DEVELOPMENT AND EVALUATION OF AUTOMATED RADAR SYSTEMS FOR MONITORING AND CHARACTERISING ECHOES FROM INSECT TARGETS

by

Timothy J. Dean BSc (Geophysics) (Hons), Curtin

A thesis submitted in fulfillment of the requirements for the degree of

Doctor of Philosophy

2007

I hereby declare that this submission is my own work and that to the best of my knowledge it contains no material previously published or written by another person, nor material which to a substantial extent has been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by colleagues, with whom I have worked at UNSW or elsewhere, during my candidature, is fully acknowledged.

I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project’s design and conception or in style, presentation and linguistic expression is acknowledged.

Timothy J. Dean 18 March 2007

i ABSTRACT This thesis describes the construction of a mobile Insect Monitoring Radars (IMR) and investigations of: the reliability of IMRs for observing insect migration in inland Australia; possible biases in IMR migration estimates; the relation between an insect’s size and its radar properties; radar discrimination between insect species; the effect of weather on the migrations of Australian plague locusts and of moths; the scale of these migrations; and here IMRs are best located.

The principles of entomological radar design, and the main features of insect migration in inland Australia, are reviewed. The main procedures used in the study are: calculation of radar performance and of insect radar cross sections (RCSs); reanalysis of a laboratory RCS dataset; statistical analysis of a four- year dataset of IMR and weather observations; and a field campaign using both two existing fixed IMRs and the new mobile unit. Statistical techniques used include correlation, multiple regression, discriminant analysis, and principal components analysis.

The original results of this work include design details of the mobile IMR, extension of radar performance calculations to IMRs and evaluation of flight speed biases, a holistic approach to IMR design, the relation of insect RCS magnitudes and polarization patterns to morphological variables, an estimate of the accuracy of the retrieved parameters, evaluations of three approaches (one- parameter, theory-based, and a novel two-stage method) to target identification, and verification of inferred target identities using results from nearby light traps. Possible sites for future IMRs are identified.

The major conclusions are that: a mobile IMR can be built with a performance equal to that of a fixed IMR but at half the cost; significant biases in the signal processing results arise from insect speed; locusts and moths can be distinguished if all RCS parameters are used; IMRs can be designed to match particular requirements; weather has a significant effect on insect migration, the best single predictor of insect numbers being temperature;moonlight has no effect; the spatial correlation of migration properties falls to 50% at a separation of 300 km; and migrating insects can be carried by the wind for 500 km in a single night.

ii CONTENTS

LIST OF TABLES...... VIII LIST OF FIGURES...... XIV PRINCIPAL SHORT NAMES AND ABBREVIATIONS ...... XXXIII ACKNOWLEDGEMENTS...... XXXIV 1 INTRODUCTION – RADAR, INSECTS, WEATHER, AND AIM OF STUDY...... 1 1.1 Preface: Radar, Insects, Study Area...... 1 1.2 Aim of the Present Study ...... 3 1.3 Monitoring Insect Flight Using Radar ...... 5 1.3.1 The Origins of Radar Entomology...... 5 1.3.2 Vertical-Beam Radars...... 8 1.3.3 Airborne, Doppler and Harmonic Radars...... 10 1.3.4 Entomological Radars in Australia...... 11 1.4 Radar Principles and Processing ...... 13 1.4.1 Pulse Operation...... 13 1.4.2 Radar Frequencies...... 14 1.4.3 Radar Identification of Insect Species ...... 15 1.4.4 Processing of Entomological Radar Signals...... 15 1.5 Effects of Weather on Insect Migration ...... 16 1.5.1 Distance and Types of Migration...... 17 1.5.2 The Effect of Wind on Insect Migration...... 18 1.5.3 Effect of Temperature on Insect Migration ...... 22 1.5.4 Effect of Humidity and Rainfall on Insect Migration...... 27 1.5.5 Orientation During Insect Migration ...... 28 1.6 Insects Studied in the Present Work...... 32 1.6.1 Australian Plague Locust...... 32 1.6.2 Spring Moths...... 40 1.7 Climate...... 45 1.7.1 Climate of the Source Area...... 45 1.7.2 The Study Area ...... 48 2 INSECT MONITORING RADARS...... 49 2.1 Development of the Fixed IMRs...... 49 2.2 Radar Configuration of the Fixed IMRs...... 53 2.3 Equipment Modules of the Fixed IMRs ...... 54 2.4 Reasons For Developing a Mobile IMR...... 55 2.5 Specifications of the IMRs ...... 55 2.6 Design of the Mobile IMR...... 57 2.7 Construction of the Mobile IMR...... 60 2.8 Equipment Modules of the Mobile IMR ...... 61 2.8.1 Control and Data-Acquisition Module ...... 63 iii 2.8.2 Microwave and Antenna Module ...... 66 2.8.3 Breakdown of Costs...... 69 2.9 Calibration of the IMRs...... 69 2.9.1 Measurement of Transmitter Power ...... 70 2.9.2 Measurement of Receiver Sensitivity...... 72 2.9.3 Estimated performance ...... 73 2.10 Locations of the Mobile IMR...... 74 2.11 Reliability of the IMRs...... 74 3 IMR PERFORMANCE, DESIGN, AND SIGNAL PROCESSING...... 77 3.1 Introduction ...... 77 3.2 Calculation of IMR Performance...... 79 3.2.1 Parameters required for Calculating IMR Performance ...... 79 3.2.2 Power Received From the Target ...... 81 3.2.3 Sensitivity of Maximum Altitude r0 to Changes in Parameters.... 85 3.3 Component Modulations of the Reflected Signal ...... 86 3.3.1 Signal Strength of Basic Components ...... 86 3.3.2 Modulation Due to Target Distance from the Beam Axis...... 88 3.3.3 Modulation due to Beam Offset...... 89 3.3.4 Modulation by RCS due to Beam Rotation ...... 90 3.4 Constraints on the Received Signal...... 91 3.4.1 Constraints Due to the Visibility Factor Vf...... 91 3.4.2 Envelope Width Across Which a Target Can Be Detected ...... 92 3.4.3 Constraints Due to Target Speed ...... 95 3.5 Calculated Performance of the Four Radars...... 102 3.6 Designing IMRs With a Specified Performance...... 105 3.6.1 Distribution of Insects in the Air ...... 105 3.6.2 Maximum Altitude...... 118 3.6.3 Beamwidth...... 119 3.6.4 Antenna Size vs. Transmitter Power...... 122 3.7 Calculating IMR Signal Components...... 124 3.7.1 Range Term...... 124 3.7.2 Trajectory Term ...... 125 3.7.3 RCS Term ...... 126 3.7.4 Wingbeat Term ...... 126 3.7.5 Calculated Total Re-radiated Signal...... 127 3.8 Processing of IMR Signals ...... 127 4 INSECT RADAR CROSS SECTION ...... 131 4.1 Introduction ...... 131 4.2 Radar Cross Section, Target Size, and Wavelength...... 133 4.3 Insect Copolar-Linear Polarisation Patterns...... 135 4.4 Constraints on Observable CLPP Forms...... 139 4.5 Ambiguity in Derived CLPP Parameter Values...... 145 4.6 Theoretical Properties of CLPPs ...... 146 4.6.1 Effect of Signal Imperfections...... 146 iv 4.6.2 Asymmetric CLPPs and θ4 – θ2 ...... 147 4.6.3 Number of CLPP Lobes...... 149 4.7 Analysis of Laboratory-Measured Insect CLPPs...... 151 4.7.1 Early Studies of Insect RCS...... 151 4.7.2 Insect Characteristics vs. Average RCS for Laboratory Data .... 153 4.7.3 Insect Characteristics vs. a2 and a4 for Laboratory Data ...... 160 4.7.4 Insect Characteristics vs. |θ4 − θ2| for Laboratory Data ...... 161 4.7.5 Insect Characteristics vs. No. of Lobes for Laboratory Data...... 164 4.8 Analysis of IMR-Measured Insect CLPPs ...... 165 4.8.1 Accuracy of Retrieved RCS Parameters...... 166 4.8.2 Insect Characteristics vs. a0, a2 and a4 for IMR Data...... 168 4.8.3 Distribution of θ2 for IMR data...... 168 4.8.4 Distribution of |θ4 − θ2| for IMR Data...... 169 4.8.5 Distribution of Number of Lobes for IMR Data...... 170 4.9 Discussion ...... 172 5 CLASSIFICATION OF INSECT TARGETS...... 174 5.1 Introduction ...... 174 5.1.1 Classification of Insects Using Wingbeat Frequency...... 174 5.1.2 Classification of Insects Using Single RCS Parameters...... 176 5.1.3 176 5.2 Multiple Regression Classification Methods...... 180 5.3 Theory-based Classification Methods...... 184 5.4 Tests of Theory-Based Classification Measures using Laboratory Data 188 5.5 A New Two-stage Approach to Classification...... 196 5.6 Tests of a New Two-Stage Approach to Classification using IMR Data 201 5.7 Discussion ...... 213 6 INSECT MIGRATION IN RELATION TO ENVIRONMENTAL FACTORS ...... 218 6.1 Introduction ...... 218 6.2 Previous Studies of Weather Effects...... 220 6.2.1 Previous Laboratory Studies of Moths and Locusts ...... 220 6.2.2 Previous Field Studies of Weather Effects on Spring Moths ..... 220 6.2.3 Previous Field Studies of Weather Effects on Plague Locusts... 222 6.2.4 More on Trough and Cold Fronts ...... 225 6.3 Approach Used in the Present Study...... 227 6.4 Weather During the Study Period ...... 228 6.5 Hypotheses to be Tested...... 234 6.6 Variables to be Tested...... 235 6.6.1 Simple Weather Variables ...... 235 6.6.2 Synoptic Weather Variables ...... 236 6.6.3 Moonlight as a Weather Variable ...... 239 6.7 Data Used for Analysis...... 242 6.7.1 Description of the Data Used for Testing ...... 243 v 6.7.2 IMR Data Fluctuations and Gaps ...... 245 6.7.3 IMR Data Trends, Clusters and Auto-Correlations ...... 247 6.7.4 IMR Data Outliers and Normality ...... 249 6.7.5 Effects of Moonlight...... 250 6.8 Methods of Analysis ...... 252 6.9 Results of Spring Moth Analyses ...... 254 6.9.1 Bivariate Correlation (Moths)...... 255 6.9.2 Multiple Regression (Moths)...... 256 6.9.3 Discriminant Analysis (Moths)...... 260 6.9.4 Principal Components Analysis (Moths)...... 263 6.10 Results of Plague Locust Analyses ...... 269 6.10.1 Bivariate Correlation (Locusts) ...... 269 6.10.2 Multiple Regression (Locusts)...... 271 6.10.3 Discriminant Analysis (Locusts) ...... 273 6.10.4 Principal Components Analysis (Locusts)...... 275 6.10.5 Locusts and Rainfall ...... 280 6.11 Discussion ...... 284 6.11.1 Discussion: Tests of Moth Hypotheses...... 284 6.11.2 Discussion: Tests of Locust Hypotheses ...... 288 6.11.3 Discussion: Moths vs. Locusts...... 290 6.11.4 Discussion: Thresholds...... 291 6.11.5 Discussion: Effects of Weather on Year-to-Year Variations in Migrant Numbers ...... 292 6.11.6 Discussion: Advantages of IMRs over Trapping Methods...... 294 7 CORRELATIONS AND THE SCALE OF MIGRANT INSECT POPULATIONS ...... 295 7.1 Introduction ...... 295 7.2 Theoretical Calculations and Computer Simulations...... 297 7.3 Previous Studies...... 300 7.4 Present Approach ...... 302 7.4.1 Fixed IMR Data Used For Analysis ...... 302 7.4.2 Mobile IMR Data Used For Analysis...... 304 7.5 Correlations between Fixed IMRs ...... 306 7.5.1 Insect Numbers at the Fixed IMRs ...... 306 7.5.2 Insect Migration Directions at the Fixed IMRs ...... 316 7.5.3 Insect Travel Speeds at the Fixed IMRs ...... 321 7.6 Correlations Between Mobile and Fixed IMRs ...... 326 7.6.1 Insect Numbers at the Mobile and Fixed IMRs...... 328 7.6.2 Insect Travel Directions at the Mobile and Fixed IMRs ...... 334 7.6.3 Insect Travel Speeds at the Mobile and Fixed IMRs...... 340 7.7 Discussion ...... 343 7.7.1 Discussion: Migration Size...... 343 7.7.2 Discussion: Optimum IMR Location...... 346 7.7.3 Discussion: IMR Reliability ...... 348

vi 8 REALISATION OF STUDY AIMS, RECOMMENDATIONS FOR FUTURE WORK, CONCLUDING REMARKS...... 350 8.1 Realisation of Study Aims...... 350 8.2 Recommendations for Future Work...... 352 8.3 Concluding Remarks...... 354 REFERENCES ...... 356 APPENDIX: INSECT RCS AND BIOMETRIC DATA...... 390

vii LIST OF TABLES

Table 2.1: ZLC-configuration entomological radar specifications at the time of this work. Further details are given in Table 3.1 in Chapter 3...... 56 Table 2.2: Measured transmitter power of the mobile IMR, proposed new Bourke IMR, and existing Thargomindah IMR using the equipment shown in Figure 2.14. The measurements of the Thargomindah IMR were made by I.T. Harman. All three IMRs use the same model 65125 transceiver..71 Table 2.3: Estimated performance of the four radars shown in Table 2.1. From top are maximum antenna gain, received power from an RCS of 1 cm2 at 500 m relative to Bourke = 100 (the smaller the number the greater the sensitivity), minimum detectable signal power (threshold), and maximum altitude at which a standard target can be detected relative to Bourke = 100 (the larger the number the greater the sensitivity)...... 73 Table 2.4: Breakdown of the causes of missing data on 93 nights for the Bourke IMR (H.K. Wang personal communication). System faults were mostly due to the hard drive becoming temporarily full before there was time to burn it to CD...... 75 Table 3.1: Parameters for calculating the performance of the four radars. For some parameters such as antenna diameter the values given are those provided by the manufacturer. For others such as transmitted power the values given are the measured values, which may differ from the manufacturer's nominal values The units shown are those of convention and where necessary require conversion to SI units before inserting in the radar equations...... 80 Table 3.2: Maximum antenna gain equation (3.3), received power equation (3.1), efficiency equation (3.7), minimum signal power (3.8) and maximum altitude (3.6) for the four radars calculated via the indicated equations and the data of Table 3.1...... 103 Table 4.1: RCS parameters vs. insect characteristics for the laboratory data. The division of masses into < 1000 mg and > 1000 mg reflects their distribution as shown in Figure 4.14. Volume = π x (width/2)2 x length. Insect width varies only slightly within the > 1000 mg group, so the correlations with width and width/length are not meaningful. Asterisks indicate the correlations that are strong, significant and consistent across masses < 1000 mg and > 1000 mg...... 159 Table 5.1: Variability (expressed as SD/Mean) within species of a0, a2 and a4. Listed in order of mass are all species in the laboratory data for which the sample size is N > 2, and data from the Bourke IMR on nights when the indicated species was dominant (but not totally dominant, so the variability will be inflated by an unknown amount). For the IMR data (spring moths and plague locusts), N = number of processed signals...... 177

viii Table 5.2: Multiple regression analysis of insect mass vs. RCS parameters for the laboratory data. As before, the insects are divided into < 1000 mg (N = 57), > 1000 mg (N = 11), and all masses (N = 68)...... 180 Table 5.3: Nights on which locusts or moths were detected by light-traps vs. the RCS prediction for the same nights...... 208 Table 5.4: Light-trap results for White Cliffs vs. those for Fowlers Gap. ‘No data’ indicates that neither locusts, moths, or mixed were recorded on nights when they were recorded at the other station. The locust totals do not agree with those in Figure 5.18 as the latter include nights when moths were also detected...... 209 Table 6.1: Hypotheses to be tested in the present work. 'Relationship' means the relationship predicted between the nightly number of insects and the weather variable, namely + positive, ? direction uncertain, x none. 'Threshold' means the threshold value below which insect flight is inhibited...... 234 Table 6.2: The study periods during which either moths or locusts were predominant, and their mean nightly counts 2000-2200 h of insects with RCS ≥ 1 cm2...... 244 Table 6.3: Results of trend and serial correlation tests for the seven insect periods. Note that the mean number of insects per night given here differ from those in Table 6.2 as the latter do not include the interpolated values...... 247 Table 6.4: Pearson correlation coefficient (r) or point-biserial correlation 1/4 coefficient (rpb) between (number of insects) and 17 weather variables during moth periods. N = 195 nights. Two-sided significance levels (P) are given if < 0.20...... 255 Table 6.5: Multiple regression analyses of the (number of insects)1/4 and weather variables for the moth periods. The three models are described in the text. P is the significance level of the regression coefficient by two- tailed t-test. SC is the change in the (number of insects)1/4 in standard deviations caused by a change of one standard deviation in the weather variable...... 259 Table 6.6: Discriminant analysis results for the moth periods. Two-sided significance levels (P) are shown if P ≤ 0.05. The three canonical coefficients for each variable show its contribution to the discrimination achieved by the three discriminant functions V1, V2 and V3. Wilks lambda is the test statistic applied to the results for each function, which allows its significance level (labelled P) to be determined. The standardised canonical coefficients (similar to the SCs in Table 6.5) show the relative effect of each variable on the result...... 262 Table 6.7: Levels predicted by the discriminant function over 195 nights vs. observed levels. The predictions achieved 68/93 = 73% success for level 1, 32/74 = 43% success for level 2, 13/24 = 54% success for level 3, and 4/4 = 100% success for level 4. Overall the success rate was (68+32+13+4)/195 = 60%. If the predictions were made at random, each cell would contain 195/16 = 12.2 counts, giving a random success rate of ix 4x12.2/195 = 25%. The contingency coefficient for this table is C = 0.60, for which P < 10−15...... 263 Table 6.8: Correlations (r x 100) between each pair of weather variables during the moth periods. Total variables = 14. The bottom two lines help to identify the main correlations and are not part of the matrix. Mean maximum |r| = 0.45...... 264 Table 6.9: A summary of the component structure when PCA is used to extract 2-6 components from the moth periods. Variables are included in a column if their loading is > 0.4. Column labelled 2: The entries are either 1 or 2, indicating that the variables conform well to a two-component structure (as confirmed by Figure 6.19). On moving across the other columns, components are added up to the limit at the top of each column, sometimes with each component evenly represented and sometimes not. For >2 components, the clearest and most even picture is given by 4 components, the same four components that are identified and interpreted in the text...... 267 Table 6.10: Loading of each variable on four components obtained by PCA of the moth periods. (These results are to allow comparison with the corresponding locust results of Table 6.16). Asterisks indicate loadings greater than 0.4...... 268 Table 6.11: Pearson correlation coefficient (r) or point-biserial correlation 1/4 coefficient (rpb) between (number of insects) and 13 weather variables during locust periods. N = 151 nights. Two-sided significance levels (P) are given if < 0.20...... 270 Table 6.12: Multiple regression analyses of the (number of insects)1/4 and weather variables for the locust periods. The three models are described in the text. P is the significance level of the regression coefficient by two- tailed t-test. SC is the change in the (number of insects)1/4 in standard deviations caused by a change of one standard deviation in the weather variable...... 272 Table 6.13: Discriminant analysis results for the locust periods. Two-sided significance levels are shown if P ≤ 0.05. The three canonical coefficients for each variable show its contribution to the discrimination achieved by the three discriminant functions V1, V2 and V3. Wilks lambda is the test statistic applied to the results for each function, which allows its significance level (P) to be determined. The standardised canonical coefficients (similar to the SCs in Table 6.12) show the relative effect of each variable on the result...... 274 Table 6.14: Levels predicted by the discriminant function over 151 nights of locust periods vs. observed levels. The predictions achieved 25/45 = 56% success for level 1, 35/71 = 49% success for level 2, 11/29 = 38% success for level 3, and 5/6 = 83% success for level 4. Overall the success rate was (25+35+11+5)/151 = 50%. If the predictions were made at random, each cell would contain 151/16 = 9.44 counts, giving a random success rate of 4x9.44/151 = 25%. The contingency coefficient for this table is C = 0.50...... 275 x Table 6.15: Correlations (r x 100) between each pair of weather variables during the locust periods. Total variables = 12. The bottom two lines help to identify the main correlations and are not part of the matrix. Mean maximum |r| = 0.58...... 276 Table 6.16: Loading of each variable on four components obtained by PCA of the locust periods. Asterisks indicate loadings greater than 0.25...... 279 Table 6.17: Multiple regression analyses of the (number of insects)1/4 and weather variables for the locust periods after excluding nights where rainfall in the previous ten days was less than 10 mm. Model 1 involves all 20 variables. Model 2 involves only those variables whose contribution to R2 exceeded 0.01, which reduced the number of variables to 8. Model 3 involves only those variables whose contribution to R2 exceeded 0.03, which further reduced the number of variables to 6. P is the significance level of the regression coefficient by two-tailed t-test. SC is the change in the (number of insects)1/4 in standard deviations caused by a change of one standard deviation in the weather variable...... 283 Table 6.18: Moth periods. Summary of weather hypotheses vs. outcomes by four methods of analysis. The weather variables have been grouped according to their loading on the components of a two-component PCA. From left to right the columns are: (1) Hypothesis from Table 6.1 where the relationship with the weather variable is predicted to be: + positive, − negative, ? uncertain, x none. (2) Bivariate correlation r from Table 6.4. (3) Regression standardised coefficients from Table 6.5 model 3. (4) If the weather variable or a related variable is among the most effective discriminators (SCC/V1 >0.35) from Table 6.6, this column identifies them. Thus H, CH means these variables discriminated well between moth numbers. Entries in parentheses indicate less effective variables (SCC/V1 = 0.30−0.35). (5) Location of the variable on the two-component PCA shown in Figure 6.19. Thus 1+ or 1− means the variable tends towards the positive or negative poles of component 1. ? = no clear tendency. (6) Whether the hypothesis is confirmed by 2 or more of the 4 results yes/no. ? = hypothesis uncertain, nevertheless weak = small effect...... 287 Table 6.19: : Locust periods. Summary of weather hypotheses vs. outcomes by four methods of analysis. The weather variables have been grouped according to their loading on the components of a two-component PCA. Column descriptions are as for Table 6.18. Column sources are (1) Table 6.1, (2) Table 6.11, (3) Table 6.12 model 3, (4) Table 6.13, (5) Figure 6.23, (7) Table 6.17. In column 6, 'thresh' = threshold effect...... 289 Table 6.20: Lower and upper thresholds for insect flight observed in the present work. Where specific thresholds could not be identified, the table shows (in parentheses) the range of values within which flight was observed, see Figure 6.5 and Figure 6.6. It seems likely that flight could occur outside the ranges shown, but the relevant observations were not available...... 291 Table 7.1: Periods >14 nights used for analysis. Each period has gaps, each gap being a single night. The predominant insects during each period were identified using the two-stage approach described in Section 5.5 in Chapter xi 5. For convenience these periods are subsequently termed 'gap-free periods'. Total nights = 172...... 304 Table 7.2: Times when each of the three IMRs were in operation during 16-23 April 2002. M: Mobile, T: Thargomindah, B: Bourke...... 305 Table 7.3: Classification count table for the data shown in Figure 7.7. The four groups into which the counts are divided were chosen to make as many cell entries > 5 as possible. The contingency coefficient for this table is 0.52...... 310 Table 7.4: Autocorrelations between nightly insect counts at the Bourke and Thargomindah IMRs for the seven gap-free periods. Total N = 172. Entries with P < 0.05 are shown in bold...... 314 Table 7.5: Crosscorrelations and their lags between nightly insect counts at the Bourke and Thargomindah IMRs for the seven gap-free periods. A lag of +1 night means that the Thargomindah counts for each period were advanced one night vs. the Bourke counts for the same period. The results for lag 0 and the correlations shown in Figure 7.8 are the same. Entries with P < 0.05 are shown in bold...... 315 Table 7.6: Circular correlations r between the mean nightly migration directions at the Bourke and Thargomindah IMRs for each of the seven gap-free periods. Four are significant (P < 0.05). Mean circular r = 0.61. Also shown are the mean migration direction θ in degrees, standard deviation, and the results of the Watson-Williams F-test of the significance of the difference between each pair of mean directions...... 320 Table 7.7: Correlations (r) between the mean nightly migration speeds at the Bourke and Thargomindah IMRs for each of the seven gap-free periods. All are significant, mean r = 0.54. Also shown are the mean migration speed v in ms-1, standard deviation, and results of the Watson-Williams F- test of the difference between each pair of means for the seven periods.323 Table 7.8: Crosscorrelations and their lags between insect travel speeds observed at the Bourke and Thargomindah IMRs for the seven gap-free periods. A lag of +1 night means that the Thargomindah speeds for each period were advanced one night vs. the Bourke speeds for the same period. Results for lag 0 and the correlations shown in Table 7.7 are the same. Entries with P < 0.05 are shown in bold...... 324 Table 7.9: Mobile IMR locations and their straight-line distances from the Bourke and Thargomindah IMRs. For example Glengeera is 26 km north of Bourke and 290 km south-east of Thargomindah. Bourke is 308 km south-east of Thargomindah...... 327 Table 7.10: Correlations for each IMR between pairs of nights where the mobile IMR position was unchanged. Each correlation is between the two sets of hourly insect counts 1900-0500 h, N = 11. ND = No Data because the IMR was either not operating or was operating for only a few hours. Entries with P < 0.05 are in bold...... 332 Table 7.11: Crosscorrelations between hourly insect counts recorded by the mobile, Bourke, and Thargomindah IMRs during the nights of 16-22 April 2002. A lag of +1 hour means that the counts for the first-named IMR xii were advanced one hour vs. the counts for the second-named IMR. ND = No data because the IMR was either not operating of was operating for only a few hours. Entries with P < 0.05 are in bold. Nights when the wind was blowing directly between IMRs are in italics...... 334 Table 7.12: Circular correlations between the hourly travel directions at each pair of IMRs during 16-23 April 2002. Each result is based on 7-11 hourly observations per night. None are significant (P < 0.05). There are fewer entries than implied by Table 7.2 because some nights (indicated by ND had insufficient data for analysis...... 336 Table 7.13: Correlations between the hourly insect speeds at each pair of IMRs during 16-23 April 2002. Each result is based on 7-11 hourly observations per night. The only significant (P < 0.05) result is shown in bold...... 341 Table 7.14: Summary of observed correlations or mean correlations between nightly insect counts observed by the Bourke and Thargomindah IMRs. In parentheses is the relevant figure or table number (t = table). N = 313 is the number of nights when both IMRs were operating during September 1999 - March 2001. N = 172 is the number of nights in the seven gap-free periods November 1999 - September 2000. Note that Pearson and circular r's are not comparable, see Section 7.5...... 344 Table A.1: Biometric data for the RCS measurements presented in Table A.2...... 391 Table A.2: Statistical summary data for the insects measured by Aldhous (1989) and Wolf et al. (1993)...... 393 Table A.3: Biometric measurements for C. terminifera and H. punctigera. ...394 Table A.4: RCS data for the insects in Table A.1...... 395

xiii LIST OF FIGURES

Figure 1.1: Climatic regions of Australia based on the 30 years of climate data from 1961 to 1990. (Koeppen classification system adapted from www.bom.gov.au). The inner circle shows the approximate area monitored by the Australian IMRs. The outer circle shows the approximate extent of the source and destination areas for the Australian plague locusts and spring moths studied in the present work...... 3 Figure 1.2: Countries where entomological studies have been conducted using ground-base radars. For examples see: Australia (Schaefer, 1976; Drake et al., 1981). Canada (Schaefer, 1976; Greenbank et al., 1980; Dickison et al., 1982; 1986; Rainey & Haggis, 1987). China (Chen et al., 1985; 1995; Riley et al., 1990; 1990b; 1991; 1991b; 1994; 1994b; 1995, Feng et al., 2003). Cyprus (Drake, 2002). Ethiopia (Schaefer, 1976; Roffey, 1972). India (Riley et al., 1992; Reynolds et al., 1999). Mali (Reynolds & Riley, 1979; 1988; Riley & Reynolds, 1986; 1990; Riley, 1989). Niger (Schaefer, 1969; 1972; 1976; see also Roffey, 1969; 1972). Philippines (Riley et al., 1987). Saudi Arabia (Riley, 1973; 1974). Sudan (Schaefer 1976; Rainey & Haggis, 1987). UK (Schaefer et al., 1985; Chapman et al., 2000b; 2000c; 2002; Smith et al., 2000). USA (Beerwinkle et al., 1994; 1995; Wolf et al., 1995). For studies using airborne radars see Section 1.3.3...... 7 Figure 1.3: A scanning entomological radar being operated in the Sudan by Loughbrough University of Technology in 1974. Photo by V.A. Drake. ..8 Figure 1.4: The original IMR configuration, as developed by Bent (1984), consisted of a static conical transmitter beam (left) with a rotating conical receiver beam (right). Reproduced from Bent (1984)...... 9 Figure 1.5: Location of the Bourke and Thargomindah IMRs. Map width = 1800 km. Green shading = 0-200 m elevation, pale yellow-green shading = 200-400 m. (From Reference Atlas for Australia and New Zealand.)...... 12 Figure 1.6: The mobile IMR with its trailer and towing vehicle in front of the fixed IMR at Thargomindah. The flat semi-arid landscape is typical of the study area. Photo by the author...... 13 Figure 1.7: Time-lapse image from a scanning radar PPI display showing individual insect tracks. Photo by W. Wolf...... 16 Figure 1.8: The three layers of the atmosphere and the day-migration of aphids. Diagram shows the initial ascent of aphids at around 0.25 ms–1 through the surface boundary layer to the planetary boundary layer, followed by wind- assisted migration via the planetary boundary layer, and final descent to the migration destination (redrawn from Irwin, 1999). Unlike some night- migrating species, the aphids do not ascend to the third layer (free atmosphere or geostrophic layer)...... 19 Figure 1.9: Observed distribution within tall grass of the night-flying grasshopper Nomadacris in Madagascar. In the dry season when xiv temperatures are generally high, the grasshoppers bask in the upper parts when cool (left), and shelter in the lower parts when hot (right). Adapted from Uvarov (1977)...... 23 Figure 1.10: Drawing from Rainey (1989) of a desert locust in flight. Males are 60-75 mm long and weigh 1.5-2 g; females are 70-90 mm long and weigh 2.5-3.5 g (Cressman, 1998). Wingspan is 100-150 mm. Fore- and hind- wings work at the same frequency, about 18 Hz, but out of phase (Rainey, 1989)...... 25 Figure 1.11: Desert locusts in flight by day, photographed from below. The swarm covered 30 sq km, reached a height of 720 m, and was estimated to contain 109 locusts with a total weight of 2000-3000 tonnes developing 10-20 megawatts of power. In this picture all locusts are oriented the same way, albeit not exactly, which suggests purposeful flight in that direction. In fact the actual travel direction was close to the wind direction, which was from right to left almost at right angles to the locust's orientation. Picture and description are from Rainey (1989)...... 29 Figure 1.12: The Australian plague locust Chortoicetes terminifera. Left: mature adult. Body colour is variable and can be grey, brown or green. Male locusts are 25-30 mm long, and females (which are larger) are 30-42 mm long. Body weight depends on conditions and can reach 600 mg. Right: final growth stage before being capable of flight. Photos and information are from www.affa.gov.au/aplc...... 33 Figure 1.13: Partial lifecycle of the Australian plague locust. The fledgling takes a further two weeks to be reproductively ready. Pictures from www.affa.gov.au/aplc...... 35 Figure 1.14: An aerial photo of Australian plague locust nymphs devastating a young wheat crop. The parallel green lines are the furrows containing young wheat, the large bare areas are the locust depredations. Serious depredations can strip areas several kilometres wide. Photo from www.affa.gov.au/aplc...... 36 Figure 1.15: Australian plague locusts taking off by day in the central highlands of Queensland. From the online version of Hunter (2004) at www.blackwell-synergy.com. Photo by Peter Spurgin...... 37 Figure 1.16: Australian plague locust. Wingspan is about twice the body length, which is up to 30 mm for males and up to 42 mm for females, and is less than half that of the African desert locust shown in Figure 1.10. Photo is from www.dpi.vic.gov.au (plague locust identification and biology)...... 38 Figure 1.17: Source area of Australian plague locusts in the arid and semi-arid interior of Australia, and their destination area in the agricultural belt of eastern Australia. Plague locusts also occur in southern parts of Western Australia but their infestations are less frequent. Adapted from Deveson & Walker (2005). Also shown are the locations of the IMRs at Thargomindah and Bourke...... 39 Figure 1.18: Moths of Helicoverpa punctigera (left) and Helicoverpa armigera (right). They are usually distinguished by the presence of the pale patch xv on the hind wings of H. armigera (circled). On average the body is 17 mm long and nearly 6 mm in diameter. Wingspan is 30-45 mm. Body weight depends on conditions but is typically about 120 mg. Photo from www2.dpi.qld.gov.au/fieldcrops/17696.html with circles imposed by the author...... 41 Figure 1.19: Moths of Helicoverpa punctigera (left) and Helicoverpa armigera (right) at rest, which emphasises their physical similarity...... 41 Figure 1.20: Lifecycle of the moths Helicoverpa punctigera and H. armigera. Images are from www2.dpi.qld.gov.au...... 42 Figure 1.21: Source area of Helicoverpa punctigera (horizontal hatching) and the major cropping areas of eastern Australia (diagonal hatching). Adapted from Gregg et al. (1995). The points labelled T and B indicate the IMRs at Thargomindah and Bourke...... 44 Figure 1.22: Annual rainfall map of eastern Australia. As shown in Figure 1.17 and Figure 1.21, the source areas of plague locusts and spring moths are generally centred on the Lake Eyre basin (outlined in red), which consists of two catchments (Cooper Creek and Georgina Diamantina) and three regions (Desert Rivers, Western Rivers and Lake Frome), covering some 1.2 million square kilometres of uniformly flat, arid and semi-arid central Australia. Lake Eyre itself is shown by the large blue dot. The major cropping areas are outlined in green. The two IMR sites at Thargomindah and Bourke are shown in black. Birdsville, shown in white, is the most isolated township in Australia and is representative of the centre of the source region...... 46 Figure 1.23: Typical landscape in the source area with characteristic clumps of grasses that in this picture are still green after previous rain. Photo from www.affa.gov.au/aplc shows a routine APLC ground survey, which typically covers 300 km a day. At regular stops every 10 km the density and species of locusts present are recorded together with their stage of development and the type and condition of the vegetation...... 47 Figure 1.24: Summer rainfall dispersing through a network of braided channels in the channel country of southwest Queensland and adjoining parts of NSW and SA, which is in the centre of the locust and moth source areas. At such times the grassy plains of the channel country (which resemble the landscape shown in Figure 1.23) become impassable. Black-and-white aerial view from The Australian Encyclopedia 1996...... 47 Figure 1.25: Average annual rainfall and average minimum and maximum temperatures at Thargomindah, Bourke and Birdsville (see Figure 1.22 for their locations)...... 48 Figure 2.1: Schematic diagram of the two fixed IMRs in inland eastern Australia...... 49 Figure 2.2: The two IMRs permanently installed at Bourke (left) and Thargomindah (right). In each case the IMR equipment is housed in the transportable cabin on the left which is air-conditioned to prevent equipment overheating. The 1.8 m radar antenna is under the radome on the right, and the whole installation is protected by barrier fencing. Each xvi IMR requires a dedicated telephone line and connection to mains power. The provision of which accounts for much of the installation cost. The cabin interiors are shown later in Figure 2.5...... 50 Figure 2.3: Website (created by H.K. Wang, a student at UNSW@ADFA- PEMS) showing a summary of results from the Bourke IMR for the night of 18/19 March 2002. Top right are plots showing the temperature, relative humidity, wind speed and wind direction recorded at ground level by the automatic weather station during the 11 hours of IMR operation. Below is a blue/green horizontal plot showing the number of insects counted at altitudes between 200 m and 1400 m. The rest of the display shows (top) the direction in which the insects are heading and their body orientation, and (bottom) their speed, wingbeat frequency and estimated mass. Different dates can be selected from the list on the left of the screen. The ‘Season’s Dynamics’ display shows in green the total number of insects detected each night (Wang et al., 2002)...... 52 Figure 2.4: Left: Plan view of the beam geometry (adapted from Drake et al., 1994). The radar beam is essentially a narrow beam whose centre traces a circular path around the vertical. The beam is polarised across the diameter of the beam, and the plane of polarisation rotates with the beam. Right: Side view of the radar beam (adapted from Smith et al., 1993) showing how the beam centre traces a circular path around the vertical. .53 Figure 2.5: The interiors of the Bourke (left) and Thargomindah (right) IMR cabins (photos by V.A. Drake). In each photo the transceivers (outlined in red) are on the floor with the controlling and signal-processing electronics on the shelves...... 55 Figure 2.6: Top: The mobile IMR during field tests near Canberra. Here the control and data-acquisition module is housed in the vehicle and is connected by cables to the microwave and antenna module in the trailer. On the ground between them is the portable generator. A closer view of the equipment when housed in the vehicle is shown in Figure 2.10. Middle Left: During operation in the study area the control and data- acquisition module is housed in a tent, shown here at Barringun. Middle Right: Where possible, locations are chosen where power is available, as here at Thyangra. Bottom Left: The mobile IMR in operation at Glengeera. Bottom Right: The mobile IMR in operation at Eulo. The building is an accommodation cabin that also provided power. The antenna is quite high up on the trailer and is well shielded, which eliminates any ground or building clutter from the beam sidelobes. Photos by the author ...... 58 Figure 2.7: Schematic plan view of the mobile IMR trailer. Clockwise from top left around the antenna mount are: petrol containers, generator, motor control, motor switch, transceiver and cables. The fuel cans and generator are located in the trailer only during transit...... 61 Figure 2.8: Schematic diagram of the mobile IMR. The upper half shows the microwave and antenna module. The lower half shows the control and

xvii data-acquisition module with its four interface cards. Dashed lines represent power. Double lines represent sections of waveguide...... 62 Figure 2.9: Oscilloscope display showing the 15 altitude gates (top), highest is on the right, and the radar return (A-scope, bottom). The radar return shows an insect traversing the beam at the height of the third gate. The initial large peak is the transmitted radar pulse...... 63 Figure 2.10: The mobile IMR's control and data-acquisition module. Top left: schematic layout. Top right: module during operation inside tent. Bottom: module during operation in rear of towing vehicle. The same components but without the restrictions of mobility can be seen inside the fixed IMR cabins shown in Figure 2.5. Photos by the author...... 64 Figure 2.11: The mobile IMR’s microwave and antenna module. Left: a view inside the trailer barrier fence. The transceiver is bottom centre. The motor controller is on the bottom right under the step. Right: Close-up of the antenna drive assembly. The rotary joint (grey-blue) is in the foreground, the rotary coupling (black) is at the top of the picture. The white cable leads to the optical tachometer. The antenna drive motor is slightly visible at the rear right. The various components are more clearly identified in Figure 2.12. Photos by the author...... 66 Figure 2.12: Side view of the Mobile IMR microwave and antenna module. Two sections of flexible waveguide connect the transceiver to the bottom of the rotary joint. The upper, turning, end of the rotary joint is attached to the rotary coupling at the base of the antenna, which is turned by a belt driven by the electric motor...... 67 Figure 2.13: Mobile IMR antenna feed in position inside the antenna. Left: The radar waves are radiated from the tip, which is offset 0.7° from the vertical. To reduce vibration and wear (the antenna feed rotates at 5 Hz), the offset is counterbalanced by two small counterweights. Right: Close- up of the attachment to the rotary coupling shown side-on in Figure 2.12. Photos by author...... 68 Figure 2.14: The equipment used to measure the mobile IMR transmitter power. Two cross-guide couplers (arrowed) were used to reduce the transmitted power to a level where it could be measured by the power meter...... 70 Figure 2.15: Receiver calibration curve for the original Bourke IMR as measured by I.T. Harman. The 53.5 dB/V line was later found to be spurious...... 73 Figure 2.16: The four mobile IMR locations in the study area. Thick black lines are sealed roads, open lines are unsealed roads, and the figures between flags are road kilometres. The four mobile IMR locations were as equally spaced between the two fixed IMRs at Bourke and Thargomindah as local settlement and the availability of power would allow...... 74 Figure 2.17: Maximum nightly peak detector temperature vs. maximum nightly air temperature. Other relationships, e.g. with average temperature, are not included as the thermometer used was capable only of recording the maximum temperature...... 76

xviii Figure 3.1: The signal from a small insect passing through the beam of the mobile IMR. The insect has taken about 4 seconds to traverse the beam, here about 20 m wide. The signal rises to a maximum on the beam axis and then falls away. Superimposed are regular variations due to the beam's rotating plane of polarisation, which is aligned with the insect's body axis twice per revolution so their frequency is 10 Hz, twice the beam’s rotation rate of 5 Hz. (The two alignment occasions differ due to the beam offset, so the amplitudes are different.) Further modulation due to the insect’s body movements associated with wingbeating is also present but is not discernible by eye. Subsequent processing of the signal showed that the insect had an RCS of 0.1 cm2 and was flying at an altitude of between 325 and 350 m in a westwards direction at 257º with a ground speed of 5 ms-1...... 78 Figure 3.2: The distribution of observed RCS values from 6,284 good-quality echoes recorded by the Bourke IMR during the night of 14 March 1999. The peak around −10 (corresponding to an RCS value of about 0.1 cm2) is largely due to a background of small insects, and the peak around 3 (corresponding to an RCS value of about 2 cm2) is largely due to spring moths and plague locusts. The shaded areas identify the RCS values that are grouped later in Figure 3.12...... 81 Figure 3.3: Calculated components of a signal reflected by an insect when traversing through the Bourke IMR radar beam. The quantities chosen for the calculation were typical of those found for insects and were: flight direction 0°, insect orientation 0°, speed 4 ms-1, radar cross section 0.1 cm2. The modulation by wingbeating is omitted for clarity but would be typically –1 to –2 dB...... 87 Figure 3.4: Change in beamwidth due to beam offset. For clarity the horizontal scale has been exaggerated about forty times. The figure shows the beam profiles at their most extreme left and right positions. To be processable the sampled width must be within the beam during the entire 360º of beam rotation. This width, here called the offset beamwidth, is shown shaded, and is (θ3dB – 2 x offset) at all altitudes. Beyond the shaded area the sampled width is within the beam for only part of the rotation and is therefore either unreliably processable or completely unprocessable, depending on the tolerance of the processing algorithm...... 89 Figure 3.5: Modulation of the RCS component calculated from the laboratory measured RCS data (n = 68) using equation (3.13). The maximum modulation is 27 dB but 95% are less than 13 dB or less...... 90 Figure 3.6: Distribution of signal modulations due to the RCS component for 4,050 insects detected by the Bourke IMR on the night of 15 March 1999 with a signal strength at least 20 dB above noise. The maximum modulation was 15 dB with 97% of signals having a modulation of 13 dB or less...... 91 Figure 3.7: The number of processed and unprocessed echoes, and the proportion processable, for a typical night’s data (in this case 15 March 1999) from the Bourke IMR. The dip in the processable proportion around xix –55 dB is due to the two-peaked distribution of RCS values, see Figure 3.2...... 92 Figure 3.8: Gaussian envelope (positions of equal gain) for a rotating beam without beam offset. Also shown is the scanned volume Vs between altitudes r1 and r2. For clarity the angle of the beam has been exaggerated about fifteen times, and the vertical altitudes represented by r1 and r2 have been omitted. (Adapted from Chapman et al., 2002.)...... 93 Figure 3.9: The length of an insect’s detectable path through an IMR beam relative to distance d from the zenith and the radius of the processable beam am...... 96 Figure 3.10: Maximum processable width vs. height for the Bourke IMR calculated by equations (3.17) and (3.18). The breakdown of observed travel speeds is from Section 7.4.3 in Chapter 7 and is for 313 nights between 1 September 1999 and 1 March 2001. For example the x-axis label of 13 ms-1 corresponds to speeds of 12.01-14.00 ms-1. The maximum mean nightly speed is about 20 ms-1...... 97 Figure 3.11: Stepwise computation of the processable proportion of signals for the Bourke IMR. There are eight gates at 150 m intervals. Each gate is 50 m in extent. The width of the scanned volume at each altitude gate is determined by the RCS and is divided into ten equal strips, each of which will allow a certain maximum speed corresponding to the minimum duration required of 0.8 seconds. If this speed is higher than the highest speed observed at Bourke, then all signals from that strip will be processable. That is, even the highest speed observed at Bourke will not exceed the capacity of the strip to process it. On the other hand, if the maximum allowable speed is only as high as the speed corresponding to, say, 25% or 50% of speeds, then on average only 25% or 50% of signals from that strip will be processable. Averaging the processable proportions across all strips then gives the processable proportion at each altitude gate shown for each RCS...... 99 Figure 3.12: Estimated numbers of insects obtained by taking the recorded numbers shown in Figure 3.2 (obtained at Bourke during the night of 14 March 1999) for each bracket of RCS values, and dividing by the average processable proportion calculated for that bracket as shown in Figure 3.11. The shaded bars correspond to the shaded parts of the distribution in Figure 3.2...... 100 Figure 3.13: The effect of speed and distance from the beam axis on the number of processable echoes for a typical night of Bourke IMR data, in this case 14 March 1999. The altitude gate is 50 m wide centred on 375 m. The dotted lines show the maximum speeds calculated by the method outlined in Figure 3.11 for the indicated RCS. The plotted speeds are the observed speeds of individual insects, and their natural variability can occasionally push them past the nominal long-term maximum of 20 ms-1 as shown in Figure 3.10, which is based on nightly averages...... 102 Figure 3.14: Beam envelopes of the VLR, Bourke, mobile and Thargomindah IMRs showing their full beamwidth. The reduced (offset) beamwidths are xx not shown. Vertical axis shows height in metres, horizontal axis shows width in metres (exaggerated about fifteen times for clarity), and shaded area shows the beam envelopes for insects of RCS 0.01 cm2 (smallest volume), 0.1, 1, and 3 cm2 (largest volume). The last two are typical of spring moths and plague locusts. Shaded bands indicate altitude gates (layers processed by the radar)...... 104 Figure 3.15: Three possible types of spatial patters. Adapted from Krebs (1989)...... 106 Figure 3.16: Distribution of insect numbers observed by a scanning pencil- beam radar in 51 filmed PPI displays 30 seconds apart during 25 minutes in northern NSW on 5 March 1979. Beam elevation 8º, height interval 129-193 m. Total insect counts are 256 (average 5.02) for the 30-degree PPI sector (left) and 102 (average 2.02) for the 10-degree PPI sector (right). In each case the observed frequencies are not significantly different from those expected if the insects were spaced at random, i.e. as predicted by a Poisson distribution. Thus a chi-squared test gives P = 0.97 df = 6 (left) and P = 0.74 df = 4 (right). Results are from Drake (1981) replotted to match the format used later in Figures 3.18 and 3.19...... 109 Figure 3.17: Example of insect numbers for the Bourke IMR from Deveson et al. (2005)...... 113 Figure 3.18: Source data are Bourke IMR insect numbers observed during 7.5- minute periods taken from the plotted results of Deveson et al. (2005). Total number of intervals = 210. Left: Observed and expected frequencies of the quantity (number of insects in each 7.5 minutes)/50 truncated to an integer. For example insect numbers of 20 and 220 are counted as 0 and 4 respectively. Right: Regression of log (variance) against log (mean) for the original data, i.e., number of insects in each 7.5 minutes not converted to an integer...... 115 Figure 3.19: Source data are Bourke IMR insect numbers observed during successive 5-minute periods on the night of 14 March 1999. Left: observed and expected frequencies for gates 225 m and 375 m combined (= data unsuitable for the purpose). Right: Same for gates 525 m and 675 m combined (= data that is more suitable)...... 116 Figure 3.20: Effect of varying antenna diameter and transmitted power to give 2 r0 = 1100 m for RCS = 0.1 cm . Left: envelopes calculated by equation (3.25) for antenna diameters of 1.8 and 1.0 m, and transmitter powers of 4 kW and 42 kW. Right: corresponding changes in the processable proportion of received signals. The lower plots show how the same equipment performs when RCS = 0.01 cm2...... 121 Figure 3.21: The combined cost of antenna and transceiver vs. maximum altitude for two different RCS values. In each case (from left to right) the three joined data points are for transmitted powers of 6, 12 and 25 kW. 123 Figure 3.22: Gaussian envelopes for a 25-kW transmitter, RCS = 0.64 cm2, and four antenna diameters...... 123 Figure 3.23: Components of the flight of an insect (I) with constant speed V and body alignment β through the IMR beam centred at C orbiting around O xxi resulting in a signal of the form given by equation (3.36). Adapted from Smith et al. (1993)...... 126 Figure 3.24: Theoretical signal based on echo intensity measured at 8, rather than 64, evenly-spaced angles. Note the under-sampling (hence loss of detail) when compared with the signal measured at 64 evenly-spaced angles in Figure 3.3...... 128 Figure 3.25: The signal amplitudes between 1 and 2 seconds overlain with parabolas fitted to the amplitudes measured at angles 0, 90, 180 and 270° around the beam. For clarity the parabolas at angles 45, 135, 225 and 315° are omitted...... 129 Figure 3.26: The sin/cosine curve fitted to the times of closest approach estimated from each of the eight fitted parabolas. Each point represents the maximum amplitude calculated from the fitted parabola for each angle around the beam...... 129 Figure 4.1: How the CLPP is formed. Left: The rotating vertical radar beam of an IMR impinges on an insect flying overhead. In this case the insect’s body axis is momentarily aligned with the plane of polarisation. Right: The insect reflects the radar beam with an intensity dependent on (1) its RCS and distance from the radar, (2) its distance from the centre of the beam and (3) the polarisation angle, here 0º. The instantaneous RCS plotted against the polarisation angle is the CLPP, bottom right...... 132 Figure 4.2: Calculated RCS (cm2) of a water sphere vs. mass (g) at a wavelength of 3.2 cm. The gradient in the Rayleigh region is about three times steeper than the gradient in the other regions, with a crossover point at a mass of roughly 0.1 g. Beyond the Rayleigh region the curve exhibits undulations due to the varying interaction between the specular reflections and the creeping wave (Skolnik, 1990)...... 135 Figure 4.3: CLPPs for various simple combinations of the fitted terms. The fitted values were chosen to emphasis their effects. For intermediate values between a2 = 0 to a2 = 1, the CLPP changes smoothly between the CLPPs shown...... 138 Figure 4.4: Boundary conditions according to equations (4.25) and (4.33) for a2/a0 and a4/a0 when θ4 − θ2 = 0, together with the corresponding form of the CLPP and the boundary between two-lobed and four-lobed CLPP forms given by a4 = a2/4. The area containing two-lobed CLPP forms is shown shaded. Above a4/a0 = 1/3 (i.e. the two points where the corresponding values of a2/a0 are ± 4/3) the boundaries imposed by equations (4.25) and (4.33) are identical, but below these two points they are notably different. In particular the values of a2/a0 that are allowed by equation (4.33) (i.e. the straight lines) are not allowed by equation (4.25) (i.e. the curved lines) below a4/a0 = 0 because symmetric forms with negative values of a4/a0 are not observable. Hence equation (4.25) imposes a more severe constraint. To save space the equations shown assume a0 = 1. If a0 ≠ 1 then all instances of a2 and a4 in the equations should be replaced by a2/a0 and a4/a0 respectively. Thus the equation top

xxii right would become a4/a0 = 0.5 + X, and X would become X = (√(1– 2 (a2/a0) /2))/2...... 142 Figure 4.5: Boundary conditions for a2/a0 and a4/a0 for particular values of θ4 − θ2. The equations describe the boundaries shown by the dotted lines. The shaded part (top) is repeated middle and bottom to help comparison. The boundary conditions imposed by equation (4.33) become inverted at intervals of θ4 − θ2 = 45º, and thus repeat at intervals of θ4 − θ2 = 90º. At intermediate values of θ4 − θ2 the boundary conditions fall between these two extremes, reaching a symmetrical shape at intervals of θ4 − θ2 = 22.5º; here there is no simple equation as in the other cases, and the equation shown has been fitted to the boundary using the form specified by equation (4.33)...... 143 Figure 4.6: Observed values of a2/a0 vs. a4/a0 for laboratory data...... 144 Figure 4.7: Observed values of a2/a0 vs. a4/a0 for the Bourke IMR. Left: good- quality echoes during the night of 14 March 1999, mainly plague locusts. Right: good-quality echoes during the night of 8 September 1999, mainly spring moths...... 144 Figure 4.8: Examples of how CLPPs with negative values of a2 or a4 are shifted by changing θ2 and θ4 but without changing the CLPP's shape. This moves the CLPP from its original quadrant to the top-right (+/+) quadrant...... 145 Figure 4.9: Examples of the fit between observed CLPPs for good-quality echoes and equation (4.16). The points are the averaged RCS values measured by the IMR at the 64 sampling angles per antenna rotation. Each smooth shape represents the equation that best fits the points, calculated using a least-squares method. In each case the major axis of the CLPP is aligned with the body axis of the insect. a0 is the mean RCS. The difference |θ4 − θ2| is a measure of asymmetry and is explained in Section 4.6.2. The insects were flying at altitudes of (clockwise from top left) 375, 525, 625 and 675 m. The four shapes may seem to differ more than the similarities in their asymmetries might suggest, but the analysis shows otherwise. Observations made at Bourke on 14 March 1999. Further examples can be found in Dean & Drake (2005)...... 147 Figure 4.10: CLPP forms vs. θ2 and θ4. The original form is for a2/a0 = 0.75 and a4/a0 = 0.17 and is shown at the centre of the plot. All forms are aligned with the horizontal (θ2) axis. Symmetric forms (i.e. where θ4 − θ2 = 0) lie on the diagonal line and are rotated by changes in θ2, whereas changing θ2 (at constant θ4) changes the shape as well. Forms that lie outside the limits of |θ4 − θ2| = ±45º are identical to a form within the limits and are retrieved by the algorithm as such. For example each vertical set of three forms within ±45º is duplicated by the set immediately above or below...... 149 Figure 4.11: Differing radar views of an insect as seen by the near-horizontal beam of a scanning radar (left) and the vertical beam of an IMR (right)...... 152 xxiii Figure 4.12: Top: The average RCS (a0) and mass for the laboratory data compared with the RCS of a water sphere from Figure 4.2. Most of the insects have an RCS that exceeds that of a water sphere, often by several times, especially for large masses...... 153 Figure 4.13: The RCS ratio insect/water for the same mass (see Figure 4.12) vs. insect width/length. As expected, the range of width/length values for insects > 1000 mg is much less than for insects < 1000 mg, probably partly because the former are for just one species (S. gregaria)...... 154 Figure 4.14: Mass vs. RCS (a0) for the laboratory data measured using a radar wavelength of 3.2 cm. There are no masses between 650 mg and 1080 mg, leading to a gap in the plotted data; for convenience masses above or below this gap are termed > 1000 mg, representing just one species (desert locusts), and < 1000 mg, representing 22 species, respectively. Left: all masses, N = 68. Right: enlargement of the plot for masses < 1000 mg, N = 57. Data are taken from Aldhous (1989) and Wolf et al. (1993)...... 156 Figure 4.15: Insect body length vs. mass for the laboratory data. The data do not include insects with lengths between 30 and 45 mm...... 157 Figure 4.16: Insect width, width/length, and volume vs. mass for the laboratory data. The insect widths show a minor gap between 2 and 3 mm but are otherwise fairly uniformly distributed, so the gap in width/length and volume is mostly due to the gap in insect length as shown Figure 4.15. Volume = π x (width/2)2 x length...... 158 Figure 4.17: Variation of |θ4 − θ2| (an indication of CLPP asymmetry) and insect mass, length, width and width/length. The first two plots show significant correlations (P < 0.01). Data from Aldhous (1989) and Wolf et al. (1993). Number of insects in each plot is 68...... 162 Figure 4.18: Four of the CLPPs measured in the laboratory by Aldhous (1989). Above each plot m, L and W indicate mass in mg, length and width in mm. The largest insect has the biggest lobes at polarisation angles of 90 and 270° rather than at 0 and 180° as for the smaller insects ...... 163 Figure 4.19: a2/4a4 vs. insect mass, length, width and width/length for the laboratory data. The CLPP has two or four lobes above or below a2/4a4 =1 respectively. Only body length and width show a significant correlation (P < 0.01)...... 165 Figure 4.20: Distribution of orientation values retrieved from good-quality echoes from the Bourke IMR during the nights of 14 March and 8 September 1999. Left two: night of 14 March, mainly plague locusts. Right two: night of 8 September, mainly spring moths. Although a small proportion of the orientation values approach 90˚, it does not represent a true 90˚ turn in body alignment. If it did, there would be a clear scatter of results on either side of 90˚, but no such scatter is evident. (This 90˚ is the angle from the mean travel direction, not the absolute retrieved angle, which as explained in the text cannot exceed 90˚.) Note that the range of orientation values is limited to 180˚, hence no values appear in the bottom half of each plot...... 169 xxiv Figure 4.21: Distribution of values of the asymmetry measure θ4 − θ2 retrieved from good-quality IMR echoes during the nights of 14 March 1999 (left) and 8 September 1999 (right) at Bourke. Values for echoes with both a2/a0 and a4/a0 > 0.2 are shown in black, for which the totals are 1122 and 409 respectively. The means and standard deviations are −1.5 ± 29º (left) and +1.5 ± 35º (right)...... 170 Figure 4.22: 10 log10(a0) vs. number of two- and four-lobed CLPPs for good- quality echoes from the Bourke IMR. Top: night of 14 March, mainly plague locusts. Bottom: night of 8 September, mainly spring moths. The former show a notably larger proportion of CLPPs with four lobes (50.5% vs. 10.3%)...... 171 Figure 5.1: Left: distribution of mass for the laboratory datasets in Table 5.1 that have N ≥ 7. For each of the four component datasets, each mass was expressed as a percentage of the mean. The percentages were then combined and plotted in the histogram. Right: distribution of a0, a2, and a4 values expressed as a percentage of the mean for each of the three component datasets (values for the H. punctigera dataset were not available, hence N is reduced from 40 to 31)...... 178 Figure 5.2: A theoretical example of how two species could be misclassified using a scheme based on the distribution of a0 values. The mean of Species A is 1 cm2 and B 2 cm2. The SD of both species is 0.5 of the mean. Overall about one-quarter of all insects are misclassified...... 179 Figure 5.3: Measured θ2 values against insect body mass. θ2 > 10º exists only for insects with masses > 1000 mg...... 181 Figure 5.4: Discrimination between species in the laboratory data by pairs of RCS parameters. The radius of each oval is equal to one standard deviation, so each oval represents 68% of one parameter and 68% of the other, and its area (after allowing for any association between parameters) will generally contain roughly half of the cases for that species. Left: a2 vs. a0. Centre: a4 vs. a0. Right: a4/a0 vs. a2/a0...... 183 Figure 5.5: Differential reflectivity of a single particle of oblate shape versus axial ratio. Adapted from Raghavan (2004)...... 185 Figure 5.6: The error in the calculation of Ψ from equation (5.4) resulting from |θ4 − θ2| values being non-zero. The resulting CLPPs are plotted at the corresponding locations. The values for the RCS parameters are taken from Aldhous (1989) for a specimen of N. pronuba (mass = 321 mg, length = 26 mm, diameter = 5 mm)...... 186 Figure 5.7: Three theory-based RCS measures superimposed on the laboratory data plotted as a4/a0 vs. a2/a0. The dotted lines reproduce the constraint boundaries shown in Figure 4.4 in Chapter 4. Bottom right: associated CLPP forms. More then half of the possible forms were not observed in the laboratory data. Laboratory data are from Aldhous (1989) and Wolf et al. (1993)...... 187 Figure 5.8: Three theory-based measures regressed against insect length, width, 2 width/length and mass, for insects with a0 < 1.9 cm (N = 57). Above each

xxv set of plots is the classification measure and its mean correlation r with the four insect measures...... 190 Figure 5.9: Three theory-based measures regressed against insect length, width, 2 width/length, and mass, for insects with a0 ≥ 1.9 cm (N = 11). Above each set of plots is the classification measure and its mean correlation r with the four insect measures...... 191 Figure 5.10: Enlargements of the three best regressions from Figure 5.8 where the body sizes of plague locusts and spring moths each have distinct ranges. Above each set of plots is the classification measure and its correlation r with the insect measure. Labelled areas show the observed range in width/length and mass for plague locusts and spring moths. ....193 Figure 5.11: The two best single classification measures superimposed on a subset of laboratory data plotted as a4/a0 vs. a2/a0. The subset consists of insects similar to plague locusts (locusts and grasshoppers, solid circles) and spring moths (moths and butterflies, crosses). Laboratory data from Aldhous (1989) and Wolf et al. (1993)...... 194 Figure 5.12: a4/a0 vs. a2/a0 for laboratory data according to mass, length, width and length/width. The dotted lines indicate the constraint boundaries shown in Figure 4.5 in Chapter 4. Laboratory data are from Aldhous (1989) and Wolf et al. (1993)...... 195 Figure 5.13: Distribution of retrieved RCS parameters. The number of cases within each area of 0.02 x 0.02 is shown as a shade of grey according to the scale shown on the right of each plot. The darker the area the greater the number of cases. Spring moths tend to concentrate below a4/a0 = 0.17 while plague locusts tend to concentrate above a4/a0 = 0.17. The value 0.17 was determined empirically to give the best discrimination between these two groups over the full dataset...... 197 Figure 5.14: CLPP forms corresponding to the area occupied by insects in Figure 5.13 and the division of the area into four regions...... 198 Figure 5.15: Distribution of retrieved RCS parameters. The number of cases within each area of 0.02 x 0.02 is shown as a shade of grey according to the scale shown on the right of each plot. The darker the area the greater the number of cases. Left: few plague locusts. Right: mainly plague locusts...... 199 2 Figure 5.16: The total number of large (a0 ≥ 1 cm ) insects and the proportion in each classification region during the Top: March and Bottom: September study periods. Upper Left: UL, Upper Right: UR, Lower Right LR, Lower Left: LL...... 200 Figure 5.17: Location map of the two APLC light traps at White Cliffs and Fowlers Gap and the two fixed IMRs at Bourke and Thargomindah...... 202 Figure 5.18: Distributions of the number of plague locusts trapped at White Cliffs and Fowlers Gap...... 203 Figure 5.19: Comparison of results for 1998 starting in May. During nights 120-300 (May-October) the insects were mainly spring moths. From night 330 (late November), as the weather became warmer, the insects were

xxvi mainly plague locusts. Weather data is for 2100 h and is from the Bureau of Meteorology...... 204 Figure 5.20: Comparison of results for 1999. Plague locusts predominate until about night 75 (mid-March), with a small transition period during nights 90-120 (April) when the insects were more mixed. Spring moths predominate until roughly night 260 (mid-September), after which the insects were more mixed with several outbreaks of plague locusts. Weather data is for 2100 h and is from the Bureau of Meteorology...... 205 Figure 5.21: Comparison of results for 2000. Plague locusts predominate the early months until about night 90 (end of March). After a transition period to about night 120 (end of April), spring moths predominate apart from a small surge in locust-like targets during nights 150-170 (first half of July). As in 1999, occasional large-scale plague locust movements began from about night 275 (early October), and by the end of the year plague locusts were again predominant. Weather data is for 2100 h and is from the Bureau of Meteorology...... 206 Figure 5.22: Comparison of results for 2001. Plague locusts predominate until about night 100 (early April), then comes a short transition period before spring moths predominate the rest of the study period from night 120 (beginning of May). Weather data is for 2100 h and is from the Bureau of Meteorology...... 207 Figure 5.23: Classification result (the percentage of targets in the Upper Left and Upper Right regions of Figure 5.14) against: Left: temperature at 2100 h. Right: relative humidity at 2100 h...... 211 Figure 5.24: Wingbeat frequencies from the Bourke IMR for mostly locusts and mostly moths. Top: 20-40 Hz. Bottom: 40-120 Hz. (H. K. Wang & V.A. Drake, personal communication)...... 212 Figure 6.1: Air temperature and the percentage of observations during which several plague locusts were seen in flight at any one time during daylight hours. Adapted from Lambert (1972). The number of observations per data point averages about 15 in the range 20-30ºC, and about 5 elsewhere...... 222 Figure 6.2: Recorded migrations of plague locusts on low-pressure systems during the years 1980-2000. Circles indicate the positions of the two fixed IMRs used in the present study. Adapted from Hunter & Deveson (2002)...... 224 Figure 6.3: An active cold front showing wind speed and temperature. Across the boundary there is a sharp change of air temperature that can result in a strong thermal upcurrent producing a relatively high-speed jet (in this case at high altitude) parallel to the boundary. Adapted from Sturman & Tapper (1996)...... 226 Figure 6.4: Distribution of wind directions. Vertical arrow indicates north, bars indicate direction wind blows from. Left: locust periods. Right: moth periods. In each case, for the purpose of calculating correlations, the 0/360º point is moved to the minimum total as shown where any split between 0 and 360 will be least disruptive...... 228 xxvii Figure 6.5: Distribution of (left to right) nightly temperature, atmospheric pressure, relative humidity, wind direction and wind speed for the (from top) 1998, 1999, 2000 and 2001 moth periods...... 230 Figure 6.6: Distribution of nightly temperature, atmospheric pressure, relative humidity, wind direction and wind speed for the (from top) 1999, 2000 and 2001 locust periods...... 230 Figure 6.7: Total 3-monthly rainfall for the general Bourke area 1998-2001. Left: January-March locust period. Right: August-October spring moth period. Adapted from www.bom.gov.au...... 232 Figure 6.8: Annual rainfall figure for the Bourke district 1891-2001. The horizontal line indicates the mean of 354 mm. Rainfall 1891-2002 varied from 57 mm in 2002 (not shown) to 856 mm in 1950. Data is from the Bourke Shire Council. A runs test above and below the median (Bendat & Piersol, 1966) showed little evidence of clustering (observed runs 54, expected runs 57, P = 0.51), a result confirmed by the serial correlation (r = 0.095, P = 0.32)...... 233 Figure 6.9: Example data, for typical weather maps for Australia illustrating typical seasonal weather patterns. Left: January-March locust period, tropical/subtropical influences. Right: August-October spring moth period, temperate influences. Adapted from www.bom.gov.au...... 233 Figure 6.10: Insect counts during the four moth periods. Nights coinciding (approximately) with the passage of a cold front, trough or both are shown in black, red or blue respectively...... 238 Figure 6.11: Distribution of unadjusted nightly insect counts (RCS ≥ 1 cm2) during moth periods (top) and locust periods (bottom). Counts are divided into 12 groups spaced about 1/600th of the total apart. Total counts are 15,058 (moths) and 63,471 (locusts)...... 245 Figure 6.12: Consecutive unadjusted nightly insect counts for the seven study periods. Interpolated nights are shown as open circles. The slope of the least-squares trend lines are given in Table 6.3...... 246 Figure 6.13: Correlograms for nightly insect counts. N = number of nights, m = mean nightly count of insects. Top: moths 1998 (N = 59, m = 144) and 2000 (N = 45, m = 64). Bottom: locusts 1999 (N = 54, m = 351) and 2001 (N = 50, m = 532). Left to right, the values of r for P = 0.05 are 0.26, 0.29 for moths and 0.27, 0.28 for locusts...... 248 Figure 6.14: Distribution of insect numbers before and after the 4th-root and 10th-root transforms. Top: moth periods. Bottom: locust periods...... 250 Figure 6.15: Effect of moonlight on average insect numbers observed by the Bourke IMR. Vertical axis = number of insects observed during periods of seven nights each centred on full moon / average number of insects observed during similar periods centred on the new moon before and after...... 252 Figure 6.16: 4th root of the nightly number of insects observed by the IMR during moth periods vs. the three most significant weather variables. N = 195. Top: atmospheric pressure. Middle: daily change in atmospheric

xxviii pressure (daily pressure minus daily pressure on the previous day). Bottom: temperature...... 256 Figure 6.17: 4th root of the predicted number of insects vs. 4th root of the actual number of insects for 195 nights during the moth periods. Results from the years 1998-2000 and 2001 are shown as points and crosses respectively. The correlation is r = 0.69 (i.e. √R2 where R2 = 0.475 see Table 6.2), for which P < 10–30...... 260 Figure 6.18: Scree plot of the first ten components of the moth period PCA. The first trend line shows the initial trend, and the second trend line shows the trend of the ‘scree’. Their point of intersection indicates the number of components to extract, in this case two...... 265 Figure 6.19: Plot of component loadings for the moth periods when the PCA is restricted to two components. The variables most relevant to each pole are circled...... 265 Figure 6.20: 4th root of the nightly number of insects observed by the IMR during the locust periods vs. rainfall. There were only two nights where rainfall = 25 mm...... 270 Figure 6.21: 4th root of the predicted number of insects vs. 4th root of the actual number of insects for 151 nights of observation during the locust periods. The correlation is r = 0.43 (i.e. √R2 where R2 = 0.188 see Table 6.12), for which P < 10–7...... 273 Figure 6.22: Scree plot of the first 10 components of the locust period PCA. The first trend line shows initial trend, and the second trend line shows the trend of the ‘scree’. Their point of intersection indicates the number of components to extract, in this case four...... 277 Figure 6.23: Plot of component loadings for the locust periods when PCA is restricted to two components. The variables most relevant to each pole are circled...... 277 Figure 6.24: Number of insects (5-point moving average) versus total rainfall in the previous 10 days (bars) for the locust periods in 1999, 2000 and 2001. Note that each year has a different vertical scale...... 280 Figure 6.25: Distribution (number of insects)1/4 during locust periods. Black bars indicate nights where the rainfall in the previous days was more than 10 mm...... 281 Figure 7.1: Insect migration vs. IMR position for known migration direction and width. (a) IMRs close together miss much of the migration. (b) IMRs too far apart miss the migration altogether. (c) The optimum distance apart is similar to the migration width and at right angles to the migrant direction (assuming width and direction are sufficiently constant for the purpose)...... 296 Figure 7.2: Possible positions of a migrating insect population (grey bars) at two IMRs A and B simultaneously as a proportion of possible positions at A or B. s = separation between IMRs, w = population width (w ≥ s), x indicates edge of population in contact with A or B. Between first x and last x the distance is (w + s), during (w – s) of which both A and B are in contact with the population, so proportion is (w – s)/(w + s)...... 297 xxix Figure 7.3: Average proportion of occasions when two IMRs separated by s metres are observing the same migrating insect population of width w metres, provided that the population is being detected by at least one IMR. Based on Figure 7.2 ith all travel directions φ being equally probable. (As described later in the text, the vertical axis turns out to be numerically equal to the mean correlation between observed insect numbers at the two IMRs.)...... 298 Figure 7.4: Distribution of the gap-free periods from 1 September 1999 to 1 March 2001 where data was acquired by both IMRs. Periods where gaps were limited to a single night are shown in white. Only periods of >14 nights (the final white bar on the right) were used for analysis. Details of these periods are shown in Table 7.1...... 303 Figure 7.5: Number of nights vs. number of large (RCS ≥ 1 cm2) insects observed by the Bourke and Thargomindah IMRs during 1 September 1999 through 1 March 2001. The correlation is r = 0.99...... 307 2 Figure 7.6: Number of large insects (a0 ≥ 1 cm vs. day number from 1 September 1999 to 1 March 2001. Left: Thargomindah IMR. Right: Bourke IMR. Counts on incomplete nights have been increased pro rata to correct for their incompleteness. Periods when the IMR was out of service are indicated by grey shading...... 308 Figure 7.7: Scatterplot of the insects plotted in Figure 7.6 during the 313 nights (57% of the total of 548 nights) when both fixed IMRs were operating. Despite the scatter a clear linear relationship is evident (r = 0.56, P < 10- 24), showing that the counts at the two IMRs tend to vary in unison...... 309 Figure 7.8: Number of large insects (RCS ≥ 1 cm2) observed during the seven gap-free periods at Bourke (solid lines and filled circles) and Thargomindah (dotted lines and open circles). Mean number of nights in each period = 25. Total nights = 172...... 312 Figure 7.9: Autocorrelation between nightly insect counts at the Thargomindah IMR for period 5 (28 nights from 30 May 2000 to 26 June 2000)...... 314 Figure 7.10: Crosscorrelation between the number of insects detected by the Bourke and Thargomindah IMRs for period 5 (28 nights from 30 May 2000 to 26 June 2000). The dotted lines indicate the correlation value where P = 0.05...... 315 Figure 7.11: Circular histograms of the mean nightly insect migration direction for the 313 nights of joint operation (57% of the total 548 nights) during 1 September 1999 through 1 March 2001. Histograms show the direction the insects are migrating towards, 0º = north, 90º = east. Left: Bourke. Right: Thargomindah...... 317 Figure 7.12: Circular histograms of the average number of insects per night according to direction for the 313 nights shown in Figure 7.11. Histograms show the direction the insects are migrating towards, 0º = north, 90º = east. Left: Bourke. Right: Thargomindah...... 318 Figure 7.13: Scatterplot of the mean migration directions for the 313 nights shown in Figure 7.10. Each point has error bars showing the associated standard deviations. The correlation is r = 0.56 (P < 10–24))...... 319 xxx Figure 7.14: Ratio of nightly insect totals at Bourke and Thargomindah over 313 nights, expressed as the mean of smallest/largest, vs. difference in nightly wind direction. The difference exceeds 50º in about 21% of cases. Cases where the difference exceeded 120º were too few to be plotted. ..321 Figure 7.15: Distribution of mean nightly insect travel speeds as measured by the IMRs at Bourke and Thargomindah for the full 313 nights...... 322 Figure 7.16: Scatterplot of the mean nightly travel speeds during the 313 nights when both fixed IMRs were operating. Each point has error bars showing the associated standard deviations. The correlation is r = 0.42 (P < 0.001)...... 323 Figure 7.17: Distances travelled during ten hours at the travel speeds and directions observed by the Bourke and Thargomindah IMRs during the 538 nights of the 1999-2001 study period. Bar length indicates the distance travelled in a 10-hour flight. Bar colour indicates total insect numbers observed travelling in the indicated direction: light grey <500, minor movement; dark grey 500-1500, average movement; black >1500, major movement. If the insects remained aloft for ten hours, the time between summer sunset and sunrise, this is where they might land...... 326 Figure 7.18: Study area with the four mobile IMR locations (Glengeera, Barringun, Eulo, and Thyangra) shown in bold type. The heavy black lines are sealed roads...... 327 Figure 7.19: Schematic view of a migration's leading edge (supposing it to be recognisable) passing over one IMR en route to another IMR several hours away. Provided the two IMRs are of equal sensitivity and are aligned with the flight direction, their results should indicate any changes in altitude and the extent to which the migration is dispersing, neither of which are measurable by a single IMR or by two IMRs separated by a relatively long distance (as Bourke and Thargomindah are)...... 328 Figure 7.20: Hourly insect counts between 1900 and 0500 h recorded by the Mobile, Thargomindah and Bourke IMRs on the nights of (from top) 16 April through 23 April 2002. The locations corresponding to each pair of plots are (from top) Glengeera, Barringun, Eulo, and Thyangra. To equalise differences between IMRs the numbers are given as a percentage of each night’s total (note that the vertical scale varies between plots). On the right is the distance between IMRs, the correlation between plots, and the total counts for the first-named IMR. Thus BT shows the total for B...... 330 Figure 7.21: Mean nightly insect travel directions at the three IMRs during 16- 23 April 2002, and wind directions measured at 2100 h at the two fixed IMR locations and at Cunnamulla (68 km east of Eulo. In each case the wind is blowing towards, and the insects are travelling towards, the direction...... 335 Figure 7.22: Three circular correlations between observed IMR travel directions. The labels above each plot identify the original entries in Table 7.11. The first hourly value is set to 0,0 degrees shown by the large dot; the line through 0,0 has been made by eye. The changes at the first-named xxxi IMR are plotted on the vertical axis. Left: a positive correlation. The changes in direction at each IMR are in the same direction. Middle and Right: two negative correlations. A small change in direction at one IMR is accompanied by a larger change in the opposite direction at the other IMR...... 337 Figure 7.23: The insect travel directions of Figure 7.21 superimposed on the geographical IMR locations shown in Figure 7.18. Top: Thargomindah and its two closest mobile IMR locations. Bottom: Bourke and its two closest mobile IMR locations. In each case the numbers are the dates in April 2002 when the mobile IMR was at that location...... 338 Figure 7.24: Average nightly travel speeds at the three IMRs during 16-23 April 2002. The speeds tended to be fairly changeable during the night, and the standard deviation over the 11 hours would be typically 8 ms–1...... 341 Figure 7.25: Travel speed vs. altitude for large (RCS ≥ 1 cm2) and small (RCS < 0.1 cm2) insects as recorded by the Bourke IMR on 20 March 1999. Total number of insects is about 2,200 (small) and 460 (large), ...... 342 Figure 7.26: Possible locations for future IMRs. For the more remote locations, open circles show areas consistent with a diameter of 300 km, this being an adequate spacing for IMRs as estimated in the text. Shaded circle show existing IMR locations...... 347

xxxii PRINCIPAL SHORT NAMES AND ABBREVIATIONS

Most abbreviations are explained as they arise. The following list is short but is given here for clarity and convenience. In parentheses is the section where first introduced or explained: locusts - Australian plague locusts (1.6.1) moths - Spring moths (1.6.2) APLC - Australian Plague Locust Commission (1.6.1) CLPP - Copolar-Linear Polarisation Pattern (4.3) IMR - Insect Monitoring Radar as used in Australia (1.3.2) RCS - Radar Cross Section (4.2) VLR - Vertical-Looking Radar as used in the UK (1.3.2)

Any non-conforming uses of the terms 'locust' and 'moth' are explained in the text as they arise.

xxxiii ACKNOWLEDGEMENTS

My supervisor, Alistair Drake and co-supervisors, David Low and Ravi Sood, from the School of Physical, Environmental and Mathematical Sciences (formerly the School of Physics), University of New South Wales at the Australian Defence Force Academy, provided formal help and encouragement. Ian Harman assisted with the operation of the radar, construction of the mobile IMR, and data processing. Staff of the electronic and mechanical workshops of the School of Physics contributed to radar design and construction. Haikou Wang assisted with the processing of data using the C++ algorithm. Staff of the Rothamsted Agricultural Research Station (UK) provided helpful advice and encouragement. Simon Cain helped with the field trial of the mobile IMR, for which respectively N. Brown, V & G Murphy, J & C Berghofer and 'Blue' Mahr kindly provided operating sites at Glengeera, Barringun, Eulo, and Thyangra. The School of Physics (Scholarship) and the University of New South Wales (Doctoral Fellowship) provided financial support.

xxxiv 1 INTRODUCTION – RADAR, INSECTS, WEATHER, AND AIM OF STUDY

Radar entomology has advanced the study of insect migration in more than a dozen countries. Two automated entomological radars have been operating in Australia since 1999. Nevertheless the field has surprisingly few exponents. Many related areas such as the discrimination between insect species and the effect of weather variables lack detailed study. The present thesis continues the work begun by V.A. Drake and others at the former School of Physics University of New South Wales at the Australian Defence Force Academy. It focuses on the radar properties of Australian plague locusts and spring moths, the effects of weather on their migrations, the optimum placement of radars for their detection, and details of the first custom- made mobile ZLC-configuration Insect Monitoring Radar. The locusts and moths breed in inland Australia and then migrate hundreds of kilometres to the agricultural areas of eastern Australia, often with devastating results.

This chapter introduces radar entomology and states the aims of the thesis. It reviews the history, principles, and types of entomological radars, and their use in Australia. It also reviews the effects of weather on insect migration in general, the characteristics of Australian plague locusts and spring moths, and their source and destination areas. Each topic is further reviewed in the chapter that deals with it. The aims of the thesis include assessing the performance of insect monitoring radars (IMRs) in characterising migrations of locusts and moths; identifying any biases; assessing the effect on migration of weather variables such as temperature, wind direction, and rainfall; determining the scale of migrations; and determining the most effective location for current and future IMRs.

1.1 Preface: Radar, Insects, Study Area

A radar (from Radio Detection and Ranging) measures the signal reflected by objects from a beam of radio waves (Skolnik, 1980). Radar technology developed rapidly during the Second World War, and is today in widespread use, including in such varied applications as air and sea navigation, weather forecasting, and law enforcement.

Insects were first identified as being capable of reflecting radar signals by Crawford (1949). Since then radar entomology - the study of insects using radar - has developed into a powerful tool. For example, it can at low cost observe the number, size, speed, direction, and body orientation of insects flying at altitudes of up to several kilometres in their natural environment, a capability currently unmatched by any other method. Indeed Dingle (1996) 1 states that it is the “tool that perhaps more than any other has advanced our knowledge of migratory movements over the past few decades”.

Radar entomology is a specialised research field with only a few groups active. During 1947-2004 there have been about 350 published studies, most of them since the 1970s, or generally less than ten a year. Many areas of the technology and its application remain open for further or more detailed investigation, some of which are addressed in the present thesis.

For example, ordinary scanning radars have been used to study insect flight and migration with considerable success (e.g. Drake & Farrow, 1983), but only now are they being automated sufficiently to be capable of acquiring the extended datasets needed for robust statistical investigations (see e.g. Wu et al., 2001). They have generally been replaced by automated Insect Monitoring Radars (IMRs) that incorporate computer processing of data (e.g. Drake et al., 2002b), but the biases that may be introduced by the analysis procedures, such as the preferential processing of particular insects, have yet to be fully evaluated.

In particular, insect migration is largely controlled by the weather (Johnson, 1969; Drake & Farrow, 1988), especially by temperature, wind, and (indirectly via its effect on pasture) rainfall. Most field studies have been based on trapping methods but interpretation is difficult because trap efficiency itself depends on weather conditions (Muirhead-Thomson, 1991). An example of an early study is that by Deal (1941), who found that there is a preferred temperature to which an insect will move in a temperature gradient. In principle IMRs can study the relation of flight and migration to weather in much greater detail than was previously possible.

The study area of the present work is in eastern Australia, an area subject to locust and moth plagues that in bad years cause losses of millions of dollars. For example in 1984, despite the use of pest control procedures, the estimated 2 crop loss was $A5 million, whereas without pest control procedures the losses might have reached $A100 million (from www.affa.gov.au/aplc). Migrating insects can travel hundreds of kilometres from their breeding grounds in inland Australia to agricultural areas in the south and east, often with devastating results. Their source and destination areas encompass parts of four states and the Northern Territory, see Figure 1.1. The area is mostly either desert or semi- arid grassland characterised by low irregular rainfall and hot summers; it is generally flat with an elevation almost entirely below 500 m. The area and its climate are described in more detail in Section 1.7.

Figure 1.1: Climatic regions of Australia based on the 30 years of climate data from 1961 to 1990. (Koeppen classification system adapted from www.bom.gov.au). The inner circle shows the approximate area monitored by the Australian IMRs. The outer circle shows the approximate extent of the source and destination areas for the Australian plague locusts and spring moths studied in the present work.

1.2 Aim of the Present Study

The present study continues the work begun by others in the former School of Physics (now part of the School of Physical, Environmental and Mathematical 3 Sciences), University of New South Wales, at the Australian Defence Force Academy, Canberra, in developing radar entomology into an established ecological monitoring tool. The present study attempts to answer such questions as: - How reliable are the present Australian IMR systems? - Can a mobile IMR for short-term observations be built and operated? - Are there biases introduced by the signal processing procedure? - Can IMRs be designed holistically to match particular requirements? - What is the relation between an insect's size and its radar properties? - Is it possible to distinguish between different types of insects from their reflectivities? - How does weather affect insect migration in inland eastern Australia? - What is the scale of such migrations and where are IMRs best located?

The resulting answers to the above questions are summarised in Chapter 8. The present study includes construction and operation of the first custom-made mobile ZLC-configuration IMR, and an assessment of weather effects on the migration of Australian plague locusts and spring moths using four years of data from the existing fixed IMRs. Weather effects are the subject of a large literature, and my main contribution to this area is their assessment using the above large and mostly continuous dataset. My hope is that the work contained in this PhD thesis (only the second in the field after Aldhous (1989)) contributes to the continuing success of radar entomology.

The rest of this introductory chapter briefly reviews the history, principles, and types of entomological radars, their present status in Australia, the effects of weather on insect migration, the insects studied in the present work (Australian plague locusts and spring moths), and their source and destination areas. Each topic is further reviewed in the chapter that deals with it.

4 1.3 Monitoring Insect Flight Using Radar

1.3.1 The Origins of Radar Entomology The first demonstration of what was to become radar occurred in 1886 when Heinrich Hertz showed that radio waves could be reflected from solid objects. There were some early successes with ionospheric reflections and proposals for ship collision avoidance systems, and then from the mid-1930s a very rapid development for air-defence applications (Bruderi, 1996). Following the end of the Second World War in 1945, meteorological radars were developed for detecting bad weather (Atlas, 1990). This resulted in the discovery of a considerable enigma. From the start, radar observations of the atmosphere had revealed phantom echoes for which no cloud, precipitation, or other identifiable targets were visible to the naked eye, which led to much debate about their cause (Hardy et al., 1966). These phantom echoes were commonly referred to as ‘angels’ (‘dot angels’ if they were discrete point targets or ‘distributed angels’ if they had substantial horizontal extent). One likely cause, namely birds, was quickly identified, and the use of radar to study bird migration became well established by the mid-1960s (Schaefer, 1966; Eastwood, 1967; Bruderer, 1997; 1997b).

The most common suggestions for other causes of angels were: (1) insects, (2) surface targets below the line of sight, and (3) direct backscatter from the air itself due to fluctuations in its index of refraction (Hardy et al., 1966). By using a searchlight linked to a vertical radar beam, and working at night, Crawford (1949) had in fact already shown that some of them were due to insects. Crawford (1949) prophetically stated that:

“The vertical-incidence radar, [however], may be a useful tool to the entomologist for observing how the density of flying insects varies with the season, time of day, weather conditions and the like.”

5 Until the 1970s, angels were the subject of significant study by radar meteorologists (scientists using radar to study the atmosphere) e.g. Bonham & Blake (1956), Tolbert et al. (1958), Plank (1960), Geotis (1964), LaGrone et al. (1964), Chernikov (1966), Glover & Hardy (1966), Hardy & Glover (1966), Hardy & Katz (1969), Hardy & Ottersten (1969). One theory held that the targets, whatever they were, would most likely have only a negligible motion through the surrounding air, so their echoes could be used to estimate wind speed and direction (e.g. Lhermite (1966)). Various workers using a variety of radars mostly concluded that the angels (and especially dot angels) were usually (but not always) due to insects.1

Other early radar observations of insects were made incidentally or using radars intended for other purposes. For example, Rainey (1955) observed a locust swarm in the Persian Gulf using a centimetric marine radar; Ramana Murty et al. (1964) and Mazumdar et al. (1969) studied locust swarms in India using a 3.2 cm meteorological radar; and Downing & Frost (1972) studied the diurnal behaviour of mosquitoes in the USA using an 18.75 mm AN/MPQ artillery locating scanning radar.

The first truly entomological radar (i.e. one purpose-built to observe insects) was constructed by G.W. Schaefer in collaboration with the Anti-Locust

1 For example, Browning & Atlas (1966) states that "practically all of the [phantom echoes] were due to insects of one kind or another", as did Lofgren & Battan (1969) and Fowler & LaGrone (1969). Deam and LaGrone (1966) concluded "in near conclusiveness" that all signals observed at vertical incidence were due to flying insects. Hardy et al. (1966) identified refractive-index fluctuations as another cause. Ottersten (1970) concluded that insects may not be the sole cause of the echoes, and that some may be due to convective bubbles 1-3 km in diameter and several hundred meters high (Hardy & Ottersten, 1969; see also Kropfli, 1983 and Chadwick & Gossard, 1983), but this was disputed by Atlas et al. (1970b), and the idea was later discarded. Campistron (1975) found links with atmospheric thermodynamics and concluded that angel echoes could be used in the investigation of the lower atmosphere. Takeda & Murabayashi (1981) investigated clear-air echoes and concluded that most were due to insects. More recent work has looked at the use of insects as markers to indicate airflow e.g. Eaton et al. (1995), which has led to the study of possible biases that could result if the insects have significant air-speeds (McLaughlin, 1993); and with the increasing use of weather radars this has become an important issue (Wilson et al., 1994; Mastrantonio et al., 1999; Venema et al., 2000; Kusunoki, 2002). 6 Research Centre (UK) and was used in Niger in 1968 (Schaefer, 1969; 1972; 1976; see also Roffey, 1969; 1972). It was a modified commercial marine radar utilising a scanning pencil-beam and a plan-position-indicator (PPI) display. When operated on the southern fringe of the Sahara Desert, it immediately established that large numbers of insects actively migrate at heights of hundreds of metres for tens or hundreds of kilometres, night after night (Schaefer, 1976). This 1968 study is considered by Reynolds (1988) to mark the real beginning of radar entomology. By 1973 Schaefer had operated similar radars in Australia, Sudan and Canada.

From the 1970s onwards, economically significant insect pests have been studied by radar in more than a dozen countries as shown in Figure 1.2. The use of entomological radars in Australia dates from 1971 and is described in Section 1.3.4.

Figure 1.2: Countries where entomological studies have been conducted using ground- base radars. For examples see: Australia (Schaefer, 1976; Drake et al., 1981). Canada (Schaefer, 1976; Greenbank et al., 1980; Dickison et al., 1982; 1986; Rainey & Haggis, 1987). China (Chen et al., 1985; 1995; Riley et al., 1990; 1990b; 1991; 1991b; 1994; 1994b; 1995, Feng et al., 2003). Cyprus (Drake, 2002). Ethiopia (Schaefer, 1976; Roffey, 1972). India (Riley et al., 1992; Reynolds et al., 1999). Mali (Reynolds & Riley, 1979; 1988; Riley & Reynolds, 1986; 1990; Riley, 1989). Niger (Schaefer, 1969; 1972; 1976; see also Roffey, 1969; 1972). Philippines (Riley et al., 1987). Saudi Arabia (Riley, 1973; 1974). Sudan (Schaefer 1976; Rainey & Haggis, 1987). UK (Schaefer et al., 1985; Chapman et al., 2000b; 2000c; 2002; Smith et al., 7 2000). USA (Beerwinkle et al., 1994; 1995; Wolf et al., 1995). For studies using airborne radars see Section 1.3.3.

Until the early 1990s entomological radars were generally scanning radars in which a rotating antenna swept the radar beam around the area of interest. An example is shown in Figure 1.3.

Figure 1.3: A scanning entomological radar being operated in the Sudan by Loughbrough University of Technology in 1974. Photo by V.A. Drake.

1.3.2 Vertical-Beam Radars In the 1990s interest shifted to vertical-beam units that were better able to automatically observe individual insects. Ottersten (1970) and Atlas et al. (1970; 1970b) were meteorologists who had detected insects in this way, the latter developing a method for estimating target speed that is a precursor of that now used in IMRs. Riley & Reynolds (1979) built the first vertical-beam entomological radar, which incorporated rotating linear polarisation to allow the determination of body shape and heading as well as speed. Bent (1984) offset the antenna feed in the parabolic dish antenna so it orbited the focal point, thus producing a conical scan, a technique dating back to the early 1940s when it was developed for use in tracking radars (Dunn et al., 1970). This combination, since termed the “ZLC-configuration” (Zenith-pointing Linearly- polarised Conical-scan) enables the determination of movement direction as 8 well as body shape, orientation, and speed from the complex signal variation that arises as an individual insect traverses the rotating beam.

Bent’s original configuration employed two antennas, one for a rotating (but not offset) transmitter beam, the other for a synchronously rotating and offset (i.e. conical-scanning) receiver beam, see Figure 1.4. Separate transmit and receive antennas are used in some recent meteorological profilers (e.g. Mead et al., 1998; Li et al., 2000; Ince et al., 2000). But entomological applications favoured a single antenna, which led to the birth of the modern VLR (Vertical- Looking Radar) and IMR (Insect Monitoring Radar). VLRs (Chapman et al., 2002) in the UK and IMRs (Drake, 2002) in Australia both use the ZLC- configuration but have minor differences in implementation. They also use different analysis procedures, so the separate names are retained.

Figure 1.4: The original IMR configuration, as developed by Bent (1984), consisted of a static conical transmitter beam (left) with a rotating conical receiver beam (right). Reproduced from Bent (1984).

In summary, the establishment and initial success of radar entomology was due largely to G.W. Schaefer's pioneering work in Niger and other counties, and to subsequent development over many decades by V.A. Drake in Australia, W.W. Wolf and K.R. Beerwinkle in the USA, and J.R. Riley, A.D. Smith and D.R. Reynolds in the UK. Accounts of the development of radar entomology

9 have been given by Lewis (1978), Riley (1979), Reynolds (1988), Reynolds & Riley (1997) and Zhai (1999).

1.3.3 Airborne, Doppler and Harmonic Radars The most widely used entomological radars are ground-based, but airborne entomological radars have been proposed and occasionally used (Taylor, 1966; Schaefer, 1979; Hobbs & Wolf, 1989; Rainey & Joyce, 1990; Wolf et al., 1990; Pair et al., 1991; Hobbs & Wolf, 1996).

Airborne radars can rapidly gather data on migration over a significant distance, effectively performing a ‘transect’, and can thus explore the structure of discrete migrating insect populations or ‘clouds’ (Hobbs & Wolf, 1996). An early version could detect insects only within a range of 500 m (Schaefer, 1979) but observations at ranges of up to 1 km are now possible (Hobbs & Wolf, 1996). The equipment used is similar to that used in a ground-based profiler and incorporates rotating polarisation and a downward-looking pencil-beam (Schaefer, 1979). Echoes are recorded and processed digitally (Hobbs & Wolf, 1989; Wolf et al., 1990). However, airborne radars are expensive to run and are therefore not suitable for long-term observations. They have never been used in Australia.

Large scanning Doppler weather radars have been used to study the mass migration of aphids in Finland (Nieminen et al., 2000), evening flights of coastal insects in France (Sauvageot & Despaux, 1996), and grasshopper and other pest migrations in the USA (Achtemeier, 1992; Westbrook et al., 1998). Such incidental studies are possible only where suitable radars happen to be located. No radars of this type are located near the present study area.

Harmonic radar observations require an insect to be tagged with a device that re-radiates a harmonic of the radar signal (Roland et al., 1996), allowing its flight to be detected near the ground despite the presence of strong echoes from 10 ground clutter (e.g. vegetation). The first use of this technique was reported by Mascanzoni & Wallin (1986), who studied the movements of carabid beetles using a handheld direction finder designed for locating avalanche victims (see also Wallin & Ekbom, 1988). A true harmonic radar (which determines range as well as direction) has since been developed for studying insects flying at low altitudes where conventional methods cannot be used due to strong ground clutter (Riley et al., 1996; 1998; 1999; Osborne et al., 1997; 1999; Capaldi & Dyer, 1999; Carreck et al., 1999; Capaldi et al., 2000; Roach, 2000; Riley & Osborne, 2001; Riley & Smith, 2002). Gibson & Torr (1999) consider it to be "the nearest we have to an ideal tool" but because it requires the target insects to be tagged before they can be tracked it cannot be used for studies of large- scale migrations.

1.3.4 Entomological Radars in Australia The use of entomological radars in Australia commenced in 1971 with a study of pests in inland New South Wales, using a 3.2-cm wavelength (see Section 1.4.2) scanning radar with data displayed on a PPI (Roffey, 1972; Schaefer, 1976). This was followed by work in Victoria (Reid et al., 1979), Tasmania (Drake et al., 1981), Queensland, South Australia, and the Northern Territory (Drake, 2002) and various sites in NSW (Drake et al., 1981; Drake, 1982; 1982b; 1983; 1984; 1985; Drake & Farrow, 1983; 1985; 1988).

Currently the Australian Plague Locust Commission is charged with monitoring and controlling locust outbreaks in eastern Australia. Given the huge area of eastern Australia over which this highly mobile pest occurs, it is difficult and expensive to monitor populations by traditional means. Hence the IMR has promise as an automatic monitor of locust migration, and of course of other pest migrations as well. Moncaster (1988), in a review of sensors used for monitoring pests, foresaw that:

11 “It is possible to envisage a network of installations to provide continuous and accurate pest warnings and substantially improved forecasts, so that farmers can be well prepared to take remedial action.”

Two IMRs have been installed for long-term operation about 800 km inland from Australia's east coast in the present study area, see Figure 1.5. At the time of the present study (2002), one unit had been operating at Bourke in northern New South Wales for about four years since May 1998; the other had been operating in southern Queensland at Thargomindah, about 300 km northeast of Bourke, for about 2.5 years since September 1999. These particular locations were selected because they were on sealed roads and had reliable electric power. Both IMRs are operated from Canberra by the University of NSW School of Physical, Environmental, and Mathematical Sciences (formerly the School of Physics). Pictures of each unit can be found in Chapter 2.

Figure 1.5: Location of the Bourke and Thargomindah IMRs. Map width = 1800 km. Green shading = 0-200 m elevation, pale yellow-green shading = 200-400 m. (From Reference Atlas for Australia and New Zealand.)

Each IMR uses a vertical 3.2 cm radar beam, of rotating polarisation, that scans through a narrow conical angle whose width is typically 20 metres at an altitude 12 of one kilometre. Consequently the beam can sample only a minute fraction of a migration, but the small beamwidth is essential to limit the number of targets within the beam because only non-overlapping signals can be reliably processed. Radiated peak power is nominally 25 kW.

Both IMRs operate largely automatically, and by 2002 they had accumulated a very large set of data (up to 180 MB per night), representing a few million individual echoes. For the present study these observations were supplemented by those from a specially constructed mobile IMR, the first of its kind, shown in Figure 1.6.

Figure 1.6: The mobile IMR with its trailer and towing vehicle in front of the fixed IMR at Thargomindah. The flat semi-arid landscape is typical of the study area. Photo by the author.

1.4 Radar Principles and Processing

1.4.1 Pulse Operation In simple (“non-coherent”) pulse radars, short bursts of energy are transmitted, and the time taken for the radar to receive echoes indicates the target’s range. The strength of the echo indicates the target's size, and if the beam is narrow then the echo can also be used to determine the target’s direction. In pulse-

13 doppler (“coherent”) radars, the phase shift of the echo is also measured and used to estimate the radial speed of the target. Transmission and reception can occur through either the same or separate antennas.

1.4.2 Radar Frequencies Radar frequencies are commonly between 100 MHz and 100 GHz (Rinehart, 1997). The lower limit is set by antenna size (low frequencies require large antennas), spectrum utilisation (the frequencies permitted by regulation), and target characteristics (the higher the frequency the smaller the target that can be detected). The upper limit is set by the availability of high-power signal generators, the tiny antenna beamwidths, and the increasing attenuation by the atmosphere as the frequency increases (Edde, 1993).

The frequencies for insect radars are determined primarily by insect size and how reflective the insect is. The effective reflecting area of the target is termed its radar cross section, or RCS, and for insects this is typically between 0.01 and 10 cm2 at insect radar frequencies. Roffey (1972) noted that an insect RCS could be modelled as an equivalent volume of water with an elongated shape, which means that its RCS will depend on the beam direction and polarisation. If the wavelength is large compared to the insect’s dimensions, almost none of the signal will be reflected. Because the reflectivity of an insect falls off roughly as the inverse fourth power of the wavelength at wavelengths longer than the target's major dimension,, a relatively short (i.e. microwave) wavelength is essential.

For example Glover et al. (1966) tested wavelengths of 3.2, 10.7 and 71.5 cm, and found that the longer wavelength failed to detect even the largest insects, whereas the shorter wavelength allowed detection of most types of insects. Fortunately equipment using a wavelength of 3.2 cm is produced for marine radars, so it is readily available at low cost and is of a manageable physical size. Consequently 3.2 cm (i.e. 9.4 GHz) has been adopted as the standard 14 wavelength for almost all entomological radars. A shorter wavelength is necessary to detect very small insects, but the equipment needed is less readily available and more expensive. An example is the 0.88 cm wavelength used by Riley (1992) to study the flight of plant-hoppers that weighed only 2 mg.

1.4.3 Radar Identification of Insect Species In principle IMRs can distinguish between different insect species. For practical applications this is important, because not all migrant insects are pests. Schaefer (1976) was the first to recognize that the modulation of echoes caused by wingbeating (or more likely by movement of the abdomen and thorax rather than by the wings themselves (Schaefer, 1976; Vaughan, 1985)), offered the possibility of identifying insect species. Wingbeat frequency has since been used as a routine diagnostic tool, although it is recognised that the overlapping of wingbeat frequency ranges means that "reliable identification of the species being observed is rarely possible" (Riley, 1989). The Australian IMRs measure wingbeat frequencies using a stationary beam for 11 minutes in each hour of operation (Drake & Harman, 2000; Drake et al., 2002).

Another method of distinguishing between species, first suggested by Riley (1978), is based on relating an insect's body shape to the variation its radar cross section with beam polarisation. Various methods have been put forward for estimating an insect's species in this way, e.g. Riley, 1985; 1992; Wolf et al., 1993; Russell & Wilson, 1997; Riley et al., 2003. However, the problem is not straightforward because body size as well as body shape has an effect.

1.4.4 Processing of Entomological Radar Signals Echoes from scanning entomological radars are usually shown on a cathode ray tube ‘plan position indicator’ (PPI) display, see Figure 1.7, and then recorded either on film (Drake, 1981) or more recently by digital image capture (Cheng et al., 2002). Until recently, data analysis has been a very time-consuming task because operators had to manually count their number (e.g. Beerwinkle et al.,

15 1988) either during the observations or from the film record. However, the advent of vertical beam radars and affordable fast computers has allowed signals to be recorded and processed automatically (Riley et al., 1992b, Beerwinkle et al., 1993). These advances, coupled with the development of signal-analysis algorithms (Smith et al., 1993, Hobbs et al., 2000, Harman & Drake, 2004) allow modern IMRs to process individual signals and determine the target's size, speed and direction without any need for human assistance.

Figure 1.7: Time-lapse image from a scanning radar PPI display showing individual insect tracks. Photo by W. Wolf.

1.5 Effects of Weather on Insect Migration

As previously mentioned, insect flight and migration are largely controlled by the weather, especially by temperature, wind, and rainfall. The effects of weather on insect behaviour have been studied in the laboratory using wind tunnels or flight mills (devices that allow tethered flight), and in the field using movie cameras, calibrated binoculars (for making timed counts of insect numbers), and light-traps. Laboratory studies have limited relevance to field conditions because many natural flight behaviours such as speed and direction

16 cannot be accurately monitored under laboratory conditions (Baker & Cooter, 1979). But even field studies can be problematic.

Thus field studies tend to rely on trapping techniques that are themselves affected by weather conditions among other factors. Light-traps are often seriously affected (e.g. Williams et al., 1956; Bowden, 1973; Bowden & Church, 1973; Dent & Pawar, 1988; Muirhead-Thomson, 1991). For example moonlight can reduce the catch by up to 50% (Morton et al., 1981, Williams, 1936; Persson, 1976; Dent & Pawar, 1988; Yela & Holyoak, 1997), as can strong winds (e.g. Harling, 1968; Mizutani, 1984). Pheromone traps are affected by many factors (Nansen et al., 2001), including temperature (via the rate of pheromone emission), trap spacing (Wall & Perry, 1980), and the timing of an insect’s appetitive response (Dent & Pawar, 1988). Suction traps (Johnson & Taylor, 1955) are affected by wind speed (Taylor, 1962).

The following subsections attempt to summarise the large literature on the effects of weather on the migration of insects in general, with special attention to the desert locust (Schistocerca gregaria) because of its relevance to the present work. (The desert locust is the best studied locust and perhaps even the best studied insect, (Cressman, 1998).) The effects of weather on the migration of Australian plague locusts and spring moths are introduced in Section 1.6 and are further explored in Chapter 6.

1.5.1 Distance and Types of Migration Insect flight is generally divided into two categories depending on its function and the distance travelled, namely trivial flight (localised movement associated with feeding, finding shelter, breeding etc:) and migration (long-distance movement from one habitat to another) (New, 1992; Dingle, 1996). Migration itself can be classified into three types depending on the breeding characteristics of the insect (Johnson, 1969; Taylor, 1986; Irwin, 1999):

17 1. Migration of short-lived insects that move to new areas for breeding and then die, e.g. Australian plague locusts and spring moths. 2. Migration of long-lived insects that leave their breeding site and undertake a reproductive hiatus before returning to their original habitat, e.g. Bogong moths. 3. Migration of immature insects that move to a different habitat to mature before the females return to the original habitat to oviposit (lay eggs).

The number of possible migrations per year depends on how many generations can occur during the breeding season. Type 1 insects generally have a relatively short lifecycle, e.g. about 65 days for Australian plague locusts and 40 days for spring moths, which leads to a sequence of peaks in migratory behaviour during the months when conditions are favourable. Type 2 and 3 insects generally have longer lifecycles and there is often a single period of migratory activity each year.

1.5.2 The Effect of Wind on Insect Migration In biological terms the atmosphere can be divided into three layers (Farrow, 1986). Wind speed typically increases with distance from the ground, and for an airborne insect there will be a level above which it will be carried downwind regardless of its activity. Below this level is the layer in which an insect can overcome the wind and thus fly in any direction (Kennedy, 1951; Westbrook & Isard, 1999). This is the first layer, variously called the surface boundary layer, the flight boundary layer, or the biological boundary layer. For small insects such as aphids this layer is rarely more than a few metres deep, see Figure 1.8. But for larger insects such as those studied in the present work, whose air speeds are around 3 ms–1 or more, it can be a few tens of metres deep (Farrow, 1986).

18

Figure 1.8: The three layers of the atmosphere and the day-migration of aphids. Diagram shows the initial ascent of aphids at around 0.25 ms–1 through the surface boundary layer to the planetary boundary layer, followed by wind-assisted migration via the planetary boundary layer, and final descent to the migration destination (redrawn from Irwin, 1999). Unlike some night-migrating species, the aphids do not ascend to the third layer (free atmosphere or geostrophic layer).

The second layer is the planetary boundary layer where high-speed winds in the third and final layer are slowed by friction with the ground. The second layer varies between day and night in ways that largely determine the height and behaviour of day-flying or night-flying insects (Pedgeley, 1982; Drake & Farrow, 1988). By day, surface heating results in convective mixing and thermal updrafts that extend the layer to 1000 m or more. By night, as the surface cools by radiation and convective mixing ceases, the layer tends to merge with the first layer and shrinks to 100-300 m thick, often with calm air at the surface. Under clear skies the surface usually cools sufficiently to reduce the temperature of the adjacent air below that at higher levels, producing a temperature inversion (i.e. where the temperature increases with height), whereas under normal conditions the air temperature decreases with height at the dry adiabatic lapse rate (i.e. under all conditions exclusive of condensation or evaporation) of 0.98 ºC per 100 m (Rainey, 1989). As shown in the next 19 section, the variation of temperature with height is a crucial variable in insect migration.

Thermal updrafts by day involve cells that, when well defined, are typically about 1 km in diameter rising at 2 ms–1 or more, which can lift insects to 1000 m or more (Farrow, 1986). On the earth's surface the passage of cells is marked by periodic wind gusts and small fluctuations in air temperature. As the sun goes down the cells die out as their energy source is removed. Therefore by night there is no possibility of external vertical assistance to insect flight except by vertical airflows due to wind convergence, as for example in a cold front where the approaching wedge of cold air can lift the overlying warm air at speeds comparable to those in thermal upcurrents (Rainey, 1989; Pedgley, 1990).

The third and final layer is the geostrophic layer or free atmosphere, extending upwards to the tropopause. It is characterised by generally strong and constant winds that exhibit an abrupt wind shear (change in wind speed) at the boundary with the second layer. This third layer offers the best opportunity for insect travel and is more easily reached at night.

Low-altitude migration within the surface boundary layer can involve travel over hundreds of kilometres, and is exhibited mainly by butterfly and moth species. Such migration can occur even if it is against the wind. For example, Abbott (1951) found that the migration of the painted lady butterfly Vanessa cardui was most commonly against the wind. But more usually insects take advantage of the wind in some way. For example Showers (1993) and Showers et al. (1993) showed that the black cutworm Agrotis ipsilon and probably other insect species use near-surface airflow to complete midcontinental migrations. Other insects can use their own power to adjust direction, for example Srygley et al. (1996) found via vector analysis that two migrating butterfly species and one migrating moth species were capable of compensating for wind drift in 20 natural free flight. The longest regular low-altitude insect migration is that of the monarch butterfly Danaus plexippus, the only lepidopteran species to make true two-way migrations by the same individual, which migrates about 4000 km from southern Canada to central Mexico every autumn (Pence, 1998).

In contrast, high-altitude flight involves more than just relatively short-distance movement in the surface boundary layer. The initial phase consists of takeoff and ascent into the atmosphere by active flying, often with the help of updrafts if flying by day (Westbrook & Isard, 1999). The insects then continue their movement within or above the planetary boundary layer shown in Figure 1.8. Small insects that use updrafts generally travel during the day, although they may continue into the night (Johnson, 1995). Other schedules are possible, for example planthoppers take off both at dawn and dusk in summer, though in the cooler weather of autumn the dawn takeoff is much reduced (Kisimoto & Sogawa, 1995). Many high-flying insects migrate at night, both to avoid predators and to take advantage of the strong, steady geostrophic winds (Drake & Farrow, 1988), generally at altitudes of a few hundred metres, which can transport them for hundreds or even thousands of kilometres. However, depending on the species, the long distances involved in most wind-borne migrations do not necessarily make them of major significance. For example Showers et al. (1989), Greenslade et al. (1999) and Loxdale et al. (1993) point out that the frequent short-distance flights of aphids have more ecological impact than their infrequent long-distance movements.

From a study of associated bird behaviour, Russell (1999) concluded that insects which ride on storms often get forced down by rain, and are prevented from re-ascending by the lack of thermal updrafts. However, they frequently re-ascend at the first opportunity, which confirms that insects use updrafts as an aid in migration rather than as something to be avoided. Once aloft, migrants can often stabilise their flying height and maintain an apparently purposeful orientation (Rosenberg, 1981; Preiss and Kramer, 1983; Riley, 1990; Riley & 21 Reynolds, 1979; Showers et al., 1993), of which more in Section 1.5.5. Early workers such as Haine (1955) considered that this ability was restricted to large insects, but the above later work has shown that this is not the case.

1.5.3 Effect of Temperature on Insect Migration Insects are cold-blooded and to survive they must maintain their body temperatures between the maximum and minimum tolerable. As the temperature falls towards the minimum tolerable, movement becomes progressively slower and less co-ordinated, and ultimately the insect becomes immobile. Conversely, as the temperature rises towards the maximum tolerable, movement becomes increasingly rapid to start with, but is then followed by reduced co-ordination, paralysis, and finally death (Chappell & Whitman, 1990).

The range of tolerable temperatures differs between species and also between individuals of the same species according to their age, nutritional status, hydration state, light intensity, humidity, and particular habitat (Uvarov, 1977). For example a locust may tolerate lower temperatures better than another of the same species some distance away because its lifecycle experienced cooler surroundings, for example because the vegetation happened to be wetter and thicker. There is also the problem of deciding, for example, exactly when co- ordinated movement begins or ends. Thus considerable variations in observed temperatures for a particular activity are to be expected (Chappell & Whitman, 1990).

Lower temperature limits vary greatly between species, but upper temperature limits are less variable because the progression from normal activity to paralysis usually occurs within a fairly narrow range. Grasshoppers and locusts typically become immobile around 10ºC, prefer 35-42ºC, and become paralysed around 47-51ºC (Uvarov, 1977; Chappell & Whitman, 1990). On the ground, insects can maintain their internal temperature within rather narrow limits, 22 despite large external changes, simply by adjusting their orientation to the wind and sun, their posture and position in the vegetation (see Figure 1.9), and their position in the temperature gradients that start at ground level (Uvarov, 1977; Chappell & Whitman, 1990; Lactin & Johnson, 1998). Among insects generally the mechanisms of thermoregulation are very diverse (Heinrich, 1995).

Figure 1.9: Observed distribution within tall grass of the night-flying grasshopper Nomadacris in Madagascar. In the dry season when temperatures are generally high, the grasshoppers bask in the upper parts when cool (left), and shelter in the lower parts when hot (right). Adapted from Uvarov (1977).

In terms of insect flight and migration, many studies over many decades have shown that flying insects choose conditions that maintain their wing muscles within the range of preferred temperatures. Thus if warmer or cooler air is required, they change altitude accordingly. Evening takeoff of locusts is rarely observed if the air temperature at sunset is below 20ºC, and large-scale takeoff is generally limited to temperatures of 25ºC or more (Uvarov, 1977; Riley & Reynolds, 1979). At low temperatures, potential migrants at dusk are sometimes seen fluttering their wings before takeoff, presumably to raise their muscle temperature into the preferred range (Farrow, 1990). Evening takeoff starts at dusk in rapidly fading light and peaks just after dark, i.e. within a relatively narrow band of light intensities that evidently provide cues for takeoff; the required band of intensities can be higher at lower temperatures;

23 later takeoffs have been observed in some moths but never in locusts (Gatehouse, 1997).

The effect of temperature on locust flight has received its most detailed study in the desert locust Schistocerca gregaria, found in Africa and Asia but not in Australia. The desert locust and the Australian plague locust are the only two locust species that regularly travel extreme distances on upper-level winds, by day and by night respectively (Farrow, 1990). The desert locust also features strongly in the laboratory data analysed later in the present work. It will therefore be described in some detail.

Desert locusts are large insects, see Figure 1.10. Their source area covers about 16 million square kilometres encompassing 30 countries in Africa, the Middle East, and Southwest Asia (Cressman, 1998). Swarms generally take off several hours after sunrise in warm weather, ascend to altitudes of up to 1500-1800 m (the upper limit of thermal updrafts over northern Africa), and fly until just before or just after sunset (Cressman, 1998). The maximum duration of flight is typically about 20 hours but has reached a remarkable 40 hours or more, and is set by the maximum size of fat reserves and their rate of consumption in flight (Rainey, 1989). The longest recorded migration occurred in 1988, after exceptional rains in the source area had led to exceptionally large swarms, when desert locusts flew within a tropical wave pattern for 4,500 km, traversing the Atlantic Ocean (Tipping, 1995). Such an exceptional combination of conditions may occur only every few centuries (Rainey, 1989).

24

Figure 1.10: Drawing from Rainey (1989) of a desert locust in flight. Males are 60-75 mm long and weigh 1.5-2 g; females are 70-90 mm long and weigh 2.5-3.5 g (Cressman, 1998). Wingspan is 100-150 mm. Fore- and hind-wings work at the same frequency, about 18 Hz, but out of phase (Rainey, 1989).

Although a total of seven authors involving over 400 measurements have reported a wide range of cruising airspeeds for the desert locust in free flight, mostly between 3 and 7 ms–1, mean 4.8 ms–1 or about 17 kph (Dean, 2003), locusts most often fly with an airspeed of about 3-4 ms–1 or about 11-14 kph (Kennedy, 1951). Maximum airspeed can reach 9 ms–1 (about 32 kph) or more and is typically observed after takeoff (Waloff, 1972; Rainey, 1989). Desert locusts frequently glide, showing a sinking speed of around 1 ms–1, which at an airspeed of 3-4 ms–1 corresponds to a lift/drag ratio of about 3-4 and a glide angle of about 14-18˚. Since thermal updrafts over northern Africa generally reach vertical speeds of 2-3 ms–1, locusts gliding by day can be carried to their cruising heights without muscular effort. Gliding may also occur when continuous flapping could lead to overheating (Rainey, 1989).

To sustain cruising flapping flight, which for a single desert locust requires about 65 kcal.kg–1hour–1 (mean of 14 locusts, Weis-Fogh, 1964), or about 0.075 watts of power per gram of body weight, the temperature of the locust's wing muscles must be between about 25º and 40ºC (Rainey, 1989). Laboratory studies (Weis-Fogh, 1956; 1976; Taylor, 1963; Waloff, 1953; 1972) found that flight was inhibited below 22ºC and above 40-42ºC. Thus locusts persuaded to fly at 40-42ºC stopped within the first minute, invariably 'panting' violently at about twice the respiratory frequency in normal flight (Weis-Fogh, 1956).

25 Solar heating by day and the metabolic heat of muscular activity can increase the muscle temperature to more than 10ºC above that of the surrounding air, which will decrease with altitude at the dry adiabatic lapse rate. Cooling will occur by radiation, convection, respiration, and (if rain is encountered) evaporation (Rainey, 1989; Chappell & Whitman, 1990).

Now, if cruising flight requires 0.075 watts of power per gram, and assuming that the observed maximum sustainable level of 0.125 watts per gram (Weis- Fogh, 1984) is applied during and after takeoff, the difference (0.05 watts per gram) would raise a locust against gravity at about 300 m per minute if aerodynamic losses and overheating are ignored. Aerodynamic losses were directly addressed by Fischer & Ebert (1999), who found that at a measured average airspeed of 4.1 ± 0.5 ms–1 for 80 adult females, a progressive increase to maximum output produced a more or less linear increase in climb angle to a maximum of about 40º with no significant change in airspeed. For 12 females there was generally little or no increase in wingbeat frequency with climb angle, e.g. from 24 to 25 Hz as the climb angle increased from 0 to 40º (Fischer & Kutsch, 1999). A climb angle of 40º at 4.1 ms–1 represents a climb rate of about 200 m per minute. To maintain these maximum climb rates would require appropriate air temperatures to maintain heat balance and may therefore be uncommon. Nevertheless it is clear that, even when convective updrafts are absent, desert locusts can reach high altitudes remarkably quickly.

Insect species other than desert locusts that have been the subject of temperature studies in the laboratory include the Monarch butterfly Danaus plexippus (Masters et al., 1988); for which the lower temperature threshold for sustained flight (airspeed around 20 kph) was between 13 and 16ºC; this study was conducted in the field but used laboratory methods such as using probes to determine body temperature. For the moth Ostrinia furnacalis (Shirai, 1988) and the rain beetles Ahasverus advena and Cryptolestes ferrugineus (Cox & Dolder, 1995); the lower temperature thresholds for sustained flight were 26 between 13 and 20ºC; all three species are found in Australia. A radar study of newly emerged armyworm moths Spodoptera exempta in Kenya revealed a mass takeoff about 15 minutes after sunset, followed by a steady climb at about 40 m per minute to heights of 600-1150 m. With a wingspan of about 30 mm and wingbeats of about 40 Hz, the moths climbed about 20 mm per wingbeat. Their airspeed was about 2.8 ms–1 or about 10 kph. Flight activity stopped about half an hour before dawn (Riley, Reynolds and Farmery, 1983). Radar studies have found rates of climb after takeoff of migratory species to be generally around 25-35 m per minute (Riley & Reynolds, 1979; Drake & Farrow, 1983; Gatehouse, 1997), but 90 m per minute has been reported for Helicoverpa zea (Gatehouse, 1997).

1.5.4 Effect of Humidity and Rainfall on Insect Migration Insect development requires two potentially conflicting requirements that are inversely related due to the effects of cloud cover, namely rainfall and sunshine. In general terms insects and their eggs cannot survive unless the soil is damp and the vegetation is green. Nor can they survive without sunshine to maintain their metabolic rate (Farrow, 1990). Where the climate is characterised by long spells of sunny weather interspersed with brief and often heavy falls of rain, as in northern Africa and eastern inland Australia, the vegetation tends to be dominated by grasses and by mosaics of grass tussocks and bare ground that, in good times, provide ideal breeding conditions. But good times, like the rainfall, are patchy and unreliable, which the insect accommodates by two complementary strategies, namely migration to another area in the hope of finding recent rainfall, and suspended development in the hope that rainfall will arrive in due course. Such migrations may not find recent rainfall and therefore tend to be hit-or-miss affairs, a point discussed further later in Section 1.6.1.

In a study of the desert locust in Mauritania using a VLR, Riley & Reynolds (1997) noted that it was widely accepted that, during periods of unfavourable conditions such as drought, the desert locust exists at low densities, behaving as 27 solitary insects. If they encounter exceptionally favourable conditions where heavy and widespread rain has fallen, they breed successfully and eventually generate the gregarious populations that lead to outbreaks. However, they also noted that heavy rain does not automatically lead to outbreaks, and suggest this may be because not enough locusts reach the favourable area. In which case the occurrence of winds to carry locusts into the favourable area is probably a critical factor, a point discussed further in Section 1.6.1. If an outbreak is followed by successive generations of gregarious breeding, the result may be a full plague. Laboratory studies (Weis-Fogh, 1956 and 1976; Taylor, 1963; Waloff, 1953 and 1972) have given results consistent with the above findings. The results showed that flight was somewhat affected by low humidity but not by high humidity. Thus long-distance migration tended to be most successful at 30ºC and 55% relative humidity.

The next topic, orientation, and its converse, dispersal, are related to the effects of weather, and to assessing the results from two radars operating simultaneously as explored in Chapter 7, so it seems appropriate to introduce orientation here.

1.5.5 Orientation During Insect Migration One of the most remarkable features of the African desert locust is the common orientation shown by individuals in the migrating swarm (Rainey, 1989). The same tends also to apply to night-migrating insects (Schaefer, 1976; Riley, 1975; Riley & Reynolds, 1979, 1983, 1986; Drake, 1983). Such orientation might suggest that the insects are attempting to navigate (Farrow, 1990). However, the apparently purposeful orientation does not necessarily indicate the actual travel direction, which except in calm conditions is largely determined by the wind direction as illustrated for the desert locust in Figure 1.11. Rainey (1989) notes how the importance of orientation in maintaining swarm cohesion is in striking contrast to its near-negligible effect on the actual travel direction. In this respect night-migrating insects would appear to have 28 little directional control, selecting only the takeoff, travel height, and landing, leading to what Deveson et al. (2005) describe as "a high-risk strategy that frequently results in high mortality".

Figure 1.11: Desert locusts in flight by day, photographed from below. The swarm covered 30 sq km, reached a height of 720 m, and was estimated to contain 109 locusts with a total weight of 2000-3000 tonnes developing 10-20 megawatts of power. In this picture all locusts are oriented the same way, albeit not exactly, which suggests purposeful flight in that direction. In fact the actual travel direction was close to the wind direction, which was from right to left almost at right angles to the locust's orientation. Picture and description are from Rainey (1989).

The mechanics of how swarms, herds, schools and flocks operate are the subject of a large body of biological and mathematical literature, yet much remains unclear (Edelstein-Keshet et al., 1998). Within the surface boundary layer, migration by day in a fixed direction is generally explained either as a light-compass response, where the sun's position (perceived either directly or via sky polarisation) is used as a compass, or as an optomotor response, where the insects adjust their orientation to keep the speed and direction of surface images constant on their retinas (Farrow, 1990). However, as migratory insects are flying within a medium that is itself moving, a given direction once selected by a compass system would not seem to be maintainable without optomotor feedback from the ground (Wehner, 1984). The locust eye is very sensitive to angular movement at high light levels, but less so at low levels, and may be insufficient for night flying at high altitude (Riley et al., 1988). Furthermore,

29 orientation patterns vary neither with altitude, as predicted by the optomotor response, nor with the level of nocturnal illumination (Riley & Reynolds, 1986).

There is some dispute over the prevalence of swarm cohesion. According to Pedgley (1990), cohesion happens with bees and locusts but has not been demonstrated in other species, although large numbers of insects flying together may give the impression of cohesion. He points out that insects moving as a cloud downwind might be expected to thin out due to dispersion, like smoke, and to individual variations in flight behaviour. In a review of wind-borne migration, Gatehouse (1997) cites studies of moths and grasshoppers indicating typically two- to three-fold reductions in density per 100 km, and concludes that such thinning must be characteristic of all wind-borne migrations except those exhibiting cohesion. Like Pedgley, he suggests there is good evidence for cohesion in day-flying locusts but not in any night-flying insects, and given their low aerial densities (his examples are for insects typically 10 m apart) he finds it difficult to see how cohesion at night could be possible.

For locusts on the ground, Buhl et al (2006) note that the standard hypothesis for the way in which individual members achieve a common orientation has been based on relative positions (Okubo and Levin 2001). Overly distant neighbours are too distant to provoke a reaction, while overly close neighbours provoke an anticrowding response. However, Buhl et al. (2006) found that the latter was not necessary to explain the common orientation. According to their mathematical model, orientation in sparse populations on the ground is unstable and short lived, but as the locust density increases to a critical level there is a transition to stable orientations. For desert locusts circling a dome in the laboratory, which imitated an endless marching swarm, the critical density was 74 m–2, or locusts roughly 12 cm apart (Couzin et al, 2005). As the group moves it meets and entrains previously unaligned individuals, so eventually all individuals adopt the same orientation. If two groups with different 30 orientations meet, the eventual orientation is that of the largest group, or of the average if both groups are similar in size (Couzin et al, 2005). However, the relevance of these findings to desert locusts flying typically 2-4 m apart in a swarm (Edelstein-Keshet et al., 1998) is unclear.

There may be other ways in which swarm cohesion is maintained. Locusts exhibit a preferred airspeed, which for African desert locusts is about 3-4 ms–1 or 11-14 kph (Kennedy, 1951), and among desert locusts flying side by side this preferred speed, together with equalisation of flight speed via an optomotor responses to the image motion of each other, seems to explain swarm cohesion, at least in daylight (Spork & Preiss, 1994). Locusta migratoria tethered in a wind tunnel showed avoidance when an approaching object subtended more than 10º of visual angle, equivalent to another locust about half a metre away, which would therefore prevent collisions in a dense swarm (Robertson & Johnson, 1993). Baker et al. (1983) filmed swarms 30-100 m wide of Locusta migratoria flying in Australia at heights mostly between 3 and 10 m, and found that few individuals flew in a straight line, with about half showing fluctuations of up to 10º in flight direction (the same fluctuations in desert locusts can be seen in Figure 1.11). Kutsch et al. (1994) found that pairs of desert locusts coupled their wingbeats when tethered in a wind tunnel 10 cm behind each other. The coupling was mainly produced via wind-receptive hairs on the rear locust's head, but again its relevance to desert locusts flying typically 2-4 m apart in a swarm is unclear. Edelstein-Keshet et al. (1998) point out that, unlike a herd grazing, an airborne swarm of desert locusts persists even though there is no nutrient gradient to provide a driving force; a mathematical model based on individuals who fly beyond the perimeter and then turn back in failed to keep the rear in tow, while a model based on individuals responding to swarm density led to unrealistically high densities.

31 1.6 Insects Studied in the Present Work

There are three Australian locust species that pose interstate threats due to their long-distance migrations. They are the plague locust, spur-throated locust, and migratory locust, of which the first is easily the most important due to the huge areas infested and the high frequency of plagues. Other Australian locust species such as the yellow-winged locust exhibit little or no migratory activity (Rentz, 1996). Of non-locust pest species that are migratory, the most important are the so-called spring moths, whose source and destination areas are similar to those for plague locusts. The present work focuses on Australian plague locusts and spring moths.

1.6.1 Australian Plague Locust The Australian plague locust Chortoicetes terminifera (Walker) is shown in Figure 1.12. The locust’s areas of infestation are greatly increased by mass migration (Hunter, 1982; Deveson & Walker, 2005). A swarm can vary in area from 1 to 25 square kilometres, and each square kilometre can contain from 4 to more than 50 million individuals, or more than 50 per square metre. The swarm can travel on the wind for more than 1500 km (Wright, 1986) easily covering several Australian states, and can cause significant damage to crops and pasture in New South Wales, South Australia, Queensland and Victoria (Wright, 1987). As a result the Australian Plague Locust Commission (APLC) was established in 1974 as a national body to monitor and control locust outbreaks in eastern Australia. Much of the information in this section is from their website www.affa.gov.au/aplc. The history and control strategies of the APLC have been described by Hunter (2004).

32

Figure 1.12: The Australian plague locust Chortoicetes terminifera. Left: mature adult. Body colour is variable and can be grey, brown or green. Male locusts are 25-30 mm long, and females (which are larger) are 30-42 mm long. Body weight depends on conditions and can reach 600 mg. Right: final growth stage before being capable of flight. Photos and information are from www.affa.gov.au/aplc.

Initially it was thought that locusts migrated mainly by day, and that infestations were therefore more or less localised and a problem only for the relevant Australian state. However, the discovery that locusts can fly long distances after sunset (Clark 1969; 1971) due to easy access to the generally strong and constant winds in the geostrophic layer now only 100-300 m above ground level, and that locusts were common in the arid interior (Clark et al., 1969; Clark 1972), made it clear that locusts invaded the agricultural zone by migrating long distances at night (Farrow 1975; 1977; Hunter, 2004). In other words locusts in one region can suddenly migrate hundreds of kilometres overnight and invade previously uninfested areas, rapidly damaging pastures and crops. Outbreaks were now an interstate concern.

The discovery of long-range migration by night revolutionised the understanding of insect populations in eastern Australia (Farrow, 1990). The evidence was hard to acquire and slow to accumulate, but the processes of takeoff, ascent, and horizontal flight, and the variables governing these processes, have now been documented for an increasing number of species. Less is know about the duration of flight and the number of migrations by individuals, and almost nothing about descent and site selection (Farrow, 1990).

33 Plague locusts have a three-stage lifecycle consisting of egg, nymph and adult as shown in Figure 1.13. Each locust egg takes 14-16 days to hatch under ideal conditions (sufficient moisture and a daily maximum temperature of 35˚C). The hatchling locust then goes through five instars over about 35 days before becoming a young adult or fledgling, at which stage migration may occur. (Instars are stages of growth between successive moults during which the wings become progressively more developed.) After a further 14 days' development the locust is reproductively ready, giving under ideal conditions a total time between generations of 6-8 weeks. Locusts can then live for several months and lay eggs three or four times.

34

Figure 1.13: Partial lifecycle of the Australian plague locust. The fledgling takes a further two weeks to be reproductively ready. Pictures from www.affa.gov.au/aplc.

Pre-adult locusts (called nymphs or hoppers) cannot fly, so their damage is limited to the immediate area. Nevertheless the nymphs can form marching bands that are commonly 200-2000 m wide, although rarely more than a few hundred metres deep, with densities ranging from under 50 m–2 at the rear to 1000-5000 m–2 at the leading edge (Hunter, 2004), which are often visible from the air as shown in Figure 1.14.

35

Figure 1.14: An aerial photo of Australian plague locust nymphs devastating a young wheat crop. The parallel green lines are the furrows containing young wheat, the large bare areas are the locust depredations. Serious depredations can strip areas several kilometres wide. Photo from www.affa.gov.au/aplc.

Locusts prefer to eat lush grasses (which after good rains are abundant in the source areas) and green cereal crops such as young wheat. A mature adult eats one-third to one-half of its body weight, or about 0.2 g, of vegetation per day, so 5000 locusts will eat about 1 kg of vegetation per day. The amount of vegetation available depends on rainfall, so rainfall is a strong determinant of locust activity and migration. In general, locusts reach plague proportions when there is a sequence of regular rains sufficient to allow 3-5 consecutive generations of breeding (Wright 1987; Hunter 1996). The rains need only be regular and do not need to be widespread. Migrating locusts that encounter areas of recent rain will normally mature and lay eggs (Hunter 1982), while those encountering dry conditions often migrate again in an attempt to find suitable conditions. Over several migrations many locusts will eventually find adequate rain areas, but the rest will fail to find adequate rain areas and will die without laying eggs (Hunter 1989).

The cruising airspeed of plague locusts has not been widely studied. According to the APLC website the airspeed of freely flying locusts in 3 ms–1. According to Clark (1969) the airspeeds determined by movie camera for about 50 individuals flying 2-4 m above the ground, corrected for wind speed, were 36 between 2.8 and 3.8 ms–1, mean 3.2 ms–1 or about 12 kph, which compares with the typical 17 kph cruising airspeed of the desert locust, which is roughly four times heavier. To sustain flapping flight similar constraints apply to the temperature of the plague locust's wing muscles. Thus plague locusts are generally inactive below 15ºC and do not take off unless the temperature is over 20ºC. Further discussion of temperature thresholds appears in Section 6.2 of Chapter 6. A photo of plague locusts taking off during the day is shown in Figure 1.15. Day flights can cover tens of kilometres but generally they cover less than a few kilometres (Farrow, 1990).

Figure 1.15: Australian plague locusts taking off by day in the central highlands of Queensland. From the online version of Hunter (2004) at www.blackwell-synergy.com. Photo by Peter Spurgin.

According to Hunter (1982), the body weight of typical adult locusts can vary from 300 to 600 mg depending on pasture conditions. According to a later study by Hunter (1989), if pasture conditions are good (i.e. green during moult through adulthood), locusts at the fledgling stage when migration is most likely to occur had a mean weight and standard error of 328 ± 41 mg, whereas mature adults had a mean weight and standard error of 550 ± 36 mg. No indication of sex was given; nor were sample sizes but the text implies several hundred. If the pasture was not green but dry, the corresponding values were 226 ± 26 mg and 437 ± 38 mg, or about a quarter less; in this case the locusts were unable to 37 accumulate enough fat to migrate and died locally without laying (Hunter, 1989). These figures indicate that natural variations due to sex, pasture conditions, and fat reserves will make any estimate of a plague locust's 'typical' weight uncertain at best.

The weight of a locust's wings is a few percent of its total body weight, is distributed over four wings, and only a fraction of this weight is water (Schaefer, 1969). In other words locust wings contain almost no water and are therefore non-reflective to radar waves, so wingspan is probably not a relevant variable. Nevertheless, as shown in Figure 1.16, the wingspan is substantial.

Figure 1.16: Australian plague locust. Wingspan is about twice the body length, which is up to 30 mm for males and up to 42 mm for females, and is less than half that of the African desert locust shown in Figure 1.10. Photo is from www.dpi.vic.gov.au (plague locust identification and biology).

The main source area for plague locusts is the arid and semi-arid channel country of New South Wales, Queensland, South Australia and the Northern Territory, an area of more than a million square kilometres. Infestations generally occur during late summer and early autumn when the locusts migrate southwards from the source area to the main cropping regions of eastern Australia (Wright, 1987). The source and destination areas are shown in Figure 1.17. During the locust plague of 1979, Symmons & Wright (1981) found that the main source area covered about 300 x 100 km, with several smaller source

38 areas covering about 100 x 50 km. It was previously thought that migratory populations build up from low-density populations during summer breeding (Wright, 1987), but more recent studies (Deveson & Walker, 2005; Deveson et al., 2005) suggest that the buildup follows migration from the south and east back into the summer rainfall areas during late spring-summer. This ‘migratory circuit’ is driven by seasonal changes that result in temporarily favourable habitats (Deveson & Walker, 2005). Thus migratory populations tend to correspond with the seasonal distribution of rainfall, and migratory behaviour with weather systems that can produce winds in almost any direction (Deveson et al., 2005).

Figure 1.17: Source area of Australian plague locusts in the arid and semi-arid interior of Australia, and their destination area in the agricultural belt of eastern Australia. Plague locusts also occur in southern parts of Western Australia but their infestations are less frequent. Adapted from Deveson & Walker (2005). Also shown are the locations of the IMRs at Thargomindah and Bourke.

39 1.6.2 Spring Moths The term ‘spring moth’ is used here to refer to several species known to migrate through the study area (Drake & Farrow, 1985; Gregg et al., 1993, 1993b). Predominant among these are two species in the genus Helicoverpa (formerly known as Heliothis), the native budworm H. punctigera (Wallengren) and the cotton bollworm H. armigera (Hubner), which are physically very similar, see Figure 1.18 and Figure 1.19.

Both Helicoverpa species are major pests. The females lay eggs, and the surviving caterpillars feed on a wide range of host plants including nearly all major field, horticultural and flower crops (Zalucki & Furlong, 2005). Both species are migratory and can move large distances (many hundreds of kilometres) between regions, or short distances within regions. Depending on the crop and season, complete loss of production can result if caterpillars are left unchecked. The migration of spring moths threatens large cropping areas of Queensland, New South Wales, Victoria and South Australia. Most management strategies rely on the use of insecticides (Zalucki & Norton, 1999).

In the inland areas where the IMRs are located, H. punctigera is the dominant migratory species arriving early in the season while H. armigera tends to come from local overwintering populations later in the season (Fitt, 1989; Fitt & Daly, 1990). As a result, during summer the numbers of H. punctigera tend to decrease while those of H. armigera tend to increase (Zalucki & Furlong, 2005). However, overall the latter generally accounts for less than 5% of individuals (Gregg et al. 1993b; Zalucki et al., 1994.

40

Figure 1.18: Moths of Helicoverpa punctigera (left) and Helicoverpa armigera (right). They are usually distinguished by the presence of the pale patch on the hind wings of H. armigera (circled). On average the body is 17 mm long and nearly 6 mm in diameter. Wingspan is 30-45 mm. Body weight depends on conditions but is typically about 120 mg. Photo from www2.dpi.qld.gov.au/fieldcrops/17696.html with circles imposed by the author.

Figure 1.19: Moths of Helicoverpa punctigera (left) and Helicoverpa armigera (right) at rest, which emphasises their physical similarity. Photos are from www.geocities.com/brisbane_noct/Budworm.htm and www.staff.it.uts.edu.au/~don/larvae/heli/armi.html, respectively.

Unlike plague locusts and their three-stage lifecycle, moths have a four-stage lifecycle consisting of egg, larva, pupa and adult as shown in Figure 1.20. The lifecycle typically lasts 35-42 days during September-April, the period when conditions are most suitable for breeding, and during this time the moths can pass through 4 to 5 generations, each with its own generation of damaging caterpillars (Zalucki & Furlong, 2005). The egg hatches in 3 days after which the larva go through 6 instars totalling about 25 days, the final instars having the greatest potential to damage crops. Once larvae are fully-grown they pupate

41 at the base of the host plant, typically for 14 days, after which the moth emerges.

Figure 1.20: Lifecycle of the moths Helicoverpa punctigera and H. armigera. Images are from www2.dpi.qld.gov.au.

The body weights of migrating spring moths are typically between 100 and 150 mg, about one-third that of a plague locust. The 9 specimens of H. punctigera listed in the Appendix had a mean length of 16.6 ± 1.4 mm, a mean diameter of 5.4 ± 0.4 mm, and a mean wing span of 35.8 ± 1.9 mm. Thus their body length is just over half that of plague locusts but their body diameter is 42 about the same. These body size/shape differences and their effect on radar reflectivity become relevant when attempts are made to distinguish between species.

The main source area for migratory spring moths is the arid and semi-arid channel country of New South Wales, Queensland, South Australia and the Northern Territory as shown in Figure 1.21, which is much the same as the source area for plague locusts. Its diversity of climatic conditions “virtually ensures that at any season of any year, there will be suitable habitat for Helicoverpa” (Gregg et al., 1995). Winter rainfall encourages the growth of many host plants (Zalucki et al., 1994) and results in 1 to 2 generations of spring moths. As the host plants dry out during spring, the moths are carried by winds ahead of cold fronts (Rochester, 1999) to the cropping areas of eastern Australia. The 35-42 day lifecycle leads to similarly spaced peaks in migratory activity (Zalucki & Furlong, 2005). The moths can infest vast areas. For example Gregg et al. (2001) estimated that in the two nights studied, 90% of immigrant moths were likely to land in areas measuring about 450 x 250 km and 800 x 350 km just west of Bourke.

43

Figure 1.21: Source area of Helicoverpa punctigera (horizontal hatching) and the major cropping areas of eastern Australia (diagonal hatching). Adapted from Gregg et al. (1995). The points labelled T and B indicate the IMRs at Thargomindah and Bourke.

The cruising airspeed of spring moths has received few studies. Rochester (1999) regressed flight speed measured by radar against windspeed measured by balloon for 331 spring moths and from the highly scattered points (r = 0.69) obtained an intercept of 6.9 ms–1 at zero wind speed, or about 25 kph. For high- flying insects in northern China that were predominantly Helicoverpa armigera, Feng et al (2005) observed airspeeds that were mostly 1.4-7.0 ms–1, or about 5-25 kph. For comparison, ten individuals of the corn earworm moth Helicoverpa zea, one of the most common and injurious pests throughout the USA whose 35-45 mm wingspan is similar to that of spring moths, reached an average speed in a wind tunnel of 7.9 ms–1 for males heading into a pheromone plume and 5.7 ms–1 in clean air (Quero et al., 2001). These airspeeds tend to be somewhat larger than the previous mean cruising airspeed of 3.2 ms–1 for the plague locust, which suggests that flight speed might be a possible source of discrimination in radar studies, although the assumption that airspeed would be 44 sufficiently constant is probably unrealistic. To sustain flapping flight much the same constraints apply to the temperature of the spring moth's wing muscles as in the case of locusts, except that flight at low temperatures is helped by an insulating coat of hairs (Church, 1960) with a corresponding increased constraint on flight at higher air temperatures. Further discussion of temperature thresholds appears in Section 6.2 of Chapter 6.

1.7 Climate

1.7.1 Climate of the Source Area The heaviest rainfall in the source area occurs in the far north, mostly as brief heavy falls in summer. Rainfall is highly variable with a long-term average of around 300 mm a year. In the rest of the source area, the long-term average is around 150 to 200 mm a year. Average annual rainfall for both source and destination areas is shown in Figure 1.22. Annual potential evaporation is generally more than 2500 mm.

45

Figure 1.22: Annual rainfall map of eastern Australia. As shown in Figure 1.17 and Figure 1.21, the source areas of plague locusts and spring moths are generally centred on the Lake Eyre basin (outlined in red), which consists of two catchments (Cooper Creek and Georgina Diamantina) and three regions (Desert Rivers, Western Rivers and Lake Frome), covering some 1.2 million square kilometres of uniformly flat, arid and semi-arid central Australia. Lake Eyre itself is shown by the large blue dot. The major cropping areas are outlined in green. The two IMR sites at Thargomindah and Bourke are shown in black. Birdsville, shown in white, is the most isolated township in Australia and is representative of the centre of the source region.

Most of the Lake Eyre basin is desert or semi-arid grassland, and is uniformly flat over vast areas, see Figure 1.23. Consequently the variable runoff forms a network of ephemeral south-flowing streams that expand into huge shallow beds often many kilometres wide. The Diamantina and the Cooper can be up to 80 km wide. The water disperses though a network of braided channels, floodplains, waterholes and wetlands (the” channel country”, see Figure 1.24) that ultimately drain into Lake Eyre (albeit only rarely) nine or ten months later. Often the only sources of water within the basin are large permanent waterholes. The basin is bordered to the east by the Main Barrier Range (in

46 New South Wales) and the Grey Range (in Queensland), but neither exceed 300 m. Lake Eyre itself is slightly below sea level.

Figure 1.23: Typical landscape in the source area with characteristic clumps of grasses that in this picture are still green after previous rain. Photo from www.affa.gov.au/aplc shows a routine APLC ground survey, which typically covers 300 km a day. At regular stops every 10 km the density and species of locusts present are recorded together with their stage of development and the type and condition of the vegetation.

Figure 1.24: Summer rainfall dispersing through a network of braided channels in the channel country of southwest Queensland and adjoining parts of NSW and SA, which is in the centre of the locust and moth source areas. At such times the grassy plains of the channel country (which resemble the landscape shown in Figure 1.23) become impassable. Black-and-white aerial view from The Australian Encyclopedia 1996.

The Lake Eyre basin is characterised by hot summers with average minima- maxima of 23-38ºC, and cool winters with average minima-maxima of 8-19ºC. The eastern area (the Cooper Catchment) has slightly cooler summers and richer grasslands that support sparse sheep and cattle grazing. The major agricultural areas are closer to the east coast in more temperate areas with greater and more consistent rainfall and are mostly devoted to growing cereals. 47 1.7.2 The Study Area The study area lies in the southeastern part of the source areas for locusts and moths. Compared with the centre of the source area, average temperatures are 1-2º lower at Thargomindah 500 km to the southeast, and 2-4º lower at Bourke. Rainfall is highly variable but averages about 100 mm higher. Average minimum-maximum temperatures at Bourke (elevation 106 m) are 21-35ºC in January and 5-20ºC in July, and the average annual rainfall is 346 mm; at Thargomindah (elevation 126 m) the equivalent figures are 23-36ºC, 6-19ºC, and 270 mm. The annual patterns of these quantities are shown in Figure 1.25.

Figure 1.25: Average annual rainfall and average minimum and maximum temperatures at Thargomindah, Bourke and Birdsville (see Figure 1.22 for their locations).

48 2 INSECT MONITORING RADARS

This chapter deals with the construction and design of insect monitoring radars (IMRs). It describes the construction of the mobile IMR, presenting this as a development of the present fixed IMRs, and describes their calibration and reliability. Parts of this chapter are expanded from Dean, Drake & Harman (2002) Monitoring winds and insect pests in the lower atmosphere using a low-cost mobile profiling radar.

From its Canberra campus the University of NSW School of Physical, Environmental and Physical Sciences (formerly the School of Physics) operates two fixed IMRs at Bourke in northern NSW and Thargomindah in southern Queensland. A third, mobile, IMR housed in a small trailer was built for just over half the cost of a fixed IMR. Their specifications of the three IMRs reflect the evolution of IMR technology since 1995. The difficulties of operation in remote areas of Australia have reduced the reliability of the IMRs, which on average have each operated on 80% of scheduled nights. The main original contributions to this chapter are the construction details of the mobile IMR.

2.1 Development of the Fixed IMRs

In the 1990s the University of NSW School of Physics (now part of the School of Physical, Environmental and Mathematical Sciences) at its Canberra campus developed, installed, and operated insect monitoring radars (IMRs) at two locations in inland eastern Australia. The IMRs are shown schematically in Figure 2.1. Brief technical details of the equipment are given in Section 2.8.

Figure 2.1: Schematic diagram of the two fixed IMRs in inland eastern Australia.

49 The first IMR was originally operated at Longreach, Queensland (23°26’S, 144°16’E; Drake et al., 1994) during 1995-96. In May 1998 it was upgraded and relocated to Bourke in northern NSW (29°48’S, 145°59’E). The second IMR was originally constructed to observe the migration of Corn Earworm moths (Helicoverpa zea) in the Lower Rio Grande Valley of Texas in June 1996 (Drake et al., 1998). In September 1999 it was upgraded and permanently installed at Thargomindah in southern Queensland (27°59’S, 143°49’E) just over 300 km north-west of Bourke. The locations of Bourke and Thargomindah are shown in Figure 1.5 in Chapter 1. The IMR installations are shown in Figure 2.2. Bourke, founded 1862, elevation 106 m, population 3000, is the railhead for a large wool-growing region and for crops (mainly cotton) grown under irrigation from the Darling River. The much smaller Thargomindah, elevation 126 m, population 270, is almost exclusively a centre for sheep and cattle raising.

Figure 2.2: The two IMRs permanently installed at Bourke (left) and Thargomindah (right). In each case the IMR equipment is housed in the transportable cabin on the left which is air-conditioned to prevent equipment overheating. The 1.8 m radar antenna is under the radome on the right, and the whole installation is protected by barrier fencing. Each IMR requires a dedicated telephone line and connection to mains power. The provision of which accounts for much of the installation cost. The cabin interiors are shown later in Figure 2.5.

50 The fixed IMRs operate automatically in conjunction with an automatic weather station and are connected to the laboratory in Canberra about 650 km (Bourke) or 950 km (Thargomindah) away via a dedicated telephone line for the exchange of data (Drake & Wang, 2000; Drake et al., 2002b). The phone line and connection to mains power accounts for much of the installation cost. The weather station provides a record of wind speed and direction, rainfall, temperature, humidity and barometric pressure. The IMRs operate for 11 hours each night year round regardless of the season. The acquired data is stored on the computer and automatically processed at the end of each working day. The results are downloaded to Canberra and then made available to farmers and pest monitoring services via an interactive web page (Drake & Wang, 2000; Drake et al., 2002b) as shown in Figure 2.3.

51

Figure 2.3: Website (created by H.K. Wang, a student at UNSW@ADFA-PEMS) showing a summary of results from the Bourke IMR for the night of 18/19 March 2002. Top right are plots showing the temperature, relative humidity, wind speed and wind direction recorded at ground level by the automatic weather station during the 11 hours of IMR operation. Below is a blue/green horizontal plot showing the number of insects counted at altitudes between 200 m and 1400 m. The rest of the display shows (top) the direction in which the insects are heading and their body orientation, and (bottom) their speed, wingbeat frequency and estimated mass. Different dates can be selected from the list on the left of the screen. The ‘Season’s Dynamics’ display shows in green the total number of insects detected each night (Wang et al., 2002).

The schedule of IMR operation is determined by insect behaviour. The two Australian IMRs operate at night time because the species of interest migrate nocturnally, whereas the two fixed Vertical-Looking Radars used for entomological work in England operate automatically for five minutes in every 15 minutes, 24 hours a day, as daytime migration is equally important there (Chapman et al., 2000; Woiwood et al, 2000).

52 2.2 Radar Configuration of the Fixed IMRs

Each of the two fixed IMRs uses a 9.4 GHz (3.2 cm) noncoherent transceiver and a pencil beam in a ZLC configuration as shown in Figure 2.4. (Measurements made with a coherent radar include the phase of the echoes allowing additional information (e.g. radial speed from the Doppler effect) to be extracted). Each IMR beam is about 1.1˚ wide and scans through a narrow conical angle of about 0.2º, which results in a beam about 20 m wide at a height of one kilometre, see Chapter 3 for details. The axis of the scanned volume is always vertical to simplify the insect's aspect as viewed by the radar beam, see Chapter 4 for details. Nominal radiated power was 32 kW at Bourke (this transmitter has since been replaced by a 25 kW model) and 25 kW at Thargomindah. From the complex pattern of signal modulations that result as an individual target passes through the beam, it is possible to retrieve the target's speed, direction of movement, alignment, size, and radar cross section (RCS) parameters.

Figure 2.4: Left: Plan view of the beam geometry (adapted from Drake et al., 1994). The radar beam is essentially a narrow beam whose centre traces a circular path around the vertical. The beam is polarised across the diameter of the beam, and the plane of polarisation rotates with the beam. Right: Side view of the radar beam (adapted from Smith et al., 1993) showing how the beam centre traces a circular path around the vertical. 53

When an insect enters the radar beam it produces an echo, the magnitude and time-variation of which is determined by the radar parameters and the insect’s size and shape, height, speed, travel direction, and orientation. (As shown in Figure 2.4, travel direction or 'displacement' is the resultant of wind direction and flight activity, and 'orientation' is the body alignment.) The equation describing these echoes is well established, and with appropriate software it is possible to retrieve the insect’s characteristics as described in Chapter 3.

2.3 Equipment Modules of the Fixed IMRs

The two fixed IMRs each consist of two modules: − Microwave and antenna module, consisting of the antenna, rotating feed assembly, drive motor, motor controller, and transceiver. − Control and data-acquisition module, consisting of a computer linked to the controlling and signal-processing electronics.

Both modules other than the antenna, drive motor and automatic weather station are housed within the cabin as shown in Figure 2.5. The antenna assembly is adjacent to the cabin under a rigid radome as shown in Figure 2.1 and Figure 2.2 and is connected to the transceiver via a rigid waveguide. Aspects of the IMR design and construction are described in Drake et al. (2002a) and Drake (2002b). They are essentially the same as for the mobile IMR which is described below together with an outline of their differences.

54

Figure 2.5: The interiors of the Bourke (left) and Thargomindah (right) IMR cabins (photos by V.A. Drake). In each photo the transceivers (outlined in red) are on the floor with the controlling and signal-processing electronics on the shelves.

2.4 Reasons For Developing a Mobile IMR

The distance between IMRs (308 km) is small compared with the roughly 1200-km diameter of the source area. Nevertheless, it may be large compared with the width of a particular migration, a point explored in Chapter 7. Add the decisive effect of wind direction and changes in wind direction, and it is easy to see how a fixed IMR could report insect numbers that are not representative. Therefore a mobile Insect Monitoring Radar was designed and constructed during 2000-2001 to help monitor insect behaviour across the study area.

2.5 Specifications of the IMRs

The specifications for the Bourke, Thargomindah and mobile IMRs reflect the evolution of IMR technology since 1995. The first unit (now at Bourke) employed a transceiver (type 65160, Decca, New Malden, UK) with a noise threshold of –87 dB. The later Thargomindah and mobile IMRs use a ‘BridgeMaster’ transceiver (type 65125, RACAL, New Malden, UK) with a lower nominal noise threshold (i.e. higher sensitivity) of –96 dB. The Bourke IMR had eight range gates, each 50 m wide, that are spaced uniformly from 200 55 to 1400 m. The more advanced Thargomindah and mobile IMRs have fifteen range gates, each 25 m range wide, which gives greater vertical resolution. In all three units the gates can be moved by one gate-width in a cycle of three steps, so that complete height coverage is achieved even when insects fly in thin layers (Drake, 2001). The upper height could be increased but few insects fly at such heights and only the largest would be detectable. Since completion of the work described in this thesis, the Bourke unit has been upgraded.

The specifications of the Bourke, Thargomindah and mobile IMRs are compared with a contemporary English Vertical-Looking Radar built mainly to detect considerably smaller insects. Perhaps the most significant differences are the better height resolution of the Thargomindah and mobile units and the broader beams of the VLR and mobile units.

Table 2.1: ZLC-configuration entomological radar specifications at the time of this work. Further details are given in Table 3.1 in Chapter 3.

Radar Bourke1 Thargo./Mobile2 VLR3 Transceiver Type pulse pulse pulse Model 651604 65125 65125 Carrier Frequency 9.4 GHz 9.4 GHz 9.4 GHz Nominal Peak Power4 32 kW 25 kW 25 kW Average Power 2 W 0.95/1.6 W 1.6 W Antenna Type parabolic parabolic parabolic Diameter 1.8 m 1.8/1.2 m 1.52 m Beamwidth 1.1º 1.1/1.64º 1.45º Sampling Range 200 - 1400 m 175 - 1275 m 150 - 1188 m Gate width 50 m 25 m 45 m Number of gates 8 15 15 1Drake et al. (1994). 2Dean et al. (2002). 3Chapman et al. (2002). 4This transceiver has since been replaced with the same model as Thargomindah/mobile (25 kW nominal peak power).

56 2.6 Design of the Mobile IMR

There were several key requirements. The mobile IMR had to be cheaper and more compact than the fixed IMRs. It had to be easily transported by trailer. Once on site, it had to be quickly set up by one person and be suitable for observations lasting one or several nights. These requirements led to considerable differences from the design for a fixed IMR.

Each component was carefully assessed to see if it was essential and if its cost was justified; if not, it was eliminated. The outcome was a mobile IMR that would easily fit into a trailer and could be set up by one person in less than 15 minutes. The associated equipment could be accommodated either in the towing vehicle for observations of one night or less (see Figure 2.6 top), or in a tent for observations over several nights (Figure 2.6, middle and bottom). Power was provided by a petrol generator (EG2200, Honda, Tokyo, Japan) rated at 2.2 kW, more than three times the power drawn by the radar. Petrol consumption was about 4 litres per night of 11 hours. The normal 1.8 m antenna and rigid radome used by the fixed IMRs was too large for the trailer, so a smaller 1.2 m antenna with a soft flat plastic radome was substituted. Altogether the mobile IMR was built for just over half the cost of a permanent unit. An itemised breakdown of costs is given in Section 2.8.3.

57

Figure 2.6: Top: The mobile IMR during field tests near Canberra. Here the control and data-acquisition module is housed in the vehicle and is connected by cables to the microwave and antenna module in the trailer. On the ground between them is the portable generator. A closer view of the equipment when housed in the vehicle is shown in Figure 2.10. Middle Left: During operation in the study area the control and data-acquisition module is housed in a tent, shown here at Barringun. Middle Right: Where possible, locations are chosen where power is available, as here at Thyangra. Bottom Left: The mobile IMR in operation at Glengeera. Bottom Right: The mobile IMR in operation at Eulo. The building is an accommodation cabin that also provided power. The antenna is quite high up on the trailer and is well shielded, which eliminates any ground or building clutter from the beam sidelobes. Photos by the author

58 Items not included in the mobile IMR but necessary for the autonomous remote operation provided by the fixed IMRs included:

− The power monitor (which measures the output power of the radar), as it was unnecessary for short-term observations. − Facilities for remote operation (telephone links, modem etc.), as the location would normally be far from the telephone network and there would always be an operator in attendance. − The automated weather station, due both to its cost and the ready availability of weather data from the Bureau of Meteorology. − Optical isolation of the drive motor, as its electrical noise level was not enough to make this necessary. − A cavity tuner, as the system could be manually tuned before the commencement of each night’s operation, and the automatic fine-tuning of the transceiver controller was capable of keeping the radar in tune through the night. − Air conditioning, as the natural air flow at night was sufficient to cool the electronics (see Section 2.11).

Two items used in the fixed IMRs had been superseded and needed to be replaced by later models. First, the motor controller for rotating the antenna feed was replaced by a new model (TSD-100, BALDOR Ltd, Fort Smith, USA) which has its own internal fan and is thus more suitable for outdoor operations. Second, two of the interface cards (both PCL830, Advantech, Taipei, Taiwan) that connect the computer with the rest of the equipment had to be replaced by a counter-timer card (CIO-CTR20HD, Measurement Computing, Middleboro, USA,) and an input/output card (CIO-DIO24, Computer Boards, Middleboro, USA). The control software had to be rewritten to accommodate these cards.

59

2.7 Construction of the Mobile IMR

The mobile IMR was constructed over a 14 month period during 2001/2002. It is only the fifth ZLC-configuration entomological radar (excluding prototypes) to be built and brought into operation, and the first to be mobile. Some components of the radar had already been constructed by I.T. Harman and members of the electronics workshop in the former School of Physics as spares for the fixed IMRs. The transceiver controller was constructed by the author to an improved design. Several other components were specially made. The change in computer interface boards made it necessary to construct several adapter cards and to rewrite significant sections of the controlling software. Equipment that had to be manufactured, or purchased, included the motor switch, inductor modules, rack enclosures, storage boxes (which double as a bench when the electronics are housed in a tent), and cabling other than that to the transceiver.

The trailer is 1.5 m wide by 5.25 m long and has enough room for boxes holding the generator and two 20-litre petrol containers. It was purchased as a standard item but with light truck tyres to make it more robust for use in the outback even though the total load was well below the design limit. A schematic plan view is shown in Figure 2.7. Retractable legs provide stability during observations and enable the trailer to be leveled. The antenna mount was designed to provide secure support for the heavy motor while keeping the top of the antenna below the level of the towing vehicle (a Mazda Bravo utility). A step built into the trailer allows easy access to the base of the antenna for attaching the feed. An enclosure of barrier fencing protects the transmitting and moving sections of the radar. The rack enclosures, monitor and oscilloscope are mounted on two flat pieces of marine ply and are easily portable; they can remain in the towing vehicle for short observations or be housed in a tent as shown in Figure 2.6. 60

Fuel Cans

Figure 2.7: Schematic plan view of the mobile IMR trailer. Clockwise from top left around the antenna mount are: petrol containers, generator, motor control, motor switch, transceiver and cables. The fuel cans and generator are located in the trailer only during transit.

2.8 Equipment Modules of the Mobile IMR

As with the fixed IMRs, the mobile IMR consists of two modules: − Control and data acquisition module, consisting of a computer interfaced to the controlling and signal-processing electronics, − Microwave and antenna module, consisting of antenna, drive motor, motor controller and transceiver. The two modules are shown schematically in Figure 2.8 and are described in the next two sections.

61

Figure 2.8: Schematic diagram of the mobile IMR. The upper half shows the microwave and antenna module. The lower half shows the control and data- acquisition module with its four interface cards. Dashed lines represent power. Double lines represent sections of waveguide.

62 2.8.1 Control and Data-Acquisition Module The mobile IMR control and data-acquisition module consists of five major components: a computer with purpose-written software to control radar operations and to store acquired data; a unit to control power-distribution; an interface between the computer and the rotating antenna feed assembly; an interface between the computer and the transceiver; and a 15-channel gated peak detector to acquire echo signals from 15 altitudes simultaneously, see Figure 2.9. These five components are carried in the towing vehicle and are shown in Figure 2.10. Time/Height

Figure 2.9: Oscilloscope display showing the 15 altitude gates (top), highest is on the right, and the radar return (A-scope, bottom). The radar return shows an insect traversing the beam at the height of the third gate. The initial large peak is the transmitted radar pulse.

63

Figure 2.10: The mobile IMR's control and data-acquisition module. Top left: schematic layout. Top right: module during operation inside tent. Bottom: module during operation in rear of towing vehicle. The same components but without the restrictions of mobility can be seen inside the fixed IMR cabins shown in Figure 2.5. Photos by the author.

The computer was an IPEX 486DX2-66 with 16-bit ISA bus and 16 MB RAM (obtained as surplus equipment), 240 and 540 MB hard drives (also obtained as surplus equipment), a 3.5” floppy disc, and a Yamaha CDR400t SCSI CD drive that was used to archive each night’s data (typically around 200 MB). The

64 computer had to be an early model to ensure bus compatibility with the available interface cards.

The four interface cards shown left to right in Figure 2.8 link the computer with the following components: 1. Transceiver (analog I/O board PC-30DS/4, Eagle Technology, Cape Town, South Africa). The transceiver generates the outgoing radar waves and detects any returned signal. The card is a variant of the PC- 30D board (see item 3 below) with the addition of simultaneous sampling (not actually required for this application). 2. Power distributor and multi-function controller (digital I/O board (CIO- DIO24, Computer Boards, Middleboro, USA). The board has 24 digital I/O lines. The power distributor controls the supply of power to the transceiver controller, peak detector and multi-function controller. The multi-function controller sets the pulse repetition frequency of the transceiver, and the sampling rate of the analog-to-digital converter in the computer. It also links the computer with the position encoder at the base of the motor unit (Harman, 1997), and with the optical tachometer (an infra-red switch that records the position of a reflective dot on the rotary joint that allows an independent check of the feed orientation). 3. Transceiver controller and antenna motor controller (analog I/O board PC-30D, Eagle Technology, Cape Town, South Africa). The card has 16 analogue input ports and a throughput of 200 kHz. The transceiver controller replicates and augments the controlling electronics found within the transceiver and allows both computer and manual control. It is similar to that used in the Thargomindah IMR but with all the circuit boards re-designed to incorporate later modifications. The antenna motor controller controls the rotation of the feed within the antenna. 4. Peak detector and multi-function controller (Interface board CIO- CTR20HD, Measurement Computing, Middleboro, USA). The peak detector enables the recording of 16 channels of data simultaneously (15 65 altitudes and the power monitor, the last unused in the mobile IMR). The gate heights can be varied both manually during operation and also automatically by the computer.

2.8.2 Microwave and Antenna Module The mobile IMR microwave and antenna module consists of a transceiver unit from a commercial marine radar, a commercial parabolic 1.2-m (4-ft) diameter microwave antenna with shielding and radome cover but with the normal feed removed, a rotating feed assembly (incorporating a microwave rotary joint, a DC electric motor, and an angle encoder), a flexible connecting waveguide, and a motor controller. The module is housed in the trailer as shown in Figure 2.11 and Figure 2.12.

a) b)

Figure 2.11: The mobile IMR’s microwave and antenna module. Left: a view inside the trailer barrier fence. The transceiver is bottom centre. The motor controller is on the bottom right under the step. Right: Close-up of the antenna drive assembly. The rotary joint (grey-blue) is in the foreground, the rotary coupling (black) is at the top of the picture. The white cable leads to the optical tachometer. The antenna drive motor is slightly visible at the rear right. The various components are more clearly identified in Figure 2.12. Photos by the author.

66

Figure 2.12: Side view of the Mobile IMR microwave and antenna module. Two sections of flexible waveguide connect the transceiver to the bottom of the rotary joint. The upper, turning, end of the rotary joint is attached to the rotary coupling at the base of the antenna, which is turned by a belt driven by the electric motor.

The transceiver (type 65125) is from a standard commercial RACAL ‘BridgeMaster’ marine radar with an interface to allow external control by the mobile IMR’s transceiver controller. The BridgeMaster rotary assembly and motor, which were housed in the same enclosure but were not needed, were discarded and the aperture sealed.

The electric motor and motor-controller are both commercial units (MT4525 BTYCN, BALDOR, Fort Smith, USA, and TSD-100 single axis servo drive, BALDOR, Fort Smith, USA, respectively). The motor has a factory-installed 512 pulse-per-revolution encoder attached to its base to allow monitoring and control of the feed rotation. Its speed is controlled by the motor controller whose output power is routed via two 400 µH inductors coupled with four 4.7 nF capacitors to reduce electrical noise from the pulse-motor drive.

67 The antenna is a commercial parabolic microwave communications antenna 1.2 m in diameter, model L1210SHP manufactured by Precision Antennas (Stratford-upon-Avon, UK), nominal frequency range 10.2 to 11.7 GHz, front- to-back ratio 68 dB. Its normal feed assembly was removed and replaced with the rotary assembly shown in Figure 2.11 and Figure 2.12. Attached to the rotary assembly is a double-dipole feed constructed in UNSW@ADFA-PEMS mechanical workshop according to the design of Silver (1949). To produce a conical scan the tip of the feed was offset from the antenna axis and balanced by a counter-weight. Figure 2.13 shows the antenna feed in position in the antenna dish.

Figure 2.13: Mobile IMR antenna feed in position inside the antenna. Left: The radar waves are radiated from the tip, which is offset 0.7° from the vertical. To reduce vibration and wear (the antenna feed rotates at 5 Hz), the offset is counterbalanced by two small counterweights. Right: Close-up of the attachment to the rotary coupling shown side-on in Figure 2.12. Photos by author.

The antenna is leveled using a spirit level before use to ensure that the axis of the radar beam is vertical. A vertical axis is necessary to simplify the insect’s aspect as viewed by the radar beam, see Chapter 4.

68 2.8.3 Breakdown of Costs The rounded cost of each component of the mobile IMR in Australian dollars as at 2001 was as follows: Transceiver 11,500 Antenna 4,500 Electronics 4,400 Rotary joint 4,000 Computer & interface boards 3,900 Trailer 2,600 Waveguide 1,500 Motor controller 1,200 Motor 900 Encoder 700 Cables 500 Total 35,700

If labour costs are included the total cost is around $95,000. The corresponding total cost for a fixed IMR is about $175,000 (Drake et al., 2002b), or nearly twice as much. This suggests that a mobile IMR is a good low-cost alternative for short observational campaigns, even when mobility is not required.

For comparison, the additional rounded costs associated with the fixed IMR at Thargomindah (as at 1998), include: Cabin 6,000 6’ Antenna 4,900 Phone connection 3,000 Electricity connection 1,500 Air conditioner 1,000 Other equipment 2,500 Total: 18,900

Note how the mobile’s use of a smaller antenna alone saved $4,900.

2.9 Calibration of the IMRs

An IMR’s transmitter power and receiver sensitivity will each have nominal values as determined by the manufacturer. But both need to be calibrated if an

69 insect’s characteristics are to be accurately measured. The transceiver of what was to become the Bourke IMR was calibrated in 1986 by V.A. Drake and W.W. Wolf. The Thargomindah IMR was calibrated in 1999 by I.T. Harman. Their calibrations have been used in the present work. The antenna components (excluding the antenna itself), transceiver, peak-detector circuits and antenna feed of the mobile IMR were identical to those of the Thargomindah IMR so these calibrations were used for the mobile IMR as well. The remaining calibrations are described below.

2.9.1 Measurement of Transmitter Power The mobile IMR’s transmitter power was measured at UNSW@ADFA’s former School of Electrical Engineering during June 2003. The equipment used is shown in Figure 2.14. The nominal transmitter power (25 kW) was too great to be measured directly, so it was reduced using two cross-guide couplers before being measured by a digital power meter (437B, Hewlett Packard, Palo Alto, USA).

Dummy Load

30 dB 20 dB Coupler Coupler

Power Meter

Transceiver

Figure 2.14: The equipment used to measure the mobile IMR transmitter power. Two cross-guide couplers (arrowed) were used to reduce the transmitted power to a level where it could be measured by the power meter.

70 The power measured by the power meter was the mean power, from which the peak power was calculated. Also measured was the transmitter power of an identical unit that has since been used to replace the type 65160 transceiver in the Bourke IMR. The results are shown in Table 2.2 together with the results previously obtained by I.T. Harman for the Thargomindah IMR.

Table 2.2: Measured transmitter power of the mobile IMR, proposed new Bourke IMR, and existing Thargomindah IMR using the equipment shown in Figure 2.14. The measurements of the Thargomindah IMR were made by I.T. Harman. All three IMRs use the same model 65125 transceiver.

Pulse Type Pulse Length (ns) Mean Power (dBm) Peak Power (kW) Mobile IMR Transmitter Short 50 31.58 ± 0.02 22.7 ± 0.1 Medium 250 39.41 ± 0.01 27.5 ± 0.1 Long 1000 41.65 ± 0.01 23.0 ± 0.1

New Bourke Transmitter Short 50 31.68 ± 0.02 23.2 ± 0.1 Medium 250 39.40 ± 0.01 27.4 ± 0.1 Long 1000 41.72 ± 0.01 23.4 ± 0.1

Thargomindah Transmitter Short 50 29.29 ± 0.07 14.2 ± 0.2 Medium 250 37.40 ± 0.02 18.3 ± 0.1 Long 1000 40.12 ± 0.04 17.1 ± 0.2

The peak powers of the (nominally identical) mobile and new Bourke transmitters are similar but not actually identical. Each is consistent with their nominal rating of 25 kW; the mean difference is 0.3 kW or just over 1%. However, the peak power of the (again nominally identical) Thargomindah transmitter is less by 6 to 9 kW, which suggests its magnetron may have degraded. The Thargomindah IMR ceased operation on 1 March 2001 due to transmitter failure, so further testing was not possible.

71 2.9.2 Measurement of Receiver Sensitivity In principle receiver sensitivity could be measured by passing a target of known RCS through the radar beam. In the present work this was attempted using a model aeroplane to tow a calibration sphere through the radar beam, but its speed was too great and its position was not precise enough, so no useful results could be obtained. Another approach might be to tilt the radar beam and aim it at a target near ground level, but attempts by others to do this have been unsuccessful due to the associated ground clutter. Therefore the sensitivity of the IMR receiver was measured by injecting a pulse from a signal generator and measuring the resulting peak size on the peak detector. This simulates the passage of an insect through the radar beam.

These sensitivity measurements were made for the Bourke IMR transceiver (model 65160) by V.A. Drake and W.W. Wolf in 1986 and for one 65125 transceiver by I.T. Harman and W.W. Wolf in 1996. Further measurements of all 65125 transceivers have recently been made by V.A. Drake and S. Hatty. The results for the original Bourke IMR transceiver are shown in Figure 2.15. The limit of sensitivity (the threshold) is –83 dBm with two apparent characteristic slopes of 53.5 dB/V and 22.5 dB/V intersecting at –77.9 dB. However, the 53.5 dB/V line was subsequently found to be spurious and the 22.5 dB/V slope appears to apply down to the threshold. The corresponding thresholds and slopes for the Thargomindah and mobile IMRs were −92.0 dBm and 27.2 dB/V, and −92.0 dBm and 29.0 dB/V, respectively. Thus sensitivity of the new units is ~7 dB better than that of the old one.

72

Figure 2.15: Receiver calibration curve for the original Bourke IMR as measured by I.T. Harman. The 53.5 dB/V line was later found to be spurious.

2.9.3 Estimated performance From the above calibrations the estimated performances of the four radars listed in Table 2.1 can be calculated. The results are briefly summarised in Table 2.3. As expected, the older Bourke IMR is the least sensitive of the four radars; otherwise they are roughly comparable in performance. Estimated sensitivities to particular insects at particular heights and further details of the four radar performances are provided in Chapter 3. They show that all three IMRs are clearly capable of characterising the insects studied later in this work.

Table 2.3: Estimated performance of the four radars shown in Table 2.1. From top are maximum antenna gain, received power from an RCS of 1 cm2 at 500 m relative to Bourke = 100 (the smaller the number the greater the sensitivity), minimum detectable signal power (threshold), and maximum altitude at which a standard target can be detected relative to Bourke = 100 (the larger the number the greater the sensitivity).

VLR Bourke Mobile Thargo. Maximum antenna gain (dB) 42 44 41 44 Received power (Bourke = 100) 26 100 14 45 Minimum signal power (dBm) −85 −72 −83 −83 Max detectable altitude (Bourke = 100) 152 100 119 154 dB = 10 log10 (gain). dBm = 10 log10 (power in mW) , so 0 dBm = 1 mW.

73 2.10 Locations of the Mobile IMR

The purpose of the mobile IMR was to make observations at locations between the two permanent IMRs. Locations adjacent to a sealed road were preferred to avoid damage to the mobile IMR in transit. Four sites were chosen as shown in Figure 2.16 with one requiring 49 km travel on an unsealed road. The unit as set up for operation at the four sites has been shown previously in Figure 2.6.

Figure 2.16: The four mobile IMR locations in the study area. Thick black lines are sealed roads, open lines are unsealed roads, and the figures between flags are road kilometres. The four mobile IMR locations were as equally spaced between the two fixed IMRs at Bourke and Thargomindah as local settlement and the availability of power would allow.

2.11 Reliability of the IMRs

During the period 1 September 1999 to 1 March 2001, a period of 548 nights, the Bourke and Thargomindah IMRs were in service on 83% and 77% of nights respectively. At Bourke the main causes of lost service were system faults and CD archiving/postal losses, accounting for 50% of failures, see Table 2.4. Installation of a larger hard drive has subsequently reduced these figures significantly by eliminating failures due to the hard drive becoming full; it has also enabled data to be kept on the hard drive until the CD has been received and checked, thus eliminating postal losses. A similar pattern of failure was observed at Thargomindah but exact figures are not available. 74

Table 2.4: Breakdown of the causes of missing data on 93 nights for the Bourke IMR (H.K. Wang personal communication). System faults were mostly due to the hard drive becoming temporarily full before there was time to burn it to CD.

Cause % of loss System faults (disk full, hardware & software faults) 25.8 CD archiving/postal loss 24.2 Power failure 19.7 Servicing 12.1 Other/unidentified 18.2

The two fixed IMRs were both fully operational on only 57% of the 548 nights, which limited the data available for comparison studies in the present work. Nevertheless during these periods a total of approximately 324,000 large (RCS >1 cm2) insects were detected at Bourke and 1,080,000 at Thargomindah. On average the C++ algorithm (Chapter 4) successfully processed 89% of echoes and failed to process 6.5%. The remaining 4.5% of echoes were too short to process.

The reliability of the mobile IMR involved additional concerns such as the hazards of travel; and the possibility of equipment overheating, especially the peak detector. When in service the temperature of the peak detector (measured at the cooling slits in its housing) was higher than the air temperature by 22 to 28°C, depending on air temperature, see Figure 2.17. However, the peak detector’s components are rated to at least 85ºC, with most rated above 100ºC, so there is little danger of overheating during the night-time observing period when the air is cool. From 16 April to 23 April 2002, during an operational period of 88 hours made up of eight 11-hour nights at four sites, the mobile IMR operated successfully for 74 hours (84%). This trial period was short but involved much road travel (about 700 km from Canberra plus 500 km from Bourke plus 700 km return, total 1900 km), so it was a severe test. Overall the mobile IMR was, if anything, slightly more reliable than the fixed IMRs.

75

Figure 2.17: Maximum nightly peak detector temperature vs. maximum nightly air temperature. Other relationships, e.g. with average temperature, are not included as the thermometer used was capable only of recording the maximum temperature.

This suggests that a mobile IMR with increased data storage could be left to operate automatically for up to a month provided mains power is available. Current proposals for upgrading include a weatherproof and cooled housing for the electronics, which will be located on the trailer in the space previously occupied by the generator and fuel cans. If mains power is not available, the generator and fuel cans could be carried in a suitable tow vehicle, but unattended operation would not be feasible.

76 3 IMR PERFORMANCE, DESIGN, AND SIGNAL PROCESSING

This chapter deals with the calculated performance of IMRs, the nature of the echoes produced by insects, how the parameters of interest are retrieved from these echoes, and how IMRs can be designed to best match the parameters of the insects under study. Parts of this chapter are expanded from Dean & Drake (2002a) Monitoring migrations of agricultural insect pests with low-cost autonomous radar profilers.

Graphical plots show how insect characteristics (altitude, speed, size, shape) affect IMR signals. Early approaches to calculating entomological radar performance are extended to IMRs. Calculations are shown for three IMRs and one VLR. Insect flight speed is a neglected variable that can seriously affect IMR performance. Limited tests indicate that the local distribution of flying insects conforms to a random (Poisson) distribution, but high densities can exceed the IMR's processing capacity. Computer processing of the received signals allows the insects' physical and flight characteristics to be determined (for overlap between species see next chapter). A simple design approach based on transmitted power and antenna diameter allows IMR performance to be matched to specific requirements. The computer processing of IMR signals is briefly described. The main original contributions in this chapter are the extension of early radar calculations to IMRs, evaluation of flight speed effects, evaluation of the local distribution of flying insects, and a holistic approach to IMR design.

3.1 Introduction

The field strength of an IMR radar beam falls off with distance from the beam's axis. Therefore the signal from an insect passing through a beam will reach a maximum on the beam's axis where the field strength is highest and fall away on either side. The beam is also polarised, rotating, and offset (Figure 2.4 in Chapter 2). Therefore the signal will be modulated by (1) the beam's rotation, because the signal is strongest when the body length is aligned with, or at right angles to, the plane of polarisation; and (2) the beam’s offset, because when the beam returns every half revolution to the same polarisation angle, but with a different distance from the zenith due to beam offset, the field strength at the target will be different.

The radar beam is reflected predominantly by the insect’s water content, so those parts of the insect that consist mainly of dry tissue such as wings (Schaefer, 1969), or which are inoperative during flight such as legs, will not 77 produce independent echoes (Riley, 1973). However, wingbeats will modulate the signal indirectly via the associated movements of the abdomen and thorax (Schaefer, 1976; Vaughan, 1985). A typical signal is shown in Figure 3.1. Its components are shown later in Figure 3.3.

Figure 3.1: The signal from a small insect passing through the beam of the mobile IMR. The insect has taken about 4 seconds to traverse the beam, here about 20 m wide. The signal rises to a maximum on the beam axis and then falls away. Superimposed are regular variations due to the beam's rotating plane of polarisation, which is aligned with the insect's body axis twice per revolution so their frequency is 10 Hz, twice the beam’s rotation rate of 5 Hz. (The two alignment occasions differ due to the beam offset, so the amplitudes are different.) Further modulation due to the insect’s body movements associated with wingbeating is also present but is not discernible by eye. Subsequent processing of the signal showed that the insect had an RCS of 0.1 cm2 and was flying at an altitude of between 325 and 350 m in a westwards direction at 257º with a ground speed of 5 ms-1.

The mathematical form of the echo from an insect was first established by Smith et al. (1993) who derived an algorithm for extracting the insect's characteristics based on the Fourier transform of the echo. This algorithm has since been used to process the data acquired by Vertical-Looking Radars (VLRs) in England (e.g. Smith & Riley, 1996). Some of the limitations of the VLR and associated processing algorithm for detecting insects have been evaluated by Chapman et al. (2002). However, similar calculations have yet to be made for IMRs, so it has not previously been possible to extend IMR observations to include, for example, accurate estimates of migrant numbers. In what follows I take Chapman et al.’s (2002) calculations, extend them to include the various modulations of the reflected signal and the constraints due

78 to noise threshold, envelope width, and target speed, and apply them to the fixed and mobile IMRs in order (among other things) to estimate their limitations in detecting and characterising insects. I then look at ways of designing IMRs with a specific performance. Finally, to provide background information relevant to signal processing, I briefly summarise the work of others in the calculation and processing of IMR signals.

3.2 Calculation of IMR Performance

What are the radar design parameters required to retrieve an insect’s size, speed, orientation and direction given a defined radar cross section, altitude and position within the radar beam? Conversely, given the radar parameters, what insects can be detected? These questions can be answered using radar theory. The first step is to derive the nominal power required to detect a given RCS at a given altitude. The second step is to adjust the nominal power for the various modulations and constraints that affect the received signal to ensure it remains above the noise threshold for the minimum required duration (at least four beam revolutions, which at 5 Hz is at least 0.8 s), and with enough margin to reject spurious signals. The first step is the subject of Section 3.2.2. The second step is the subject of Sections 3.3-3.4. The findings are then applied in Section 3.6 to the design of IMRs with a specified performance.

3.2.1 Parameters required for Calculating IMR Performance The parameters required for calculating IMR performance from radar theory are listed in Table 3.1 for the VLR of Chapman et al. (2002) in the UK, the two fixed IMRs, and the mobile IMR. The VLR was designed to detect insects considerably smaller than those for which the IMRs were designed. Table 3.1 also includes the equation numbers where the parameters are first cited.

79 Table 3.1: Parameters for calculating the performance of the four radars. For some parameters such as antenna diameter the values given are those provided by the manufacturer. For others such as transmitted power the values given are the measured values, which may differ from the manufacturer's nominal values The units shown are those of convention and where necessary require conversion to SI units before inserting in the radar equations.

Symbol Equation No. Description VLR1 Bourke Mobile Thargo.

pt (3.1) Transmitted Power (kW) 25 32 22.7 14.2 λ (3.1) Wavelength (cm) 3.2 3.2 3.2 3.2

Da (3.7) Antenna Diameter (m) 1.52 1.8 1.2 1.8

θ3dB (3.2) Beamwidth (º) 1.45 1.1 1.64 1.1

LS (3.6) System Losses (dB) 1.58 1.62 1.37 1.62 B (3.8) Bandwidth (MHz) 20 18 18 18 2 Nf (3.8) Noise Figure (dB) 3.5 18 5.5 5.5 PRF (3.9) Pulse Repetition Freq. (Hz) 1500 2500 1270 1270

In (3.9) Integration Factor (dB) 3.5 4.5 3 3 3 Vf (3.8) Visibility Factor (dB) 15 15 15 15 ∆ (3.12) Beam offset (°) 0.15 0.2 0.2 0.2 ∆r Range gate width (m) 45 50 25 25 Range gate spacing (m) 71 150 50 50 1Data from Chapman et al. (2002). 2Nominally 12 dB but measurements indicated 18 ± 1 dB. This discrepancy may indicate a degradation in receiver performance or unaccounted power loss (I.T. Harman, personal communication). 3The value used by Chapman et al. (2002) was 13 dB, but 15 dB is used here for consistency with the IMRs.

The RCS values that the IMRs encounter in the study area depend on the insect species and season and are generally between 0.01 and 10 cm2. An example of their distribution is shown in Figure 3.2. Another example is shown in Figure 4.22 in Chapter 4.

80

Figure 3.2: The distribution of observed RCS values from 6,284 good-quality echoes recorded by the Bourke IMR during the night of 14 March 1999. The peak around −10 (corresponding to an RCS value of about 0.1 cm2) is largely due to a background of small insects, and the peak around 3 (corresponding to an RCS value of about 2 cm2) is largely due to spring moths and plague locusts. The shaded areas identify the RCS values that are grouped later in Figure 3.12.

3.2.2 Power Received From the Target

The power reflected by a point target and received back at the radar (pr) is given by the radar range equation (see e.g. Rinehart, 1997) p g 2λ 2 σ p = t (W) (3.1) r π 3 4 64 rr where: rr is the range or altitude (m), σ is the RCS of the target (Radar Cross 2 Section, m ), λ is the wavelength (m), pt is the transmitted power (W) and g is the antenna gain at an angular distance θ (radians) from the beam axis as approximated by the Gaussian equation (Skolnik, 1990):

 θ 2  g= g exp() − 4ln 2  (3.2) 0 θ   3dB   where θ3dB is the beamwidth in radians, expressed as the angle between the half-power points in the radar beam, and g0 is the maximum gain on the beam axis. The –4 term accommodates the difference between θ (measured from the beam axis) and θ3dB (measured across the width). For example, if the half- 81 power points (i.e. where g = 0.5 g0) are θ radians from the beam axis, θ3dB = 2θ, 2 and the antenna gain g = g0 exp(−4 ln2 (0.5) ) = 0.5 g0 in accordance with the definition.

The maximum gain on the beam axis is given by π 2k 2 g = a . (3.3) 0 θ φ b b

2 Here ka is a measure of the radar illumination pattern and is a constant dependent on the type of antenna, θb is the horizontal beamwidth (radians) and φ 2 b is the vertical beamwidth. For circular reflectors ka = 1, and the horizontal and vertical beamwidths are both equal to θ3dB. The value of θ3dB is provided by the antenna manufacturer and is inversely proportional to antenna diameter (Rudge, 1982).

For the Bourke and Thargomindah IMRs, where θ3dB = 1.1° (0.0192 radians), the maximum gain is π 2 g = = 26,777, which in dB = 10 log (26,777) = 44.3 dB. (3.4) 0 π 10 (1.1 )2 180

Combining equations (3.1), (3.2) and (3.3), and replacing pr with pm, the minimum power to be received for successful operation and for the time being ignoring all losses, gives

2 πp λ σ 2 r 4 = t exp− 8ln 2()θ θ  (3.5) r θ 4  3dB  64 3dBp m where rr is the altitude corresponding to power level pm when the target is at angle θ from the beam axis.

An alternative expression for the maximum altitude r0 at which an insect can be detected on the beam axis can be found by rearranging equation (3.1) and including the system one-way loss (LS) consisting of the waveguide, duplexer, 82 rotation joint and radome losses incurred by the outgoing beam (the same one- way loss will be incurred by the returning beam), the antenna diameter (Da, m) and efficiency (ρa, see equation (3.7)), and the minimum signal power required by the radar receiver in order to register the target (Smin, see equation (3.8)); which gives

0.25 pπ D4 ρ 2 σ  r = t a a  (m) (3.6) 0 2λ 2 64LSS min 

In the numerator, ρa is the efficiency given by g λ 2 ρ = 0 . (3.7) a π 2 2 Da

In the denominator, Smin is the minimum signal power (W) required to register the target and is given by

B ()NVI+ − /10 S= k T ×10 f f n (3.8) minB 0 0.76 -23 -1 -1 where kB is Boltzmann’s constant (1.3807 x 10 WHz K ), T0 is the absolute temperature of the receiver input (taken to be 293 K, i.e. 20ºC), B is the receiver bandwidth (Hz), and Nf is the measured equipment noise figure (dB), typically around 5 dB.

Vf is the visibility factor (dB), the safety margin above noise required to detect a certain proportion of targets, and which is normally set to ensure a defined low false alarm rate. According to Chapman et al. (2002), if the insect is to be detected 90% of the time, the corresponding required value of Vf is 5 dB. However, when allowance is made for signal variations due to changes in the target's RCS with changing beam polarisation, they estimate a Vf for analysis (as opposed to detection) of 13 dB, which they used for their VLR. In practice the optimum value of Vf can be determined empirically as described in Section 3.4.1 after consideration of the various modulations in Section 3.3. In Table 3.2 all values of Vf are 15 dB.

83 In is the integration factor (dB), the gain in signal strength due to signal sampling. Instead of emitting a constant radar beam, IMRs and VLRs send pulses at a certain frequency called the pulse repetition frequency or PRF, typically 1250-2500 Hz. During each pulse the power may be around fifty times the continuous power. The received signals are sampled at 64 evenly spaced angles around the beam, which is rotating at 5 Hz, giving a sampling frequency of 320 Hz. The sampling frequency is less than the PRF and therefore allows accumulation and integration of the signal samples. In represents the improvement in the signal-to noise ratio due to this accumulation and (before conversion to dB) is

PRF I = . (3.9) n 320 For the Bourke IMR, inserting the values of Table 3.1 into the above equations gives the following results: 26,777× 0.0322 Efficiency ρ = = 0.8575 a π 2×1.8 2 2500 Integration factor I = = 2.795, or 10log( 2.795) = 4.5dB as given in n 320 10 Table 3.1.

6 − 18× 10 ()+ − Minimum signal power S =1.3807 × 1023 × 293 × × 10 18 15 4.5 /10 min 0.76 = × −11 ×−11 = − − 6.782 10 W, or10log10 ( 6.782 10) 101.7dBWor 71.7dBm .

=1.62 10 = System one-way loss LS 10 1.4521.

 ×π ×4 ×2 ×σ 0.25 = 32,000 1.8 0.8575 Maximum altitude r0  −   43 × 1.45212 × 0.0322 × 6.782 × 10 11 

0.25 2 2 =16,963 ×σ m. If RCS = 1 cm , σ = 0.0001 m and r0 = 1,696 m.

Comparison of equations (3.5) and (3.6) indicates that = 2 pm L S Smin (3.10)

84 However the above calculations do not take into account the drop in signal strength due to modulation by target position and beam offset, or to high flight speeds, all of which are considered in subsequent sections.

3.2.3 Sensitivity of Maximum Altitude r0 to Changes in Parameters

How sensitive is r0 to changes in the various parameters? It depends on the parameter. A change in antenna diameter Da cancels out in equations (3.6) and

(3.7) but changes the beamwidth θ3dB in proportion to 1/diameter, which then affects r0. According to the above equations, the following changes in parameters each increase r0 by about 1% for all four radars:

− 4% increase in transmitter power pt, radar cross section σ, or

integration factor In

− 4% decrease in minimum signal power Smin, bandwidth B, visibility

factor Vf, or temperature T − 2% increase in wavelength λ

− 2% decrease in one-way loss LS

− 1% decrease in beamwidth θ3dB (equivalent to a 1% increase in

antenna diameter Da)

(The above changes in In, Smin, Vf, and GL are as power, not dB.)

Some of the above changes are readily predicted via the power to which the parameter is raised in the relevant equations. Others, such as the effect of In and Vf, are less obvious. Overall, r0 is fairly insensitive to most parameters, which has clear implications if large changes are required. This topic is further explored in Section 3.6 (designing IMRs with a specified performance). The accuracy of the calculated r0 will depend on how much effect a given parameter has and on how precisely it is measured. Here beamwidth θ3dB (1.1º - 1.64º in Table 3.1) has proportionately the most effect and is nominally the least precisely measured. However, assuming that the equipment parameters remain stable during operation, the only variable influence on r0 other than σ will be

85 temperature. On average a 12º fall in receiver temperature, as might occur in the absence of air conditioning during the passage of a cold front, will reduce r0 by 1%. None of the radars listed in Table 3.1 operate up to heights close to r0, so for them the effect of temperature on r0 is of no consequence.

3.3 Component Modulations of the Reflected Signal

This section considers the modulations caused by the target and by the beam configuration. Constraints on the signal due to the noise threshold, processable width, and target speed are considered in Section 3.4.

3.3.1 Signal Strength of Basic Components The signal reflected by the target back to the radar contains several component frequencies as shown in Figure 3.3. The main component is a rise and fall due to the insect crossing the beam, with smaller components due to beam rotation, beam offset, and (smallest of all) wingbeating. The way in which these components are calculated for the purpose of processing is described later in Section 3.7, and the way in which the signal is processed to disentangle these components is described in Section 3.8. The immediate sections look at the signal strength of these components and the effects of beam offset and high flight speeds. The calculated performance of the four radars is then given in Section 3.5. Sections 3.4 and 3.5 summarise the work of others and are included only to provide the equations and background information relevant to the other sections in this chapter.

86 Components of a reflected signal N Plan view: Western half of a rotating IMR beam at an altitude of 225 m. The dotted line indicates the path of a sphere (plots 1 and 2) or insect (plots 3 and 4) moving across the beam from south to north at 4 ms-1. The altitude and speed are illustrative only but are well within the range typically found for insects. The form of the reflected signal is illustrated below.

Plot 1. Signal for a sphere moving through a stationary IMR beam. Because the target is spherical there is no modulation due to varying target geometry. The reflected signal shows a broad rise and fall as the target traverses the beam.

Plot 2. Signal for a sphere moving through a rotating linearly-polarised beam. A smaller oscillation is imposed on the signal seen in Plot 1 due to the variation in distance between target and beam axis due to beam offset. The beam rotates at 5 revolutions/second so the peaks are spaced 0.2 s apart.

Plot 3. Additional signal modulation imposed on plot 2 due to variation of the insect's RCS with beam polarisation angle. The major peaks are spaced 0.1 s apart as the maxi- mum reflection of the beam by the symmetric insect occurs twice per revolution.

Plot 4. Resultant of the signals in plots 2 and 3. This is the type of signal that an insect would produce. The value of the signal at 1.5 s (–42 dB) is the resultant of –33 dB (resultant of range, radar power and sensitivity) plus –2 dB (plot 2) plus –7 dB (plot 3). The signal is clipped at the noise floor of –83 dB.

Figure 3.3: Calculated components of a signal reflected by an insect when traversing through the Bourke IMR radar beam. The quantities chosen for the calculation were typical of those found for insects and were: flight direction 0°, insect orientation 0°, speed 4 ms-1, radar cross section 0.1 cm2. The modulation by wingbeating is omitted for clarity but would be typically –1 to –2 dB.

87

3.3.2 Modulation Due to Target Distance from the Beam Axis

If the radar beam is without offset, the variation in gain with distance θ of the target from the beam axis is described by equation (3.2). The modulation md of the signal due to the change in distance between distances θ1 and θ2 is

 θ 2  θ 2   2 1  m =exp − 8ln 2  −    (θ1 < θ2) (3.11) d  θ θ   3dB  3 dB  

2 If θ1 = 0 and θ2 = θ3dB/2, then md = exp(−8ln2 x (0.5) ) = 0.25, or as dB

10 log10(0.025) = –6.0 dB.

However, when the beam is offset, a target distant from the beam axis may be inside the beam for only part of the rotation. If the processing algorithm has zero tolerance of incomplete sampling of the 64 sampling angles, the effective beamwidth for an offset beam is less than the nominal beamwidth by two times the offset, as shown in Figure 3.4 for the Bourke IMR with a 0.1 cm2 target. In fact both this algorithm and the frequency-domain one used for the English VLRs (A.D. Smith personal communication 2007) tolerate a small number of samples that fall to the noise level (although the accuracy of the extracted parameters is reduced), so Figure 3.4 tends to slightly underestimate the effective beamwidth. That is, the processable width is reduced by twice the offset, and the maximum altitude is reached when the processable width reaches zero. Beam offset does not affect signal strength within the beam, so the beamwidth to use when calculating signal strength is still θ3dB, not (θ3dB – 2 x offset).

88

Figure 3.4: Change in beamwidth due to beam offset. For clarity the horizontal scale has been exaggerated about forty times. The figure shows the beam profiles at their most extreme left and right positions. To be processable the sampled width must be within the beam during the entire 360º of beam rotation. This width, here called the offset beamwidth, is shown shaded, and is (θ3dB – 2 x offset) at all altitudes. Beyond the shaded area the sampled width is within the beam for only part of the rotation and is therefore either unreliably processable or completely unprocessable, depending on the tolerance of the processing algorithm.

3.3.3 Modulation due to Beam Offset If the insect is θº from the zenith, the minimum and maximum angular distances from the beam axis are (θ − ) and (θ + ), where is the beam offset in degrees (see Table 3.1), and by equation (3.2) the change in gain (i.e. gain 2/gain 1) is

 2θ  2∆  m∆ =exp() − 8ln 2  (3.12) θ  θ   3dB  3 dB  where m is the modulation of the reflected signal due to beam offset. For the Bourke IMR and θ = 1º, which corresponds roughly to the full beamwidth that 2 RCS = 1 cm would create at 600 m, m = exp(−8ln2 x 1.82 x 0.32) = 0.04, or as dB 10 log10(0.04) = –14 dB. 89

In terms of the form of the received signal, the modulations due to target distance from beam axis and to beam offset are traditionally not separated, and are collectively referred to as the trajectory component.

3.3.4 Modulation by RCS due to Beam Rotation

The modulation of the radar cross section component mRCS due to beam rotation depends on the two principal scattering terms of the target (σXX and σYY, see Section 4.3 in Chapter 4) and is given by σ  m =10log XX (dB). (3.13) RCS 10 σ  YY  Equation (3.13) can be evaluated using the laboratory data for 68 individual insects given in the Appendix, and observed data from the Bourke IMR. Values calculated for the laboratory data using equation (3.13) are shown in Figure 3.5. Bourke IMR results for 4,050 insects are shown in Figure 3.6. The maximum modulation for the former is 27 dB but 95% (for which the mean is 7 dB) are 13 dB or less. The maximum modulation for the latter is 15 dB, the mean is 8 dB, and 97% are 13 dB or less. When allowance is made for the very large insects in the laboratory data that are not found in the Bourke area, the two sets of results show acceptable agreement.

Figure 3.5: Modulation of the RCS component calculated from the laboratory measured RCS data (n = 68) using equation (3.13). The maximum modulation is 27 dB but 95% are less than 13 dB or less.

90

Figure 3.6: Distribution of signal modulations due to the RCS component for 4,050 insects detected by the Bourke IMR on the night of 15 March 1999 with a signal strength at least 20 dB above noise. The maximum modulation was 15 dB with 97% of signals having a modulation of 13 dB or less.

3.4 Constraints on the Received Signal

3.4.1 Constraints Due to the Visibility Factor Vf To be reliably processable, the received radar signal or echo must remain above the noise threshold for at least the minimum processable signal length, i.e. at least four beam revolutions, which at 5 Hz is at least 0.8 seconds. The signal must also be sufficiently above the noise threshold to accommodate the modulations due to distance from the beam axis (e.g. –12 dB), beam offset (e.g. –7 dB), wingbeating (e.g. –2 dB), and the variation in radar cross section due to beam rotation (e.g. –8 dB), which is where Vf comes in.

The optimum safety margin or visibility factor Vf can be evaluated by comparing the proportion of successfully processed echoes against signal strength. The procedure is illustrated in Figure 3.7, which shows the number of successfully processed and unprocessed echoes for a typical night’s data from the Bourke IMR, and the proportion that was successfully processed. As expected, the proportion of successfully processed echoes increases with maximum signal strength, in this case from around 5% to nearly 70% as the

91 maximum signal strength increases from –80 dB to –35 dB. The average processable proportion was 38% for a total of nearly 19,000 echoes, and was reached when the maximum signal amplitude was about –73 dB, or 10 dB above noise (–83 dB), which implies that any processing biases will not be intrusive if the safety margin or visibility factor Vf is set to 10 dB. In other words setting Vf to 10 dB means that something like the worst half or two- thirds (here 100% – 38% = 62%) of the echoes will be automatically rejected during processing. However, in the present work, given the need for accurate analyses of the RCS parameters (Chapters 4 and 5), Vf was increased to 15 dB. No allowance is necessary for the 5 dB suggested on probability grounds by Chapman et al. (2002), see Section 3.2.2, because it is already incorporated in the 15 dB limit.

Figure 3.7: The number of processed and unprocessed echoes, and the proportion processable, for a typical night’s data (in this case 15 March 1999) from the Bourke IMR. The dip in the processable proportion around –55 dB is due to the two-peaked distribution of RCS values, see Figure 3.2.

3.4.2 Envelope Width Across Which a Target Can Be Detected Equation (3.2) shows how the antenna gain varies in Gaussian fashion with angular distance from the beam axis. For a rotating beam without beam offset, the Gaussian envelope (positions of equal gain) will be as shown in Figure 3.8, which also shows the scanned volume VS between altitudes r1 and r2.

92

Figure 3.8: Gaussian envelope (positions of equal gain) for a rotating beam without beam offset. Also shown is the scanned volume Vs between altitudes r1 and r2. For clarity the angle of the beam has been exaggerated about fifteen times, and the vertical altitudes represented by r1 and r2 have been omitted. (Adapted from Chapman et al., 2002.)

According to Chapman et al. (2002), from whom equations (3.14) to (3.16) are reproduced, the scanned volume for a beam without offset is given by

3 3 2     πθ  r   r   r r  3 V= 3dB  r32 −  1   +3 r 3 ln0 − r 3 ln 0  (m ) (3.14) S 18ln 2 0 r r  2r 1 r  0   0    2 1  where r0 is the maximum altitude at which targets can be detected. If r0 happens to lie in the middle of the highest range gate (i.e. r2 > r0), which is not an approach used in the present work, then (3.14) can be evaluated by putting r2 = r0, so that

3 2   πθ  r   r  V= 3dB  r31−1   − 3 r 3 ln 0  (m3). (3.15) S 18ln 2 0r  1 r  0   1 

The scanned volume resembles the frustum of a right circular cone. If the sides show no appreciable bulge, as is the case for a narrow beam and r1 ~ r2, the mean horizontal radius am (m) of the scanned volume is then given with good accuracy by

93 V a = S (3.16) m π ()− r2 r 1

The Bourke IMR's range gate width of 50 m is the largest of the four radars in Table 3.1 and should therefore show the largest inaccuracies when using equation (3.14). But except at altitudes below 300 m or within 200 m of r0, the difference between the mean radius according to (3.16) and the actual radius in the middle of the gate was generally less than 0.05% for all r0's between 1000 m and 2000 m, while the difference between the mean radius and the upper or lower radius averaged 2% and was rarely more than 5%. Halving the range gate width halved the differences.

The above equations do not allow for beam offset ∆, which reduces the processable width (depending on the tolerance of the processing algorithm) by up to twice the beam offset as shown earlier in Figure 3.4. It also reduces the maximum altitude r0 from the value given by equation (3.6), i.e. the value when am = 0, to the value when the processable width becomes zero as described in Section 3.3.2. The reduction in maximum altitude due to beam offset is generally only a few percent. Beam offset ∆ also reduces the position of maximum width from about 61% of r0 at = 0º to 54% of r0 at = 0.175º, the reduction being roughly proportional to and independent of RCS and Smean.

An alternative envelope calculation to that of Chapman et al. (2002), but giving the same results, is to use equation (3.5), in which the key quantity is pm, the minimum power to be received for successful operation. Once pm has been specified along with the parameters pt, λ, σ, and θ3dB , the envelope within which the target can be detected can be found by rearranging equation (3.5) to give (recall that θ is measured from the beam axis whereas θ3dB is a width)

94   4 (π λ2 σ θ 4 )  ln rr p t 64 3dB p m   θ= θ   (3.17) 3dB −8ln 2   which allows θ to be determined for any valid value of rr. The beamwidths that define the envelope are then given by

Full beamwidth = 2 rrtanθ Distance between beam centres 180º of rotation apart = 2 rrtan (3.18) Offset beamwidth = 2 rrtanθ − 2 rrtan

 4 (π λ2 σ θ 4 ) Equation (3.17) is solvable only if ln rr p t 64 3dB p m  is negative, which applies up to the maximum range r0 given by equation (3.6).

3.4.3 Constraints Due to Target Speed Chapman et al. (2002) did not consider the need for signals to be long enough, not just strong enough, to be processable. In Section 3.4.1 the visibility factor

Vf was set at 15 dB to avoid processing bias, which means that to be successfully processed the signal amplitude must remain 15 dB above the noise threshold for at least 0.8 s. At low altitudes the beam is quite narrow, and the target may cross it in less time than is required for signal processing, either because of high target speed or because the flight path is near the edge of the beam. Either way, the result is a reduction in the processable volume to less than that described by equations (3.14) and (3.15).

The above reduction has hitherto not been mentioned in the literature. The maximum speed at distance d from the zenith consistent with a signal lasting not less than 0.8 s is given by

2 a2− d 2 m (ms-1) (3.19) 0.8 where am is now the radius of the processable beam, see Figure 3.9.

95

Figure 3.9: The length of an insect’s detectable path through an IMR beam relative to distance d from the zenith and the radius of the processable beam am.

Thus the maximum processable speed is reduced to 75% for a flight path that is two-thirds of the processable radius out from the zenith, and to 50% for a flight path that is 87% out. For the Bourke IMR with a target RCS of 1 cm2, using beamwidths calculated by equation (3.18), the variation of processable width with altitude and RCS is shown in Figure 3.10. The processable width increases with altitude and then decreases, the maximum width being reached at 61% of the maximum altitude for the full beam and 54% for the offset beam. There is a notable reduction in processable width between the full beam and the offset beam, but the effect is less than the variation due to altitude. It is also less than the variation due to differences in RCS. For example reducing the target RCS from 1 cm2 to 0.1 cm2 nearly halves the processable widths.

Thus far, Figure 3.10 shows little that is not already implied by Figure 3.8. But Figure 3.10 also shows the distribution of travel speeds observed at Bourke and Thargomindah during 1999-2001, and it is here that the picture changes. To detect an insect travelling at the mean observed speed of 12.5 ms-1 requires a processable width of 12.5 x 0.8 = 10 m, which for RCS = 0.1 cm2 is not attainable by the offset beamwidth. Insects flying at 19 ms-1 will generally not be detected unless their RCS exceeds 1 cm2, which suggests that the distribution of observed speeds (and indeed the distribution of observed

96 altitudes) may well be less determined by actual speed and altitude than by a progressive inability of the IMR to detect insects travelling at higher speeds.

Figure 3.10: Maximum processable width vs. height for the Bourke IMR calculated by equations (3.17) and (3.18). The breakdown of observed travel speeds is from Section 7.4.3 in Chapter 7 and is for 313 nights between 1 September 1999 and 1 March 2001. For example the x-axis label of 13 ms-1 corresponds to speeds of 12.01-14.00 ms-1. The maximum mean nightly speed is about 20 ms-1.

There is another way of looking at the situation. Divide the width W into n strips where the ith strip has width Wi. The mean width is of each strip is therefore

n → π ∑Wi / n W 4 for large n i=1 (error is 1% for n = 10). Since width is symmetrical, using n = n/2 strips over the half-width gives the same answer. The maximum processable speed corresponding to Wi is Wi/0.8 so the mean of the maximum speeds that the beam widths can process in 0.8 seconds is n  = v∑ Wi / 0.8  n . i=1 

97 Therefore the proportion of processable signals PPS averaged across all width elements and all observed speeds will be = × PPS v Fs .

Where Fs is the the cumulative frequency distribution of the observed travel speeds v. For example, if the maximum beam width W is 20 m then the average maximum processable speed across the beam is 19.7 ms-1. If only 28% of speeds are at or below 19.7 ms-1 then the mean proportion of processable signals will be only 28%. Of course the beamwidth depends on the RCS of the target and thus it is necessary to do multiple calculations based on varied RCS values.

Wi is a function of RCS and IMR sensitivity as described by equations (3.17), (3.18) and (3.19). The computation of PPS for the Bourke IMR and various values of RCS is illustrated in Figure 3.11. For each RCS the proportion of processable signals at the lowest altitude is small and is largely determined by travel time effects. The processable proportion then increases with altitude as travel time effects become less severe, levels off, and eventually returns to zero when the altitude exceeds the maximum processable altitude r0 for that RCS as determined by equation (3.6). If travel time had no effect, all processable proportions would be unity for all altitudes below r0. But the travel time effect reduces the processable proportion, averaged over applicable altitude gates for RCS values of 10, 1, 0.5, 0.1, 0.05 and 0.01 cm2, to 0.88, 0.80, 0.74, 0.46, 0.29 and 0.05 respectively, assuming the processing algorithm is able to process the full beamwidth. If the algorithm can process only the offset beamwidth then the processable proportion is further reduced as shown in Figure 3.11 for an RCS of 0.5 cm2. The average processable proportions corresponding to the six RCS values above are now 0.82, 0.69, 0.49, 0.16, 0.07, and 0.00 respectively, roughly one-third less on average. The above levels for the full and offset beamwidths are in general agreement with the 0.39 observed for a total of

98 20,800 simulated signals based on typical echoes received by the Bourke IMR, see Section 4.8.1 in Chapter 4 for more details.

Figure 3.11: Stepwise computation of the processable proportion of signals for the Bourke IMR. There are eight gates at 150 m intervals. Each gate is 50 m in extent. The width of the scanned volume at each altitude gate is determined by the RCS and is divided into ten equal strips, each of which will allow a certain maximum speed corresponding to the minimum duration required of 0.8 seconds. If this speed is higher than the highest speed observed at Bourke, then all signals from that strip will be processable. That is, even the highest speed observed at Bourke will not exceed the capacity of the strip to process it. On the other hand, if the maximum allowable speed is only as high as the speed corresponding to, say, 25% or 50% of speeds, then on average only 25% or 50% of signals from that strip will be processable. Averaging the processable proportions across all strips then gives the processable proportion at each altitude gate shown for each RCS.

99 If the procedure illustrated in Figure 3.11 is run in reverse and applied to the recorded numbers of insects for each RCS, the result is an estimate of the insect numbers that would be recorded if travel time effects did not apply. When applied to the Bourke data shown earlier in Figure 3.2, the resulting estimates are as shown in Figure 3.12. As expected, differences are small for RCS values > 0.5 cm2, but become large or very large as RCS values fall below 0.5 cm2. At RCS values around 0.01 cm2 only 5% of the insects are being recorded, and this is just for altitudes below the applicable r0 (around 450-500 m) and for the good-quality echoes that make up the dataset. If all echoes (not just good- quality ones) for small insects are considered, plus the small insects that could be flying above 500 m but which the Bourke IMR cannot detect, the actual proportion of small insects being recorded could be considerably less.

Figure 3.12: Estimated numbers of insects obtained by taking the recorded numbers shown in Figure 3.2 (obtained at Bourke during the night of 14 March 1999) for each bracket of RCS values, and dividing by the average processable proportion calculated for that bracket as shown in Figure 3.11. The shaded bars correspond to the shaded parts of the distribution in Figure 3.2.

The limitations revealed by Figure 3.10, Figure 3.11, and Figure 3.12 are serious. The travel time effect causes massive reductions in the theoretical ability of IMRs to detect small insects, and even for large insects the reductions are appreciable. The effect is clearly visible in the Bourke IMR data plotted in

100 Figure 3.13, which shows for different RCS values how the number of processable echoes varies with increasing distance from the zenith and with insect speed. Most of the RCS values in Figure 3.13 are between 0.05 and 5 cm2 (Figure 3.2), which suggests (Figure 3.11 and Figure 3.12) that overall perhaps one half or more of the otherwise processable signals have escaped processing due to travel time effects. Furthermore, each cloud of data points in Figure 3.13 is concentrated below the maximum speed predicted by travel time effects. In principle plots like this could be used in reverse to calculate the effective beamwidth, that is, the beamwidth corrected for beam offset and for tolerance in the processing algorithm, except that this requires a very high level of measurement accuracy that will be unrealistic in the absence (as here) of actual field calibrations using targets of known RCS. Thus measurement error readily accounts for the small discrepancies seen in Figure 3.13 between observed and predicted maximum speeds, which are most noticeable at the lowest RCS values where the relative effect of measurement error is highest.

A reduced detection rate due to travel time effects will be serious for studies of height distributions, when corrections may be needed to avoid misleading results, but less so for pest monitoring, where numbers and directions are the most important results and nights of large-scale migration are very unlikely to escape detection. Errors in flight speed will affect the predicted landing area but this is already subject to uncertainty about flying time. Ways of reducing travel time effects are discussed in Section 3.6.3.

101

Figure 3.13: The effect of speed and distance from the beam axis on the number of processable echoes for a typical night of Bourke IMR data, in this case 14 March 1999. The altitude gate is 50 m wide centred on 375 m. The dotted lines show the maximum speeds calculated by the method outlined in Figure 3.11 for the indicated RCS. The plotted speeds are the observed speeds of individual insects, and their natural variability can occasionally push them past the nominal long-term maximum of 20 ms-1 as shown in Figure 3.10, which is based on nightly averages.

3.5 Calculated Performance of the Four Radars

The performances of the four radars, calculated from the relevant equations using the parameters given in Table 3.1, are shown in Table 3.2. Profiles of the calculated beam envelopes are shown in Figure 3.14. The results show that, as expected, the radars do differ in performance, but not dramatically so. In particular, as might be expected given their long pedigree, all three IMRs are clearly capable of characterising the spring moths and plague locusts (RCS typically 1-3 cm2) studied later in this work

102 Table 3.2: Maximum antenna gain equation (3.3), received power equation (3.1), efficiency equation (3.7), minimum signal power (3.8) and maximum altitude (3.6) for the four radars calculated via the indicated equations and the data of Table 3.1.

VLR Bourke Mobile Thargo.

Maximum gain (dB) g0 41.9 44.3 40.8 44.3 Received power for 2 p −78.1 −72.3 −80.8 −75.8 RCS = 1 cm at 500m (dBm) r

Efficiency ρa 0.692 0.858 0.868 0.858

Minimum signal power (dBm) Smin −84.7 −71.7 −82.7 −82.7

Max altitude (m) ) full beam r0 1448 954 1138 1466 2 for RCS = 0.1cm ) offset beam r0 1420 922 1121 1416

Max altitude (m) ) full beam r0 2575 1696 2024 2608 2 for RCS = 1 cm ) offset beam r0 2524 1638 1993 2519 dB = 10 log10 (gain). dBm = 10 log10 (power in mW), so 0 dBm = 1 mW.

103

Figure 3.14: Beam envelopes of the VLR, Bourke, mobile and Thargomindah IMRs showing their full beamwidth. The reduced (offset) beamwidths are not shown. Vertical axis shows height in metres, horizontal axis shows width in metres (exaggerated about fifteen times for clarity), and shaded area shows the beam envelopes for insects of RCS 0.01 cm2 (smallest volume), 0.1, 1, and 3 cm2 (largest volume). The last two are typical of spring moths and plague locusts. Shaded bands indicate altitude gates (layers processed by the radar).

104 3.6 Designing IMRs With a Specified Performance

An IMR must be able to detect specific targets up to their expected maximum altitude, and for long enough that statistically significant numbers can be obtained. On the other hand, at each gate, the volume scanned must not be so large that more than one insect is detected at a time, as this results in unprocessable overlapping signals. Therefore an important preliminary step in the design process is to establish the number, size, and altitude of insects that the IMR is required to detect, to which their distribution in space is immediately relevant. (The parameters that could be varied operationally such as range gate width and antenna diameter are considered later in Section 3.6.2 onwards.) The mechanisms by which flying insects could be concentrated by the wind or by temperature inversions have received some study, e.g. by Farrow (1990) and Pedgley (1990), but not their general distribution in space. The following section attempts to fill the gap.

3.6.1 Distribution of Insects in the Air The distribution of insects on the ground is the subject of a large literature. We might reasonably expect that the processes associated with living and breeding would make such distributions non-random. Nevertheless randomness is often taken as a starting point, for which the Poisson distribution is the appropriate model (Krebs, 1989) since it describes the distribution of random events in time or space, and conversely the number of times a random event occurs in a given interval of time or space. For example, over a range of densities from 15 to 140 grasshoppers per square metre, which represents an average distance apart of respectively 26 cm and 9 cm, the proportion of 0.05-m2 samples (defined by a wire ring positioned at random in the vegetation in advance of counting) containing 0, 1, 2, 3… grasshoppers conformed to a Poisson distribution (Onsager, 1991; Legg et al., 1995). In a Poisson distribution the probability P(r) of exactly r occurrences is given by P( r) = e−µ µ r /! r (3.20) 105 where = mean number of occurrences per occasion, formally given by = Np where N = number of occasions and p = probability of occurrence. In many cases it may be impossible to define N and p realistically, for example where p = probability of a football team scoring a goal, but their product Np = (here the average goals/match) can be well defined. The variance of occurrences that conform to a Poisson distribution is equal to their mean, . The mean will depend on the sampling interval, but there are no universal guidelines to say what that interval should be if there is a choice (Krebs, 1989); essentially it can be whatever gives workable results, determined if necessary by pilot trials.

The spacing of discrete objects and events in time or space generally conform to one of three spatial patterns, namely random, aggregated (also called clumpy, lumpy, patchy or clustered), and uniform, as shown in Figure 3.15. Aggregated patterns can come in many varieties, for example small clusters widely spaced, or large clusters randomly spaced with individuals either randomly distributed or uniformly distributed within each cluster. Many tests of patterns are available, e.g. Simpson et al., 1960; Green, 1979; Krebs, 1989; Richter & Sondgerath, 1990.

Figure 3.15: Three possible types of spatial patters. Adapted from Krebs (1989).

106

Poisson distributions tend to apply when insect densities on the ground are low, indicating that the insect spacing tends to be random. But at high densities the spacing usually becomes more aggregated and departs from a Poisson distribution, that is, the variance now exceeds the mean (Taylor, 1961). Conversely, if the spacing becomes more uniform, the variance falls below the mean. For example, if the three boxes shown in Figure 3.15 are each divided into 36 equal areas by a grid 4 wide and 9 tall, and the dots are counted in each area, the values of variance/mean are 1.0 for random, 1.7 for aggregated, and 0.5 for uniform. At high densities the variance can be related to the mean by variance = mean + mean2/k, where k is a constant (Shepard & Carner, 1976) widely used as an index of clustering despite being dependent on sample size (Richter & Sondgerath, 1990). This dependence means that if the sample is very large and contains very many clusters then the property bestowed by clustering will tend to be lost (Richter & Sondgerath, 1990).

Another widely used expression is variance = a x meanb, where a and b are constants (Taylor, 1961; Taylor, 1984). Values of b = 1, b > 1, or b < 1 indicate that the spacing between individuals tends to be random, aggregated, or uniform respectively. If expressed in the form log (variance) = log a + b log (mean), a and b can be obtained by linear regression. Thus analysis by linear regression of 156 sets of field data covering 102 species including shellfish, insects, fish, birds, animals, and people in US populations gave a mean b of 1.45 SD 0.39 (Taylor, 1978). In general, spacing was random only at low densities, and only 2 of the 102 species were spaced randomly at all densities. For the others the value of variance/mean changed with population density. However, the behaviour at high densities was species-specific and not predictable by extrapolation from lower densities, which led Taylor (1978) to conclude that the spacing between individuals was density-dependent and reflected a fundamental life process.

107 In a later study Taylor (1982) found similar results for 97 species of aphids, 263 species of moths, and 84 species of birds, all sampled throughout Great Britain in the 1960s and 1970s. The mean b values for the distribution in time were 1.99, 1.55, and 1.30 respectively, and for the distributions in space they were 2.14, 2.24, and 1.79. The results were based on trap counts for aphids and moths, and census counts for birds made by observers. No studies addressed the distribution of insects flying in the air.

So how might flying insects be distributed in the air? The variation with altitude and time is usually observed as part of most radar studies, e.g. Drake and Farrow (1983), but it has proved difficult to find attempts to evaluate the fine- scale distribution of flying insects even though this would seem to be an evaluation uniquely suited to radar methods. One attempt was reported by Drake (1981) who filmed the echoes shown on the PPI display (see Figure 1.7 in Chapter 1 for an example) of a scanning pencil-beam radar over a series of 25-minute sequences in northern NSW 300 km southeast of Bourke in March 1979. The beam rotated twenty times a minute at an elevation of 8º, and the PPI display for each rotation (i.e. 3 seconds worth) was captured on sequential frames of 16-mm cine film. The display was divided into sectors in widely separated locations around the PPI that allowed the number of echoes visible in a given sector to be counted on each frame at 10-frame intervals, i.e. every 30 seconds, analogous to the grid used to count the distributions shown in Figure 3.15. (The separation of sectors in space and time was to avoid the counts of one sector being contaminated later by the counts of another.) Only one sequence showed a level of insect activity that was sufficiently constant during 25 minutes, but the counts showed an excellent fit to a Poisson distribution, see Figure 3.16. The insects were not precisely identified but were thought to be probably grasshoppers.

108

Figure 3.16: Distribution of insect numbers observed by a scanning pencil-beam radar in 51 filmed PPI displays 30 seconds apart during 25 minutes in northern NSW on 5 March 1979. Beam elevation 8º, height interval 129-193 m. Total insect counts are 256 (average 5.02) for the 30-degree PPI sector (left) and 102 (average 2.02) for the 10-degree PPI sector (right). In each case the observed frequencies are not significantly different from those expected if the insects were spaced at random, i.e. as predicted by a Poisson distribution. Thus a chi-squared test gives P = 0.97 df = 6 (left) and P = 0.74 df = 4 (right). Results are from Drake (1981) replotted to match the format used later in Figures 3.18 and 3.19.

The average insect density during the above observations can be estimated from the volume scanned during one rotation, which was about 60 x 106 m3 for insects with an RCS similar to that for locusts (Drake, 1981), or 5 x 106 m3 for the 30-degree sector, and is thus about 0.1 per 100,000 m3, which is low when compared with the numbers during peak migration periods.

To explore in more detail the distribution of insects in the air we therefore need some idea of the maximum density of flying insects. Reported maximum numbers of insects per 100,000 m3 are 200-480 for aphids, 3-120 for moths, 1- 150 for grasshoppers, and 100-5000 for desert locusts, the latter having reached an estimated 1,500,000 in a swarm close to the ground (Rainey, 1989; Farrow, 1990; Pedgley, 1990; Gatehouse, 1997). In a November 1979 scanning radar study of plague locusts 300 km southeast of Bourke, Drake & Farrow (1983) observed maximum densities of 1-37 per 100,000 m3 that peaked around 225 m once the locusts had reached their cruising altitude. Much higher densities were observed immediately after takeoff when the insects were still close to the 109 ground, the density reaching 600 per 100,000 m3 in one instance at an altitude of 50-75 m (Drake & Farrow, 1983). The agreement between observed densities vs. those predicted from local measurements of locust density on the ground varied from good to fifty times lower, the discrepancy being attributed to errors in estimating (1) locust density on the ground over wide areas, and (2) the proportion of locusts taking off (estimates were 5-20%). Higher maximum densities, say 100 or more per 100,000 m3, comparable with the above data for moths and grasshoppers, would seem likely during the usual January-February peak in plague locust activity.

If the flying insects are assumed to be evenly spaced 90º from each other at the corners of a cube, the above ranges translate into mean distances apart of 6-8 m, 10-30 m, 9-45 m, and 3-10 m respectively, and 14-45 m for plague locusts (or 10-45 m using the above higher estimate). If the insects are assumed to be evenly spaced 60º from each other at the corners of a tetrahedron, which uses space more efficiently than a cube thus allowing a greater distance apart for the same density, the mean distances apart are roughly doubled. (Let one insect in 1000 m3 = one insect at the corner of a cube of side x. Solving for x, we get x3 (volume of cube) = 1000 m3, so x = 10 m. Alternatively, let one insect in 1000 m3 = one insect at the corner of a tetrahedron of side y. Solving for y, we get y3(√2)/12 (volume of tetrahedron) = 1000 m3, so y = 20.4 m.)

How do the above ranges compare with those observed in the present work? At 225 m the Bourke radar beam is about 10 m wide, so the gate has a side area of about 10 x 50 = 500 m2. (For the present purpose the difference between full beamwidth and offset beamwidth shown in Figure 3.4 is of little importance, as is the effect of RCS on beamwidth, so both can be ignored.) At the mean observed groundspeed at Bourke of 12 ms–1 (see Section 7.4.3 in Chapter 7), the gate will sample a volume of about 500 x 12 x 3600 = 21,600,000 m3 every hour, which at a density of, say, 100 insects per 100,000 m3 will deliver 21,600 insects per hour or 6 per second, well beyond the gate's maximum processing 110 capacity of 1 per 0.8 second. Therefore insects at such densities could not be processed without loss, a point already addressed under speed and travel time effects in Section 3.4.3. Where the beamwidth increases with increasing altitude, so will the volume sampled, thus making the problem worse at the same density. For example at 625 m the width of the Bourke radar beam is roughly twice that at 225 m, so under the above conditions a 625 m gate would be receiving about 12 insects per second.

The above finding can be checked by referring to the total targets recorded for each night at Bourke during 1998-2001 as shown in Figures 5.19-5.22 in Chapter 5. During this period there are 26 occasions when the raw totals per night (not the totals that were successfully processed, which were typically about one-third of the raw total) exceeded 30,000; unfortunately these individual peaks are not discernible in Figures 5.19-5.22 due to the use of a moving average. On such nights the maximum number of insects per unit gate- volume was usually observed at the lowest gate (225 m) covering the 200-250 m range in altitude, whereas the maximum number of insects was usually observed at higher gates with their larger beamwidths. On such nights the maximum hourly count at the 225 m gate (corrected for time not spent on counting targets) was around 2500, which in a volume of 21,600,000 m3 = 6 insects per 100,000 m3, well below the above (nominal) 100, which confirms that insects at such densities could not be processed without loss.

Nevertheless, even at 100 insects per 100,000 m3, the mean distance between insects is still around 10 m, which at 1 insect per 100,000 m3 increases to around 45 m. Compared with the mean distances of 0.1-1 m between migrating locusts on the ground (see Sections 1.5.5 and 1.6.1), such densities would certainly qualify as ‘low’, i.e. they are densities at which the Poisson distribution would most likely apply. Furthermore, insects flying at night will have reduced visual cues to their position within the swarm, and will be subject to wind gusts and air turbulence causing random variations in individual 111 orientation (clearly visible in Figure 1.11 and in the results of Section 4.8.3), speed (visible in the results of Section 7.5.2), and direction (visible in the results of Section 7.5.3). Further randomising influences will arise from differences in size and species. Gatehouse (1997) argues that it is difficult to see how cohesion among night-flying insects could be possible, and that a degree of dispersal must therefore attend all their migrations. He cites three radar studies of migration that suggest decreases in airborne density of around 20-50% per 100 km, depending on local conditions.

It therefore seems likely that within a single IMR gate the arrival of an insect will be an event whose occurrence will be described by the Poisson distribution. That is, we can realistically calculate the mean arrivals in unit time, but we cannot say anything about the probability of an arrival at a particular moment or the number of such moments. The Poisson distribution will clearly not apply to periods in which there are substantial non-random changes in density, as would occur for example at the edge of a swarm or (typically) over several hours during the course of a night. However, our immediate interest is in the distribution of insects when such conditions are absent.

Data suitable for testing the fit of IMR observations to a Poisson distribution are provided by Deveson et al. (2005), who present plots of the insect numbers recorded during consecutive 7.5-minute periods by the Bourke IMR on 15 November 1999 and 3 December 1999. On each night the insect numbers over seven consecutive hours (18h through 00h on 15 November 1999 and 22h through 04h on 3 December 1999) for gates 200-350 m, 350-500 m, and 500- 650 m were extracted from enlargements of their plots. Each hour provided five 7.5-minute periods with insect numbers (the remaining time was devoted to other measurements) giving a total of 210 periods for the two nights. The insect numbers for the 200-350 m gate on 15 November 1999, for example, which recorded the highest counts, are shown in Figure 3.17. (The combined insect numbers are analysed later in Figure 3.18.) 112

Figure 3.17: Example of insect numbers for the Bourke IMR from Deveson et al. (2005)

The above 7-hourly periods were chosen because the insect numbers recorded during each 7.5 minutes were fairly uniform and free of large increases or decreases. Nevertheless, of the six sets of insect numbers (2 nights x 3 gates), four show a decreasing trend over the seven hours and two show an increasing trend, although none of the trends are significant. Furthermore, the gaps in the data as illustrated in Figure 3.17 introduce uncertainty, so it might be unrealistic to expect a perfect fit to a Poisson distribution. On the other hand, the mean number of insects recorded in 7.5 minutes corresponds to about 2 insects per 100,000 m3 and an average distance apart of about 37 m, which suggests that a marked deviation from a Poisson distribution would indicate a hard-to-explain level of cohesion among these particular flying insects.

In fact, as shown in Figure 3.18, the fit to a Poisson distribution is very good. Left, the observed and expected frequency distributions of the quantity (number of insects in each 7.5 minutes)/50 truncated to an integer are not significantly different (by chi-squared test P = 0.74, df = 8). Here the x-axis values of 0, 1, 2, … 8 are equivalent to insect counts of 0-49, 50-99, 100-149, … 350+. The raw frequencies cannot be tested directly for their fit to a Poisson distribution because the degrees of freedom (given by maximum count – 1) are then too many to allow an effective test. So 50 is an arbitrary divisor equivalent to

113 grouping the data (or choosing a suitable grid size for the sparse data in Figure 3.15) that adjusts the degrees of freedom to allow the most effective test. As already noted (Krebs, 1989) there are no universal guidelines to say what the grouping should be if there is a choice, essentially it can be whatever gives workable results. Here the ratio Variance/mean = 0.96, close to the 1.00 expected for a Poisson distribution. Changing the arbitrary constant to values between 43 and 57 made no appreciable difference.

For Figure 3.18 right, the value of b in Taylor's (1961) expression variance = a x meanb is equal to the slope of log (variance) vs. log (mean), and is not significantly different from the value of b = 1 expected for a random distribution. However, there is a potential artifact in such a plot that reduces its value as an indicator of randomness. Given that insect numbers tend to decrease above a certain altitude, the values of log (mean) and log (variance) will also tend to decrease, which when plotted against each other will necessarily show a trend similar to that in Figure 3.18 (right) regardless of the underlying distribution of insects. This artifact will tend to intrude whenever the plot involves data from different altitudes, as is the case here. Consequently the comparison of observed and expected frequencies, as in Figure 3.18 (left), is the more reliable indicator of randomness. In this case the results indicate that the spacing between recorded insect arrivals at the Bourke IMR on these two nights was not significantly different from random, which compares well with the results of Drake (1981) shown earlier in Figure 3.16.

114

Figure 3.18: Source data are Bourke IMR insect numbers observed during 7.5-minute periods taken from the plotted results of Deveson et al. (2005). Total number of intervals = 210. Left: Observed and expected frequencies of the quantity (number of insects in each 7.5 minutes)/50 truncated to an integer. For example insect numbers of 20 and 220 are counted as 0 and 4 respectively. Right: Regression of log (variance) against log (mean) for the original data, i.e., number of insects in each 7.5 minutes not converted to an integer.

Checking this finding with Bourke IMR data from the present work proved to be less than straightforward. Extracting insect numbers over the short time intervals needed for a Poisson test required further data processing, which was time consuming. Nights meeting the requirements of sufficient insect numbers, sufficient periods without longer-term changes in numbers, and freedom from equipment breakdown, were not easy to locate, especially as these qualities were not reliably predicted by an examination of the existing nightly counts. The need for uniformity in insect numbers over the observation period has been stressed by Drake (1981) following his Poisson tests using a scanning radar, who concluded that observations where these conditions are not met "would undoubtedly have deviated from the Poisson form".

The effect of failure to meet the above requirements is illustrated by the insect numbers recorded by the Bourke IMR on the night of 14 March 1999 during a peak in the abundance of plague locusts in which a total of 19,442 insects were processed. At the 225-m gate insect numbers were high during 18-19h and 01- 02 h, and low at other times. At the 375-m gate more than one-third of the observations were lost due to equipment failure. In contrast, the insect numbers

115 at the 525-m and 675-m gates tended to be high and uniform. In other words this night conveniently provides two sets of data for testing conformity to a Poisson distribution, the one from the 225-m and 375-m gates being clearly unsuitable, and the other from the 525-m and 675-m gates being more suitable.

Poisson plots for the 225-m and 375-m gates combined, and for the 525-m and 675-m gates combined, for consecutive 5-minute periods (excluding time devoted to other measurements) during the ten hours between 18h and 03h (a total of up to 80 periods per gate) are shown in Figure 3.19. The arbitrary constant used to produce the 0-8 range in counts was 15 and 13 respectively. The unsuitable data (left) shows a poor fit to the Poisson distribution, despite which the observed and expected plots are still largely symmetrical, which suggests that Poisson may still be a useful first approximation. The more suitable data (right) shows a much better fit (P = 0.09 df = 8, or P = 0.31 df = 6 when the extreme cell pairs are collapsed to keep expectancies above 5). The value of variance/mean = 1.02, close to the 1.00 expected for a Poisson distribution. In both cases the insect density was roughly half that observed by Deveson et al (2005) as plotted in Figure 3.17.

Figure 3.19: Source data are Bourke IMR insect numbers observed during successive 5-minute periods on the night of 14 March 1999. Left: observed and expected frequencies for gates 225 m and 375 m combined (= data unsuitable for the purpose). Right: Same for gates 525 m and 675 m combined (= data that is more suitable).

116 The good fit to a Poisson distribution shown in Figure 3.18 (left) and Figure 3.19 (right) confirms the observations of Drake (1981) shown in Figure 3.16, and would seem to merit further study of the distribution of insects in the air using IMRs capable of recording targets over short time intervals without processing losses. It would also seem to justify the following new approach to assessing processability:

If flying insects are distributed in accordance with a Poisson distribution, the probability P of observing 0 or 1 insect (i.e. not more than one insect) in t seconds will be 1 e−µ µ r P =∑ =exp()() −µ µ + 1 where = 1/t (3.21) r=0 r! (Cox & Lewis, 1966), which gives the following outcomes: t 1 2 3 4 5 6 8 10 P 0.736 0.910 0.955 0.974 0.982 0.988 0.993 0.995

(Note that, although t is measured in seconds, it is actually a measure of insect density. That is, , the mean number of insects per interval, is defined as 1/t, so as t increases the number decreases and the probability of observing not more than one insect increases, rather than decreases as might appear at first sight.)

In other words, if at a single gate we want to observe not more than one insect during t seconds for 95.5% or 97.4% of the time, the mean interval between insects needs to be not less than three or four times the minimum processable interval. Thus if the minimum processable interval is 0.8 seconds, the mean interval between insects needs to be not less than 2.4 or 3.2 seconds at the maximum travel speed. (In practice this means the maximum processable travel speed, as explained previously in Section 3.4.3.) As already noted, the above interval of 2.4-3.2 seconds is much longer than the interval between insects arriving at peak periods, which suggests that insect numbers should not be ignored in the preliminary steps of IMR design.

117 If excessive insect numbers are likely, they can be avoided simply by reducing the vertical gate width. The gate heights themselves are determined by the altitudes of interest. For example, if the insects being studied tended to migrate mostly at the top of a temperature inversion, the gates could be narrower and occupy a smaller range of heights. If few of the insects fly at high altitudes, for example at Bourke fewer than 5% fly above 1,000 m, then high-altitude gates could be dispensed with. Essentially the choice of gate height and vertical width is an empirical matter best decided by trial and error in the field.

3.6.2 Maximum Altitude Insect size (i.e. RCS) and maximum altitude are mutually co-determined in a way that is easily seen by rearranging equations (3.3), (3.6) and (3.7) to give πp λ2 σ r 4 = t (3.22) 0 θ 4 2 64 3dBLS S min which indicates the relative effect that each parameter will have on r0. Thus 4 increasing r0 by a factor of 1.5 corresponds to multiplying pt by 1.5 = 5, θ3dB 2 4 by 1/1.5 = 0.67, LS by 1/1.5 = 0.44, Smin by 1/1.5 = 0.20, or (less obviously) In by 4 (the last three as power, not dB). At first sight a small reduction in θ3dB seems to be a better option for increasing maximum altitude than a large increase in transmitted power. But a reduction in θ3dB requires a proportionate increase in antenna diameter, which may cost more than the cost of increased power (see below).

If sensitivity is crucial, are there ways of increasing it other than via transmitted power and antenna diameter? In principle reducing the radar losses in equation (3.6), increasing the bandwidth in equation (3.8), and reducing the noise in equation (3.8), can increase sensitivity. But the former requires changes to the waveguide that at best allow only marginal improvements, while the latter are inherent properties of the transceiver and cannot easily be changed. Similarly, as explained in Section 1.4.2, changes to λ may not be legal or may require equipment that is commercially unavailable or unaffordable. 118 3.6.3 Beamwidth The relationship with beamwidth, and with the associated travel time effects, is especially important and can be explored by expressing beamwidth in terms of simple geometry as =θ ≈ θ θ θ beamwidth 2rr tan 2 rr ( in radians, error < 0.04% for < 2º) (3.23) where rr = altitude and θ = distance from beam axis. θ is given by equation (3.17), which results in

( 4θ 4 2 )() π λ2 σ  ln rr 64 3 dB L S S min pt  beamwidth= 2r θ (3.24) r3 dB −8ln 2

ln (ξr 4 θ 4 σ ) = 2rθ r3 dB (3.25) r3 dB −8ln 2 ξ 2 π λ 2 where is a constant = 64LS Smin pt

Thus once the radar equipment has been chosen, the relation between maximum altitude, width and RCS is completely determined. One can be varied independently of the others only by changing the equipment. However, equation (3.25) does not give an easily-grasped picture of how width might be varied. One can see that the attainable width increases with RCS and attainable height, but only in a general way, and only for a given radar.

Some idea of the interdependencies can be obtained by keeping θ3dB constant, and then increasing r0 (by whatever means) by factor f. This increases the maximum width by factor f and increases its altitude by factor f, but superimposing the two envelopes shows that the effect at any given altitude is not nearly as simple. In terms of the mean maximum altitude of the two envelopes, the proportionate increase in width changes progressively from almost zero at the lowest altitude to f around halfway, then continues to increase until curtailed at the top of the envelope. In other words the increase is greatest at higher altitudes where (as shown in Figure 3.10) extra width may not

119 be needed, and least at lower altitudes where extra width may be most needed.

If extra width is needed at lower altitudes, then increasing r0 is not an effective approach.

However, as might be expected, an effective way to increase width at the lower altitudes is to increase θ3dB according to equation (3.24), which also reduces r0 according to equation (3.6). (Increasing θ3dB is effectively the same as decreasing antenna diameter in the same proportion.) At first sight this might seem to be an unnecessary complication. In fact the outcomes become remarkably simple if, on changing θ3dB or antenna diameter, the transmitted power is adjusted to prevent the change in r0 indicated by equation (3.24). Under such conditions a decrease in antenna diameter produces a proportional increase in beamwidth that is the same for all values of RCS and for all altitudes within the envelope. For example, if such manipulations are applied to the mobile IMR (that is, if all equipment parameters are left unchanged except antenna diameter and transmitted power), and we need to detect RCS = 0.1 cm2 at an altitude of 1000 m (which means that to leave room for an altitude gate we adjust antenna diameter and transmitted power to give r0 = 1100 m at RCS = 0.1 cm2), the outcomes are as shown in Figure 3.20. A decrease in antenna diameter requires a large increase in transmitted power to compensate, roughly 4 in proportion to 1/Da , but achieves a dramatic increase in the processable proportion of received signals. As shown in the next subsection, the cost differences on either side are roughly similar and therefore tend to cancel out.

120

Figure 3.20: Effect of varying antenna diameter and transmitted power to give 2 r0 = 1100 m for RCS = 0.1 cm . Left: envelopes calculated by equation (3.25) for antenna diameters of 1.8 and 1.0 m, and transmitter powers of 4 kW and 42 kW. Right: corresponding changes in the processable proportion of received signals. The lower plots show how the same equipment performs when RCS = 0.01 cm2.

Figure 3.20 suggests that, in principle, the tailoring of envelopes to particular requirements should be a simple matter, but in practice the options are limited by the commercial availability of suitable equipment. Furthermore, it would clearly not be worth increasing the radar’s sensitivity if it were required only for detecting large insects. Indeed, it would be advantageous to reduce the sensitivity so that small insects would tend to be ignored. In other words the challenge of radar design lies with the smallest insects and their travel speeds. The above approach allows useful simplifications, but for a precise assessment there may be no reasonable alternative to carrying out the various calculations, including the calculation of processable proportions, and then systematically varying the parameters, or at least varying them as much as the availability of affordable commercial equipment will allow.

121 3.6.4 Antenna Size vs. Transmitter Power Section 2.8.3 in Chapter 2 showed how the two most expensive electronic components were the transceiver and antenna. If sensitivity needs to be increased then increasing antenna size is roughly twice as expensive as increasing transmitter power. For example, costs in Australian dollars in 2001 for a 1.8-m antenna and 25-kW transceiver were about $9,400 and $11,500 respectively. Reducing the antenna size to 1.2 m would have saved $4,900, whereas doubling the transceiver power would have cost about the same. Figure 3.21 shows the relationship between maximum altitude and the combined cost of antenna and transmitter for RCS values of 0.64 cm2 (corresponding approximately to the dip between the two peaks in Figure 3.2) and 0.0064 cm2. In each case the smaller antenna with the largest transceiver achieves much the same maximum altitude as the larger antenna with the smallest transceiver, but at considerably less cost, and as a bonus the beam is generally about 50% wider.

122

Figure 3.21: The combined cost of antenna and transceiver vs. maximum altitude for two different RCS values. In each case (from left to right) the three joined data points are for transmitted powers of 6, 12 and 25 kW.

If transmitted power is kept constant at 25 kW, Figure 3.22 shows how the Gaussian envelope for RCS = 0.64 cm2 varies with antenna diameters of 0.6 - 1.8 m. With a diameter of 0.6 m the maximum altitude is severely reduced but the beamwidth is dramatically increased. The largest scanned volume is for a diameter of 1.2 m but, as will by now be apparent, volume alone is not necessarily a good indication of the processable proportion.

Figure 3.22: Gaussian envelopes for a 25-kW transmitter, RCS = 0.64 cm2, and four antenna diameters.

123 3.7 Calculating IMR Signal Components

This and the next section summarise the work of others (Smith et al 1993, Drake et al 2002, and Harman & Drake 2004) and are included only to provide the equations and background information relevant to the other sections in this chapter.

The components of the IMR signal were explained in the various parts of Section 3.2. The present section looks at how they are calculated for the purpose of processing. The form of the signal produced by an insect passing through an IMR beam was first published by Smith et al. (1993). As shown by equation (3.1), the received power is a function of the range, the RCS, the antenna gain, and the wavelength and power of the transmitted signal. The logarithmic form of equation (3.1) is ( ) = ( ) +( ) +(λ) +( σ ) − 10log10 pr 10log10 pt 20log10 g 20log10 10log10 − π − 30log10 ( 4) 40log10 (rr ) (3.26) The situation with an IMR is, however, more complicated due to the offset rotating beam. When an IMR echo is expressed in logarithmic terms, the total received signal (prL) is given by = + + + + prL S c S r S t Sσ Sw (dBm). (3.27) where Sc is the radar sensitivity defined as shown below, and Sr, St, Sσ and Sw are the range, trajectory, RCS and wingbeat modulation terms respectively, the ( ) ( ) (σ ) first three terms are analogous to the 40log10 rr , 20log10 g , 10log10 terms in equation (3.26).

3.7.1 Range Term

The altitude or range term (Sr) defines the radar sensitivity in terms of the signal received from a target at altitude h = 1000 m. = −  ( ) − ( ) Sr 40log 10 h log10 1000  (dB). (3.28)

124 3.7.2 Trajectory Term

The trajectory term (St) combines the modulations due to distance from the beam axis and to beam offset. It relates the distance of the target from the centre of the beam (rt) to the power received, allowing for the Gaussian nature of the antenna gain r 2 S= −10log ( e ) k t (dB) (3.29) t 10 θ 2 ()3dBh

2 where k = 8ln2, e = 2.7183 and rt is given by

2 = −2 + − 2 rt( X I X C) ( Y I Y C ) (3.30) where XI and YI are the x- and y-components of the insect’s position and XC and

YC are the x- and y-components of the beam axis, as shown in Figure 3.23. If the path of an insect through the IMR beam is straight, at constant speed (v), direction (γ), and body alignment (β); if its distance of closest approach to the zenith (p) occurs at time (τ), on the χ side of the beam (right is +1, left is –1); and if the IMR beam centre (C) orbits about the zenith O with constant offset (∆ in m for the given altitude) and speed (Ω in rad/s), the distance of the insect from the centre of the beam at instantaneous time t is given by:

2 =[ γ + − τ γ ][] − ∆ Ω2 + rt { psin0 v ( t )sin sin t } [ γ+ − τ γ ][] − ∆ Ω 2 { pcos0 v ( t )cos cos t } (3.31)

= ∆++2p 2 [ v( t −τ )]2 +[ 2 χp ∆Ω−− sin( t γ )] [ 2( v t −∆ τ )cos( Ω− t γ )] (3.32)

where γ0 is the direction from the zenith to the insect when the latter is at its point of closest approach (modulo of γ − χ 90° + 360°, 360°). Combining equation (3.32) with equation (3.29) gives: = − × St 10log( e ) k

∆++2 2 [][ −τ2 + χ ∆Ω−−γ][ −∆ τ Ω− γ ] p v( t ) 2p sin( t ) 2( v t )cos(t ) (3.33) ()θ 2 3dBh

125 rt

Y

X

Figure 3.23: Components of the flight of an insect (I) with constant speed V and body alignment β through the IMR beam centred at C orbiting around O resulting in a signal of the form given by equation (3.36). Adapted from Smith et al. (1993).

3.7.3 RCS Term

The RCS term (Sσ) relates the polarisation pattern of the insect with orientation β to the orbital position of the beam centre (Ωt) = +( Ω −β ) +( Ω − β ) Sσ 10log a0 a 2 cos 2 t a4 cos 4 t  (3.34) where a0, a2 and a4 are RCS constants determined by the size and shape of the 2 2 insect. a0 is the average RCS cm value in general use. a2 and a4, also in cm , describe how the reflected signal varies according to the angle between the insect and plane of polarisation. These terms are detailed in the next Chapter.

3.7.4 Wingbeat Term

If the modulation in the time-averaged RCS (a0) due to wingbeating has magnitude µ at time t, then SW (Drake et al., 2002) is given by: = [µ ] SW 10log (t ) . (3.35) 126 3.7.5 Calculated Total Re-radiated Signal We now have everything needed to evaluate equation (3.27) except a particular value for Sc. Taking the Bourke IMR as our example, we revisit Section 3.2.2 and obtain Sc = −59 dBm. Evaluating Sr, St, Sσ and Sw by equations (3.28), (3.33), (3.34) and (3.35) respectively, equation (3.27) now becomes = − + − ()() −  − × prL 59{ 40log h log1000} 10log()e k

∆++−2p 2 [][ v( t τ )2 + 2 χ p ∆Ω−− sin( tγ )][ 2( v t −∆ τ )cos( Ω−t γ )] + θ 2 ()3dBh +µ ( )   +( Ω −β ) +( Ω − β ) 10log 1 t   a0 a 2 cos 2 t a4 cos 4 t  . (3.36)

This is consistent with the result given in Smith et al. (1993), which differs only in having an opposite sign for Ωt due to their radar beam rotating in the opposite direction to that shown in Figure 3.23.

3.8 Processing of IMR Signals

The processing of IMR signals has been described in detail by Harman & Drake (2004). What follows is a simplified description necessary only to understand the points raised at various times in the present work concerning the processing of IMR signals.

The reflected radar signals are processed in three stages to extract the insect’s characteristics. (1) From the continuous data signals, extract those individual signals whose amplitude is greater than the preset limit as detailed in Table 3.1 using a C++ program running on a Pentium 3-800 computer. (2) Transfer the extracted signals to a SUN Ultra 10 UNIX server, 440 MHz, 384MB RAM, running Solaris 7. (3) Process the extracted signals using the algorithm described below.

The algorithm in step (3) was originally developed and written in C++ by I.T. Harman for a single platform. It was later re-written in MATLAB by 127 V.A. Drake to enable a more thorough analysis but needed three separate processing steps (the first step in C++). For details see Harman & Drake (2004). Processing using either algorithm is slow. For example processing the Bourke data for 1998-2001 took several months of computer time. Details of processing speeds are given at the end of this section.

To simplify the explanation, the following example measures the echo intensity of 8 evenly-spaced angles with a beam rotation rate of 5 Hz, giving a sample rate of 40 Hz, whereas in reality 64 evenly-spaced angles are measured at 5 Hz giving a sampling rate of 320 Hz. The example signal is shown in Figure 3.24 below. The radar sensitivity (Sc) is a constant value and the range term (Sr, equation (3.28)) depends on altitude, which leaves only the trajectory term (St, equation (3.33)) and RCS term (Sσ, equation (3.34)) to be determined.

Figure 3.24: Theoretical signal based on echo intensity measured at 8, rather than 64, evenly-spaced angles. Note the under-sampling (hence loss of detail) when compared with the signal measured at 64 evenly-spaced angles in Figure 3.3.

The first step of the algorithm is to fit a parabola to the echo power of each successive scan at each of the angles around the beam as shown in Figure 3.25. Each parabola is thus freed from the fluctuations due to the rotating offset beam.

128

Figure 3.25: The signal amplitudes between 1 and 2 seconds overlain with parabolas fitted to the amplitudes measured at angles 0, 90, 180 and 270° around the beam. For clarity the parabolas at angles 45, 135, 225 and 315° are omitted.

The slower the insect the longer the time spent near the centre of the beam and the flatter the parabola. Hence we can calculate the velocity of the insect from the beamwidth and the time2 term of the parabolic fit.

The maximum amplitude occurs when the insect is closest to the beam centre, so if we plot the times of the maxima for each of the (in this case) eight angles against the angles, then by fitting a sine/cosine curve as show in Figure 3.26, we can estimate the time and distance of closest approach and the direction.

Fitted equation: Time = 1.5 + 0.15 cos(angle) – 0.01 sin (angle) Time(s)

Figure 3.26: The sin/cosine curve fitted to the times of closest approach estimated from each of the eight fitted parabolas. Each point represents the maximum amplitude calculated from the fitted parabola for each angle around the beam.

Once the speed, direction, and time and distance of closest approach are known, the trajectory term (St, equation (3.33)) can be calculated and removed from the signal, leaving only the RCS term (Sσ, equation (3.34)). The individual RCS variables are extracted from the RCS term using the normal least-squares matrix-inversion method (Drake, 2002).

129 The slowest step in this processing procedure was the MATLAB processing which ran at a speed of about 56 signals/minute (3,360 signals/hour), so a heavy night’s data of about 20,000 signals took about 6 hours to process. Delimiting the signals ran at about 550 signals/minute or about 37 minutes for 20,000 signals. Transfer using the FTP program (WS-FTP 4.5, John A. Junod, Ipswitch Software, USA) ran at about 286 signals/minute or about 70 minutes for 20,000 signals. The total processing time was therefore nearly 8 hours, or about 75% of the time taken to acquire the data (about 11 hours).

The overall processing rate for the MATLAB algorithm was therefore about 43 signals/minute. In contrast the C++ algorithm ran at about 133 signals/minute on a 486DX2-66, or three times faster, making it more suitable for processing the multiple-year datasets used in Chapters 4-7.

130 4 INSECT RADAR CROSS SECTION

This chapter deals with the properties of insect RCS and their shape variations with polarisation of the IMR beam. It is divided into the development of theory and the analysis of radar data. Parts of this chapter are expanded from Dean & Drake (2005) Monitoring insect migration with radar and its potential for target identification.

Insects reflect a rotating IMR beam with an intensity dependent on their RCS and flight path through the beam. After subtraction of the flight-path component, the reflected signal traces the instantaneous RCS values in a pattern (called the Copolar-Linear Polarisation Pattern or CLPP) that can be fitted to an equation derived from radar theory. The processing algorithm extracts three fitted constants (a0, a2, a4) and two fitted angles (θ2, θ4) that together describe the insect's CLPP. The characteristics of the CLPPs and their relationship to the five fitted variables are explored using published laboratory data and selected nights of IMR data. Broad discrimination between insect masses seems possible based on average RCS values but not between insect species, a point further explored in the next chapter. Neither the retrieval algorithm nor body shape asymmetry (for example due to rolling in flight) appears to introduce any systematic bias. The main original contributions to the present chapter are the explorations of: the properties and limitations of CLPPs, their relationship to the five fitted variables, the accuracy of the retrieved five fitted variables, and the relationships between an insect's size, shape, and average RCS values.

4.1 Introduction

In an Insect Monitoring Radar or IMR the beam direction is vertical and the reflected signal is received at the same polarisation angle used for transmission. The effective area of the target that reflects the radar signal is called the Radar Cross Section or RCS, and is usually greatest when the plane of polarisation coincides with the insect’s body axis. If the insect’s flight path is level and unbanked, the beam sees only the insect’s underside, so there are no changes in aspect (such as those that occur for scanning radars) to complicate matters. The beamwidth is very small, around one degree, so the target’s aspect will be effectively independent of the target’s horizontal position within the beam.

The RCS of an insect crossing the beam will therefore depend only on its orientation to the (rotating) plane of polarisation. The reflected signal will depend on the RCS and how close the insect’s flight path is to the centre of the beam. Once the flight path has been determined, as described in Chapter 3, its contribution to the reflected signal can be subtracted, leaving the variation of

131 RCS due to beam rotation. The beam rotates five times a second, so the insect is usually within the beam for several full rotations, each of them providing a pattern of flight-path-corrected reflections that can be averaged to improve the accuracy of the retrieved result.

When the observed instantaneous RCS is plotted against the polarisation angle (the angle between the insect’s body axis and the plane of polarisation) the result is a distinctive RCS pattern called the Copolar-Linear Polarisation Pattern or CLPP, that conforms to the pattern predicted by radar theory, see Figure 4.1. Processing consists of fitting the theoretical equation to the observed pattern.

Figure 4.1: How the CLPP is formed. Left: The rotating vertical radar beam of an IMR impinges on an insect flying overhead. In this case the insect’s body axis is momentarily aligned with the plane of polarisation. Right: The insect reflects the radar beam with an intensity dependent on (1) its RCS and distance from the radar, (2) its distance from the centre of the beam and (3) the polarisation angle, here 0º. The instantaneous RCS plotted against the polarisation angle is the CLPP, bottom right.

132 4.2 Radar Cross Section, Target Size, and Wavelength

A target exposed to electromagnetic energy scatters the energy in all directions. Since the IMR transmitter and receiver use the same antenna, the only scattering direction of interest is back to the IMR. The intensity of the energy scattered back to the source of the wave, referred to as backscattering, is described by the RCS (σ) of the object. Skolnik (2002) defines the RCS of a target as "the (fictional) area intercepting that amount of power which, when scattered equally in all directions, produces an echo at the radar equal to that from the target", which he also defines formally (Skolnik, 1990) as

E 2 σ= lim 4 π R2 s (4.1) R→∞ 2 E0 where E0 is the electric field strength of the transmitted wave at the target at range R and ES is the electric field strength of the reflected wave at the radar.

In practice the target is usually sufficiently distant for the reflected signal ES to vary inversely with the distance R, which means that the R2 term in the numerator is cancelled by an implicit R2 term in the denominator. Consequently the dependence of RCS on R disappears along with the need to calculate a limit. So RCS is more usually expressed in terms of incident and reflected power, and is thus independent of the actual power.

RCS has the dimension length2 and is thus an area. In non-insect work the RCS values are typically expressed in m2, the SI unit of area, but in insect work the RCS values are usually expressed in cm2 due to the small sizes involved, typically 0.01-10 cm2. In the present work the species of interest (plague locusts and spring moths) have RCS values that are typically 1-3 cm2.

Roffey (1972) noted that an insect’s RCS could be modelled as an equivalent volume of water that was elongated, and whose ability to reflect the radar beam

133 depended as usual on its size with respect to the radar wavelength. As the size of the target increases from small to large relative to the wavelength, three regions of response can be identified. According to Trebits (1989), the approximate limits of these three regions for a water sphere of radius r measured at wavelength λ are: Rayleigh region λ> 2 π r (4.2) Resonance region 2πr≥ λ ≥ 2 π r 10 (4.3) Optical region λ< 2 π r 10 (4.4)

Radius is an awkward measure to apply to insects, so in radar entomology RCS measurements are usually referred not to radius but to insect mass. Figure 4.2 shows the calculated RCS for λ = 3.2 cm and water spheres of masses between 10-3 and 104 g, superimposed on the three regions detailed above. The masses of the larger insects that are detected by the IMRs, and the masses of the laboratory-measured insects analysed in Section 4.7, are on or close to the border between the Rayleigh and Resonance regions.

134

Figure 4.2: Calculated RCS (cm2) of a water sphere vs. mass (g) at a wavelength of 3.2 cm. The gradient in the Rayleigh region is about three times steeper than the gradient in the other regions, with a crossover point at a mass of roughly 0.1 g. Beyond the Rayleigh region the curve exhibits undulations due to the varying interaction between the specular reflections and the creeping wave (Skolnik, 1990).

4.3 Insect Copolar-Linear Polarisation Patterns

However, a water sphere would not react to the changes in polarisation angle that are an essential feature of IMRs. Thus if a water sphere were to pass over an IMR, the returned signal would be the same for all polarisation angles, and the CLPP would be a circle. In contrast, for more complex targets such as insects (which are also generally less than a wavelength long), reflectivity can be considerably more complicated as waves are reflected or ‘scattered’ with polarisation components cross-polarised to the illumination direction. The multiple polarisation properties of a target can be fully described by the scattering matrix S (e.g. Huynen, 1965; Kell & Ross, 1970)

135  σ σ eiα  S = eiφ  XX XY  (4.5)  σiα' σ i β   YXe YY e  where X denotes polarisation in the X direction, Y denotes polarisation at right angles to X, σ is the RCS of the relevant element, and α, α’, β and φ are phase angles. The four components of the matrix represent the transformation of the transmitted polarised components of the signal into the equivalent received components (Huynen, 1965).

According to Aldhous (1989), see also Hobbs & Aldhous (2006), the RCS of an insect is given by

σ = * 2 hr.S h t . (4.6) where ht and hr are the transmitting and receiving polarisations, respectively. For linearly polarised radars with the plane of linear polarisation at angle φ to the insect’s body axis cosφ  ==   hh rt   . (4.7)  sinφ  An insect seen from below is generally symmetrical about its body axis (Lawrence et al., 1991). Baker et al. (1984) filmed from below swarms of Locusta migratoria flying at heights mostly between 3 and 10 m. Of several hundred individuals, each observed in 10-20 consecutive frames, less than 1% had noticeably curved abdomens. For a symmetrical insect the XY and YX σiα = σ iα ' components of the scattering matrix S are equal, that is, XY eYX e . Substituting this equality into equation (4.5) and the combined result into equation (4.6), gives the following expression for σ( φ ) , the RCS at polarisation angle φ (Aldhous, 1989)

2  σ σ iα  φ XX XY e cos  σ( φ )= [ cos φ , sin φ]     (4.8) σiα σ i β sinφ  XYe YY e   

136 2 = σ2 φ+ σiβ 2 φ+ σiα φ φ XX cos YY e sin 2XY e cos sin (4.9) += φ + φ + φ + φ aa 110 a12 a21 a22 4sin4cos2sin2cos (4.10) where: =σ + σ + σ + σ σ β a0 (1/ 8)(3XX 3 YY 4 XY 2XX YY cos ) (4.11) =σ − σ a11 (1/ 2)(XX YY ) (4.12) = σ σ α+ σ α − β a12 XY( XX cosYY cos( )) (4.13)

=σ + σ − σ − σ σ β a21 (1/ 8)( XX YY4 XY 2XX YY cos ) (4.14) a = (1/ 2) σ( σcos α− σ cos( α − β )) . (4.15) 22 XY XX YY

Which in turn can be rewritten as σ φ = ±φ − θ ± φ − θ ()a0 a 2 cos2(2 )a 4 cos4(4 ) . (4.16) where:

=2 + 2 a2 a 11 a 12 (4.17)

=2 + 2 a4 a 21 a 22 (4.18)

θ = −1 2 (1/2)tan (a12 / a 11 ) (4.19) θ = −1 4 (1/4)tan (a22 / a 21 ) (4.20) where a0 is the mean RCS, a2 and a4 are fitted constants, and θ2 and θ4 are fitted angles. The nature of these fitted variables is discussed later.

Equation (4.16) is the starting point for the analyses that follow. Negative values of a2 and a4 were ignored by Aldhous (1989) and Hobbs & Aldhous (2006) but are included in the current analysis as discussed in Section 4.5. Note that in place of the a0, a2, a4, φ, θ2, θ4 symbols used here, Aldhous (1989) and

Hobbs & Aldhous (2006) use a0, a1, a2, θ, θ1, θ2 respectively.

The CLPPs produced by various combinations of the fitted terms in equation (4.16) are illustrated in Figure 4.3. However, the relationship between equation 137 (4.16) and the CLPP forms actually observed is not as straightforward as the few examples of Figure 4.3 might suggest, since there are various constraints imposed by radar theory that are not immediately apparent in equation (4.16). These constraints are discussed in the next section.

Figure 4.3: CLPPs for various simple combinations of the fitted terms. The fitted values were chosen to emphasis their effects. For intermediate values between a2 = 0 to a2 = 1, the CLPP changes smoothly between the CLPPs shown.

138 4.4 Constraints on Observable CLPP Forms

There are two constraints imposed by radar theory that limit the CLPP forms that can be observed. The first constraint applies to symmetric CLPPs (i.e. where θ2 = θ4), the second constraint applies to asymmetric CLPPs (i.e. where

θ2 ≠ θ4). The first constraint can be derived as follows.

For backscattering from a mirror-symmetric target, S has the simple form

 σ 0  S =  XX  . (4.21)  iβ   0 σYY e  When combined with plane-polarised radiation, this form leads to a simplification of equation (4.16), namely σ φ = ±φ − θ ± φ − θ ()a0 a 2 cos2( )a4 cos4( ) (4.22) where θ = θ2 = θ4. The constraint arises because of the way a0, a2 and a4 are constrained in the expression for the phase angle β, whose cosine is given by (Dean & Drake, 2005) a− 3 a cos β = 0 4 . (4.23) 2− 2 + 2 + a0 a 2 a 42 a 0 a 4 The cosine can have values only in the range –1 to +1, at which extremes ()−2 =2 − 2 + 2 + a03 a 4 a 0 a 2 a 42 a 0 a 4 . (4.24) Rearranging gives = ±() − a2 8 a4 a 0 a 4 (4.25) and, via the usual solution for quadratic equations,

a± a2 − a 2 2 a = 0 0 2 . (4.26) 4 2

Equations (4.25) and (4.26) constrain the maximum values that either a2/a0 or a4/a0 can assume, given the other. In particular, the observed values of a2 and a4 are constrained to the following limits. = = maximuma2 2 a 0 at a4 a 0 2 (4.27) 139 = − minimuma2 2 a0 (4.28) = maximum a4 a 0 (4.29)

a− a2 − a 2 2 maximum a = 0 0 2 for 0

a+ a2 − a 2 2 maximum a = 0 0 2 for 0.5a< a < a (4.31) 4 2 0 4 0 = minimuma4 0 . (4.32)

The above constraints are those that apply via equation (4.22), which requires that θ2 = θ4, therefore the constraints apply only to symmetric CLPPs. However, the retrieval process is based not on equation (4.22) but on equation (4.16), which does not automatically exclude asymmetric CLPPs and will therefore accept θ2 ≠ θ4. This leads to the second (and weaker) of the two constraints, which can be derived as follows:

The RCS is an area, and negative areas cannot exist. Therefore the RCS given by equation (4.16) has to be positive at all polarisation angles. However, certain combinations of the variables in equation (4.16) can give negative RCS values even though they are still mathematically acceptable. For example, values of a0 = 1, a2 = −1, and a4 = −0.5 could theoretically give a maximum

RCS (given by a0 + a2 + a4 as shown in Figure 4.3) of –0.5, which is negative and therefore cannot be observed in practice. A procedure based directly on the scattering matrix (Hobbs & Aldous 2006) eliminates these non-physical combinations and may be preferable for future work.

The boundary conditions that equation (4.16) must satisfy in order to give positive values of σ( φ ) for all values of the polarisation angle φ can be obtained by solving ±φ − θ ± φ − θ = a0 a 2 cos2(2 )a 4 cos4(4 ) 0 (4.33)

140 for all possible combinations of a0, a2, a4 θ2 and θ4. Which of these variables could have an effect on boundary conditions? Inspection of equation (4.33) indicates that, when θ2 = θ4, changes to θ2 merely rotate the CLPP pattern as shown in Figure 4.3 without effect on the boundary conditions. Changing the sign in front of the a2 and a4 terms is equivalent to a change in the corresponding cosine terms of 90˚ or 45˚ respectively, which is equivalent to a change in θ2 which again has no effect on the boundary conditions. The variables that could have an effect are thus reduced to θ4 − θ2 and the three a terms, or two a terms when expressed as a2/a0 and a4/a0.

The above complexity can be further untangled by comparing equations (4.25) and (4.33). The boundary conditions imposed by equation (4.25), which apply only when θ2 = θ4, and by equation (4.33), which apply generally, are sometimes equal and sometimes overlapping, as shown in Figure 4.4 and Figure

4.5. For example, equation (4.33) allows a0 = 1, a2 = 1, and a4 = 0, but these values when inserted into equation (4.25) give cos(β ) = 1 0 , which of course cannot be evaluated. Equation (4.33) also allows a0 = 1, a2 = 1, and a4 = 0.1, but in equation (4.25) they give cos(β ) = 0.7 0.03 = 4 , which again cannot be evaluated. In other words neither case is allowed by equation (4.25).

Figure 4.4 and Figure 4.5 show that the constraint imposed by equation (4.33), and therefore its overlap with equation (4.25), depends on θ4 − θ2. So the constraint that applies under any given combination of variables will be either equation (4.25) or equation (4.33), depending on target symmetry. In short, as shown by these Figures, only certain combinations of a2/a0 and a4/a0 can be observed, and the observable combinations depend on θ4 − θ2.

141

Figure 4.4: Boundary conditions according to equations (4.25) and (4.33) for a2/a0 and a4/a0 when θ4 − θ2 = 0, together with the corresponding form of the CLPP and the boundary between two-lobed and four-lobed CLPP forms given by a4 = a2/4. The area containing two-lobed CLPP forms is shown shaded. Above a4/a0 = 1/3 (i.e. the two points where the corresponding values of a2/a0 are ± 4/3) the boundaries imposed by equations (4.25) and (4.33) are identical, but below these two points they are notably different. In particular the values of a2/a0 that are allowed by equation (4.33) (i.e. the straight lines) are not allowed by equation (4.25) (i.e. the curved lines) below a4/a0 = 0 because symmetric forms with negative values of a4/a0 are not observable. Hence equation (4.25) imposes a more severe constraint. To save space the equations shown assume a0 = 1. If a0 ≠ 1 then all instances of a2 and a4 in the equations should be replaced by a2/a0 and a4/a0 respectively. Thus the equation top right would become 2 a4/a0 = 0.5 + X, and X would become X = (√(1– (a2/a0) /2))/2.

142

Figure 4.5: Boundary conditions for a2/a0 and a4/a0 for particular values of θ4 − θ2. The equations describe the boundaries shown by the dotted lines. The shaded part (top) is repeated middle and bottom to help comparison. The boundary conditions imposed by equation (4.33) become inverted at intervals of θ4 − θ2 = 45º, and thus repeat at intervals of θ4 − θ2 = 90º. At intermediate values of θ4 − θ2 the boundary conditions fall between these two extremes, reaching a symmetrical shape at intervals of

θ4 − θ2 = 22.5º; here there is no simple equation as in the other cases, and the equation shown has been fitted to the boundary using the form specified by equation (4.33).

The adherence of insect CLPPs to the constraints for symmetric targets, i.e. where θ1 = θ2, is verified in Figure 4.6 for the laboratory data of Aldhous 143 (1989) and Wolf et al. (1993), and in Figure 4.7 for data from the Bourke IMR. None of the points in Figure 4.6 and very few of the points in Figure 4.7 fall beyond the constraint of equation (4.33) shown by the dashed lines; those that do can be explained by imperfections in the processed signal as illustrated in Section 4.8.1. The fit to this constraint is thus very good. Rather more points in both Figures fall beyond the constraint of equation (4.25) shown by the solid curves, perhaps too many to be plausibly explained by imperfections in the processed signal alone, so at least some of them are probably due to the effects of θ4 − θ2, i.e. to instances where the insect as seen by the radar from below is not symmetrical, as for example where the insect is banking or subject to turbulence. The effects of θ4 − θ2 are detailed in Section 4.6.2.

Figure 4.6: Observed values of a2/a0 vs. a4/a0 for laboratory data.

Figure 4.7: Observed values of a2/a0 vs. a4/a0 for the Bourke IMR. Left: good-quality echoes during the night of 14 March 1999, mainly plague locusts. Right: good-quality echoes during the night of 8 September 1999, mainly spring moths. 144 4.5 Ambiguity in Derived CLPP Parameter Values

The presence of the two fitted angles in equation (4.16) introduces ambiguity into the derived CLPP parameter values. Inspection of equation (4.16) shows that changing the sign of the a2 or a4 terms has the same effect as incrementing

θ2 or θ4 by multiples of 90˚ or 45˚ respectively, see Figure 4.8. Aldhous (1989) avoided this ambiguity by restraining the values of a2 and a4 to be ≥ 0 (i.e. the

+/+ quadrant of Figure 4.8) through appropriate changes to the values of θ2 and/or θ4. This restriction of a2 and a4 values may, however, reduce the ability to distinguish between insect species simply because different species that might otherwise plot in different quadrants will be overlain when moved to the +/+ quadrant.

Figure 4.8: Examples of how CLPPs with negative values of a2 or a4 are shifted by changing θ2 and θ4 but without changing the CLPP's shape. This moves the CLPP from its original quadrant to the top-right (+/+) quadrant.

145 4.6 Theoretical Properties of CLPPs

The previous sections have shown how the observed CLPPs can be broadly described according to radar theory by equation (4.16) and the fitted terms a0, a2, a4, θ2 and θ4. The present section examines the theoretical properties of CLPPs in more detail, starting with a look at the effect of signal imperfections. Subsequent sections extend the findings with empirical measurements using laboratory and field data, in preparation for attempts in the next chapter to characterise insects by their CLPPs.

4.6.1 Effect of Signal Imperfections Equation (4.16) is derived from radar theory to describe the variation of RCS with polarisation angle. Within the constraints discussed in the previous section, we therefore expect IMR observations to accurately fit the shapes allowed by the equation (as opposed to seeing the equation as merely one way of fitting a shape to the observations). And indeed the observed CLPPs for good-quality echoes do fit the equation very well, see Figure 4.9. The CLPPs in Figure 4.9 show two main lobes, and (in three of the four examples) two smaller lobes at right angles. The number of lobes is discussed later in Section 4.6.3.

Imperfections in the calculated flight-path component due to equipment noise, to interference from a nearby target, or to fluctuations associated with any statistical curve fitting, lead to imperfections in the remaining signal used to calculate the RCS. So the occasional small deviations evident in Figure 4.9 from a perfect fit could have many causes and do not necessarily imply that equation (4.16) is incorrect. A shape can be fitted even if some angular measurements are missing, for example due to the reflected signal strength being too low, and in normal practice the observations are rejected on sampling grounds only if more than half of the 64 sampling points are excluded.

146

Figure 4.9: Examples of the fit between observed CLPPs for good-quality echoes and equation (4.16). The points are the averaged RCS values measured by the IMR at the 64 sampling angles per antenna rotation. Each smooth shape represents the equation that best fits the points, calculated using a least-squares method. In each case the major axis of the CLPP is aligned with the body axis of the insect. a0 is the mean RCS. The difference |θ4 − θ2| is a measure of asymmetry and is explained in Section 4.6.2. The insects were flying at altitudes of (clockwise from top left) 375, 525, 625 and 675 m. The four shapes may seem to differ more than the similarities in their asymmetries might suggest, but the analysis shows otherwise. Observations made at Bourke on 14 March 1999. Further examples can be found in Dean & Drake (2005).

4.6.2 Asymmetric CLPPs and θ4 – θ2

The CLPP is symmetric whenever θ4 – θ2 = 0, which indicates that the insect (as seen by the radar from below) is symmetric about its body axis. Inspection of equation (4.16) shows that this applies for all values of θ2, so |θ4 – θ2| is essentially a detector of, and a measure of, asymmetry in the insect. However, although equation (4.16) determines the CLPP’s shape, the cos2 and cos4 terms

147 of equation (4.16) prevent it from differentiating between opposite directions on the insect’s body axis. So only the alignment (not direction) of the body axis can be retrieved, which means that the head-tail orientation of the insect remains ambiguous. Fortunately the ambiguity can usually be easily resolved by considering wind direction, assuming that insects tend to fly with the wind rather than against it (see Section 1.5.5 in Chapter 1).

By the same token, only bilateral (left-right) asymmetry will be detectable in the CLPP. Such asymmetry can arise either because the insect’s anatomy is not perfectly symmetric, or because the insect is banking or rolling, perhaps as the result of turbulence. In such cases |θ4 – θ2| will be a measure of the insect’s asymmetry. Results presented later in Sections 4.7.4 (laboratory data) and 4.8.4

(IMR data) indicate that asymmetry is generally negligible (|θ4 – θ2| < 3˚) for all but the largest insects (> 650 mg), although it can exceed 10˚ for insects > 1000 mg. The occurrence of asymmetric CLPP forms is investigated using laboratory data in Section 4.7.4 and IMR data in Section 4.8.4.

Non-zero values of θ4 – θ2 distort the CLPP into asymmetry. The distortions produced by various combinations of θ2 and θ4 are shown in Figure 4.10 for a CLPP typical of those observed by the Bourke IMR. The diagonal line indicates θ4 = θ2, so the forms on this line are symmetric. Away from the diagonal, the forms become increasingly distorted up to |θ4 – θ2| = 45º, after which the distortion decreases until the original undistorted form is reached at

|θ4 – θ2| = 90º. As shown earlier in Figure 4.3, changes in θ2 (where θ2 = θ4) merely rotate the form by the same amount.

148

Figure 4.10: CLPP forms vs. θ2 and θ4. The original form is for a2/a0 = 0.75 and a4/a0 = 0.17 and is shown at the centre of the plot. All forms are aligned with the horizontal (θ2) axis. Symmetric forms (i.e. where θ4 − θ2 = 0) lie on the diagonal line and are rotated by changes in θ2, whereas changing θ2 (at constant θ4) changes the shape as well. Forms that lie outside the limits of |θ4 − θ2| = ±45º are identical to a form within the limits and are retrieved by the algorithm as such. For example each vertical set of three forms within ±45º is duplicated by the set immediately above or below.

4.6.3 Number of CLPP Lobes

If the insect is symmetric, i.e. θ4 – θ2 = 0, equation (4.16) can be written as σ φ = ±φ − θ ± φ − θ ()a0 a 2 cos2( )a4 cos4( ) (4.34) where θ = θ2 = θ4. Here the form of the CLPP (as opposed to its size and orientation) depends only on a2 and a4. As noted by Aldhous (1989) and shown in Figure 4.4, the patterns can have either two lobes (i.e. one pair of maxima and one pair of minima) or four lobes (i.e. two pairs of each). Differentiating equation (4.34) with respect to φ gives

dσ( φ )  a  = −8a sin 2()φ − θ 2 ±cos 2()φ − θ (4.35) φ 4   d  4a4 

149 which is zero at each stationary point, i.e. at maxima and minima. It is evident that such points occur whenever one of the following two conditions applies: − sin 2(φ− θ ) = 0 i.e. at φ− θ =0,90 ° ,180 ° or90 ° , giving two maxima

and minima and thus two lobes. a − 2 = ±cos 2(φ − θ ) . (4.36) 4a4 The cos term cannot exceed ±1, so the expression has a solution only when a 2 ≤1 (Aldhous, 1989). (4.37) 4a4

≥ That is, if a4 a 2 4 , there will be a second set of four minima and maxima and ≥ thus two lobes in addition to the existing two lobes, but only if a4 0 . If < a4 0 there will still be a second set of lobes, but this time they distort the existing two-lobe pattern into a butterfly shape as shown in the lower part of Figure 4.4. However, as shown previously in Section 4.4, there are constraints < that do not allow symmetric CLPPs with a4 0 to be observed in practice. Therefore in general terms with respect to the shape of the CLPP:

− a2 = 0 and a4 = 0 produce a circle of radius a0.

− a2 > 0 distorts the circle into a two-lobe dumb-bell shape.

− Increasing a2/a0 makes the dumb-bell shape more pronounced. − ≥ a4 a 2 4 adds two smaller lobes at a polarisation angle of 90˚ to that of the main lobes.

− Increasing a4/a0 makes the smaller lobes larger.

150 4.7 Analysis of Laboratory-Measured Insect CLPPs

The measurements used in this Section, here termed ‘laboratory data’, were made at a wavelength of 3.2 cm and are taken from Aldhous (1989) and Wolf et al. (1993). The data are listed in the Appendix. The measurements made by Aldhous (1989) for one of two specimens of Tipula oleracea give a slightly negative minimum RCS, which by definition is not observable and is therefore probably due to measurement or rounding errors. (This specimen is #2 in the 2 Appendix, Table 4, for which measured a0 = 0.18 cm , a2 = 0.23, a4 = 0.049, so minimum RCS = a0 − a2 + a4 = −0.001.) This specimen has therefore been excluded from my analysis. Altogether the analysis is of 68 insects from 23 species in order to identify trends across species. (See next chapter for the analysis of differences between species.)

Notable at the heavy end of the laboratory data are 11 specimens of the desert locust Schistocerca gregaria, the world's largest locust, which is described in Sections 1.5.3-1.5.5 of Chapter 1. The 11 specimens are so large (masses range from 1,084 mg to 3,094 mg) that there is no overlap with the rest of the data in physical measures or radar properties. (In the rest of the data, 60% of the individuals are C. brunneus, N. pronuba or A. urticae, with the rest being spread over 19 species.) As we shall see, this separates desert locusts from the other insects in every analysis of the laboratory data, often raising problems of interpretation. But first a brief look at early studies of insect RCS.

4.7.1 Early Studies of Insect RCS Since the 1970s there have been several major experimental studies of insect RCS, most of them confined to a limited number of species (Russell & Wilson, 1997). Early studies measured insect RCS from the sides (measurements made with the E field of the beam orientated parallel and/or perpendicular to the insect’s body) and the end (measurements made with the E field of the beam orientated perpendicular to the insect’s body) because these were the aspects viewed by the near-horizontal beam of the scanning radars used in early studies,

151 see Figure 4.11 (left). Ten individuals of different species were measured in this way by Hajovsky et al. (1966), and a further two species by Richter & Jensen (1973).

Later, the angular variation of the RCS about a vertical axis was measured for five individuals from three species by Riley (1973) and for a further six species by Schaefer (1976). Recent studies (Riley, 1985; Aldhous, 1989; Wolf et al., 1993) have measured the insect’s RCS from below as in vertically pointing IMR beams, see Figure 4.11 (right). Their measurements were made at different polarisation angles to fully utilise the IMR’s rotating polarisation. Unfortunately Riley (1985) gives his RCS measurements as five small graphs so his data could not be included in my analyses.

Scanning Radar IMR

Figure 4.11: Differing radar views of an insect as seen by the near-horizontal beam of a scanning radar (left) and the vertical beam of an IMR (right).

Most studies have used anaesthetised (usually by CO2) or freshly killed insects to avoid the rapid loss of body moisture following death, which can greatly affect the observed RCS (Hajovsky et al., 1966). In an alternative approach, Richter & Jensen (1973) attached live unanaesthetised insects to a tethered balloon by a small piece of thread that allowed them to fly. Radar wavelengths used were typically 3.2 cm, as in most entomological radars, and antennas were typically oriented vertically to reduce the effects of extraneous reflections.

152 4.7.2 Insect Characteristics vs. Average RCS for Laboratory Data

The average RCS values (a0) for the laboratory data are plotted against mass in Figure 4.12 together with the RCS of a water sphere as shown previously in Figure 4.2. Although there is a broad correspondence, most of the insects have RCS values larger than that of a water sphere, often several times larger, especially for large insects where there is no tendency for the insect’s RCS to follow the first dip in the Resonance Region. The RCS ratio insect/water for the same mass is plotted against insect width/length in Figure 4.14. As width/length increases, i.e. as the insect becomes more circular, there is a clear tendency for the RCS ratio insect/water to decrease, which suggests (as expected) that elongated insects are better reflectors of radar waves than circular ones of the same mass.

Figure 4.12: Top: The average RCS (a0) and mass for the laboratory data compared with the RCS of a water sphere from Figure 4.2. Most of the insects have an RCS that exceeds that of a water sphere, often by several times, especially for large masses.

153

Figure 4.13: The RCS ratio insect/water for the same mass (see Figure 4.12) vs. insect width/length. As expected, the range of width/length values for insects > 1000 mg is much less than for insects < 1000 mg, probably partly because the former are for just one species (S. gregaria).

Despite the scatter shown in Figure 4.12, several studies have suggested that an insect’s mass can be roughly estimated from its RCS, e.g. Riley (1973, 1985, 1992), Riley et al. (2003), Russell & Wilson, (1997). Within the limits of 2 σXX > 0.0032 and a0 < 0.25 cm , Chapman et al. (2002) suggest the relation = 2 5 2 a0 6.4 m 10 (cm ) (4.38) where m is the insect's mass in mg. Here the predicted a0 varies as the square 2 of the insect's mass. At their limit of a0 = 0.25 cm the value of m is 62 mg, only 4 insects of the laboratory and field insects analysed here have masses below this limit (see Table 5.1 in the next chapter). Indeed, for most of the Rayleigh Region of Figure 4.2, the slope of log(RCS of water sphere) vs. log(mass of water sphere) is a uniform 2.0, indicating that in this region RCS varies as the square of the water sphere's mass; which might seem to provide support for equation (4.38). However, around the boundary with the Resonance Region, in the range of insect masses for the laboratory data (see also Figure 4.12), the slope is no longer uniform, suggesting unpredictable departures from the above relationship. Another way of approaching the problem is as follows:

154

It is easy to show that the volume of a sphere is proportional to area3/2 regardless of whether the area is cross sectional area or surface area. The volume of a cylinder with a constant width/length ratio is also proportional to area3/2 (ignoring the end areas), again regardless of whether the area is cross sectional area or surface area. Only if the cylinder length is constant is the volume proportional to area2 (ignoring the end areas). However, for the laboratory data neither length nor width/length ratio is constant (see Figure 4.15 and Figure 4.16 respectively), and width/length shows only a modest correlation with length (r = –0.57 across all 68 points, falling to –0.28 (P = 0.035) when masses >1000 mg are excluded), indicating that the specimens tend to get proportionately thinner as length increases. Computer simulation with and without end areas, using typical ranges of length and width/length, showed that the proportionality power was much closer to 3/2 than to 2, values being typically in the range 1.47-1.62 with a mean of 1.55.

In other words, if an insect's mass across all species was proportional to volume, if its RCS was proportional to body area, and if radar waves were perfectly reflected by body area independent of wavelength, all of which may or may not be a reasonable first approximation, we would expect a0 to vary as mass3/2 and not as mass2 as suggested by equation (4.38).

However, this prediction is not supported by the laboratory data, which shows 3/2 2 no clear tendency for a0 to vary either as mass or as mass , the relationship being more linear, see Figure 4.14. The correlation between a0 and mass is a −34 3/2 respectable r = 0.95 (P < 10 ) for a0 and 0.90 for a0 across all masses −13 3/2 (N = 68), falling to r = 0.81 (P < 10 ) for both a0 and a0 when the 11 masses > 1000 mg are excluded. About two-thirds of masses > 1000 mg vary 3/2 3/2 according to a0 , but the remaining third (excluded when fitting the a0 plot) vary equally well according to a0. As previously noted, masses > 1000 mg consist of just one species (desert locusts), whereas masses < 1000 mg consist 155 of 22 species, a difference that confounds any comparison of the two mass ranges and makes any interpretation uncertain.

There is a general tendency for mass to increase as a0 increases, but the scatter 3/2 is too great (and the sample size too small) to distinguish between a0 and a0

(or any other power of a0) as the best generalised estimator of mass. The deficiencies of r = 0.81 as an accurate predictor become apparent when the scatter is examined for masses < 400 mg, i.e. for masses typical of those observed in the study area (see Table 5.1 in Chapter 5). Thus in broad terms 2 the masses in Figure 4.14 are about 100 mg for a0 values < 1.2 cm , 200 mg for 2 2 a0 values around 1.5 cm , and 300 mg for a0 values around 2 cm , but a finer and more reliable discrimination would not seem attainable via a0 alone.

Figure 4.14: Mass vs. RCS (a0) for the laboratory data measured using a radar wavelength of 3.2 cm. There are no masses between 650 mg and 1080 mg, leading to a gap in the plotted data; for convenience masses above or below this gap are termed > 1000 mg, representing just one species (desert locusts), and < 1000 mg, representing 22 species, respectively. Left: all masses, N = 68. Right: enlargement of the plot for masses < 1000 mg, N = 57. Data are taken from Aldhous (1989) and Wolf et al. (1993).

How well does a0 reflect insect characteristics other than mass, such as width and length? The relationship between insect mass and body length for the laboratory data is shown in Figure 4.15, and is far from uniform. As expected, length increases generally with mass, but there is considerable scatter. There is 156 also (in these data) an absence of insect lengths between 30 mm and 45 mm, which introduces a gap in the plotted points and makes it unclear whether lengths above or below the gap follow separate linear trends or follow the same (curvilinear) trend. The linear correlation between length and mass is 0.78 before the gap (masses < 650 mg) and 0.94 after the gap (masses > 1080 mg).

Figure 4.15: Insect body length vs. mass for the laboratory data. The data do not include insects with lengths between 30 and 45 mm.

Much the same trends and gaps appear in the plots of width vs. mass, width/length vs. mass and volume vs. mass (here volume = π x (width/2)2 x length), again with considerable scatter, see Figure 4.16. The correlations between RCS parameters and insect characteristics for the laboratory data are summarised in Table 4.1.

157

Figure 4.16: Insect width, width/length, and volume vs. mass for the laboratory data. The insect widths show a minor gap between 2 and 3 mm but are otherwise fairly uniformly distributed, so the gap in width/length and volume is mostly due to the gap in insect length as shown Figure 4.15. Volume = π x (width/2)2 x length.

158 Table 4.1: RCS parameters vs. insect characteristics for the laboratory data. The division of masses into < 1000 mg and > 1000 mg reflects their distribution as shown in Figure 4.14. Volume = π x (width/2)2 x length. Insect width varies only slightly within the > 1000 mg group, so the correlations with width and width/length are not meaningful. Asterisks indicate the correlations that are strong, significant and consistent across masses < 1000 mg and > 1000 mg.

Observed correlation r for insect masses of Comparison < 1000 mg N = 57 > 1000 mg N = 11 all masses N = 68 **mass vs. length 0.78 0.94 0.94 **mass vs. width 0.84 0.84 0.46 mass vs. width/length 0.18 0.36 −0.44 **mass vs. volume 0.92 0.90 0.86

**a0 vs. a2 0.60 0.86 0.87

*a0 vs. a4 0.77 0.68 0.86

**a2 vs. a4 0.68 0.93 0.91

a2 / a0 vs. a4 / a0 0.33 0.57 0.39

**a0 vs. mass 0.81 0.89 0.95

**a0 vs. length 0.81 0.88 0.89

**a0 vs. width 0.72 0.83 0.47

a0 vs. width/length 0.06 0.40 −0.41

**a0 vs. volume 0.76 0.89 0.85

a2 vs. mass 0.12 0.91 0.80

**a2 vs. length 0.16 0.84 0.70

a2 vs. width 0.42 0.70 0.28

a2 vs. width/length −0.27 0.23 −0.40

a2 vs. volume 0.01 0.78 0.62

**a4 vs. mass 0.57 0.73 0.85

*a4 vs. length 0.61 0.60 0.80

a4 vs. width 0.35 0.46 0.38

a4 vs. width/length −0.17 0.08 −0.43

a4 vs. volume 0.40 0.56 0.71

a2 / a0 vs. mass −0.72 −0.56 −0.45

a2 / a0 vs. length −0.39 −0.44 −0.49

a2 / a0 vs. width −0.76 −0.32 −0.73

a2 / a0 vs. width/length −0.48 −0.02 −0.14

a2 / a0 vs. volume −0.82 −0.38 −0.71

a4 / a0 vs. mass 0.11 −0.22 −0.15

a4 / a0 vs. length 0.19 −0.39 −0.10

a4 / a0 vs. width −0.10 −0.45 −0.16

a4 / a0 vs. width/length −0.33 −0.37 −0.18

a4 / a0 vs. volume −0.09 −0.40 −0.21 ** Correlations have P < 0.01 and are consistent across N = 57 and N = 11. * Correlations have P < 0.05 and are consistent across N = 57 and N = 11.

159 In Table 4.1, the insect characteristics mass, length, width and volume cohere strongly among themselves but less well with width/length. The parameters a0, a2 and a4 also cohere strongly among themselves. Of the correlations for a0, those vs. mass, length or volume are consistently strong, typically 0.8 or more, and vs. width are almost as strong. The strong correlations vs. volume are perhaps surprising given that volume depends on the two quantities width2 and length and will therefore be sensitive to measurement errors in both, and of course to differences between the actual insect volume and the cylindrical 2 volume represented by π x (width/2) x length. The correlations between a0 and width/length are weak and erratic, which is disappointing given that width/length or squatness would seem to be a distinctive attribute of insects, but is perhaps unsurprising given that, in dimensional terms, width/length effectively cancels out the very area that a0 is representing. The correlations with a2 and a4 are discussed in the next section.

4.7.3 Insect Characteristics vs. a2 and a4 for Laboratory Data Hitherto no studies have looked in detail at the relationship between insect characteristics and the fitted variables a2 and a4. Figure 4.4 in Section 4.4 illustrates how positive values of a2 elongate the CLPP while positive values of a4 add a secondary small elongation at right angles, which suggests that a2 and a4 might show stronger correlations with width and length than a0 does. In fact the opposite is the case. As shown in Table 4.1, a0 generally shows the strongest and most consistent correlations with mass, length and volume (r’s

0.8 to 0.9), a2 shows the weakest and most erratic correlations (r’s 0.0 to 0.8), while a4 shows moderate correlations (r’s 0.4 to 0.7).

If a2/a0 and a4/a0 are substituted for a2 and a4, the correlations with insect characteristics become even more erratic. Overall, the strongest and most consistent correlations are shown by a0, which therefore emerges as the best single predictor of insect characteristics. However, the occasionally strong albeit erratic correlations observed for a2 and a4 suggest that all three 160 parameters (in a combination yet to be determined) might be a better predictor than a0 alone. This suggestion is explored in the next chapter.

4.7.4 Insect Characteristics vs. |θ4 − θ2| for Laboratory Data

In Section 4.6.2 it was shown that |θ4 − θ2| is a measure of an insect's bilateral symmetry. Aldhous (1989) found that |θ4 − θ2| was negligible (< 3º) for all but the largest insects (> 650 mg) that he measured, and was roughly proportional to insect size. This finding is verified for the laboratory data in Figure 4.17, which shows |θ4 − θ2| plotted against mass, length, width and width/length. Two of the four plots show a significant correlation (P < 0.01). The correlation with mass supports Aldhous's findings (r = 0.37 P = 0.002), although the correlation with length is slightly stronger (r = 0.42 P = 0.0004). The distributions are not uniform and appear to contain outliers, so the correlations may be inflated and therefore should be interpreted with caution. The values of

|θ4 − θ2| that exceed 5º are generally limited to large insects > 1000 mg in mass and > 45 mm in length, i.e. desert locusts. Furthermore, the above results are for just 23 species and may or may not apply to other species.

161

Figure 4.17: Variation of |θ4 − θ2| (an indication of CLPP asymmetry) and insect mass, length, width and width/length. The first two plots show significant correlations (P < 0.01). Data from Aldhous (1989) and Wolf et al. (1993). Number of insects in each plot is 68.

Aldhous (1989) noted that insects with masses > 1000 mg have CLPPs with four lobes, with the biggest lobes at 90/270° rather than the 0/180° consistently observed for smaller insects, see Figure 4.18 for examples. Indeed, in his data all insects with masses > 640 mg (namely one specimen of Noctua fimbriata and 11 specimens of Schistocerca gregaria) exhibit this 90/270° alignment.

162

Figure 4.18: Four of the CLPPs measured in the laboratory by Aldhous (1989). Above each plot m, L and W indicate mass in mg, length and width in mm. The largest insect has the biggest lobes at polarisation angles of 90 and 270° rather than at 0 and 180° as for the smaller insects

If studies of insects with alignments of 90/270° assume (incorrectly) that the alignment is 0/180° then the implied body orientation will be at right angles to the actual direction. One way to identify insects with a 90/270° alignment might be to identify those insects whose orientation differs by 90° from the rest of the sample, because orientations are usually highly consistent; e.g. see Riley (1979), Reynolds (1988), Reynolds & Riley (1997) and Zhai & Zhang (1999), albeit with small variations due to individual differences and air turbulence (Baker et al., 1984). However, as shown in Section 4.5, an alignment of

90/270° is equivalent to changing the sign of the a2 term in equation (17), with no effect on the resulting RCS. If the sign of the a2 term is constrained to be positive by the retrieval algorithm (as is the case here), then the retrieved θ2 will be artificially rotated 90°, and therefore so will the observed orientation. If this constraint is removed, a2 can assume negative values as required, and the observed orientation will be correct.

163 4.7.5 Insect Characteristics vs. No. of Lobes for Laboratory Data Aldhous (1989) found that, at a 3.2 cm wavelength, insects with masses < 250 mg have a CLPP with just two lobes, which suggests that the number of lobes may be a broad indicator of mass. Earlier, Section 4.6.3 showed that the number of lobes was determined by a2 and a4. Thus if a4 < a2/4 the result was always two lobes; if a4 ≥ a2/4 the result was always four lobes. However, a4 in both the laboratory and IMR data is rarely much above a2/4, so as shown in Figure 4.4 the second set of lobes is usually small in size, and in borderline cases it may be difficult to reliably tell if a second set is present.

Aldhous's finding is checked in Figure 4.19, which shows the value of a2/4a4 for the laboratory data plotted against insect mass, length, width and width/length. The results for mass show a general tendency for insects with four lobes to be heavier than insects with two, which is in agreement with Aldhous’s finding. But there are numerous exceptions, perhaps too many to make the number of lobes a reliable guide to mass.

The only significant (P < 0.01) correlations are with body length (r = −0.23) and width (r = −0.26), showing that insects with four lobes tend to be longer and wider than those with two lobes. However, the observed correlations are clearly subject to outliers and should therefore be interpreted with caution.

164

Figure 4.19: a2/4a4 vs. insect mass, length, width and width/length for the laboratory data. The CLPP has two or four lobes above or below a2/4a4 =1 respectively. Only body length and width show a significant correlation (P < 0.01).

The above analysis of laboratory data has so far looked at the measured variables taken one at a time. The next section repeats more or less the same analysis on IMR data to see how well the findings replicate. The next chapter extends the analysis to combinations of variables.

4.8 Analysis of IMR-Measured Insect CLPPs

The same analyses as in Section 4.7 were applied to observed RCS parameters from the Bourke IMR on two nights, each with large numbers of good quality

165 echoes for which all retrievable parameters were therefore available. The two nights were 14 March 1999 with 6,284 echoes (mainly plague locusts), and 8 September 1999 with 1,581 echoes (mainly spring moths). In each case smaller but unknown species were also present. Results for the night of 15 November 1999 (4,042 good-quality echoes) are given in Dean and Drake (2005).

The first step in analysing the IMR data was to check the accuracy of the RCS parameters retrieved by the processing algorithm. This check occupies the next subsection, after which come the analyses proper.

4.8.1 Accuracy of Retrieved RCS Parameters The accuracy of the retrieved RCS parameters was evaluated by two methods each using computer-generated data. The first used perfect CLPPs generated directly. The second used simulated radar signals with a distribution similar to those observed by the Bourke IMR. In each case the starting point was a set of RCS parameters that could then be compared with the parameters retrieved by the processing algorithm. The procedure implemented by the processing algorithm is described in Section 3.8 in Chapter 3.

Method 1. CLPPs were generated that spanned the entire set of CLPPs shown previously in Figure 4.4, including negative values of both a2 and a4. The negative values of a2 and a4 were subsequently made positive by appropriate changes to θ2 and θ4 during their retrieval by the processing algorithm, as shown previously in Figure 4.8. The total number of CLPPs thus generated was 600.

Errors in the retrieved a2 and a4 were generally very low (< 0.1%). Errors in the retrieved θ2 and θ4 were also generally low (< 1º) when respectively a2/a0 or a4/a0 were > 0. When both a2/a0 and a4/a0 were = 0, i.e. the CLPP was a circle as shown previously in Figure 4.3 and Figure 4.4, the values of θ2 and θ4 should have been undefined but were not. When only a2/a0 = 0, i.e. the CLPP was 166 shaped like a cross as shown in Figure 4.4, the output value of θ4 was correct but θ2 within 5º of either –90º or 90º only when a4/a0 was greater than 0.1.

When only a4/a0 = 0, i.e. the CLPP was shaped like a dumbbell as shown in

Figure 4.4, the output value of θ2 was within 5º of either –45º or 45º only when a2/a0 was greater than 0.1. (Had the retrieval been without error then the above values of ± 90º and ± 45º would have been exact rather than ‘close to’.) As for uncertainty in the retrieved parameters, Harman & Drake (2004) report about 1º for the angles θ2 and θ4, and better than 2% for a0 and speed when these are 2 -1 0.0005 to 1.3 cm and 5 to 15 ms respectively, rising to 15% when a4 is small.

Method 2. The first 100 good-quality echoes on the night of 15 November 1999 were used to provide a realistic set of flight-path parameters as well as values for a0 and θ2. The value of θ4 − θ2 was always zero. Values of a2 and a4 were then chosen uniformly from the range allowed by a positive RCS (Figure

4.4), including zero values for a2 and a4. For each combination, variants were created to match each of eight nominal altitude gates ranging from 225 m to 1,275 m, for four beam rotations (duration 0.8 s), using equation (1) of Harman and Drake (2004). 0-1 dB of noise was injected at random. Further details of the simulation are given in Dean and Drake (2005).

The result was a total of 20,800 simulated signals of which 8,035 (39%) produced good-quality CLPPs. The remainder failed, either because the signals were too weak and thus fell below the noise threshold, or because the signal was too short. For a2/a0 (8,035 comparisons) and a4/a0 (5,368 comparisons with non-zero a4), 98% of the retrieved values were within 0.02 of their initial values. For |θ4 − θ2| (4,400 comparisons with non-zero a2/a0 and non-zero a4/a0), 98% were within 2º of the initial value of 0º (positive a2/a0) or 45º

(negative a2/a0).

The results of Methods 1 and 2 are in good agreement. They show that the algorithm can accurately retrieve RCS parameters from CLPPs in which they 167 are present in every possible combination. For θ4 − θ2 the retrieval is least accurate when a2 or a4 approach zero, but the accuracy of the retrieved a2 or a4 is not affected. If RCS parameters can be related to insect characteristics (a point explored below and in the next chapter), then IMRs have the clear potential to discriminate between insects of different shapes and sizes.

4.8.2 Insect Characteristics vs. a0, a2 and a4 for IMR Data Unlike the laboratory data, the IMR data does not contain insects whose characteristics have been independently measured. Therefore no comparison of a0, a2, and a4 with insect characteristics is possible, even though the distribution of a2/a0 and a4/a0 values was found to be well described by the constraints, see Figure 4.6 and Figure 4.7 in Section 4.4. Instead, the present analysis compares the distribution of θ2, θ4 − θ2, and number of lobes between nights when either plague locusts or spring moths were the main species. This analysis occupies the next three sections.

4.8.3 Distribution of θ2 for IMR data

Recall that values of θ2 = 90˚ were observed in the laboratory data for one specimen of mass 648 mg (N. fimbriata) and 11 specimens of mass 1,064- 3,094 mg (the desert locust S. gregaria). Neither species are found in Australia. In contrast, probably less than 1% of the IMR measured insects had an estimated mass > 650 mg, and the typical plague locust or spring moth is much smaller than the above laboratory-measured specimens, see Table 5.1 in Chapter 5. On this basis there seems no reason to suppose that orientations of 90˚ should be observed in the two sets of Bourke IMR data. And indeed this was confirmed by the results. The two sets of IMR data showed no evidence that some of the insects had an orientation at 90˚ to the rest. As shown in Figure 4.20, all insects were strongly oriented in the same direction, with minor variations that can be attributed to air turbulence and wind gusts. As explained in Section 4.6.2, the presence of cos2 and cos4 terms in equation (4.16) means that IMR data indicate only the orientation of the body axis and not which way

168 the insect is facing, but the ambiguity is easily resolved by assuming the insect is flying with the wind rather than against it.

Mass > 400 mg Mass < 400 mg Mass > 400 mg Mass < 400 mg

Figure 4.20: Distribution of orientation values retrieved from good-quality echoes from the Bourke IMR during the nights of 14 March and 8 September 1999. Left two: night of 14 March, mainly plague locusts. Right two: night of 8 September, mainly spring moths. Although a small proportion of the orientation values approach 90˚, it does not represent a true 90˚ turn in body alignment. If it did, there would be a clear scatter of results on either side of 90˚, but no such scatter is evident. (This 90˚ is the angle from the mean travel direction, not the absolute retrieved angle, which as explained in the text cannot exceed 90˚.) Note that the range of orientation values is limited to 180˚, hence no values appear in the bottom half of each plot.

4.8.4 Distribution of |θ4 − θ2| for IMR Data To recap, the IMR data being analysed are the retrieved RCS parameters for 6,284 good-quality echoes (mainly plague locusts) and 1,581 good-quality echoes (mainly spring moths) from the Bourke IMR. And as shown in Section

4.4, |θ4 − θ2| is a measure of an insect's asymmetry.

The distribution of |θ4 − θ2| values for the two sets of IMR data is shown in Figure 4.21. Both means are close to zero, which suggests that neither the observed asymmetries nor the retrieval algorithm are introducing any systematic bias. There is a tail of larger values in both directions but no indication of the peaks around ± 45º that might be expected if forms corresponding to a4 < 0 were present, nor around ± 90º if forms corresponding to a2 < 0 were present. There is a small tendency for the larger values of

|θ4 − θ2| to occur when a2/a0 and a4/a0 are small, as shown by the unshaded 169 portion of Figure 4.21. Thus for the first sample, 61% of the 737 echoes with

|θ4 − θ2| > 10˚ have either a2/a0 or a4/a0 < 0.1, rising to 68% at |θ4 − θ2| > 22.5º.

In both cases the corresponding proportion at |θ4 − θ2| = 0 is about 30%. These results are consistent with the results presented in Section 4.8.1, and with the weakening (when a2/a0 or a4/a0 are small) of the constraints imposed by equations (4.25) and (4.26).

Figure 4.21: Distribution of values of the asymmetry measure θ4 − θ2 retrieved from good-quality IMR echoes during the nights of 14 March 1999 (left) and 8 September 1999 (right) at Bourke. Values for echoes with both a2/a0 and a4/a0 > 0.2 are shown in black, for which the totals are 1122 and 409 respectively. The means and standard deviations are −1.5 ± 29º (left) and +1.5 ± 35º (right).

In summary, the distributions shown in Figure 4.7, Figure 4.20 and Figure 4.21 indicate that the insects in these two IMR samples are approximately symmetric and without a 90º change in alignment between CLPP and body axis.

4.8.5 Distribution of Number of Lobes for IMR Data The distribution of the number of lobes in the CLPP is shown for each of the two sets of IMR data in Figure 4.22. On 14 March (top, mainly plague locusts) there were notably more CLPPs with four lobes than on 8 September (bottom, mainly spring moths), 50% vs. 10%. It also shows a higher proportion of 2 CLPPs with a0 ≥ 1 cm (10 log10(a0) ≥ 0), namely 50% vs. 40 %.

170 Analysis of the data from the further periods 14-25 March and 7-18 September show that the proportion of four-lobed CLPPs averaged 37% when plague locusts were predominant, compared to 11% when spring moths were predominant. In the March data there was a significant correlation between a0 and the proportion of four-lobed CLPPs (r = 0.87, P < 0.001), which is consistent with the results for laboratory data shown previously in Figure 4.19. The September data contained insufficient CLPPs with four lobes to allow a similar analysis.

Figure 4.22: 10 log10(a0) vs. number of two- and four-lobed CLPPs for good-quality echoes from the Bourke IMR. Top: night of 14 March, mainly plague locusts. Bottom: night of 8 September, mainly spring moths. The former show a notably larger proportion of CLPPs with four lobes (50.5% vs. 10.3%).

171 4.9 Discussion

The IMR and laboratory observations reported here confirm two things. First, that the CLPPs of insects follow, within observational error, the form derived from theory and described by equation (4.16). Second, that any changes in aspect due to voluntary movements, air turbulence, or geometry while traversing the beam, are not sufficient to cause systematic bias.

Small natural variations in orientation within the swarm (e.g. Baker et al. 1984) and natural variations in wind direction lead to a generally small scatter in travel directions, which is readily detected (Figure 4.20) and is in agreement with previous radar observations of high-altitude nocturnal insect migration (e.g. Riley, 1975; Schaefer, 1976; Harman & Drake, 2004). Nevertheless the near-constancy is still noteworthy given that, in different circumstances, many insects are capable of rapid manoeuvring in flight (Dudley, 1997). The present results do not throw light on the possible ways in which insects might achieve this near-constancy (e.g. optomotor control vs. wind convergence).

Locating CLPPs on an a4/a0 vs. a2/a0 plot that includes negative a2 and a4 values (e.g. Figure 4.8) avoids the need to take into account rotation of the CLPP due to asymmetry or orientations not aligned with the insect's body axis. Such plots would in effect be opposed to normal practice, where the retrieval algorithm shifts the CLPP to the +a2/+a4 quadrant by adjusting the corresponding θ2 and θ4 values. However, such rotation of the CLPP applied only to the heaviest insects in the laboratory data, none of which are found in Australia, and not at all to the IMR data. Consequently no allowance needs be made in the present work for these shifts in the retrieved CLPPs, whose retrieved shape information can be presented straightforwardly and unambiguously by a point on the plot of a4/a0 vs. a2/a0 as in Figure 4.4.

172 The relationships between the three main CLPP types (four-lobed, asymmetric, and oriented at 90˚) and insect body size and shape found by Aldhous (1989), were generally confirmed using the laboratory and IMR data. I found less definite limits on the insect mass that showed four lobes (Aldhous found four lobes only if mass > 250 mg), otherwise there were no significant disagreements.

What insect characteristic might best discriminate between species? The characteristic most commonly used is mass, but length and width would also be potential discriminators if they correlated strongly with RCS parameters. They also have the advantage of a relative variability within a given species that is typically less than half the variability for mass, see Table 5.1 in Chapter 5. Unfortunately, analysis of the relationship between individual RCS parameters and insect characteristics gave generally disappointing results. Broad discrimination between insect masses seemed possible (r = 0.90 for a0 vs. mass), but discrimination between species did not seem possible. However, this was for RCS parameters taken individually. Given that a2/4a4 determines the number of CLPP lobes, and that large insects tend to have four lobes, it seems possible that RCS parameters taken in combination could discriminate between species. This potential is investigated in the next chapter.

173 5 CLASSIFICATION OF INSECT TARGETS

This chapter deals with classifying insect targets according to their RCS properties. Parts of this chapter are expanded from Dean & Drake (2005) Monitoring insect migration with radar and its potential for target identification.

Methods with the potential to discriminate between plague locusts and spring moths using RCS parameters are reviewed. Multiple regression and five theory-based methods (all involving various combinations of RCS parameters) were examined and tested on published laboratory data, but their discrimination was unsatisfactory. A new two-stage approach to classification gave acceptable results when tested against four years of IMR data and independent light-trap data. It involved initially dividing the data according to the value of a0 followed by a further division according to the values of a2/a0 and a4/a0. Although evaluation of its performance vs. alternative approaches was hindered by the poor reliability of independent light-trap data, it seems clear that the new two-stage approach is superior to approaches based on a0 alone. Wingbeat frequencies of plague locusts and spring moths from IMR data overlap too much to allow even a modest discrimination. The main original contributions to this chapter are a statistical evaluation based on laboratory data of single-parameter discrimination methods, tests of theory-based methods, the derivation and testing of a new two-stage approach to discrimination, and a comparison of results from light traps 135 km apart.

5.1 Introduction

If migrating species can be precisely identified in addition to the insect numbers, speed and direction routinely provided by the IMR, it would greatly help the planning of pest management procedures whose aim is to prevent a damaging infestation. To date the approaches that have been proposed for identifying insect species by radar have involved either wingbeat frequency or simple RCS parameters.

5.1.1 Classification of Insects Using Wingbeat Frequency Schaefer (1976) was the first to recognise that the modulation of echoes by wingbeating (whether caused directly or via associated movements of the abdomen and thorax, see also Vaughan, 1985) might help to discriminate between insect species. Wingbeat frequency can vary from less than 10 Hz to over 200 Hz, depending on insect size and species, and has been used in attempts to identify species. However, there is a considerable spread of

174 frequencies even for the same species, for example Grodnitsky & Morozov (1993) give 37−107 Hz for the bug Pitedia juniperina, 30−40 Hz for the cotton moth Helicoverpa armigera, 38−70 Hz for the crane fly Tipula oleracea, and 90−120 Hz for the house fly Musca domestica.

As a further example, Riley & Reynolds (1979) present a plot of wingbeat frequencies for 21 species of locusts and grasshoppers found in the middle Niger area of Mali, most of them estimated using the wingbeat frequency formula of Schaefer (1976), namely WBF = 400 L–0.78 Hz, where L = wing length in mm. The frequencies range from 15 Hz for the African red locust to 45 Hz for small grasshoppers, and for each adjacent pair there is an almost complete overlap, which means that discrimination by wingbeat frequency would be clearly impossible. Even important non-adjacent pairs such as the desert locust (15−19 Hz) and the migratory locust (16−25 Hz) show too much overlap for them to be distinguishable by wingbeat frequency alone. (For comparison, later direct measurement of the African migratory locust gave ranges of 18−26 Hz (Baker et al., 1981), 15−27 Hz (Kutsch & Stevenson, 1981), and 16−23 Hz (Foster & Robertson, 1992).) Because of this general overlap, Riley (1989) concluded that "reliable identification of the species being observed is rarely possible".

Measurement of wingbeat frequency by the Bourke and Thargomindah IMRs is made by ceasing beam rotation for about 10 minutes each hour. These stationary beam observations are well suited to detecting the variation of echo intensity with wingbeating as targets traverse the beam (Drake & Harman, 2000; Drake et al., 2002). Beam rotation is stopped during such measurements because it was originally thought that the 5-Hz rotation frequency and its harmonics, and especially the continually changing polarisation, would overwhelm and distort the usually small wingbeat signal. However, Wang & Drake (2004) have shown that wingbeat frequencies can be extracted from

175 rotating-beam data, at least for good-quality echoes, with only a small reduction in the rate of successful processing due to the more complex signals.

During a single night of IMR operation the result can be many hundreds of observations. At Bourke the observed frequencies vary widely but tend to be between 20 and 70 Hz (Wang & Drake, 2004). As shown in Section 5.6 wingbeat frequencies for locusts and spring moths overlap too much to provide even modest discrimination, so wingbeat frequencies were not considered further.

5.1.2 Classification of Insects Using Single RCS Parameters Riley (1978) was the first to suggest that an insect's RCS parameters might discriminate between species. As described in the previous chapter, his suggestion was followed up by Wolf et al. (1993) using their own laboratory- measured RCS parameters of 14 individual insects (mass 9-254 mg) representing 6 species together with those of Aldhous (1989) who measured 54 individuals (mass 45-3094 mg) representing 18 species. Unfortunately there have been no further laboratory studies reported in the literature, nor have there been any systematic attempts to relate RCS parameters and CLPP forms to insect species (as opposed to insect characteristics). However, the acquisition of RCS parameters and CLPP forms by IMRs now makes it possible to apply this approach to field observations. In what follows the use of RCS parameters and CLPP forms to discriminate between insect characteristics and insect species will be explored using the laboratory data of Aldhous (1989) and Wolf et al. (1993). Methods to discriminate between plague locusts and spring moths will then be explored using four years of Bourke IMR data.

The previous chapter looked at the relationship between simple combinations of retrieved RCS parameters (a0, a2, a4, θ2, θ4 − θ2) and insect characteristics (mass, length, width). The results allowed broad discrimination between insect masses and lengths and (less successfully) widths, for which the best single

176 parameter was a0, but the results were too scattered to allow precise discrimination between species. Some idea of the discrimination that might be possible using the single parameters a0, a2 and a4 can be obtained from a consideration of their variability (expressed as their coefficient of variation, or SD/Mean, a dimensionless number useful for comparing variances in populations with different means) as shown in Table 5.1.

Table 5.1: Variability (expressed as SD/Mean) within species of a0, a2 and a4. Listed in order of mass are all species in the laboratory data for which the sample size is N > 2, and data from the Bourke IMR on nights when the indicated species was dominant (but not totally dominant, so the variability will be inflated by an unknown amount). For the IMR data (spring moths and plague locusts), N = number of processed signals.

SD/Mean as percentage

Insect Mean mass (mg) N a0 a2 a4 Spring moths 121 * 2667 70 71 77 A. gamma 125 3 53 56 45 Honeybees ** 160 4 66 51 89 C. brunneus 161 7 49 54 56 Plague locusts 328 * 7999 48 49 54 N. pronuba 401 13 25 59 34 S. gregaria 1838 11 51 83 59 Mean variability 52 60 59

* Average masses as measured by respectively J.E. Dowse and M.J. Stores (Table 3 in the Appendix for H. punctigera); and by Hunter (1989) for the plague locust fledgling stage when migration is most likely to occur. The actual masses of insects detected by the Bourke IMR could not be measured. ** Workers and drones.

The number of species in Table 5.1 is small, as are the sample sizes for the laboratory data, nevertheless the variabilities of a0, a2 and a4 are roughly similar and consistently large, typically just over 50% of the mean. The distribution of mass, a0, a2, and a4 is shown in Figure 5.1. The sample sizes are too small for statistical reliability, and combining datasets for different species might not be justified if there was a better alternative. But as they stand the distributions for mass and a0 are not significantly non-normal (P = 0.74 and 0.33 respectively by the Shapiro-Wilk test of normality), whereas the distributions for a2 and a4 are

177 significantly non-normal (P = 0.01 and 0.03 respectively), although perhaps not enough to disqualify an assumption of normality as a first approximation.

Figure 5.1: Left: distribution of mass for the laboratory datasets in Table 5.1 that have N ≥ 7. For each of the four component datasets, each mass was expressed as a percentage of the mean. The percentages were then combined and plotted in the histogram. Right: distribution of a0, a2, and a4 values expressed as a percentage of the mean for each of the three component datasets (values for the H. punctigera dataset were not available, hence N is reduced from 40 to 31).

How well would such variable parameters discriminate between two species A 2 and B that have mean a0 values of, say, 1.0 and 2.0 cm , and SDs that are 50% of the mean? To answer this question, suppose the criterion is set midway at a0 = 1.5. That is, all a0 values < 1.5 will be classified as species A, and all a0 values > 1.5 will be classified as species B. As shown in Figure 5.2, the criterion of 1.5 is 1.0 SD higher than A's mean a0 of 1.0 (SD = 0.5), and 0.5 SD lower than B's mean a0 of 2.0 (SD = 1.0). Assuming that the a0's are normally distributed (Figure 5.1), 68% of A's a0's will lie within ± 1.0 SD of A's mean, so

(100 – 68)/2 = 16% will be > 1.5, and 38% of B's a0's will lie within ± 0.5 SD of B's mean, so (100 – 38)/2 = 31% will be < 1.5. If there are equal numbers of A and B, then on average about (16% + 31%)/2 or one-quarter of the insects will be misclassified.

178

Figure 5.2: A theoretical example of how two species could be misclassified using a 2 scheme based on the distribution of a0 values. The mean of Species A is 1 cm and B 2 cm2. The SD of both species is 0.5 of the mean. Overall about one-quarter of all insects are misclassified.

In practice the mean a0 values are likely to be less far apart, in which case the average misclassification rate will be increased, for example to more than one- third if the mean a0's are 1.0 and 1.5 and the criterion is midway at a0 = 1.25.

For plague locusts and spring moths, the same calculation based on the figures given in Table 5.1 suggests that, when equal numbers are present, classification by a0 would lead to misclassification about 35−40% of the time. Accordingly, the present chapter looks at more complex combinations of the retrieved RCS parameters to see if the discrimination between species can be improved.

179 5.2 Multiple Regression Classification Methods

Ideally the simplest way of identifying insect species would be to combine the RCS parameters into a single measure that discriminates between species. For the laboratory data analysed in Chapter 4 (N = 68), a multiple regression analysis between insect mass and RCS parameters including a2 and a4 gave useful improvements over a0 alone, see Table 5.2. In this regression, insects whose θ4 − θ2 value was close to ± 90º were assigned negative values of a2, which involved 12 insects in total, all with masses > 600 mg. Insects whose

θ4 − θ2 value was close to ± 45º were assigned negative values of a4 which involved a single specimen of N. pronuba of mass = 538 mg2.

Table 5.2: Multiple regression analysis of insect mass vs. RCS parameters for the laboratory data. As before, the insects are divided into < 1000 mg (N = 57), > 1000 mg (N = 11), and all masses (N = 68).

Adjusted R2 and r for insect masses of RCS parameters used in < 1000 mg > 1000 mg All masses the multiple regression N = 57 r N = 11 r N = 68 r

0.649 0.81 0.764 0.87 0.903 0.95 a0

0.834 0.91 0.833 0.91 0.927 0.96 a0, a2

0.841 0.91 0.871 0.93 0.926 0.96 a0, a2, a4

0.843 0.92 0.885 0.94 0.935 0.97 a0, a2, a4, θ2

0.840 0.92 0.875 0.94 0.937 0.97 a0, a2, a4, θ2, |θ4 − θ2| "Adjusted R2" means that R2 has been adjusted to allow comparison between R2 values for different samples independent of sample size. In general the effect is to slightly reduce R2 for small samples. r = √R2.

2 From Aldhous (1989), which is a PhD thesis. It is not clear why this specimen of N. pronuba (θ4 – θ2 = –46.6º) should be so different from his twelve other specimens of N. pronuba (mean θ4 – θ2 = –2.6º SD 4.5º) other than being easily the heaviest (mean mass of his other specimens = 390 mg, SD 75, range 321-495 mg) and thus close to other heavy specimens such as N. fimbriata (648 mg) and S. gregaria (1084-3094 mg) that show values of θ4 – θ2 close to ± 90º. Aldhous’s thesis (page 160) says the specimen was misaligned during measurement on a turntable, implying a surprising level of misalignment (angles are reported to 0.1º), but the same result appears unchanged in Hobbs and Aldhous (2006) without any mention of misalignment, which suggests that Aldhous did not regard misalignment as sufficient cause for the result. For the present purpose the result has been retained to provide an example of a negative value of a4. 180 The results of Table 5.2 show that, by including a2 and a4, the already strong correlation between a0 and mass can be usefully increase from r = 0.81 to r = 0.92 for masses < 1000 mg. However, this strong correlation is with insect mass over a wide range of masses, and it does not necessarily translate into good discrimination between insect species. Indeed, when the insect species have identical masses, it is obvious that no discrimination via mass will be possible. The same argument applies to all other insect characteristics such as length.

Including θ2 in the regression gave small improvements that were appreciable only when masses > 1000 mg were included; θ2 has no effect on CLPP shape and should therefore have no effect on the regression, so the observed effect was probably due to the presence of θ2 values > 10˚ for masses > 1000 mg, see

Figure 5.3. Nevertheless for completeness θ2 is included in the analyses.

Including |θ4 − θ2| slightly worsened the regression, which adds to the suspicion that the earlier small but possibly spurious (due to outliers) correlation between

|θ4 − θ2| and mass (Figure 4.17 in Section 4.7.4) is indeed spurious.

Figure 5.3: Measured θ2 values against insect body mass. θ2 > 10º exists only for insects with masses > 1000 mg.

181 Similar regressions against log10(mass) using either the same RCS parameters or log10(parameters) usually gave good fits, but across the three mass groups none were consistently better than those shown in Table 5.2. Because the plot of mass vs. a0 in Figure 4.14 in Chapter 4 hints that the relationship might possibly be curvilinear over the whole range of insect masses, the all-masses 2 group was also regressed with curvilinear components, for example a0, a0 , a2, 2 a4 and |θ4 − θ2|, but in general the fit was not appreciably improved. However, 2 2 just including a0 with a0 appreciably increased the R value against mass from

0.903 to 0.922, which is comparable with including a2 and a4 with a0 (which increased the R2 values to 0.926).

To get a better idea of the discrimination between species that might be possible via simple combinations of a0, a2 and a4, their means and standard deviations are plotted against each other in Figure 5.4 for each species in the laboratory data for which the sample size is N > 2. The results show that adding a second parameter does tend to improve the discrimination, but unless there are already large differences between species (as between S. gregaria and the others), considerable overlap between species still seems inevitable. In some cases, notably for S. gregaria, an unwise choice of plot (here right vs. left or centre) can make the discrimination worse.

182

Figure 5.4: Discrimination between species in the laboratory data by pairs of RCS parameters. The radius of each oval is equal to one standard deviation, so each oval represents 68% of one parameter and 68% of the other, and its area (after allowing for any association between parameters) will generally contain roughly half of the cases for that species. Left: a2 vs. a0. Centre: a4 vs. a0. Right: a4/a0 vs. a2/a0.

A survey of the variabilities of mass, length, and width similar to that for the RCS parameters in Table 5.1 indicates that SD/Mean has a considerable range and averages 22% for mass, 11% for length and 12% for width. The smaller variability for length and width is as expected, given that both are factors in volume and therefore mass. Length (but not width) correlates with RCS parameters almost as strongly as mass does, so its smaller variability might seem to favour it ahead of mass as a potential predictor of species. But this approach leads nowhere because the variability of the observations (whether a0, a2 or a4) remains decisively larger than the variability of any insect characteristic. Furthermore, as already noted, no discrimination between insect species is possible if the species are similar in their target characteristics whether mass, length or width.

Accordingly, what is required is some combination of RCS parameters that can be related directly to species, or at least to some combination of insect characteristics that is adequately species-specific, and which might escape the limitations imposed by RCS variability as described above. As shown in the next section, there seem to be three possibilities.

183 5.3 Theory-based Classification Methods

Here "theory-based" means that the methods use various combinations of RCS parameters that are suggested by general CLPP theory (Chapter 4) rather than combinations that are derived empirically (Section 5.5).

Perhaps the most obvious theory-based measure is the ratio between the lengthwise and crosswise components of the RCS pattern, that is, between the

RCS value when the plane of polarisation is aligned with (σXX) vs. orthogonal to the body axis (σYY), because this should relate to the insect’s shape. As shown in Chapter 4 this ratio can be written as σ a+ a + a XX = 0 2 4 (5.1) σ − + YY a0 a 2 a 4 This ratio is similar to the ratio of reflectivities used to calculate the maximum differential radar reflectivity parameter (ZDR), which is used in meteorological radar studies to discriminate between airborne particles (e.g. Sauvageot & Despaux, 1996), = ( ηη ) Z DR log10 VH (5.2) where ηH and ηV are the horizontal and vertical copolarised reflectivity factors.

Figure 5.5 shows how ZDR varies with axial ratio for rain, hail, sleet, and snow.

The observed values of ZDR have a very wide range, hence ZDR is usually expressed in dB.

184

Figure 5.5: Differential reflectivity of a single particle of oblate shape versus axial ratio. Adapted from Raghavan (2004).

Another single parameter (Ψ), first introduced by Wolf et al. (1993) is based on the relative difference between the maximum RCS value and a0, ( − ) RCSmax a 0 Ψ = (5.3) a0

For most insects RCSmax coincides with the body axis and is given by + + a0 a 2 a 4 provided that (as is usually the case at Bourke, see Figure 4.21 in

Section 4.8.4) |θ4 − θ2| is approximately zero. Substitution of this result into equation (5.3) gives (a+ a ) Ψ = 2 4 (5.4) a0

If |θ4 − θ2| is substantially far from zero then the pattern is distorted, see Figure 4.10 in Section 4.6.2; in this case equation (5.4) becomes progressively less reliable as a single measure of body shape, see Figure 5.6. But such differences were seldom observed by the Bourke IMR and only for the largest insects

> 1000 mg in the laboratory data. When |θ4 − θ2| = 0 the parameter θ2 rotates the CLPP but does not change its shape, that is, it does not affect the retrieved a0, a2 or a4 values, so θ2 by itself will not discriminate between species. In

185 principle an exception occurs when the species have θ2 values close to ± 90º (which as previously mentioned applies only to the laboratory data with masses > 1000 mg and does not apply at Bourke), but not in practice because radar observations cannot directly determine whether θ2 is 0º or 90º.

Figure 5.6: The error in the calculation of Ψ from equation (5.4) resulting from |θ4 − θ2| values being non-zero. The resulting CLPPs are plotted at the corresponding locations. The values for the RCS parameters are taken from Aldhous (1989) for a specimen of N. pronuba (mass = 321 mg, length = 26 mm, diameter = 5 mm).

A further theory-based measure (Θ), introduced here for the first time, is based on the extent to which the CLPP exhibits four lobes, which as shown in Section 4.6.3 can be expressed as a Θ = 2 (5.5) 4a4 where Θ < 1 (i.e. a4 ≥ a2/4) indicates four lobes.

The way in which these three theory-based measures partition the laboratory data when the data are plotted as a4/a0 vs. a2/a0 is shown in Figure 5.7, for which the theoretical maximum observable values are 1.00 and 1.41 respectively (see Section 4.4). As the partition lines become more and more parallel to an axis, they will necessarily discriminate less and less between data 186 on that axis. Similarly, the closer the partition lines are to being at 45º to both axes the more they will discriminate between data on both axes. Only Ψ maintains a consistent 45º angle to both axes, and a consistent separation, whereas σXX/σYY and Θ vary considerably and become much closer together as their value increases. The latter can be countered by using their log10 values as in equation (5.5). On the other hand, these comments apply only to discriminating between data, whereas we are more interested in discriminating between species. These three theory-based measures will now be tested against the laboratory data.

Figure 5.7: Three theory-based RCS measures superimposed on the laboratory data plotted as a4/a0 vs. a2/a0. The dotted lines reproduce the constraint boundaries shown in Figure 4.4 in Chapter 4. Bottom right: associated CLPP forms. More then half of the possible forms were not observed in the laboratory data. Laboratory data are from Aldhous (1989) and Wolf et al. (1993).

187 5.4 Tests of Theory-Based Classification Measures using Laboratory Data

The single CLPP classification measures (a0 + a2 + a4)/(a0 − a2 + a4), its log10,

(a2 + a4)/a0, its log10, and a2/4a4 were regressed against insect length, width, width/length and mass for the laboratory data of Aldhous (1989) and Wolf et al. (1993). Because small insects had simple CLPP patterns and large insects had complex CLPP patterns, the laboratory data were divided into two sets, one set ‘small’ with mass < 1000 mg (N = 57) and the other set ‘large’ with mass > 1000 mg (N = 11), corresponding to the clear gap in masses shown in the 2 preceding figures. The corresponding values of a0 are roughly < 1.9 cm and > 1.9 cm2. These results are shown in Figure 5.8 and Figure 5.9 respectively.

In Figure 5.8 (mass < 1000 mg) all 20 correlations are negative, indicating that the larger the insect’s length, width and mass the smaller the single classification measure; 18 of the correlations are individually significant (P < 0.05), often very highly so, and 11 are significant when corrected approximately for the number of tests (P < 0.05/20) using the Bonferroni method (Townend, 2002). The most consistently high correlations are with log10[(a0 + a2 + a4)/(a0 − a2 + a4)], mean r = −0.57, and log10[(a2 + a4)/a0], mean r = −0.55. The correlations with width are always higher than with width/length, and are nearly always higher than with length or mass. For completeness other combinations of the physical parameters, such as mass/(length x diameter2), a proxy for density, were tested but none were better than those shown in Figure 5.8.

However, the results shown in Figure 5.9 are almost the reverse of those shown in Figure 5.8. All but two of the correlations are positive, whereas they were previously all negative; only 5 of the correlations are individually significant (P < 0.05), and none are significant when corrected approximately for the number of tests (P < 0.05/20). The most consistently high correlations are with 188 a2/4a4, mean r = +0.67, which previously showed the weakest correlations, mean r = −0.18. The correlations with width are consistently higher than with width/length, but are now nearly always less than with length or mass. Again other combinations of parameters were checked but none were better than those shown in Figure 5.9.

189 (a0 + a2 + a4)/(a0 − a2 + a4), mean r = −0.22

log10[(a0 + a2 + a4)/(a0 − a2 + a4)], mean r = −0.57

(a2 + a4)/a0, mean r = −0.51

log10[((a2 + a4)/a0], mean r = −0.55

a2/4a4, mean r = −0.18

Figure 5.8: Three theory-based measures regressed against insect length, width, 2 width/length and mass, for insects with a0 < 1.9 cm (N = 57). Above each set of plots is the classification measure and its mean correlation r with the four insect measures.

190 (a0 + a2 + a4)/(a0 − a2 + a4), mean r = +0.42

log10[(a0 + a2 + a4)/(a0 − a2 + a4)], mean r = +0.42

(a2 + a4)/a0, mean r = +0.17

log10[((a2 + a4)/a0], mean r = +0.16

a2/4a4, mean r = +0.67

Figure 5.9: Three theory-based measures regressed against insect length, width, 2 width/length, and mass, for insects with a0 ≥ 1.9 cm (N = 11). Above each set of plots is the classification measure and its mean correlation r with the four insect measures.

191 The differences between Figure 5.8 (small insects) and Figure 5.9 (large insects) make it clear that these particular single classification measures could not succeed unless there was an initial division on size. Furthermore, even the highest correlations (r ~0.7) are barely adequate for reliable classification. For example, if the level of correct classification made by chance is 50%, r = 0.5 would increase the level to only 75% (Rosenthal & Rubin, 1982). The prospects might be better if a0 values could be used to decide which regression should be used, except this implies a requirement for advance knowledge of the species you are about to detect. (That is, although we can get a0 from the radar observations, it will be of no help unless we know to which species it applies, in which case there would be no need of the present explorations.) Furthermore, when the three best regressions from Figure 5.8 are applied to plague locusts and spring moths, the variation within each group is considerably more than the variation between groups, see Figure 5.10. In other words the scatter in the classification measure (y-axis) within each labelled area is too great to allow discrimination between labelled areas, so these predictors would fail to reliably discriminate plague locusts from spring moths.

192

Figure 5.10: Enlargements of the three best regressions from Figure 5.8 where the body sizes of plague locusts and spring moths each have distinct ranges. Above each set of plots is the classification measure and its correlation r with the insect measure. Labelled areas show the observed range in width/length and mass for plague locusts and spring moths.

The reason for this failure becomes evident in Figure 5.11, where the single parameter partitions of Figure 5.7 are superimposed on insects similar to plague locusts (other locusts and grasshoppers) and spring moths (moths and butterflies). In each case there is reliable separation only at extreme values of a2/a0, with a clear overlap at intermediate values. So the partitions come nowhere near separating insects similar to plague locusts from insects similar to 193 spring moths. However, this conclusion does not necessarily generalise to all possible insects. The failure of the partitions shown in Figure 5.11 to reveal useful separation is limited to insects similar to moths and locusts. Useful separation of other insect types may still occur, as shown in Figure 5.4.

a2/4a4 (a0 + a2 + a4)/(a0 – a2 + a4)

Figure 5.11: The two best single classification measures superimposed on a subset of laboratory data plotted as a4/a0 vs. a2/a0. The subset consists of insects similar to plague locusts (locusts and grasshoppers, solid circles) and spring moths (moths and butterflies, crosses). Laboratory data from Aldhous (1989) and Wolf et al. (1993).

If the entire set of laboratory data is included, the analysis becomes more complex as shown in Figure 5.12. In this figure, insects with θ4 − θ2 = ± 90º were assigned negative values of a2 (12 insects in total, all with masses > 600 mg). Insects with θ4 − θ2 = ± 45º were assigned negative values of a4 (a single insect, mass = 538 mg, see footnote in Section 5.2). Top left, as insect mass increases (the mass scale is logarithmic) the a2/a0 values decrease (r = −0.78, P < 0.0001) until, at a mass of around 650 mg, they become negative. The a4/a0 values remain more or less the same for all masses with no significant relationship evident (r = −0.07, P = 0.61) and are all limited to less than 0.4 except for two Queen honeybees and four grasshoppers C. brunneus, all with masses between 185 and 214 mg.

Top right and bottom left, consistent with the relationship found for mass, as body length and diameter increase a2/a0 values decrease (r = −0.87, P < 0.0001 194 and r = −0.59, P < 0.0001 respectively). Although there is no significant correlation between a4/a0 and length (r = −0.14, P < 0.27) there is between a4/a0 and diameter (r = −0.30, P = 0.02). The only insect with a negative a4/a0 value has the third widest body (7.8 mm). Bottom right, neither a2/a0 nor a4/a0 show any consistent variation with width/length. Insects with large width/length ratios tend to have higher a2/a0 values although the relationship is relatively weak (r = 0.32, P = 0.013), and again there is no significant relationship with a4/a0 (r = −0.20, P = 0.13).

Figure 5.12: a4/a0 vs. a2/a0 for laboratory data according to mass, length, width and length/width. The dotted lines indicate the constraint boundaries shown in Figure 4.5 in Chapter 4. Laboratory data are from Aldhous (1989) and Wolf et al. (1993).

195 5.5 A New Two-stage Approach to Classification

The previous section attempted to discriminate between species by partitioning the a4/a0 vs. a2/a0 plot in three theory-based ways. But when applied to plague locusts and spring moths, there was too much overlap, and none of the partitions succeeded in discriminating between the two groups. However, all three approaches are theory based, and they all involve the division of parameters by parameters, thus losing information that may be present in the undivided parameter. For example, both a0 and a2 show strong correlations with mass, information which is then largely lost if either a0 or a2 is replaced by a2/a0. Previously it was argued that a correlation between mass and a0 is of no value when species have similar a0 values. Nevertheless it could provide a useful filter to eliminate other species, leaving a cleaner set of data for subsequent analysis. This then would be the first stage in an improved two- stage approach to discriminating between species. However, rather than use mass to determine regression coefficients as explained in the previous section, the second stage would be to partition the a4/a0 vs. a2/a0 (or similar) plot in whatever empirical way would best discriminate between species in question.

An exploration of this approach was made using data from the Bourke IMR for 14−25 March and 7−21 September 1999, when the predominant insects were respectively plague locusts and spring moths. For these periods a total of over 116,000 and 56,000 signals were processed, from which the RCS parameters were successfully retrieved for an average of over 3,700 and 1,200 signals per night.

2 The observed a0 values are typically ≥ 1 cm for plague locusts and spring moths, each (as already noted) with a wide range and therefore with considerable overlap. So the value of a0 for the first-stage filter was set at 1.0 cm2 to divide "small" insects from "large" insects (see Figure 3.2 in Chapter 3). 196

The distribution of RCS parameters on two typical nights are analysed in Figure 5.13. When combined with similar analyses for the other nights, the results showed that almost all the small (< 1 cm2) insects occur in the region 2 0.4 < a2/a0 < 0.95, a4/a0 < 0.17. In contrast, most of the large (≥ 1 cm ) insects in March (mainly plague locusts) occur above this region, generally where a4/a0 > 0.17, while most of those in September (mainly moths) occur in the region 0.7 < a2/a0 < 0.95, a4/a0 < 0.17, see Figure 5.13. Figure 5.14 shows the CLPP forms corresponding to the occupied area of Figure 5.13 and a division of the occupied area into four regions.

Figure 5.13: Distribution of retrieved RCS parameters. The number of cases within each area of 0.02 x 0.02 is shown as a shade of grey according to the scale shown on the right of each plot. The darker the area the greater the number of cases. Spring moths tend to concentrate below a4/a0 = 0.17 while plague locusts tend to concentrate above a4/a0 = 0.17. The value 0.17 was determined empirically to give the best discrimination between these two groups over the full dataset.

197

Figure 5.14: CLPP forms corresponding to the area occupied by insects in Figure 5.13 and the division of the area into four regions.

Further inspection of Figure 5.13 suggests that the overlap between large and small insects is generally restricted to the Lower Right region of Figure 5.14, and that the Lower Left region is generally empty of large insects. The main difference is that about half the plague locusts extend to larger a4/a0 values than the other insects

Tests of this general finding occurred on the night of 22 March 1999, when the ground temperature (17˚C) was below previously observed threshold for plague locust flight (17.5−21˚C; Clark, 1969 and 1971; Farrow, 1979) so it was unlikely that plague locusts would be present and on the night of 25 March 1999, when the wind direction was rather dramatically different (165˚) from the previous night bringing a different population of insects. The distribution of retrieved RCS parameters for both nights is shown in Figure 5.15. In the first case there are notably few large insects, a point supported by a large decrease (about 80%) in the number of large insects compared to the previous night (which is shown later in Figure 5.16). In the second case the data are less scattered than usual, and the concentration of large insects in the Upper Right region of Figure 5.14 (a2/a0 > 0.95, a4/a0 > 0.17) is pronounced.

198

Figure 5.15: Distribution of retrieved RCS parameters. The number of cases within each area of 0.02 x 0.02 is shown as a shade of grey according to the scale shown on the right of each plot. The darker the area the greater the number of cases. Left: few plague locusts. Right: mainly plague locusts.

The difference between the distributions of plague locusts and spring moths in the plot of a4/a0 vs. a2/a0 can be further explored by looking at the number of targets that fall within the four areas for each night of the March and September study periods. These numbers are shown as a bar graph in Figure 5.16 and exhibit two main features. First, despite the huge variation in the number of insects detected each night, the proportion falling in the combined Upper regions is fairly constant (except for 22 March). Second, the proportion of targets in the combined Upper regions observed in March (mean 60%, SD 7%), when plague locusts were predominant, is strikingly different from that for spring moths in September (mean 12%, SD 6%).

199

2 Figure 5.16: The total number of large (a0 ≥ 1 cm ) insects and the proportion in each classification region during the Top: March and Bottom: September study periods. Upper Left: UL, Upper Right: UR, Lower Right LR, Lower Left: LL.

The above results suggest that the proposed two-stage approach is worth testing further. However, while a0 would seem to be the best (or at least most logical) parameter for the first-stage filter, it is not clear whether a4/a0 vs. a2/a0 is the best plot for the second stage. Accordingly the same Bourke IMR data were submitted to an a4 vs. a2 plot, an a2 − a4 vs. a4/a2 plot, and an a2 − a4 vs. a2 + a4 plot, each being suggested by an examination of the correlations presented in Chapter 4 rather than by consideration of radar theory. However, the areas

200 occupied by moths and plague locusts in these plots show considerable overlap, more than on Figure 5.13, so their use here is unwarranted.

Given the encouraging results from the new classification method for these short periods of data, the method will now be applied to longer datasets and verified against other, independent, data sources.

5.6 Tests of a New Two-Stage Approach to Classification using IMR Data

The new approach to classification described in the previous section was applied to Bourke IMR data for the period June 1998 to October 2001, which thus covered the times of peak pest activity in four successive years. Altogether the data from 1,247 nights of IMR operation were analysed out of the 1,408 nights possible (the difference being due to loss of service mainly caused by system and power faults as described in Section 2.11).

2 For each night of operation the percentage of detected insects with a0 ≥ 1 cm that had a4/a0 > 0.17 was calculated, corresponding to the percentage in the Upper region of Figure 5.14. The resulting percentage was then interpreted as follows, based on the observations for March and September 1999 reported in the previous section: < 30% Mainly spring moths, 30 - 50% Mixed or identification is uncertain, > 50% Mainly plague locusts.

The indicated occurrence of plague locusts (i.e. nights where the above percentage was >50%) for each night of observation was then compared with results from light traps operated by the Australian Plague Locust Commission at White Cliffs 290 km SW of Bourke, and Fowlers Gap 420 km SW of Bourke, see Figure 5.17, and periods of high locust densities reported in the 201 APLC's monthly bulletins (www.affa.gov.au/aplc). Each light trap consists of a 250W mercury vapour lamp that attracts night-flying insects that then fall into a water-filled base 3 m in diameter. The insects are retrieved, identified, and counted the following morning. The light traps provide unambiguous identification, but probably detect migrants only after arrival rather than before departure (www.affa.gov.au/aplc). Furthermore, the light traps and IMRs are several hundred km apart, so they might not be sampling the same population, even though their separation is relatively small compared with the large size of the source area. Either way, gaps in the light-trap data will affect the counts shown in Figures 5.18-5.21.

Figure 5.17: Location map of the two APLC light traps at White Cliffs and Fowlers Gap and the two fixed IMRs at Bourke and Thargomindah.

202 Nightly trap counts ranged from less than ten to over a thousand. However, plague locusts were detected on only 5% of nights, mostly unevenly, see Figure 5.18. Consequently only a few comparisons with the IMR results could be made.

Figure 5.18: Distributions of the number of plague locusts trapped at White Cliffs and Fowlers Gap.

The percentage of targets in the combined Upper regions each night as a 7-point moving average, the light trap plague locust counts, and the temperature and relative humidity at 2100 h are shown for each of the four years 1998−2001 in Figures 5.19-5.22 respectively. Each figure has a detailed caption that identifies the main features. The species listed as 'other' in the light-trap legends are not identified in the original reports but were mostly grasshoppers (H.K. Wang personal communication).

The results show that the total insect numbers followed the same broad pattern each year, peaking in the warmer months at the start and end of each year, and falling away in the cooler months to less than 5% of the maxima. The dominant classification (based on the proportion of targets in the combined Upper regions) was plague locusts in the warmer months and spring moths in the cooler months.

203

Figure 5.19: Comparison of results for 1998 starting in May. During nights 120-300 (May-October) the insects were mainly spring moths. From night 330 (late November), as the weather became warmer, the insects were mainly plague locusts. Weather data is for 2100 h and is from the Bureau of Meteorology.

204

Figure 5.20: Comparison of results for 1999. Plague locusts predominate until about night 75 (mid-March), with a small transition period during nights 90-120 (April) when the insects were more mixed. Spring moths predominate until roughly night 260 (mid- September), after which the insects were more mixed with several outbreaks of plague locusts. Weather data is for 2100 h and is from the Bureau of Meteorology.

205

Figure 5.21: Comparison of results for 2000. Plague locusts predominate the early months until about night 90 (end of March). After a transition period to about night 120 (end of April), spring moths predominate apart from a small surge in locust-like targets during nights 150-170 (first half of July). As in 1999, occasional large-scale plague locust movements began from about night 275 (early October), and by the end of the year plague locusts were again predominant. Weather data is for 2100 h and is from the Bureau of Meteorology.

.

206

Figure 5.22: Comparison of results for 2001. Plague locusts predominate until about night 100 (early April), then comes a short transition period before spring moths predominate the rest of the study period from night 120 (beginning of May). Weather data is for 2100 h and is from the Bureau of Meteorology.

207 Although the light-trap locust counts in Figures 5.19-5.22 are very infrequent, and (as shown below) unreliable, they tend to parallel the fluctuations in the combined number of targets in the Upper Left and Upper Right regions. Thus all the circles denoting light-trap locusts in Figures 5.19-5.22 occur during periods of high target numbers, and none occur during periods of low target numbers. To quantify the relationship, the nights on which locusts or moths were captured by the light-traps were compared to the RCS predictions for the same nights. The results (Table 5.3) show that plague locusts were not misidentified as moths on any night. From the Fowlers Gap results (but not White Cliffs), moths were misidentified as plague locusts on one night. However, on this night the migration direction was not towards Fowlers Gap, so the light trap and IMR may have been observing different populations.

Table 5.3: Nights on which locusts or moths were detected by light-traps vs. the RCS prediction for the same nights.

Detected by Predicted by RCS Light-Trap Locust Mixed Moth Total Hits Misses Uncertain Fowlers Gap Locust 11 9 0 20 Mixed 6 8 0 14 Moth 1 22 2 25 Total 18 39 2 59 21 (36%) 1 (2%) 37 (62%) White Cliffs Locust 20 10 0 30 Mixed 0 0 1 1 Moth 0 0 1 1 Total 20 10 2 32 21 (66%) 0 (0%) 11 (34%)

The above comparison assumes that light-trap results are a reliable criterion for assessing IMR results. However, when the light-trap results are compared in a table similar to that in Table 5.3, they are clearly not reliable at all (Table 5.4), even though the two locations are closer to each other (135 km) than they are from Bourke (289 km and 423 km). For example, of the 53 nights with locusts 208 recorded at White Cliffs only 13 were recorded as locust nights at Fowlers Gap. Even worse, of the 46 nights with moths recorded at Fowlers Gap, none were recorded as a moth night at White Cliffs. Overall only 20.5% of the nights with moths or locusts recorded at one site were also recorded at the other. Indeed, the 3x3 contingency coefficient between Fowlers Gap and White Cliffs for the locust, mixed, and moth totals in Table 5.4 is only 0.23 (P = 0.76), or –0.21 (P = 0.88) if the frequencies are collapsed into a 2x2 table (locusts vs mixed plus moths), both suggesting an extremely poor reliability that may have attenuated the IMR success rates shown in Table 5.3.

It is possible that the above poor agreement may be due to insufficient insects at trap level, so they may have escaped trapping on a particular night even though they were in the area. To check this possibility the period during which the trap results were counted was widened from the original one night to three nights and five nights centred on the target night. But if anything the agreement was even poorer − instead of the above 20.5% for one-night periods it was 19.0% for both three-night and five-night periods, confirming an extremely poor reliability that would have attenuated the IMR success rates shown in Table 5.3.

Table 5.4: Light-trap results for White Cliffs vs. those for Fowlers Gap. ‘No data’ indicates that neither locusts, moths, or mixed were recorded on nights when they were recorded at the other station. The locust totals do not agree with those in Figure 5.18 as the latter include nights when moths were also detected.

Detected at Detected at Fowlers Gap White Cliffs Locust Mixed Moth No data Total Locust 13 18 1 21 53 Mixed 0 0 0 1 1 Moth 1 0 0 1 2 No data 12 29 45 0 86 Total 26 47 46 23 142

A further check on the new approach is possible via temperature. As detailed in Table 6.1 in Chapter, the lower temperature limits observed for moth flight are

209 well below those observed for locust flight (3-11ºC vs. 17.5-21ºC) which therefore predicts that locusts should predominate during the warmer months – a point confirmed by the results shown in Figures 5.19-5.22. Thus a plot of the percentage of total insect numbers observed in the combined Upper Left and Upper Right regions vs. temperature should show a positive correlation, and in fact the correlation is strongly positive (r = 0.62, N = 920) and very highly significant (P < 10-12), see Figure 5.23 left. In contrast the corresponding plot of total insect numbers (not just those in the upper regions) vs. temperature shows only a small non-significant correlation in the wrong direction, r = −0.054 (P = 0.06, N = 1,172), which supports the validity of the first result. (A small non-significant correlation for total insect numbers vs. temperature may seem implausible at first sight given the seasonal patterns of the two variables in Figures 5.19-5.22, but two opposing trends are involved here, one where warm temperatures encourage locusts and discourage moths, and one where cool temperatures encourage moths and discourage locusts, which is why there is no significant overall relationship.)

The weather investigations presented in the next chapter suggest that, in general terms, humidity is favoured more by locusts than by moths. So at first sight a similar plot vs. relative humidity should show a positive correlation. But Figures 5.19-5.22 show that relative humidity is highest when temperature is lowest, and vice versa, which (given that insects react more to temperature than to humidity) generally explains the weak, negative (r = −0.26, N = 918) but still very highly significant (P < 10-6) correlation found.

210

Figure 5.23: Classification result (the percentage of targets in the Upper Left and Upper Right regions of Figure 5.14) against: Left: temperature at 2100 h. Right: relative humidity at 2100 h. Finally, wingbeat frequencies from the Bourke IMR for mostly plague locusts and mostly spring moths (H.K. Wang & V.A. Drake, personal communication) are plotted in Figure 5.24 top). The mean wingbeat frequencies and standard deviations are 34.7 Hz SD 16.2 (N = 6,624) for locusts and 37.4 Hz SD 20.1 (N = 6,018) for moths, which clearly overlap too much to provide useful discrimination, even though the difference between means is highly significant (P < 10–12 by t-test) due to the very large sample sizes. Thus the procedure shown earlier in Figure 5.2 indicates that a classification based on these wingbeat frequencies when equal numbers are present would lead to misclassification about 47% of the time compared to 50% expected by chance. There is also no evidence of any significant peaks in the distributions above 40 Hz (Figure 5.24 bottom) that may be diagnostic.

211

Figure 5.24: Wingbeat frequencies from the Bourke IMR for mostly locusts and mostly moths. Top: 20-40 Hz. Bottom: 40-120 Hz. (H. K. Wang & V.A. Drake, personal communication).

212 5.7 Discussion

The results from the laboratory data seem clear. RCS parameters (a0, a2, a4,

|θ4 − θ2|) in a multiple regression show a strong correlation with insect mass

(r ≥ 0.9), most of it due to a0, which might suggest they would also usefully discriminate between species. In fact the same parameters, either alone or in three theory-based combinations, failed to do so, at least not unless the species had very different masses (e.g. by a factor of ten). These approaches failed because the variation of RCS parameters within a given species (standard deviation typically 50−60% of the mean) was usually larger than the variation between species, i.e. the distributions overlapped.

The above findings are based on a limited amount of laboratory data, namely 38 individual insects spread over just five species whose mean masses range from 125 mg to 1838 mg. Nevertheless the variations of parameters as a proportion of the mean are similar (and high) for each species. They are also consistent with the variations observed by the Bourke IMR for thousands of individual spring moths and plague locusts. So it seems reasonable to conclude that the above limitations may apply generally rather than just to the species that happened to be studied in the present work.

The above limitations were overcome, albeit not completely, by a new two- stage approach that was tested by using it to classify IMR data into moth, mixed and plague locust periods and comparing these with light-trap catches.

The first stage divided the data according to size (i.e. a0). The second stage divided the high-a0 data according to its position on an a4/a0 vs. a2/a0 plot. In each case the best parameter, and the best value for the division, were decided empirically. The comparison showed that this approach successfully discriminates between groups. However, comparisons of the light-trap results revealed that these agreed very poorly with each other, which makes them rather unsatisfactory as a criterion for testing IMR observations − a point 213 unsuspected when the present study was designed. The results were also consistent with the expected effects of temperature preferentially boosting locust numbers during the warm months. The effects of weather conditions on insect numbers are investigated further in the next chapter.

The new approach classified up to one half of all nights as mixed, which might seem to limit its application. However, the number of insects observed during these mixed nights was generally low, so they are usually of little ecological significance. For nights classified as “plague locusts”, when numbers were high, there were usually clear changes in the number of insects in the Upper Left and Upper Right regions of Figure 5.14. For example during October 2000 the proportion changed from around 20% to over 60%, indicating plague locust outbreaks that were later confirmed by the light-trap results.

The above results apply only to the Bourke IMR and to spring moths vs. plague locusts. In other areas with other radars and other species it is possible that an alternative first stage (e.g. one based on different values of a0, or on a2 rather than a0) and an alternative second stage (e.g. one based on a4 vs. a2 rather than a4/a0 vs. a2/a0), would give better results, in the same way that the choice of plot in Figure 5.4 could improve or worsen the discrimination between species. It seems unlikely that the best solution for any given set of target species could be predicted on the basis of the present work. Rather, it would need to be established empirically using the approach described here.

Some single-stage classification procedures may require RCS parameters to be more accurately measured than is reasonably possible. For example, the value of (a0 + a2 + a4)/(a0 − a2 + a4), calculated for the values of a0 = 0.18, a2 = 0.23 and a4 = 0.049 given for Tipula oleracea by Aldhous (1989), is −459 (0.459/−0.001), well outside the ranges typically observed (1-20 for small insects and 1-6 for large insects, see Figure 5.8 and Figure 5.9) but easily explained by errors in the measurement of a0 and a2, normally acceptable, 214 which in this case lead to a much larger, and therefore unacceptable, relative error in their difference a0 − a2. Such differences do not arise in the present two-stage approach, so the requirement for high accuracy in the measurement of RCS parameters is reduced.

As noted in Section 5.1, the other commonly used technique for identifying species, wingbeat frequency, has poor reliability (e.g. Riley, 1989) due to the considerable overlap between species. This can be attributed to changes in frequency due to variation in flight characteristics such as angle of ascent (Vogel, 1967; Wolf, 1993; Fischer & Kutsch, 1999), altitude and especially speed (which has the most significant effect). For example Baker et al. (1981) found that the wingbeat frequency of Locusta migratoria in Australia increased from about 17 Hz to 26 Hz (an increase of 50%) as speed increased from about 3.7 to 5.1 ms-1 (these are the regressed values for 38 specimens) or 13-18 kph. Kutsch & Stevenson (1981) found that the wingbeat frequency of Locusta migratoria decreased when climbing by about 5 Hz due to the use of more powerful wing flapping.

Wingbeat frequencies also vary with temperature, typically 1 Hz/˚C (Farmery, 1982; Unwin & Corbet, 1984; Vaughan, 1985; Foster & Robertson, 1992; Hyatt & Maughan, 1994; May, 1981; 1995; Roberts et al., 1998; Moore & Miller, 2002), ultrasound noise levels (Skals & Surlykke, 2000), the insect’s sex (Fischer & Kutsch, 2000), the insect’s size and shape (May, 1981; Riley & Reynolds, 1979 and 1983; Unwin & Corbet, 1984; Oertli, 1991; Hyatt & Maughan, 1994; Wootton et al., 2000), and the insect's maturity (for example Kutsch & Stevenson 1981 found that Locusta migratoria juveniles had wingbeat frequencies that averaged 7 Hz less than those of mature specimens). For both the desert locust (Kutsch et al., 1994) and Locusta migratoria (Camhi et al., 1995), wingbeat frequencies became synchronised if the locusts were 10 cm behind each other. For tethered Locusta migratoria wingbeat frequencies were about 7 Hz less than when free flying (Kutsch & Stevenson, 1981), which 215 illustrates the hazards of applying laboratory findings to field conditions. Finally, wingbeating will of course disappear altogether when the insect is gliding.

Given the general overlap between wingbeat frequencies, and given that most of the above modifiers are not susceptible to present radar measurement, it would seem that classification by wingbeat frequency alone is justified only in situations where the overlap is insignificant (which is not the case here).

In contrast, RCS parameters are unaffected by the insect’s altitude and speed, and (except in terms of interfering with radar echoes) by the presence of other insects. The two-stage approach described here is used in the next chapter to classify the insects observed by the Bourke IMR as either spring moths or plague locusts, prior to investigating the effect of weather on their migrations.

One final question remains: to what extent does the new two-stage approach to classification perform better than approaches based on a0 and on wingbeating? For plague locusts vs. spring moths present in equal numbers, the level of misclassification was estimated to be about 35-40% by a0 (Section 5.1.2) and 47% by wingbeating (Section 5.6), both on statistical grounds as illustrated in Figure 5.2. Because the new two-stage approach starts with a division based on a minimum value of a0, its level of misclassification will be less, but the actual level could not be determined due to the poor reliability of light-trap results. Nor could it be determined by comparison with wingbeat frequencies, which like light-trap results were too unreliable for the purpose.

Adding a2 and a4 to a0 improved the regression against mass in the laboratory data from r = 0.649 to 0.841 (Table 5.2), but as already noted this does not necessarily translate into improved discrimination between species. Although adding a second parameter can improve discrimination in some cases (Figure 5.4), significant overlap between species seems inevitable unless there are

216 already large differences between species. Indeed, an unwise choice of parameter can make the discrimination worse. If other parameters are to be added it would seem preferable to do so via the new two-stage approach.

All approaches could in principle be dismissed on the grounds of merely predicting locusts in summer and moths in spring, which is something we already know. But inspection of Figures 5.18-5.21 shows that the timing of locust and moth outbreaks varies somewhat from year to year, and therefore could not be reliably predicted by something as vague as summer vs. winter, even when translated into night temperature (which, due to considerable variability, not to mention the variability in local insect numbers, is scarcely less vague than summer vs. winter).

In summary, it seems that we can conclude with some confidence that the new two-stage approach to classification will be better than approaches based on a0 or on wingbeating. This conclusion is tested in the next chapter, where the new two-stage approach is used to successfully classify the insects observed by the Bourke IMR as either spring moths or plague locusts prior to investigating the effect of weather on their migrations.

217 6 INSECT MIGRATION IN RELATION TO ENVIRONMENTAL FACTORS

This chapter deals with relations between IMR observations and weather variables. It builds on the classification of targets and general data quality validations described in previous chapters. Parts of this chapter are expanded from Dean & Drake (2002a) Monitoring migrations of agricultural insect pests with low-cost autonomous profiling radars.

The effects of weather on insect migration are of much interest but have not been systematically studied using long-term IMR data. After a review of previous studies, four years of Bourke IMR data are systematically analysed to determine the effect of weather variables over three periods totalling 151 nights of mainly plague locusts, and four periods totalling 195 nights of mainly spring moths. The distribution of insect numbers was highly skewed and was normalised by using their 4th root. The methods of analysis were mainly bivariate correlation (including auto-correlation), multiple regression, discriminant analysis, and principal components analysis. The results were generally consistent with the results of previous studies. Three variables (temperature, pressure, days since rain) in decreasing order of effect) accounted for 48% of the variance in the 4th root of moth numbers. Four variables (humidity, wind direction, wind speed, change in humidity) accounted for 19% of the variance in the 4th root of locust numbers, but once sufficient rain had fallen to stimulate takeoff, six variables (temperature, humidity, rainfall, wind speed, rainfall in the preceding ten days, pressure) accounted for 38% of the variance. The best single predictor of insect numbers was temperature. Moths tended to prefer dry conditions while locusts tended to prefer damp conditions (but not too damp). Moonlight had no significant effect. The main original contributions in this chapter are the tests and results that occupy most of the chapter.

6.1 Introduction

It is generally accepted that “climate, to a first approximation, is the major determinant of insect abundance and distribution” (Zalucki & Furlong, 2005). Insects will thrive wherever the climate is conducive to food and breeding, and the feasibility of predicting the former from the latter has been confirmed in many studies (Zalucki & Furlong, 2005). For example, the same authors have shown that a climatic model (essentially temperature and moisture) fitted to the distribution of Helicoverpa armigera in Australia predicts a worldwide distribution that agrees well with the known distribution. The model also predicts areas such as South America where the species could establish if introduced. Similar worldwide predictions for Helicoverpa punctigera cannot be tested because it is essentially confined to Australia. 218 However, predicting pest pressure for a migratory species is far from straightforward because it is influenced by the vagaries of weather at three critical points: (1) in the source area, (2) at the time of migration, and (3) in the destination area. Predictions of the date of emergence or fledging of populations in breeding areas can be made several months in advance using rainfall and temperature forecasts, for example see Oertel et al (1999) for spring moths and Hunter (1989, 1996) for plague locusts, but the prediction of emergence is not the focus here.

The relationship between insect migrant numbers and weather variables has been of interest to entomologists for many years (see Johnson, 1969; Pedgley, 1982; Johnson, 1995). Most of the field studies have used various types of insect trap, but with limited success because their capture efficiency can depend on weather conditions such as wind, temperature and moonlight (Muirhead- Thomson, 1991). Entomological radars have offered an important new approach because they can observe insects flying at high altitudes in their natural environment. Scanning radars have been used with some success (e.g. Drake & Farrow, 1983) but their lack of automation makes them unsuitable for acquiring extended datasets.

Overall, the effects of the weather on insect migrations in eastern Australia has been the subject of many studies during the last fifty years and are now fairly well understood, see e.g. Farrow (1990) and Gatehouse (1997) for reviews. In principle the long continuous datasets provided by IMRs should allow weather effects to be studied in much greater detail than was previously possible, but this potential has yet to be confirmed.

The present chapter reviews previous studies of weather effects on plague locusts and spring moths, and then explores this potential using four years of data from the Bourke IMR, specifically to determine the extent to which

219 weather variables influence their migration. Similar long-term datasets were not available for the Thargomindah IMR.

6.2 Previous Studies of Weather Effects

Previous studies of weather effects on insect migration can be divided into laboratory studies, where the insects are observed in wind tunnels or on flight mills (devices allowing tethered flight), and field studies, where the insects are observed using movie cameras, calibrated binoculars (for making timed counts of insect numbers), and light, pheromone and suction traps. Chapter 1 reviewed previous studies of weather effects but left the details for plague locusts and spring moths to the present section, which includes a separate sub-section on troughs and cold fronts.

6.2.1 Previous Laboratory Studies of Moths and Locusts Only a handful of insect species have been studied using laboratory methods, which generally established limits of temperature and humidity for active flight, see Section 1.5 in Chapter 1. Furthermore, the relevance of laboratory studies to field conditions is limited because many natural flight behaviours such as speed and direction cannot be accurately monitored under laboratory conditions (Baker & Cooter, 1979). Other than a laboratory study by Lambert (1982) of Australian plague locusts suspended in a wind tunnel, which found that flight activity increased with reduced feeding (suggesting that poor pasture could stimulate migration), there have been no laboratory studies of plague locusts or spring moths.

6.2.2 Previous Field Studies of Weather Effects on Spring Moths Winter rainfall encourages growth of many host plants (Zalucki et al., 1994) and results in 1-2 generations of spring moths. As the host plants dry out during spring, the moths are carried by winds to areas that include the cropping area of eastern Australia. The amount of damage depends on the area, the number of moths, the eggs they lay, and the number surviving to become

220 caterpillars. (The caterpillars do the damage; the moths themselves have no mouthparts capable of damaging vegetation.) Their 35-42 day lifecycle leads to similarly spaced peaks in migratory activity (Zalucki & Furlong, 2005). The effect of humidity itself is uncertain, although high humidity may increase moth abundance (Gregg et al., 1994).

Migratory takeoff will generally not occur if the air temperature is outside the range necessary for biological functioning, see Section 1.5.3 in Chapter 1. Studies using tower-mounted traps (e.g. Gregg et al., 1994), ground-based traps (e.g. Persson, 1974; Morton et al., 1981), aerial trapping (Drake & Farrow, 1985), and scanning entomological radars (Drake & Farrow, 1985) have found minimum temperatures for active flight of between 3 and 11°C (Dent & Pawar, 1988; Gregg & Wilson, 1991; Coombs, 1993), which is about 10°C lower than the 13-20°C reported for the moth Ostrinia furnacalis (Shirai, 1988) and the rain beetles Ahasverus advena and Cryptolestes ferrugineus (Cox & Dolder, 1995), all of which are found in Australia. The maximum temperature for takeoff has not been widely studied. Zalucki & Furlong (2005) report a preferred temperature range of 15-33ºC and an upper lethal limit of 40ºC for H. punctigera, and 20-31ºC and 37ºC for H. armigera. Moth abundance has been observed to increase with temperature (Persson, 1976; Morton et al., 1981) but sometimes only slightly (Gregg et al., 1994).

Wind direction and disturbed weather are again important factors. Takeoff has been observed in wind speeds of 1.3 to 3.6 ms-1 (5-13 kph) measured at a height of 2 m (Drake & Farrow, 1983). Catch numbers depended on wind direction (Gregg et al., 1994) and decreased with increasing wind speed (Gregg et al., 1994; Persson, 1976; Morton et al., 1981). Migration frequently takes place in the warm northwesterly airflow associated with cold fronts (Drake & Farrow, 1985; Rochester, 1999) and troughs and depressions (Gregg et al., 1994).

221 6.2.3 Previous Field Studies of Weather Effects on Plague Locusts As with spring moths, migratory takeoff will generally not occur if the temperature is outside a favourable range. Studies have suggested that the minimum temperature for takeoff is between 17.5 and 21°C (Clark, 1969 and 1971; Farrow, 1979). This is consistent with laboratory studies of the desert locust Schistocerca gregaria using wind tunnels and flight mills, which found that flight was inhibited below 22°C (Weis-Fogh, 1956; 1976; Taylor, 1963; Waloff, 1953 and 1972), and field studies of grasshoppers in Mali, which suggested that flight was inhibited below 23-24°C (Riley & Reynolds, 1979). Lambert (1972) observed the proportion of day flying by plague locusts in relation to temperature on 133 occasions in northern NSW during late October to mid December 1969. No flight was observed below 19ºC, whereas flight always occurred above 30ºC. Intermediate temperatures produced intermediate results as shown in Figure 6.1.

Figure 6.1: Air temperature and the percentage of observations during which several plague locusts were seen in flight at any one time during daylight hours. Adapted from Lambert (1972). The number of observations per data point averages about 15 in the range 20-30ºC, and about 5 elsewhere.

However, minimum surface temperatures can be misleading because night- flying locusts and other insects tend to become concentrated in the temperature inversion layer 100-250 m above ground level where air temperatures are about

222 5-10°C higher than near the ground. Examples and vertical profiles are given by Drake & Farrow (1983) for plague locusts and Riley & Reynolds (1979) for grasshoppers in Mali. Insects who take off promptly at dusk and climb into the warmer air at the top of the inversion layer could thus continue flying despite a subsequent fall of surface temperature below the threshold for takeoff.

Layers can also form at higher altitudes due to temperature ceiling effects, where the fall in air temperature due to the adiabatic lapse rate is more than can be compensated by thoracic heating. However, neither low-altitude nor high- altitude layering is within the scope of the present chapter.

The maximum air temperature for takeoff has been reported as 34°C (Clark, 1971), although laboratory observations of S. gregaria flying in temperatures of 40-42°C (Weis-Fogh, 1956; 1976) suggest this limit may be too low. However, maximum temperatures tend to be of limited relevance because large-scale migrations occur mostly at night when temperatures are generally less than 35°C (Clark, 1969 and 1971; Farrow, 1979).

The effect of humidity is uncertain. Two observed lower limits for plague locusts are 60% (Clark, 1969) and 8% (Clark, 1971) whose difference suggests that humidity effects may be confounded by temperature effects. For example, laboratory studies of S. gregaria have found that migration is somewhat affected by low humidity, but not high humidity, the most favourable conditions being about 30°C and 55% relative humidity (Weis-Fogh, 1956 and 1976).

Wind speed, wind direction and disturbed weather are important factors. Flight can occur in wind speeds up to 6.4 ms-1 (23 kph) measured by a Shepherd three-cup anemometer at a height of about 5 m (Clark, 1969 and 1971) but may be inhibited by higher speeds. Migration can even take place in northward airflows blowing away from the main destination areas (Drake & Farrow, 223 1983), which helps to redistribute populations between the better-known southward migrations. Indeed, the Australian Plague Locust Commission reports that migration can occur in any direction, but those towards the east or southeast (the agricultural areas) pose the biggest threat. Major migrations tend to occur during periods of disturbed weather ahead of low-pressure troughs or cold fronts (Clark, 1969 and 1971), see Figure 6.2. These conditions are similar to those favouring the migration of spring moths.

Figure 6.2: Recorded migrations of plague locusts on low-pressure systems during the years 1980-2000. Circles indicate the positions of the two fixed IMRs used in the present study. Adapted from Hunter & Deveson (2002).

Rainfall has a decisive long-term effect because it determines the food supply and thus the population pressures that lead to migration. But rainfall also has a 224 short-term effect because migrations often occur after rain (Clark, 1969; Hunter, 1982; Hunter & Elder, 1999) or involve movements towards areas of recent rainfall (Hunter & Deveson, 2002). However, insects generally do not fly in the rain, and rain is generally associated with low temperatures that tend to inhibit flight, so a simple relationship seems unlikely.

6.2.4 More on Trough and Cold Fronts As noted above, major migrations tend to occur during periods of disturbed weather ahead of low-pressure troughs or cold fronts. A front is the boundary between two air masses of different temperatures. It may be stationary or moving, in which case the front is named for the advancing air mass. The classic model of a cold front is of an advancing cold air mass pushing into the existing air mass, causing the air at the boundary to rise and consequently form cloud and rain. The surface separating the two masses is not vertical but sloping, the slope being typically 1 in 100, and may extend right up through the troposphere. At the boundary within a cold front there is a marked drop in temperature, a sudden increase in humidity, an abrupt wind change, and a marked pressure rise (Forsdyke, 1969; Sturman & Tapper, 1996).

However, the classic model seldom applies in NSW and southern Queensland because the existing air mass may not be moist enough to form cloud or rain when forced to rise, and the advancing cold air mass can be very shallow especially in summer, which results in just a change of wind direction and a drop in temperature. Fronts move at speeds that average around 35 kph but may sometimes exceed 50 kph. A front may be hundreds of kilometres wide (Sturman & Tapper, 1996).

Low-level jets that travel at relatively high speed parallel to a front can occur in the warm air ahead of cold fronts at altitudes of 100-300 m, analogous to the high-level jet shown in Figure 6.3. Insects flying in these jets can travel much

225 faster than insects flying at altitudes just a few tens of metres above or below them (Farrow, 1986).

Figure 6.3: An active cold front showing wind speed and temperature. Across the boundary there is a sharp change of air temperature that can result in a strong thermal upcurrent producing a relatively high-speed jet (in this case at high altitude) parallel to the boundary. Adapted from Sturman & Tapper (1996).

A trough is a region of relatively low pressure that often precedes and moves with a cold front. Troughs are generally more prevalent in the warmer months, and in summer the most significant wind changes are associated with troughs that precede cold fronts. Troughs can intensify rapidly, generally at the expense of the cold front, leading to a strengthening of northerly winds ahead of a cool change (Sturman & Tapper, 1996).

The converging air masses at a front produce upward airflows and changes in wind direction that can carry insects for long distances. Scorer (1990) points out that insects which are being shovelled up in this way will stop flying when the temperature of the air being cooled adiabatically in the updraft reaches the lower threshold for flight, leading to their concentration in layers. He also suggests that convergence could maintain coherence in locust swarms larger than could be held together by a flight behaviour in which random direction becomes inwards at the edges.

226 Although only cold fronts are considered in the present study, converging air currents can occur anywhere there is an undercutting of warm air by cool air, for example cool air produced by the evaporation of falling rain or by horizontal variations in the radiation balance of the ground, all of which could in principle lead to local concentrations of flying insects (Pedgley, 1990).

6.3 Approach Used in the Present Study

The approach consisted essentially of comparing insect numbers with weather variables in order to determine their relationship over the long continuous time periods that only an IMR can feasibly provide.

The comparison of data over time suggests that time series analysis should be appropriate. However, time series analysis leads to the identification of trends and cycles as a function of time (a single variable), allowing us to predict ahead (Chatfield, 1996), whereas what we want here is to identify insect outcomes as a function of weather (many variables). In other words time series analysis would tend to tell us only what we already know, such as locust numbers show cyclic trends that generally peak in summer. Also, the identification of cyclic components does not establish that the data was generated by a cyclical process; thus even random data can be decomposed into cycles that are nevertheless meaningless (Bloomfield, 2000).

Furthermore, a time series analysis can in principle be applied only if the data is continuous and without gaps, which for IMR data is seldom the case. (In this case gaps comprise 13% of the study period.) There are various ways of filling occasional gaps to allow otherwise incomplete sets of data to be analysed, e.g. see Little & Rubin, (1987), for example the gap can be filled using the grand mean, the local mean, or the best fit to a curve, the best gap-filler being the one that does the least violence to the actual data. But missing data is still missing data that nothing can bring back. The perils of an over-reliance on gap-filling are vividly described by Kendall (1959).

227

Consequently the data were analysed by more appropriate techniques, namely bivariate correlation (including auto-correlation, which is also used in time series analysis), multiple regression, discriminant analysis, and principal component analysis. They were applied to periods that the Bourke IMR had identified as consisting of mostly plague locusts (January-March) or mostly spring moths (more variable but here nominally August-October), which are referred to as ‘locust periods’ and ‘moth periods’ respectively. The following sections describe in turn the hypotheses, variables, data, methods, and results, starting with an overview of the weather during the study period.

6.4 Weather During the Study Period

The following overview looks mainly at wind direction, wind speed, temperature, and rainfall, all of which are known determinants of insect migrations. Other than a few small differences explainable by the statistical variability of small samples, the weather during the study period was essentially what would be regarded as typical for the study area.

The distribution of wind directions was much the same for both the spring moth periods and the summer locust periods (Figure 6.4).

Figure 6.4: Distribution of wind directions. Vertical arrow indicates north, bars indicate direction wind blows from. Left: locust periods. Right: moth periods. In each case, for the purpose of calculating correlations, the 0/360º point is moved to the minimum total as shown where any split between 0 and 360 will be least disruptive. 228

However, other weather conditions were more variable during the spring moth periods than during the summer locust periods. They also showed appreciable differences between moths and plague locusts consistent with their season, see Figure 6.5 and Figure 6.6. Compared with the summer locust periods, mean nightly temperatures for the spring moth periods were lower (18-22°C vs. 29- 34°C), wind speeds were lower (1.8-3.2 ms-1 vs. 4.1-4.5 ms-1), air pressures were higher (1015-1017 hPa vs. 1009-1012 hPa), and humidities were higher (36-69% vs. 31-44%), all as expected except for wind speed where the Bureau of Meteorology long-term means for spring and summer are more nearly equal, which suggests that the present difference is the result of statistical variations in these particular (limited) samples.

In a survey of statistical methods in environmental biology, Green (1979) points out that assumptions such as normality are almost certainly not valid for any set of real data, a point confirmed by Micceri (1989) in a survey of 440 large-sample (N > 400) datasets in the social sciences, yet they are nearly valid for many sets of data. He suggests as a rule of thumb that Pearson correlations will be valid for any dataset if the distribution shows a single peak and N >10, which applies to nearly all the distributions shown in Figure 6.5 and Figure 6.6, and that F-tests and t-tests will generally be valid even on extremely non- normal datasets.

A Shapiro-Wilk test of normality applied to the above distributions showed no significant (P < 0.01) departure from normality for the key weather variables temperature and pressure. The most serious departure was (as expected) for wind direction. Gross deviations from normality as in a very highly skewed distribution will generally reduce the observed correlations (an example is given later in Section 6.9.2), which means that the indications will generally be conservative (Zar, 1984).

229

Figure 6.5: Distribution of (left to right) nightly temperature, atmospheric pressure, relative humidity, wind direction and wind speed for the (from top) 1998, 1999, 2000 and 2001 moth periods.

Figure 6.6: Distribution of nightly temperature, atmospheric pressure, relative humidity, wind direction and wind speed for the (from top) 1999, 2000 and 2001 locust periods. 230 As for rainfall in the area immediately surrounding Bourke, in the long-term there is about a third more rain in January-March than in August-October (see Figure 1.22 in Chapter 1), but for the present locust and moth periods the rainfall patterns were generally similar, with rainfall highest on the coast and diminishing with distance from the coast, see Figure 6.7. Annual rainfall in the Bourke district is very erratic but was consistently higher than average for 1998-2000 and below average for 2001-2002, see Figure 6.8.

The weather pattern during January-March (Figure 6.9 left) was characterised by the circulation of air around slowly-moving high-pressure systems resulting in light, variable winds or light westerlies (Tapper & Hurry, 1993). The weather pattern during August-October (Figure 6.9 right) was characterised by the passage of cold fronts. These cold fronts result in cool, moist south- westerlies within the study area (Tapper & Hurry, 1993), but as just noted, without a notable increase in rainfall.

231 1998

1999

2000

2001

Figure 6.7: Total 3-monthly rainfall for the general Bourke area 1998-2001. Left: January-March locust period. Right: August-October spring moth period. Adapted from www.bom.gov.au.

232

Figure 6.8: Annual rainfall figure for the Bourke district 1891-2001. The horizontal line indicates the mean of 354 mm. Rainfall 1891-2002 varied from 57 mm in 2002 (not shown) to 856 mm in 1950. Data is from the Bourke Shire Council. A runs test above and below the median (Bendat & Piersol, 1966) showed little evidence of clustering (observed runs 54, expected runs 57, P = 0.51), a result confirmed by the serial correlation (r = 0.095, P = 0.32).

Figure 6.9: Example data, for typical weather maps for Australia illustrating typical seasonal weather patterns. Left: January-March locust period, tropical/subtropical influences. Right: August-October spring moth period, temperate influences. Adapted from www.bom.gov.au.

233 6.5 Hypotheses to be Tested

To allow systematic testing, hypotheses about weather effects were derived from the above results and from reasonable assumptions. For example, strong winds should pass more insects per unit time over the IMR, thus increasing their counts even though no special increase is predicted from the above results (provided of course that the wind does not inhibit takeoff or lead to reduced processing as described in the previous chapter). Similarly, the observed effect of rain in the study area might be due to the associated troughs and cold fronts rather than to the rain itself. The various single-variable hypotheses derived in this way, for investigation in the present work both individually and in combination, are listed in Table 6.1.

Table 6.1: Hypotheses to be tested in the present work. 'Relationship' means the relationship predicted between the nightly number of insects and the weather variable, namely + positive, ? direction uncertain, x none. 'Threshold' means the threshold value below which insect flight is inhibited.

Weather Variable Spring Moths Plague Locusts Temperature T - relationship + + - threshold 3 - 11ºC 17.5 - 21ºC Humidity H - relationship + x - threshold ? x Wind Speed WS - relationship + + - threshold > 0 ms-1* > 0 ms-1* Wind Direction WD - relationship ? + Synoptic Weather - trough + + - cold front + + Pressure P - relationship ? ? Rainfall RF - relationship ? +

*A threshold value might be expected for wind speed if insects preferred takeoff into or with the wind, but this threshold has not been evaluated in previous studies. 234

6.6 Variables to be Tested

The weather variables to be tested consisted of 13 simple weather variables and various synoptic weather variables. A simple weather variable is one that can be measured in the field such as temperature and pressure. A synoptic weather variable such as a trough or cold front is one that can be obtained only from a synoptic weather map. As a precaution, consideration was also given to moonlight as a potential confounding variable.

6.6.1 Simple Weather Variables The 13 simple weather variables were as follows: P Atmospheric Pressure hPa S Wind Speed ms-1 H Relative Humidity % T Temperature ºC CP Daily Change in atmospheric Pressure hPa CS Daily Change in wind Speed ms-1 CH Daily Change in relative Humidity % CT Daily Change in Temperature ºC RF RainFall in the previous 24 hours mm DR Days since Rainfall of >0 mm RD Rain in the previous 24-hour Day (yes or no) WD Wind Direction 0º, 90º = towards N, E CWD Change in Wind Direction º

Daily change = daily value minus daily value on previous day. The two rainfall variables attempt to determine whether it is the presence of rain (RD) or the amount (RF) that has an effect. The following simple weather variables were also tested but were found either to be without clear effect or to confound the analysis with superfluous auto-correlations. So they have been excluded from the subsequent analysis: Days since rain -1 day (rain occurred at 1) Days since rain -2 days (rain occurred at 2) Rain in previous 24 hours exceeded 5 mm (yes or no) Rain in previous 24 hours exceeded 10 mm (yes or no)

235 Surface weather conditions (temperature, relative humidity, pressure, wind speed, and wind direction) as measured by the Bourke Automatic Weather Station (or manually prior to 1 February 1999) were obtained from the Bureau of Meteorology. Data prior to 1 February 1999 were available at intervals of three hours, hence the weather data at 1900 h (the IMR start time) and at 2000- 2200 h (the interval for counting insect numbers) were interpolated from those at 1800, 2100 and 2400 h. Subsequent data were available at intervals of one hour, making interpolation unnecessary.

Wind direction is a circular variable and therefore not usually analysable directly. Previous studies have solved this problem in various ways including separation into two variables (e.g. Nisbet & Drury (1968), Richardson (1974)) or by using a quadratic fit (Able, 1973). For the present analysis a new method was devised where potential problems due to significant totals being split by the 0/360º point (so part of the total appears at 0º and the rest at 360º) were avoided by moving the 0/360º point to the lowest total. In other words any split was confined to the area where it mattered least. The approach is illustrated in Figure 6.4.

Rainfall in the area immediately surrounding Bourke was estimated from the Bureau of Meteorology daily rainfall maps. This method was preferred to relying on a single reading from the Bourke weather station itself, which might not record rain falling nearby. The rainfall values on these maps were given as 0, 1, 5, 10, 15, 25, 50…mm (the maximum for the present dataset was 25 mm).

6.6.2 Synoptic Weather Variables The synoptic weather variables that were considered were the passage of cold fronts, passage of troughs, and the Weather Index adapted from Able (1973) where 1 = East of low pressure system, 2 = West of low pressure system, 3 = Transitional weather (moving from high pressure to low pressure or vice verse), 4 = West of high pressure system, and 5 = East of high pressure system. 236 The effect of troughs and cold fronts on insect migration were briefly reviewed in Section 6.2.4.

Cold fronts and troughs were included to test whether migration occurred in the days following their passage, to compare their effect with that of rainfall, and to see whether their effect was more than could be explained by the associated changes in temperature and wind conditions. However, during the locust periods, cold fronts and troughs occurred on only 3 and 9 nights respectively, compared with 26 and 14 nights respectively for the moth periods (which were in a cooler part of the year). So there was insufficient data for synoptic variables to be used for the locust-period analyses, and barely enough for the moth-period analyses.

For the moth-period analyses the passage of cold fronts and troughs was determined by examining the Bureau of Meteorology weather maps retrieved from www.bom.gov.au (or, before January 2000, the Bureau’s Monthly Weather Review). The maps showed all troughs simply as troughs regardless of their location or origin. Unfortunately the resulting data were rather subjective, being my interpretation of the Bureau's interpretation of weather data, and their timing was imprecise as they were available only at 12-hour intervals. Consequently, as a precaution, these synoptic data were examined graphically to assess their utility. Plots of the results are shown in Figure 6.10.

237

Figure 6.10: Insect counts during the four moth periods. Nights coinciding (approximately) with the passage of a cold front, trough or both are shown in black, red or blue respectively.

In Figure 6.10 there are a total of 26 cold fronts and 14 troughs. Of the 14 troughs, 7 show a connection with cold fronts (3 coincide with a cold front, 3 occur on the next day, 1 on the previous day), and the remaining 7 show no consistent connection. These results diverge somewhat from the accepted view that fronts are often preceded by troughs, but this may merely reflect statistical variations due to the small number.

As a further precaution the synoptic data were examined for temperature effects on insect numbers. The studies reviewed in Section 6.2.2 suggest that moths favour warm weather. So moth numbers might be expected to decrease on the night after a cold front, or (given the uncertainty in timing) on the night after 238 that. Such an effect is evident in Figure 6.10 for each of the four years. In total, out of 26 cold fronts 18 show such an effect, 5 show the opposite, and 3 are uncertain due to missing data. A similar tendency is observed for troughs in the first three years but is consistently reversed in the fourth year, which also has the most data.

The above finding indicates that the results of any analysis involving these synoptic variables are likely to be misleading due to their imprecision and small number (compared to the precision and number of simple weather variables). The number of troughs (14) is especially small.

The four synoptic variables analysed were therefore limited to: CF Cold Front present (yes or no) TR Trough present (yes or no) DCF Days since Cold Front (cold front passes at 0) DT Days since Trough (trough passes at 0)

For completeness, variations of the above were also tested, such as days before a cold front or trough, or days following the day after, as were variables based on the Weather Index, but they were either without clear effect or were clearly dominated by statistical artifacts (for example a cross-correlation between measures on adjacent days cannot fail to give r = 1 at lag 1 day), so they have been excluded from the analyses.

6.6.3 Moonlight as a Weather Variable Moonlight is not normally considered to be a weather variable. Nevertheless, in terms of insect numbers, the following review suggests that moonlight has the potential to act like one. Because moonlight is rarely considered in IMR studies the review is appropriately detailed.

Moonlight can reduce the catch made by light-traps by up to 50% (Morton et al., 1981; Dent & Pawar, 1988; Yela & Holyoak, 1997). In northern latitudes,

239 as at Rothamsted (52º N) where much of the classic work on light trapping of moths was carried out, there are many complicating factors such as extensive and variable cloud cover obscuring the moon, variable angular elevation of the moon, and marked seasonal changes in night length and insect numbers (Muirhead-Thomson, 1991). However, in the tropics, the lengths of day and night are more constant, and each lunar cycle follows a similar pattern regardless of season (Muirhead-Thomson, 1991). Of the many light-trap studies carried out in many different countries under a variety of insect and climate conditions, almost all have confirmed a general pattern in which the moon competes with the light source from the trap and renders it less effective. In general, catches are 3-4 times higher around new moon or at periods of no moon, than at full moon, albeit with a few notable exceptions, for example instead of 3-4 times it was 10 times for pyralid moths and 0.3 times for bostrychid beetles (Muirhead-Thomson, 1991).

A direct biological effect of moonlight, especially on marine organisms, is supported by a substantial literature (Cumming 1990, Burns 1997). Moonlight can vary from 0.001 lux at a new moon to 0.1 lux at full moon (daylight is normally more than 10,000 lux, see Refinetti, 2006), but the variation is not uniform. Thus the light intensity at half moon is not half that at full moon but only 9% (Danthanarayana, 1986). An effect of moonlight on some plants has been well-established by stomatal studies. Some animal life responds in a similar manner, and birds are perhaps the easiest to observe. Pre-dawn light has a high blue component (Zeiger et al. 1981), and at very low light intensities blue light can be several times as biologically effective as red light (Zeiger et al., 1981; Lee & Downum, 1991). With low dense cloud and cool conditions, clear patterns are not generally established.

The biological effects of moonlight are generally those than can be explained by its intensity, even though the mechanism can be indirect. For example, some studies of bats have found their activity to be unaffected by moonlight 240 (e.g. Hayes, 1997; Leonard & Fenton, 1983), while others have found a decreased activity at full moon that was explained by higher predator activity (e.g. Meyer et al., 2004; Fenton et al., 1977).

Lunar and daily periodicities were found in the numbers of light brown apple moths Epiphyas postvittana, a harmful pest of fruit crops in Australia, caught during suction-trap studies in orchards near Melbourne (Danthanarayana, 1976). Apple moths are predominantly nocturnal flyers. Their numbers showed a peak at full moon, and two more peaks just before and just after new moon. However, the findings were based on 444 moths caught over seven lunar cycles, or just over 200 consecutive nights, so the nightly count was well below that required for statistical reliability. In a cotton-growing region of New South Wales the full moon reduced light-trap catches of spring moths by 49% for H. armigera but were without effect for H. punctigera (Morton et al., 1981).

Danthanarayana (1986) reviewed the evidence for lunar effects on the flight and migration of 61 insect species, and concluded that the moon was more closely implicated than previously suspected. Using suction traps he found that mosquitoes (Culex pipiens australicus) and cabbage moths (Plutella xylostella) were most active around full moon, corresponding to a sharp peak in light intensity (as already noted, the half moon gives only 9% of the light of the full moon), and around a few days before or after new moon, corresponding to peaks in moonlight polarisation. He notes that (1) many insects are known to be sensitive to polarisation, for examples mosquitoes stop travelling as soon as overhead polarisation is interrupted, and to the polarisation of light by natural reflective surfaces such as wet or waxy plant leaves, (2) the observed pattern could not be explained by weather variables such as temperature, humidity, rainfall, or wind speed, and (3) when obliteration of the full moon peak is allowed for in light-trap results, the evidence suggests that a similar trimodal lunar periodicity may be common in insects generally.

241 But in terms of insect migration, other authors are less convinced. In a radar study of plague locusts migrating at night in NSW, Drake (1983) found no evidence that the moon provided a directional cue. Wehner (1984) points out that using the moon's position as a cue for celestial navigation is problematic because of the complex way in which its elevation and azimuth vary with time. Riley and Reynolds (1987) note that there is general agreement among radar observers that the orientation of high-flying insects is unaffected by the presence of the moon as a celestial cue. Furthermore, their own radar observations suggest that polarisation by itself cannot account for orientation at night. Unfortunately none of the forty or so studies of moonlight effects on insect behaviour published since Danthanarayana's review have addressed polarisation effects.

The relevance of moonlight to high-flying insects is therefore unclear. Nevertheless the possibility that it could confound the effect of other weather variables in the present study has to be recognised. For example, even if the moon is not used as a directional cue, bright moonlight might still inhibit the migrations of night-flying insects whose takeoff is triggered by low light levels. Accordingly, the effect of moonlight on insect numbers in the present IMR data was explored. The (negative) results are presented at the end of the next main section.

6.7 Data Used for Analysis

The hypotheses were tested using Bourke IMR data for 1 May 1998 through 31 October 2001, a period for which IMR observations were available on a total of 1,281 nights or 87% of the maximum possible. The IMR data were used to identify periods where the insects with an average RCS ≥ 1 cm2 (see Section 5.5 in Chapter 5) were either mostly plague locusts or mostly spring moths. This reduced the period of observations from a total of 1,281 nights to a total of 363 nights for locusts and moths combined, see next section for details.

242 The active period for plague locusts varied somewhat according to year but was fairly consistently January-March. In contrast, the active period for spring moths was longer and more variable, reflecting a habitat in which it can breed in almost any season (see Section 1.6.2 in Chapter 1), and the period with the least missing data was nominally August-October. The above periods are here referred to as ‘locust periods’ and ‘moth periods’ respectively.

The number of insects was taken as the total number of insects observed between 2000 and 2200 h, because insects at these hours can safely be assumed to have taken off near Bourke under the weather conditions reported for the Bourke area. Conversely, insects observed at, say, 0100 h would have been flying for roughly six hours from areas 50-100 km away, which clearly might not share the same weather conditions as at Bourke.

Rain in the IMR beam produces echoes that reduce the radar’s ability to monitor insects, therefore intervals where rain was detected at the IMR site had to be excluded from the dataset. Fortunately, the brevity of the monitoring window (only two hours) improved the chances of avoiding showers and patchy rain, and only 9% of the nights that had to be excluded were due to rain (the rest were due to missing data).

6.7.1 Description of the Data Used for Testing The mean number of insects observed each night (i.e. during 2000-2200 h) for each period is shown in Table 6.2. The four moth periods 1998-2001 were variable with mean nightly insect numbers of 27-148, with similarly variable totals in each of the three-month parent periods of 2,200-7,300 (rounded). The three locust periods 1999-2001 were more consistent with mean nightly insect numbers of 310-536, with similarly consistent totals in each of the three-month parent periods of 18,000-25,000 (rounded). Unfortunately no period was free of missing data. The proportion of nights with missing data can be ascertained from Table 6.2 and is 11% for moths and 25% for locusts. Nights with full data 243 totalled 198 for moths and 165 for locusts, or 195 and 151 after outliers were removed, see Section 6.7.4.

Table 6.2: The study periods during which either moths or locusts were predominant, and their mean nightly counts 2000-2200 h of insects with RCS ≥ 1 cm2.

Nights with Total Mean Adjust. Start End data nights insects/night Factor Locusts 13-Jan-1999 31-Mar-1999 52 78 343 1.56 1-Jan-2000 31-Mar-2000 66 91 310 1.72 21-Jan-2001 12-Mar-2001 47 51 536 1.00 Moths 1-Sep-1998 31-Oct-1998 55 61 133 1.11 6-Sep-1999 26-Sep-1999 20 21 148 1.00 1-Aug-2000 20-Sep-2000 41 51 64 2.31 3-Aug-2001 31-Oct-2001 82 90 27 5.56

To give equal weight to each period for the purpose of analysis, the nightly counts within each period were subsequently adjusted to the same mean by multiplying by (maximum mean number per night)/(mean number per night), whose values are shown in the last column of Table 6.2. (The possibility of bias due to these multipliers is checked later in Section 6.9.2 with negative results.) Unless otherwise indicated, the terms 'insect numbers' or 'insect counts' in the rest of this chapter refer to the adjusted numbers of insects observed during 2000-2200 h with RCS ≥ 1 cm2.

The distribution of unadjusted nightly insect counts for each period is shown in Figure 6.11. The distributions within each group were not significantly different, mean P by Kolmogorov-Smirnov test being 0.50 for moths and 0.56 for locusts. As shown in Figure 6.11, the nightly counts for moths tend to be either low or high, whereas those for locusts are relatively more even.

244

Figure 6.11: Distribution of unadjusted nightly insect counts (RCS ≥ 1 cm2) during moth periods (top) and locust periods (bottom). Counts are divided into 12 groups spaced about 1/600th of the total apart. Total counts are 15,058 (moths) and 63,471 (locusts).

6.7.2 IMR Data Fluctuations and Gaps The unadjusted insect counts including interpolated counts for nights with missing data are plotted in Figure 6.12. They show large night-to-night fluctuations that tend to hide the trends expected due to the natural increase or decrease in seasonal activity over periods that are up to three months long. The interpolated counts mean that some artificial contributions to the clustering evident in Figure 6.12 are inevitable. However, the fluctuations (which we might reasonably assume are due to weather effects and immigration and emigration events) are generally so extreme that the effects of trend and interpolation are unlikely to be serious. In any case, interpolated data was used only for the plots in Figure 6.10 and Figure 6.12 and was not used in later analyses.

245

Figure 6.12: Consecutive unadjusted nightly insect counts for the seven study periods. Interpolated nights are shown as open circles. The slope of the least-squares trend lines are given in Table 6.3.

246 6.7.3 IMR Data Trends, Clusters and Auto-Correlations Prior to the planned analyses, the data plotted in Figure 6.12 were examined for trend, clustering, auto-correlation, outliers and normality. Trend was tested by the reverse arrangements trend test (Bendat & Piersol, 1966). Clustering was tested by the runs test and by serial correlation (Bendat & Piersol, 1966). As expected, the results show significant trends for 4 of the 7 periods, and significant serial correlations for 6 of the 7 periods, see Table 6.3. However, the trends and serial correlations are uncorrelated (r = 0.02, N = 7), nor are there any consistent variations with the proportion of interpolated nights, which together support the previous expectation that interpolation is unlikely to have serious effects on Figure 6.10 and Figure 6.12. Not shown are the results of the runs tests, which revealed clustering consistent with the serial correlations.

Table 6.3: Results of trend and serial correlation tests for the seven insect periods. Note that the mean number of insects per night given here differ from those in Table 6.2 as the latter do not include the interpolated values.

No. of Nights No. of Insects Serial A B C % M Trend P r P Moth 1998 59 55 4 7 144 1.5 0.04 0.58 <0.0001 Moth 1999 20 20 0 0 148 8.6 0.12 0.45 0.048 Moth 2000 45 41 4 9 64 1.9 0.003 0.16 0.31 Moth 2001 90 82 8 9 28 0.6 <0.0001 0.43 <0.0001 All moths 214 198 16 7 112 −0.7 <0.0001 0.57 <0.0001

Locust 1999 54 52 2 4 351 −9.9 <0.0001 0.41 0.002 Locust 2000 90 66 24 27 311 1.7 0.09 0.49 <0.0001 Locust 2001 50 47 3 6 532 2.6 0.54 0.32 0.024 All locusts 194 165 29 15 379 1.1 0.01 0.44 <0.0001 A = nights in period analysed, B = nights in A with data, C = nights in A filled by interpolation, % = C/A percent. M = mean unadjusted number of insects per night. Trend = insects/night. Negative if trend is downwards. Serial r = correlation between insect numbers on successive pairs of nights.

Auto-correlation (Chatfield, 1996) was tested by correlating the number of insects on each night with the number of insects on previous nights and displaying the results as a correlogram, a plot of correlation coefficients vs. the

247 separation (lag) in nights (Chatfield, 1996). However, few of the periods were adequately long and gap-free to allow reliable analysis. Results for the four periods that combined the largest mean nightly count of insects with the largest number of nights are shown in Figure 6.13. The auto-correlations at lag 1 are of course identical to the serial correlations for the same periods given in Table 6.3, and all but one are significant. The only consistent effect is the decrease in auto-correlation from lag 1 to lag 2, which is consistent with the migrating insects being drawn from a limited population, that is, migration depletes the potential migrant numbers and leads to a reduction in the number of migrants on the following nights. Strong but not reproducible auto-correlations for lags of more than a few nights are probably fortuitous, for example in locusts 1999 the strong but not reproducible peak at lag 6 is due to the several peaks that happen to be spaced six nights apart in Figure 6.12.

Figure 6.13: Correlograms for nightly insect counts. N = number of nights, m = mean nightly count of insects. Top: moths 1998 (N = 59, m = 144) and 2000 (N = 45, m = 64). Bottom: locusts 1999 (N = 54, m = 351) and 2001 (N = 50, m = 532). Left to right, the values of r for P = 0.05 are 0.26, 0.29 for moths and 0.27, 0.28 for locusts.

248

6.7.4 IMR Data Outliers and Normality Outliers are observations far removed from the rest of the sample that can seriously distort statistical outcomes (Zar, 1984), especially if those outcomes depend (as here) on assumptions of normality. The unadjusted nightly counts were therefore tested for outliers using Hotelling's T2 test (the multivariate analogue of an independent samples t-test, see e.g. Everitt, 2005) based on the Mahalanobis distance of each point from the variable mean (the Mahalanobis distance is essentially a distance measure between points that is comparable to the R2 in regression, see e.g. McGarigal et al., 2000). Following convention the probability limit was set to P = 0.05. The outliers thus identified were removed, which reduced the number of moth and locust nights (previously 198 and 165) to 195 and 151 respectively. There were proportionately more locust outliers than moth outliers. The mean counts for locusts before and after removal were similar (379 vs. 326), but the SDs were notably different (367 vs. 255), consistent with the presence of outliers.

Normality was not met by the raw insect counts or the adjusted counts, which showed a marked skew. Therefore normality was achieved by mathematically transforming the adjusted counts. Consistent with similar studies (e.g. Nisbet & Drury, 1968), five different transforms were applied, namely the 10th, 4th, and 2nd roots, the natural logarithm, and the square. As suggested by Nisbet & Drury (1968), multiple regression was used to provisionally rank the transforms by R2 value, a measure of the relationship between insect numbers and weather variables. The highest R2 values were obtained using the 4th and 10th roots, a result consistent with the results of Nisbet & Drury (1968). Each transform was then tested for normality by the Shapiro-Wilk test, which has excellent power when testing departures from normality, see Shapiro, Wilk & Chen (1968). The 4th root transform gave results closest to a normal distribution (P < 0.2 by the

249 Shapiro-Wilk test) and was therefore adopted for subsequent analyses. The raw and transformed distributions are shown in Figure 6.14.

Figure 6.14: Distribution of insect numbers before and after the 4th-root and 10th-root transforms. Top: moth periods. Bottom: locust periods.

6.7.5 Effects of Moonlight As already noted, if moonlight is a potential confound in the study of weather effects on insects, then weather effects are a confound in the study of moonlight effects. Furthermore, weather variables can change completely in the 29-day interval between one full moon and the next. The issue is therefore a complex and challenging one, but one to which IMR data seem well suited.

The four years of Bourke IMR data contain insect numbers for 47 periods of seven nights centred on a full moon, and insect numbers for 50 periods of seven nights centred on a new moon, which would seem to be sufficient to allow non- moonlight effects to cancel out. (These are counts for the full night, not just for 2000-2200 h.)

250 An exact full moon occurs when the moon is exactly opposite the sun, so an exact full moon will necessarily be visible in the sky after the sun has set, i.e. when the IMR begins operating. On the other hand, three days before full moon, the moon would rise on average about half an hour after the start of IMR operations at 2000 h, but over all nights with full moon this represents a loss of hours x full moon of less than 1%. The average insect count for the 47 full- moon periods was 7,158 ± 6,527. That for the 50 new-moon periods was 7,191 ± 6,507. By a t-test the difference is non-significant (P = 0.98, i.e. the means are significantly the same). If anything the counts are less at new moon than at full moon, the opposite of what might be expected if bright moonlight was inhibiting the takeoff of night flyers.

The full-moon and new-moon periods can also be analysed in terms of their ratio, which over four years is notably erratic, see Figure 6.15. However, the erratic variations seem no more than might be expected from the large changes in insect numbers that can occur in the 14-day interval between full and new moons (a view supported by the above large standard deviations), and which probably account for the apparent downward trend as the new-moon count increases. The reason seems straightforward – at unusually low new-moon counts the full-moon count, because it is 14 days away, is likely to be not unusually low, giving ratios >1, and conversely for unusually high new-moon counts, giving ratios <1. But the ratio shows no consistent bias as might be expected if moonlight had a positive or negative effect on migration, a point confirmed by the average counts given above. For these high-flying insects moonlight had no evident effect and could therefore be disregarded as a potential confound.

251

Figure 6.15: Effect of moonlight on average insect numbers observed by the Bourke IMR. Vertical axis = number of insects observed during periods of seven nights each centred on full moon / average number of insects observed during similar periods centred on the new moon before and after.

6.8 Methods of Analysis

The statistical methods used to analyse the data included bivariate correlation, multiple regression, discriminant analysis and principal component analysis. All analyses were performed using NCSS software (J. Hintze, Number Cruncher Statistical Systems, Kaysville, USA). Variations of each technique are available in this software, all generally aimed at fine-tuning the precision of statistical prediction. However, the present work is less concerned with prediction and more concerned with gaining a broad picture of weather effects. Furthermore, as pointed out by Berk (1990), even variations designed to be robust can still produce outcomes that disagree in detail. Consequently the initial analyses were limited to the above four techniques. As it happened, the outcomes were sufficiently in agreement for the present purpose to make further diversification unwarranted, at least not until more complete datasets become available.

252 Bivariate correlation involved calculating the Pearson correlation coefficient r (e.g. see Bhattacharya & Johnson, 1977) between each weather variable and the 4th root of the insect numbers. For dichotomised weather variables (those with a value of either yes or no) the point-biserial correlation coefficient was used instead. The latter measures the relationship between two variables when one variable has only two values (Wallnau & Gravetter, 2004).

Multiple regression involved fitting the weather variables collectively to the 4th root of the insect numbers using a linear regression equation of the form 1/ 4 = + + + + N I cWW1 W1 c 2 W 2 cW 3 W 3 .... (6.1) where N is the number of insects adjusted as explained in Section 6.7.1, I is the value of the intercept, and cWn is the coefficient of the weather variable Wn. Initially all variables were included in the model. The analysis was then repeated after removing the least significant variables (a process known as stepwise regression) in order to maximise the statistical fit to the data, as measured by the coefficient of determination (R2) (Thorndike, 1978). Stepwise regression simplifies the final equation and eliminates variables that are correlated with each other. Such intercorrelations (also called multicollinearity) can make the results an unrealistic estimate of the true regression and should therefore be avoided.

Discriminant analysis looks at the difference between two or more groups of data (here the different levels of migratory activity) and then determines which variables best discriminate between groups (Klecka, 1980), thus predicting the level of a particular night’s migratory activity (giving a result that is within a range of values rather than an exact value). The result of discriminant analysis is a set of functions fD, one for each group, whose values are a linear combination of the discriminating variables similar to that for multiple regression, namely = + + + fDWW c1 W1 c2 W 2 cW 3 W 3 .... (6.2)

253 The estimated migratory level for a night is then determined by finding the highest scoring discriminant function.

Principal component analysis transforms the data to a new set of variables, the principal components or factors, that are as uncorrelated as the data will allow and which are ordered so that the first few account for most of the variance present in the original variables (Kim & Mueller, 1978; Lawley & Maxwell, 1971; Goddard & Kirby, 1976). The correlation between a particular variable and a particular component is known as the loading of that variable on that component; the higher the loading the stronger the variable's influence. In statistical terms the of principal component analysis is a function fPC whose values are a linear combination of the underlying variables, again similar to that for multiple regression, namely = + + + fPC c W1 W1 c W 2 W 2 cW 3 W 3 ..... (6.3) Principal component analysis is similar to discriminant analysis but the latter maximises the difference between values of the dependent variable whereas principal component analysis maximises the variance across all the dependent variables accounted for by the factor. In the next two sections the above methods will be used to investigate the effects of weather on the migratory behaviour of spring moths and plague locusts.

6.9 Results of Spring Moth Analyses

The analyses treat the four moth periods totalling 195 nights as a single sample and compares the 4th root of the number of insects (adjusted as in Table 6.2) observed each night between 2000 and 2200 h with 17 weather variables (13 simple, 4 synoptic), both separately and together, using four different techniques. The aim is to discover the extent to which each weather variable affects nightly moth numbers.

254 6.9.1 Bivariate Correlation (Moths) The correlations between the 4th root of nightly insect numbers and each of the 17 weather variables were calculated. Point-biserial correlation coefficients were calculated for the three dichotomous variables (those with a value of either yes or no). The results are shown in Table 6.4. The highest and most individually significant (P < 0.001) correlations were with atmospheric pressure P (r = −0.52), change in pressure CP (r = −0.33), and temperature T (r = 0.59). Also individually significant (P < 0.05) were the correlations with wind speed (r = 0.17), change in wind speed (r = 0.19), change in temperature (r = 0.17), and number of days since rain (r = −0.17). When the significance levels are corrected for the number of tests using the Bonferroni method (Townend, 2002), the three highest correlations are still highly significant (P < 0.001). Their scatterplots are shown in Figure 6.16.

Table 6.4: Pearson correlation coefficient (r) or point-biserial correlation coefficient (rpb) between (number of insects)1/4 and 17 weather variables during moth periods. N = 195 nights. Two-sided significance levels (P) are given if < 0.20.

Variable r P P Atmospheric Pressure −0.52 < 10-14 S Wind Speed 0.17 0.02 H Relative Humidity −0.13 0.07 T Temperature 0.59 < 10-20 CP Change in Pressure −0.33 < 10-5 CS Change in Wind Speed 0.19 0.008 CH Change in Humidity −0.01 CT Change in Temperature 0.17 0.02 RF Rainfall in previous 24 h −0.02 DR Days since rainfall > 0 mm −0.17 0.02 WD Wind Direction 0.02 CWD Change in Wind Direction 0.03 DCF Days since Cold Front 0.12 0.09 DT Days since Trough −0.07 RD Rain in previous 24 hours 0.02* CF Cold Front Present 0.11* 0.13 TR Trough Present −0.02*

* point-biserial correlation coefficient (rpb), for which the weather variable is yes/no.

255

Figure 6.16: 4th root of the nightly number of insects observed by the IMR during moth periods vs. the three most significant weather variables. N = 195. Top: atmospheric pressure. Middle: daily change in atmospheric pressure (daily pressure minus daily pressure on the previous day). Bottom: temperature.

6.9.2 Multiple Regression (Moths) As already noted, multiple regression allows weather variables to be assessed in combination. The results are shown in Table 6.5 for three models. Model 1 involves all 17 weather variables. Model 2 involves only those variables whose inclusion increased the R2 value by at least 0.005, which reduced the number of variables to 7. Model 3 involves only those variables whose inclusion increased the R2 value by at least 0.01, which further reduced the number of variables to 3.

256 As shown later in Table 6.8 there were strong intercorrelations (r ≥ 0.35) between wind speed S and change in wind speed CS (r = 0.59), pressure P and change in pressure CP (r = 0.39), temperature T and change in temperature CT (r = 0.43), humidity H and change in humidity CH (r = 0.38), and humidity H and rainfall RF (r = 0.37). However, none of these pairs appear in Model 3, which suggests that the outcome has not been affected by these intercorrelations (multicollinearity). The regression equation for Model 3 is 1/ 4 = − − + NM 69.8 0.023DR 0.068P 0.118T (6.4) where DR is measured in days, P in hPa and T in °C.

As shown in Table 6.5, R2 for this equation is 0.475, which means that it accounts for 47.5% of the variance in the 4th root of the observed moth numbers. The corresponding r is 0.69, which is impressive even though the relation is with the 4th root of the number of moths in which case it could be argued that r = 0.69 is an overestimate of the relation with their actual number. To follow this argument, imagine three pairs of data with regression values of 2, 3, 4 and N1/4 values of 2, 4.1, 3. For these three pairs r = 0.476, whereas between the same regression values and the corresponding N values (16, 283, 81), r = 0.233, apparently confirming that r = 0.476 is an overestimate. But the argument is invalid because r = 0.233 is the result obtained with highly skewed data (in this case more skewed than any in Figure 6.5 and Figure 6.6), and skew is known to reduce the observed r. In such a situation one approach is to use a non-parametric measure of association such as Spearman's coefficient of rank correlation (Zar, 1984), which in this case is 0.50, which does not support the view that r = 0.476 is an overestimate.

On the other hand, multiple regression capitalises upon any chance fluctuations in the data that favour high multiple correlation. The resulting value of R2 is therefore an inflated value (Kachigan, 1986). If the same regression weights were applied to a new sample, the observed R2 would probably be smaller than

257 the original R2. A common way of ‘shrinking’ the original R2 to a more realistic value is by the formula (Kachigan, 1986) RealisticR2 = 1 −( 1 − R2 )( N − 1/) ( N − n) (6.5) where N = sample size and n = number of variables. Given N and n, the value of R2 expected by chance alone (Kachigan, 1986) is ChanceR2 =( n − 1) /( N − 1) (6.6)

False correlations exist even when the sample consists of random numbers. For example Freedman (1983) analysed ten sets of random data, each having 50 predictors and a sample size of 100. The mean overall correlation between criterion and combined predictors (i.e. between noise and noise) should have been zero, but thanks to false correlations it was an impressive R2 = 0.48, in agreement with the 0.48 predicted by equation (6.6).

In the present case N = 214 and maximum n = 17, which shrinks the observed R2 = 0.534 to a minimum of R2 = 0.494, hardly a decisive difference. The corresponding value of R2 expected by chance is 16/213 = 0.075.

The relative effect of each variable can be assessed using the standardised coefficients (SC), which is the change in N1/4 in standard deviations caused by a change of one standard deviation in the weather variable (Schroeder et al., 1986). The SCs for each variable in Models 2 and 3 are shown in Table 6.5. The variable with the greatest effect is temperature T, which has about 1.2 times the effect of the atmospheric pressure P and about 4.3 times the effect of the number of days since rain DR. These three variables account for about 48% of the variance in the 4th root of spring moth numbers.

258 Table 6.5: Multiple regression analyses of the (number of insects)1/4 and weather variables for the moth periods. The three models are described in the text. P is the significance level of the regression coefficient by two-tailed t-test. SC is the change in the (number of insects)1/4 in standard deviations caused by a change of one standard deviation in the weather variable.

Model 1 Model 2 Model 3 Variable Coeff. P Coeff. P SC Coeff. P SC CF (Y/N) −0.115 0.000 CH −0.008 0.556 −0.007 0.107 −0.113 CP −0.045 0.057 −0.055 0.003 −0.227 CS 0.010 0.018 CT −0.062 0.792 −0.068 0.007 −0.213 CWD 0.001 0.015 DCF −0.004 0.162 DR −0.027 0.843 −0.033 0.006 −0.163 −0.023 0.037 −0.111 DT −0.007 0.050 H 0.007 0.272 P −0.055 0.095 −0.054 0.000 −0.273 −0.068 0.000 −0.341 RD (Y/N) 0.254 0.000 0.302 0.089 0.111 RF −0.031 0.229 S 0.062 0.255 T 0.133 0.216 0.125 0.000 0.508 0.118 0.000 0.477 TR (Y/N) 0.417 0.000 WD 0.000 0.078 Intercept 55.4 55.8 69.8 R2 0.534 0.507 0.475

The 4th root of the number of insects predicted by Model 3 for the 195 nights of observations is compared with the 4th root of the actual number of insects in Figure 6.17. Despite considerable scatter the correspondence is clearly evident as indicated by r = 0.69 and P < 10−30. The results for 2001, despite their adjustment factor being significantly higher than for the other years (5.56 vs. 1.00-2.31, see Table 6.2), are not noticeably displaced from the results for 1998-2000, which indicates that the adjustment factor is not biasing the results.

259

Figure 6.17: 4th root of the predicted number of insects vs. 4th root of the actual number of insects for 195 nights during the moth periods. Results from the years 1998-2000 and 2001 are shown as points and crosses respectively. The correlation is r = 0.69 (i.e. √R2 where R2 = 0.475 see Table 6.2), for which P < 10–30.

6.9.3 Discriminant Analysis (Moths) Whereas multiple regression attempts to predict the number of moths, or at least the 4th root of their number, from the weather variables, discriminant analysis attempts to predict the migratory level or group into which the number will fall. Consequently it is necessary to define suitable migratory levels in terms of the number of insects observed between 2000 and 2200 h each night. Suitable levels were determined by inspection of the distribution shown earlier in Figure 6.11. Four levels seemed sufficient, as follows. N = number of cases (see later in Table 6.7). 1. Up to 30 individuals, N = 93 2. 31 - 90 individuals, N = 74 3. 91 - 147 individuals, N = 24 4. More than 147 individuals. N = 4

260 From the insect numbers and weather variables within each of these four levels, multiple discriminant analysis calculates three uncorrelated functions and then ranks them in order of their eigenvalues (Klecka, 1986). The first discriminates as best it can, the second function improves the discrimination as best it can, and the same for the third function. The final result is a list of weather variables that best discriminate between the four levels of insect numbers.

The results for 14 weather variables are shown in Table 6.6 (the 3 remaining variables had to be excluded as they can only have values of yes or no). The results of Table 6.6 show that the first discriminant function was significant (P < 0.0001), but not the second (P = 0.623) or third (P = 0.718), both of which can therefore be discarded. Overall, 4 of the 14 variables had significant effects (P < 0.05) on the discrimination. The standardised canonical coefficients (indicating which variables have the greatest proportionate effect on the result) show that the variable with the greatest effect was temperature T, which has about 2.8 times the effect of atmospheric pressure P, 3.3 times the effect of wind direction WD, and 3.6 times the effect of the number of days since a trough DT, which is consistent with the multiple regression results.

261 Table 6.6: Discriminant analysis results for the moth periods. Two-sided significance levels (P) are shown if P ≤ 0.05. The three canonical coefficients for each variable show its contribution to the discrimination achieved by the three discriminant functions V1, V2 and V3. Wilks lambda is the test statistic applied to the results for each function, which allows its significance level (labelled P) to be determined. The standardised canonical coefficients (similar to the SCs in Table 6.5) show the relative effect of each variable on the result.

Variable P Canon. Coeff. Std. Canon. Coeff. V1 V2 V3 V1 V2 V3 P <0.001 0.07 0.03 −0.05 0.39 0.15 −0.26 S 0.06 0.13 −0.57 0.10 0.21 −0.92 H −0.04 −0.04 −0.01 −0.73 −0.74 −0.24 T <0.001 −0.27 0.04 0.01 −1.09 0.16 0.05 CP −0.04 0.00 0.02 −0.16 −0.01 0.07 CS −0.01 −0.11 0.37 −0.03 −0.22 0.74 CH 0.02 0.05 0.02 0.44 0.89 0.32 CT 0.19 0.07 0.04 0.62 0.23 0.14 RF 0.01 −0.03 −0.17 0.02 −0.07 −0.47 WD 0.021 0.00 0.00 0.00 −0.33 0.44 0.01 CWD 0.00 0.00 0.00 −0.06 0.17 0.19 DCF 0.00 0.05 −0.17 −0.01 0.16 −0.59 DR 0.00 −0.14 −0.07 0.03 −0.71 −0.36 DT 0.003 0.03 −0.01 0.00 0.30 −0.07 −0.04 Intercept 0.06 0.13 −0.57 W. lambda 0.491 0.892 0.958 P <10−5 0.623 0.718

The levels predicted by the discriminant function over 195 nights are compared with the observed levels in Table 6.7. The results show that the discriminant function successfully predicted the actual level on 117 nights or 60% vs. 25% for random prediction.

262 Table 6.7: Levels predicted by the discriminant function over 195 nights vs. observed levels. The predictions achieved 68/93 = 73% success for level 1, 32/74 = 43% success for level 2, 13/24 = 54% success for level 3, and 4/4 = 100% success for level 4. Overall the success rate was (68+32+13+4)/195 = 60%. If the predictions were made at random, each cell would contain 195/16 = 12.2 counts, giving a random success rate of 4x12.2/195 = 25%. The contingency coefficient for this table is C = 0.60, for which P < 10−15.

Actual Predicted Count Count 1 2 3 4 Total 1 68 16 2 7 93 Level 1, N ≤ 30 2 16 32 13 13 74 Level 2, 31- 90 3 0 6 13 5 24 Level 3, 91 – 147 4 0 0 0 4 4 Level 4, >147 Total 84 54 28 29 195

6.9.4 Principal Components Analysis (Moths) Unlike the previous three methods that predict moth numbers or level of numbers, principal components analysis (PCA) identifies the main components that underlie the weather variables. It begins with a correlation matrix between all possible pairs of weather variables as shown in Table 6.8.

263 Table 6.8: Correlations (r x 100) between each pair of weather variables during the moth periods. Total variables = 14. The bottom two lines help to identify the main correlations and are not part of the matrix. Mean maximum |r| = 0.45.

P S H T CP CS CH CT RF DR WD CWD DCF DT P Atmos press −22 12 −35 39 −14 −4 −13 −7 13 −15 −4 16 −9 S Wind speed −22 −37 14 2 59 −1 −10 3 7 6 1 3 10 H Rel humidity 12 −37 −39 −8 −14 38 −22 37 −37 7 8 −8 −17 T Temperature −35 14 −39 −29 16 −9 43 1 −5 −16 8 −23 7 CP Change in P 39 2 −8 −29 −18 −19 −51 −9 3 2 −5 −4 −4 CS Change in S −14 59 −14 16 −18 −13 13 6 2 3 10 2 −4 CH Change in H −4 −1 38 −9 −19 −13 −37 31 −2 −12 −10 5 8 CT Change in T −13 −10 −22 43 −51 13 −37 −13 2 0 10 −4 6 RF Rainfall −7 3 37 1 −9 6 31 −13 −29 3 6 −14 1 DR Ds after RF 13 7 −37 −5 3 2 −2 2 −29 −32 −15 43 32 WD Wind direc −15 6 7 −16 2 3 −12 0 3 −32 27 −18 23 CWD Ch in WD −4 1 8 8 −5 10 −10 10 6 −15 27 −13 −12 DCF Ds after cf 16 3 −8 −23 −4 2 5 −4 −14 43 −18 −13 −6 DT Ds after tr −9 10 −17 7 −4 −4 8 6 1 32 23 −12 −6 Max Correl (+) 39 59 38 43 39 59 38 43 37 43 27 27 43 32 Max Correl (−) −35 −37 −56 −39 −51 −18 −37 −51 −29 −37 −48 −15 −23 −17

The results of Table 6.8 show that each variable is appreciably correlated with at least one of the other variables (Gleason-Staelin redundancy measure is 0.29). Thus the mean maximum |r| for 14 variables is 0.45, range 0.27 to 0.59, which indicates that each variable contributes something to the overall weather conditions, so none should be omitted. Accordingly, the entire matrix was submitted to PCA. A scree plot (Cattell, 1966) of the first ten components is shown in Figure 6.18, which suggests restricting the PCA to two components. The PCA results for two components are shown in Figure 6.19.

264

Figure 6.18: Scree plot of the first ten components of the moth period PCA. The first trend line shows the initial trend, and the second trend line shows the trend of the ‘scree’. Their point of intersection indicates the number of components to extract, in this case two.

Figure 6.19: Plot of component loadings for the moth periods when the PCA is restricted to two components. The variables most relevant to each pole are circled.

The results of Figure 6.19 show that the variables tend to fall into four clusters, each defining a pole of the two components. In terms of the variables with the highest loadings, Component 1 runs from (days since cold fronts, days since rain) on the left to (humidity, rainfall, wind direction) on the right, or simplistically from dry to wet. Component 2 runs from (temperature, change in 265 temperature) at the top to (pressure, change in pressure) at the bottom. In Figure 6.19 pressure correlated –0.35 with temperature, so simplistically Component 2 runs from hot to cold.

As we shall see, the PCA analysis for locusts produced four components (see Section 6.10.4), so to allow comparison with locusts the PCA analysis for moths was repeated with four components, which subsequently gave the clearest and most even picture when compared to 3-6 components, see Table 6.9. The four components with their main contributing variables are shown below in order of magnitude together with their interpretation. The loadings of each variable on the four components are shown in Table 6.8. − Component 1 (WD, −DR, −DCF). Approaching troughs or cold fronts that bring rain. − Component 2 (−CP, CT, T, −P). Changes in temperature and pressure, possibly due to contact with a trough or cold front. − Component 3 (−CH, −H, −RF, CT, DR). Humidity, recent rain, moisture content. − Component 4 (−S, −CS, H). High and increasing wind.

As expected, the four components reflect the two-component results shown in Figure 6.19. Thus the strong dependence on temperature and change of temperature in the two-component plot of Figure 6.19 is still evident in Component 2 where they are the second and third strongest loadings in Table 6.10.

266 Table 6.9: A summary of the component structure when PCA is used to extract 2-6 components from the moth periods. Variables are included in a column if their loading is > 0.4. Column labelled 2: The entries are either 1 or 2, indicating that the variables conform well to a two-component structure (as confirmed by Figure 6.19). On moving across the other columns, components are added up to the limit at the top of each column, sometimes with each component evenly represented and sometimes not. For >2 components, the clearest and most even picture is given by 4 components, the same four components that are identified and interpreted in the text.

Number of Components Variables 2 3 4 5 6 P 2 2 2 2 2 S 2 2 4 4 4 H 1, 2 1, 3 3, 4 1, 3 1, 3 T 2 2 2 2 1, 2 CP 2 2 2, 4 2 2 CS 2 2 4 4 CH 3 3 3 3 CT 2 2, 3 2, 3 2, 3 2, 3 RF 3 3 3 3 DR 1 1, 3 1, 3 5 5 WD 1 1 1 1 1, 5 CWD 5 DCF 1 1 5 5 DT 5 6

267 Table 6.10: Loading of each variable on four components obtained by PCA of the moth periods. (These results are to allow comparison with the corresponding locust results of Table 6.16). Asterisks indicate loadings greater than 0.4.

Component Variables 1 2 3 4 P −0.01 −0.56* 0.20 0.38 S −0.072 −0.05 0.00 −0.88* H 0.40 −0.16 −0.62* 0.47* T −0.11 0.72* 0.13 −0.23 CP −0.03 −0.76* 0.15 −0.12 CS 0.19 0.11 0.08 −0.63* CH −0.21 −0.05 −0.75* 0.09 CT 0.13 0.73* 0.46* 0.17 RF 0.16 0.08 −0.69* −0.09 DR −0.53* −0.17 0.43* 0.04 WD 0.74* −0.10 0.1 −0.19 CWD 0.40 0.13 0.04 −0.15 DCF −0.42* −0.24 0.17 0.13 DT 0.01 0.01 0.15 −0.14

When (number of insects)1/4 is included in the two-component PCA shown in Figure 6.19, it loads most strongly (0.75) on Component 2 where it aligns with temperature (that is, it appears on the plot near the temperature end of Component 2) and is opposite atmospheric pressure. When (number of insects)1/4 is included in the four-component PCA shown in Table 6.10, it loads most strongly, albeit moderately (0.26), on Component 2, changes in temperature and pressure possibly due to contact with a trough or cold front. Both results are consistent with the results of the previous bivariate, regression and discriminant analyses.

268 6.10 Results of Plague Locust Analyses

The analyses treat the three locust periods totalling 151 nights as a single sample and compares the 4th root of the number of insects (adjusted as in Table 6.2) observed each night between 2000 and 2200 h with 13 weather variables, both separately and together, using the same statistical techniques as for the moth periods. The aim is to discover the extent to which each weather variable affects nightly locust numbers.

Locusts and moths are active mainly during different seasons, so we cannot assume that the effects of weather will be identical in both cases. Also, other differences will complicate their comparison – locusts feed on pasture, moths do not; which can upset comparisons based on rainfall; locusts are known to migrate regardless of wind direction, forming a 'migratory circuit' (see Section 1.6.1 in Chapter 1) that in effect enlarges their source area, whereas the same is not known to apply to moths. Finally, fewer variables were included for the locust period, which will necessarily limit a direct comparison.

6.10.1 Bivariate Correlation (Locusts) The correlations between the 4th root of nightly insect numbers and each of the 13 weather variables were calculated. Point-biserial correlation coefficients were calculated for the three dichotomous variables (those with a value of either yes or no). The results are shown in Table 6.11. The highest and most individually significant (P = 0.0001) correlation was with rainfall (r = −0.31). Also individually significant (P < 0.05), although too small to be useful, were the correlations with wind speed (r = 0.20), temperature (r = 0.19), change in humidity (r = −0.19), and change in temperature (r = 0.17). When the significance level for the highest correlation (rainfall) is corrected for the number of tests, it is still highly significant (corrected P = 0.001). However, the strength of this relationship is very dependent on the two extreme values (r drops to −0.15 when the two nights with rainfall of 25 mm are excluded). The

269 scatterplot for rainfall is shown in Figure 6.20. Overall the locust period results show weaker relationships with the environmental variables than those for the moth period shown in Table 6.4.

Table 6.11: Pearson correlation coefficient (r) or point-biserial correlation coefficient 1/4 (rpb) between (number of insects) and 13 weather variables during locust periods. N = 151 nights. Two-sided significance levels (P) are given if < 0.20.

Variable r P P Atmospheric Pressure −0.11 0.18 S Wind Speed 0.20 0.01 H Relative Humidity −0.06 T Temperature 0.19 0.02 CP Change in Pressure 0.02 CS Change in Wind Speed 0.09 CH Change in Humidity −0.19 0.02 CT Change in Temperature 0.17 0.04 RF Rainfall in previous 24 hours −0.31 0.0001 DR Days since rainfall > 0 mm −0.05 WD Wind Direction −0.11 0.18 CWD Change in Wind Direction 0.03 RD* Rain in previous 24 hours −0.11 0.18

* point-biserial correlation coefficient (rpb), for which the weather variable is yes/no.

Figure 6.20: 4th root of the nightly number of insects observed by the IMR during the locust periods vs. rainfall. There were only two nights where rainfall = 25 mm.

270 6.10.2 Multiple Regression (Locusts) The data for the locust periods were analysed in a similar manner to that for the moth periods (Section 6.9.2). The results are shown in Table 6.12 in terms of three models. Model 1 involves all 13 variables. Model 2 involves only those variables whose inclusion increased the R2 value by at least 0.001, which reduced the number of variables to 8. Model 3 involves only those variables whose inclusion increased the R2 value by at least 0.03, which further reduced the number of variables to 4. The resulting equation for Model 3 is 1/ 4 = − − NL 0.212 0.018CH+0.029H+0.198S+0.089T (6.7) where CH and H are measured in %, S in ms−1, and T in ºC.

As shown in Table 6.12, R2 for this equation is 0.188, which means that the four variables account for only 18.8% of the variation in 4th root of the observed locust numbers. The corresponding r is 0.43, considerably smaller than the r of 0.69 observed for moths.

As shown by the standardised coefficients in Table 6.12, the variable with the greatest influence is humidity H, which has about 1.3 times the effect of night temperature T, 1.6 times the effect of wind speed S, and 2.1 times the effect of changes in humidity CH. Of these, only temperature T was among the three variables with the greatest influence on moth numbers (the other two were atmospheric pressure P and days since rain DR).

271 Table 6.12: Multiple regression analyses of the (number of insects)1/4 and weather variables for the locust periods. The three models are described in the text. P is the significance level of the regression coefficient by two-tailed t-test. SC is the change in the (number of insects)1/4 in standard deviations caused by a change of one standard deviation in the weather variable.

Model 1 Model 2 Model 3 Variable Coeff. P Coeff. P SC Coeff. P SC CH −0.017 0.131 −0.016 0.021 −0.200 −0.018 0.008 −0.217 CP 0.081 0.171 0.054 0.288 0.086 CS −0.042 0.507 −0.046 0.451 −0.072 CT 0.008 0.889 CWD 0.001 0.457 DR 0.019 0.568 H 0.040 0.000 0.037 0.000 0.567 0.029 0.000 0.449 P −0.019 0.619 RD (Y/N) 0.234 0.541 RF −0.098 0.464 −0.175 0.073 −0.161 S 0.262 0.001 0.252 0.000 0.361 0.198 0.000 0.284 T 0.100 0.011 0.107 0.000 0.415 0.089 0.002 0.345 WD 0.001 0.323 0.002 0.089 0.141 Intercept 17.140 −1.497 −0.212 R2 0.246 0.236 0.188

The 4th root of the number of insects predicted by Model 3 for the 151 nights of observations is compared with the 4th root of the actual number in Figure 6.21. The relationship is somewhat less strong than it was for the moths in Figure 6.17 (r = 0.43 vs. r = 0.69).

272

Figure 6.21: 4th root of the predicted number of insects vs. 4th root of the actual number of insects for 151 nights of observation during the locust periods. The correlation is r = 0.43 (i.e. √R2 where R2 = 0.188 see Table 6.12), for which P < 10–7.

6.10.3 Discriminant Analysis (Locusts) Discriminant analysis was applied to the locust period using the same method as for the moth period (Section 6.9.3). Suitable levels were determined by inspection of the distribution shown earlier in Figure 6.14. Again, four levels seemed sufficient, as follows. N = number of cases (see Table 6.14). 1. Up to 200 individuals, N = 45 2. 201 - 800 individuals, N = 71 3. 801 - 1800 individuals, N = 29 4. More than 1800 individuals, N = 6 The results for 12 weather variables are shown in Table 6.13. These results show that only the first discriminant function was significant (P = 0.037), so the other two (P > 0.8) can be discarded. Overall, only one of the 12 variables had a significant effect (P < 0.05) on the discrimination, namely wind speed S with temperature T and rainfall RF next. The standardised canonical coefficients (indicating which variables have the greatest proportionate effect on the result)

273 show that humidity H and temperature T had more effect than wind speed S (which is consistent with the regression results), with rainfall RF and wind direction WD next, even though they failed to reach significance.

Table 6.13: Discriminant analysis results for the locust periods. Two-sided significance levels are shown if P ≤ 0.05. The three canonical coefficients for each variable show its contribution to the discrimination achieved by the three discriminant functions V1, V2 and V3. Wilks lambda is the test statistic applied to the results for each function, which allows its significance level (P) to be determined. The standardised canonical coefficients (similar to the SCs in Table 6.12) show the relative effect of each variable on the result.

Variable P Canon. Coeff. Std. Canon. Coeff. V1 V2 V3 V1 V2 V3 Constant −4.00 136.44 246.20 P −0.01 −0.14 −0.24 −0.03 −0.50 −0.88 S < 0.05 0.45 −0.32 0.07 0.72 −0.52 0.12 H 0.08 0.01 −0.01 1.49 0.29 −0.23 T 0.23 0.04 −0.19 1.10 0.20 −0.94 CP 0.10 0.09 0.30 0.22 0.21 0.68 CS −0.12 −0.01 0.19 −0.23 −0.02 0.35 CH −0.02 0.04 0.01 −0.25 0.58 0.13 CT 0.08 0.05 0.16 0.27 0.17 0.54 RF −0.22 −0.15 0.15 −0.50 −0.34 0.34 DR 0.00 −0.07 0.11 0.02 −0.28 0.43 WD 0.00 0.01 0.00 0.33 0.43 −0.06 CWD 0.00 0.00 0.00 0.24 −0.20 0.18 Constant −4.00 136.44 246.20 P 0.037 0.804 0.836 Wilk’s lambda 0.691 0.892 0.960

The levels predicted by the discriminant function over 151 nights are compared with the observed levels in Table 6.14. The results show that the discriminant function successfully predicted the actual level on 76 nights or 50%, vs. 25% for random prediction, considerably less than the 72% achieved for moths. But nearly all major outbreaks (>1800 individuals) were correctly identified.

274 Table 6.14: Levels predicted by the discriminant function over 151 nights of locust periods vs. observed levels. The predictions achieved 25/45 = 56% success for level 1, 35/71 = 49% success for level 2, 11/29 = 38% success for level 3, and 5/6 = 83% success for level 4. Overall the success rate was (25+35+11+5)/151 = 50%. If the predictions were made at random, each cell would contain 151/16 = 9.44 counts, giving a random success rate of 4x9.44/151 = 25%. The contingency coefficient for this table is C = 0.50.

Actual Predicted Count Count 1 2 3 4 Total 1 25 10 5 5 45 Level 1, N ≤ 200 2 14 35 13 9 71 Level 2, 201 – 800 3 7 6 11 5 29 Level 3, 801 – 1800 4 0 1 0 5 6 Level 4, >1800 Total 46 52 29 24 151

6.10.4 Principal Components Analysis (Locusts) Locusts and moths are active mainly during different seasons, so we cannot assume that the components that underlie the weather variables for both migration periods will be identical. Also, fewer variables were included for the locust period, which will necessarily limit a direct comparison. The correlation matrix on which the principal components analysis (PCA) is based is shown in Table 6.15.

275

Table 6.15: Correlations (r x 100) between each pair of weather variables during the locust periods. Total variables = 12. The bottom two lines help to identify the main correlations and are not part of the matrix. Mean maximum |r| = 0.58.

P S H T CP CS CH CT RF DR WD CWD P Atmos press −11 42 −60 32 −12 −2 −5 9 −20 −22 −7 S Wind speed −11 −5 2 0 57 −5 −3 3 −18 −16 −17 H Rel humidity 42 −5 −77 18 −2 28 −27 48 −46 −11 −7 T Temperature −60 2 −77 −23 12 −18 27 −36 23 1 10 CP Change in P 32 0 18 −23 −15 18 −41 26 −20 14 3 CS Change in S −12 57 −2 12 −15 −7 7 −1 −6 −8 −21 CH Change in H −2 −5 28 −18 18 −7 −78 35 0 17 6 CT Change in T −5 −3 −27 27 −41 7 −78 −38 10 −23 −10 RF Rainfall 9 3 48 −36 26 −1 35 −38 −37 0 −16 DR Ds after RF −20 −18 −46 23 −20 −6 0 10 −37 12 1 WD Wind direc −22 −16 −11 1 14 −8 17 −23 0 12 36 CWD Ch in WD −7 −17 −7 10 3 −21 6 −10 −16 1 36 Max Correl (+) 42 57 48 27 32 57 35 27 48 23 36 36 Max Correl (−) −60 −18 −77 −77 −41 −21 −78 −78 −38 −46 −23 −21

The results of Table 6.15 show that each variable is appreciably correlated with at least one of the other variables (the Gleason-Staelin redundancy measure is 0.26). Thus the mean maximum |r| for 12 variables is 0.58, range 0.36 to 0.78, which indicates that each variable contributes something to the overall weather conditions, in agreement with the corresponding results for the moth periods. Accordingly, the entire matrix was submitted to PCA. A scree plot of the first 10 components is shown in Figure 6.22 and suggests that four components exist. However, to allow comparison with the moth results, the PCA was first restricted to two components, with the results shown in Figure 6.23.

276

Figure 6.22: Scree plot of the first 10 components of the locust period PCA. The first trend line shows initial trend, and the second trend line shows the trend of the ‘scree’. Their point of intersection indicates the number of components to extract, in this case four.

Figure 6.23: Plot of component loadings for the locust periods when PCA is restricted to two components. The variables most relevant to each pole are circled.

The results of Figure 6.23 show that the variables tend to fall into four clusters, each defining a pole of the two components. In terms of the variables with the highest loading, Component 1 runs from (humidity, recent rainfall, pressure) on the left to (temperature, days since rainfall) on the right, or simplistically from

277 cold/wet to hot/dry. Component 2 runs from (wind direction, daily change in wind direction) at the top to (wind speed, daily change in wind speed) at the bottom, or simplistically from wind direction to speed. Other than the emphasis on wind direction and speed, the results have some resemblance to the two moth components (simplistically dry-wet vs. hot-cold).

When the PCA was expanded to four components as suggested by the scree test, a clear picture emerged. The four components with their main contributing variables are shown below together with their interpretation. As expected, they reflect the two-component results shown in Figure 6.23. The loading of each variable on the four components are shown in Table 6.16. − Component 1 (−P, T, −CP, −H, DR). High temperature, decreasing pressure and humidity. − Component 2 (CH, −CT, RF). Increasing humidity, decreasing temperature, recent rain. − Component 3 (S, CS). High and increasing wind speed. − Component 4 (−CP, −WD, −CWD). Decreasing pressure, stable wind direction.

278 Table 6.16: Loading of each variable on four components obtained by PCA of the locust periods. Asterisks indicate loadings greater than 0.25.

Component Variables 1 2 3 4 P −0.45* −0.23 0.01 −0.10 S −0.06 −0.03 0.58* −0.10 H −0.25* 0.12 −0.05 0.17 T 0.35* −0.01 0.01 −0.02 CP −0.27* −0.05 0.18 −0.42* CS 0.01 0.00 0.52* 0.00 CH 0.15 0.44* −0.06 0.02 CT −0.03 −0.36* −0.06 0.16 RF 0.01 0.34* −0.03 0.24 DR 0.63* 0.04 0.40* −0.17 WD 0.08 0.06 0.03 −0.41* CWD −0.06 −0.13 −0.04 −0.52*

When (number of insects)1/4 is included in the two-component PCA of Figure 6.23, it loads −0.34 on Component 2 and 0.07 on Component 1, aligning with wind speed S and opposing wind direction WD. The opposition to wind direction seems unremarkable because locusts are known to migrate on all wind directions, i.e. there is no preferred wind direction. When (number of insects)1/4 is included in the four-component PCA shown in Table 6.16, it loads the most strongly (−0.54) on Component 3, high and increasing wind speed. Both results are consistent with the results of the previous bivariate and multivariate analyses, for which one important variable was wind speed.

279 6.10.5 Locusts and Rainfall Previous studies have found that plague locust migration can be triggered by rainfall (Hunter, 1982; Hunter & Elder, 1999; Hunter & Deveson, 2002), and at first sight the present data seem to support this influence. For example, the plot of insect numbers and rainfall during locust periods shown in Figure 6.24 suggests that locust numbers tend to vary according to rainfall. albeit not consistently. Similarly, the distribution of insect numbers (not numbers1/4) during locust periods shown in Figure 6.25 suggests that the higher numbers tend to be associated with proportionately more rainfall. For example >85% of migrations involving more than 800 individuals occurred on nights where the total rainfall in the previous ten days was greater than 10 mm.

Figure 6.24: Number of insects (5-point moving average) versus total rainfall in the previous 10 days (bars) for the locust periods in 1999, 2000 and 2001. Note that each year has a different vertical scale.

280

Figure 6.25: Distribution (number of insects)1/4 during locust periods. Black bars indicate nights where the rainfall in the previous days was more than 10 mm.

However, although the bivariate correlation between (number of insects)1/4 and rainfall RF was the highest of the correlations with weather variables shown in Table 6.11, it was negative (r = –0.31), which is in the wrong direction as well as being highly significant (P = 0.0001). The correlation with days since rain DR was also negative (–0.05) as was that with rain in the previous 24 hours (−0.11) although neither was significant. In the multiple regression analysis rainfall was also negative (−0.098), although rain the previous day (yes/no) was now positive (0.23), as was humidity (the most effective of the top four variables). Rainfall was also a moderately strong positive component in the four-component PCA, loading 0.34 on Component 2 (humidity, decreasing temperature, recent rain).

In other words, rainfall emerges with both negative and positive effects. What could cause these inconsistent results? One possible explanation is that, when it is occurring, rainfall suppresses both migration and the IMR observation of this suppression, thus preventing a consistent relationship from emerging. On the other hand, such an effect was not evident in the moth results, where days since rain DR (but not rainfall RF) was in the top three variables, but this may merely

281 reflect their reduced sensitivity to immediate pasture conditions - locusts and caterpillars need to feed on pasture but moths do not.

Alternatively, it seems possible that the rainfall variable RF (mm in previous 24 hours taken from daily rainfall maps of the study area) was unrepresentative of the rainfall pattern needed to stimulate locust migration. Or perhaps the rainfall was too patchy in the takeoff area upwind of the IMR.

Consequently further analyses were undertaken using a threshold model with interaction, i.e. a model that attempts to predict migrant numbers once sufficient rain has fallen to stimulate takeoff. First, from inspection of Figure 6.24, the threshold for total rainfall over the previous ten days was set at 10 mm (finer discrimination was not possible because rainfall values were available only to the nearest 5 mm). Nights were then excluded where rainfall in the previous ten days was less than 10 mm, which reduced the dataset size by 47% to N = 71. Multiple regression was then applied to the remaining data with the addition of the following variables, making a total of 20 weather variables: RF(+5) - Rainfall in the following five days (mm). RF(+10) - Rainfall in the following ten days (mm). RF(-5) - Rainfall in the preceding five days (mm). RF(-10) - Rainfall in the preceding ten days (mm). RF(C9) - Rainfall in the preceding and following four days (mm). RF(>5) - Rainfall in the preceding day was greater than 5 mm. RF(>10) - Rainfall in the preceding day was greater than 10 mm.

The results of the regression analysis are shown in Table 6.17. The R2 value of for Model 3 (6 variables) was 0.378, twice the R2 value previously obtained (0.188 for 4 variables). The regression equation was: 1/ 4 = − + + − − − + + NL 76 0.028H 0.073 P 0.092 RF 0.015 RF ( 10) 0.198ST 0.185 (6.8)

282 Table 6.17: Multiple regression analyses of the (number of insects)1/4 and weather variables for the locust periods after excluding nights where rainfall in the previous ten days was less than 10 mm. Model 1 involves all 20 variables. Model 2 involves only those variables whose contribution to R2 exceeded 0.01, which reduced the number of variables to 8. Model 3 involves only those variables whose contribution to R2 exceeded 0.03, which further reduced the number of variables to 6. P is the significance level of the regression coefficient by two-tailed t-test. SC is the change in the (number of insects)1/4 in standard deviations caused by a change of one standard deviation in the weather variable.

Model 1 Model 2 Model 3 Variable Coeff. P Coeff. P SC Coeff. P SC CH −0.002 0.907 CP 0.092 0.251 0.105 0.084 0.214 CS −0.040 0.663 CT 0.033 0.712 0.058 0.147 0.189 DR −0.018 0.830 WD −0.072 0.536 CWD 0.064 0.410 H 0.028 0.173 0.028 0.024 0.515 0.028 0.024 0.515 P 0.031 0.637 0.073 0.110 0.203 RD 0.275 0.646 RF −0.190 0.013 −0.136 0.018 −0.529 −0.092 0.008 −0.358 RF(+10) 0.006 0.855 RF(+5) 0.037 0.267 RF(−10) −0.009 0.441 −0.010 0.236 −0.149 −0.015 0.080 −0.224 RF(−5) 0.034 0.037 RF(C9) −0.031 1.000 RF(>10) −0.737 0.438 −0.835 0.284 −0.225 RF(>5) −0.308 0.719 S 0.236 0.066 0.202 0.014 0.284 0.198 0.017 0.278 T 0.186 0.024 0.165 0.003 0.624 0.185 0.001 0.701 Intercept −33.745 −1.100 −76.011 R2 0.430 0.401 0.378

As shown by the standardised coefficients in Table 6.17, under Model 3 the variables with the greatest influence in this revised regression are temperature T and humidity H; next are total rainfall RF, wind speed S, total rainfall in the previous 10 days RF(−10), and atmospheric pressure P. The two rainfall items are negative (the rest are positive), which implies that once sufficient rain has fallen to promote takeoff, further rain is counterproductive. This would explain

283 why, in the original multiple regression analysis (Model 1), rainfall in previous 24 hours RF was negative (coefficient −0.098) while rain the previous day RD (yes/no) was positive (0.234). Thus the main influence of rainfall on locust migration appears to be a threshold influence only.

6.11 Discussion

The results show that the use of IMRs enables studies of weather effects on insect populations flying at altitudes of up to a kilometre or more. The present study has confirmed a diversity of relationships that were previously known such as the dominant effect of temperature, and has uncovered at least one not previously known, namely a rainfall threshold effect for locusts. As predicted in Section 6.10, the results for moths and locusts often differed for what seems like straightforward reasons. The need to divide the data into calibration and validation subsets to avoid spurious results due to chance fluctuations was tested in Section 6.9.2 (equations 6.5 and 6.6). Such a division might be counterproductive unless the subsets were well matched, which (given the number of variables) would be difficult to achieve, especially as the number of nights was not large enough to both estimate the regressions and independently validate them, at least not without introducing worse spuriousness due to small sample sizes. Fortunately the test indicated that spurious results were unlikely to be a problem. The following subsections discuss in turn the results for moths, locusts, moths vs. locusts, thresholds, year-to-year variations, and the advantages of IMRs over trapping methods.

6.11.1 Discussion: Tests of Moth Hypotheses The hypotheses tested for the moth periods, and the outcome by four methods of analysis, are compared in Table 6.18, which groups them according to the location of the variables on the four-component PCA. The results of Table 6.18 show good agreement between the major outcomes of the four methods of analysis, which (since the same data are being analysed in each case) is not unexpected. Thus the variables found to be the most important by one method

284 (for example temperature T and atmospheric pressure P) are found to be the most important by the other methods. Where there are differences they are generally limited to borderline variables such as wind direction WD.

Since temperature T and atmospheric pressure P are also associated with the synoptic variables troughs and cold fronts, an association with these synoptic variables might be expected. However, as pointed out in Section 6.6.2, troughs could not be timed precisely enough, and were too infrequent for the results involving measures such as days since trough DT to be meaningful. For example, the 14 troughs in the moth periods were not consistently followed by either high or low moth numbers, but one trough in 1998 and three in 2001 happened to be followed by very high moth numbers. Consequently the regression analysis revealed a strong effect for a variable representing one-day- since-trough, which was strong enough to persist along with temperature and pressure into Model 3 but arose from just four exceptional values. Cold fronts were somewhat more numerous, although the timing of them was still imprecise, and as shown in Section 6.6.2 their effect tended to be in the predicted direction, an outcome that is also reflected in Table 6.18.

Taken together, these findings indicate that migration tends to take place in the warm low-pressure airflows preceding a cold front, which is in agreement with the observations of Drake and Farrow (1985) and Gregg et al. (1994), and with the expectancy that low temperature might inhibit takeoff, even though the reported temperature threshold for takeoff is a low 3-11ºC. Cold fronts would seem to have an effect beyond that of the associated changes in temperature and wind direction, simply because of the associated wind convergence, updrafts, and shovelling effects described in Section 6.2.4, but the precise outcome will depend on the particular case.

The correlation between temperature T and pressure P, and between T and changes in pressure CP, are −0.35 and −0.29 respectively (Table 6.8), which is 285 consistent with warm air being associated with low pressure. Normally one would expect warm air to be associated with anticyclones and therefore with high pressure, but here the analysis is evidently reacting to the change accompanying a cold front, which, significantly, can be accompanied by the shovelling of insects into concentrated layers mentioned above, a point that is supported by the negative correlation with wind direction (–0.16). So this may be an example of how traditional meteorological expectations can be upset by the particular mechanisms of insect migration.

The rain-related variables have a weak negative correlation with insect numbers (Table 6.4, r = −0.02 for rainfall in previous 24 hours RF and r = −0.13 for relative humidity H). Nevertheless the discriminant analysis (Table 6.6) shows H to be a good discriminator. This is explained by the intercorrelations (Table 6.8), which show that H is inversely related to temperature T (r = −0.39), and by the PCA results (Figure 6.19) which show that H and T have opposite signs on both Components 1 and 2. In other words high temperature, low pressure, and low humidity tend to occur together, and it is these conditions that promote moth migrations. Moths tend to stay put when it is cold and damp.

The wind-related variables have a generally weaker effect than expected. Wind speed S was strongly correlated (r = 0.59) with changes in wind speed CS (Table 6.8), showing as expected that very windy days tend to follow less windy days, and was independent of wind direction WD (r = 0.06) and changes in wind direction CWD (r = 0.01). Nevertheless S and WD loaded on Component 1 in opposite directions (Figure 6.19), suggesting that wind tended to be effective only if it was in the right direction, either to favour migration or to favour flight over the IMR, both of which may be no more than a logical consequence of the dependence on insect numbers to give positive results.

286

Table 6.18: Moth periods. Summary of weather hypotheses vs. outcomes by four methods of analysis. The weather variables have been grouped according to their loading on the components of a two-component PCA. From left to right the columns are: (1) Hypothesis from Table 6.1 where the relationship with the weather variable is predicted to be: + positive, − negative, ? uncertain, x none. (2) Bivariate correlation r from Table 6.4. (3) Regression standardised coefficients from Table 6.5 model 3. (4) If the weather variable or a related variable is among the most effective discriminators (SCC/V1 >0.35) from Table 6.6, this column identifies them. Thus H, CH means these variables discriminated well between moth numbers. Entries in parentheses indicate less effective variables (SCC/V1 = 0.30−0.35). (5) Location of the variable on the two- component PCA shown in Figure 6.19. Thus 1+ or 1− means the variable tends towards the positive or negative poles of component 1. ? = no clear tendency. (6) Whether the hypothesis is confirmed by 2 or more of the 4 results yes/no. ? = hypothesis uncertain, nevertheless weak = small effect.

Moth Periods Corr Regr Best 2comp Hypoth Weather Variable Hypoth. r SC Discr PCA conf? 1 2 3 4 5 6 Relative Humidity H + –0.13 H,CH 1+ Yes Rain in previous 24h RF ? –0.02 1+ ? Wind Direction WD ? 0.02 (WD) 1+ Weak

Days since rain DR – –0.17 –0.11 1− Yes Days since Trough DT + –0.07 (DT) 1− ? Days since Cold F DCF + 0.12 1− Weak

Temperature T + 0.59 0.48 T,CT 2+ yes Wind Speed S + 0.17 2+ weak

Atm. Pressure P ? –0.52 –0.34 P 2− yes

287 6.11.2 Discussion: Tests of Locust Hypotheses The hypotheses tested for the locust periods, and the outcomes by four methods of analysis (of which one, regression, had two variants), are compared in the same way as they were for the moth periods Table 6.19. This time there are only six variables because there were insufficient days to allow synoptic variables to be tested. As with the moth periods, the variables found to be the most important by one method (for example temperature T and wind speed S) are found to be the most important by the other methods. But unlike the moth periods, the relationships between the other variables tend to be less clear-cut, or at least more complicated.

The variables with the strongest effects are temperature T (positive), relative humidity H (interpreted as positive from the standardised coefficient (0.52) rather than the much weaker bivariate correlation (−0.06)), and recent rainfall RF (negative). As already noted in Section 6.10.4, the opposite effects of H and RF became stronger and more consistent when days with <10 mm rain were excluded, which implies that rain has a threshold effect. That is, once sufficient rain has fallen to promote takeoff, further rain has no effect. The positive effect of rain is in agreement with the observations of Clark (1969), Hunter (1982), Hunter and Elder (1999), and Hunter and Deveson (2002), but the threshold effect is a new finding.

Temperature T was strongly inversely correlated with pressure P (Table 6.15, r = −0.60), more so than in the moth periods (r = −0.35), which suggests the same situation, namely that these results are consistent with airflows preceding cold fronts that were found to be associated with migration by Clark (1969 and 1971) and Drake and Farrow (1983).

Wind direction WD and wind speed S have moderate but opposite effects, and are at opposite ends of Component 2, which opposition is unremarkable for the 288 reasons outlined in Section 6.10. Here the effect of wind speed is positive if the wind is towards the north (see Figure 7.9 in Chapter 7 which shows the majority of migrations in this data heading north), which is consistent with previous observations of northwards migration on winds from the south (Drake and Farrow, 1983). In other words the conditions that promote locust migration are high temperature, high humidity, and good winds. Locusts tend to stay put when it is cold, dry, and calm.

In Table 6.19, with one clear exception, all hypotheses for the locust periods were confirmed, two strongly and three weakly, showing that the results were generally consistent with previous observations and with reasonable assumptions. The exception was that no relationship was expected for humidity whereas a strong positive relationship was found. The hypothesis that rainfall in the previous 24 hours RF would have a positive effect on insect numbers emerged as a threshold effect rather than the predicted quantitative effect. The column labelled 'Reg2' shows that the threshold data improved the relationship not only with rainfall but also with the other variables, while remaining largely consistent with the full regression in the column labelled ‘Regr’. No clear link with rainfall RF was observed for the moth periods, nor was one predicted.

Table 6.19: : Locust periods. Summary of weather hypotheses vs. outcomes by four methods of analysis. The weather variables have been grouped according to their loading on the components of a two-component PCA. Column descriptions are as for Table 6.18. Column sources are (1) Table 6.1, (2) Table 6.11, (3) Table 6.12 model 3, (4) Table 6.13, (5) Figure 6.23, (7) Table 6.17. In column 6, 'thresh' = threshold effect.

Locust Periods Corr Regr Best 2comp Hypoth Reg2 Weather Variable Hypoth r SC Discr PCA conf? SC 1 2 3 4 5 6 7 Temperature T + 0.19 0.35 T 1+ yes 0.70

Relative Humidity H x –0.06 0.45 H 1– no 0.52 Rain in previous 24h RF + –0.31 RF 1– thresh –0.36 Atm Pressure P ? –0.11 1– weak 0.20

Wind Direction WD + –0.11 (WD) 2+ weak

Wind Speed S + 0.20 0.28 S 2– yes 0.28 289 6.11.3 Discussion: Moths vs. Locusts Some individual comparisons of moth vs. locust results have been briefly noted in the previous section. But how do they compare overall? In both cases the best single predictor of insect numbers was temperature, which is consistent with the previous studies of temperature summarised in Section 6.2. Both showed a moderate dependence on wind speed and direction, which may reflect the mechanism suggested by Riley & Reynolds (1997), namely that when heavy rain does not automatically lead to outbreaks (as is the case here), the occurrence of winds allowing access to rainfall areas may be critical. Since (as far as is known) only locusts have a 'migratory circuit' that leads to migrations on any wind direction, one might have expected to see a clear difference in the wind results for moths and locusts, but none was observed, possibly because the sampling windows were too short (and too localised at particular times of the year) to adequately sample the full range of existing flight behaviours.

The above preferences were reflected in the best discriminators based on standardised canonical coefficients, which for moths were T, H, and P, and for locusts were H, T, S, and RF. The differences between the moth and locust results seem to largely reflect the difference in season, namely cool calm conditions (moths) vs. hot windy conditions (locusts), even though the difference in wind conditions seems characteristic of these datasets only, see Section 6.4. Nevertheless the analyses confirm that temperature and moisture are collectively important in determining the migratory conditions for both moths and locusts. Moths tended to prefer dry conditions while locusts tended to prefer damper conditions (but not too damp). The order of their relevance in any particular case will most likely depend on the insect species, the area, and the season.

290 6.11.4 Discussion: Thresholds The thresholds that could be identified were limited by the weather conditions that happened to exist during the study period, and in many cases only a range of values consistent with flight were observed rather than actual thresholds. The results are summarised in Table 6.20.

Table 6.20: Lower and upper thresholds for insect flight observed in the present work. Where specific thresholds could not be identified, the table shows (in parentheses) the range of values within which flight was observed, see Figure 6.5 and Figure 6.6. It seems likely that flight could occur outside the ranges shown, but the relevant observations were not available.

Weather Variable Spring Moths Plague Locusts Temperature (7 - 30°C) (19 - 41°C) Humidity (13 – 97%) (12 – 97%) Pressure (1001 – 1029 hPa) (1001-1019 hPa) Wind Speed (0 - 9.2 ms-1) (0.5 - 9.8 ms−1) Rainfall none > 10mm in previous 10 days

For moths the minimum temperature did not reach the previously found lower threshold (3ºC), there was no evident upper or lower humidity threshold, and the upper speed at which flight was observed can be increased from the 3.6 ms-1 reported by Drake and Farrow (1985) to 9.2 ms−1 (33 kph) as measured at a height of 2 m.

For locusts no lower temperature threshold was found at temperatures down to 19ºC, there was no evidence of an upper or lower humidity threshold, or of the upper wind speed threshold of 6.4 ms−1 reported by Clark (1969 and 1971). Consistent with previous studies (e.g. Hunter, 1982) rainfall >10mm in the previous 10 days was important for large-scale locust migration, as was high humidity, but higher rainfall tended to inhibit migration. These rainfall effects may be a result of moisture being required for the vegetation growth that allows locusts to mature their eggs and oviposit (Hunter, 1982; Hunter & Elder, 1999).

291 6.11.5 Discussion: Effects of Weather on Year-to-Year Variations in Migrant Numbers For spring moths three weather variables accounted for 47.5% of the variance in the 4th root of insect numbers. For locusts, once sufficient rain had fallen to stimulate takeoff, six weather variables accounted for 37.8% of the variance. For both moths and locusts it seems likely that weather conditions act in concert, first to provide conditions that induce takeoff, and second to encourage the surface food supplies required to support migration. One might therefore expect weather conditions to be generally predictive of variations in migration from year to year.

But how well do they perform in practice? How well can between-year variations in insect numbers (Table 6.2) be explained by differences in weather? Do weather differences support Zalucki & Furlong's (2005) premise (which included spring moths) that "climate, to a first approximation, is the major determinant of insect abundance and distribution"? Or Riley & Reynolds’s (1997) suggestion, based on desert locusts, that rainfall will have a (delayed) effect only if enough locusts can reach the rainfall area to begin gregarious breeding? As already noted, the strongest positive influence on moth numbers was temperature. The mean temperature in 2000 was 3ºC lower than during the other three moth years, which suggests that 2000 should have the lowest moth numbers. In fact they were larger than in 2001 (averaging 64 vs. 27). For the other important weather variables there were no consistent differences between years. So weather on its own seems unable to account for the observed between-year variations in moth numbers, at least not without including factors not considered here such as regional rainfall, rainfall in adjoining regions, and the particular stage in adjoining regions of insect population growth, although it will still trigger migration if population size permits.

292 For locusts the between-year variations are more easily explained. Thus the increase in locust numbers in 2001 compared with the previous two years can be explained by a significant increase in the proportion of days when it rained (35% vs. 20%, P < 0.05), which would increase the growth of vegetation and thus the opportunities for locusts to oviposit and mature their eggs, which in turn would increase their numbers, a point illustrated previously in Figure 6.24, and which is also consistent with Riley & Reynolds’s (1997) suggestion. Consistent with a threshold model there was no major difference in average daily rainfall between the three years (1.5, 1.6 and 1.1 mm/day for 1999, 2000 and 2001 respectively). Furthermore, as shown previously in Figure 6.6, the proportion of summer nights with temperatures >40ºC was appreciably higher in 2001 than during the previous two years, which would have further boosted locust numbers.

In summary, it seems self-evident that long-term prediction of insect migrations in any particular case (not just moths and locusts) will depend on the insect species, the area, the season, and the stage of population growth. Hints can be obtained from the behaviour of particular species, but the present work suggests it is unwise to assume that they will generalise to other species. In any case, conclusions can hardly be reached from an incomplete sampling of just three or four seasons. Among the issues that in hindsight seem pertinent yet remain unresolved are the effect of changes in the sampling window (here 2000- 2200 h), the effect of restricting the analysis to particular altitudes (here incompatible with the need for large sample sizes), and especially the effect of changing IMR location (similar long-term datasets were not available for the Thargomindah IMR). Nevertheless, as discussed in the next section, IMRs are probably the only practicable way of obtaining the long-term datasets needed to establish these types of relations.

293 6.11.6 Discussion: Advantages of IMRs over Trapping Methods Although IMRs may not allow the reliable identification of species if many species migrate at the same time, they do have distinct advantages over conventional trapping methods. No other method can measure migratory activity at altitudes of more than a kilometre. They are deliberately unresponsive to insects flying below 200 m, thus avoiding trivial near-ground flights that would contaminate trapping methods.

IMRs can also disentangle weather effects that upset trapping methods. For example moonlight can reduce light-trap catches by up to 50%, so light traps are unable to determine whether moonlight affects insect flight. Some trap- based studies claim to have found positive effects, but the four years of Bourke IMR data showed nothing significant. The previous chapter also found evidence of serious unreliability in light-trap performance.

Lastly, IMRs can operate unattended and continuously. They are non-invasive and therefore do not affect the results. Sample sizes are large, free of contamination, and are easily analysed. IMR construction costs are high but running costs are low, certainly very much lower than would be required for labour-intensive trapping methods returning similar sample sizes.

294 7 CORRELATIONS AND THE SCALE OF MIGRANT INSECT POPULATIONS

This chapter deals with correlations between IMR observations at different locations, and their relevance to estimating migration size and direction. Parts of this chapter are expanded from Dean & Drake (2002a) Monitoring migrations of agricultural insect pests with low-cost autonomous radars and Dean & and Drake (2002b) Properties of biotic targets observed with an X-band radar profiler and the potential for bias in winds retrieved from Doppler weather radars.

The value of an Australian IMR network depends on its ability to characterise insect movements over large areas. Theory and computer simulations suggest a simple relationship between observed correlations and the geometry of migrating populations. The characteristics of migrating populations (width, length, direction, speed) were investigated using 313 nights of data from two fixed IMRs 308 km apart, with a subset of 172 nights divided into seven gap-free periods for investigating autocorrelations, and 8 nights of hourly data from the two fixed IMRs and one mobile IMR variously in between. The results showed that the two fixed IMRs were sampling the same peak migration on roughly 50% of occasions, on which the migrations were about 600 km in width, and that peak migrations were up to 100 km in length on roughly 75% of occasions, and perhaps up to 200 km for the rest. A migrating population could be carried by the wind for 500 km or more in a single night. The few occasions on which two IMRs were aligned with the wind direction gave valuable insight into the relevance of flight times. Overall the results are consistent with those of previous studies and help to decide the optimum location of IMRs, for which a number of suggestions are made. The chapter ends with a discussion of reliability issues in light of the experience gained with the mobile IMR and especially with operating three IMRs together. The main original contributions in this chapter are the tests and results that occupy most of the chapter.

7.1 Introduction

The ultimate purpose of collecting insect movement data is to understand and predict the spatial dynamics of insect populations (Turchin, 1998). Thus the value of a network of fixed IMRs depends on its ability to characterise insect movements over large areas from observations at a limited number of sites.

For example, Gatehouse (1997) notes how the use of two ground-based radars aligned with wind direction makes it possible to follow migrations over long distances and thus estimate rates of dispersal during flight, but the normal day- to-day fluctuations in wind direction make alignment difficult to achieve, so in practice the number of such studies is small (he cites two). An airborne radar

295 would avoid alignment requirements by following the migration directly, but such radars are expensive to run and are therefore not suitable for long-term observations. Airborne radars have never been used in Australia.

In terms of detecting a migration of an assumed width, the optimum separation of two ground-based IMRs at right angles to the insect travel direction (their most sensitive position for monitoring width) will be similar to the migration width (see Figure 7.1). But how to accommodate the inevitable variations in migration width, position, and direction? How might the length and width of each varying migration be determined by ground-based IMRs?

Figure 7.1: Insect migration vs. IMR position for known migration direction and width. (a) IMRs close together miss much of the migration. (b) IMRs too far apart miss the migration altogether. (c) The optimum distance apart is similar to the migration width and at right angles to the migrant direction (assuming width and direction are sufficiently constant for the purpose).

In principle the determination of migration length and width might require dozens of equally-spaced IMRs operating simultaneously, which would be both impractical due to lack of sites with reliable power and phone communications, and prohibitively expensive. Therefore the aim of this chapter is to see whether inadequate tools (one mobile and two fixed IMRs) can nevertheless provide some estimate of migration sizes (width and length), their main direction, and the optimum location for IMRs. As in the previous chapter, the outcome is a large number of results that are brought together in the subsequent discussion. But first a brief excursion into theory.

296 7.2 Theoretical Calculations and Computer Simulations

Imagine a migrating population of insects approaching two IMRs A and B at right angles to the line joining them as shown in Figure 7.2. Let w = migration width and s = separation between IMRs. For detection at either IMR, the location of the migration can extend (laterally) over a distance w + s; for detection at both IMRs the distance is w – s (or 0 if w ≤ s). So, of the migrations that are detected by either IMR, a proportion (w-s)/(w+s) will be detected by both. For example, when w = 1s, 1.5s, 2s, 3s, 4s, this proportion is about 0, 0.20, 0.33, 0.50, 0.60, respectively.

Figure 7.2: Possible positions of a migrating insect population (grey bars) at two IMRs A and B simultaneously as a proportion of possible positions at A or B. s = separation between IMRs, w = population width (w ≥ s), x indicates edge of population in contact with A or B. Between first x and last x the distance is (w + s), during (w – s) of which both A and B are in contact with the population, so proportion is (w – s)/(w + s).

If the migrating population approaches the two IMRs not at 90º but at angle φ, the separation between IMRs becomes effectively s.sinφ. If all values of φ (i.e. all travel directions) are equally probable, the average proportion of occasions when both IMRs will be observing the same population will be the mean of (w – s.sinφ)/(w+ s.sin φ) over the range φ = 0-179º, provided that negative values of (w – s.sinφ), i.e. negative widths, which have no physical meaning, are replaced by zero. (The range 180-359º need not be included since it is merely reverses the 0-179º directions and therefore adds nothing to the outcome. Indeed, as explained shortly, 0-89º could replace 0-179º, but here 0-179º is easier to visualize.) As a useful rule of thumb the average proportion so

297 calculated is roughly equal to n/4 for n < 2 or (n – 1)/n for n > 2, where n = w/s, see Figure 7.3.

Figure 7.3: Average proportion of occasions when two IMRs separated by s metres are observing the same migrating insect population of width w metres, provided that the population is being detected by at least one IMR. Based on Figure 7.2 ith all travel directions φ being equally probable. (As described later in the text, the vertical axis turns out to be numerically equal to the mean correlation between observed insect numbers at the two IMRs.)

If n = 2 (so the migration width is twice the separation between IMRs), if all travel directions are equally probable, if the migration is uniform across its width, and provided the migration is detected by at least one IMR, it will be detected by the other IMR about one-half of the time.

Computer simulations that compared sets of random data representing insect counts from two IMRs A and B showed that correlation r would be observed if 1 in 1/r of the B counts were made equal to the A counts, as for example might occur if A and B were observing the same migration, regardless of how the counts were distributed (e.g. normal or uniform). For example a correlation of 298 r ~ 0.25 was observed if 1 in 4 of the B counts were made equal to the A counts, any difference between the observed r and an exact 0.25 being due to whatever correlation happened to exist between the remaining A and B counts. (Obviously if all counts are made equal then r = 1, and if all are made random then r ~ 0.) This means that if r is the observed mean correlation between two IMRs, then on average about 1 in 1/r counts are being observed at both IMRs, that is, 1/(1/r) = r is an estimate of the average proportion of occasions when both IMRs are observing the same population. Thus the vertical axis in Figure 7.3 is numerically equal to the observed mean r. Since our previous rule of thumb suggests that this proportion is roughly equal to n/4 or (n – 1)/n for values of n below or above 2 respectively, where n = w/s, it follows that r ~ n/4 or r ~ (n – 1)/n respectively, which on rearranging give w/s ~ 4r or w/s ~ 1/(1 – r) for values of r below or above 0.5 respectively, both surprisingly simple expressions for estimating w/s from r.

Unfortunately this simplicity comes at the expense of possibly unrealistic assumptions such as migration uniformity and (less obviously) by the requirement that no wind direction should automatically bring migrations to an IMR. If some winds violate this, the lateral edge of the migrating population cannot be defined, so neither can the width, which means the above expression is no longer valid for all occasions. On the other hand, the requirement that all insect travel directions be equally probable is less unrealistic than it may seem, because equal probability is required only of φ between 0º and 90º, not of travel directions between 0º and 360º, which means equal probability between 0º and 90º when the four quadrants of travel directions are superimposed, which tends to cancel out inequalities. Thus when the quadrants of the travel directions at Bourke and Thargomindah (shown later in Figure 7.10) are superimposed, their original non-uniformity largely disappears.

A more serious objection is the ambiguity of the observed r's. Given that insect counts show consistent seasonal variations, being high in summer and low in 299 winter, this would tend to produce a positive r between two IMRs even if they never shared the same migrating population. However, as shown later, this objection can be overcome by appropriate choice of test conditions.

The r to be used in the above expression is the r that would be observed if there was no dispersal of insects over the distance between the two IMRs. Dispersal of the migrating population between IMRs was simulated as follows. Instead of making, say, 1 in 4 of the B data equal to the A data, 1 in 4 was made equal to the A data x d, where d is a dispersing factor ranging from 0 (total dispersal, no insects from A reach B on that night) to 1 (no dispersal, all insects from A reach B on that night). This reduced the observed correlation to a value that was generally within 10% of dr provided the data means were similar. For example if d = 0.6 was applied to a simulation that was producing an observed correlation of r, the observed correlation fell to approximately 0.6 r. The correlation that would be observed if there was no dispersal is then (observed r)/d, which in this case is (0.6 r)/0.6. Allowing d to vary at random about its average value, e.g. by ± (1 – d), made only minor differences.

7.3 Previous Studies

Two VLR sites are in operation in the UK. One is at the Rothamsted agricultural research station near Harpenden about 35 km northwest of London, the other is at Chilbolton about 100 km to the southwest of Rothamsted. The sites were selected mainly for practical reasons − Rothamsted because much insect-monitoring data from suction and light traps was already available there, and Chilbolton because various meteorological instruments were based there. The two radars tend to show similar, but not identical, patterns (A.D. Smith personal communication 2006). The Chilbolton radar was previously at Malvern, 130 km west of Rothamsted, and comparisons of activity at the two sites have been made. For example, similar vertical distributions of insects occurred at both sites on some nights (Reynolds et al., 2005) and also during some early mornings (D.R. Reynolds personal communication, 2006). The 300 above results indicate that, in this part of the UK, simultaneous observations at VLRs 100-130 km apart can have qualitative similarities, which suggests that the associated insect populations could be of like dimensions.

In Australia, Symmons and Wright (1981) studied the severe 1979 outbreak of plague locusts and found that the major source area measured about 300 x 100 km with several smaller source areas measuring about 100 x 50 km. These areas are similar in size to the areas over which heavy rain can fall and which can be 300-500 km across. Such a similarity is to be expected because rainfall has a critical influence on insect numbers, both as a takeoff trigger and as a vegetation promoter. So the dimensions of a migrating population will tend to parallel the dimensions of the area over which rain has previously fallen.

Gregg et al. (2001) studied the migration of several moth species from inland Australia to an area just west of Bourke. The predicted fallout areas (regions where 90% of immigrant moths were predicted to land) for the two nights studied measured about 450 x 250 km and 800 x 350 km. When small numbers of insects are migrating individually rather than collectively, which is more typical of moths than of locusts (Rochester, 1999), the migration boundaries may be difficult to determine.

A single radar can observe flight direction, duration and density, and thus provide some estimate of population movement. For example Drake & Farrow (1983), using a scanning radar 300 km southeast of Bourke during November 1979, observed plague locusts originating up to 200 km away that, in terms of numbers crossing a line one kilometre wide, varied from about 30 to 3000 per second. But the estimation of actual migration boundaries requires some correlation between observations at two or more radars, which (assuming there are no confounding seasonal effects) will establish that the dimensions of the migration are at least comparable to the separation between radars. Given the substantial insect counts during locust and moth outbreaks, estimating the 301 migration boundaries with present IMR data should be straightforward. On the other hand, as shown in Figure 6.2 in Chapter 6, many outbreaks occur in areas distant from the two fixed IMRs, so the estimates thus obtained may not apply outside the present study area.

7.4 Present Approach

The Bourke and Thargomindah IMRs are fixed and cannot be moved, so two indirect approaches were used to estimate the scale of the populations observed and the distribution of their lengths and widths: 1. Correlating the observations made by the two fixed IMRs. A strong correlation would suggest that the IMRs are unnecessarily close as in Figure 7.1a, resulting in over-sampling. A weak relationship would suggest the opposite as in Figure 7.1b. 2. Using the mobile IMR to make observations at locations between the two fixed IMRs. A generally strong correlation with one of the fixed IMRs might suggest they are appropriately spaced as in Figure 7.1c.

7.4.1 Fixed IMR Data Used For Analysis The fixed IMR data used for analysis came from the Bourke and Thargomindah IMRs for each night that both the IMRs were operating during the period 1 September 1999 to 1 March 2001 (after which the Thargomindah IMR ceased operating). During this period the Bourke and Thargomindah IMRs operated on 83% and 77% of the 548 nights respectively with both IMRs operating on 313 or 57% of nights. A summary of the causes of missing data at Bourke is given in Section 2.11 of Chapter 2 and a summary of the processing procedure is given in Section 3.6 of Chapter 3. Due to the large volume of data involved, processing took several months and was carried out with the help of H. K. Wang using the C++ algorithm (see Section 3.6).

Many of the analyses involved tests of autocorrelation and crosscorrelation which requires data without gaps. However, only one period contained more

302 than 14 nights of gap-free data from both IMRs. Therefore gaps of only one night were filled by interpolation, which increased the number of such periods to seven as shown in Figure 7.4.

Using the classification scheme developed in Chapter 5 the predominant migratory insects during these seven periods were identified as spring moths (four periods), plague locusts (two periods) and mixed (one period). These periods, as detailed in Table 7.1, and subsequently termed 'gap-free periods', were then used for statistical analysis.

Figure 7.4: Distribution of the gap-free periods from 1 September 1999 to 1 March 2001 where data was acquired by both IMRs. Periods where gaps were limited to a single night are shown in white. Only periods of >14 nights (the final white bar on the right) were used for analysis. Details of these periods are shown in Table 7.1.

303 Table 7.1: Periods >14 nights used for analysis. Each period has gaps, each gap being a single night. The predominant insects during each period were identified using the two-stage approach described in Section 5.5 in Chapter 5. For convenience these periods are subsequently termed 'gap-free periods'. Total nights = 172.

No. Total no of Average nightly Likely of missing Nights insect counts* ID Start Date Finish Date Identity Nights Bourke Thargo. Bourke Thargo. 1 06-Nov-99 26-Nov-99 Locusts 21 1 2 182 463 2 28-Dec-99 25-Jan-00 Locusts 29 1 2 390 332 3 08-Apr-00 06-May-00 Mixed 29 1 4 162 176 4 10-May-00 27-May-00 Moths 18 1 1 76 90 5 30-May-00 26-Jun-00 Moths 28 0 4 31 66 6 07-Jul-00 22-Jul-00 Moths 16 0 3 20 36 7 15-Aug-00 14-Sep-00 Moths 31 0 2 138 113

*Insects with RCS ≥ 1 cm2 recorded during 1900-0500 h

7.4.2 Mobile IMR Data Used For Analysis The mobile IMR data used for analysis was acquired during the period 16-23 April 2002 between 1900 h and 0500 h for two nights at each of four sites located between the two fixed IMR sites and accessible by mostly sealed roads (driving on rough unsealed roads for long distances was likely to damage the mobile IMR). The locations are pictured in Section 2.10 of Chapter 2 and are described later in Section 7.6.

Of the 88 one-hour mobile IMR study periods, the mobile, Thargomindah and Bourke IMRs operated successfully for 84%, 80% and 76% of periods respectively. The last two values are consistent with the reliabilities observed during 1 September 1999 through 1 March 2001, see Section 2.11 in Chapter 2.

Any two IMRs operated concurrently on 31% of periods (excluding the periods where all three operated concurrently), and all three operated concurrently on 55% of periods. The details are shown in Table 7.2. During the mobile IMR study period (all three IMRs operating), the mobile IMR counted a total of about 48,000 insects (about 643 h-1), the Thargomindah IMR counted about 4,400 insects (63 h-1), and the Bourke IMR counted about 2,200 insects (33 h-1). 304 Of these about 30%, 30%, and 45%, respectively, were successfully processed. These success rates were lower than usual and were due to (1) using the MATLAB processing algorithm, which has a more rigorous acceptance criteria than the C++ algorithm used for the fixed IMR data of 1999-2001, and (2) including all echoes (not just large RCS ≥ 1 cm2 echoes) in an attempt to increase the number of insects detected during these relatively brief study periods, which resulted in an increase in weak signals that were less likely to be processable. Similarly the lower success rate for the Mobile and Thargomindah IMRs compared with Bourke is due to the acquisition of weak signals (due to their higher sensitivity) that are less likely to be processable. The difference between the number of targets observed by the IMRs is discussed later in Section 7.6.1.

Table 7.2: Times when each of the three IMRs were in operation during 16-23 April 2002. M: Mobile, T: Thargomindah, B: Bourke.

Time 16 17 18 19 20 21 22 23 Total 19 TB MTB MTB MTB MTB MTB MTB M 20 TB MTB MTB MTB MTB MTB MT M 21 TB MTB TB MTB MTB MTB MT M 22 TB MTB TB MTB MTB MTB MT M 23 TB MTB TB MTB MTB MTB MT M 0 MTB MTB TB MTB MTB MTB MT M 1 MTB MTB TB MTB MTB MTB MT M 2 MTB MTB TB MTB MTB MTB MT M 3 MTB MTB TB MTB MTB MTB MT M 4 MTB MTB TB MTB MTB MTB MT M 5 MB MB B MB MB MB M M M 6 11 2 11 11 11 11 11 74 T 10 10 10 10 10 10 10 0 70 B 11 11 11 11 11 11 1 0 67 MT 0 0 0 0 0 0 9 0 9 MB 1 1 0 1 1 1 0 0 5 TB 5 0 8 0 0 0 0 0 13 MTB 5 10 2 10 10 10 1 0 48

305

7.5 Correlations between Fixed IMRs

This first part of the analysis (this section) looks at the correlations between the two fixed IMRs in terms of insect numbers, direction and speed. The second part of the analysis (next section) looks at the correlations between the fixed and mobile IMRs. For circular data the correlations are circular correlations, which although analogous to Pearson r correlations in ranging from 0 (no correlation) to ± 1 (perfect and perfect inverse correlation), do not measure the same thing and are therefore not directly comparable (Fisher & Lee, 1983; Jones, 2006). In particular they need to be larger to reach the same significance level. For example, to reach P = 0.05 with N = 100 requires Pearson r = 0.197 but circular r = 0.308. The P values given later for circular correlations are approximate if N ≤ 30.

7.5.1 Insect Numbers at the Fixed IMRs The number of large (RCS ≥ 1 cm2) insects observed by the Bourke and Thargomindah IMRs during 1 September 1999 through 1 March 2001 are distributed as shown in Figure 7.5. At both IMRs the number of nights rapidly decrease as the nightly number of insects increase, and the distributions are very similar (r = 0.99, P < 10-6).

306

Figure 7.5: Number of nights vs. number of large (RCS ≥ 1 cm2) insects observed by the Bourke and Thargomindah IMRs during 1 September 1999 through 1 March 2001. The correlation is r = 0.99.

The insect numbers shown in Figure 7.5 are plotted against date in Figure 7.6. The results reflect the seasonal nature of insect migration in the study area, with numbers at a minimum during winter and a maximum during summer, see Figures 5.19-5.22 in Chapter 5.

307

2 Figure 7.6: Number of large insects (a0 ≥ 1 cm vs. day number from 1 September 1999 to 1 March 2001. Left: Thargomindah IMR. Right: Bourke IMR. Counts on incomplete nights have been increased pro rata to correct for their incompleteness. Periods when the IMR was out of service are indicated by grey shading.

308

A scatterplot of the counts for the 313 nights when both IMRs were operating is shown in Figure 7.7. A clear linear relationship is evident (r = 0.56, P < 10-24), showing that the counts at the two IMRs tend to vary in unison. When the nightly counts were divided into four ranges (<30, 30-150, 151-1000, >1000) the resulting classification table confirmed this trend, see Table 7.3. The contingency coefficient is C = 0.52 (P < 10–15), confirming a strong association between the insect numbers at Bourke and Thargomindah, and the hit rate (expressed as the sum of the diagonal entries/total number of entries) is 50% compared to the 25% expected by chance.

Figure 7.7: Scatterplot of the insects plotted in Figure 7.6 during the 313 nights (57% of the total of 548 nights) when both fixed IMRs were operating. Despite the scatter a clear linear relationship is evident (r = 0.56, P < 10-24), showing that the counts at the two IMRs tend to vary in unison.

309

Table 7.3: Classification count table for the data shown in Figure 7.7. The four groups into which the counts are divided were chosen to make as many cell entries > 5 as possible. The contingency coefficient for this table is 0.52.

Number of Insects (Bourke) < 30 30-150 151-1000 > 1000 Total < 30 47 31 11 0 89 Number 30-150 23 51 47 4 125 of Insects 151-1000 3 17 57 11 88 (Thargo.) > 1000 0 1 7 3 11 Total 73 100 122 18 313

However, it seems likely that at least part of the above correspondence between the two IMRs is due to seasonal effects. Thus locusts will tend to increase in the warmer months and moths will tend to increase in the cooler months regardless of whether the two IMRs are actually observing the same population. That is, seasonal effects may be swamping any genuine correlations between the two IMRs. The two cases could be differentiated if (1) the source of each population was already known, which does not apply here, or (2) a third IMR was available between the two fixed IMRs, which applies here and is discussed later in Sections 7.6 and 7.7. But for the moment the results raise two key questions:

The first key question is: Are the same trends shown in the seven gap-free periods? The number of large insects (RCS ≥ 1 cm2) detected each night by the Bourke and Thargomindah IMRs during the seven gap-free periods are shown in Figure 7.8. On nights when there are clear peaks at either Bourke or Thargomindah, there is sometimes a clear correspondence, for example night 23 in the second moth period and night 24 in the fourth moth period, and sometimes no evident correspondence, for example night 18 in the first locust period and night 6 in the second locust period. Sometimes both can occur on

310 consecutive nights, as in nights 3 and 4 of the first moth period, and sometimes it is hard to decide either way, as in the last half of the third moth period.

Altogether there are about 14 nights with clear peaks, of which 7 show a clear correspondence and 7 show no evident correspondence, which suggests as a first approximation that the two IMRs are sampling the same migrating population on something like 50% of occasions. This then is our first clue to the adequacy of their 300-km separation.

In Figure 7.8 the mean correlations are r = 0.20 for the two locust periods, r = 0.38 for the single mixed period, and r = 0.64 for the four moth periods, or r = 0.49 for all seven periods, a total of 172 nights, which again shows that the counts at the two IMRs do indeed tend to vary in unison. The above correlations are clearly not explainable by seasonal effects because the periods are only 16-31 nights long. The correlations are also consistent with the two IMRs observing the same population on 50% (1 in 2) of occasions, which the previous computer simulations in Section 7.2 suggest would be observed if r = 0.50.

311 Mixed

Figure 7.8: Number of large insects (RCS ≥ 1 cm2) observed during the seven gap-free periods at Bourke (solid lines and filled circles) and Thargomindah (dotted lines and open circles). Mean number of nights in each period = 25. Total nights = 172.

312 The second key question is: How strongly are the insect counts on one night related to counts on the next night, for (1) the same IMR and (2) between IMRs? To answer (1), inspection of the 14 clear peaks in Figure 7.8 shows that about one-third last for 1 night, one-third last for 2 nights, and one-third last for 3-5 nights. These results are supported by the autocorrelations shown in Table 7.4, where the means show that the strongest autocorrelations tend to occur at lag –1 night, but without a steep falling away at higher lags. The results for Thargomindah period 5 are shown in Figure 7.9.

According to Chatfield (1996), unless there is reason to suspect a correlation between the same variable many days apart (as for persistent sunspots which tend to reappear every 27 days due to solar rotation), there is usually little point in calculating autocorrelations beyond lag N/4, which in this case is 28/4 = 7 nights. In general, once beyond any short-term autocorrelation, the autocorrelations will tend to vary at random above and below zero, and may (spuriously) show occasional large values at increasingly higher lags, not only because more results mean a greater chance of an apparently significant result but also because the number of paired data is becoming increasingly too small and is thus increasingly open to statistical fluctuations due to small sample sizes. These characteristics are visible in Figure 7.9.

313 Table 7.4: Autocorrelations between nightly insect counts at the Bourke and Thargomindah IMRs for the seven gap-free periods. Total N = 172. Entries with P < 0.05 are shown in bold.

Bourke Thargomindah r for P = 0.05 −1 −2 −3 −4 −5 −1 −2 −3 −4 −5 1 0.43 0.02 −0.04 −0.24 −0.11 −0.34 0.52 0.09 −0.08 −0.05 −0.17 2 0.37 0.23 −0.06 −0.25 −0.15 −0.12 0.41 0.10 −0.15 −0.33 −0.16 3 0.37 0.12 −0.07 0.07 0.25 −0.05 0.37 0.14 −0.25 −0.27 −0.20 4 0.47 −0.46 −0.05 −0.11 −0.02 −0.01 0.48 0.00 −0.12 −0.09 −0.03 5 0.37 0.40 −0.10 −0.08 −0.09 −0.02 0.51 0.09 −0.21 −0.21 −0.07 6 0.50 0.13 −0.24 −0.10 −0.03 −0.09 −0.04 −0.42 0.13 −0.20 0.08 7 0.36 0.21 0.01 −0.04 −0.12 −0.18 0.31 −0.10 −0.22 −0.09 0.07 |mean r | 0.22 0.08 0.13 0.11 0.12 0.38 0.13 0.17 0.18 0.11 Total (P < 0.05) 1 0 0 0 0 5 0 0 0 0 Total (P < 0.20) 2 0 1 1 1 6 1 1 2 0

Figure 7.9: Autocorrelation between nightly insect counts at the Thargomindah IMR for period 5 (28 nights from 30 May 2000 to 26 June 2000). To answer (2), crosscorrelations were calculated between the two IMRs for the seven gap-free periods and are shown in Table 7.5. In general the strongest crosscorrelations occur at a lag of 0 nights (|mean r| = 0.49, P ~ 0.01), with appreciable but nonsignificant crosscorrelations at lags of +1 and –1 (|mean r| = 0.29, P ~ 0.15). The results for period 5 are typical and are plotted in Figure 7.10, to which the same comments about high lags apply as for Figure 7.9.

314 Table 7.5: Crosscorrelations and their lags between nightly insect counts at the Bourke and Thargomindah IMRs for the seven gap-free periods. A lag of +1 night means that the Thargomindah counts for each period were advanced one night vs. the Bourke counts for the same period. The results for lag 0 and the correlations shown in Figure 7.8 are the same. Entries with P < 0.05 are shown in bold.

Lag (Nights) r for P = 0.05 −2 −1 0 1 2 1 0.43 0.12 0.31 0.42 −0.07 −0.15 2 0.37 0.60 0.34 −0.02 −0.25 −0.31 3 0.37 0.07 0.24 0.38 0.33 0.15 4 0.47 −0.09 0.13 0.49 0.71 −0.15 5 0.37 −0.06 0.35 0.89 0.53 0.13 6 0.50 −0.58 −0.25 0.45 0.01 −0.28 7 0.36 0.17 0.27 0.77 0.21 −0.07 |mean r | 0.24 0.27 0.49 0.30 0.18 Total (P < 0.05) 2 0 4 2 0 Total (P < 0.20) 2 5 6 4 1

Figure 7.10: Crosscorrelation between the number of insects detected by the Bourke and Thargomindah IMRs for period 5 (28 nights from 30 May 2000 to 26 June 2000). The dotted lines indicate the correlation value where P = 0.05.

When combined with the previous results in answer to (1), the above results suggest as a first approximation that each IMR was sampling a population on the ground whose takeoff at peak times was generally enough to occupy up to two nights on roughly two-thirds of occasions, and up to 3-5 nights on the rest. The above results also suggest that on perhaps one-third of peak occasions one IMR was reacting to the insects that the other IMR reacted to on the night

315 before or the night after. This then is our second clue to the adequacy of the IMRs 308-km separation.

7.5.2 Insect Migration Directions at the Fixed IMRs Insect migration directions as measured by an IMR are the resultant of wind direction and flying direction, of which the former is invariably the most dominant at the usual altitudes of night-flying insects. This section compares the insect migration directions at the two fixed IMRs. Notable differences may indicate that the populations being sampled are from different source areas.

Circular histograms of the mean nightly insect migration directions at Bourke and Thargomindah are shown in Figure 7.11 for the 313 nights of joint operation (57% of the total 548 nights) during the period 1 September 1999 to 1 March 2001. The distributions are only broadly similar, with Thargomindah having more south-westward (90º to 180º), almost no south-eastward, and fewer north-westward directions, and by circular statistics (Batschelet, 1981) the mean directions at Bourke (332°; S.D. 98°) and Thargomindah (301°; S.D. 86°) are significantly different (chi-squared value 67.9, N = 16, P < 10–6). The circular correlation is 0.603 consistent with their broad similarities, but neither distribution is uniform (Rayleigh uniformity P < 10–30 in both cases), showing that there is a preferred direction in each case.

316

Figure 7.11: Circular histograms of the mean nightly insect migration direction for the 313 nights of joint operation (57% of the total 548 nights) during 1 September 1999 through 1 March 2001. Histograms show the direction the insects are migrating towards, 0º = north, 90º = east. Left: Bourke. Right: Thargomindah.

Circular histograms of the mean number of insects per night according to direction (Figure 7.12) migration patterns that are slightly different from those shown in Figure 7.11, with a peak 22% of nights at Bourke having a south- westward (180º to 270º) direction but only 6% at Thargomindah, while 25% of nights at Thargomindah have a south-eastward direction but only 11% at Bourke. Furthermore, the overall pattern of migration in Figure 7.12 is different, with a predominance of movement (i.e. large-scale migration) to the west at Bourke and roughly north-south at Thargomindah. Nevertheless the circular correlation between Bourke and Thargomindah is 0.77 (N = 16, P = 0.05) consistent with their broad similarities, but neither distribution is uniform (Rayleigh uniformity P < 10–30 in both cases), showing that there is a preferred direction in each case.

317

Figure 7.12: Circular histograms of the average number of insects per night according to direction for the 313 nights shown in Figure 7.11. Histograms show the direction the insects are migrating towards, 0º = north, 90º = east. Left: Bourke. Right: Thargomindah.

A scatterplot of the 313 mean nightly migration directions at Bourke and Thargomindah is shown in Figure 7.13. The results show a clear linear relationship, circular r = 0.56 (P < 10–24) (circular r is used instead of Pearson r to accommodate the continuity at 0/360º and to avoid the use of an arbitrary origin, thus the small cluster of data top left is a continuation of the data top right). The weather systems that determine wind direction are much larger than the 308 km between IMRs, so we might expect a higher correlation between travel directions than between raw insect counts. On the other hand, the wind trajectory maps given by Deveson et al. (2005) for 9-hour flights at 600 m during dates in November 1999 and 2000 relevant to northward migrations of plague locusts show differences of up to nearly 90º in wind trajectories between Bourke and Thargomindah, which might moderate our expectation. In fact the two correlations are the same (r = 0.56 vs. 0.56 in Figure 7.7). As with the raw insect counts, it is possible that the correlation has been inflated by seasonal effects even though the seasonal differences in wind direction are notably less than the orders-of-magnitude seasonal differences in insect counts (see Figures 5.19 - 5.22 in Chapter 5). So again the key question is: Are the same trends shown in the seven gap-free periods?

318 The corresponding circular correlations for the seven gap-free periods are shown in Table 7.6. They range from 0.22 to 0.86, mean 0.58, four of them significant (P < 0.05), showing that on any given night the migration directions at Bourke and Thargomindah do indeed tend to be similar. Table 7.6 also shows the mean migration directions for the seven periods and the results of the Watson-Williams F-test directional differences (Batschelet, 1981), all but two of which are non-significant (P > 0.05), which indicates that the mean migration directions tend to be not significantly different. So again, seasonal effects do not explain the observations.

Figure 7.13: Scatterplot of the mean migration directions for the 313 nights shown in Figure 7.10. Each point has error bars showing the associated standard deviations. The correlation is r = 0.56 (P < 10–24)).

319 Table 7.6: Circular correlations r between the mean nightly migration directions at the Bourke and Thargomindah IMRs for each of the seven gap-free periods. Four are significant (P < 0.05). Mean circular r = 0.61. Also shown are the mean migration direction θ in degrees, standard deviation, and the results of the Watson-Williams F- test of the significance of the difference between each pair of mean directions.

No. Bourke Thargomindah r P of r F P of F

θ SD θ SD 1 11 78 333 65 0.45 0.26 2.596 0.12 2 344 63 325 69 0.55 0.02 1.066 0.31 3 319 62 290 77 0.76 0.01 2.154 0.15 4 349 86 328 73 0.85 0.02 0.507 0.48* 5 352 67 315 64 0.86 0.0001 3.901 0.05 6 111 69 101 119 0.36 0.98 0.045 0.83* 7 138 58 261 90 0.22 0.22 6.489 0.01*

* Result is unreliable because the distribution of directions at Bourke or Thargomindah was too uniform to allow a robust mean to be identified.

Compared with the correlations for insect travel direction, the correlations for insect numbers are perhaps more informative because they arise both from weather systems (which affect takeoff behaviour and flight duration) and from the existence of flight-capable populations (which is determined mainly by population processes and rainfall patterns). To explore the extent to which similarity in insect numbers depends on similarity in wind direction, the ratio of average nightly counts at Bourke and Thargomindah (expressed as the mean of smallest/largest) is plotted against differences in wind direction in Figure 7.14. That is, for each night with insect counts at both Bourke and Thargomindah we calculate the quantity (nightly insect count at Bourke or Thargomindah, whichever is the smallest) / (nightly insect count at the other location). This quantity measures the difference in counts between Bourke and Thargomindah regardless of which is the larger, and expressing it as smallest/largest keeps it in the range 0-1. We then calculate for each difference in mean nightly wind direction the mean of these quantities, and plot the results in Figure 7.14.

If similar winds tend to produce similar counts, then dissimilar winds should tend to produce dissimilar counts, in which case the ratio smallest/largest 320 should decrease as the winds diverge in direction, a trend clearly supported by the results of Figure 7.13. However, the difference has to exceed 40-60º before the effect becomes noticeable, which suggests that the effect is not a strong one, in keeping with the results showing that seasonal effects do not dominate.

In stable conditions the horizontal wind direction near the surface can vary significantly over short distances (for example due to storm outflows) even though the wind speed may be very low. For example at Bourke during the study period the average change in surface wind direction and speed over three hours was 35˚ and 2.4 ms-1 respectively. However, fluctuations in surface wind conditions seem unlikely to have much effect at the high altitudes preferred by migrating insects, see Section 1.5.2 in Chapter 1.

Figure 7.14: Ratio of nightly insect totals at Bourke and Thargomindah over 313 nights, expressed as the mean of smallest/largest, vs. difference in nightly wind direction. The difference exceeds 50º in about 21% of cases. Cases where the difference exceeded 120º were too few to be plotted.

7.5.3 Insect Travel Speeds at the Fixed IMRs The distribution of mean nightly insect travel speeds for the full 313 nights is shown in Figure 7.15. The Bourke speeds showed a significant non-normal distribution (P < 0.001 by Shapiro-Wilk test) with heavier tails and a longer right tail than a normal distribution. The Thargomindah speeds also showed a

321 significant non-normal distribution (P = 0.04 by Shapiro-Wilk test), with symmetrical but lighter tails than a normal distribution.

The means of the mean nightly insect travel speeds are 12.0 SD 2.3 ms-1 for Bourke and 12.9 SD 2.4 ms-1 for Thargomindah, each for the full 313 nights. An autocorrelation analysis for each set of IMR speeds showed that the mean nightly speed was significantly correlated (P < 0.05) at a lag of one night during periods 2 and 3 at Bourke (r = 0.38 and 0.43 respectively), and period 3 at Thargomindah (r = 0.54), indicating an occasional tendency for the nightly travel speed to be related to the previous nightly speed, which would be expected whenever wind conditions were stable for more than a night or two.

Figure 7.15: Distribution of mean nightly insect travel speeds as measured by the IMRs at Bourke and Thargomindah for the full 313 nights.

A scatterplot of the mean nightly travel speed on each of the 313 nights is shown in Figure 7.16, for which r = 0.42, P < 10-12. The corresponding correlations for the seven gap-free periods are shown in Table 7.7. They range from 0.39 to 0.72, mean 0.54, all of them significant (P generally < 0.05), showing that on any given night the travel speeds at Bourke and Thargomindah

322 tend to be similar. Table 7.7 also shows the mean nightly travel speeds for the seven periods and results of the Watson-Williams F-test of the significance of the difference between each pair, but all are non-significant (P > 0.05), which indicates that the mean nightly travel speeds are not significantly different.

Figure 7.16: Scatterplot of the mean nightly travel speeds during the 313 nights when both fixed IMRs were operating. Each point has error bars showing the associated standard deviations. The correlation is r = 0.42 (P < 0.001).

Table 7.7: Correlations (r) between the mean nightly migration speeds at the Bourke and Thargomindah IMRs for each of the seven gap-free periods. All are significant, mean r = 0.54. Also shown are the mean migration speed v in ms-1, standard deviation, and results of the Watson-Williams F-test of the difference between each pair of means for the seven periods.

No. Bourke Thargomindah r P F* v SD v SD 1 11.9 2.3 11.9 1.9 0.47 0.03 0.451 2 12.8 1.9 13.1 1.7 0.52 0.004 0.616 3 12.2 2.7 14.7 2.7 0.39 0.04 0.888 4 11.5 2.0 12.8 1.7 0.58 0.01 0.466 5 12.1 2.1 12.5 1.4 0.48 0.01 0.033 6 10.7 1.9 10.6 2.0 0.72 0.002 0.860 7 12.5 2.9 13.0 3.0 0.61 0.0003 0.959

* All values of F are non-significant (P > 0.05) 323

The above correlations between mean nightly insect travel speeds are supported by the corresponding crosscorrelations in Table 7.8, which show an occasional tendency for nightly speeds at one IMR to correlate with speeds at the other IMR on the preceding or following night (|mean r | = 0.21, P = 0.31).

Table 7.8: Crosscorrelations and their lags between insect travel speeds observed at the Bourke and Thargomindah IMRs for the seven gap-free periods. A lag of +1 night means that the Thargomindah speeds for each period were advanced one night vs. the Bourke speeds for the same period. Results for lag 0 and the correlations shown in Table 7.7 are the same. Entries with P < 0.05 are shown in bold.

Lag (Nights) r for P = 0.05 −4 −3 −2 −1 0 1 2 1 0.43 −0.41 −0.16 0.20 0.41 0.47 0.36 0.07 2 0.37 0.10 0.37 0.56 0.27 0.52 0.17 −0.01 3 0.37 −0.02 −0.03 −0.01 0.10 0.39 0.26 0.06 4 0.47 −0.15 −0.03 −0.05 0.46 0.58 −0.25 −0.45 5 0.37 −0.21 −0.01 −0.17 0.13 0.48 0.16 −0.21 6 0.50 −0.16 −0.11 0.13 0.01 0.72 −0.01 −0.21 7 0.36 −0.03 −0.24 −0.15 −0.12 0.61 0.23 −0.08 mean r | 0.15 0.14 0.18 0.21 0.54 0.21 0.16 Total (P < 0.05) 0 1 1 0 7 0 0 Total (P < 0.20) 1 2 1 3 7 3 1

The above speed results are consistent with the earlier travel direction results shown in Table 7.6. In other words, on any given night, the wind carrying insects over Bourke tends to be similar (but by no means identical) in speed and direction to the wind carrying insects over Thargomindah. This of course is based on using insects as tracers of the wind. Comparisons between wind data reported by the IMR's weather stations show similar results but are less relevant because (1) the data are necessarily for altitudes well below those at which insects migrate, and (2) the concern here is insect travel direction. But as an example, a comparison using more than 500 nights of high altitude (200- 1500 m) wind data between Cobar (about 160 km south of Bourke) and

324 Charleville (about 570 km north of Cobar) showed good agreement for mean nightly wind direction and moderate agreement for mean nightly wind speed.

The distances that a migrating population could travel in ten hours, given the directions and speeds observed by the Bourke and Thargomindah IMRs during the study period, assuming they start at the IMRs, are shown in Figure 7.17. The results indicate that migrating insects could move 500 km or more in any direction in a single night, which together with some short-range movements from the landing area explain why their depredations can extend over many hundreds of kilometres more or less at the same time. Unfortunately little is known about the actual duration of a night's flight and the number of times that a night flight occurs during an insect's lifetime (Farrow, 1990). The above ten hours is based on the APLC website, which states that plague locusts seem to land before sunrise, giving a maximum of 9-10 hours in the air.

325

Figure 7.17: Distances travelled during ten hours at the travel speeds and directions observed by the Bourke and Thargomindah IMRs during the 538 nights of the 1999- 2001 study period. Bar length indicates the distance travelled in a 10-hour flight. Bar colour indicates total insect numbers observed travelling in the indicated direction: light grey <500, minor movement; dark grey 500-1500, average movement; black >1500, major movement. If the insects remained aloft for ten hours, the time between summer sunset and sunrise, this is where they might land.

7.6 Correlations Between Mobile and Fixed IMRs

This, the second part of the analysis, introduces the mobile IMR to explore the spatial gap between the two fixed IMRs. It was used in four locations in which the distance between the mobile IMR and the nearest fixed IMR varied from 26 to 122 km. Unfortunately there was insufficient time for the mobile IMR to be located next to a fixed IMR as a control, or with a small separation along the

326 wind direction. The locations are shown in Table 7.9 and Figure 7.18. Pictures of each location are shown in Figure 2.6 in Chapter 2.

Table 7.9: Mobile IMR locations and their straight-line distances from the Bourke and Thargomindah IMRs. For example Glengeera is 26 km north of Bourke and 290 km south-east of Thargomindah. Bourke is 308 km south-east of Thargomindah.

Dates Name Latitude Longitude Bourke Thargomindah (April 2002) Dist. (km) Dir. Dist. (km) Dir. 16-17 Glengeera 29° 48’S 145° 59’E 26 N 290 SE 18-19 Barringun 29° 01’S 145° 43’ E 116 N 216 SE 20-21 Eulo 28° 10’S 145° 03’E 226 NW 122 E 22-23 Thyangra 28° 10’S 143° 23’ E 325 NW 49 W

Figure 7.18: Study area with the four mobile IMR locations (Glengeera, Barringun, Eulo, and Thyangra) shown in bold type. The heavy black lines are sealed roads.

The analysis looks at the correlations between the mobile and two fixed IMRs in terms of insect numbers, direction, and speed. Unfortunately an extended field operation was outside the scope and resources of the present work, and the mobile IMR's study period had to be restricted to just eight nights during April 2002 spread over the four locations. Equally unfortunately the study period coincided not only with the decline in insect numbers between summer and winter (see Figures 5.19 - 5.22 in Chapter 5) but also with winds that were 327 blowing generally towards (rather than away from) the centre of the source areas shown in Figure 1.17 and Figure 1.21 of Chapter 1. Consequently the insect numbers available for analysis were too small for statistical reliability. So the results presented below are more to demonstrate the mobile IMR's potential. Nevertheless, as we shall see, there are a number of useful outcomes.

7.6.1 Insect Numbers at the Mobile and Fixed IMRs The analyses below compare the hourly insect counts at each IMR, whereas the previous comparisons between fixed IMRs were of nightly counts. Because the distance between IMRs is now reduced, the leading edge (supposing it to be recognisable as shown in Figure 7.19) of a group of insects taking off at sunset will most likely (given a favourable wind direction) pass over the IMRs a few hours apart on the same night, something not routinely possible with the fixed IMRs, which in principle should allow population characteristics to be more precisely investigated.

Figure 7.19: Schematic view of a migration's leading edge (supposing it to be recognisable) passing over one IMR en route to another IMR several hours away. Provided the two IMRs are of equal sensitivity and are aligned with the flight direction, their results should indicate any changes in altitude and the extent to which the migration is dispersing, neither of which are measurable by a single IMR or by two IMRs separated by a relatively long distance (as Bourke and Thargomindah are).

On the other hand, compared with nightly counts over 313 nights, the hourly counts over 8 nights were very much smaller, not merely because the sampling period was smaller but also for the reasons mentioned previously, and were insufficient for statistical reliability. There were also large differences in IMR sensitivity (see below), so the IMRs would not be reacting to the same species

328 (selection via RCS windows as in Chapters 5 and 6 could not be used because it reduced sample sizes too much), so the estimation of dispersal and changes in altitude would not be possible. In short, we should expect our hourly counts to give correlations that tend to be erratic and inconsistent.

The number of insects detected each hour by the three IMRs is shown in Figure 7.20. To equalise differences in sensitivity between IMRs the numbers of insects are plotted as a percentage of each total, with the totals listed under N in the rightmost column. The average hourly insect counts are very different (20 at Bourke, 63 at Thargomindah, 450-500 at the mobile IMR) but the differences are readily explained. Firstly, transmitter ageing had reduced the performance of the Thargomindah IMR. Secondly, most of the detected insects were small and at altitudes of 200 - 600 m, where the scanned volume of the mobile IMR was about four times larger than that of the fixed IMRs. Thirdly, the wider beamwidth of the mobile IMR increased the processable proportion of signals due to flight speed effects (see Section 3.4.3 in Chapter 3).

329 16 km r N BT 308 0.88 331 MB 26 0.16 1,945 TM 290 0.01 227

17 km r N BT 308 -0.12 579 MB 26 -0.36 8,143 TM 290 -0.07 333

18 km r N BT 308 -0.36 708 MB 116 nd 13,449 TM 216 nd 291

19 km r N BT 308 -0.27 190 MB 116 -0.19 3,658 TM 216 0.08 229

20 km r N BT 308 0.37 238 MB 226 0.20 2,874 TM 122 0.29 215

21 km r N BT 308 0.61 155 MB 226 -0.10 2,468 TM 122 -0.64 834

22 km r N BT 308 nd 22 MB 325 nd 11,338 TM 49 0.91 2,301

23 km r N BT 308 nd MB 325 nd 3,674 TM 49 nd

Figure 7.20: Hourly insect counts between 1900 and 0500 h recorded by the Mobile, Thargomindah and Bourke IMRs on the nights of (from top) 16 April through 23 April 2002. The locations corresponding to each pair of plots are (from top) Glengeera, Barringun, Eulo, and Thyangra. To equalise differences between IMRs the numbers are given as a percentage of each night’s total (note that the vertical scale varies between plots). On the right is the distance between IMRs, the correlation between plots, and the total counts for the first-named IMR. Thus BT shows the total for B.

330 The most common trend in Figure 7.20 is a general decline during the later part of the night, which is hardly unexpected. Nevertheless there are appreciable differences. Thus insect numbers peaked between 1900 h and 2000 h on all seven nights at Bourke, but on only two nights at Thargomindah and one at the mobile IMR. The mean correlation between hourly counts was r = 0.19 SD 0.51 (N = 6) for Bourke-Thargomindah and r = 0.03 SD 0.40 (N = 11) for mobile-fixed IMRs, mean r = 0.09, not enough to justify the assumption that sunset takeoff effects will generally dominate any relationship between IMRs.

About 20 peaks can be identified in Figure 7.20, of which about three-quarters were 2-3 hours long, in agreement with the 2-3 hours observed by Drake & Farrow (1983) for six nights during November 1979 when the insects were mostly plague locusts. The rest were 4-5 hours long. At the mean insect travel speed of 35 kph (see later in Section 7.6.3) these results suggest that the main part of the migrations was up to 100 km long for roughly 75% of occasions, and perhaps up to 200 km long for the rest. Since takeoff occurs during a short period after dusk and before dark (Section 1.5.3), the source areas are likely to be of similar dimensions.

On the other hand, any source area immediately downwind of the IMR will be excluded, in which case the above estimate will be too low. Furthermore, if the flight time varies considerably within the population then the estimation of migration extent may be further compromised.

If the main part of migrations are several hours long, there should be a tendency for hourly insect counts to correlate with those of the hour before, that is, the serial correlations between insect counts should tend to be positive. Across all 19 nights all but three serial correlations were positive (mean serial r = 0.285 SD 0.248, N = 19), although only one exceeded the r = 0.60 needed to reach significance (P = 0.05), which probably reflects the tiny sample size in each case (N = 11 hours). 331

The previous analyses between fixed IMRs 308 km apart showed a clear tendency for their counts to vary in unison, so we might expect the tendency to increase as the distance apart decreases provided the travel direction is favourable. The last is especially critical when the study period is short, and as shown later in the next section, travel directions that happen to be unfavourable during a short study period give misleading results. Thus at first sight the correlation between r values and the distance between mobile and fixed IMRs of –0.17 (N = 5) for Bourke and 0.02 (N = 6) for Thargomindah would seem to indicate no consistent tendency for the similarity in counts to increase as the distance between IMRs decreases. But as we shall see in the next section (7.6.2), this changes once travel direction is taken into account.

Nevertheless, for pairs of nights when the mobile IMR position was unchanged, do the hourly insect counts on the first night correlate with those on the second night? (This is not the same as the serial correlation analysis above, which was concerned only with counts within the same night.) If the wind direction remains the same (which in this case was only roughly true), and if the source population is still active (which seems doubtful given the time of year and winds blowing towards the main source areas), positive results might be expected. In this case the relevant correlations for each IMR are shown in Table 7.10. The correlations are erratic, range −0.46 to 0.87 for 9 results, although always positive (mean 0.76) for the 4 results with P ≤ 0.05.

Table 7.10: Correlations for each IMR between pairs of nights where the mobile IMR position was unchanged. Each correlation is between the two sets of hourly insect counts 1900-0500 h, N = 11. ND = No Data because the IMR was either not operating or was operating for only a few hours. Entries with P < 0.05 are in bold.

Nights Mobile Thargomindah Bourke April 2002 r P r P r P 16/17 0.39 0.39 −0.46 0.19 0.58 0.05 18/19 ND ND 0.32 0.37 0.87 0.0005 20/21 0.85 0.001 −0.26 0.46 0.75 0.008 22/23 0.075 0.83 ND ND ND ND 332

Hourly insect counts between IMRs are explored via the crosscorrelations shown in Table 7.11. Provided the insect travel direction was directly from one IMR to the other, the crosscorrelations at lags of a few hours were generally higher than at hour 0 consistent with the expected effect of flight times. The effect of flight times are analysed in the next section but an example from Table 7.11 can be mentioned here. On 20-21 April the mobile IMR was at Eulo 122 km from Thargomindah. On the first night the migration speed was 40 kph towards Thargomindah at an angle of about 21º to the line joining the IMRs, giving a flight time between IMRs in the travel direction of about 122/40 x cos(21) = 2.8 hours, in agreement with the significant correlation at lag –2. On the second night the wind had changed by almost 180º and was now blowing towards Eulo, in agreement with the significant correlation at lag +3.

333 Table 7.11: Crosscorrelations between hourly insect counts recorded by the mobile, Bourke, and Thargomindah IMRs during the nights of 16-22 April 2002. A lag of +1 hour means that the counts for the first-named IMR were advanced one hour vs. the counts for the second-named IMR. ND = No data because the IMR was either not operating of was operating for only a few hours. Entries with P < 0.05 are in bold. Nights when the wind was blowing directly between IMRs are in italics.

April Lag (hours) −4 −3 −2 −1 0 1 2 3 4 Mobile/Bourke 16 −0.09 −0.22 −0.12 −0.14 0.00 0.21 0.03 −0.09 0.18 17 0.04 0.01 −0.10 −0.42 −0.51 −0.26 0.12 0.71 0.81 18 ND ND ND ND ND ND ND ND ND 19 −0.07 −0.10 −0.10 −0.16 −0.27 0.48 0.61 −0.07 0.05 20 −0.31 −0.26 0.19 0.48 0.14 −0.32 −0.05 0.53 0.29 21 −0.22 −0.28 −0.19 0.04 −0.16 −0.48 0.04 0.48 0.36 22 ND ND ND ND ND ND ND ND ND Thargomindah/Mobile 16 −0.03 −0.15 −0.10 −0.06 −0.06 0.06 −0.11 −0.01 −0.04 17 0.03 0.03 −0.17 −0.22 −0.05 0.08 0.17 −0.01 −0.41 18 ND ND ND ND ND ND ND ND ND 19 0.48 −0.31 0.08 0.54 0.10 −0.52 −0.08 −0.10 −0.14 20 −0.23 0.24 0.68 0.74 0.28 −0.35 −0.61 −0.43 −0.17 21 −0.06 −0.07 −0.10 −0.31 −0.65 −0.39 0.37 0.64 0.41 22 −0.15 0.07 0.29 0.51 0.92 0.43 0.39 0.02 −0.01 Bourke/Thargomindah 16 0.20 −0.09 0.11 0.26 0.88 0.26 −0.15 0.02 −0.16 17 0.15 0.23 0.07 −0.41 −0.14 −0.06 0.25 0.19 −0.22 18 −0.01 0.04 0.07 −0.08 −0.35 −0.38 0.00 0.67 0.60 19 0.04 −0.06 −0.15 −0.01 −0.26 −0.53 −0.10 0.17 −0.05 20 −0.17 −0.43 −0.30 0.03 0.39 0.02 −0.14 −0.27 0.10 21 0.09 0.09 0.15 −0.07 0.59 0.69. 0.03 −0.04 −0.12 22 ND ND ND ND ND ND ND ND ND |mean r | 0.14 0.16 0.17 0.26 0.34 0.32 0.19 0.26 0.24 P < 0.2 1 1 1 5 5 6 2 6 2

7.6.2 Insect Travel Directions at the Mobile and Fixed IMRs The mean nightly insect travel directions at each of the three IMRs are shown in Figure 7.21. As the mobile IMR moves from a location close to Bourke (at far left) to a location close to Thargomindah (at far right), so the associated travel directions move from Bourke-like to Thargomindah-like. By circular 334 statistics the Rayleigh Uniformity Test results were all significant (P < 0.001), showing that there was a preferred direction on each night (the direction shown in Figure 7.21). Nightly variations in the travel direction averaged 35º SD 24º and 33º SD 18º for the Bourke and mobile IMRs respectively, and were a notably larger 96º SD 59º at Thargomindah. The increase at Thargomindah was largely due to changes of more than 90º in travel direction during the nights of 16, 20, 21 and 22 April, all of which occurred at late hours when insect counts were low.

Figure 7.21: Mean nightly insect travel directions at the three IMRs during 16-23 April 2002, and wind directions measured at 2100 h at the two fixed IMR locations and at Cunnamulla (68 km east of Eulo. In each case the wind is blowing towards, and the insects are travelling towards, the direction.

335 The results of Figure 7.21 show that the mean hourly insect travel directions measured by the IMRs tended (with notable exceptions) to be similar to the mean surface wind directions recorded at 2100 h. Interestingly, on 20 April a change in nightly travel direction was recorded at all three IMRs (the whole night was different from the previous night, see Figure 7.21), even though the surface wind direction showed little change, which indicates that on that night the IMRs were sampling insects at altitudes where the wind direction differed markedly from that at the surface.

Circular correlations between mean hourly travel directions at each pair of IMRs for each of the seven nights are shown in Table 7.12. The correlations vary considerably from −0.76 to +0.67, mean r = +0.06, but none are significant (P < 0.05). A negative correlation arises when the wind direction at one IMR changes only slightly while the travel direction at the other IMR changes significantly. Such changes are not what we might expect, so Figure 7.22 gives two examples together with a positive correlation for comparison.

Table 7.12: Circular correlations between the hourly travel directions at each pair of IMRs during 16-23 April 2002. Each result is based on 7-11 hourly observations per night. None are significant (P < 0.05). There are fewer entries than implied by Table 7.2 because some nights (indicated by ND had insufficient data for analysis.

Date (April 2002) 16 17 18 19 20 21 22 M/T 0.31 −0.23 ND −0.76 0.40 0.65 0.3 M/B −0.74 0.45 ND ND −0.66 0.31 ND B/T 0.32 −0.37 0.67 ND −0.34 0.60 ND

336

Figure 7.22: Three circular correlations between observed IMR travel directions. The labels above each plot identify the original entries in Table 7.11. The first hourly value is set to 0,0 degrees shown by the large dot; the line through 0,0 has been made by eye. The changes at the first-named IMR are plotted on the vertical axis. Left: a positive correlation. The changes in direction at each IMR are in the same direction. Middle and Right: two negative correlations. A small change in direction at one IMR is accompanied by a larger change in the opposite direction at the other IMR.

Instructive results arise when the insect travel direction happens to be from one IMR to the other. At Thargomindah this occurred on two occasions. The first occasion was the night of 20 April when the travel direction was from Eulo to Thargomindah and the night of 21 April when the travel direction was from Thargomindah to Eulo, see Figure 7.23. In both cases there were significant crosscorrelations at lags equivalent to the flight time between the locations (Table 7.11). On the night of 21 April a sharp strong Thargomindah peak occurred at 1900 and 2000 h, falling to almost nothing for the rest of the night, whereas the mobile registered a broad but much weaker peak three hours later (Figure 7.20) consistent with the calculated three-hour flying time between the two sites. On the night of 22 April, when the direction was from Thyangra to Thargomindah, a distance of only 49 km, the two locations had a significant crosscorrelation (r = 0.92) at a lag of 0 hours, consistent with the two IMRs observing the same population.

337

Figure 7.23: The insect travel directions of Figure 7.21 superimposed on the geographical IMR locations shown in Figure 7.18. Top: Thargomindah and its two closest mobile IMR locations. Bottom: Bourke and its two closest mobile IMR locations. In each case the numbers are the dates in April 2002 when the mobile IMR was at that location.

The next two examples illustrate the problems of interpretation arising from (1) differences in sensitivity, and (2) uncertainty in wind direction.

(1) At Bourke (see Figure 7.23) the wind directions were generally away from the mobile IMR locations except on 17 April when the wind was blowing at 36 kph directly towards the mobile IMR at Glengeera 26 km away, less than one hour's flight time. (Data from the first night at this location is not available

338 because operation of the mobile IMR was delayed.) The Bourke IMR recorded a sharp initial peak at 1900-2000 h, falling away to nothing, then a lesser peak at 0100-0200 h, whereas the mobile IMR recorded steady numbers that hardly changed during the night. The peaks at Bourke suggest the passage of two populations 2-3 hours (70-100 km) in extent separated by 3-4 hours (100-140 km) almost free of insects, which seems incompatible with the mobile IMR results. However, the mobile IMR was more sensitive than the Bourke IMR and was counting nearly five times as many insects (mostly small), enough to swamp the peaks (mostly due to plague locusts) registered by the Bourke IMR. The same problem also applied to the Thargomindah and mobile IMRs in the example above, where the same swamping effect is evident, but (since the Thargomindah IMR was more sensitive than the Bourke IMR) not enough to entirely suppress the features noted above.

(2) On 16 April, when the travel direction at Bourke was generally aligned with Thargomindah 308 km away, both IMRs recorded a sharp initial peak (Figure 7.20) that could only be due to local takeoff at sunset. On that night the flight time between IMRs was about 12 hours, too long for the Bourke peak to make Thargomindah before sunrise, which explains why no late peak was observed at Thargomindah. But on 18 April, when the travel directions at both IMRs differed from each other and from the Bourke-Thargomindah direction, although the latter was roughly aligned with their mean, only Bourke recorded an initial peak. Thargomindah recorded a later broader peak at lags of +3 and +4 (Table 7.11), which if produced by the same insects implies a travel speed of about 308/4 = 77 kph, which is unlikely but perhaps not unrealistically high for a low-level jet. What did the mobile IMR results show? On that night it was at Barringun roughly one-third of the way between Bourke and Thargomindah, and seemingly well placed to monitor the situation. Like Bourke, it recorded an initial peak, but the travel direction was almost at right angles to that at both Bourke and Thargomindah (Figure 7.21), so no conclusion was possible.

339 The changeable travel directions uncovered in this section could be due to features of the passing weather system such as fronts or depressions, or to localised effects on wind direction such as localised convections and surface topography (e.g. see Pedgley, 1990). They make it difficult to accurately track insects between IMRs no matter how precise the individual IMR observations may be. The implications should be obvious – the full value of a mobile IMR is unlikely to be realised (even when sensitivities are the same) unless it has enough operational time at each location to accommodate the vagaries of weather and insect activity.

7.6.3 Insect Travel Speeds at the Mobile and Fixed IMRs The mean nightly insect travel speeds at each of the three IMRs are shown in Figure 7.24. The average speeds in ms-1 over all nights were mobile 12.1 SD 4.0, Bourke 8.1 SD 1.0, Thargomindah 8.5 SD 1.2 (N = 8). The speeds tended to be changeable during the night, the average variation (maximum hourly value – minimum hourly value)/2 being between 2.4 and 2.7 ms-1 for the three locations with the maximum variation usually being recorded at around 2200 h. In Figure 7.24, the mean insect speeds recorded by the mobile IMR show notably more variations than those recorded by the fixed IMRs, and as it moves from a location close to Bourke (at far left) to a location close to Thargomindah (at far right), the speeds show no tendency to move from Bourke-like to Thargomindah-like. The mean travel speed over all three locations was 9.7 ms−1 (35 kph), somewhat less than the mean travel speed of 12.5 ms-1 observed for the 313 nights (Figure 7.15).

340

Figure 7.24: Average nightly travel speeds at the three IMRs during 16-23 April 2002. The speeds tended to be fairly changeable during the night, and the standard deviation over the 11 hours would be typically 8 ms–1.

The correlations between the hourly insect speeds for each pair of IMRs are shown in Table 7.13. The r values range from −0.43 to +0.63, mean +0.08, but only one of the fifteen (on 20 April for Mobile-Thargomindah) is significant (P < 0.05) due to speeds at 2400 h at both sites being about 50% greater than the speeds at the beginning and end of the night.

Table 7.13: Correlations between the hourly insect speeds at each pair of IMRs during 16-23 April 2002. Each result is based on 7-11 hourly observations per night. The only significant (P < 0.05) result is shown in bold.

Date (April 2002) 16 17 18 19 20 21 22 M/T 0.16 0.34 ND 0.15 0.63 −0.24 0.35 M/B −0.31 0.30 ND ND −0.05 0.01 ND B/T −0.43 −0.05 −0.13 ND 0.38 0.23 ND

As mentioned in previous chapters, IMR data show the insect travel direction but not which way the insect is facing, which in principle can be resolved by assuming that insects tend to fly with the wind rather than against it. An empirical question remains – how good are surface winds as an indicator of

341 insect travel direction? Given that the average air speed of moths and locusts is around 12 kph (see Sections 1.6.1 and 1.6.2 in Chapter 1), the difference in wind speed between flying upwind and flying downwind for the same travel speed would be around 2 x 12 = 24 kph, which seems ample for a determination of which way the insect is facing. However, the surface wind speed is usually very different from that at altitude especially at night, see Section 1.5.2 in Chapter 1, so in practice the idea cannot be reliably tested.

However, if it is reasonably assumed that small insects have insignificant airspeeds, they can be used as 'tracers' to give an idea of wind speed for comparison with the travel speed of large insects. An example of such a comparison made by the Bourke IMR is shown in Figure 7.25. If the large insects on this occasion were flying with the wind, their travel speed should exceed that of the tracers – and it does. In principle the smaller the tracers the closer their travel speed is to the wind speed, but tracers small enough to a have an insignificant airspeed may be too small to be detectable by an ordinary IMR at the heights where large insects tend to be concentrated. Conversely, tracers large enough to be detectable may have an appreciable air speed, so in Figure 7.25 the speed difference between the two plots may underestimates large insect air speed.

Figure 7.25: Travel speed vs. altitude for large (RCS ≥ 1 cm2) and small (RCS < 0.1 cm2) insects as recorded by the Bourke IMR on 20 March 1999. Total number of insects is about 2,200 (small) and 460 (large),

342 7.7 Discussion

The aim of this chapter was to estimate the width and length of migrating insect populations, their main direction, and the optimum location for the IMRs using nearly two years of data from the two fixed IMRs and a further eight nights of data involving a third, mobile, IMR in intermediate locations. However, there were only five nights on which all three IMRs were in service for a sufficient duration. During this period the distance between the mobile IMR and the nearest fixed IMR ranged from 26 to 122 km, and the comparisons were between hourly insect counts rather than nightly counts

A period of five nights is comparable with the observation periods in several studies conducted using scanning radars, but as expected it was still too short to give the insect numbers required for statistical reliability, especially when the wind was away from the source area.

7.7.1 Discussion: Migration Size The theoretical calculations and computer simulations in Section 7.2 suggested that the width w of a migratory population, the separation s between two IMRs, and the correlation r observed between IMR insect counts over a variety of occasions could be roughly related by the expressions w/s ~ 4r or w/s ~ 1/(1 – r) for r below or above 0.5 respectively. A strong correlation (provided it was not caused by concurrent events regardless of migration size such as the sunset takeoff) would suggest that the migration width was large compared with the IMR separation and that the migration was being over-sampled. A weak correlation would suggest the opposite.

The relevant observations for the fixed IMRs are summarised in Table 7.14. For N = 313 nights the correlation between insect counts was r = 0.56, and for N = 172 nights spread over seven gap-free periods the mean correlation was r = 0.49. The average period was 24 nights, too short for seasonal effects to dominate. In addition, the average correlation between hourly counts for the 343 fixed and mobile IMRs was r = 0.09 (N = 17), too low for sunset takeoff effects to dominate, although in each case a contribution cannot be ruled out.

Table 7.14: Summary of observed correlations or mean correlations between nightly insect counts observed by the Bourke and Thargomindah IMRs. In parentheses is the relevant figure or table number (t = table). N = 313 is the number of nights when both IMRs were operating during September 1999 - March 2001. N = 172 is the number of nights in the seven gap-free periods November 1999 - September 2000. Note that Pearson and circular r's are not comparable, see Section 7.5.

Type of Insect Travel Travel N correlation counts Direction speed 313 Pearson 0.56 (7.5) 0.56 (7.11) 0.42 (7.14) 313 Circular – 0.60 (7.9) 0.77 (7.10) 172 Pearson 0.49 (7.6) – – 172 Circular – 0.61 (7.6t) 0.54 (7.7t)

The agreement between the insect counts at the two IMRs 308 km apart is all the more impressive given that the results from APLC light-traps 130 km apart show poor agreement, namely 13 hits in 142 trials, see Table 5.4 in Chapter 5. So it seems reasonable to conclude that the counts at the two IMRs tended to vary in unison to an extent not explainable by purely seasonal or sunset takeoff effects. That they did so over all possible wind directions, including disadvantageous wind directions, suggests that their distance apart (308 km) was at least similar to the average migration width, whose estimate is further refined below.

For N = 313 nights there was also a strong positive correlation between the migration directions measured at the fixed IMRs of r = 0.56, and a less-strong correlation between migration speeds of r = 0.42 (Table 7.14). Both are similar to the correlation between insect numbers (r = 0.56). Together they suggest that migration characteristics (not just numbers) are consistent across a distance of 308 km. Such consistency over such a large distance is itself a remarkable feature of these migrations.

344 Putting s = 300 km and r = 0.50 into the expressions linking w, s, and r suggests that the two IMRs were sampling the same population on something like 1 in 1/0.50 or 50% of occasions, and that the average migration width on those occasions was something like 600 km. Had the result been 10% we could have concluded that the two IMRs were too far apart and that the migration width on those occasions was smaller than 600 km. Conversely, had the result been nearer 100%, we could have concluded that the two IMRs were too close together and that the migration width was larger than 600 km.

Is there a preferred migration travel direction? Unsurprisingly, the results show that insects necessarily travel in whatever general direction the wind happens to be blowing. So after allowing for small variations due to flight activity, their 'preferred direction' necessarily coincides with wind direction during their periods of activity. For moths and locusts this means they can move in almost any direction (Figure 7.17). There is more on this topic in the next section.

What do the results reveal about migration length? The duration of the peaks in the hourly insect counts indicated that peak migrations were up to 100 km long for roughly 75% of the time, and perhaps up to 200 km long for the rest. But again, this was towards the end of the season when the migrations would be smaller in extent. In other words during major outbreaks the migration length could be considerably larger, a point supported by the studies reviewed in Section 7.2 which observed migrating populations with width's ranging from 100 to 800 km, and lengths ranging from 50 km to 350 km. (Depending on which way the wind is blowing, a 'width' seen on the ground could become a 'length' in the air, and vice versa.)

Equally instructive were the occasions when the wind was blowing directly from one IMR to the other, when the strongest correlations tended to occur at lags consistent with the flight times between IMRs (Table 7.10). Unfortunately the large and unplanned differences in IMR sensitivity prevented evaluation of 345 a major unknown, namely migration dispersal. Nevertheless the present study has demonstrated that the mobile IMR could operate in almost any location with results at least equal to those from the fixed IMRs.

7.7.2 Discussion: Optimum IMR Location What is the optimum compass bearing from one IMR to the other? In the present study the main long-term migration directions at Thargomindah were generally north and south and were fairly clear cut, while those at Bourke were generally southwest and northwest and were less clear cut (Figure 7.11). For major outbreaks the directions at Thargomindah were also generally north and south while those at Bourke were generally north or northwest (Figure 7.17). In both locations the least-favoured migration direction was east towards the coast, which would therefore appear to be the optimum orientation for a fixed two- IMR system, since its weakest orientation (i.e. with one IMR directly behind the other) would then align with the least-favoured migration direction. In the present study the orientation of the two IMRs was southeast-northwest, some 45 degrees different, which may have somewhat reduced their joint efficacy.

However, there are two additional factors to be considered. (1) East is the least-favoured direction by only a small margin. Indeed, the scatter of directions whether over two years (Figure 7.11 and Figure 7.17) or twenty years (Figure 6.2 in Chapter 6) is so marked that almost any orientation would be as good as any other provided the IMRs were located within the source areas or adjacent to them. (2) Suitable locations with power, communications, and accessibility by sealed road are infrequent in inland areas. The practicality of maintaining the units in reliable operation must carry considerable weight when choosing locations.

Given that a separation of 300 km seems to be about right, potentially suitable locations accessible by sealed (or partially sealed in the case of Tibooburra) roads are shown in Figure 7.26. Circles indicating the areas consistent with a

346 diameter of 300 km have been applied to the more widely separated locations. Of the places shown, Wilcannia (330 km south-west of Bourke) has reasonable access from Canberra and is well situated for detecting southwards invasions, while Windorah (310 km north of Thargomindah) is in the source area and is thus well situated for purely entomological studies. Perhaps the clearest message to emerge from the diversity of choices shown in Figure 7.26 is an emphasis on the advantages of a mobile IMR, which if nothing else allows the characteristics of a particular site to be sampled in advance without any commitment to permanence.

Figure 7.26: Possible locations for future IMRs. For the more remote locations, open circles show areas consistent with a diameter of 300 km, this being an adequate spacing for IMRs as estimated in the text. Shaded circle show existing IMR locations.

347 7.7.3 Discussion: IMR Reliability An initial discussion of IMR reliability appeared in Section 2.11 of Chapter 2, to which the following comments can be added in light of the experience gained with the mobile IMR and especially with operating three IMRs together.

Studies such as the present one that require the simultaneous operation of two or more IMRs have an especial need for reliability. However, the present IMRs performed rather poorly in this regard. The observations reported in Chapter 2 showed that, over a period of 548 nights, the fixed IMRs were individually capable of successful operation on an average of 80% of nights, range 76% - 84%, that is, with an average of 20% downtime, most of which was due to the difficulties of operation and maintenance in remote areas. The figure is inflated by postal losses that occasionally resulted in the loss of a sequence of nights of CD-recorded data in one go even though the IMRs had operated normally. Nevertheless 80% compares poorly with the reliability of about 95% observed for the English VLRs, where most of the downtime is due to errors generated in the analogue-to-digital system (A. Smith, 2002, Natural Resources Institute, personal communication).

For the present study period of eight nights, each of 11 hours during 18-23 April 2002 (see Table 7.2), the average reliability was again 80%, range 76% (Bourke) to 84% (mobile), with at least two IMRs in service 85% of the time, and all three in service 55% of the time. The figures predicted on the basis of an individual reliability of 80% are 64% and 51%, respectively, which suggests that such predictions can be indicative even when, as here, the time scale is too short for long-term reliabilities to apply with any confidence. If equipment and procedures could be improved to the point where failures follow the expected Poisson distribution (see e.g. Walpole (2002)), prediction of short-term reliability might also improve, but that day may be some time away especially for IMRs in remote areas.

348 Similarly, if an overall reliability of 80% is required, the individual reliabilities would need to be at least 89% for two IMRs and 93% for three IMRs. The gap- free datasets required for statistical analysis (but not for routine operation) would further limit the proportion of usable data. For example, on only 172 nights of the present study (31% of the total 548) were both IMRs working sufficiently reliably for their results to be included in the gap-free datasets shown in Table 7.1.

The causes of IMR failure at Bourke (Table 2.4 in Chapter 2) indicate that they break down into system faults (26%), CD archiving/postal losses (24%), power failure (20%), servicing (12%), and other/unidentified (18%). The first two account for a total of 10% of nights out of service. If this could be reduced to 4% of nights, and given small improvements in the other/unidentified failure rate, then these higher reliabilities could be achieved. Uninterruptable power supplies have recently been incorporated into the existing IMRs, offering protection against short-term power failure. A decrease in servicing seems inadvisable because it would most likely lead to an increase in other faults.

349 8 REALISATION OF STUDY AIMS, RECOMMENDATIONS FOR FUTURE WORK, CONCLUDING REMARKS

This short chapter contains a summary of the study aims and how well each has been realised (that is, brief answers, all positive, are given to the questions raised in Section 1.2 in Chapter 1), recommendations for future work (devise ways to calibrate IMRs in the field, improve reliability, make more laboratory measurements of insects, make longer field studies with the mobile IMR, study other areas and species), and concluding remarks.

8.1 Realisation of Study Aims

The present study has continued the work begun by others at the University of New South Wales (in the former School of Physics, now part of the School of Physical, Environmental and Mathematical Sciences, ADFA campus, Canberra) in developing radar entomology. Its specific aims, given in Section 1.2 of Chapter 1, are listed below together with a brief indication of how well each aim has been realised.

How reliable are the present Australian IMR systems? See Section 2.11 in Chapter 2. The average observed reliability (proportion of time in service) was 80%, which is too low to produce the long continuous datasets needed for efficient analyses and inter-IMR comparisons, although adequate to produce the shorter, albeit erratic, datasets analysed in the present work.

Can a mobile IMR for short-term observations be built and operated? See Chapters 2 and 7. A mobile IMR was successfully constructed at a cost almost half that of a fixed IMR. The mobile IMR was then successfully used in the field for a period of eight nights, the maximum that resources allowed. As shown in Chapter 7, its mobility did not adversely affect its performance, which

350 proved to be at least equal to that of the fixed IMRs.

Are there biases introduced by the signal processing procedure? See Chapter 3. No biases were found in the signal processing procedures themselves, but a substantial bias was found at high insect speeds due to the insect's time within the beam being less than the minimum required for signal processing. The bias increased with decreasing beamwidth and was thus especially marked at low altitudes. A procedure for estimating its effect was devised.

Can IMRs be designed holistically to match particular requirements? See Section 3.6 in Chapter 3. First establish the number, size, and altitude of insects that the IMR is required to detect. The IMR can then be holistically tailored to suit by simultaneously adjusting antenna diameter and transmitted power to maintain the required maximum altitude and maximise the processable proportion of received signals. The choice of gate height and width is best decided by field trials.

What is the relation between an insect's size and its radar properties? See Chapter 4. In broad terms, the larger the insect the larger its RCS and the more complex its CLPP. Previous investigations have been limited by their focussing on only one of the four CLPP quadrants. The use of all four CLPP quadrants (even though the others are not retrievable by the algorithms presently in use) has clarified some previously obscure relationships such as those between RCS parameters and insect size and shape.

Is it possible to distinguish between different types of insects from their reflectivities? See Chapter 5. Existing methods gave generally disappointing results. A new method based on all RCS characteristics (not just the average RCS value) was successful in distinguishing between Australian plague locusts and spring moths.

351 How does weather affect insect migration in inland eastern Australia? See Chapter 6. Weather has a significant effect on the migration of Australian plague locusts and spring moths, especially rainfall on the migration of locusts. Overall three weather variables (temperature, pressure, days since rain) accounted for 48% of the variance in moth numbers. Once sufficient rain had fallen to stimulate takeoff, six weather variables (temperature, humidity, rainfall, wind speed, rainfall in the preceding ten days, pressure) accounted for 38% of the variance in locust numbers. The best single predictor of insect numbers was temperature. Moonlight had no significant effect.

What is the scale of such migrations and where are IMRs best located? See Chapter 7. The use of two fixed IMRs 308 km apart and a mobile IMR variously in between suggested that the two fixed IMRs were sampling the same peak migration on roughly 50% of occasions, on which the migrations were about 600 km in width, and that peak migrations were up to 100 km in length on roughly 75% of occasions, and perhaps up to 200 km for the rest. A migrating population could be carried by the wind for 500 km or more in a single night in almost any direction. Possible sites for future IMRs are identified and discussed in Section 7.7.2.

8.2 Recommendations for Future Work

Despite the success of radar entomology much remains to be explored. IMR methods have been strong on remote sensing but weak on reliability, location, and species classification. Reliability is essentially a matter of technology and is therefore in principle solvable. Location is less of a problem if mobile IMRs are available. Target classification appears possible at the level of groups (e.g. locusts vs. moths as in the present study), and between species whose radar properties are naturally distinct (e.g. very large insects vs. very small insects). But classification in general remains the most difficult problem.

352 The following five recommendations for future work are aimed at areas that the present work has identified as being in need of attention. Each recommendation represents a sizable research project.

1. Field calibration of IMRs. All the IMRs constructed to date have been calibrated as a subsystem in laboratories, not as a full system in the field.. Therefore methods are needed that will calibrate an IMR under field conditions. One possible approach might be to suspend known radar targets from a tethered balloon or from a support linking two tethered balloons, although the IMR's narrow vertical beam makes all such approaches difficult. Mobile IMRs should also be tested next to each fixed IMR.

2. IMR Reliability. Priority should be given to reducing hardware and software faults, and at improving IMR data transmission from remote areas. Modern computer technology such as high-capacity hard drives, DVD burners, and broadband satellite connections offer practicable solutions.

3. Laboratory RCS data. Laboratory measurements of individual locusts, spring moths and other Australian migratory insects should be made. Their radar properties are fundamental to our understanding of IMR observations, so it is surprising that relatively few studies have been made. No equipment currently exists in Australia for this specific purpose but it may be possible to adapt existing facilities including one at the UNSW Canberra campus.

4. Longer mobile IMR studies. The scale of insect migration within the study area should be further investigated with the mobile IMR over a much longer time period than the eight nights of the present study. (The present mobile IMR needs a cooled weatherproof housing for the electronics so it can operate unattended for a month or so. A submission for the required funds has already been made.)

353 5. Extend study area. The present study should be extended to other areas and perhaps to other insect species. Mobile or fixed IMRs should be operated in areas where large-scale migrations are likely, together with biological surveys to provide an entomological basis for the IMR observations.

8.3 Concluding Remarks

The new era of radar entomology predicted by Drake (1993) seems to be well underway. The previous era (roughly 1968 - 1990) involved mostly scanning radars in studies of insect behaviours and their relation to the atmosphere. These studies were seen as a major advance in insect migration research. For example, according to Reynolds (1988), the scanning radar:

Opened the door to a secret world, remote from our everyday, earth- bound experience, and provided a glimpse as startling in some ways as the first views through the microscope.

In the new era the use of entomological radars is being extended beyond simple insect studies into season-long monitoring of insect pests. This new application arose from the 1990s development of automated IMRs that allowed continuous observation of pest movements over many months, which was an observing schedule not achievable with the earlier manually-operated scanning radars. Subsequent advances in radar technology, plus the evolution of digital technology, allowed the results from IMR sites to be rapidly disseminated to pest-management organisations. Although the Australian IMR network was limited to two IMRs, it was the first to fulfill the vision of Bent (1984), who, when writing of aphid monitoring in the UK, commented:

It is envisaged that a number of these automatic systems will be strategically sited … and be linked directly … over the telephone system. In operation each radar will collect information about the numbers of insects in different categories flying at the various monitoring heights. … At suitable times the radar computer will be contacted via its modem and the stored information relayed to a host computer. … The data will then be used … to produce up to the minute pest warnings and for improved forecasts. 354 Today, thanks to the Internet, the information produced by IMRs is even more readily disseminated than Bent envisaged, and can now be readily accessed by farmers, researchers, and pest-management organisations. Indeed, the volume and quality of information on insect behaviour acquired by IMRs over periods of several years, at relatively low cost, is allowing insect flight to be studied to a level of detail that was not considered possible thirty years ago. For example Fowler and LaGrone (1969), in an early comparison of insect and radar characteristics, commented:

It does not seem likely that one could predict the orientation of an insect in flight at altitudes at which dot angel [phantom] echoes have been observed … The polarisation dependence of insect orientation offers little hope of positively identifying insects…

The last may not be true, but much research needs to be done before we can be sure. For example, even insect flight speed was recently considered to be "one of the least known features of flight performance" (Dudley, 1997). Indeed, the largest study of insect free flight made up to the 1990s followed a total of 270 individuals over a lake using a boat, and took ten months spread over three years (Dudley and Srygley, 1994). Today IMRs routinely observe thousands of insects in free flight every night.

The present work has shown that insect targets can be classified by IMRs into categories related to size and shape (categories which can be related to particular species when only those species are known to be present), that their movements over large areas can be quantified, and that fixed and mobile IMRs make possible hitherto unfeasible studies of insect migration including the effects of weather, in locations almost without limit. The "secret world" of high-altitude insect flight seems certain to be revealed still further.

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389 APPENDIX: INSECT RCS AND BIOMETRIC DATA

390 Table A.1: Biometric data for the RCS measurements presented in Table A.2.

Source Species Mass (mg) Length (mm) Width (mm) Aldhous, 1989 1T. oleracea 45 17.7 1.7 2T. oleracea 49 18.7 1.6 3A. repandata repandata 52 18.9 2.9 4M. secalis 53 14 3 5C. brunneus 68 15.6 2.1 6N. janthina 80 15.5 4.5 7H. sylvina 82 15.5 3 8N. janthina 82 17 4 9C. brunneus 97 16.9 1.9 10O. plecta 100 14.2 4.1 11X. xanthaographa 102 16.3 3.2 12A. gamma 107 20.5 4.4 13A. tragopoyinis 110 17.9 4.3 14H. sylvina 113 17.3 3.5 15A. gamma 118 19.4 4.4 16X. c-nigrum 125 17.5 5 17X. xanthaographa 126 17.8 4.2 18A. urticae 128 21.5 4.2 19N. comes 133 18.5 4.5 20A. gamma 149 22.9 4.7 21A. urticae 160 21.2 3.6 22C. brunneus 173 20.2 2.9 23N. comes 176 19.7 4.9 24C. brunneus 188 22 2.9 25C. brunneus 190 20.8 3 26C. brunneus 200 21.3 3 27A. exclamationis 208 19 5.5 28C. brunneus 214 21.7 2.9 29N. pronuba 270 27.3 6.6 30N. pronuba 295 23 5.7 31D. plexxippus 305 30.2 3.7 32N. pronuba 321 26 5 33N. pronuba 333 24.5 7 34N. pronuba 337 25 6.5 35N. pronuba 400 26.8 6.2 36N. pronuba 419 25.8 7.1 37N. pronuba 443 26.9 6.7 38N. pronuba 451 26 7.5 39N. pronuba 457 27 7.6 40N. pronuba 459 25.5 7 41N. pronuba 495 28.8 7.5 42N. pronuba 538 27.5 7.8 43N. fimbriata 648 24.5 9

391

Source Species Mass (mg) Length (mm) Width (mm) 44S. gregaria 1084 46.6 4.8 45S. gregaria 1133 50.4 5.6 46S. gregaria 1371 48.3 5.4 47S. gregaria 1494 47.5 5.1 48S. gregaria 1532 50.7 5 49S. gregaria 1713 54.5 6.5 50S. gregaria 1751 51.2 5.4 51S. gregaria 2241 56.7 6.1 52S. gregaria 2326 55.4 6.8 53S. gregaria 2474 58.1 6.6 54S. gregaria 3094 62.3 6.9 Wolf et al., 1993 55L.c.s borer 9 8 1.4 56Boll weevil 10 5 2 57Boll weevil 11 5 2 58L.c.s borer 14 10 2 59Honeybee worker 99 11 4 60Fall armyworm 100 14.5 3.5 61Stink bug 132 14.5 8 62Honeybee worker 150 11 4 63Honeybee drone 182 14 5 64Honeybee queen 185 16 4.5 65Honeybee queen 196 16 4.5 66H. zea male 206 14.5 3.5 67Honeybee drone 208 14.5 5.5 68H. zea female 254 17 5

392 Table A.2: Statistical summary data for the insects measured by Aldhous (1989) and Wolf et al. (1993).

Species No. Mass (mg) Length (mm) Width (mm) Ave. SD. Ave. SD. Ave. SD. Aldhous, 1989 T. oleracea 2 47.0 2.8 18.2 0.7 1.7 0.1 A. repandata repandata 1 52.0 18.9 2.9 M. secalis 1 53.0 14.0 3.0 C. brunneus 7 161.4 56.0 19.8 2.5 2.7 0.5 N. janthina 2 81.0 1.4 16.3 1.1 4.3 0.4 H. sylvina 2 97.5 21.9 16.4 1.3 3.3 0.4 O. plecta 1 100.0 14.2 4.1 X. xanthaographa 2 114.0 17.0 17.1 1.1 3.7 0.7 A. gamma 3 124.7 21.8 20.9 1.8 4.5 0.2 A. tragopoyinis 1 110.0 17.9 4.3 X. c-nigrum 1 125.0 17.5 5.0 A. urticae 14 113.0 23.9 18.2 2.6 4.1 0.6 N. comes 2 154.5 30.4 19.1 0.8 4.7 0.3 A. exclamationis 1 208.0 19.0 5.5 N. pronuba 13 401.4 82.8 26.2 1.5 6.8 0.8 D. plexxippus 1 305.0 30.2 3.7 N. fimbriata 1 648.0 24.5 9.0 S. gregaria 16 1416.1 825.2 44.9 12.9 6.2 1.3 Wolf et al., 1993 L.c.s borer 2 11.5 3.5 9.0 1.4 1.7 0.4 Boll weevil 2 10.5 0.7 5.0 0.0 2.0 0.0 Fall armyworm 1 100.0 14.5 3.5 H. zea female 2 230.0 33.9 15.8 1.8 4.3 1.1 Honeybee drone 2 195.0 18.4 14.3 0.4 5.3 0.4 Honeybee queen 2 190.5 7.8 16.0 0.0 4.5 0.0 Honeybee worker 2 124.5 36.1 11.0 0.0 4.0 0.0 Stink bug 1 132.0 14.5 8.0

393 Table A.3: Biometric measurements for C. terminifera and H. punctigera.

Index Sex Body length Body Width Weight Wing Span (mm) (mm) (mg) (mm) C. terminifera1 1 F 26.5 7.1 2 F 28.3 6.9 3 M 26.0 6.7 4 F 28.8 7.2 5 M 27.5 6.8 6 F 29.4 6.4 7 M 27.3 6.2 8 M 26.7 6.6 9 F 25.0 6.3 10 F 27.6 7.1 11 F 30.0 7.1 12 F 30.1 7.8 13 F 30.1 7.5 14 F 30.8 7.4 15 M 22.4 6.4 16 M 22.2 5.3 H. punctigera2 1 17.00 5.61 151.5 38.60 2 16.10 5.30 140.3 37.65 3 17.21 5.55 101.4 34.00 4 16.50 5.65 109.0 35.28 5 19.72 6.00 107.4 37.20 6 15.47 5.00 108.4 35.08 7 16.00 5.11 128.8 36.80 8 14.52 5.05 130.6 34.27 9 16.95 5.04 109.2 33.10 1Measured by the author on 11 Feb 2003 at the Australian Plague Locust Commission. 2Measured by J.E. Down and M.J. Storer on 17 October 1980 at the CSIRO Division of Entomology.

394 Table A.4: RCS data for the insects in Table A.1.

Source σXX σYY 2 2 2 2 2 a0 (cm ) a2 (cm ) a4 (cm ) θ2 (°) θ4-θ2 (°) (cm ) (cm ) Aldhous, 1989 1 0.25 0.25 0.028 -21.9 4.2 0.528 0.028 2 0.18 0.23 0.049 -2.4 1 0.459 -0.001 3 0.28 0.24 0.036 -26.1 -1.4 0.556 0.076 4 0.091 0.091 0.002 10 -13.4 0.184 0.002 5 0.63 0.56 0.13 -14.3 -4.2 1.32 0.2 6 0.73 0.59 0.078 -2.7 -4 1.398 0.218 7 0.14 0.13 0.029 2 2.8 0.299 0.039 8 0.33 0.2 0.053 6.3 0.5 0.583 0.183 9 0.39 0.44 0.1 -4.8 -3.6 0.93 0.05 10 0.7 0.66 0.14 1.5 -0.2 1.5 0.18 11 0.83 0.82 0.15 -3.5 -2.1 1.8 0.16 12 0.49 0.52 0.13 5.1 -0.2 1.14 0.1 13 0.98 0.97 0.2 -1.6 -0.2 2.15 0.21 14 0.28 0.25 0.054 4.4 0.9 0.584 0.084 15 0.88 0.82 0.18 -1.5 1.5 1.88 0.24 16 1.2 1.36 0.34 -5 0.4 2.9 0.18 17 1.03 1.16 0.29 -0.3 0.8 2.48 0.16 18 1.26 1.31 0.31 8.2 0.3 2.88 0.26 19 1.51 1.67 0.37 1.2 -1.6 3.55 0.21 20 1.5 1.58 0.31 -6.6 -0.7 3.39 0.23 21 1.22 1.11 0.21 -13.5 5.8 2.54 0.32 22 2.36 3.08 0.85 5.1 -0.2 6.29 0.13 23 1.62 1.75 0.38 -2.3 -0.6 3.75 0.25 24 1.73 2.26 0.74 0.1 0.4 4.73 0.21 25 2.07 2.63 0.84 3.3 0 5.54 0.28 26 1.57 2 0.87 -2.6 1.3 4.44 0.44 27 1.85 1.36 0.25 0.7 -2.1 3.46 0.74 28 1.52 1.95 0.73 4.9 0.2 4.2 0.3 29 1.84 1.54 0.31 0.4 -0.6 3.69 0.61 30 1.66 1.35 0.41 -3.8 0.4 3.42 0.72 31 2.21 1.96 0.37 4.9 -0.7 4.54 0.62 32 0.97 0.87 0.31 3.5 1 2.15 0.41 33 2.72 2.03 0.14 -3.6 -8.3 4.89 0.83 34 1.59 0.85 0.38 -4.8 2.3 2.82 1.12 35 1.88 1.74 0.28 -0.5 -2 3.9 0.42 36 1.84 0.7 0.43 -1.6 0.9 2.97 1.57 37 2.33 0.77 0.5 -3.1 2 3.6 2.06 38 2.28 0.29 0.52 -1.8 1.1 3.09 2.51 39 2.71 0.36 0.62 -11.6 10.4 3.69 2.97 40 1.77 0.98 0.62 -8.7 2.1 3.37 1.41

395

Source σXX σYY 2 2 2 a0 (cm ) a2 (cm ) a4 (cm ) θ2 (°) θ4-θ2 (°) (cm2) (cm2) 41 2.55 0.71 0.55 4 0.9 3.81 2.39 42 2.49 0.19 0.55 -46.6 -1.1 3.23 2.85 43 2.16 0.22 0.36 -89.4 -1.2 2.74 2.3 44 4.11 2.22 1.17 -86.8 -1.8 7.5 3.06 45 4.58 1.6 0.83 -80.8 -5.7 7.01 3.81 46 4.69 1.67 1.17 -75.3 -11.5 7.53 4.19 47 5.3 2.55 1.22 -78.5 -7.2 9.07 3.97 48 4.88 0.88 0.6 -60.2 -20.1 6.36 4.6 49 9.24 2.05 0.37 -75.9 -12.8 11.66 7.56 50 5.44 4.15 1.32 -83.7 -2.4 10.91 2.61 51 9.64 4.61 0.97 -89.5 -2 15.22 6 52 10.9 4.96 1.34 -78.1 -7.1 17.2 7.28 53 7.17 6.42 1.76 88.3 -2.2 15.35 2.51 54 16.8 12.5 3.21 -89 -2.1 32.51 7.51 Wolf et al., 1993 55 0.0127 0.0125 0.0034 -1.4 0 0.0286 0.0036 56 0.005 0.0044 0.00064 -0.5 2.2 0.01004 0.00124 57 0.0129 0.0103 0.00074 -0.8 2.2 0.02394 0.00334 58 0.081 0.087 0.015 1.6 -0.7 0.183 0.009 59 0.41 0.38 0.049 0.7 -1.9 0.839 0.079 60 0.53 0.6 0.149 1.5 -3 1.279 0.079 61 1.48 0.98 0.175 1 -2.3 2.635 0.675 62 0.15 0.14 0.023 -0.7 1.7 0.313 0.033 63 0.78 0.54 0.243 0.1 -0.3 1.563 0.483 64 1.03 1.06 0.495 -0.6 0.9 2.585 0.465 65 0.82 0.88 0.328 -0.5 1 2.028 0.268 66 0.41 0.39 0.071 0.9 -1.9 0.871 0.091 67 1.04 0.64 0.285 0.9 -1.4 1.965 0.685 68 1.79 1.62 0.291 -1.2 2.7 3.701 0.461

396