Remote Sensing Tropical Cyclone Rainfall Over the Southwest Pacific Region

Remote Sensing Tropical Cyclone Rainfall over the Southwest Pacific Region

Anil Deo

Submitted in total fulfilment of the requirements for the degree of

Doctor of Philosophy

School of Earth Sciences The University of Melbourne Melbourne, Australia

18 April 2018

This thesis is dedicated to my wife Madhu Malti Devi and daughter Adria Vaneesha Deo.

Without their support and patience, the successful completion of this work would not have

been possible.

Abstract

The south-west Pacific (SWP) region is susceptible to the catastrophic effects of tropical cyclones (TCs). The region, therefore, has received adequate attention in terms of scientific research pertaining to TC genesis, tracks and intensity. It (especially the island countries), nonetheless, has not received much attention, in comparison to studies elsewhere

(e.g. the Atlantic and western North Pacific region), on additional important aspects of TCs such as rainfall estimation and characteristics of the TC-related rainfall drop size distribution

(DSD). The latter has implications for radar rainfall estimation and cloud modelling studies.

In this thesis, we first validate the Tropical Rainfall Measuring Mission (TRMM) Multi- satellite Precipitation Analysis (TMPA) 3B42 quantitative precipitation estimates (QPEs) during the passage of TCs over New Caledonia and Fiji.

It is shown that TMPA has skill in representing the rainfall during the passage of TCs over New Caledonia and Fiji. TMPA overestimates light rainfall and underestimates moderate to heavy daily rainfall. The skill deteriorates with increasing elevation, as underestimation is greater at large altitudes. The ability of TMPA also varies with TC intensity and distance from the TC centre, whereby it is more skilful for less intense TCs

(category 1-2) and near the TC centre than in the outer rainbands.

The rainfall DSD during the passage of TCs over Darwin, Australia, is evaluated next and this is compared with the DSD associated with non-tropical cyclone (non-TC) events. It is shown that the TC-related DSD is statistically different from the non-TC related DSD, the former encompassing a larger concentration of small to moderate size drops. The TC related drop diameter is lower than the non-TC values at all rain rates and also for the different precipitation types (convective, transition and stratiform). The TC DSD also varies with distance from the TC centre, as rainfall near the TC centre comprises of relatively smaller drops which are strongly evident at small to moderate rainfall rates (< 30 mm hr-1). These

iii variations in the DSD have implications for the parameters used in the algorithm that converts radar reflectivity to rainfall rate, as well as for the analytical expressions used in describing the observed DSD employed in cloud modelling parameterizations.

Finally, the feasibility of estimating the DSD parameters using (i) the TRMM precipitation radar (PR) and (ii) a combined PR and TRMM Microwave Imager (TMI) algorithm (COM) is investigated using the Darwin C-band dual polarised (C-POL) ground radar (GR) as the reference. The correspondence of the TRMM instruments with the GR is generally dependent on the precipitation type: the PR and the COM usually overestimate

(underestimate) the reflectivity and the rainfall rate from events that are highly stratiform

(convective) whereas they mostly overestimate the median volume diameter (Do) of all rainfall types whereby the overestimation increases with an increase in the percentage of convective fraction. Also, the COM reflectivity estimates are similar to the PR estimates but it has a smaller bias in the Do for most of the greater stratiform events. This suggests that combining the TMI with the PR adjusts the Do towards the “correct” direction if the GR is taken as the reference. Moreover, for the TC events considered in this study, the association of the TRMM estimates with the GR is similar to the highly stratiform non-TC events (there is no significant difference) but it differs largely from the majority of the highly convective non-TC events.

Declaration

This is to certify that:

(i) this thesis comprises only my original work towards the Doctor of Philosophy except

where indicated,

(ii) due acknowledgement has been made in the text to all other material used,

(iii) the thesis is less than 100,000 in words in length, exclusive of tables, maps,

bibliographies and appendices.

______

Acknowledgements

This research would not have been successful without the kind support of various people and institutions. A sincere appreciation is extended to the Australian Government

Department of Education for funding my PhD at the University of Melbourne through the

Endeavour Postgraduate Award. A hearty thanks to my supervisor Prof. Kevin Walsh for his expert guidance and support during my candidature. Thanks, also to the two PhD panel members, Dr. Robyn Schofield and Dr. Richard Dare, for their guidance and advice. I would also like to extend my gratitude to Dr. Stephen Munchak of the Goddard Space Flight Centre

(GSFC), NASA and Dr. Alexander Peltier of Meteo-France, New Caledonia for their kind contribution to certain aspects of this thesis. Thanks to Dr. Ravin Deo of Monash University,

Dr. Savin Chand of Federation University Australia, Dr. Visagaperuman Ramachandran of

Fiji National University and Prof. Sushil Kumar of the University of the South Pacific for their support and guidance during the PhD application process.

I would also like to thank Drs. Alain Protat, Michael Whimpey, Valentin Louf, Yen Jun

Chen, and Surendra Rainuyar from the Bureau of Meteorology and Dr. Robert Warren of

Monash University for their support on certain aspects of this project. Thanks to the Fiji

Meteorological Services and Swastika Sharan from the same institution and the Australian

Bureau of Meteorology for providing the necessary data.

I would also like to acknowledge the Melbourne International Fee Remission

Scholarship for covering the tuition gap. Thanks to the ARC Centre of Excellence for

Climate System Science and its respective institutions for funding my attendance to workshops, winter school and a visit to the GSFC NASA laboratory. Special thanks to Dr.

Munchak and Jasmine Smith from GSFC for providing the necessary support during my visit.

Thanks to the members of the School of Earth Sciences especially Toni Fraser,

Charlotte Mcloughlin and Katrina Swell for their administrative support. My appreciation

vi also to Cheryl Goult, Laveena Lobo and Ashleigh Cook from Scope Global Pty Limited, responsible for managing the Endeavour Awards, for their caring and support.

Finally, a sincere graduate to my parents, Mrs. Gyan Wati and Late Mr. Prem Deo, who passed away during my final year of candidature, my wife Madhu Devi, my daughter Adria

Deo, my brother Ashneel Deo and my in-laws Mr. and Mrs. Anand Kumar for their continued support.

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Publications

The thesis comprises the following manuscripts which are either published or submitted for publication in international referred journals:

Chapter 4: Deo, A., Walsh, K.J.E., Peltier, A., 2016. Evaluation of TMPA 3B42

precipitation estimates during the passage of tropical cyclones over New

Caledonia. Theor. Appl. Climatol.1-17.

Chapter 5: Deo, A., Walsh, J.E., 2016. Evaluation of TRMM multi-satellite precipitation

analysis during the passage of tropical cyclones over Fiji. Journal of Southern

Hemisphere Earth Systems Science, 66, 442-456.

Chapter 6: Deo, A., Walsh, K.J.E., 2016. Contrasting tropical cyclone and non-tropical

cyclone related rainfall drop size distribution at Darwin, Australia. Atmos.

Res., 181, 81-94.

Chapter 7: Deo, A., Munchak, S.J., Walsh, K.J.E., 2018. Cross-validation of rainfall

characteristics estimated from the TRMM PR, a combined PR-TMI algorithm

and a C-POL ground-radar during the passage of tropical cyclone and non-

tropical cyclone events over Darwin, Australia. J. Atmos. Oceanic Technol

(Accepted for Publication, October 2018)

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Contents

1 Introduction and Objectives ...... 1

1.1 Introduction ...... 1

1.2 Aims and Objectives ...... 4

1.3 Thesis Outline ...... 5

2 Literature Review ...... 6

2.1 TC Genesis ...... 7

2.2 Quantitative Precipitation Estimation (QPE) during the passage of TCs ...... 7

2.2.1 Evaluation of TRMM-based precipitation products during the passage of TCs .. 9

2.3 Cloud Dynamics and Microphysics ...... 11

2.3.1 Warm Clouds (liquid phase) ...... 11

2.3.2 Cold clouds (mixed phase) ...... 13

2.3.3 Dynamical and Microphysical Processes in Stratiform and Convective

Precipitation ...... 16

2.4 Empirical Formulation of the DSD ...... 19

2.4.1 Rainfall DSD and Weather Radar Rainfall Estimation ...... 20

2.4.2 DSD Characteristics during the Passage of TCs ...... 22

2.5 Comparison of rainfall characteristics measured from the TRMM PR and Dual-

Polarised Ground Radars ...... 24

3 Data and Methodology ...... 28

3.1 Evaluation of the TRMM 3B42 estimates over Fiji and New Caledonia ...... 29

3.2 Tropical Cyclone and non-Tropical Cyclone related Rainfall Drop Size Distribution

over Darwin ...... 29

3.3 Comparison of the rainfall characteristics estimated from the TRMM PR, COM and

the Darwin C-POL radar ...... 30

3.3.1 Darwin C-POL Radar ...... 30

3.3.2 TRMM PR ...... 31

3.3.3 TRMM COM ...... 33

3.3.4 Methodology for Aligning the PR and the GR ...... 34

3.3.5 Statistical Metrics ...... 36

4 Evaluation of TMPA 3B42 Precipitation Estimates during the Passage of

Tropical Cyclones over New Caledonia ...... 38

4.1 Introduction ...... 40

4.2 Data and Methodology ...... 43

4.2.1 TMPA ...... 43

4.2.2 New Caledonia Rain Gauge Data ...... 45

4.2.3 Methodology ...... 47

4.3 Results...... 50

4.3.1 Skill With Respect To Elevation ...... 52

4.3.2 Skill with respect to TC intensity, distance from TC centre and position of TC

centre with respect to the island ...... 59

4.3.3 Case Studies ...... 66

4.4 Discussion and Summary ...... 71

5 Evaluation of TRMM Multi-satellite Precipitation Analysis during the passage

of Tropical Cyclones over Fiji ...... 77

5.1 Introduction ...... 78

5.2 Data and Methodology ...... 79

5.2.1 TMPA ...... 79

5.2.2 Fiji Rain Gauge Data ...... 81

5.2.3 Methodology ...... 81

5.3 Results...... 85

5.3.1 Case Studies ...... 90

5.4 Discussion and Summary ...... 93

6 Contrasting Tropical Cyclone and non-Tropical Cyclone related Rainfall Drop

Size Distribution at Darwin, Australia ...... 97

6.1 Introduction ...... 98

6.2 Data and Methodology ...... 100

6.3 Results...... 106

6.3.1 Individual TCs ...... 106

6.3.2 Contrasting TC and non-TC DSD ...... 111

6.3.3 TC distance stratification ...... 117

6.3.4 Comparison of TC DSD between Darwin and other Regions ...... 119

6.3.5 Radar Z-R Parameters ...... 120

6.3.6 Analytical Expression - Gamma Function ...... 124

6.4 Summary ...... 130

7 Cross-validation of rainfall characteristics estimated from the TRMM PR, a

combined PR-TMI algorithm and a C-POL ground-radar during the passage of

tropical cyclone and non-tropical cyclone events over Darwin, Australia ...... 134

7.1 Results and Discussion ...... 135

7.1.1 Case Descriptions ...... 135

7.1.2 Comparison of Reflectivity ...... 137

7.1.3 Comparison of Do ...... 146

7.1.4 Comparison of Rainfall Rate ...... 150

8 Summary and Recommendations for Future Work ...... 155

References ...... 160

Tables

Table 4.1 Contingency Table...... 48

Table 4.2 Rainfall categories and thresholds. Column 1 is used for analysing the RMSE,

column 2 for the relative bias and column 3 for the categorical statistics...... 49

Table 4.3 TC categories and their corresponding central pressure as used by Australian

BOM...... 49

Table 4.4 Pattern matching statistics for comparison of TMPA estimates with rain gauge

observations. The entries in the bracket are the 95 % confidence interval...... 51

Table 4.5 The four extreme gauge rainfalls with their corresponding TMPA rain estimates

for TC Vania (2011), Innis (2009) and Erica (2003). The rainfalls are in mm

day-1 ...... 70

Table 5.1 Contingency Table ...... 83

Table 5.2 Rainfall categories and thresholds. Column 1 is for the relative bias and column

2 for the categorical statistics...... 84

Table 5.3 Pattern matching statistics for comparison of TMPA estimates with rain gauge

observations. The entries in the bracket are the 95 % confidence interval...... 86

Table 6.1 Disdrometer and rain gauge accumulated rainfall (AR) of the seven TCs...... 103

Table 6.2 RMSE between the observed and estimated drop concentration using moments

M234, M246 and M346...... 105

Table 6.3 Rainfall rate classes or categories...... 106

Table 6.4 Liquid water content (LWC), rain rate (R) and Dm around reflectivity 40 dBZ

(39 – 41) of TCs over Darwin compared with that over the western Pacific;

Atlantic; and Bay of Bengal (BOB - India) during the southwest and northeast

monsoon (SWM and NEM) seasons...... 120

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Table 6.5 Z-R relation (Z = ARb) coefficient (A) and power (b) of TCs over different

regions. The values presented are without rainfall type (convective, stratiform or

transition) stratification...... 123

Table 6.6 TC and non-TC mean and median gamma parameters. The values in the

brackets accompanying the mean are the 95 % confidence interval...... 125

-1 Table 6.7 TC and non-TC mean and median slope, Λ (mm ); shape, μ and intercept, No

(m-3mm-1), parameters of the convective, transition and stratiform rainfall types.

...... 128

Table 7.1 TC (numbers 1 and 2) and non-TC (numbers 3 – 13) overpass events and their

corresponding TRMM orbit number ...... 137

Table 7.2 PR and GR rainfall rate comparison from previous studies...... 154

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Figures

Figure 2.1 TC formation basins: 1 - North Atlantic, 2 - Eastern North Pacific, 3 – Western

North Pacific, 4 – North Indian, 5 – Western South Indian, 6 – Eastern South

Indian, and 7 – Western South Pacific basin (the region enclosing the Pacific

Island countries). Source: http://www.aoml.noaa.gov/hrd/tcfaq/F1.html ...... 7

Figure 3.1 Schematic of the volume matching technique. (a) Averaging of PR bins in the

vertical at the intersection of the PR with the GR and (b) averaging of the GR in

the horizontal at the intersection of the PR with the GR...... 34

Figure 4.1 Location of New Caledonia (enclosed in the dashed red rectangular box) in the

south-west Pacific basin ...... 43

Figure 4.2 Rain gauge locations on the main island, Grande Terre, New Caledonia. The

blue crosses are stations with elevation less than 300 m and the red circles are

stations with elevation greater than 300 m. The numbers in the grid boxes are

the GPCC Monitoring Product Version 6 gauge-based analysis number of

stations per 1º grid for year 2012 (January – December) over the New Caledonia

region...... 46

Figure 4.3 2D histogram of TMPA against rain gauge data together with the line of perfect

agreement for the period 1998 – 2012. The colour bar shows the number of

observations in each bin...... 50

Figure 4.4 (a) RMSE and relative RMSE between the TMPA estimates and the gauge

observations as a function of rainfall (mm day-1). The error bars indicate a 95 %

confidence interval. (b) Percentage rainfall at each of the rainfall categories.... 52

Figure 4.5 (a) Relative bias as a function of gauge rainfall (yellow squares with solid line)

on the island sites. The sites are further separated into two subgroups according

to elevation: elevation less than 300 m (red circles with solid line) and elevation

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greater than 300 m (green diamonds with dashed line). The error bars indicate

the 95 % confidence interval. (b) Percentage rainfall at each of the rainfall

categories for the three groups computed with respect to the total rainfall of the

respective group...... 54

Figure 4.6 (a-d) Categorical statistics: (a) POD; (b) FAR; (c) FBI and (d) ETS over the

island (yellow squares with solid line). The sites are further separated into two

subgroups according to elevation: elevation less than 300 m (red circles with

solid line) and elevation greater than 300 m (green diamonds with dashed line).

The error bars indicate the 95 % confidence interval. (e) Percentage rainfall

above each of the rainfall thresholds for the three elevation groups computed

with respect to the total rainfall of the respective group...... 56

Figure 4.7 Average TC rainfall of gauge observations (a), TMPA estimates (b) and the

relative bias (c) at station sites which have at least 10 samples...... 59

Figure 4.8 (a-d) Categorical statistics: (a) POD; (b) FAR; (c) FBI and (d) ETS for category

1-2 (cat12, yellow squares) and category 3-5 (cat 35, red circles) TCs. The error

bars indicate the 95 % confidence interval. (e) Percentage rainfall above each of

the rainfall thresholds for the two intensity groups computed with respect to the

total rainfall of the respective group...... 61

Figure 4.9 (a‒d) Categorical statistics: (a) POD; (b) FAR; (c) FBI and (d) ETS for TCs

with centres less than 200 km (yellow squares) and greater than 200 km (red

circles). The error bars indicate the 95 % confidence interval. (e) Percentage

rainfall above each of the rainfall thresholds for the two distance groups

computed with respect to the total rainfall of the respective group...... 62

Figure 4.10 (a‒d) Categorical statistics: (a) POD; (b) FAR; (c) FBI and (d) ETS for east

(yellow squares) and west (red circles) TCs. The error bars indicate the 95 %

confidence interval. (e) Percentage rainfall above each of the rainfall thresholds

for the two position groups computed with respect to the total rainfall of the

respective group...... 65

Figure 4.11 Average distance of TC centres from gauge stations for TC days 1, 2, 3,4 and 5

for east (yellow squares) and west (red circles) TCs. The TC days are days (24

hours) counted from the time a TC first enters within the 500 km zone from any

gauge station...... 66

Figure 4.12 (a) Mean gauge rainfall, the corresponding mean TMPA estimates and the

relative bias of the 12 TCs that have at least 10 observations and whose spatial

correlation coefficient (r) between the TMPA estimates and gauge observations

are statistically significant at 95% confidence level. The TCs are arranged in the

order of ascending average gauge rainfall. The TCs used as case studies to

demonstrate the ability of TMPA are shown in the brackets (name and year).

The error bars indicate the 95% confidence interval. (b) RMSE, relative RMSE

and the spatial correlation coefficient (r) of the 12 TCs shown in panel (a)...... 67

Figure 4.13 24 hour accumulated gauge and TMPA estimate rainfall of TC Vania (a and b

respectively), Innis (c and d respectively) and Erica (e and f respectively) on the

landfall day (landfall date and time of each TC are respectively shown in the

TMPA estimate panel). The black dashed line shows the track of the TCs...... 69

Figure 4.14 Categorical statistics (a) POD; (b) FAR; (c) FBI and (d) ETS of land-falling

TCs shown in Figure 4.13 (i.e. Vania (2011), Innis (2009) and Erica (2003)).

The error bars indicate a 95 % confidence interval...... 71

Figure 5.1 Location of Fiji (enclosed in the dashed red rectangular box) in the south west

Pacific basin...... 80

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Figure 5.2 Rain gauge locations over Fiji. The crosses are stations with elevation less than

300 m and the circle is the station with elevation greater than 300 m. The

numbers in the grid boxes are the GPCC Monitoring Product Version 6 gauge

based analysis number of stations per 1º grid for year 2012 (January –

December) over the Fiji region...... 82

Figure 5.3 2D histogram of TMPA against rain gauge data together with the line of perfect

agreement for the period 1998 – 2012. The colour bar shows the number of

observations in each bin...... 86

Figure 5.4 Relative bias as a function of gauge rainfall. The error bars indicate the 95 %

confidence interval...... 87

Figure 5.5 Categorical statistics: POD; FAR; FBI and ETS at rainfall thresholds 5, 15, 30,

45, 75 and 100 mm day-1.The error bars indicate the 95 % confidence interval.

...... 88

Figure 5.6 Average TC rainfall of gauge observations (a), TMPA estimates (b) and the

relative bias (c) at station sites which have at least 10 samples...... 89

Figure 5.7 Categorical statistics (a) POD; (b) FAR and (c) ETS for rain within 200 km of

the TC centre and greater than 200 km from the TC centre. The error bars

indicate the 95 % confidence interval...... 90

Figure 5.8 Mean gauge rainfall, the corresponding mean TMPA estimates and the relative

bias of the 15 TCs that have at least 10 observations and whose spatial

correlation coefficient (r) between the TMPA estimates and gauge observations

are statistically significant at 95% confidence level. The TCs are arranged in the

order of ascending average gauge rainfall. The TCs used as case studies (Figure

5.9) to demonstrate the ability of TMPA are shown in the brackets (name and

year). The error bars indicate the 95% confidence interval. b) The spatial

xvii

correlation coefficient (r) and number of samples (spatial data points) of the

individual TCs...... 92

Figure 5.9 24 hour accumulated gauge and TMPA estimate rainfall of TC Cliff (a and b

respectively), Gene (c and d respectively) and Tomas (e and f respectively). The

black dashed lines show the track of the TCs...... 93

Figure 6.1 Tracks of the 7 TCs passing over Darwin (location is shown by a red dot) for the

period 2006 to 2013...... 102

Figure 6.2 Root mean square error (RMSE) in the drop concentration, N(D), between

observed and the gamma fitted distributions using moments two, three and four

(M234); two, four and six (M246) and three, four and six (M346) of the TC and

non-TC drop spectra...... 105

Figure 6.3 Time series (UTC) of drop concentration (N(D) ‒ coloured plot), Dm (black line

with N(D)), distance from TC centre (solid red line), wind speed (solid blue

line) and rainfall rate (black line with distance and wind speed plot) of TC

Carlos (a) and George (b). The colour bar denotes the drop concentration of the

respective TC and the secondary y-axis shows the magnitudes of Dm, distance

and rainfall rate...... 108

Figure 6.4 Average drop concentration (N(D)) of individual TCs with respect to rainfall

rates (a) 0.1 – 0.3, (b) 0.3 – 0.5, (c) 0.5 – 1, (d) 1 – 3, (e) 3 – 5, (f) 5 – 10, (g) 10

– 20, (h) 20 – 30, (i) 30 – 60 and (j) > 60 mm hr-1 for the 20 diameter classes.

(k) Average Dm of non-TC and individual TC DSD spectra with respect to the

10 rainfall classes. The error bars are the 95 % confidence interval...... 111

Figure 6.5 Average drop concentration of the TC and the non-TC rainfall DSD spectra with

respect to the 20 diameter classes. The error bars are the 95 % confidence

interval...... 112

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Figure 6.6 (a) Normalised frequency distribution of rain rates of TC and non-TC drop

spectra. Average DSD of (b) TC and (c) non-TC rainfall events. (d) TC versus

non-TC ratio of average DSD with respect to rain rate and diameter class. .... 114

Figure 6.7 (a) Average Dm of TC and non-TC drop spectra for the 10 rainfall classes. The

error bars are the 95 % confidence interval. (b) Normalised frequency

distribution of Dm with respect to convective (black), transition (blue) and

stratiform (red) rainfall type of TC (solid lines) and non-TC (dashed lines) drop

spectra...... 115

Figure 6.8 Mean Dm of TC and the three distance groups from TC centre (< 60 km, 60 –

200 km and > 200 km) with respect to the 10 rainfall classes. The error bars are

the 95 % confidence interval...... 118

Figure 6.9 Radar rainfall estimation parameters. (a) Pre-factor, A, and (b) power, b, for TC

and non-TC (i.e. All) and rainfall types (convective, transition and stratiform) of

TC and non-TC; and pre-factor, A (red plot) and power, b (blue plot) with

respect to (c) distance from TC centre...... 122

Figure 6.10 Normalised frequency distribution of (a) slope, Λ; (b) shape, μ; and (c)

intercept, No, gamma fitted parameters calculated using moments two, three and

four (M234) of the of TC and non-TC drop spectra...... 124

Figure 6.11 Distribution of (a) slope, Λ; (b) shape, μ; and (c) intercept, log10(No), gamma

fitted parameters (calculated using M234) of the of TC and non-TC drop spectra

with respect to rain rate...... 126

Figure 6.12 Frequency distribution of (a) slope, Λ; (b) shape, μ; and (c) intercept, log10(No),

gamma fitted parameters (calculated using M234) of the of TC and non-TC drop

spectra with rainfall type (black plot – convective, blue plot – transition and red

plot – stratiform)...... 128

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Figure 6.13 Distribution of (a) slope, Λ; (b) shape, μ; and (c) intercept, log10(No), gamma

fitted parameters of the < 60 km, 60 – 200 km and > 200 km distance groups

against rain rate...... 130

Figure 7.1 GR reflectivity at a constant altitude of 3.5 km for the two TC Carlos events (15

February 2011 and 17 February 2011) and for two non-TC widespread events

(13 January and 13 March 2012). The plot in red in a) shows the track of TC

Carlos...... 135

Figure 7.2 Matched reflectivity profiles (in dBZ) from the GR (left), PR (middle) and

COM (right) for the events shown in Figure 7.1 at the 1.3º GR elevation sweep.

...... 138

Figure 7.3 Scatter plot of the matched reflectivity profiles (in dBZ) for altitude less than 4

km from the PR (left) and the COM (right) against the GR for the events shown

in Figure 7.1...... 139

Figure 7.4 Statistics of r (left), RMSE (middle) and Bias (right) of the matched reflectivity

profiles for the events shown in Figure 7.1 for altitude less than 4 km. Events

have been further separated into convective (Conv), stratiform (Strat), over the

land and over the ocean. The error bars show the 95 % confidence interval. .. 141

Figure 7.5 Statistics of (a) r, (b) RMSE and (c) Bias for the TC and non-TC events for

altitude less than 4 km. Panel (d) shows the percentage of convective rainfall of

each event. The TC events are marked as red (the first red point from the left

(event 5) is the 15 February 2011 event and the second red point (event 7) is the

17 February 2011 event). The error bars show the 95 % confidence interval. . 142

Figure 7.6 Reflectivity difference with respect to the GR at the 3 km altitude (a) for the PR

and (b) for the COM for TC 1 (20110214)...... 144

Figure 7.7 Same as Figure 7.5 except for altitude greater than 4 km...... 145

Figure 7.8 Same as Figure 7.3.except for Do...... 147

Figure 7.9 Same as Figure 7.4 except for Do...... 148

Figure 7.10 Same as Figure 7.5 except for Do...... 149

Figure 7.11 Same as Figure 7.3 and Figure 7.8 except for rainfall rate...... 151

Figure 7.12 Same as Figure 7.4 and Figure 7.9 except for rainfall...... 152

Figure 7.13 Same as Figure 7.5 and Figure 7.10 except for rainfall rate...... 153

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1 Introduction and Objectives

1.1 Introduction

It is well established that tropical cyclones (TCs) are associated with extreme amounts of rainfall that has a significant impact on the total rainfall climatology of the affected region.

While there are benefits such as supporting agriculture (Knight and Davis, 2007; Lee et al.,

2010) and filling inland river systems and dams (Middelmann, 2007), the torrential rainfall often causes widespread flooding (Gao et al., 2009; Nogueira and Keim, 2010) that inflicts colossal damage (Kunkel et al., 1999; Elsberry, 2002; Dong et al., 2010) and threatens life

(Rappaport, 2000). The south-west Pacific island region is vulnerable to these drastic consequences of TC heavy precipitation. Therefore, a study is necessary to further investigate the various aspects pertaining TC precipitation such as the quantitative precipitation estimation (QPE) and the rainfall characteristics which could aid in disaster preparedness and/or mitigation over this region.

Considerable advancement in precipitation estimation has been achieved with the advent of remote sensing instruments onboard various orbiting satellites. This has significantly increased the availability of precipitation datasets, which would not have been possible through surface-based measurements alone over much of the globe, particularly in oceanic, remote or developing regions. This improvement in datasets has become highly desirable for disaster mitigation, such as those related to heavy precipitation during the passage of TCs and for validation of models that simulate and forecast these rainfall events.

These precipitation datasets, however, are indirect estimates of rainfall, depending on the properties of the cloud top (in the case of IR algorithms) and the path-integrated hydrometeor content (in the case of passive microwave algorithms) (Wilheit, 1986; Janowiak et al., 2001;

Huffman et al., 2007). To use these rainfall estimates appropriately and confidently for TC

related studies, it is important to estimate their accuracy and expected error characteristics, which could be achieved by validating them against “ground truth” data from rain gauge and/or radar observations.

A popular source of precipitation estimates is the Tropical Rainfall Measuring Mission

(TRMM) multi-satellite precipitation analysis (TMPA) product. TMPA estimates of TCs have been validated over various regions such as China (Yu et al., 2009), Taiwan (Chang et al.,

2013), USA (Habib et al., 2009), Australia (Chen et al., 2013b) and the Pacific atolls and islands (Chen et al., 2013c). The respective studies have shown that TMPA on average has a reasonable ability in representing the spatial and temporal distribution of TC rainfall, yet care should be taken when using it for TC studies as its performance varies under different conditions, for example, the magnitude of rainfall, topography, latitude, intensity of TC, season, and distance from the TC centre. A comprehensive validation, similar to those performed in the regions mentioned above, however, is lacking over specific island nations in the south-west Pacific region which is urgently needed before we can confidently use these data.

Estimates from numerical weather prediction (NWP) models and weather radars are also important sources of precipitation information during the passage of TCs. The rainfall drop size distribution (DSD) plays an important role in numerical models and radar rainfall estimation (Tokay and Short, 1996; Radhakrishna and Rao, 2010; Handwerker and Straub,

2011; Tang et al., 2014). The pre-factor A and exponent b of the widely used radar reflectivity (Z) to rainfall rate (R) (Z-R) algorithm (Z=ARb) are strongly dependant on the

DSD. In cloud-modelling studies, knowledge of the DSD is important for understanding rainfall growth mechanisms through different microphysical processes (such as evaporation, collision and coalescence) and for parameterization of these processes. As such, knowledge of the rainfall DSD is essential for accurate representation of rainfall especially by (i)

platforms employing radar remote sensing, for example satellite platforms (e.g. the Global

Precipitation Measurement (GPM) system; Hou et al. (2014)) and ground-based weather stations, and (ii) NWP models (Niu et al., 2010; Gatlin et al., 2015).

Several studies have investigated the rainfall DSD (Tokay and Short, 1996; Tokay et al., 1999; Bringi et al., 2003; Rosenfeld and Ulbrich, 2003; Ulbrich and Atlas, 2007;

Radhakrishna et al., 2009; Niu et al., 2010; Konwar et al., 2014; Thurai et al., 2016) and have shown that the DSD differs for different rainfall regimes. The DSD has a spatial- temporal variation not only within a storm system but also from storm to storm and over different climatic regimes. In a recent study, Radhakrishna and Rao (2010) have shown that the TC DSD differs statistically from the non-TC DSD over the Gadanki, India, region and the associated radar and the gamma distribution parameters between TC and non-TC environments differ. This study thus seeks to establish if there is any difference between the

TC and the non-TC related DSD over the south-west Pacific region and if there is a difference it will have implications for radar rainfall estimation and cloud-modelling studies.

DSD characteristics are usually obtained from ground-based disdrometers (Joss and

Waldvogel, 1969; Tokay and Short, 1996), dual-polarised radars (Bringi and Chandrasekar,

2001) and dual-frequency profilers (Bringi et al., 2009). Performing these measurements over remote regions, for example over the oceans where the TC duration is generally the greatest, is difficult, however. Algorithms have been developed to estimate DSD parameters from the

TRMM precipitation radar (PR) and these could be used to fill the gap. A few studies have cross-validated the PR derived DSD characteristics against dual-polarised ground-radar (GR) estimates, for example over the United States of America (Chandrasekar et al., 2003a;

Chandrasekar et al., 2003b) and over the Kwajalein Atoll (Bringi et al., 2012), to ascertain the error characteristics. These studies show that the PR has a reasonable estimate of the DSD characteristics with respect to the GR (for example Bringi et al. (2012) report a relative bias

of about 11.7 – 24.6%). A similar comprehensive study that could provide more information on the PR derived DSD characteristics, but is lacking for the south-west Pacific region. Also, the studies over the other regions have only used non-TC events and there is a lack of study involving TCs. Thus, in this study, we use TC events together with non-TC events to compare and contrast the rainfall characteristics estimated from the PR, a combined PR and

TRMM Microwave Imager (TMI) algorithm (hereafter referred to as COM; Munchak and

Kummerow (2011)) and the Darwin, Australia, based C-band dual-polarised (C-POL) ground- radar.

1.2 Aims and Objectives

The aims of the study are as follows. First, it seeks to evaluate the TMPA 3B42 estimates during the passage of TCs over Fiji and over New Caledonia. Second, it seeks to compare and contrast the rainfall DSD characteristics associated with TC and non-TC events.

Finally, it seeks to cross-validate the rainfall characteristics estimated using the TRMM PR, the COM and a C-POL ground-radar during the passage of TCs over Darwin. More specifically, the study would seek to answer the following questions:

(i) Evaluation of TRMM 3B42 over Fiji and over New Caledonia

o How the TRMM 3B42 performs during heavy rainfall?

o How does the performance vary with topography, intensity and distance from

TC centre?

(ii) Comparison of TC and non-TC DSD characteristics

o Is there any difference between TC and non-TC related DSD over this region

and also under different precipitating systems (e.g. convective and stratiform)

during the Australian summer monsoon season?

o Does the TC DSD vary with distance from the TC centre?

o If there is a difference between the TC and the non-TC DSD, then how does it

relate to the radar rainfall estimation parameters and the analytical expression

(the gamma function) used to represent the observed DSD?

(iii) Cross-validation of rainfall characteristics estimated using the PR, the COM, and the

Darwin C-POL ground-radar

o How do the rainfall characteristics such as the radar reflectivity, the rainfall

rate and the DSD parameter (median volume diameter, Do) estimated from the

PR, the COM and the ground-radar inter-compare?

o Do the estimates from each platform vary with precipitation type (i.e.

convective and stratiform type rainfall)?

1.3 Thesis Outline

The structure of the thesis is as follows. Chapter 2 provides an overview of the relevant literature on TCs, satellite-based remote sensing of precipitation, the microphysics and dynamics that dictate the rainfall DSD and remote sensing of rainfall characteristics using the

TRMM PR. Chapter 3 presents the data and methodology and Chapter 4 and 5 present the evaluation of the TMPA during the passage of TCs over New Caledonia and over Fiji respectively (the manuscripts accepted in peer-reviewed journals are presented). Note that only a brief overview of the TMPA 3B42 is provided in Chapter 3; a detailed description is given in the data and methodology section of Chapter 4 (i.e. section 4.2). Chapter 6 presents the study on the differences in the TC and the non-TC DSD characteristics (the manuscript accepted in a peer-reviewed journal is presented) and Chapter 7 presents the results on the comparison of the rainfall characteristics estimated from the PR, the COM and the GR for TC and non-TC events. Finally, Chapter 8 summarises the main findings of this research and provides some recommendations for future work. The next chapter presents the literature review.

2 Literature Review

Summary

The various aspects of precipitation characteristics and their measurement (or estimation) during the passage of TCs are well documented in the scientific literature. This section, commencing with an introduction of TCs, reviews the available satellite rainfall products, with an explicit emphasis on the TRMM 3B42 product and its performance during TCs. It further provides an insight into the cloud dynamics and microphysics (that dictate the DSD), the mathematical formulation of the DSD and the relation between DSD and radar-rainfall estimation. Finally, it presents the comparison of the rainfall characteristics estimated using the TRMM PR and dual-polarised ground radars.

2.1 TC Genesis

TCs form over regions that broadly satisfy the following environmental conditions: a relatively warm ocean with temperatures greater than 26ºC, some low-level vorticity, a non- zero Coriolis parameter, a small vertical wind shear, a conditionally unstable atmosphere and a large relative humidity (Gray, 1975, 1979; Menkes et al., 2012). The importance of upper- level divergence has also been suggested (Fett, 1966; Gray, 1988). The ocean basins that exhibit these environmental characteristics favourable for TC genesis are shown in Figure

2.1.

Figure 2.1 TC formation basins: 1 - North Atlantic, 2 - Eastern North Pacific, 3 –

Western North Pacific, 4 – North Indian, 5 – Western South Indian, 6 –

Eastern South Indian, and 7 – Western South Pacific basin (the region

enclosing the Pacific Island countries). Source:

http://www.aoml.noaa.gov/hrd/tcfaq/F1.html

2.2 Quantitative Precipitation Estimation (QPE) during the passage of TCs

and numerical weather model evaluation (Ebert et al., 2007; Yu et al., 2009). Accurate estimates of TC rainfall are also of interest to marine biologists in relation to the health of coral reefs which have a narrow tolerance limit to deviations in sea salinity (Jury et al., 2010).

Yet having an adequate network of surface-based systems to accurately measure precipitation is difficult over oceanic regions, and in remote and developing countries (Ebert et al., 2007;

Huffman et al., 2007; Scheel et al., 2011), for example, the island countries in the south-west

Pacific region. This gap can be filled by satellite-based precipitation estimates providing coverage at fine spatial and temporal resolutions.

Precipitation-related information is available from a number of passive microwave

(MW), visual (VIS) and infrared (IR) sensors onboard various satellites. The IR instruments sense the cloud-top temperature (TB) and are available globally almost all the time, but these observations are weakly related to the underlying precipitation (Joyce et al., 2004). On the other hand, low-frequency MW signals sense the emission spectra of raindrops while higher frequency MW signals sense the scattering spectra of ice particles, hence giving a better estimate of precipitation. Some popular MW capable instruments include the Advanced

Microwave Scanning Radiometer-E (AMRS-E) on the Aqua satellite, the TRMM Microwave

Imager (TMI), Special Sensor Microwave Imager (SSMI) and Special Sensor Microwave

Imager/Sounder (SSMI/S) on the US Defence Meteorological Satellite Program (DMSP), the

Advanced Microwave Sounding Unit-B (AMSU-B) on the US National Oceanic and

Atmospheric Administration (NOAA) satellite series and the Microwave Humidity Sounders

(MHS) on the later NOAA-series satellites, the European Operational Meteorological

(MetOp) satellite and the Global Precipitation Measurement (GPM) Microwave Imager

(GMI).

To meet the requirements for advanced climate modelling, initialisation of NWP models and for other meteorological applications necessitated the need for a better spatial and

temporal resolution precipitation product. The intermittent coverage of the MW sensors falls short of this requirement hence scientists have progressively moved towards blending the

MW data with the less-optimal IR data. A number of techniques have been developed to achieve this but they could be separated into two distinct categories. The first method uses the

IR data to compute a motion vector which is then used to propagate the MW precipitation features in between MW satellite passes (i.e. it is an exclusively MW only blended product).

The second method uses the MW data to calibrate the IR precipitation estimates which are then used to fill the gaps in between MW satellite passes.

Some common blended precipitation products include the Tropical Rainfall Measuring

Mission (TRMM) Multi-satellite Precipitation Analysis (TMPA) (Huffman et al., 2007;

Huffman and Bolvin, 2014), the Climate Prediction Centre morphing method (CMORPH)

(Joyce et al., 2004), the Naval Research Laboratory-Blended satellite Technique (NRL) (Turk and Miller, 2005; Turk and Mehta, 2007), the Precipitation Estimation from Remotely Sensed

Information Using Artificial Neural Networks (PERSIANN) (Sorooshian et al., 2000) and the recent Integrated Multi-satellitE Retrievals for GPM (IMERG) (Huffman et al., 2014;

Huffman et al., 2015). The CMORPH and the PERSIANN are examples of the former blending technique while the NRL, the TMPA and the IMERG are examples of the latter type. Apart from the MW and IR data, the monthly rain gauge analysis, which includes the

Global Precipitation Climatology Centre (GPCC) analysis, is also applied to the TMPA and the IMERG products to minimise the bias (Huffman et al., 2007; Huffman et al., 2017). Next, we present an evaluation of TMPA during the passage of TCs.

2.2.1 Evaluation of TRMM-based precipitation products during the passage of TCs

Under a program of the International Precipitation Working Group (IPWG) and the more comprehensive study called the Pilot Evaluation of High-Resolution Precipitation Products

(PEHRPP), several satellite-based precipitation products have been validated over various

regions. Among these include validations of the TMPA products (Ebert et al., 2007; Zhou et al., 2008; Koo et al., 2009; Kubota et al., 2009; Sapiano and Arkin, 2009; Tian et al., 2009;

Dinku et al., 2010; Buarque et al., 2011; Kidd et al., 2012).

Several studies have also evaluated the TMPA 3B42 estimates during the passage of

TCs over regions such as mainland China (Yu et al., 2009), Taiwan (Chang et al., 2013; Chen et al., 2013a), USA (Habib et al., 2009), India (Prakash et al., 2012) and the Australian region

(Chen et al., 2013b). 3B42 has also been evaluated over the ocean (at atoll sites – assumed to be similar to open ocean conditions) as well as for “coastal and inland sites” in the Pacific basin (Chen et al., 2013c). These studies, in general, show that TMPA has skill in revealing the overall band structures within the TCs, but it tends to underestimate the moderate and heavy rainfall events while overestimating the very light rainfall. The skill of TMPA also varies under different conditions such as latitude (Yu et al., 2009; Chen et al., 2013b), TC intensity, distance from TC centre (Chen et al., 2013b) and terrain (Chang et al., 2013; Chen et al., 2013b, c). TMPA performs quite well at lower latitudes, for intense TCs and near the

TC centre. Chen et al. (2013c) explicitly show that a difference exists in the skill of TMPA over the ocean and over the land, where it tends to overestimate heavy rain frequency on atoll sites and underestimate heavy rain frequency on coastal and island sites. Moreover, this study shows that TMPA’s skill at coastal and island sites decreases with increasing elevation, suggesting that TMPA has difficulty in representing orographically-enhanced rainfall during

TC landfall, as also reported by Chang et al. (2013).

While the above studies advance our knowledge about the skill of TMPA over the aforementioned regions, a similar study has not yet been undertaken to quantitatively evaluate the TMPA estimates of TC rainfall over New Caledonia and the Fiji region. Such an evaluation is needed before TMPA can be confidently used for TC-related studies in these locations. New Caledonia and the Fiji are situated in the south-west Pacific region, have

mountainous islands and atolls and frequently experience TCs (Dowdy et al., 2012).

Estimates of predicted TC rainfall over these regions are highly dependent on the use of satellite-based estimates over the open ocean for approaching storms, but these estimates do not capture the effect of orographic enhancement. Thus evaluation of satellite-based estimates of rainfall over them is needed. Ideally, satellite-based rainfall estimates could be effectively used during the passage of TCs and post TC events such as for numerical weather prediction model verification. The section next explores the formation of precipitation.

2.3 Cloud Dynamics and Microphysics

Clouds form from saturated moist air that is accomplished through vertical motions

(thermal, orographic, or frontal boundaries) that lift air parcels up in the atmosphere resulting in expansion and adiabatic cooling of air (Wallace and Hobbs, 2006). This leads to condensation of water vapour and formation of cloud particles (liquid or ice).

The present section, following Houze (2014a), discusses the microphysics and dynamics of precipitation formation in warm (temperature above 0ºC) and cold clouds

(temperature below 0ºC). Since precipitating systems include convective and stratiform elements (Steiner and Smith, 1998), these cases are also presented.

2.3.1 Warm Clouds (liquid phase) a) Nucleation

The process by which the cloud particles form from water vapour is referred to as nucleation. For example, several water vapour molecules could collide to form a pure water droplet. This case is known as homogenous nucleation, distinguished from heterogeneous nucleation which involves collection of water vapour onto an aerosol particle.

The critical radius, Rc, for the survival of an embryonic pure water droplet is dependent on the humidity of the environment as illustrated by Kelvin’s formula (Wallace and Hobbs,

2006; Houze, 2014a), given as

2 vl Rc  (2.1)  e  n1kBT ln   es 

where  vl is the surface tension, n1 is the number of water molecules per unit volume in the drop, kB is Boltzmann’s constant, e is the vapour pressure and es is the saturated vapour pressure over a plane surface of water at temperature T. Note that Rc is a function of temperature and and es are also functions of temperature but the dependence of Rc on temperature at atmospheric temperatures is weak (Houze, 2014a); instead it is dependant largely on the humidity. More importantly, the air must be supersaturated (relative humidity, e/es, greater than 1) for a droplet to form through the homogenous nucleation process and via the principles of quantum mechanics, the rate of nucleation of drops exceeding Rc requires super-saturation in the order of 400 – 500 % (Houze, 2014a). Super-saturation in the atmosphere rarely exceeds a few percent, hence, droplets in natural clouds do not form through homogenous nucleation of pure water. They rather form through the heterogeneous nucleation process. The physics of the homogenous process, however, is relevant for the discussion of the latter process, presented later.

The atmosphere contains numerous aerosol particles and water vapour molecules could deposit on the surface of the aerosol particles at much lower super-saturation than in the homogenous process. This “heterogeneous” process eventuates when the aerosol particle is “wettable”, that is the surface tension between the aerosol particle and the water vapour is small. These aerosol particles are known as cloud condensation nuclei (CCN).

The nucleation process is more efficient if the CCN is soluble. Liquid solutions have lower saturation vapour pressure than pure water which increases the relative humidity (e/es)

(Houze, 2014a). Following (2.1), this reduces the Rc and the nucleation process becomes much easier. For cases where a CCN is insoluble, a larger aerosol particle is required to

increase the survival of a drop that has formed around it. Thus, the composition and the size of the CCN play a crucial role in the size distribution of droplets in the clouds. b) Growth and Breakup of Drops in Warm Clouds

Once formed, water droplets continue to grow in size through vapour deposition.

Droplets also grow by collection of other droplets through collision, referred to as coalescence. Since the fall speed of particles increases with an increase in size (Beard and

Pruppacher, 1969; Beard, 1976), the larger falling drops (collector drops) will collide and collect smaller droplets in their path. The collection efficiency (E) is a product of the collision efficiency (E1) and the coalescence efficiency (E2) (Houze, 2014a). The collision efficiency

E1 is dependent on the relative air motion (the streamlines) around the falling drop (Wallace and Hobbs, 1977). Smaller droplets could be advected away from the path of a large falling drop (efficiency < 1) or smaller droplets not in the path of a large falling drop could collide with the large drop if pulled into its wake (efficiency > 1). The existence of a coalescence efficiency shows that not every collision will result in coalescence.

In addition, drops could also reduce in size. They can reduce in size through evaporation depending on the level of air saturation. Drops also reduce in size through breakup: drops become unstable when they attain a certain size and breakup spontaneously into smaller drops (Srivastava, 1971). In addition, an imperfect collision-coalescence process at times may produce small drops as a by-product. Laboratory experiments show that when small raindrops collide with larger drops, the resulting coalescence produces “satellite” droplets from the merger of the colliding drops (Brazier-Smith et al., 1972, 1973).

2.3.2 Cold clouds (mixed phase) a) Nucleation of ice particles

Ice particles may form directly from the water vapour phase when enough vapour molecules come together so that the embryonic ice particle is large enough to survive and

grow. This is analogous to homogenous nucleation of pure water drops from water vapour.

The process, however, is dependent strongly on the temperature and the degree of super- saturation. Theoretical and laboratory experiments show that temperatures below – 65ºC and super-saturation in the order of 1000 % are necessary for homogenous nucleation of ice particles from the vapour phase (Houze, 2014a). Super-saturation of this magnitude does not exist in the atmosphere, thus homogenous nucleation of ice particles directly from the vapour phase is not dominant in the formation of natural ice clouds.

Homogenous nucleation of ice particles rather occurs directly from supercooled liquids, in a manner analogous to nucleation of drops from the vapour phase. Though the temperature of cold clouds is below 0ºC, it is well observed that water droplets exist in the liquid phase at these temperatures as supercooled liquids (Houze, 2014a). The critical radius for the formation of ice particles from water drops is given by an expression similar in form to equation 2.1. The critical radius depends strongly on the temperature and the degree of super- saturation. Theoretical and laboratory results show that temperatures lower than ~ – 35ºC are required for homogenous nucleation of ice particles (Mason, 1971). This suggests that homogenous nucleation of ice particles from the liquid phase occur only in higher clouds.

Ice particles in natural clouds, however, do exist at temperatures between 0ºC to – 35ºC

(Houze, 2014a). Hence, heterogeneous nucleation must be responsible for the occurrence of ice particles at these temperatures. Similar to heterogeneous nucleation of liquid drops, heterogeneous nucleation of ice particles requires aerosol particles that reduce the critical radius for the formation of ice particles. Aerosol particles that act in this manner are known as ice nuclei. There are several methods by which ice nuclei could trigger the formation of ice particles. An ice nucleus suspended in a supercooled drop could trigger the formation of an ice particle if the temperature of the drop is lowered to a point where the ice nucleus is activated. This could occur in two ways: (i) if the nucleus on which the drop forms is an ice

nucleus, a process known as condensation nucleation and (ii) if the formation of ice particles is caused by some other nucleus suspended in supercooled water, a process known as immersion freezing. Ice particles also form when ice nuclei in the atmosphere come into contact with supercooled water, a process known as contact nucleation. Ice particles could also form on an ice nucleus directly from the vapour phase, a mechanism known as deposition nucleation. b) Growth of Ice Particles in Cold Clouds

Once formed, the ice particles grow through deposition, aggregation and riming.

Growth through deposition involves diffusion of the ambient water vapour onto the ice particle. Aggregation involves ice particles collecting other ice particles and is strongly dependant on the temperature: the process is more efficient at temperatures greater than – 5ºC where the surface of ice crystals becomes adhesive (Hobbs et al., 1974). There is an absence of aggregation at temperatures below – 20ºC (ice crystals become less adhesive). The shape of the ice crystal also affects aggregation: dendrite shaped crystals (i.e. branched in shape) with intertwined branches are more efficiently aggregated (Hobbs et al., 1974). Another factor that influences aggregation is the magnitude of super-saturation which affects the dampness and adhesiveness of ice crystals (Wallace and Hobbs, 2006). Larger values of super-saturation correlate with a larger degree of aggregation (Mitchell, 1988).

The riming process involves ice particles collecting supercooled liquid drops that freeze upon contact whereby the collection efficiency depends strongly on the size of the liquid drops and the fall speed of the collector ice (Wang and Ji, 2000). Results show that the collection is more efficient for moderate-sized cloud droplets (maximum diameter around 20

– 30 μm; Reinking (1979) and Mosimann et al. (1994)) rather than for tiny droplets (< 10

μm) and also more efficient at large fall speeds (Wang and Ji, 2000). The degree of riming significantly affects the shape of the collector ice crystal. Light to moderately rimed crystals

retain the shape of the collector crystal whereas heavily rimed crystals lose the collector identity and the particle is known as graupel (Mosimann et al., 1994). Extremely rimed crystals are known as hail.

Further, large ice crystals may break into smaller pieces. This increases the concentration of ice particles in clouds, a mechanism known as secondary production of ice particles (i.e. separate from nucleation) or ice enhancement. Secondary production can happen through collision, known as fragmentation, or due to a structural breakdown during the melting process (Mitra et al., 1990). During the riming process, ice splinters may also break away (Hallett and Mossop, 1974) and produce several ice particles. This process, in particular, is known to greatly enhance the concentration of ice particles in natural clouds

(Black and Hallett, 1986). As an ice crystal falls, it encounters several thousand supercooled droplets that freeze upon contact, each with the potential of producing numerous splinters.

2.3.3 Dynamical and Microphysical Processes in Stratiform and Convective

Precipitation

Precipitation systems can be classified into convective and stratiform rainfall types.

This classification is often characterised in terms of the magnitude of the updraft (vertical motion) that determines the character and the amount of precipitation from the two types

(Steiner and Smith, 1998; Houze, 2014a). The updraft determines the time cloud particles stay aloft to grow by the various microphysical processes.

Stratiform precipitation originates from nimbostratus clouds that rise well above the

0ºC isotherm and involves ice particles in the early phase of development. Thus, for convenience, the dynamics of stratiform and convective rainfall are described often in terms of the fall speed of ice particles (Steiner and Smith, 1998; Houze, 2014a). Stratiform precipitation systems are defined as regions that have on average weaker vertical motions (w,

usually in the order of a few centimetres per second) relative to the fall speeds of ice particles

(~ 1 – 3 ms-1) and that satisfy the condition:

0  w  vice (2.2)

where w is the area averaged vertical velocity and vice is the typical fall velocity of ice particles or snow. It is important to emphasise here that the local vertical motions could exceed the typical fall velocity of ice particles, but a stratiform precipitation system is defined as regions large enough to satisfy equation 2.2 on average.

A schematic of the basic features of a typical stratiform precipitation system is shown in Figure 2.2a. Once the ice particles are introduced into the system (through nucleation or advection from nearby systems), they start to grow through deposition. The mean vertical motion maintains the super-saturation by condensation while the ice particles grow through deposition as they fall. In particular, ice particles introduced at higher altitudes have more time to grow by deposition. Once the ice particles descend to within 2.5 km above the 0ºC isotherm, the ice particles may grow through aggregation and form large crystals

(snowflakes). A vertical motion of a few ms-1 could at times also suspend some supercooled liquid drops, allowing the crystals to grow further though riming. Upon descending to 0ºC and below, the crystals start melting, forming large falling raindrops. This melting layer in the stratiform precipitation system is observed as a bright band with a large horizontal extent on radar images.

The basic features of a typical convective system are shown in Figure 2.2b. The average vertical motion w in convective systems does not satisfy equation 2.2 as the vertical velocity is typically in the order of 1 – 10 ms-1, which matches or surpasses the typical fall speed of ice crystals. Studies show that precipitation in convective systems forms in a relatively shorter time, usually less than half an hour, compared with stratiform systems where it usually takes 1 – 3 hours (Houze, 2014a). Such a short time indicates that the initial

cloud particles will originate not far from the base of the cloud when they form (time to) and

they start to grow from that point as they are carried upward by the strong updrafts until

heavy enough to fall under the influence of gravity. The only growth mechanism that

supports such a rapid growth is collection of liquid water (accretion, where liquid water

collects liquid water, or riming, where ice particles collect supercooled liquid water). The

strong updrafts condense large amounts of liquid water: large particles will grow though the

collection of liquid water. These regions are usually narrower in scale and appear as narrow

vertical cores of strong radar echoes.

During the dissipating phase (after t5), the strong vertical motion in the convective

precipitating system diminishes and ceases to carry/suspend precipitating particles aloft. The

falling particles could then take the form of a stratiform precipitation system characterised by

a bright radar echo.

a) Cloud top Vapour

⃰ ⃰ ⃰ ⃰⃰ ⃰ deposition ⃰⃰⃰ ⃰ ⃰ ⃰ ⃰ ⃰ ⃰ Aggregation ~ 1 km 0 ºC ⃰ ⃰ ⃰ ⃰ ⃰ ⃰ ⃰⃰ ⃰⃰ ⃰ ⃰ Melting ⃰⃰⃰ ⃰⃰⃰ ⃰ ⃰ ⃰ ⃰ ⃰ ⃰ ⃰ ⃰ ⃰ ⃰ ⃰ ⃰ ~ 1 - 1 km ⃰ ⃰ ⃰ ⃰⃰ ⃰ ⃰⃰⃰ ⃰ ⃰ ⃰ ⃰ ⃰ ⃰ 8

“Bright Band”

Earth’s surface Radar echo boundary

Height b) Radar echo boundary ~ 5 km

Collectional growth 0 ºC

Earth’s

t0 t1 t2 t3 t4 t5 tn-1 tn surface

Figure 2.2 Features of a) stratiform and b) convective precipitation. The shaded region

shows large radar echoes, with darker shading indicating intense radar

echoes. The convective precipitation (b) is illustrated in succession of times

t0 to tn. Cloud particles grow, while being lifted due to the strong updraft,

till t2 and then falls towards the ground under the influence of gravity,

reaching the surface just before t5. After t5 the cloud may start to recede or

continue in a steady state before dissipation commences from tn-1. An

evaporated cloud is shown at tn. Adapted from Houze (1981).

2.4 Empirical Formulation of the DSD

The mathematical formulation of the size distribution of raindrops (or the DSD) has been of great interest to researchers over the past several decades. In an early study, Marshall and Palmer (1948) indicated that the DSD could be closely approximated using an exponential function given as

N(D)  Noe D 0  D  Dmax  2.3

where N(D) is the number of raindrops per unit volume per unit diameter, D (unit: m-

3 -1 -3 -1 - mm ), No is the intercept parameter (unit: m mm ) and Ʌ is the slope parameter (unit: mm

1 0.21 ). They reported that Ʌ is related to the rainfall rate as   41R and that No is constant (

3 -3 -1 No  810 m mm ). Other studies also showed that the DSD can be closely approximated by the exponential relation (Laws and Parsons, 1943; Best, 1950). However, studies such as

Waldvogel (1974) reported deviations of the underlying DSD from the exponential function with significant “jumps” in the No. Hence, there was a need for a better formulation to represent the actual shape of the DSD that arise primarily through the rainfall microphysical processes. In a later study, Ulbrich (1983) showed that the DSD can be better approximated using the gamma function as:

 N(D)  No D e D 2.4

where μ (unit less) is the shape parameter. This formulation is versatile. It could be used to represent a wide range of DSD shapes (concave upward i.e. μ < 0 or concave downward

i.e. μ > 0) usually observed under different precipitation systems. Moreover, it reduces to the exponential function for μ = 0. Next, we explore the relationship between the DSD and radar- rainfall estimation.

2.4.1 Rainfall DSD and Weather Radar Rainfall Estimation

A weather radar is an integral component of atmospheric remote sensing. It transmits a series of MW pulses towards the target (i.e. cloud or precipitating systems) and then receives and processes the back-scattered signal to discern the information. The formulation of this process in terms of the received power and in absence of attenuation is given as (Battan,

1973)

C K 2 Z P  2.5 r r 2

where Pr is the average received power scattered from rainfall at a range r, C is the radar constant, K is a constant related to the dielectric coefficient of water and Z is the radar reflectivity factor (more commonly known as radar reflectivity).

The Z is related to the DSD of the remotely sensed precipitating column as (Battan,

1973)

 Z   D 6 NDdD 2.6 0

Hence, Z is exclusively a meteorological quantity and it could be estimated using radar remote sensing via equation 2.5. The accuracy depends on the satisfaction of the assumptions such as Rayleigh scattering and absence of attenuation and beam shielding.

The rainfall rate (R) of the sampled volume is also a function of the DSD. For a stationary rainfall rate (i.e. in an absence of wind interactions such as up or downdrafts and turbulence), with no collisions between raindrops, this relation is (Battan, 1973)

 R  6 104  D3vDNDdD 2.7 0

where v(D) is the terminal drop fall speed as a function of D.

The most widely used formulation of the terminal drop speed is a power law of the form

2.8

where c is the and γ are the constants. The direct proportionality between D, v and R implies that larger rainfall rates are characterised with larger drops and greater fall speeds.

Equations 2.6 and 2.7 demonstrate that the rainfall rate is related to the radar reflectivity via the DSD. Empirical computations based on observations show that this Z-R relation strongly assumes a power law of the form (Battan, 1973)

Z  AR b 2.9

where A and b are the coefficient of the power law. For a gamma DSD, the empirical relation between the coefficients and the DSD is given as (Ulbrich and Atlas, 2007):

106 7  N 2.33/4.67  A  o 2.10 33.314.67 17 /4.67 

7   and b  2.11 4.67  

where (x) is the complete gamma function.

The Z-R relation is the principal basis of estimating rainfall from single frequency radars, distinguished from multiple frequency radars which utilise more than one frequency or polarisation. On the other hand, multiple frequency radars have the advantage of providing additional information that is deduced from the difference between the signals across the different channels (the polarisations). Some of these parameters include the differential reflectivity factor (Zdr), the specific differential propagation phase (Kdp) and the co-polar correlation coefficient (ρhv). Advanced radar algorithms utilise Z-R relations together with the

Kdp information to estimate rainfall. The Zdr, which is the difference in the power scattered from a drop’s semi-major and semi-minor axis, provides the DSD information of the radar

sample. A complete information on assumptions and techniques for DSD and rainfall retrieval from multiple frequency radars can be found in Bringi and Chandrasekar (2001) and the references therein.

A major challenge to obtaining an accurate estimate of radar rainfall is attenuation, which is a gradual loss of the intensity of the transmitted signal as it propagates through precipitation. This causes an error in the estimated rainfall and therefore appropriate algorithms are required to correct for this. The attenuation tends to increase profoundly with an increase in the frequency (or a decrease in the wavelength) of the radar signal and also the intensity of the rainfall (Doviak and Zrnić, 1993). At a given intensity of rainfall, the TRMM

PR signal (wavelength of ~ 2.2 cm) would attenuate more in comparison to an X-band radar

(~ 3.2 cm) or a C-band (~ 5.4 cm) or an S-band (~ 10 cm) radar, with the last having the least attenuation. Appropriate algorithms are developed to correct for the attenuation and the readers are referred to Bringi et al. (2001) and Iguchi et al. (2009) for a complete description of the attenuation correction relating to the C-band Darwin radar and the TRMM PR respectively. Having reviewed the relationship between the DSD and radar rainfall estimation, next we present the literature on the DSD during the passage of TCs.

2.4.2 DSD Characteristics during the Passage of TCs

Considerable research has evaluated the DSD characteristics and the associated Z-R relations for different rainfall systems and over different regions (Tokay and Short, 1996;

Tokay et al., 1999; Bringi et al., 2003; Rosenfeld and Ulbrich, 2003; Ulbrich and Atlas, 2007;

Radhakrishna et al., 2009; Niu et al., 2010; Konwar et al., 2014; Thurai et al., 2016). These studies show that the DSD has a spatial-temporal variation not only within a storm system but also from storm to storm and over different climatic regimes and that there is no unique value for the Z-R coefficients.

Studies have also evaluated the DSD characteristics during the passage of TCs and they report an abundance of small to medium-sized drops with fewer large drops during the passage of TCs (Merceret, 1974; Wilson and Pollock, 1974; Jorgensen and Willis, 1982;

Willis, 1984; Ulbrich and Lee, 2002; Maeso et al., 2005; Tokay et al., 2008; Chang et al.,

2009; Radhakrishna and Rao, 2010; Bhattacharya et al., 2013). A recent study by

Radhakrishna and Rao (2010), on the difference in DSD between TC and non-TC events during the southwest and northeast monsoon season at Gadanki (India), shows that the TC

DSD differs statistically from the non-TC DSD and that the TC DSD also varies seasonally and over different regions. It is shown that TC rainfall, in comparison to non-TC rainfall, comprises a greater concentration of small to medium size drops (i.e. less than 3 mm) with almost an absence of large drops (greater than 3 mm).

The above studies advance our understanding of TC DSDs, especially over the

Atlantic, the northwest Pacific, and the north Indian Ocean basins. The same topic, however, has received little attention over the Australian and the southwest Pacific region, despite these regions being vulnerable to the catastrophic effects of TC heavy rainfall (Dare et al., 2012;

Chen et al., 2013b; Dare, 2013). This study thus evaluates the DSD during the passage of TCs over Darwin, Australia. It seeks to establish if there is any difference between TC and non-

TC related DSD over this region and also under different types of precipitating systems (e.g. convective and stratiform) during the Australian summer monsoon season. We pose the following question: if there is a difference, then how does it relate to the radar rainfall estimation parameters and the analytical expression (the gamma function) used to represent the observed DSD? The next section provides an overview of the cross-validation of the rainfall characteristics estimated from the TRMM precipitation radar (PR) and GRs.

2.5 Comparison of rainfall characteristics measured from the TRMM PR and Dual-

Polarised Ground Radars

The PR (the first space-borne weather radar) has successfully provided estimates of rainfall for the tropics and subtropics (38ºN – 38ºS) during its operational period from 1998 –

2015 (limited data were available in 2015). For a reliable estimate of precipitation, functions of calibration were implemented in the PR to ensure that the measured reflectivity Z is unbiased compared to a known reference (Kozu et al., 2001). Nonetheless, there could still be biases in the Z-R relationship or the retrieval algorithm and routine cross-validation against ground-based measurements is instrumental for diagnosing the performance of the satellite- based estimates. Central to the evaluation of the PR measurements is the TRMM ground validation (GV) programme which produces quality controlled ground-radar (GR) data using

GR at Houston, Texas (HSTN), Melbourne, Florida (MELB), Darwin, Australia (DARW), and Kwajalein Atoll, Marshall Islands (KWAJ).

The cross-validation of the PR reflectivities has been performed by several studies (Wang and Wolff, 2009; Wen et al., 2011; Park et al., 2015; Li et al., 2017). For example, Wang and

Wolff (2009) compared the PR reflectivities against the four TRMM GV sites. They found that the PR suffers from significant attenuation at lower altitudes, especially in convective rainfall, and an attenuation correction tends to perform quite well for convective rainfall but it slightly over-corrects for stratiform rainfall. The offset between the PR and GR reflectivities were also found to be dependent on the reflectivity magnitude (a larger offset at larger reflectivities). The PR and the GRs at HSTN, MELB, and the KWAJ sites were found to be within ± 1dB whereas the DARW GR was found to be within +1 to – 5 dB (bias of 6 to – 18

% with respect to the GR). In another study, Park et al. (2015) used four widespread and four convective events to compare the PR over the Korean Peninsula. For the widespread cases they showed that the PR attenuation-corrected reflectivity at lower altitudes (i.e. below the

melting layer) matches closely with the GR whereas for the convective events the PR underestimates the GR by 1 – 3 dB. Using stratiform precipitation events over China, Li et al.

(2017) found that the PR underestimates the GR at higher altitudes (above the bright band) but it overestimates at low altitudes. The bias between the PR and GR was also found to be largely correlated with the magnitude of the reflectivity. The above studies, in general show, that the disagreement between the PR and GR is larger at larger reflectivities which is usually observed in convective events. Moreover, the magnitude of difference varies between radars over different regions, most likely due to different calibration offsets.

Cross-validation of the PR rainfall rate has also been performed by some studies (Liao et al., 2001; Wolff and Fisher, 2008; Liao and Meneghini, 2009). Under the TRMM GV programme, Wolff et al. (2005) developed rainfall products from the GR and rain gauge data at MELB and KWAJ using the Window Probability Matching Method (WPMM). The

WPMM matches the probabilities of the radar reflectivities and the gauge rainfall in such a way that the probability density function (PDF) of the radar-derived rainfall matches with the

PDF of the gauge rainfall on a monthly scale. Wolff et al. (2005) compared the WPMM product with the PR over a 6-month period. They found that the PR overestimates the rainfall at KWAJ by 6% whereas at MELB it underestimates the rainfall by 9%. In a follow-up study,

Wolff and Fisher (2008) compared the WPMM to the individual PR footprints over a 5-year period and found that the PR underestimates the rainfall by 13.7 % at KWAJ (an oceanic site). At MELB, the PR was found to overestimate the rainfall over the ocean by 4.1% and underestimate the rainfall over the land and the coast by 7 and 8% respectively. In another study, Liao and Meneghini (2009) compared the PR rainfall with the rainfall from the MELB

GR. A conditional-based comparison (i.e. rainfall rates compared at pixels at which both the

PR and the GR detect rainfall) showed that the PR overestimates stratiform rainfall by 9 % and underestimates convective rainfall by 19 %. These studies provide some insight into the

association of PR and GR rainfall rates, nonetheless, a clear consensus in the association between the two is missing.

The PR is a single frequency radar hence DSD information retrieval is not straightforward. Algorithms have been developed to estimate drop size parameters from the

PR and a few studies have compared these with dual-polarised GR estimates (Chandrasekar et al., 2003a; Chandrasekar et al., 2003b; Bringi et al., 2012). In an early study, Chandrasekar et al. (2005) compared the drop size parameters estimated from S-band polarimetric (S-POL)

GRs with the respective coincident TRMM overpass events. The PR attenuation adjustment factor, , and the attenuation corrected reflectivity (Zc) were utilised to compute the median volume diameter, Do, of the rainfall estimated from the PR. The study was performed using two overpass events and the GR measurements were taken from the Texas and Florida Under

Flight Experiment (TEFLUN) and the Large Scale Biosphere-Atmosphere (LBA) field campaigns. Chandrasekar et al. (2005) found that the PR underestimates the Do by 8 %. In a recent study, Bringi et al. (2012) compared the Do estimated from the KWAJ S-POL GR with those estimated from the PR and a combined TRMM Microwave Imager (TMI) and PR algorithm (Munchak and Kummerow, 2011) for two overpass events. The PR Do was estimated using the method described by Kozu et al. (2009). Bringi et al. (2012) found that the PR overestimates the Do by 11.7 – 24.6% while the combined algorithm had a relatively smaller bias (– 0.8 – 9.7%). These studies advance our knowledge on the estimation of DSD parameters using the PR but, similar to the cross-validation of rainfall rates, a consensus between the association of PR and GR estimated DSD parameters, over different regions, has not been established.

The primary aim of the GV programme is to understand the differences in the precipitation retrievals for different meteorological and hydrological regimes (Schwaller and

Morris, 2011). The skill of the 2A25 algorithm varies over different terrains (ocean/land

surface) and precipitation types: it is more reliable over the oceans and during intense rainfall events (Meneghini et al., 2000; Meneghini et al., 2004). DSD cross-validation studies have only used non-TC events and there is a lack of study involving extreme events like TCs.

Moreover, a comprehensive study, similar to Bringi et al. (2012), that compares the rainfall rate and DSD parameters for the DARW GR is lacking.

This study uses TCs together with non-TC events to compare the precipitation characteristics (namely the radar reflectivity, the DSD and the rainfall) estimated using the

PR and the Munchak and Kummerow (2011) TMI and PR combined algorithm (hereafter referred to as COM) with the DARW GR. A new framework that differs in several ways from the methodology used by the existing combined algorithm (2B31) and which is expected to provide an improved estimation of rainfall characteristics is utilised by the COM (Munchak and Kummerow, 2011). This study seeks to investigate if there is an added advantage of using the MW estimates with the PR in estimating the rainfall characteristics. For the cross- validation, a recalibrated DARW GR data (Alain Protat, BOM, Personal Communication) is used. The next section (section 3) presents the data and methodology utilised to evaluate the

TMPA, examine the DSD and cross-validate the PR and COM during the passage of TCs.

Note that some of the literature presented here in Chapter 2 is repeated in the sections to follow.

3 Data and Methodology

Summary

This section describes the data used and the methodology employed to accomplish the objectives of this research. It commences with a brief overview of the TRMM data and the approach employed for its evaluation. Next, a brief overview of the disdrometer data and the methodology employed to evaluate the DSD is given. Finally, an overview of the Darwin

GR, the PR, the COM and a detailed description of the cross-validation approach utilised for this study are given.

3.1 Evaluation of the TRMM 3B42 estimates over Fiji and New Caledonia

The TRMM 3B42 version 7 product is used in this study. It is the latest version that incorporates several changes from its predecessor (version 6) such as a new IR data set, uniformly reprocessed input data using current algorithms and additional output fields

(Huffman and Bolvin, 2014).

The New Caledonia and the Fiji rain gauge daily data are used to verify the TMPA estimates. For this study, the TMPA data are verified directly against the rain gauge observations by interpolating the TMPA data to the gauge stations using inverse distance weighting (IDW) (Shepard, 1968). A suite of validation statistics such as continuous variable statistics (namely the correlation coefficient, the relative bias, and the root mean square error) and categorical statistics (namely the probability of detection, the false alarm ratio, the frequency bias and the equitable threat score) are then used for the verification. For a more detailed description of the data and the methodology see section 4.2 (for the evaluation over

New Caledonia) and 5.2 (for the evaluation over Fiji).

3.2 Tropical Cyclone and non-Tropical Cyclone related Rainfall Drop Size

Distribution over Darwin

The main instrument we use for this study is the impact type Joss-Waldvogel disdrometer (JWD) (Joss and Waldvogel, 1969) model RD-80 located at the Atmospheric

Radiation Measurement (ARM) research facility, Darwin, Australia. The JWD sorts the drops into 20 diameter classes (or bins) in the range 0.3 to 5.5 mm every 1 minute. Using these 1- min data, the integral rainfall parameters of drop concentration, rainfall rate, reflectivity and the mass-weighted mean diameter are computed. To describe the observed DSD, we employ here the widely used gamma function (Ulbrich, 1983; Kozu and Nakamura, 1991; Tokay and

Short, 1996) with an analytical expression given as:

 ND  No D exp D (3.1)

where N(D) is the number of raindrops per unit volume per unit diameter, D (unit: m-3mm-1)

-1 -3 -1 and No (mm m ), μ (dimensionless) and Λ (mm ) are respectively the intercept, shape and slope parameters. These parameters are computed using a moment-based method that utilises three moments of the gamma DSD function (Tokay and Short, 1996; Smith, 2003). A more detailed description of the data and methodology is given in section 6.2

3.3 Comparison of the rainfall characteristics estimated from the TRMM PR, COM

and the Darwin C-POL radar

3.3.1 Darwin C-POL Radar

The DARW C-band dual-polarised radar, located at 12.248°S and 130.925°E and operated by the Australian Bureau of Meteorology (BOM), is part of the TRMM GV programme and provides information on tropical rainfall (Keenan et al. (1998) and the references therein). A detailed description of the radar system is provided by Keenan et al.

(1998). The base outputs of this radar system are the horizontal polarised equivalent reflectivity factor (Zh), the differential reflectivity factor (Zdr), the differential propagation phase (Φdp), the co-polar correlation coefficient (ρhv), the Doppler velocity and the spectrum width. Data from the DARW GR has a varying range resolution between 0.25 – 1 km for every 1º in azimuth (the distance to the first gate from the radar is 1 km after which the range resolution is 0.25 km). For the computation of the rainfall rate and DSD parameters the Zh, Zdr and Φdp parameters are used, where the last is also used to compute the specific differential propagation phase (Kdp). In the C-band, the signal suffers from significant attenuation which is corrected for by the BOM using the Bringi et al. (2001) method.

A set of algorithms, developed by Bringi et al. (2009), is employed to retrieve the radar-based DSD parameter, Do. The algorithm was developed using 6 months of disdrometer data during the Darwin wet season (November to March). Note that the wet season would consist of TC and non-TC related DSD cases so the algorithm gives a climatological

representation. Previous studies have shown that there is a statistically significant difference between TC and non-TC related DSDs which necessitates the implementation of a variable

DSD algorithm for rainfall retrieval (Radhakrishna and Rao, 2010; Deo and Walsh, 2016).

Implementing these changes in the DARW GR, the PR and the COM for a more accurate cross-validation is, however, beyond the scope of this study. The Do algorithms for different

Zdr thresholds are as follows:

4 3 2 Do  0.0203Zdr 0.1488Zdr  0.2209Zdr 0.5571Zdr 0.801; (mm) (3.2)

‒ 0.5 ≤ Zdr ≤ 1.25 dB

3 2 Do  0.0355Zdr  0.0321Zdr  1.0556Zdr 0.6844; (mm) (3.3)

1.25 ≤ Zdr ≤ 5 dB

d The algorithm for estimating Nw follows the power law relation Zh/Nw = c (Do) as discussed by Bringi et al. (2002) which has been adapted for the C-band radar and is given as:

Z h 7.319 0.056Do (3.4) N w

6 -3 -1 -3 where the units of Zh and Nw are mm m and mm m respectively.

For the computation of the rainfall rate from the DARW GR, the BOM employs the hybrid method of Thompson et al. (2017) that utilises Zh, Zdr and Kdp variables.

3.3.2 TRMM PR

We use version 7 (V7) of the TRMM PR rain profiling algorithm (also known as

2A25). The following PR data are used: attenuation corrected reflectivity, Zc (2A25); rainfall rate, R (2A25); rainfall type (2A23) and attenuation adjustment factor,  (2A25). A detailed description of the rainfall profiling algorithm is given by Iguchi et al. (2009).

At 13 GHz, the PR suffers from significant attenuation and this is corrected using a combination of the surface reference technique (SRT) and the Hitschfeld-Bordan method

(Iguchi et al., 2000). Briefly, the attenuation adjustment factor is used to adjust the initial

coefficient 0 in the relation between attenuation coefficient k and effective radar reflectivity

 factor Ze ( k  0 Z e ) in such a way that the path integrated attenuation (PIA) estimated using the SRT matches with the PIA estimated using the Hitschfeld-Bordan method.

Kozu et al. (2009) note that estimating the attenuation adjustment factor is approximately related to estimating the DSD. Hence, using their appendix and following

Bringi et al. (2012) we derive the Do estimator for convective and stratiform rainfall fields and which are given as follows:

lnDo    0.100.185 lnR 1.81 log10   Convective rainfall (3.5a)

lnDo   0.05140.1631lnR1.6743 log10   Stratiform rainfall (3.5b)

Note that Kozu et al. (2009) used TRMM V6 to derive the parameters whereas we use

V7 here. The set of parameters in their appendix is still valid for convective rainfall in V7, but it differs for stratiform rainfall (Toshio Iguchi, National Institute of Information and

Communications Technology, Personal Communication). A new set of parameters (provided by Toshio Iguchi) are used here for the stratiform rainfall. The accuracy in estimating Do using equations 3.5a and b also differ: Kozu et al. (2009) note that the estimation is more accurate for convective rainfall where the SRT-based path attenuation is generally more reliable. The SRT is based on the notion that a difference between the measurements during rain and rain-free periods (a reference background) provides the information about the PIA.

The method is more reliable during heavy precipitation since there is a significant contrast between the raining column and the background reference (the attenuation is large) unlike during weak precipitation when the contrast is weaker. Moreover, ocean surfaces have less variability than land surfaces hence the reliability is also larger over the former (Meneghini et al., 2000; Meneghini et al., 2004).

3.3.3 TRMM COM

At the core of the Munchak and Kummerow (2011) TRMM PR+TMI combined algorithm (COM) is a Hitchfeld-Bordan reflectivity profiling algorithm, similar in many respects to the 2A25. Instead of Z-R and Z-k power laws, Z-Do power laws are fit to the 2A25

Z-R relationships for stratiform and convective rain. From these power laws and a gamma distribution

 3.67      ND  N o D exp  (3.6)  Do  with shape parameter μ equal to 3, all integral parameters can be determined including R, k, and the extinction coefficient, single-scatter albedo, and asymmetry parameter at each TMI frequency which are input to the delta-Eddington radiative transfer model (Kummerow,

1993). The TMI brightness temperatures are simulated at the PR resolution then convolved to

TMI resolution.

In each PR profile three parameters are retrieved: εDSD, εICE, and εCLW. εDSD modifies

b the Z-Do power law such that Do = εDSDaZ . Likewise, εICE modifies the Z-Do relationship in ice phase regions of the profile and εCLW modifies the cloud liquid water profile. Because of the large size (approximately 40 × 70 km at 10 GHz) of the TMI field-of-view (FOV), an optimal estimation technique (Rodgers, 2000) is used to optimize εDSD, εICE, and εCLW over

FOVs containing many PR profiles. TMI brightness temperatures and SRT PIA estimates are used as observational inputs to the optimal estimation procedure. Alternatively, the COM algorithm has the flexibility to run in radar-only mode, where only εDSD is modified to match the SRT PIA inputs (this is henceforth referred to as the “PIA” algorithm). The flexibility allows us to examine the impact of the TMI observations on the Do retrieval without having to account for subtle algorithm differences between COM (in radar-only mode) and 2A25.

3.3.4 Methodology for Aligning the PR and the GR

Due to the difference in the measurement geometry of the PR and the GR (Figure 3.1), the observations from both the instruments need to be transformed onto a common coordinate system for a meaningful comparison. We accomplish this using the Schwaller and Morris

(2011) volume matching method which computes the PR and the GR averages at the geometric intersection of the PR with the individual GR rays. Unlike some of the other techniques, that are mostly gridded approaches (Bolen and Chandrasekar, 2000; Schumacher and Houze, 2000; Bolen and Chandrasekar, 2003; Wang and Wolff, 2009), this method computes the averages where there are actual observations in other words there is no interpolation, extrapolation or oversampling of observations.

a) b)

Figure 3.1 Schematic of the volume matching technique. (a) Averaging of PR bins in

the vertical at the intersection of the PR with the GR and (b) averaging of

the GR in the horizontal at the intersection of the PR with the GR.

For a coincident overpass rainfall event, we compute the distance between each of the

PR rays and the DARW GR and examine the corrected reflectivity values of the PR rays. For the analysis, we then use only those PR rays which are within 100 km from the GR site and have at least one bin above the reflectivity threshold of PR (i.e. 18 dBZ). The 18 dBZ is considered to be the minimum sensitivity level of the PR (Schwaller and Morris, 2011). Next, we compute the height above the ground level, including the GR vertical beamwidth (at the half power points) and the PR horizontal beamwidth, at which a PR ray intersects a GR sweep.

The matching process then involves computing the averages for each PR ray at each

GR sweep intersection. The along ray average of the PR at the intersection is computed in the vertical and includes those bins (at a resolution of 0.250 km) that fall within the vertical resolution (beamwidth) of the GR sweep (Figure 3.1a). Only those bins with values greater than (or equal to) 18 dBZ (or rain rate greater than 0.01 mm hr-1) are used for the average.

We keep a note of the total number of bins expected from a geometric standpoint (which is a function of the GR elevation and the range of the intersecting column from the GR) and the number of bins rejected.

The GR average at the intersection is computed in the horizontal, centred around the

PR ray footprint (Figure 3.1b) and within the PR horizontal beamwidth. If all the GR bins within this PR footprint are below 15 dBZ (a threshold chosen to match the minimum sensitivity level of the PR and allowing for a GR calibration offset of 3 dBZ) then the GR average is flagged ‘below threshold’. Otherwise, a weighted average using the Barnes

Gaussian weighting (Barnes, 1973) is computed (0 dBZ readings are included in the computation). We keep a track of the total number of bins expected from a geometric standpoint and the number of these bins below the 15 dBZ threshold.

In essence, the above procedure reduces the PR vertical resolution to that of the number of GR sweeps and the GR horizontal resolution to the number of PR rays. For further statistical analysis, we use only those data points that have less than 5 % of the bins rejected when computing the averages. This minimises the effects of non-uniform beam filling

(NUBF) and biases related to the sensitivity level of the PR (Schwaller and Morris, 2011).

NUBF is the presence of non-uniformity in the reflectivity within a radar field of view that would lead to error in the estimates. For a detailed description of the volumetric matching method see Schwaller and Morris (2011).

3.3.5 Statistical Metrics

For the comparison to the PR, with the DARW GR taken as the reference, we use a combination of statistics. The Pearson correlation coefficient (r) is used to measure the degree of linear association, the root mean square error (RMSE) to measure the average magnitude of error; and the bias (and relative bias) measures the difference between the average PR and GR values. The formulae of the statistics are as follows:

PR  PRGR  GR r   (3.7) 2 2 PR  PR GR  GR

n PRi  GRi  Bias= i1 (3.8) n

Bias Relative bias= (3.9) GR

n 1 2 Root mean square error (RMSE) = PRi  GRi  (3.10) n i1

RMSE Relative RMSE= (3.11) GR where PR and GR are the mean of the PR and GR measurements.

The uncertainty in these statistics is computed using a bootstrapping method (Efron and Tibshirani, 1993) that involves re-sampling of the data. About 10,000 re-samples are created upon which bootstrapping is applied at the 95 % confidence level. The 50th percentile is presented as the statistic and the 2.5th and 97.5th percentile as the upper and lower bound for the errors (confidence intervals). The next chapter is the evaluation of TMPA over New

Caledonia and we present the manuscript that has been published.

4 Evaluation of TMPA 3B42 Precipitation Estimates during the Passage of Tropical Cyclones over New Caledonia Anil Deo1, Kevin J. E. Walsh1, Alexandre Peltier2

Anil Deo, School of Earth Sciences, The University of Melbourne, Victoria 3010, Australia

([email protected], Ph: +61 (0)3 8344 7675, Fax: +61 (0)3 8344 7761)

Kevin J. E. Walsh, School of Earth Sciences, The University of Melbourne, Victoria 3010,

Australia

Alexandre Peltier, Meteo-France, New Caledonia

1School of Earth Sciences, The University of Melbourne, Victoria 3010, Australia

2Meteo-France, New Caledonia, 5 Rue Vincent Auriol, BP 151, 98845 Noumea Cedex

Abstract

This study evaluates the Tropical Rainfall Measuring Mission (TRMM) Multi-Satellite

Precipitation Analysis (TMPA) 3B42 version 7 (V7) estimates of tropical cyclone (TC) rainfall over New Caledonia using the island rain gauge observations as the ground-truth reference. Several statistical measures and techniques are utilised to characterise the difference and similarity between TMPA and the gauge observations. The results show that

TMPA has skill in representing the observed rainfall during the passage of TCs. TMPA overestimates light rainfall events and underestimates moderate to heavy rainfall events. The skill deteriorates with increasing elevation, as underestimation by TMPA is greater at large altitudes. The ability of TMPA also varies with TC intensity and distance from the TC centre, whereby it is more skilful for less intense TCs (category 1-2) and near the TC centre than in the outer rainbands. The ability of TMPA varies from case to case but a better performance is shown for TCs with a larger average rainfall. Finally, case studies of TC Vania (2011), TC

Innis (2009), and TC Erica (2003) show that TMPA has the ability to represent the spatial distribution of the observed rainfall, but it tends to underestimate the larger rainfall rates.

4.1 Introduction

Heavy rainfall associated with tropical cyclones (TCs) has been related to disastrous natural hazards such as flooding, landslide and related health and socio-economic problems

(Dare 2013 and the references therein). As an example, severe tropical cyclone Erica (2003), struck New Caledonia and caused estimated damage of US$15.0 million, two deaths and injured hundreds (Regional Specialised Meteorological Centre Fiji, 2003; Australian

Government Bureau of Meteorology, 2003). It also increased the chance of spreading dengue fever which was already endemic on the island (United Nations Office for the Coordination of Humanitarian Affairs, 2003). Extreme rainfall over parts of the island was around 200 mm day-1. These consequences place a heavy socio-economic burden on the Pacific island countries (Terry et al., 2008).

Accurate measurement of precipitation during the passage of TCs is highly important as it has applications that would significantly aid in disaster mitigation and risk analysis. Such applications include better precipitation forecasting through improved model initialization and numerical weather model evaluation (Ebert et al., 2007; Yu et al., 2009). Accurate estimates of TC rainfall are also of interest to marine biologists in relation to the health of coral reefs which have a narrow tolerance limit to deviations in sea salinity (Jury et al., 2010).

Yet having an adequate network of surface-based systems to accurately measure precipitation is difficult over oceanic, remote and developing countries (Ebert et al., 2007; Huffman et al.,

2007; Scheel et al., 2011), for example, the island countries in the south-west Pacific region.

This gap could be filled by satellite-based precipitation estimates providing coverage at fine spatial and temporal resolution.

To increase the quality of satellite-based precipitation estimates, scientists have progressively moved towards using a combination of remote sensing instruments onboard various satellites. These include the Tropical Rainfall Measuring Mission (TRMM) Multi-

Satellite Precipitation Analysis (TMPA) (Huffman et al., 2007; Huffman and Bolvin, 2014), the Climate Prediction Centre morphing method (CMORPH) (Joyce et al., 2004), the Naval

Research Laboratory-Blended satellite Technique (NRL) (Turk and Miller, 2005; Turk and

Mehta, 2007), the Precipitation Estimation from Remotely Sensed Information Using

Artificial Neural Networks (PERSIANN) (Sorooshian et al., 2000) and the recent Integrated

Multi-satellitE Retrievals for Global Precipitation Measurement (GPM) (IMERG) (Huffman et al., 2014; Huffman et al., 2015).

These precipitation datasets, however, have a shortcoming in that they are indirect estimates of precipitation where some physical quantity is measured (e.g. cloud top temperature for infrared-based measurement and emission/scattering of microwave signals by hydrometeors for microwave-based measurements) using satellite remote sensing techniques and is then correlated with precipitation (Janowiak et al., 2001; Wilheit, 2003; Huffman et al.,

2007). Thus, the satellite-based estimate needs to be validated using surface-based “ground truth” rain gauge data or (alternatively) calibrated radar data to evaluate its accuracy and limitations before it could be confidently used (Ebert et al., 2007; Yu et al., 2009; Chen et al.,

2013b, c). Under a program of the International Precipitation Working Group (IPWG) and the more comprehensive study called the Pilot Evaluation of High-Resolution Precipitation

Products (PEHRPP) (Arkin et al., 2006), work has been conducted to validate nearly all operational satellite precipitation products (Ebert et al., 2007).

Several studies have evaluated the TMPA 3B42 estimates (hereafter referred to as

TMPA) related to heavy precipitation associated with TCs over various regions such as over mainland China (Yu et al., 2009), Taiwan (Chang et al., 2013; Chen et al., 2013a), USA

(Habib et al., 2009), India (Prakash et al., 2012) and the Australian region (Chen et al.,

2013b). Chen et al. (2013c) also evaluated TMPA over the ocean (at atoll sites – assumed to be similar to open ocean conditions) as well as for “coastal and inland sites” in the Pacific

basin. These studies, in general, show that TMPA has skill in revealing the overall band structures within the TCs, but it tends to underestimate the moderate and heavy rainfall events while overestimating the very light rainfall. These studies further show that the skill of

TMPA varies under different conditions such as latitude (Yu et al., 2009; Chen et al., 2013b),

TC intensity, distance from TC centre (Chen et al., 2013b) and terrain (Chang et al., 2013;

Chen et al., 2013b, c). TMPA performs quite well at lower latitudes, for intense TCs and near the TC centre. Chen et al. (2013c) explicitly show that a difference exists in the skill of

TMPA over the ocean and over the land, where it tends to overestimate heavy rain frequency on atoll sites and underestimate heavy rain frequency on coastal and island sites. Moreover, this study shows that TMPA’s skill at coastal and island sites decreases with increasing elevation, suggesting that TMPA has difficulty in representing orographically-enhanced rainfall during TC landfall, as also reported by Chang et al. (2013).

While the above studies have advanced our knowledge about the skill of TMPA over the aforementioned regions, a similar study has not yet been undertaken to quantitatively evaluate the TMPA estimates of TC rainfall over New Caledonia. Such an evaluation is needed before TMPA can be confidently used for TC-related studies in this location. New

Caledonia (Figure 4.1) is situated in the south-west Pacific region, has mountainous islands and atolls and frequently experiences TCs (Dowdy et al., 2012). New Caledonia has a rain gauge network that is spread almost over the entire island (Figure 4.2), with several gauges also located over high terrain. Estimates of predicted TC rainfall over New Caledonia are highly dependent on the use of satellite-based estimates over the open ocean for approaching storms, but these estimates do not capture the effect of orographic enhancement. Thus evaluation of satellite-based estimates of rainfall over New Caledonia is needed. Ideally, satellite-based rainfall estimates could be effectively used during the passage of TCs and post

TC events such as for numerical weather prediction model verification.

The objectives of the study are as follows: (i) to evaluate the skill of TMPA for different altitudes, TC intensity, distance from TC centre and position of TCs with respect to the island and (ii) to examine the skill of TMPA during the passage of individual TCs. The paper is organised as follows. Section 2 introduces the data and methodology, section 3 presents the results of the composite TC data for the different conditions (i.e. altitude, TC intensity, distance from TC centre and position of TCs) followed by case studies. Section 4 contains a discussion and summary.

Location of New Caledonia 10

-10

-20

Latitude

-30

-40

-50 110 120 130 140 150 160 170 180 -170 Longitude Figure 4.1 Location of New Caledonia (enclosed in the dashed red rectangular box) in

the south-west Pacific basin

4.2 Data and Methodology

4.2.1 TMPA

This study utilises the research version of the TMPA product. While the TRMM satellite was retired in October 2014, it has left behind a wealth of data for much of the globe over the period 1998 – 2014.

The TMPA product is a 3 hourly, 0.25º × 0.25º latitude-longitude resolution gridded product generated using the following datasets: the TRMM combined instrument (TCI) dataset comprising the TRMM Microwave Imager (TMI) and the TRMM precipitation radar

(PR, 2B31) used as the source of calibration, the microwave (MW) data, the window-channel infrared (IR) data and gridded monthly rain gauge data (Huffman et al., 2007).

The precipitation-related MW data are collected from Low Earth Orbit (LEO) satellites which include the Advanced Microwave Scanning Radiometer-E (AMRS-E) on the Aqua satellite, the TRMM Microwave Imager (TMI), Special Sensor Microwave Imager (SSMI) and Special Sensor Microwave Imager/Sounder (SSMIS) on the US Defence Meteorological

Satellite Program (DMSP), the Advanced Microwave Sounding Unit-B (AMSU-B) on US

National Oceanic and Atmospheric Administration (NOAA) satellite series and the

Microwave Humidity Sounders (MHS) on later NOAA-series satellites and the European

Operational Meteorological (MetOp) satellite. The AMRS-E, TMI and SSM/I fields of view

(FOVs) are then converted to precipitation estimates using the Goddard Profiling Algorithm

(GPROF) (Kummerow et al., 2001). The GPROF precipitation estimation technique differs over the ocean and over the land (Wilheit, 1986). The ocean surface has a lower emissivity and appears “cold” to the MW radiometer in relation to a “warm” emission signature of hydrometeors above. Thus differentiating the two is possible using the emission signature.

The land surface, on the other hand, has a larger and variable emissivity, thus making the emission mode measurement challenging. Hence, over land, the scattering mode is utilised.

MW emission is dominated by liquid hydrometeors which have a direct physical relationship with surface rainfall, while MW scattering is dominated by frozen hydrometeors which have a less direct physical relationship with surface rainfall. Hence, estimation over the land is less accurate than that over the ocean. With the presence of liquid hydrometeors, which have a strong emission signature, the errors in the estimation over the land become more significant.

For the AMSU-B and MHS, the Zhao and Weng (2002) and Weng et al. (2003) algorithms are used. While the algorithms can differentiate between precipitating and non- precipitating ice-bearing clouds, they have difficulty with clouds that lack the ice phase. The conical scanners (TMI, AMRS-E, SSM/I) have similar limitations over land, so AMSU-B and MHS estimates are roughly comparable.

The window-channel infrared (IR) data used in the TMPA are the merged Climate

Prediction Centre (CPC-NOAA) half-hourly 4 km × 4 km latitude-longitude resolution IR data collected by the international constellation of geosynchronous earth orbit (GEO) satellites (Janowiak et al., 2001; Huffman et al., 2007). The rain gauge data utilised by TMPA are the GPCP monthly rain gauge analysis, developed by the Global Precipitation

Climatological Centre (GPCC) (Rudolf, 1993). As an illustration, Figure 4.2 shows the

GPCC gauges over New Caledonia in 2012.

The TMPA estimates are produced in four stages. First, the MW estimates from individual sensors are calibrated using the TCI and then combined. Second, the IR estimates are created with MW calibration. Third, the MW and IR data are combined such that the MW estimates are taken “as is” with the IR estimates used to fill the gaps. Finally, the monthly rain gauge analysis is applied to minimise the bias, and this step has been shown to improve the accuracy of the estimation (Huffman et al., 2007).

The latest version (version 7 or V7) of TMPA, released in 2012, incorporates several changes from its predecessor (version 6) such as a new IR data set, uniformly reprocessed input data using current algorithms and additional output fields (Huffman and Bolvin, 2014).

A detailed description of the TMPA product is given by Huffman et al. (2007).

4.2.2 New Caledonia Rain Gauge Data

The New Caledonia island rain gauge daily data are used to verify the TMPA estimates.

As shown in Figure 4.2, which is a plot of the location of the rain gauges on Grande Terre,

the main island of New Caledonia used in this study, the island has gauge stations that are spread almost over the entire island, with several of them also located at high elevations. The climate division of Meteo-France, New Caledonia, collects and performs quality control on the data. Data that have been verified by the division are used for this study.

New Caledonia Mainland stations

-20

1 1 1

-21

Latitude 0 0 0

-22

0 0 2

-23 164 165 166 167 Longitude Figure 4.2 Rain gauge locations on the main island, Grande Terre, New Caledonia. The

blue crosses are stations with elevation less than 300 m and the red circles

are stations with elevation greater than 300 m. The numbers in the grid

boxes are the GPCC Monitoring Product Version 6 gauge-based analysis

number of stations per 1º grid for year 2012 (January – December) over the

New Caledonia region.

(Source:https://www.esrl.noaa.gov/psd/data/gridded/data.gpcc.html#detail)

Rain gauge data are known to have systematic and random errors with possible sources from wind, wetting, splashing, evaporation and calibration (Habib et al., 2008). The wind- related error, which increases with increasing wind magnitude, is the principal source of the systematic error (Nešpor and Sevruk, 1999; Habib et al., 2008; Wang et al., 2008). Under TC conditions, the wind-induced error would be quite significant and this has to be taken into consideration in our arguments and discussions, given that we do not have the requisite data to correct the gauge measurements. Nonetheless, gauge data are still considered to be the most accurate and direct measurement of rainfall and the optimal choice for evaluation of satellite precipitation estimates (Ebert et al., 2007; Chen et al., 2013b, c).

4.2.3 Methodology

TMPA estimates can be verified directly against the gauge data (grid to point) or against gridded analysis of the gauge data. High resolution gridded observation data, however, are not available for New Caledonia. Studies (e.g. Ensor and Robeson 2008) have also shown that interpolating to a grid tends to increase the frequency of light precipitation events while decreasing the incidence of heavy events. As this study is focusing on heavy rainfall during the passage of TCs, actual values of heavy precipitation are essential.

Therefore, a ‘grid to point’ method has been employed here. The TMPA data are verified directly against the rain gauge observation by interpolating the TMPA data to the gauge stations using inverse distance weighting (IDW) (Shepard, 1968).

As the focus of this study is on the heavy precipitation associated with TCs, TCs that made landfall and those having centres less than 200 km from any one station at any point in time during their passage are considered for this study. A total of 13 TCs, for the period 1998

– 2012, match these criteria. The dates and positions of TC centres are obtained from the

International Best Track Archive for Climate Stewardship data (IBTrACS) (Knapp et al.,

2010) portal. The data have a temporal resolution of 6 hours.

Rainfall at a gauge station is considered to be TC related, and the particular day for the station considered being a “TC day” if a TC centre, at any point in time during the daily accumulation period, is within 500 km from the gauge station. The 500 km criterion for TC related rainfall is consistent with other studies such as Lonfat et al. (2004), Lau et al. (2008),

Jiang and Zipser (2010), Nogueira and Keim (2010) and Chen et al. (2013b, c). For the various declared “TC days”, the TMPA 3 hourly data, for the gauge accumulation period, are summed up to match the accumulation times of the daily gauge rainfall data.

Several statistical measures are used to validate TMPA. For rainfall pattern matching, the correlation coefficient (r), the relative bias, the root mean square error (RMSE) and relative RMSE are utilised (Wilks, 2011). To evaluate the skill of the TMPA estimates, the four common categorical statistics used in validation studies, namely the probability of detection (POD), the false alarm ratio (FAR), the frequency Bias (FBI) and the equitable threat score (ETS), are calculated using a contingency table (Table 4.1). These categorical statistics are based on different rain thresholds that define the transition between a rain and no-rain event. The rainfall thresholds used in this study are shown in Table 4.2 and the formulae of the various statistics are given in Appendix A. Each statistic provides partial information about the error, hence combinations of statistical measures are typically employed for an overall evaluation (Ebert, 2007; Wilks, 2011).

Table 4.1 Contingency Table.

Gauge Rain ≥ Threshold Gauge Rain < Threshold TMPA ≥ Threshold Hit false alarm TMPA < Threshold Miss correct negatives

Table 4.2 Rainfall categories and thresholds. Column 1 is used for analysing the

RMSE, column 2 for the relative bias and column 3 for the categorical

statistics.

Rainfall categories Rainfall categories Rainfall Threshold (mm day-1) (mm day-1) (mm day-1) 5 – 15 5 – 15 5 15 – 30 15 – 30 15 30 – 45 30 – 45 30 45 – 75 45 – 75 45 75 – 100 75 – 100 75 100 – 150 > 100 100 > 150

The skill of TMPA is evaluated for different altitudes, TC intensity, distance from TC centre and position of TCs with respect to the island. The categories of TC intensity used here are those used in the south-west Pacific region by the Fiji Bureau of Meteorology and the

Australian Government Bureau of Meteorology (BOM) (Table 4.3). Note this classification scheme differs from the Saffir-Simpson scale (Simpson, 1974).

Table 4.3 TC categories and their corresponding central pressure as used by

Australian BOM.

Category Central pressure (hPa) 1 > 985 2 985 – 970 3 970 – 955 4 955 – 930 5 < 930

The confidence intervals on some of the validation statistics are evaluated at a 95 % level using the bootstrapping technique (Efron and Tibshirani, 1993) which involves re- sampling of the data. Some 15,000 random re-samples, with replacement, are constructed on which the bootstrapping is applied. The 50th percentile (median) is presented as the validation statistic and the 2.5th and 97.5th percentile as the 95 % confidence interval.

4.3 Results

To examine the overall quality of the TMPA estimates over the 15 year period, a 2D histogram of TMPA against gauge data (Figure 4.3) is presented first. A moderate positive linear association between the two is evident with a considerable number of outliers. While numerous TMPA samples occur above the 1:1 reference line at all observed gauge rainfall categories, more are below the reference line; for larger rain rates (greater than 100 mm day-

1) almost all are below the reference line. For data with a threshold of zero, cases of missed detections (Gauge > 0, TMPA = 0) and false alarms (Gauge = 0, TMPA > 0) are evident.

While missed detections do not occur for observed rain events greater than 40 mm day-1, numerous false alarms exist for moderate to large TMPA estimates, with some occurring for estimates greater than 100 mm day-1. This could partly result from a mismatch between point gauge and areal TMPA estimate (Tan et al., 2016).

2D histogram of TMPA against gauge rainfall 1000 >=20 18

) 100 16 -1 14 12 10 10 8

1 observations of number TMPA rainfall (mm day TMPArainfall(mm 6 4 2 0 0 1 10 100 1000 Gauge rainfall (mm day-1) Figure 4.3 2D histogram of TMPA against rain gauge data together with the line of

perfect agreement for the period 1998 – 2012. The colour bar shows the

number of observations in each bin.

Table 4.4 Pattern matching statistics for comparison of TMPA estimates with rain

gauge observations. The entries in the bracket are the 95 % confidence

interval.

Mean Gauge Rainfall (mm day-1) 30.0 (28.34, 31.80) Mean TMPA Rainfall (mm day-1) 27.50 (26.04, 29.04) Relative Bias -0.0836 (-0.1232, -0.0408) RMSE (mm day-1) 34.33 (32.27, 37.25) Relative RMSE 1.15 (1.08, 1.24) Correlation Coefficient 0.68 (0.65, 0.70) Number of Samples 2,645

To compare TMPA with the gauge data, the continuous verification statistics of mean rain rate, bias, RMSE, relative RMSE and r were computed next and are given in Table 4.4.

TMPA has a lower mean rain rate than the gauge which shows, on average, an underestimation by TMPA. Correspondingly, the bias is -0.0836 (-8.36%) which shows underestimation by TMPA. This underestimation could be larger since there may be wind induced under-catch associated with rain gauges as the quality controlled data does not include this correction. TMPA has a moderate linear association with the gauge data (r =

0.68). However, the RMSE value of 34.33 (relative RMSE of 1.15 or 115%), which measures the average magnitude of the error, shows a large deviation in the TMPA estimates. A plot of

RMSE and the relative RMSE against seven categories of rainfall (rainfall categories are listed in column 1 of Table 4.2) is shown in Figure 4.4a. The RMSE increases with increasing rainfall, giving magnitudes of 20 – 55 mm day-1 for rainfall less than 150 mm day-1 and 112 mm day-1 for events greater than 150 mm day-1. The relative RMSE (the RMSE divided by the mean gauge), on the other hand, decreases with increase in rainfall. For rain rates less than 45 mm day-1 it is greater than 1 (or 100 %) and as large as 2.2 (220 %) for the 5 – 15 mm day-1 category, which shows large deviations in the estimates with respect to the average rainfall.

For rainfall greater than 45 mm day-1 the relative RMSE ranges from 0.75 – 0.5 (75 – 50 %).

Although this is large with respect to the average rainfall, it is still lower than that at lower rain rates.

To assess the relative importance of the RMSE statistic, a plot of percentage rainfall in each of the rainfall categories is shown in Figure 4.4b. The percentage ranges from 6 – 19 %, with 19 % of the total rainfall occurring for rare rainfall events (greater than 150 mm day-1).

This shows that the rare events (heavy rainfall) are important for the total rainfall.

(a) RMSE and Relative RMSE 150 3 125 RMSE 2.5 Relative RMSE 100 2 75 1.5 RMSE 50 1

25 0.5 RelativeRMSE

0 0 (b) Rainfall percentage 20 15 % 10 5 5-15 15-30 30-45 45-75 75-100 100-150 >150 Rain Range: (mmday-1)

Figure 4.4 (a) RMSE and relative RMSE between the TMPA estimates and the gauge

observations as a function of rainfall (mm day-1). The error bars indicate a

95 % confidence interval. (b) Percentage rainfall at each of the rainfall

categories.

4.3.1 Skill With Respect To Elevation

The ability of TMPA under different conditions such as elevation, TC intensity, distance from the TC centre and position of TC centre with respect to the island is also investigated. A combination of validation statistics, namely the relative bias and the four commonly used categorical statistics (POD, FBI, FAR and ETS) are used. Samples were

grouped according to elevation less than 300 m and greater than 300 m. This threshold is established based on studies (e.g. Sinclair (1994), Roe (2005) and Smith et al. (2009)) that show clear orographic enhancement at 300 m. It is also consistent with Chen et al. (2013b) who report a difference in the skill of TMPA above and below this elevation threshold.

Figure 4.5a shows the relative bias of TMPA estimates against the gauge data for different elevations for six categories of rainfall (the rainfall categories are listed in column 2 of Table

4.2). Under all-terrain conditions (that is without partitioning for different elevations), the bias is positive for rain rates below 45 mm day-1 and negative for rain rates above 45 mm day-

1. This shows that TMPA overestimates the observed light rainfall but it tends to underestimate moderate to heavy rainfall events, in agreement with other validation studies

(e.g. Yu et al. 2009; Chen et al. 2013b,c).

Considering the partitioning for different elevations, for lower elevation (less than 300 m) TMPA overestimates light rainfall (less than 45 mm day-1) and underestimates moderate to heavy rainfall (greater than 45 mm day-1). On the other hand, for higher elevation (greater than 300 m) there is an underestimation by TMPA at all rain thresholds which worsens with increasing threshold. The underestimation of moderate to heavy rainfall (greater than 45 mm day-1) at higher elevation is also slightly larger than that for lower elevation. A possible reason for this could be the inability of TMPA to detect short-lived extreme rainfall events due to the orographic enhancement usually observed at higher elevation, as pointed by Chang et al. (2013) and Chen et al.(2013b, c).

To assess the relative importance of these statistics, a plot of percentage rainfall in each of the rainfall categories is shown in Figure 4.5b. The percentage rainfall of each group is computed with respect to the total rainfall in each group. The percentage contribution increases with increase in rainfall category. The rare rainfall events (greater than 100 mm day-1), however, have a relatively larger contribution (greater than 35 %) to the total rainfall

at all elevations and it is more pronounced at higher elevation (50 %). These results show that the heavy rainfall events are important for the total rainfall, especially at higher elevations.

Figure 4.5 (a) Relative bias as a function of gauge rainfall (yellow squares with solid

line) on the island sites. The sites are further separated into two subgroups

according to elevation: elevation less than 300 m (red circles with solid

line) and elevation greater than 300 m (green diamonds with dashed line).

The error bars indicate the 95 % confidence interval. (b) Percentage rainfall

at each of the rainfall categories for the three groups computed with respect

to the total rainfall of the respective group.

Figure 4.6 (a–d) shows the categorical statistics for all-terrain conditions (i.e. without elevation stratification) and the less than 300 m and greater than 300 m elevation groups as a function of six rain thresholds (the rainfall thresholds are listed in column 3 of Table 4.2).

Considering all-terrain conditions, the POD (Figure 4.6a) decreases with increasing rain threshold but it remains above 0.5. Under different elevations, the POD is consistently larger for lower elevation (less than 300 m) than for higher elevation (greater than 300 m) which shows that the ability of TMPA decreases with increasing elevation.

The FAR (Figure 4.6b) over the island (without elevation stratification) increases with increase in rainfall but its response differs when stratified with respect to high and low elevations. While the FAR for lower elevations (less than 300 m) is similar to that of the

“without elevation stratification” group, the FAR for higher elevations (greater than 300 m) is consistently smaller than the lower elevation group at all rainfall thresholds. The response at the higher elevation data to changing thresholds is also different: the FAR increases from 5 –

30 mm day-1 and then there is a sharp decrease for thresholds greater than 30 mm day-1. This signifies that for the estimates made at a higher elevation, relatively fewer events (in comparison with lower elevation) are false alarms and this becomes more pronounced at moderate to large rainfall thresholds (greater than 30 mm day-1).

The FBI score (which measures relative frequencies; Figure 4.6c) for all-terrain conditions is less than 1 for light rain thresholds (less than 15 mm day-1) and approximately 1 for moderate to heavy rainfall. This shows that the TMPA estimates correspond well with the observed frequency of moderate to heavy rainfall. At lower elevation, TMPA underestimates the frequency of light rainfall (less than 15 mm day-1) and it slightly overestimates (FBI ~

1.15) moderate to heavy rainfall (greater than 30 mm day-1). On the other hand, at higher elevations, TMPA significantly underestimates the frequency of the observed rainfall events,

which shows the inability of TMPA to capture the observed rainfall at higher altitudes, in agreement with our earlier findings.

Figure 4.6 (a-d) Categorical statistics: (a) POD; (b) FAR; (c) FBI and (d) ETS over the

island (yellow squares with solid line). The sites are further separated into

two subgroups according to elevation: elevation less than 300 m (red circles

with solid line) and elevation greater than 300 m (green diamonds with

dashed line). The error bars indicate the 95 % confidence interval. (e)

Percentage rainfall above each of the rainfall thresholds for the three

elevation groups computed with respect to the total rainfall of the respective

group.

The ETS, which is a measure of relative accuracy with respect to random chance

(Figure 4.6d), can be used to evaluate the skill under different conditions. For all elevations, the ETS is approximately equal to 0.37 for rain thresholds between 15 and 75 mm day-1 whereas, for thresholds greater than 75 mm day-1 (i.e. at rainfall rates typical of TCs), it is slightly lower (~ 0.3). Considering elevation, the ETS of the greater than 300 m group is less than that of the less than 300 m group for rainfall thresholds less than 75 mm day-1 but for rainfall thresholds 75 mm day-1 and above the ETS is approximately the same for the two groups. This shows that the relative accuracy of TMPA at small to moderate rainfall rates

(less than 75 mm day-1) at higher elevations is less than that at lower elevations but at large rainfall rates (greater than 75 mm day-1) the relative accuracy of the two groups are almost the same. The latter could be attributed to a significantly smaller FAR at higher elevation arising from a smaller FBI. Overall, the ETS over the island ranges from 0.2 to 0.4 and is approximately 0.3 and above during moderate to heavy rainfall events. This is somewhat larger than that reported by some studies (e.g. Yu et al. 2009 and Chen et al. 2013c). For example, the study by Chen et al. (2013c) over the islands and atolls reports ETS to be zero during heavy rainfall events over land with high elevation. Similarly, Yu et al. (2009) report

ETS to be zero during heavy rainfall events over mainland China. The ETS shown here is comparable with that over Australia (Chen et al., 2013b), however.

To show the relative importance of the computed statistics, Figure 4.6e shows the percentage rainfall above each of the rainfall thresholds for the different elevations (the percentage rainfall below each threshold is simply 100 % minus the “percentage above”). The percentage rainfall decreases with an increase in the rainfall threshold but it is consistently

larger for the greater than 300 m group at most of the rainfall thresholds. The percentage contribution by heavy rainfall events (greater than 100 mm day-1) to the total rainfall occurring in the elevation groupings is larger (50 %) for the greater than 300 m group. As discussed before, these results show that the higher rainfall events are more important for the total rainfall at higher elevations than at lower elevations.

The above set of results (Figure 4.5 and 4.6), in general, shows that when all rain intensity categories are considered, the performance of TMPA deteriorates with increasing elevation with a general behaviour of underestimation of observed rainfall events. To further investigate this, we examined the mean gauge rain, the mean TMPA rain and the relative bias at each station (Figure 4.7). Results show greatest rain gauge averages over higher altitudes

(Figure 4.7a), likely due to orographic enhancement. Comparatively, mean TMPA rainfall is commonly less than the mean gauge rainfall with pronounced underestimation at higher elevations (Figure 4.7b). This is clearly shown by the relative bias (Figure 4.7c) which is generally smaller and negative at higher elevation stations in comparison with lower elevations. These results further confirm that the ability of TMPA deteriorates with increasing elevation.

(a) Gauge Average (b) TRMM Average )

) 30 30

-1 -1

20 20

10 10

MeanRainday (mm MeanRainday (mm

0 0 0 200 400 600 800 1000 0 200 400 600 800 1000 Height (m) Height (m) (c) Relative Bias 1

0.5

RelativeBias -0.5

-1 0 200 400 600 800 1000 Height (m) Figure 4.7 Average TC rainfall of gauge observations (a), TMPA estimates (b) and the

relative bias (c) at station sites which have at least 10 samples.

4.3.2 Skill with respect to TC intensity, distance from TC centre and position of TC

centre with respect to the island

To evaluate TMPA under different TC intensity (category), the samples are grouped according to category 1 – 2 (cat12) and category 3 – 5 (cat35). The four categorical statistics

(POD, FAR, FBI, and ETS) are computed and are shown in Figure 4.8 (a–d). The POD

(Figure 4.8a) for each category group is similar especially at moderate to large rain rates. On the other hand, the FAR (Figure 4.8b) is larger for higher category TCs (cat35) than for lower category TCs (cat12). Similarly, the FBI (Figure 4.8c) is larger for cat35 than cat12. The FBI for cat35 is always above 1 for all rain thresholds and it increases with increasing rain threshold, while for cat12 it is always below 1. This shows that TMPA overestimates the frequency of observed rain events in higher category TCs and that the overestimation

increases with increase in rainfall magnitude, while it generally underestimates the frequency of rain events in lower category TCs. The ETS (Figure 4.8d) is relatively larger for the cat12 group in comparison with cat35, which could be attributed to lower false alarms for the lower category TCs, hence a better skill of TMPA during the passage of less intense TCs. This is in contrast to the results of Chen et al. (2013b) which showed better ETS for higher category

TCs over mainland Australia. Further information regarding the skill as a function of TC intensity is provided in section 4.

Figure 4.8e shows the percentage rainfall above each of the rainfall thresholds for the different intensity groups. The percentage rainfall for the cat12 group is consistently larger than the cat35 group at almost all of the rainfall thresholds (except for the first). This larger percentage rainfall for the cat12 group is related to the higher contribution from the heavy rainfall events (45 % contribution from the greater than 100 mm day-1 rainfall events compared to 23 % from the same threshold for the cat35 group) which shows that the heavy rainfall events are more important for the total rainfall during the passage of less intense TCs.

Figure 4.8 (a-d) Categorical statistics: (a) POD; (b) FAR; (c) FBI and (d) ETS for

category 1-2 (cat12, yellow squares) and category 3-5 (cat 35, red circles)

TCs. The error bars indicate the 95 % confidence interval. (e) Percentage

rainfall above each of the rainfall thresholds for the two intensity groups

computed with respect to the total rainfall of the respective group.

While heavy rainfall also occurs in the TC outer rainbands, the most intense rainfall typically occurs close to the centre of the storm. Accordingly, we examined the performance of TMPA with respect to distance from the TC centre where samples are grouped according to distance less than 200 km and greater than 200 km from the TC centre and the four

categorical skill scores (POD, FAR, FBI and ETS) are calculated. Figure 4.9 (a‒d) shows the results for the two groups.

Figure 4.9 (a‒d) Categorical statistics: (a) POD; (b) FAR; (c) FBI and (d) ETS for TCs

with centres less than 200 km (yellow squares) and greater than 200 km

(red circles). The error bars indicate the 95 % confidence interval. (e)

Percentage rainfall above each of the rainfall thresholds for the two distance

groups computed with respect to the total rainfall of the respective group.

The POD (Figure 4.9a) for TC centres near the island (less than 200 km) is higher than that for distant TCs (greater than 200 km). This shows that TMPA has a better performance closer to the TC centre. The FAR (Figure 4.9b) is higher for larger distance whereas there is a marginal difference in the FBI (Figure 4.9c). The ETS (Figure 4.9d) is larger closer to the TC centre which shows that TMPA has better skill when TCs are closer to the island. This is in agreement with findings of Chen et al. (2013b) which showed that TMPA performs better in locations closer to the TC centre.

Figure 4.9e shows the percentage rainfall above each of the rainfall thresholds for the two distance groups. The percentage rainfall of the less than 200 km group is consistently larger than the greater than 200 km group at most of the rainfall thresholds (except for the first threshold) which could be attributed to the higher contribution from the heavy rainfall events for the less than 200 km group (47 % contribution from the greater than 100 mm day-1 rainfall events compared to 26 % from the same threshold for the greater than 200 km group).

This shows that the heavy rainfall events are more important for the total rainfall for stations closer to the TC centre.

TCs approach the Grande Terre Island from both the eastern and western side.

Therefore, the performance of TMPA is also examined with regards to the position of the

TCs with respect to the island (East or West). TC days are grouped as east TC (days when

TCs had centres on the eastern side of the island) and west TC (days when TCs had centres on the western side of the island) and the various categorical statistics (POD, FAR, FBI and

ETS) are calculated and shown in Figure 4.10 (a‒d). The POD (FAR) of the western TCs is larger (smaller) than the eastern TCs at all rain thresholds. This shows that TMPA has a better performance when the TCs are on the western side of Grande Terre at least for the sample of TCs analysed here. The FBI of the eastern TCs is larger (greater than 1) than the western TCs for rain thresholds between 15 and 75 mm day-1. A large ETS is observed for

western TCs which shows that TMPA has better skill when TCs are on the western side of the island. To explain the above results, the average distance of TC centres from the gauge stations is calculated for the respective TC days (Figure 4.11). TC days 1 to 5 refer to the consecutive days when the average distance of a TC is less than 500 km from the gauges i.e.

1 is the first day, 2 is the second day and so on. Results show that, on average, the western

TCs are much closer to the island than the eastern TCs, which could be the reason for the better performance of TMPA for western TCs in our sample. This further confirms that

TMPA performs better closer to the TC centres. Another possible explanation is that slopes on the western side of Grande Terre are not as steep as on the eastern side, thus orographic enhancement is less and so TMPA performs better, although further analysis would be required to confirm this.

Figure 4.10e shows the percentage rainfall above each of the rainfall thresholds for the east and west groups. The percentage rainfall of the western TCs is consistently larger than the eastern TCs at majority of the rainfall thresholds (except for the first threshold) which could be attributed to the higher contribution from the heavy rainfall events (45 % contribution from the greater than 100 mm day-1 rainfall events compared to 27 % from the same threshold for the eastern TCs). This shows that the heavy rainfall events are more important for the total rainfall for western TCs.

Figure 4.10 (a‒d) Categorical statistics: (a) POD; (b) FAR; (c) FBI and (d) ETS for east

(yellow squares) and west (red circles) TCs. The error bars indicate the 95

% confidence interval. (e) Percentage rainfall above each of the rainfall

thresholds for the two position groups computed with respect to the total

rainfall of the respective group.

TC days distance distribution 250 TC east TC west 200

150 Distance (km)

100 0 1 2 3 4 5 TC day

Figure 4.11 Average distance of TC centres from gauge stations for TC days 1, 2, 3,4

and 5 for east (yellow squares) and west (red circles) TCs. The TC days are

days (24 hours) counted from the time a TC first enters within the 500 km

zone from any gauge station.

4.3.3 Case Studies

Figure 4.12a shows the gauge average, TMPA average and the relative bias of TCs that have at least ten samples and whose spatial correlation coefficient (r) between the gauge and

TMPA is significant at the 95 % confidence level (12 such cases). The position of the TCs in this plot is based on the ascending order of average gauge rainfall. A varying association between the gauge rainfall and TMPA is evident. Excellent association (a low relative bias) between the TMPA averages and the gauge averages are evident near the larger tail of the rainfall distribution (TCs 6 – 11 except 7) whereas cases of significant underestimation and overestimation (large relative bias) are more usual near the lower tail of the rainfall distribution (TCs 1 – 5). The spatial correlation between the gauge rainfall and TMPA

(Figure 4.12b) varies among the TCs and ranges from 0.3 to 0.8. A majority (nine) of the TCs have r greater than 0.5, of which six (50 %) are greater than 0.7, while three are less than 0.5.

The higher r is prominent with TCs comprising heavy average rainfall. TCs 1 – 6 (except 3) are cases with a low average rainfall and have r less than 0.6, whereas TCs 7 – 12, cases with

a high average, have r greater than 0.6. This shows a better representation of the pattern of

observed rainfall for TCs with higher average rainfall.

(a) Average rain rate and relative bias of individual TC 100 -1 Gauge 80 TMPA 1

), RMSE ), relative bias -1 60 0.5 (Vania, 2011)

40 0 relativebias 20 (Erica, 2003) -0.5

(Innis, 2009) Rainfallday (mm 0 -1 1 2 3 4 5 6 7 8 9 10 11 12

(b) RMSE, Relative RMSE and r for individual TC 50 2

1.6 40 RMSE 1.2 30 Relative RMSE

RMSE r 0.8 20

0.4 Relativeand r RMSE

10 0 1 2 3 4 5 6 7 8 9 10 11 12 Individual TC

Figure 4.12 (a) Mean gauge rainfall, the corresponding mean TMPA estimates and the

relative bias of the 12 TCs that have at least 10 observations and whose

spatial correlation coefficient (r) between the TMPA estimates and gauge

observations are statistically significant at 95% confidence level. The TCs

are arranged in the order of ascending average gauge rainfall. The TCs used

as case studies to demonstrate the ability of TMPA are shown in the

brackets (name and year). The error bars indicate the 95% confidence

interval. (b) RMSE, relative RMSE and the spatial correlation coefficient

(r) of the 12 TCs shown in panel (a).

The RMSE and the relative RMSE between the gauge and TMPA estimates of the 12

TC cases are shown in Figure 4.12b. The RMSE (relative RMSE) increases (decreases) with increasing average rainfall. This shows that the absolute error in the estimation of heavy rainfall rate is large, but it is relatively small (in comparison with light rainfall) when normalised with respect to the corresponding average rainfall.

TC 7 (Vania, 2011), TC 9 (Innis, 2009) and TC 11 (Erica, 2003) are used to present the performance of TMPA for some individual TC cases. These TCs are chosen on the basis of varying bias, where the first has a large negative bias and the latter two have a small bias

(Figure 4.12a). In addition, these are land-falling cases, hence they present the skill of TMPA when TCs hit land. TC tracks are shown in Figure 4.13. TC Vania made landfall on the south eastern coast of Grande Terre on January 14 at 2300 New Caledonia Time (NCT) (1200

UTC) as a category 1 (980hPa) TC with wind speeds of 83.3 km hr-1. TC Innis made landfall on the north eastern side on February 17, 2009, at 1100 hrs NCT (0000 UTC) as a category 1

(997 hPa) TC with an average wind speed of 56 km hr-1 (IBTrACs archive). In contrast, Erica was a high-intensity TC that reached category 5 on 13 March at 0700 NCT (12 March 1800

UTC) peaking with wind speeds of 240 km hr-1 on 13 March at 1700 NCT (0600 UTC). On the same day, Erica closely paralleled the southwest coast of Grande Terre, before making landfall on the south western coast on March 14 at 1100 NCT (0000 UTC) as a category 4 TC with wind speeds around 185 km hr-1. After passing the island, Erica underwent extra-tropical transition, weakening as it moved southwards (Australian Government Bureau of

Meteorology, 2003).

Figure 4.13 shows the 24 hour accumulated gauge and TMPA-estimated rainfall of the above three TCs for the landfall day. TMPA (Figure 4.13b, d, f) in general shows a spatial distribution that almost resembles the observed rainfall (Figure 4.13a, c, e), with regions

receiving large gauge rainfall also captured to some extent. There is, however, a disparity

between the observed and the estimated extreme values, with general underestimation shown

for the TMPA data. Table 4.5 lists four extreme observed gauge rainfall events and their

corresponding TMPA estimates for each TC. The maximum observed (estimated) rainfalls

are 450.7 (127.4), 326.9 (76.2) and 200.0 (164.57) mm day-1 respectively for TC Vania, Innis

and Erica. These results show that though TMPA is able to represent the regions of heavy

rainfall events, the magnitude is mostly underestimated. This underestimation could be larger

due to the wind-induced error in the gauge measurements that have not been corrected here.

(a) TC Vania - Gauge (c) TC Innis - Gauge (e) TC Erica - Gauge 200 15/01/2011 0500 hrs NCT 400 300 150 300 200 100 200 17/02/2009 100 100 1100 hrs NCT 50 14/03/2003, 1100 hrs NCT 0 0 0 (b) TC Vania - TMPA (d) TC Innis - TMPA (f) TC Erica - TMPA 200 300

-20 400 )

150 -1 300 -21 200 100

200 Latitude -22 100

100 50 Rainfall(mmday

-23 0 0 0 164 165 166 167 Longitude

Figure 4.13 24 hour accumulated gauge and TMPA estimate rainfall of TC Vania (a and

b respectively), Innis (c and d respectively) and Erica (e and f respectively)

on the landfall day (landfall date and time of each TC are respectively

shown in the TMPA estimate panel). The black dashed line shows the track

of the TCs.

Table 4.5 The four extreme gauge rainfalls with their corresponding TMPA rain

estimates for TC Vania (2011), Innis (2009) and Erica (2003). The rainfalls

are in mm day-1

TC Vania TC Innis TC Erica Gauge TMPA Gauge TMPA Gauge TMPA 450 127 327 76 200 165 426 134 275 171 192 123 385 134 244 111 179 117 383 141 215 72 172 118

Figure 4.14 shows a plot of the four categorical statistics of the three TCs for all the TC days. TC Vania shows a smaller POD (especially for rain thresholds less than 75 mm day-1), a smaller FAR (for rainfall greater than 15 mm day-1) and a smaller FBI (consistently less than 1 at all rain thresholds) than the other two TCs. The ETS (or relative accuracy) of TC

Vania, on the other hand, is larger than that of TC Erica (Innis) at all rain thresholds (greater than 45 mm day-1). The FBI values i.e. less than 1, ~ 1, and values partially above and below

1 are consistent with the large negative bias of TC Vania and negligible bias of TC Erica and

Innis respectively (Figure 4.12a). These results, together with Figure 4.12 and 4.13, show that the skill of TMPA varies from case to case.

(a) POD (b) FAR 0.6 1 VANIA 0.8 INNIS 0.4 ERICA

0.6

FAR POD 0.4 0.2 0.2

0 0 0 5 15 30 45 75 100 0 5 15 30 45 75 100 Rain Threshold: (mm day-1) Rain Threshold: (mm day-1) (c) FBI (d) ETS 0.8 1.5 0.6 1

0.4

FBI ETS

0.5 0.2

0 0 0 5 15 30 45 75 100 0 5 15 30 45 75 100 Rain Threshold: (mm day-1) Rain Threshold: (mm day-1) Figure 4.14 Categorical statistics (a) POD; (b) FAR; (c) FBI and (d) ETS of land-falling

TCs shown in Figure 4.13 (i.e. Vania (2011), Innis (2009) and Erica

(2003)). The error bars indicate a 95 % confidence interval.

4.4 Discussion and Summary

This study has evaluated the ability of the TMPA 3B42 research product (version 7) to

represent the 24 hour accumulated gauge rainfall associated with TCs affecting New

Caledonia with the aim of providing insight into the accuracy and limitations of the TMPA

3B42 data. Combinations of statistics are used to demonstrate the disparity and similarity

between the TMPA and gauge rainfall.

Overall, the study shows that TMPA has a moderate skill (relative accuracy or ETS

around 0.3 – 0.4 for moderate to high rainfall events) in estimating rainfall associated with

TCs over the island. TMPA generally overestimates light rainfall events and underestimates

heavy rainfall events, in agreement with other validation studies, for example, Yu et al.

(2009), Chang et al. (2013) and Chen et al. (2013b,c). TMPA has a spatial correlation (r) of

0.68 with the observations with large deviations (RMSE=34.33 mm day-1). This correlation is slightly larger than that reported by Chen et al. (2013c) over coastal and island sites (r=0.55).

It is comparable with that obtained over mainland China (r=0.66) (Yu et al., 2009), however, it is smaller than that over Australia (r =0.86) (Chen et al., 2013b). While the ETS (relative accuracy) over the island is comparable with that over Australia, it is larger than that over

China and the coastal and island sites. The difference in the skill over different regions could be attributed, to some extent, to the varying skill of satellites with latitude: Ebert et al. (2007) report that satellite estimates have a better skill over lower latitudes during summer. China encompasses higher latitudes than New Caledonia which could explain the difference. Over the Australian region, the TC days are heavily concentrated over lower latitude regions (Chen et al., 2013b), which could be a reason for a comparatively larger r than that obtained over

New Caledonia.

The skill of TMPA also varies under different conditions such as elevation, distance from TC centre, TC intensity and TC location (east or west) with respect to the island. Under different terrain conditions, results show that the skill of TMPA decreases with increasing elevation, which could be due to TMPA’s inability to capture short-lived orographic enhanced rainfall. A possible factor for this could be the resolution of TMPA (3 hourly and

0.25° × 0.25°) which is not high enough to resolve the rapidly evolving small scale orographic enhancements over the small-scale mountainous terrain of the island, as also suggested by studies in other locations (e.g. Chang et al. 2013; Chen et al. 2013b,c).

Considering distance from the TC centre, TMPA is in better agreement with the observations near the TC centre, consistent with the findings of Chen et al. (2013b). This could be attributed to the more organised convection and greater concentration of liquid and

frozen hydrometeors in the vicinity of the eye-wall (usually the region of the extreme rainfall) than in the outer rainbands, leading to a relatively stronger scattering of MW signal which is then better correlated with surface rainfall.

With respect to TC intensity, results show that TMPA has a better skill (relatively large

ETS) for less intense TCs. This could largely be due to the low number of false alarms (FAR) during the passage of these TCs which in turn is related to the low FBI (underestimation of the frequency of the observed rainfall). The reason for a low FBI could be that lower category

TCs have much weaker organised convection and cloud cover (usually few hydrometeors) which correlates with weak MW scattering that could lead to an underestimation of the frequency of the observed rainfall. A low FBI thus leads to fewer false alarms. This better skill of TMPA for less intense TCs, however, is in contrast to the findings of Chen et al.

(2013b) who reports better skill for higher category TCs over Australia. To ascertain the exact reason for the difference with that over Australia requires additional statistical information such as POD, FAR and FBI for the same region, which are not available. A further investigation is needed that is outside the scope of this paper.

Considering the TC centre location with respect to the island, TMPA is more skilful for western than for eastern TCs. A distance analysis shows that the former are relatively closer to the island than the latter. This therefore is likely an indication of better performance of

TMPA closer to the TC centre, as shown previously.

The skill of TMPA, however, varies from case to case. TCs with large (small) average rainfall are mostly associated with a small (large) relative bias, a high (low) spatial correlation, a high (low) RMSE and a small (large) relative RMSE. TCs with large average rainfall could have more organised convection and greater concentration of hydrometeors aloft than TCs with low average rainfall. As discussed previously, this will lead to a relatively stronger scattering of MW signal which may then be better correlated with surface rainfall.

TC Vania (2011), Innis (2009) and Erica (2003), which are land-falling TCs with the former having a large negative bias and the latter two having a negligible bias, are chosen as case studies to demonstrate the ability of TMPA. While TMPA is able to show the spatial distribution of the observed rainfall pattern, it significantly underestimates the heavy rainfall events. In relation to Innis and Erica, TC Vania (i) has a lower POD (for rain rates less than

75 mm day-1) and FBI, which could be related to the large negative bias, and (ii) a large ETS

(especially for rain rates greater than 45 mm day-1) likely due to the less false alarms.

In summary, this study shows that TMPA is able to represent (with moderate skill) the observed TC rainfall over the island of Grande Terre. As an application for future TC related studies, the TMPA estimates could be blended with rain gauge data, which would take advantage of the strengths and mitigate the shortcomings of each data set, by producing blended gridded precipitation estimates for New Caledonia. Methods for such blending have been presented by several studies, for example, Mitra et al. (2009), Vila et al. (2009), Li and

Shao (2010) and Renzullo et al. (2011). Radar rainfall estimates could also be actively used in such blending but a prior thorough accuracy and error analysis of this data set would be required. In the near future, the GPM based precipitation product (Hou et al., 2014; Huffman et al., 2015), which is the successor of the TRMM based product, could also be incorporated.

Such a blended dataset is expected to provide a better precipitation estimate for New

Caledonia.

Appendix A

For comparison between TMPA estimates and the gauge observations, the statistics of correlation coefficient (r), relative bias and relative root mean square error (RMSE) are used

(Wilks, 2011). In addition, four categorical statistics commonly used in validation studies, that is the probability of detection (POD), the false alarm ratio (FAR), the frequency Bias

(FBI) and the equitable threat score (ETS) (Wilks, 2011), are calculated using a contingency table (Table 4.1).

The correlation coefficient (r) measures the linear association between the observation and the estimates. It does not take bias into account, therefore is used with other statistics.

E  EO  O r   (A.1) 2 2 E  E O  O

The relative mean error (relative bias) measures the difference between the average observed and estimated values.

E  O Relative Bias = (A.2) O

The root mean square error (RMSE) measures the average magnitude of error weighted according to the square of the error.

n 1 2 RMSE = Ei  Oi  (A.3) n i1

RMSE and the Relative RMSE = (A.4) O where E = TMPA estimate; O = gauge observation and n = number of samples

The POD is the ratio of correct estimates to the number of observed “yes” events and ranges from 0 to 1 with 1 being the perfect score. It is sensitive to hits and the climatological frequency of the event, however ignores false alarms. Thus it is usually used together with the FAR.

hits POD  (A.5) hits  misses

The FAR is the fraction of false alarms to the number of estimated “yes” events and ranges from 0 to 1 with 0 being the perfect score. It is sensitive to false alarms and the climatological frequency of the event but ignores misses. It must be used together with the

POD.

falsealarms FAR  (A.6) hits  falsealarms

The FBI is the ratio of number (frequency) of estimated “yes” events to the number of observed “yes” events and ranges from 0 to ∞ with 1 being the perfect score. An FBI less than 1 indicates underestimation and greater than 1 indicates overestimation.

hits  falsealarms FBI  (A.7) hits  misses

The ETS is a measure of relatively accuracy with respect to hits due to random chance.

The score ranges from -1/3 to 1 with 0 being no skill and 1 a perfect score.

hits  hits ETS  random (A.8) hits  misses  falsealarms  hitsrandom

hits  misseshits  falsealarms where hits  (A.9) random hits  misses  falsealarms  correct negatives

Having presented the accuracy and limitations of TMPA over New Caledonia we next examine the same over Fiji. The manuscript accepted for publication is presented.

5 Evaluation of TRMM Multi-satellite Precipitation Analysis during the passage of Tropical Cyclones over Fiji Anil Deo1, Kevin J. E. Walsh1

Anil Deo, School of Earth Sciences, The University of Melbourne, Victoria 3010, Australia

([email protected], Ph: +61 (0)3 8344 7675, Fax: +61 (0)3 8344 7761)

Kevin J. E. Walsh, School of Earth Sciences, The University of Melbourne, Victoria 3010, Australia

1School of Earth Sciences, University of Melbourne, Victoria 3010, Australia

Abstract

Fiji is prone to the devastating effects of heavy rainfall during the passage of tropical cyclones (TCs) and as such accurate measurement of rainfall during these events is urgent for effective disaster mitigation and risk analysis. Fiji, however, has a sparse distribution of rain gauges, thus there is a deficiency in the accurate measurement of rainfall. This gap could be filled by satellite-based rainfall estimates but before they are used, they need to be validated against a reference dataset for their accuracy and limitations. This study hence validates the

TRMM based Multi-satellite Precipitation Analysis (TMPA) estimates over the island of Fiji.

The study shows that TMPA has moderate skill in estimating rainfall during the passage of

TCs over the island of Fiji. This skill is also highly variable as it decreases with an increase in rainfall intensity, increase in distance from the cyclone centre and increasing terrain elevation.

The ability of TMPA also varies case by case but we report a general underestimation of rainfall by TMPA during the passage of TCs with a larger rainfall rate (defined in our case as those TCs with average daily rainfall greater than 25 mm day-1).

Keywords

Validate, TMPA, rainfall estimates, disaster response

5.1 Introduction

Extreme rainfall during the passage of tropical cyclones (TCs) causes devastating impacts such as flooding, landslide and death (Dare, 2013). The widespread flooding during the passage of TC Evan (2012, a category 4 TC) over Fiji inflicted colossal damage and threatened lives over parts of the country (Government of Fiji, 2013). Extreme rainfall during the passage of the TC exceeded 200 mm day-1.

Accurate information on the magnitude and distribution of rainfall during such events is crucial for effective disaster mitigation and risk analysis particularly by better precipitation forecasting through improved model initialization and numerical weather model evaluation

(Ebert et al., 2007; Yu et al., 2009). Fiji (geographical location shown in Figure 5.1) has a sparse distribution of rain gauges (see Figure 5.2) and accurate spatial and temporal representation of rainfall over this region is limited. This gap could be addressed by utilising satellite-based rainfall estimates.

These estimates, however, need to be evaluated against reference rainfall data, such as rain gauge or calibrated radar data, for their accuracy and limitations before they can be confidently used (Ebert et al., 2007). Under a program of the International Precipitation

Working Group (IPWG) and the more comprehensive study called the Pilot Evaluation of

High Resolution Precipitation Products (PEHRPP) (Arkin et al., 2006), work has been conducted to validate nearly all operational satellite precipitation products (Ebert et al.,

2007).

In addition, some studies have evaluated the Tropical Rainfall Measuring Mission

(TRMM) Multi-satellite Precipitation Analysis (TMPA) 3B42 estimates (hereafter referred to as TMPA) of extreme rainfall during the passage of TCs (Habib et al., 2009; Yu et al., 2009;

Chen et al., 2013a; Chen et al., 2013c, b; Deo et al., 2016). These studies are over mainland

China (Yu et al., 2009), Taiwan (Chang et al., 2013; Chen et al., 2013a), USA (Habib et al.,

2009), India (Prakash et al., 2012), the Australian region (Chen et al., 2013b), Pacific atoll and “coastal and inland” sites (Chen et al., 2013c) and over New Caledonia (Deo et al.,

2016). These studies in general show that TMPA has moderate skill in representing the observed rainfall but the skill is variable with respect to the magnitude of rainfall, geographical terrain, latitude, structure of the TC and TC intensity.

The above evaluations have broadened our understanding of the skill of TMPA during heavy rainfall events caused by the passage of TCs over the respective regions, but no such information is available for the Fiji region. In this study we evaluate the TMPA estimates over Fiji and show that TMPA has moderate skill in representing rainfall during the passage of TCs over Fiji. We also show that the skill statistics over Fiji differ from those other regions. Thus, this evaluation gives users some insight into the accuracy and limitations of the TMPA product over Fiji.

5.2 Data and Methodology

5.2.1 TMPA

TMPA is a 3 hourly, 0.25º × 0.25º latitude-longitude resolution gridded product which makes use of the following datasets: the TRMM combined instrument (TCI) data comprising the TRMM Microwave Imager (TMI) and the TRMM precipitation radar used as the source of calibration; microwave (MW) data from several Low Earth Orbit (LEO) satellites; the

Climate Prediction Centre (CPC-NOAA) infrared (IR) data and the Global Precipitation

Climatology Project (GPCP) gridded monthly rain gauge data (Huffman et al., 2007).

TMPA is produced in four stages. First, the MW estimates from individual sensors are calibrated using the TCI and then combined. Second, the IR estimates are created with MW calibration. Third, the MW and IR data are combined such that the MW estimates are taken

“as is” with the IR estimates used to fill the gaps. Finally, the monthly rain gauge analysis, which includes the Global Precipitation Climatology Centre (GPCC) analysis, is applied to

minimise the bias (Huffman et al., 2007). There certainly is some overlap between the Fiji gauge data and the monthly gauge analysis used for TMPA. The number of Fiji stations used by GPCC varies each year but they are about 4 – 9 (out of 16) stations especially for years

2000 – 2012, which is the duration of this study (information obtained from the GPCC website: http://www.esrl.noaa.gov/psd/data/gridded/data.gpcc.html). Hence, the Fiji gauge data could be considered as the more accurate rainfall data for this region. The number of Fiji gauge stations used for the GPCC land-surface precipitation monthly product for the year

2012 (when the number of Fiji gauges used is 9) per 1º × 1º grid is shown in Figure 5.2.

This study utilises the research version (version 7 or V7) of TMPA. The reader is referred to Huffman et al. (2007) for a detailed description of the TMPA.

Location of New Caledonia 10

-10

-20 Latitude

-30

-40

-50 110 120 130 140 150 160 170 180 -170 Longitude

Figure 5.1 Location of Fiji (enclosed in the dashed red rectangular box) in the south

west Pacific basin.

5.2.2 Fiji Rain Gauge Data

We use the Fiji rain gauge daily data to verify the TMPA estimates. The rain gauges, though, are sparsely distributed (Figure 5.2). The data is quality controlled by the Fiji

Meteorological Service (Fiji Met) and only data that have been verified by Fiji Met are used for this study.

Rain gauge data are known to have errors (both systematic and random) with possible effects from obstruction, wind, wetting, splashing, evaporation and calibration (Habib et al.,

2008). The wind-induced error is the primary source of a systematic error that increases with an increase in wind speed (Nešpor and Sevruk, 1999; Habib et al., 2008; Wang et al., 2008).

As such, the wind-related error will be large during the passage of TCs and this has to be taken into consideration when comparing with TMPA. Accurate observations during extreme weather conditions are further difficult as there is a chance of some degree of uncertainty and propagation of gross, systematic and random errors due to instrumental malfunction during such weather conditions. Nonetheless, gauge data are still considered to be the most accurate and direct measurement of rainfall and the optimal choice for evaluation of satellite precipitation estimates (Ebert et al., 2007; Chen et al., 2013b, c).

5.2.3 Methodology

Satellites estimates could be evaluated using a grid to grid approach or a grid to point approach where the satellite estimates in the latter approach are interpolated to the gauge stations for a direct comparison. In this study we use the grid to point method (congruent with studies such as Chen et al. (2013c) and Yu et al. (2009) ) to evaluate TMPA because a grid based rain gauge dataset is not available for Fiji. TMPA estimates are interpolated to the gauge stations using the inverse distance weighting (IDW) technique (Shepard, 1968) that uses the weighted average of data in the neighbourhood of a grid cell. A power function value of 2 is typically used in the IDW. As discussed by Chen et al. (2013c) and Yu et al. (2009),

we acknowledge that the interpolation will inevitably introduce some errors since TMPA is an areal-averaged product.

Rain gauge stations - Fiji -16

0 0 0 0 1 0

-17

0 1 1 0 0 1

-18

0 0 1 0 0 1

Latitude -19

0 0 1 1 0 0

-20

0 0 0 0 0 1

-21 176 177 178 179 180 181 182 Longitude

Figure 5.2 Rain gauge locations over Fiji. The crosses are stations with elevation less

than 300 m and the circle is the station with elevation greater than 300 m.

The numbers in the grid boxes are the GPCC Monitoring Product Version 6

gauge based analysis number of stations per 1º grid for year 2012 (January

– December) over the Fiji region.

(Source:https://www.esrl.noaa.gov/psd/data/gridded/data.gpcc.html#detail)

The comparison is performed on a daily (24-hour accumulated) basis. The 24-hour rainfall at a gauge station is considered to be TC related and the day is considered to be a “TC day” if the centre of a TC is within 500 km from the gauge station anytime during the accumulation period. The use of the 500 km criteria follows from studies such as Lonfat et al.

(2004), Lau et al. (2008), Jiang and Zipser (2010), Nogueira and Keim (2010) and Chen et al.

(2013b, c) who define TC rainfall to be mostly within this region. The position and the dates of a TC are obtained from the International Best Track Archive for Climate Stewardship data

(IBTrACS) (Knapp et al., 2010) repository that has a 6 hour temporal resolution. A total of

15 TCs for the period 1998 – 2012 satisfied the above criteria. For the declared TC days, the

3-hour TMPA estimates are summed up to match the gauge accumulation period.

A suite of validation statistics, comprising continuous variable statistics and categorical statistics, is used for the evaluation. The continuous variable statistics used here are the correlation coefficient (r), the relative bias and the root mean square error (RMSE). The categorical statistics used here are the probability of detection (POD), the false alarm ratio

(FAR), the frequency bias (FBI) and the equitable threat score (ETS). The categorical statistics are computed using a contingency table (Table 5.1) that depends on a rainfall threshold to determine a rain and no rain event. The rainfall thresholds used in this study are shown in Table 5.2 and the formulae of the statistics (Wilks, 2011) are given in the

Appendix.

Table 5.1 Contingency Table

Gauge Rain ≥ Threshold Gauge Rain < Threshold TMPA ≥ Threshold Hit false alarm TMPA < Threshold Miss correct negatives

Table 5.2 Rainfall categories and thresholds. Column 1 is for the relative bias and

column 2 for the categorical statistics.

Rainfall categories Rainfall Threshold (mm day-1) (mm day-1) 5 – 15 5 15 – 30 15 30 – 45 30 45 – 75 45 75 – 100 75 > 100 100

The uncertainty associated with some of the validation statistics are computed using the bootstrapping technique (Efron and Tibshirani, 1993) which involves re-sampling of the data.

We construct 10,000 re-samples with replacement onto which bootstrapping is applied at a 95

% confidence level. The 50th percentile is presented as the validation statistic and the 2.5 and

97.5 percentile as the 95 % confidence interval.

5.3 Results

After combining all the TC data, a two dimensional histogram of the data is constructed first and shown in Error! Reference source not found.. Some notable observations are as ollows. There is a general positive linear trend between the TMPA and gauge measurements but still numerous data points have large deviations from the line of perfect agreement (1:1 line). Cases of extreme disagreement, such as a gauge measurement of 0 mm day-1 compared with a TMPA of 100 mm day-1, are evident. Even so, the bins with a larger frequency of rainfall events (green, yellow or red bins) fall on the line of perfect agreement. Interestingly, for observed rainfall events greater than 100 mm day-1, a majority of the TMPA estimates are below this value which shows that TMPA generally underestimates heavy rainfall.

Table 5.3 presents the results of the continuous variable statistics. The correlation coefficient between TMPA and gauge is 0.6 which is a weak linear association between the two. The overall relative bias is -0.015 (1.5%), an underestimation but small in magnitude.

The RMSE between the TMPA estimates and the gauge is 38.71 mm day-1. This, when compared to the gauge average of 27.07 mm day-1 (a relative RMSE of 1.43), shows that there are large deviations in the TMPA estimates from the actual ground observations.

Figure 5.4 shows the relative bias for six categories of rainfall (the rainfall categories are listed in column 1 of Table 5.2). It is evident that TMPA overestimates light to moderate rainfall events (less than 75 mm day-1) and underestimates large rainfall events. This is consistent with the findings of most of the earlier studies (Yu et al., 2009; Chen et al., 2013c, b).

2D histogram of TMPA against gauge rainfall 1000 >=20

100 )

-1 14

12 10 10

numberof observations TMPA rainfall TMPA day (mm 1 6

2 0 0 1 10 100 1000 Gauge rainfall (mm day-1)

Figure 5.3 2D histogram of TMPA against rain gauge data together with the line of

perfect agreement for the period 1998 – 2012. The colour bar shows the

number of observations in each bin.

Table 5.3 Pattern matching statistics for comparison of TMPA estimates with rain

gauge observations. The entries in the bracket are the 95 % confidence

interval.

Mean Gauge Rainfall (mm day-1) 27.07 ( 23.53, 31.36) Mean TMPA Rainfall (mm day-1) 26.65 (23.81, 29.91) Relative Bias -0.015 (-0.133, 0.101) RMSE (mm day-1) 38.71 (32.50, 53.18) Relative RMSE 1.43 (1.20, 1.96) Correlation Coefficient 0.60 (0.51, 0.66) Sample Size 574

The categorical statistics (POD, FAR, FBI and ETS) as a function of six rainfall thresholds (the rainfall thresholds are listed in column 2 of Table 5.2) are presented in Figure

5.5. The POD and the ETS decrease with increasing rainfall rate which shows that TMPA has more difficulty in detecting larger rainfall rates. The FBI is around unity at all rain rates which shows that the number of events estimated to occur is almost the same as the number of events that have actually occurred with respect to the given rainfall thresholds. The FAR on the other hand increases with an increase in rain rate threshold which shows that of the events estimated to occur more are false alarms at larger rain rates. These results in general show that the skill of TMPA decreases with increasing rainfall rate.

Relative Bias 1

0.5

0 RelativeBias -0.5

-1 0 5-15 15-30 30-45 45-75 75-100 >100 -1 Rain Range (mm day )

Figure 5.4 Relative bias as a function of gauge rainfall. The error bars indicate the 95

% confidence interval.

Categorical Statistics

1.4 POD FBI 1.2 FAR ETS 1

0.8

0.6 CategoricalStatistics 0.4

0.2

0 0 5 15 30 45 75 100 -1 Rain Threshold: (mm day )

Figure 5.5 Categorical statistics: POD; FAR; FBI and ETS at rainfall thresholds 5, 15,

30, 45, 75 and 100 mm day-1.The error bars indicate the 95 % confidence

interval.

It is known that TMPA has varying skill with terrain, where the skill decreases with increasing elevation (Chen et al., 2013b). Hence, we examine the data for the same behaviour over Fiji. To facilitate this, we compute the average TMPA and gauge rainfall and the relative bias at each station and these are shown in Figure 5.6. While there is only one gauge station at higher elevation (800 m at Monasavu) it nonetheless shows that TMPA has less skill at higher elevation. The TMPA average (20 mm day-1) at the higher elevation is significantly smaller than the observation (55 mm day-1) with a relative bias of -0.55 (55 %), the largest underestimation in comparison to other, lower elevation stations. The observed rainfall at

Monasavu is also the largest which could be associated with orographic enhancements.

(a) Gauge Average (b) TRMM Average

70 70 )

) 60 60

-1 -1 50 50 40 40 30 30

20 20 MeanRainday (mm MeanRainday (mm 10 10 0 0 0 200 400 600 800 1000 0 200 400 600 800 1000 Height (m) Height (m) (c) Relative Bias 1

0.5

RelativeBias -0.5

-1 0 200 400 600 800 1000 Height (m)

Figure 5.6 Average TC rainfall of gauge observations (a), TMPA estimates (b) and the

relative bias (c) at station sites which have at least 10 samples.

Given that most of the heavy rainfalls occur closer to the TC centre, we therefore examine the skill of TMPA with respect to the distance from the TC centre. Samples are grouped into distances < 200 km and > 200 km. This criteria follows studies such as Lonfat et al. (2004) who note that TC regions < 200 km on average could be considered as eye-wall and inner rainfall regions and regions > 200 km as outer rainfall regions. The size and structure of an individual TC would vary however (Kimball and Mulekar, 2004). For the 15

TCs considered here, heavy rainfall does occur closer to the TC centre as we note that the average rainfall for the < 200 km group is 53.2 mm day-1 whereas for the > 200 km group it is

14.7 mm day-1. Figure 5.7 shows the POD, FAR and the ETS statistics. It is evident that

TMPA has more skill near the TC centre (< 200 km). The POD (FAR) of the < 200 km group is larger (smaller) than that of the > 200 km at all rainfall rates and the ETS of the < 200 km group is larger than that of the > 200 km group especially at larger rainfall rates.

(a) POD (b) FAR 1 1 <200 km 0.8 0.8 >200 km

0.6 0.6 FAR POD 0.4 0.4

0.2 0.2

0 0 0 5 15 30 45 75 100 0 5 15 30 45 75 100 Rain Threshold: (mm day-1) Rain Threshold: (mm day-1) (c) ETS 0.6 0.5 0.4

0.3 ETS 0.2 0.1

0 0 5 15 30 45 75 100 Rain Threshold: (mm day-1)

Figure 5.7 Categorical statistics (a) POD; (b) FAR and (c) ETS for rain within 200 km

of the TC centre and greater than 200 km from the TC centre. The error bars

indicate the 95 % confidence interval.

5.3.1 Case Studies

Figure 5.8a shows the average TMPA and gauge rainfall and the relative bias of individual TCs. The average gauge rainfall of the individual TCs does not differ much as

most of them (13 out of 15) have values between 20 and 30 mm day-1. Comparing the gauge with TMPA, it is shown that the TMPA average is mostly larger (smaller) than the gauge average for TCs with relatively smaller (larger) gauge average. Correspondingly, for TCs with a smaller average rainfall (TC 1 – 8) we get a relative bias that is mostly larger than zero

(an overestimation by TMPA) and a relative bias of mostly less than zero (an underestimation by TMPA) for TCs with a larger average rainfall (TC 9 and above). Yet the confidence intervals for the satellite and gauge values overlap in each case, which suggests that the

TMPA values are reasonable estimates of the observed rainfall. The correlation (Figure 5.8b) is highly variable except that it is weakest for TC 1 which has the lowest average rainfall.

Note that the samples of individual TCs (the size of which is shown in Figure 5.8b) will not be completely independent with each other that is, for each TC day, the errors in the satellite estimates will not be independent of each other.

(a) Average rain rate and relative bias of individual TC 100 Gauge TMPA relative bias

80 1 ), RMSE ), -1 60 0.5

40 0 relativebias

20 -0.5 Rainfallday (mm 0 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Individual TC

(b) Correlation coefficient and number of samples 1 r number of samples 80 0.8 70 60

r 0.6 50 40

0.4 numberof samples 30

0.2 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Individual TC

Figure 5.8 Mean gauge rainfall, the corresponding mean TMPA estimates and the

relative bias of the 15 TCs that have at least 10 observations and whose

spatial correlation coefficient (r) between the TMPA estimates and gauge

observations are statistically significant at 95% confidence level. The TCs

are arranged in the order of ascending average gauge rainfall. The TCs used

as case studies (Figure 5.9) to demonstrate the ability of TMPA are shown

in the brackets (name and year). The error bars indicate the 95% confidence

interval. b) The spatial correlation coefficient (r) and number of samples

(spatial data points) of the individual TCs.

Figure 5.9 shows the spatial distribution of the 24-hour TMPA and gauge rainfall for

TC Cliff (2007), Gene (2008) and Tomas (2010). These are land-falling TCs or TCs that have

tracks close to mainland Fiji. It is evident that TMPA is able to show the overall distribution

of the observed rainfall, yet it tends to underestimate the magnitude of the heavy rainfall

events.

(a) TC Cliff - Gauge (c) TC Gene - Gauge (e) TC Tomas - Gauge

250 160 300 200 120 200 150 80 100 100 40 50 0 0 0 (b) TC Cliff - TMPA (d) TC Gene - TMPA (f) TC Tomas - TMPA -15 250 -16 160 ) 300 -1 200 -17 120 -18 200 150 80 Latitude -19 100 100

-20 40 50 Rainfall(mmday -21 0 0 0 176 177 178 179 180 181 182 Longitude

Figure 5.9 24 hour accumulated gauge and TMPA estimate rainfall of TC Cliff (a and b

respectively), Gene (c and d respectively) and Tomas (e and f respectively).

The black dashed lines show the track of the TCs.

5.4 Discussion and Summary

The above set of results show that TMPA has skill in representing the 24 hour observed

rainfall during the passage of TCs over Fiji. Yet a correlation (r) of only 0.6 shows that the

linear association between the TMPA estimates and the observations is weak. Also the

average deviation between the TMPA estimates and the observations is large (RMSE = 38.7

mm day-1). Moreover, during moderate to extreme rainfall events, which are of greatest

concern during the passage of TCs, there is a significant underestimation by TMPA. The

reasons for the fairly weak association of TMPA with the observations could include the

retrieval error of the satellite algorithm, the sampling error related to generating daily values from satellite "snapshots", small sample size (due to a small number of gauges) and gauge under-catch.

Comparing the ability of TMPA over different regions, the r obtained here is smaller than that over Australia (r greater than 0.72; Chen et al. (2013b)) but it is comparable with that over China (r = 0.62 to 0.66; Yu et al. (2009)), the Pacific coastal and inland sites (r =

0.55; Chen et al. (2013c)) and New Caledonia (r = 0.66; Deo et al. (2016). Considering the heavier rainfall events (usually greater than 75 mm day-1 and which are of greatest concern during TCs), the ETS we report here approaches zero which is comparable with that over the

Pacific coastal and inland sites (Chen et al., 2013c) and that reported over mainland China

(Yu et al., 2009). The ETS for the same rainfall events over Australia (Chen et al., 2013b) and

New Caledonia (Deo et al., 2016) however is greater than zero.

Considering the effects of terrain and the structure of the TC, TMPA is less skilful at higher elevations and at distances further from the TC centre. The decrease in the skill of

TMPA with elevation is also reported by other studies (Chen et al., 2013a; Chen et al., 2013c, b) and this has been attributed to the inability of TMPA to capture short-lived orographically enhanced rainfall. In particular, the resolution of TMPA (3 hourly and 0.25° × 0.25°) might not be enough to resolve the rapidly evolving small scale orographic enhancements over the small scale mountainous terrain in Fiji. Similarly, previous studies (Chen et al., 2013b) also show better skill of TMPA closer to the centre of TCs. This could be attributed to the more organised convection and greater concentration of liquid and frozen hydrometeors in the vicinity of the eye-wall (usually the region of the extreme rainfall) than in the outer rainbands, leading to a relatively stronger scattering of MW signal which is then better correlated with surface rainfall.

The implication of this study is that it provides users of TMPA with information over

Fiji on the accuracy and limitation of this product, for use in NWP model evaluation, for example. Moreover, TMPA could be used to create a blended gauge-satellite gridded rainfall product for Fiji that will exploit the strengths and mitigate the limitations of each product.

Methods for such blending have been discussed by some studies such as Mitra et al. (2009),

Vila et al. (2009), Li and Shao (2010) and Renzullo et al. (2011).

TRMM was retired from operations and the Global Precipitation Measurement (GPM) mission Integrated Multi-satellite Retrievals for GPM (IMERG) provides the next-generation global rainfall estimates (Hou et al., 2014). The satellite constellation and blending algorithm in the GPM are not very different from what was used in TMPA (Hou et al., 2014), hence the estimates from TMPA and IMERG over Fiji may be comparable, as shown by some studies over other regions: for example, (Tang et al. (2016)) over southeast China (this study is not related to TCs though). A more confident answer, however, would require an evaluation of

IMERG during the passage of tropical cyclones over Fiji in the near future.

Disclaimer

The findings made and views expressed in this paper are not necessarily those of the

Fiji Meteorological Service.

Acknowledgements

The authors thank the Australian Research Council Centre of Excellence for Climate

System Science and their respective institutions for supporting this work. The authors also thank the Fiji Meteorological Service for providing the rain gauge data and Mr. Bipen

Prakash of Fiji Meteorological Service for his positive comments on the paper. Anil Deo also acknowledges the Australian government–sponsored Endeavour Postgraduate Award for funding his doctorate degree at the University of Melbourne.

Appendix B

E  EO  O Correlation coefficient r   (B.1) 2 2 E  E O  O

E  O Relative Bias = (B.2) O

n 1 2 RMSE = Ei  Oi  (B.3) n i1

RMSE Relative RMSE = (B.4) O where E = TMPA estimate; O = gauge observation and n = number of samples

hits POD  (B.5) hits  misses

falsealarms FAR  (B.6) hits  falsealarms

hits  falsealarms FBI  (B.7) hits  misses

hits  hits ETS  random (B.8) hits  misses  falsealarms  hitsrandom

hits  misseshits  falsealarms where hits  (B.9) random hits  misses  falsealarms  correct negatives

Having examined the skill of the TMPA precipitation estimates over some of the

Pacific Island Countries, we next present the evaluation of the DSD during the passage of

TCs over Darwin, Australia, and explore some of its implications for remote sensing and cloud-modelling parameterisations. The manuscript accepted for publication is presented.

6 Contrasting Tropical Cyclone and non-Tropical Cyclone related Rainfall Drop Size Distribution at Darwin, Australia Anil Deo1, Kevin J. E. Walsh1

Anil Deo, School of Earth Sciences, University of Melbourne, Victoria, 3010, Australia

([email protected], Ph: +61 (0)3 8344 7675, Fax: +61 (0)3 8344 7761)

Kevin J. E. Walsh, School of Earth Sciences, University of Melbourne, Victoria 3010, Australia

1School of Earth Sciences, University of Melbourne, Victoria, 3010, Australia

Abstract

In this study the rainfall drop size distribution (DSD) during the passage of seven tropical cyclones (TCs) over Darwin is compared and contrasted with that associated with non-tropical cyclone (non-TC) events, using the impact disdrometer data at the Darwin

Atmospheric Radiation and Measurement (ARM) site. The disparity of the DSD with respect to rainfall types (between TC and non-TC conditions) and distance from TC centre is also examined. It is shown that TC DSDs are statistically different from the non-TC DSDs, the former encompassing a larger concentration of small to moderate drop sizes. The TC mass- weighted mean diameter (Dm) is lower than the non-TC values at all rain rates and also for the different precipitation types (convective, transition and stratiform). The TC DSD varies with distance from the TC centre, as rainfall near the TC centre (< 60 km) comprises of relatively smaller drops which are strongly evident at small to moderate rain rates (< 30 mm hr-1). Such variations in the DSD have implications for the parameters used in the algorithm that converts radar reflectivity to rainfall rate in TCs, as well as for the analytical expressions used in describing the observed DSD employed in cloud modelling parameterizations.

Keywords

Disdrometer, Cloud microphysics, Mass-weighted mean diameter, Drop concentration

6.1 Introduction

The rainfall drop size distribution (DSD) plays an important role in radar rainfall estimation and cloud-modelling studies (Tokay and Short, 1996; Radhakrishna and Rao,

2010; Handwerker and Straub, 2011; Tang et al., 2014). The pre-factor A and exponent b of the widely used radar reflectivity (Z) to rainfall rate (R) (Z-R) algorithm (Z=ARb) are strongly dependant on the DSD. In cloud-modelling studies, knowledge of the DSD is important for understanding rainfall growth mechanisms through different microphysical processes (such as evaporation, collision and coalescence) and for parameterization of these processes. As such, knowledge of the rainfall DSD is essential for accurate representation of rainfall especially by (i) platforms employing radar remote sensing, for example satellite platforms

(e.g. the GPM; Hou et al. (2014)) and ground-based weather stations, and (ii) numerical weather prediction models (NWP) (Niu et al., 2010; Gatlin et al., 2015).

The challenge, however, is that there is no unique DSD for different rainfall regimes.

Several studies have shown that the rainfall DSD has spatial-temporal variation not only within a storm system but also from storm to storm and over different climatic regimes

(Tokay and Short, 1996; Tokay et al., 1999; Bringi et al., 2003; Rosenfeld and Ulbrich, 2003;

Ulbrich and Atlas, 2007; Radhakrishna et al., 2009; Niu et al., 2010; Konwar et al., 2014;

Thurai et al., 2016). Such variability in the DSD corresponds to variation in the radar rainfall algorithm and cloud modelling parameterization and, therefore, it becomes important to investigate the DSD characteristics of different rainfall regimes and over different regions.

Synoptic scale systems such as tropical cyclones (TCs) are associated with copious amounts of rainfall which often causes devastating effects such as widespread flooding, landslide and fatalities (Rappaport, 2000; Dare et al., 2012; Dare, 2013). Rainfall information during such events which aids in disaster mitigation and risk analysis is mainly derived from radar platforms (space-borne and ground-based) and NWP model forecasts. A better

understanding of the TC-related DSD is thus one of the aspects for improvement in rainfall representations from these platforms. TC-related rainfall DSD has been examined by some studies (Merceret, 1974; Wilson and Pollock, 1974; Jorgensen and Willis, 1982; Willis, 1984;

Ulbrich and Lee, 2002; Maeso et al., 2005; Tokay et al., 2008; Chang et al., 2009;

Radhakrishna and Rao, 2010; Bhattacharya et al., 2013) using aircraft (airborne foil impactors and probes) and ground-based disdrometer measurements. An excellent review of the early studies is presented by Tokay et al. (2008). Most of these studies show an abundance of small to medium-sized drops with fewer large drops in TCs. A recent study by

Radhakrishna and Rao (2010), on the difference in DSD between TC and non-TC events during the southwest and northeast monsoon season at Gadanki (India), shows that the TC

DSD differs statistically from the non-TC DSD and that the TC DSD also varies seasonally and over different regions. A variation in the radar rainfall estimation and the gamma distribution parameters between TC and non-TC environments has been established by

Radhakrishna and Rao (2010).

The above studies have advanced our understanding of TC DSDs, especially over the

Chen et al., 2013b; Dare, 2013). TCs are known to contribute significantly to the total climatological rainfall over the Australian region, as high as 50 % over some areas (Jiang and

Zipser, 2010; Dare et al., 2012; Dare, 2013). Accurate representation of rainfall is important for this region as it has direct implications for disaster mitigation, agriculture and energy

(Dare et al., 2012). Moreover, rain gauge data are sparse over a significant portion of

Australia (Jones et al., 2009), especially the northern and western regions which are prone to

TCs (Dare and Davidson, 2004). In these regions, remote sensing data become even more important.

This study thus examines the TC DSDs using the Atmospheric Radiation and

Measurement (ARM) disdrometer data at the Darwin (Australia) site. It seeks to establish if there is any difference between TC and non-TC related DSD over this region and also under different types of precipitating systems (e.g. convective and stratiform) during the Australian summer monsoon season. Differences in the TC DSD with distance from the TC centre are also investigated. We pose the following question: if there is a difference, then how does it relate to the radar rainfall estimation parameters and the analytical expression (the gamma function) used to represent the observed DSD? The following section (section 2) describes the data and methodology, followed by results and discussion in section 3 and finally the summary in section 4.

6.2 Data and Methodology

The primary instrument we use for this study is the impact type Joss-Waldvogel disdrometer (JWD) (Joss and Waldvogel, 1969) model RD-80 located at the ARM research facility, Darwin (130.90E, 12.43S), Australia. The JWD uses a piezoelectric mechanism where the impact of a raindrop on a Styrofoam cone is converted to an electric pulse proportional to the size of the raindrop. The JWD sorts the drops into 20 diameter classes (or bins) in the range 0.3 to 5.5 mm every 1 minute. The bins have varying diameter intervals ranging from 0.1 to 0.5 mm. The JWD is a reliable standalone instrument but as with any other measurement instrument, it suffers from some limitations and the reader is referred to

Tokay et al. (2001) and Tokay et al. (2002) for a detailed description. Briefly, the major limitations include its inability to resolve larger drops (e.g. greater than 5.5 mm, where they are assigned to the largest bin size) and its underestimation of small drops during intense rainfall due to the ringing of the cone upon the impact of the drops (which is known as

100

disdrometer recovery dead time) and an increase in the background acoustic noise during such intense events (the small drops cannot be distinguished from the noise). Nonetheless, the

JWD is widely used for DSD studies (Kozu and Nakamura, 1991; Tokay and Short, 1996;

Tokay et al., 2001; Ulbrich and Atlas, 2007; Radhakrishna and Narayana Rao, 2009;

Radhakrishna and Rao, 2010; Giangrande et al., 2014).

The integral rainfall parameters of drop concentration (N(D)), rain rate (R), reflectivity (Z) and the mass-weighted mean diameter (Dm) are computed using the standard formulae (Sharma et al., 2009) as follows:

ni -3 -1 NDi   (m mm ) (6.1) F.t.vDi Di

 3.6 1 20 R  n D3 (mm hr-1) (6.2) 6 103 Ft i1 i i

6 -3 (mm m ) (6.3)

20 N D D4D i1  i  i i Dm  20 (mm) (6.4) N D D3D i1  i  i i where ni is the number of drops measured in drop size class i, F is the Styrofoam cone area

-2 (50 cm ), t is the sampling time (60 s), Di is the average diameter (mm) of the drops in class

-1 i, ΔDi is the diameter (mm) interval of drop class i and v(Di) is the fall velocity (m s ) (Gunn and Kinzer, 1949) of a drop with diameter Di.

The study period spans 2006 – 2013 and a total of 7 TCs passed within 500 km of the

Darwin site (tracks shown in Figure 6.1) during this period. The date and position of the TCs were obtained from the IBTrACS archive (Knapp et al., 2010) where the data has a temporal resolution of 6 hours. A 1-min rainfall spectrum is considered to be TC-related if a TC centre came within 500 km of the ARM site. This 500 km criterion is consistent with other studies such as Lonfat et al. (2004), Dare et al. (2012) and Chen et al. (2013b). Following Tokay and

101

Short (1996), Tokay et al. (2001) and Cao and Zhang (2009), spectra with R < 0.1 mm hr-1 are

considered to be within the noise level and therefore are eliminated for this study.

Cyclone tracks over Darwin

-8 Alessia George -12 Helen Carlos Laurence Latitude -16 Grant Twenty

-20 110 120 130 140 150 160 Longitude Figure 6.1 Tracks of the 7 TCs passing over Darwin (location is shown by a red dot)

for the period 2006 to 2013.

Given the limitations of the JWD instrument, a comparison is made between the

accumulated JWD and the rain gauge TC rainfall to evaluate the quality of the data. A

Novalynx tipping-bucket rain gauge (model 260-2500E-12) that has a sampling resolution

period of 1-min is collocated with the JWD at the ARM site. Note that tipping bucket rain

gauges are known to also have errors and the reader is referred to studies of Chen and

Chandrasekar (2015), Habib et al. (2008) and Wang et al. (2008) for an understanding of their

accuracy and limitations. Table 6.1 shows the dates of the TCs and the JWD and tipping

bucket (TB) accumulated rainfall (AR) for rainfall rates greater than 0.1 mm hr-1. Except for

TC George (2007) and Carlos (2011), there is a good correspondence between the two sets of

AR. Differences for TC George and Carlos were still less than 10 %. In addition, during the

passage of TC George, the rain gauge had 19 minutes of missing records which explains the

discrepancy during this TC. This comparison validates the disdrometer data used for the

study.

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Table 6.1 Disdrometer and rain gauge accumulated rainfall (AR) of the seven TCs.

Cyclone Dates (UTC) Disdrometer AR (mm) Tipping bucket AR (mm) George 02 – 04/03/2007 397.54 367.00 Helen 29/12/2007 109.50 103.20 Laurence 11– 13/12/2009 323.40 315.60 Carlos 14 – 18/02/2011 729.00 777.41 Twenty 27 – 31/03/2011 104.98 111.00 Grant 23/12/2011 43.35 45.00 Alessia 23 – 24/11/2013 72.21 69.60 Total = 1780.00 Total = 1788.81

We employ here the widely used gamma function (Ulbrich, 1983; Kozu and

Nakamura, 1991; Tokay and Short, 1996) as the analytical expression to describe the observed DSD:

 ND  No D exp D (6.5)

-1 -3 -1 where No (mm m ), μ (dimensionless) and Λ (mm ) are respectively the intercept, shape and slope parameters. These gamma DSD parameters could be effectively used to study the natural variations in the characteristics of precipitation (Konwar et al. (2014) and the references therein). The μ parameter describes the breadth and the shape of the DSD where less (greater) than 1 denotes concave upward (downward) shape and zero denotes an exponential shape (Ulbrich, 1983). The Λ parameter describes the truncation of the DSD tail along D i.e. a larger (smaller) Λ truncates the DSD towards smaller (larger) D. The No parameter is the drop concentration (N(D)) when D approaches its minimum value.

The gamma DSD parameters are computed using a moments-based method that utilises three moments of the gamma DSD function (Tokay and Short, 1996; Smith, 2003). One of the issues with this moments method is that bias could be introduced in the estimated parameters (Smith and Kliche, 2005) and thus spectra with a sufficient number of drops are recommended. To minimise this issue of small sample size, an extra criteria of eliminating spectra with less than 10 drops is implemented, consistent with other studies (Tokay and

103

Short, 1996; Tokay et al., 2001; Tokay et al., 2002; Cao and Zhang, 2009; Radhakrishna and

Narayana Rao, 2009; Niu et al., 2010; Lam et al., 2015). Considering a sample size of > 10 drops together with rainfall rate > 0.1 mm hr-1 and the TC rainfall distance criteria of < 500 km, a total of 33,211 1-min spectra, constituting of 14,164 TC related and 19,047 non-TC related spectra, are used.

Different combinations of moments have been suggested, e.g. 3rd, 4th, and 6th (Kozu and

Nakamura, 1991; Tokay and Short, 1996), 2nd, 3rd and 4th (Smith, 2003; Cao and Zhang,

2009) and 2nd, 4th and 6th (Ulbrich and Atlas, 1998) (referred to as M346, M234 and M246 respectively) to estimate the gamma parameters. Smith (2003) and Cao and Zhang (2009) suggested using middle order moments, e.g. M234, as they showed that these are associated with a lower least square error. We, therefore, utilise M234 to estimate the TC and non-TC gamma parameters. Smith (2003) and Cao and Zhang (2009) utilise non-TC DSDs; hence to further justify the use of M234 we compute the root mean square error (RMSE) between the observed and estimated drop concentration for both TC and non-TC events, using each moment combination (the formulae are given in Appendix A), which demonstrates that M234 has a lower error (Table 6.2). Interestingly, the error in estimating the TC DSDs is larger than for the non-TCs for the different moment combinations. The RMSE is also stratified with respect to rainfall rate (rainfall classes shown in Table 6.3) and is shown in Figure 6.2. A notable difference between the TC and non-TC related error is evident especially for rainfall rates < 20 mm hr-1 (class 7) where the RMSE related to the latter is lower than the former.

Nonetheless, of the combination of moments used, both the TC and non-TC events show the smallest RMSE for M234 at almost all rainfall rates.

To ascertain the statistical significance of some of the results, the two-sample

Kolmogorov-Smirnov (2KS) test (Press et al., 2007) at the 95 % confidence level is utilised.

The 2KS test tests the null hypothesis that two samples are from the same population. The

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uncertainty (error) on some of the statistics is also evaluated at the 95 % confidence interval

calculated using a bootstrapping technique (Efron and Tibshirani, 1993) which involves re-

sampling of the data. Some 10,000 random re-samples, with replacement, are constructed on

which the bootstrapping is applied. The 50th percentile (median) is presented as the statistic

and the 2.5 and 97.5 percentile as the 95 % confidence interval.

Table 6.2 RMSE between the observed and estimated drop concentration using

moments M234, M246 and M346.

RMSE (mm-3m-1) M234 M246 M346 TC 197.13 225.90 246.4 Non-TC 116.17 137.2 155.65

RMSE 350 TC M346 300 TC M234 TC M246 250 non-TC M346 non-TC M234 200 non-TC M246

RMSE 150

100

0 1 2 3 4 5 6 7 8 9 10

Rainfall classes (mm h-1)

Figure 6.2 Root mean square error (RMSE) in the drop concentration, N(D), between

observed and the gamma fitted distributions using moments two, three and

four (M234); two, four and six (M246) and three, four and six (M346) of

the TC and non-TC drop spectra.

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Table 6.3 Rainfall rate classes or categories.

Class Rainfall rates (mm hr-1) 1 0.1 – 0.3 2 0.3 – 0.5 3 0.5 – 1 4 1 – 3 5 3 – 5 6 5 – 10 7 10 – 20 8 20 – 30 9 30 – 60 10 > 60

6.3 Results

6.3.1 Individual TCs

The time series of the drop concentration (N(D)), Dm, R, surface wind speed and distance from the TC centre to the site for the 7 TCs are examined first. As an illustration,

Figure 6.3 shows the time series for TC Carlos (Figure 6.3a) and George (Figure 6.3b) which have the highest accumulated rainfall amount (AR – see Table 6.1). The 1-min surface wind speed data were obtained from the ARM surface observation instrument and the IBTrACS 6- hourly time and position were linearly interpolated to obtain the 1-min resolution data. Some notable observations are as follows. The N(D) is larger closer to the TC centre. The Dm is mostly below 3 mm (with a large frequency of 1 – 2 mm); nonetheless, there are some cases of > 3 mm, for example during TC Laurence and TC Alessia (figure not shown). The Dm, however, is observed to be strongly dependent on the rain rate R, with generally higher values for higher R (see Figure 6.4k).

When stratified with respect to rainfall rate or reflectivity, the DSDs should appear similar (Radhakrishna and Rao (2010) and the references therein). Hence for an explicit comparison, we stratified the DSD of each TC into 10 rainfall rate categories (the rainfall categories are listed in Table 6.3). The average N(D) for each rainfall rate category was computed and is shown in Figure 6.4 (a‒j). Smaller rain rates (especially rain rates < 1 mm

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hr-1) are dominated by smaller drops (fewer moderate drops) whereas moderate and larger rainfall rates generally have a combination of small and moderate size drops. There is a systematic gain of drop concentration by moderate diameter classes with an increase in rainfall rate. The magnitude of the peaks, however, varies for each rainfall group where the higher rain rates tend to have a larger drop concentration. As evident, the peaks at lower rain rates (< 1 mm hr-1) are lower (below 400 m-3mm-1 for the majority of the TCs) whereas for rain rates > 1 mm hr-1 the peaks are around 400 m-3mm-1 and above. The peaks systematically shift slightly towards the moderate diameter classes with increasing R. An interesting observation is that the distribution systematically shifts from mono-modal (single peak) to bimodal (two peaks) with an increase in rain rate. This bi-modal nature is dominant for rainfall rates 3 – 60 mm hr-1.

The average DSD varies among the TCs and with rain rate. Examining TCs with higher rainfall contributions, TC Carlos (black solid line), with the highest accumulated rainfall amount (AR) of 777 mm (Table 6.1), has a higher drop concentration at low to moderate rain rates (< 20 mm hr-1) and a relatively lower drop concentration at higher rain rates (> 20 mm hr-1). TC George (red solid line) with second highest AR (367 mm) encompasses mostly moderate drop concentration at all rain rates. TC Laurence, with third highest AR (315 mm), has almost the lowest drop concentration at all rain rates.

The corresponding average drop diameter (Dm) with respect to rain rates R is shown in

Figure 6.4k. The Dm is lower at lower rain rates and increases systematically with an increase in R for all TCs. There is no statistical difference between the Dm of most TCs for the majority of the rainfall rates (except for TC Alessia and to some extent TC Laurence). The

Dm of TCs is also compared with the non-TCs (solid blue line) which show that except for

TC Alessia and to some extent TC Laurence, the other five TCs have statistically lower Dm

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values than the non-TC values. This result points towards a difference between TC and non-

TC DSD which is discussed in detail in the subsequent section.

(a) TC Carlos, 14-15/02/2011

) 5.37 -1 (i)

3.54 mm 1e+03 -3 2 2.26 1e+02 1.33 Dm (mm) Dm 1e+01

Diameter(mm) 0.66

0.36 0 1e+00 Concentration(m

) -1

200

) 16 (ii) -1 12 8 100

4 WindSpeed (ms 0 0 00 04 08 12 16 20 00 04 08 12 16 20 00

Time (UTC) Distance(m)Rain Ratehr (mm

(b) TC George,02-03/03/2007

) 5.37 -1 (i) Dm 3.54 1e+03 mm 2 -3 2.26 1e+02 1.33 Dm (mm) Dm 1e+01

Diameter(mm) 0.66

0.36 0 1e+00 Concentration(m

) -1

) 16 (ii) Wind speed -1 300 TC distance 12 (b) Rain rate 200 8

(i) 4 100 WindSpeed (ms 0 0 00 04 08 12 16 20 00 04 08 12 16 20 00

Time (UTC) Distance(m)Rain Ratehr (mm

Figure 6.3 Time series (UTC) of drop concentration (N(D) ‒ coloured plot), Dm (black

line with N(D)), distance from TC centre (solid red line), wind speed (solid

108

blue line) and rainfall rate (black line with distance and wind speed plot) of

TC Carlos (a) and George (b). The colour bar denotes the drop concentration of the respective TC and the secondary y-axis shows the magnitudes of Dm, distance and rainfall rate.

109

1200 1200

(a) 0.1-0.3 (b) 0.3-0.5

) ) -1

-1 800 800

mm mm

-3 -3

400 400

N(D)(m N(D)(m

1 2 3 4 5 1 2 3 4 5 Diameter (mm) Diameter (mm) 1200 1200

) ) -1

-1 800 800

mm mm

-3 -3

400 400

N(D)(m N(D)(m

1 2 3 4 5 1 2 3 4 5 Diameter (mm) Diameter (mm) 1200 1200 (e) 3.0-5.0 (f) 5.0-10.0

) ) -1

-1 800 800

mm mm -3 -3

400 400 N(D)(m N(D)(m

1 2 3 4 5 1 2 3 4 5 Diameter (mm) Diameter (mm) 1200 1200

(g) 10.0-20.0 (h) 20.0-30.0

) ) -1

-1 800 800

mm mm

-3 -3

400 400

N(D)(m N(D)(m

1 2 3 4 5 1 2 3 4 5 Diameter (mm) Diameter (mm)

110

1200 1200 George

(i) 30.0-60.0 (j) >60 Helen

)

) -1 -1 Laurence 800 800

Carlos

mm -3 -3 Twenty Grant 400 400

Alessia

N(D)(m N(D)(m

1 2 3 4 5 1 2 3 4 5 Diameter (mm) Diameter (mm) (k) Dm of Individual TC

2.4

2 George Helen Laurence (mm) 1.6

m Carlos D Twenty 1.2 Grant Alessia non TC 0.8 1 2 3 4 5 6 7 8 9 10 Rainfall classes

Figure 6.4 Average drop concentration (N(D)) of individual TCs with respect to

rainfall rates (a) 0.1 – 0.3, (b) 0.3 – 0.5, (c) 0.5 – 1, (d) 1 – 3, (e) 3 – 5, (f) 5

– 10, (g) 10 – 20, (h) 20 – 30, (i) 30 – 60 and (j) > 60 mm hr-1 for the 20

diameter classes. (k) Average Dm of non-TC and individual TC DSD spectra

with respect to the 10 rainfall classes. The error bars are the 95 %

confidence interval.

6.3.2 Contrasting TC and non-TC DSD

The TC DSDs are combined to ascertain how their average compares with the non-TC

DSD. Figure 6.5, a plot of average TC and non-TC DSD, shows that the TC DSDs are

statistically different from the non-TC DSDs, with TCs demonstrating a higher drop

concentration at lower diameter classes (< 2.6 mm) and the non-TCs demonstrating a higher

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concentration than the TCs for diameters > 2.6 mm. This implies that TCs have a larger concentration of small to medium size drops in comparison to non-TCs, as also reported by

Radhakrishna and Rao (2010) over India.

(a) Average DSD 4 10 TC nTC 2

) -1

mm 0

-3 10 N(D) (mN(D) -2 10

-4 10 1 2 3 4 5 6 Diameter (mm)

Figure 6.5 Average drop concentration of the TC and the non-TC rainfall DSD spectra

with respect to the 20 diameter classes. The error bars are the 95 %

confidence interval.

How do the TC and non-TC DSD compare with respect to the rain rates? First we compare the relative frequencies of the rain rates of the TC and non-TC 1-min DSDs as shown in Figure 6.6a. The two distributions are found to be statistically different (using the

KS test). Non-TCs tend to have a higher frequency at lower rain rate (< 2 mm hr-1) whereas

TCs have a higher frequency for low to moderate rain rates (2 – 40 mm hr-1). Above 40 mm hr-1, a significant difference is absent. This could be related to the small sample size at higher rain rates that then gives a noisier data set, thus removing the signal. This result, as anticipated, demonstrates that TCs typically have larger rain rates than non-TCs.

Second, we compare the DSDs with respect to the rain rates. To accomplish this, drop concentrations of each diameter class are grouped into the 10 rainfall classes (classes listed in

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Table 6.3) and for each rainfall and diameter class the average TC and non-TC DSD and the ratio (TC/non-TC), to compare the latter two averages, are computed and are shown in Figure

6.6 (b‒d). Results show that there is a systematic shift in the maximum drop concentration from lower diameter to higher diameter as rain rate increases (in both TC and non-TC events) as discussed in section 3.1. It is quite evident, in both the TC (Figure 6.6b) and non-TC

(Figure 6.6c) average DSD plots, that lower rain rates tend to have a larger drop concentration at smaller diameter classes, which shows that smaller drops dominate at smaller rain rates. As rain rate increases, the peak (or maximum) concentration shifts to moderate diameter classes, with small concentrations at smaller diameters especially at higher rain rates (> 20 mm hr-1). Overall, both the TC and the non-TC rainfall have maximum drop concentration around 1 – 30 mm hr-1. Comparing the two averages, Figure 6.6d shows that the ratio (TC/non-TC) at lower rain rates (< ~ 10 mm hr-1) is > 1 (as high as 2.6) at small diameters (< ~ 1 mm) whereas for rain rates > 10 mm hr-1 the > 1 ratio systematically shifts to moderate diameters (1 – 3 mm). The contour lines show regions where the ratio is > 1. The above results signify that at lower rain rates (< 10 mm hr-1) TCs have relatively more small drops (< 1 mm) whereas the non-TCs have more moderate to large drops (> 1 mm) and at higher rain rates (> 10 mm hr-1) TCs have more moderate drops (1 – 3 mm) with almost negligible concentration of large drops (> 3 mm), whereas the non-TCs have more large drops (> 3 mm).

To further verify the above results, the corresponding average drop diameter (Dm) at each rainfall class for the TC and non-TC rain is computed and is shown in Figure 6.7a. The

Dm of both TC and non-TC events are smaller at smaller rain rates and increases with an increase in the rainfall rate. However, a statistically significant difference in the magnitude of the Dm is observed with the TC Dm consistently lower than the non-TC values at all rainfall

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classes. This affirms that TCs comparatively have smaller drop sizes than the non-TCs at all rain rates.

(a) Normalised frequency of Rain Rate 0 10 TC -1 nTC 10

-2 10

-3

10 NormalisedFrequency -4 10 0 1 2 10 10 10 Rain Rate (mm hr-1) (b) Average DSD for different rain rates (TC)

)

-1 800

) -1

10 600 mm 1 400 -3

200 N(D)(m

Rainrate hr (mm 0.1 (c) Average DSD for different rain rates (nTC)

)

-1 800

) -1

10 600 mm 1 400 -3

200 N(D)(m

Rainrate hr (mm 0.1 (d) Ratio of TC and nTC DSD Vs Rain Rates

)

-1 1.2 1 1.2 1 3 1.2 1 10 1.5 2 1.2

2 Ratio 1 1.2 1 1 1

Rainrate hr (mm 0.1 1 2 3 4 5 Diameter (mm)

Figure 6.6 (a) Normalised frequency distribution of rain rates of TC and non-TC drop

spectra. Average DSD of (b) TC and (c) non-TC rainfall events. (d) TC

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versus non-TC ratio of average DSD with respect to rain rate and diameter

class.

(a) TC and nonTC average Dm with rain rate

2.5 TC nonTC 2

1.5 mean Dm (mm) mean Dm 1

0 0.1-0.3 0.3-0.5 0.5-1 1-3 3-5 5-10 10-20 20-30 30-60 >60 Rainfall rate (mm hr-1)

(b) Normalised frequency of Dm - Precipitation type

convec TC 0.12 convec nTC strati TC strati nTC transi TC 0.08 transi nTC

0.04 NormalisedFrequency

0 0 0.5 1 1.5 2 2.5 3 3.5 4 Dm (mm)

Figure 6.7 (a) Average Dm of TC and non-TC drop spectra for the 10 rainfall classes.

The error bars are the 95 % confidence interval. (b) Normalised frequency

distribution of Dm with respect to convective (black), transition (blue) and

stratiform (red) rainfall type of TC (solid lines) and non-TC (dashed lines)

drop spectra.

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DSDs are known to vary with precipitation types (Rosenfeld and Ulbrich, 2003), such as convective, transition and stratiform rainfall, hence we examine the TC and non-TC DSD for these variations. Following Rao et al. (2001), samples are grouped respectively into convective, stratiform or transition rainfall if the Dm/R ratio is less than 0.1, greater than 0.5 or in between the latter two thresholds. Figure 6.7b, a plot of the relative frequency of Dm for the different rainfall types, shows that the TC and non-TC DSDs differ for the three rainfall types. TCs have a relatively higher frequency of smaller Dm for the three rainfall types

(statistically significant at the 95 % level using the KS test).

The above set of results implies that there have to be some differences in the precipitation formation mechanism or the cloud microstructure between TCs and non-TCs which would lead to such differences in the DSD. It is well known that the precipitation formation is governed mostly by the cloud microphysical processes and that the latter is a function of the dynamics (the updraft/vertical wind motion (Rosenfeld and Ulbrich, 2003;

Houze, 2014b). Comparing TC and non-TC updrafts, the study by Heymsfield et al. (2010), on convective precipitation, shows a significantly weaker TC updraft than in non-TCs (both over the land and over the ocean) at low to mid altitudes (3 – 11 km). These altitudes are the crucial regions for the microphysical processes (Houze, 2014b). A stronger updraft could affect the drop sizes in two ways. The first is drop sorting, in which the small drops could be advected high up in the updrafts with the larger drops falling under the influence of gravity.

Second, the large updrafts could suspend the drops aloft, therefore increasing the time for the collision and coalescence process which would then increase the drop sizes. Above the 0°C isotherm, the suspension of drops (liquid or ice) by the updraft would also allow growth of particles through riming. These mechanisms thus could shift the non-TC DSD towards relatively larger drop diameters.

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In addition to stronger updrafts, relatively higher temperatures could also shift the DSD towards larger drops by evaporating the smaller drops. To investigate this, we compute the surface temperature and relative humidity distribution over Darwin for the TC and non-TC events (figure not shown). Non-TCs have a higher frequency of higher temperatures (TC and non-TC means of 23.4 and 24.5 °C respectively) and lower humidity (TC and non-TC means of 96 and 88 % respectively). Relatively larger temperatures and drier conditions during non-

TC events imply more evaporation of smaller drops.

6.3.3 TC distance stratification

The distribution of precipitation varies within a TC system, with heavy rainfall generally occurring in the vicinity of the eye-wall. We therefore investigate if there is any difference in the TC rainfall DSD with respect to the distance from the TC centre.

To examine the differences in the DSD with respect to the distance from the TC centre, samples are grouped into distance < 60 km, 60 – 200 km and > 200 km. These criteria distinguish TC regions, dividing the storm approximately into eye-wall, inner rainband and outer rain band (Lonfat et al., 2004; Yokoyama and Takayabu, 2008). Note that individual

TC structure would vary, however (see discussion at the end of the section). The average Dm of the distance groups with respect to the rainfall rate (Figure 6.8) shows that rainfall closer to the TC centre, in comparison with further from the TC centre, has relatively smaller drop diameters at low to moderate rain rates (this is statistically significant). It is apparent from

-1 Figure 6.8 that the Dm of the < 60 km group at rain rates < 30 mm hr is lower than the Dm of the other two groups. For the same rain rate range, the Dm differences of the 60 – 200 km and the > 200 km groups, however, are mixed whereby for rain rates < 1 mm hr-1 the two groups

-1 have almost the same Dm and for rain rates 1 – 30 mm hr the 60 – 200 km has slightly larger values. Above 30 mm hr-1 there is an absence of a statistically significant difference between the Dm of the three groups.

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While the above results point to a variation in the DSD with distance from the TC centre, it should be noted that these are based on a small sample of TCs (7 TCs). Moreover, the distance considered here is average values that distinguish eye-wall and outside eye-wall regions and that the actual TC size and structure would vary, with some TCs having much smaller eye-wall radii (e.g. Kimball and Mulekar (2004)). A more detailed analysis could consider the variation in the actual size of TCs but this is outside the scope of this study.

(d) TC Dm with distance from TC centre and rain rate 3 TC 2.5 <60 km 2 60-200 km >200 km 1.5

mean Dm (mm) mean Dm 1

0.5 0.1-0.3 0.3-0.5 0.5-1 1-3 3-5 5-10 10-20 20-30 30-60 >60 Rainfall rate (mm hr-1)

Figure 6.8 Mean Dm of TC and the three distance groups from TC centre (< 60 km, 60

– 200 km and > 200 km) with respect to the 10 rainfall classes. The error

bars are the 95 % confidence interval.

The actual reason for the difference between the DSD with distance, especially the presence of relatively smaller drops near the TC centre, is not clear at the moment. A possible factor could be the presence of a large quantity of small size liquid or ice particles aloft that subsequently fall as raindrops. The presence of a large quantity of small ice particles aloft near the TC centre has been reported by some studies, for example, the study by Houze et al.

(1992), who analysed the mesoscale distribution of ice particles in the inner core of hurricane

Norbert (1984). Using aircraft observations at an altitude of 6 km, they report the presence of a high concentration of small ice particles at the edge of the eye-wall region. The authors attribute the above observation as likely resulting from secondary ice particle production through the riming mechanism at ~0 to -5ºC by the process identified by Hallett and Mossop

118

(1974) (see Houze (2010) and the references therein). A large concentration of ice particles is produced by this process (Black and Hallett, 1986). Thus, the above process could partially explain the observation of smaller drops near the centre of TCs observed over Darwin.

Another possibility for this observation could be that smaller drops at distances further from the TC centre evaporate, thus shifting the DSD more towards relatively larger drops, especially at low to moderate rain rates where the smaller drops are in abundance. A humidity and temperature analysis (figure not shown) show that the relative humidity decreases with an increase in distance from the TC centre (a relatively lower mean at larger distances) and the temperature is somewhat higher at distances further from the TC centre. Thus, a relatively drier environment and a higher temperature could cause more evaporation of the smaller drops at larger distances, which shifts the DSD at low to moderate rain rates towards relatively larger drops.

6.3.4 Comparison of TC DSD between Darwin and other Regions

Radhakrishna and Rao (2010) have demonstrated the variation of TC DSD over different regions. Hence, we compare the TC DSD at Darwin with those over India

(Radhakrishna and Rao, 2010), the Atlantic (Tokay et al., 2008) and the western Pacific

(Chang et al., 2009). To facilitate this, we group together data having reflectivity between 39 to 41 dBZ (around 40 dBZ) following Tokay et al. (2008) and compute the average liquid water content (LWC), rain rate R and Dm. Table 6.4 shows the respective TC rainfall parameters (LWC, R and Dm) over Darwin and for the regions mentioned above. The parameter values over Darwin are somewhat similar to those over the Atlantic and during the north-east monsoon season (NEM) over the Bay of Bengal (BOB-India) but they are quite different from those over the western Pacific and during the south-west monsoon (SWM) season over the BOB. As evident, the LWC and the average rain rate at Darwin are higher and the Dm is lower than those over the western Pacific and during the SWM season over the

119

BOB. The difference in the rainfall parameters between the western Pacific and the Atlantic

(or for that matter over Darwin) could be correlated with terrain-influenced convective systems during the passage of TCs over western Pacific (Chang et al., 2009). Over the BOB, the microphysical processes related to stronger updrafts during the SWM have been attributed to the variation in the rainfall parameters compared to those occurring during the NEM. With the parameters over Darwin similar to those over NEM, these arguments could also hold to explain the difference between that over Darwin and SWM. As discussed previously, stronger updrafts shift the DSD towards relatively larger Dm.

Table 6.4 Liquid water content (LWC), rain rate (R) and Dm around reflectivity 40

dBZ (39 – 41) of TCs over Darwin compared with that over the western

Pacific; Atlantic; and Bay of Bengal (BOB - India) during the southwest

and northeast monsoon (SWM and NEM) seasons.

-3 -1 Region LWC (gm ) R (mm hr ) Dm (mm)

Darwin 0.80 16.65 1.75

Western Pacific - 12.1 1.88 (Chang et al., 2009) Atlantic 0.90 18.5 1.67 (Tokay et al., 2008) SWM BOB ~ 0.64 ~ 13.7 ~ 1.89 (Radhakrishna and Rao, 2010) NEM BOB ~ 0.82 ~ 17 ~ 1.72 (Radhakrishna and Rao, 2010)

6.3.5 Radar Z-R Parameters

A difference in the DSD between TC and non-TC related rainfall events implies that the parameter A and b of the radar rainfall estimation algorithm Z=ARb will also differ.

Hence, we examine the degree of variation in the radar rainfall estimation parameters between TC and non-TC related events and also with respect to the different precipitation types and distance from the TC centre. A simple linear regression between the Z and the R is

120

used to compute the values of the coefficients. The coefficient A indicates the size of the drops (larger A for larger drops) and the power b indicates the microphysical processes. A larger b (greater than 1) signifies size or mixed controlled case, namely collision and coalescence, whereas b ~ 1 signifies number controlled case (collision, coalescence and breakup) that produces equilibrium DSD (Atlas et al., 1999; Rosenfeld and Ulbrich, 2003;

Sharma et al., 2009). Figure 6.9 shows the A and b parameters of TC and non-TC related rainfall events and for the different conditions (rainfall types and distance from the TC centre). Non-TCs have larger A than TCs, with values of 310 and 234 respectively (Figure

6.9a), but there is no difference in the b values (Figure 6.9b). Under different rainfall types, a statistically significant difference exists between the TC and non-TC A parameter for the convective and stratiform types (Figure 6.9a; non-TC values are larger) and the b parameter for the transition type (Figure 6.9b; non-TC value is larger). A larger coefficient A implies larger drops during non-TC events, consistent with our previous results. A relatively larger b during non-TC events (particularly for the transition type) implies that rainfall processes during those events are governed by more size-controlled processes.

The TC Z-R relation reported here differs from that obtained in other regions. For a comparison, we present some of these relations in Table 6.5 (these are without separation into convective, stratiform and transition types). The coefficient A of TCs over Darwin (234) is comparatively lower than that over the Atlantic (which generally has a higher value compared to other regions) and the BOB SWM season but it is higher than that over Taiwan and the BOB NEM season. The power b (1.3) is lower than that over other regions (except during the passage of TC Debbie over the Atlantic). These differences in the Z-R relation could be attributed to the inherent differences in the nature of the TC DSDs.

Figure 6.9c shows the radar parameters for the three distance groups. The A of the two

> 60 km groups is almost similar (~ 250) but it is smaller for the < 60 km group (~ 125). The

121

b of the < 60 km group (1.40) is larger than the > 60 km groups (1.32 and 1.30 for 60 – 200

and > 200 km respectively). A smaller A for the < 60 km group denotes smaller drops near

the TC centre, consistent with our earlier findings. A larger b near the TC centre implies that

rainfall processes have more size-controlled processes.

(a) TC non-TC Coefficient A (c) Distance Coefficient 400 300 1.6 A

300 250 b 1.5

b A 200 A 200 1.4

100 TC 150 1.3 nonTC 0 All Conv Trans Strat <60 60-200 >200 Rain type Distance (km) (b) TC non-TC Coefficient b 1.8 TC nonTC

1.6 b

1.4

All Conv Trans Strat Rain type

Figure 6.9 Radar rainfall estimation parameters. (a) Pre-factor, A, and (b) power, b, for

TC and non-TC (i.e. All) and rainfall types (convective, transition and

stratiform) of TC and non-TC; and pre-factor, A (red plot) and power, b

(blue plot) with respect to (c) distance from TC centre.

122

Table 6.5 Z-R relation (Z = ARb) coefficient (A) and power (b) of TCs over different

regions. The values presented are without rainfall type (convective,

stratiform or transition) stratification.

Region Studies A b Scott (1974) TC Felice (1970) 300 1.24 Atlantic TC Debbie (1969) 260 1.35 Wilson and Pollock (1974) 350 1.35 Jorgensen and Willis (1982) 300 1.35 Western Pacific Chang et al. (2009) 207 1.45 Radhakrishna and Rao (2010), BOB SWM 275 1.39 India Radhakrishna and Rao (2010), BOB NEM 142 1.55

While these results point to a variation in the radar parameters with distance, as mentioned before, the variation in TC DSD (hence the radar parameters) could be a function of the TC sample size and depend very much on the actual size and structure of the TC.

These results also contrast with those of Jorgensen and Willis (1982), who did not find any statistical difference in the radar parameters for TC Fredric (1979) when stratified into eye- wall and outside eye-wall regions. A possible reason could be a difference in the TC rainfall

DSD between the two regions as smaller drops at distances near the TC centre is observed here. Another possibility could be the difference in the instruments being used (or the measurement methodology) and thus the representation of the actual DSD on the surface.

While we use the ground-based disdrometer measurements, Jorgensen and Willis (1982) used drop size measurements made from optical array spectrometer probes onboard a research aircraft. Friedrich et al. (2012) report that DSD measurements made aloft (such as using radar) do not usually represent the DSD observed at the surface as processes that occur close to the surface (e.g. raindrop breakup or evaporation) cannot be captured by these instruments.

Hence, the difference in the Z-R relation between Jorgensen and Willis (1982) and that obtained here could also be due to the above factor.

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6.3.6 Analytical Expression - Gamma Function

As discussed in section 2, we use M234 to estimate the TC and non-TC gamma

distribution parameters. Figure 6.10 shows the frequency distribution of the gamma

parameters. The TC and non-TC distributions are statistically different at the 95 % level. It is

apparent that TCs have larger frequencies of slope (μ; mm-1), shape (Λ) and intercept

-3 -1 (log10No(m mm )) parameters at values 4 – 14, 4 – 15 and 4 – 10 respectively, whereas non-

TCs have a higher frequency at parameter values < 4. There is a negligible difference at

larger parameter values. Correspondingly, the TC mean and median values are larger than for (a) Slope parameter (a) Slope parameter 0.15 0.15the non-TCs as shown in Table 6.6. Physically, a larger μ and Λ respectively indicates a TC TC 0.1 0.1 narrower DSD shape for TC and a truncationnTC of the tail of the DSD towards smaller D. The nTC 0.05 0.05 larger No indicates a larger concentration of smaller drops in TCs. These are consistent with 0 0 our0 previous findings.10 20 0 10 20 -1 Slope parameter (mm-1) Slope parameter (mm ) (b)(a) ShapeSlope parameter (b) Shape parameter 0.15 0.1 TC 0.1 0.1 nTC 0.05 0.05

0 0 0 10 20 0 10 20 -1 SlopeShape parameter parameter (mm ) Shape parameter (c)(b) Intercept Shape parameter parameter (c) Intercept parameter 0.3 0.3 0.1 0.2 0.2 0.05 0.1 0.1 0 0 00 10 20 0 10 20

0 10 20 NormalisedFrequency

NormalisedFrequency -3 -1 Shape parameter-3 -1 log [N (m mm )] log [N (m mm )] 10 o (c) Intercept10 o parameter 0.3Figure 6.10 Normalised frequency distribution of (a) slope, Λ; (b) shape, μ; and (c) 0.2 intercept, No, gamma fitted parameters calculated using moments two, three 0.1 124 0

0 10 20 NormalisedFrequency log [N (m-3 mm-1)] 10 o

and four (M234) of the of TC and non-TC drop spectra.

Table 6.6 TC and non-TC mean and median gamma parameters. The values in the

brackets accompanying the mean are the 95 % confidence interval.

TC Non-TC Mean Λ (mm-1) 10.79 (10.54, 10.89) 10.47 (10.30, 10.62) μ 7.87 (7.71, 8.01) 7.82 (7.70, 7.95) -3 -1 75 60 52 49 No (m mm ) 5.09 ×10 (3.57 ×10 , 2.11 ×10 (1.17 ×10 , 1.52 ×1076) 6.38×1052 Median Λ(mm-1) 7.42 6.94 μ 6.18 5.66 -3 -1 5 5 No (m mm ) 4.26×10 1.39×10

Figure 6.11 shows the gamma parameters with respect to the rainfall rate (using the 10 rainfall classes). Overall, the Λ, μ and No parameter values decrease with an increase in rain rate which respectively shows that with an increase in rain rate the tail of DSD shifts towards larger D, the breadth of the DSD shape increases and the concentration of smaller drops decreases.

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) (a) Slope parameter -1 30 TC 20 nonTC

0 SlopeParameter (mm (b) Shape parameter 18

ShapeParameter 0

80 60 40 20

InterceptParameter 0 1 2 3 4 5 6 7 8 9 10 rainfall classes (mm hr-1)

Figure 6.11 Distribution of (a) slope, Λ; (b) shape, μ; and (c) intercept, log10(No),

gamma fitted parameters (calculated using M234) of the of TC and non-TC

drop spectra with respect to rain rate.

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Comparing the TC and non-TC distributions, the Λ parameter of the two (Figure

6.11a), is statistically different, with the TC values consistently larger than the non-TC at all rain rates. This indicates that the tail of the TC DSD truncates more towards relatively smaller D than non-TCs at all rain rates. Comparing the μ parameter (Figure 6.11b), TCs have higher averages than non-TCs at most of the rain rates (except at classes 2, 3 and 6 where there is no significant difference). A larger deviation between the two is prominent at higher rain rates. This shows that TCs have a relatively narrower DSD than non-TCs at most of the rain rates but is more pronounced at higher rainfall rates. Comparing the intercept parameter, there is no statistical difference between the TC and non-TC distribution (Figure 6.11c) at most of the rainfall classes, except at classes 1, 4 and 5 where the TC values are higher than the non-TC. Physically, this means that TCs have a relatively larger concentration of smaller drop at lower rain rates, in agreement with our earlier findings.

Figure 6.12 shows the frequency distribution of the gamma parameters with respect to rainfall types (convective, transition and stratiform). Overall, the stratiform and transition distributions are more spread and right-skewed than the convective distribution which is relatively narrower, has only small to moderate parameter values and nearly normally distributed. The distribution of the parameters of the three rainfall types for the TC and non-

TC events are also statistically different at the 95% level. The corresponding average and median values of each parameter are shown in Table 6.7. TCs tend to have a larger average and median values than non-TCs for the three rainfall types.

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Table 6.7 TC and non-TC mean and median slope, Λ (mm-1); shape, μ and intercept,

-3 -1 No (m mm ), parameters of the convective, transition and stratiform

rainfall types.

Precipitation Type Convective Transition Strati. TC(non-TC) TC(non-TC) TC(non-TC) Mean Λ (mm-1) 6.8 (5) 8.2 (7.4) 14 (12.3) μ 8.42 (6.10) 6.64 (6.35) 8.86 (8.59) -3 -1 5 4 6 5 7 6 No (m mm ) 4.70×10 (6.40×10 ) 1.53×10 (5.35×10 ) 5.24×10 (9.40×10 ) Median Λ (mm-1) 6.60 (4.74) 6.75 (6.21) 8.85 (8.16) μ 8.15 (5.76) 5.51 (5.38) 6.05 (5.75) -3 -1 5 4 6 5 5 5 No (m mm ) 3.70×10 (5.41×10 ) 1.53×10 (5.35×10 ) 5.74×10 (2.02×10 )

(a) Slope Parameter (b) Shape Parameter 0.25 0.2 convec TC 0.2 convec nTC 0.15 0.15 strati TC strati nTC 0.1 0.1 transi TC transi nTC 0.05

0.05

NormalisedFrequency NormalisedFrequency 0 0 0 10 20 30 40 50 0 10 20 30 40 50 Slope Parameter (mm-1) Shape Parameter (c) Intercept Parameter

0.4

0.3

0.2

0.1 NormalisedFrequency 0 0 10 20 30 40 Intercept Parameter log [N (m-3 mm-1)] 10 o

Figure 6.12 Frequency distribution of (a) slope, Λ; (b) shape, μ; and (c) intercept,

log10(No), gamma fitted parameters (calculated using M234) of the of TC

and non-TC drop spectra with rainfall type (black plot – convective, blue

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plot – transition and red plot – stratiform).

6.3.6.1 Gamma Parameter with TC Distance

Given that the TC DSD shows variation with distance from the TC centre, accordingly, we have investigated the variation in the gamma parameters with distance from TC centre.

Figure 6.13 shows a plot of the gamma DSD parameters of the three distance groups against rain rainfall rate. The plot shows that the gamma DSD parameters of the three distance groups differ to some extent. The Λ parameter of the less than 60 km group is larger for rainfall rates less than 10 mm hr-1 (class 6); the μ parameter of the less than 60 km group is larger at most of the rain rates (except for groups 5, 6 and 10 where there is no statistical difference) and the No parameter of the three groups differs at class 1 where the less than 60 km group has a lower value.

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) (a) Slope parameter -1 60 <60 40 60-200 >200 20

0 SlopeParameter (mm (b) Shape parameter

ShapeParameter 0

InterceptParameter 0 1 2 3 4 5 6 7 8 9 10 rainfall classes (mm hr-1)

Figure 6.13 Distribution of (a) slope, Λ; (b) shape, μ; and (c) intercept, log10(No),

gamma fitted parameters of the < 60 km, 60 – 200 km and > 200 km

distance groups against rain rate.

6.4 Summary

In this study we have compared and contrasted the rainfall DSD between TC and non-

TC related events using the ARM impact disdrometer data at Darwin, Australia, for the period 2006 – 2013, with the aim of establishing if there is any significant difference between

TC and non-TC rainfall DSD and also the relationship with rainfall type and distance from

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TC centre. We also wish to determine that if there is a difference in the DSD, then how does it impact on the parameters of the widely used radar reflectivity (Z) to rainfall rate (R) relationship (Z=ARb) and the gamma DSD model, the latter mostly used for cloud-modelling parameterizations.

Results show that statistically significant differences exist between the DSD of TCs and non-TCs with TCs, comparatively, having smaller drop diameters. The drop diameter (Dm) of both types of rainfall events increases with increase in rain rate, however, the TC drops are consistently smaller than the non-TCs at all rain rates. A similar pattern is observed when the data are partitioned into rainfall types (convective, transition, and stratiform) with TCs having a larger frequency of smaller Dm than the non-TCs for the three rainfall types.

Moreover, it is shown that the TC DSD varies with distance from TC centre. While the

Dm of each distance group increases with rain rate, the Dm of the < 60 km group at low to moderate rain rates (< 20 mm hr-1) is statistically smaller than that further from the TC centre.

A comparative analysis using data at 40 dBZ reflectivity shows that the TC DSD at

Darwin differs from that during the SWM over the BOB (India) and from that over the western Pacific (Taiwan). Possible factors could be the strength of the updrafts and the influence of geography (e.g. terrain).

Variation in the DSD thus induces variation in the radar rainfall estimation and the gamma DSD model parameters. A statistically significant difference in the radar parameters exists between the TC and non-TC rainfall, under different rainfall types and with respect to distance from TC centre. The TC Z-R relation obtained here differs from other regions.

Differences in the gamma DSD model parameters are evident for the different conditions. TCs have higher slope and shape parameter values than non-TCs, the former observed at all rain rates and the latter at moderate to high rainfall rates. However, there is an absence of significant difference in the intercept parameter. With precipitation type, a

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difference in the distribution is observed at small and moderate values of the gamma parameters with TCs (non-TCs) generally having a higher frequency of moderate (low) values. TCs thus have larger average values of the respective gamma parameters. With respect to distance, the slope parameter value of the less than 60 km group is significantly larger than the greater than 60 km groups at small to moderate rain rates (less than 20 mm hr-

1). The shape parameter values of the former group are also higher than the latter group at almost all rain rates but there is no major difference in the intercept parameter between the groups.

The inherent differences in the Z-R relation parameters and the gamma DSD parameters between TC and non-TC rainfall events and also under different condition (e.g. rainfall types and distance from TC centre) suggests that a dynamic Z-R and gamma DSD relation should be utilised in radar rainfall retrievals and cloud microphysical parameterisations, based on the dynamical and microphysical context of the rainfall. Similar suggestions have been made by other studies such as Bringi et al. (2003) and Atlas and Ulbrich (2006).

Appendix C

The formulae to compute the shape, μ (dimensionless), slope, Λ (mm-1), and intercept,

-1 -3 No (mm m ), gamma fitted parameters using moments M234, M246 and M346 are as follows:

(a) for M234 (Smith, 2003):

M 2 M 4   2 (C.1) M 3

th where Mk is the k moment of the gamma function given as:

20 M k   Di NDi Di (C.2) i1 and Di is the average diameter (mm) of the drops in class i, ΔDi is the diameter (mm) interval of drop class i and N(Di) is the drop concentration of drop class i.

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3 4  3 M 2 M 2   (C.3);   (C.4); No  (C.5)  1 M 3  1   3

(b) for M246 (Ulbrich and Atlas, 1998):

M 2   4 (C.6) M 2 M 6

1 7 11[7 112  4 130 12]2   (C.7) 2 1

1 2 M 2   3  4     (C.8)  M 4 

M 3 N  2 (C.9) o   3

M 2   4 (C.10) M 3M 6

1 11 8 [  8]2   4   (C.11);   (C.12) 21 Dm

M 4 N  3 (C.13) o   4

The root mean square error (RMSE) of the drop concentration, N(D), from observed and the gamma fitted distribution is computed as:

n 1 2 RMSE  NDi e  NDi o  (C.14) n i1

where NDi e and NDi o are the gamma fitted and observed drop concentration respectively at drop class i for each drop spectra.

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7 Cross-validation of rainfall characteristics estimated from the TRMM PR, a combined PR- TMI algorithm and a C-POL ground-radar during the passage of tropical cyclone and non- tropical cyclone events over Darwin, Australia

Summary

After presenting a thorough understanding of the DSD associated with TC and non-TC events, the related dynamical and cloud microphysical aspects and some of the implications for radar rainfall estimation and cloud-modelling parameterisations in the previous chapter, this chapter moves on to present the cross-validation of the rainfall characteristics, including the DSD, estimated from the TRMM PR, the COM and the Darwin GR. Note that this study has not yet been published hence the format of presentation is different from the above three chapters. This chapter is presented as a standard thesis chapter which comprises only the results and discussion, the introduction and the data and methodology of which has already been presented in Chapter 2 (i.e. section 2.5) and Chapter 3 (i.e. section 3.3) respectively.

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7.1 Results and Discussion

7.1.1 Case Descriptions

Overpass events during the passage of TC Carlos (year 2011) are used as case studies for the cross-validation of PR and COM rainfall characteristics during the passage of TCs. TC

Carlos, after forming near Darwin (track shown in Figure 7.1a), stayed in the vicinity of

Darwin for more than a day before heading southwest. During its passage, the TC brought a copious amount of rainfall in excess of 300 mm day-1 over the Darwin region

(http://www.bom.gov.au/cyclone/history/carlos.shtml).

Figure 7.1 GR reflectivity at a constant

altitude of 3.5 km for the two TC

Carlos events (15 February 2011

and 17 February 2011) and for

two non-TC widespread events

(13 January and 13 March 2012).

The plot in red in a) shows the

track of TC Carlos.

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Two TRMM overpass events over the Darwin site occurred during the passage of TC

Carlos: (i) on 15 February 2011 and (ii) on 17 February 2011. Figure 7.1a and b respectively show the GR reflectivity plan position indicators (PPIs, which is a display of measurements at a radial distance from the GR) of the two TC events at an altitude of 3.5 km. The 15

February event (Figure 7.1a) has a larger spatial coverage of rainfall than the 17 February event (Figure 7.1b) which could be related to the distance of the TC centre from the Darwin station as the former is closer (112 km) than the latter (167 km).

In addition to these two TC events, eleven non-TC events are also used to examine the correspondence of the space-borne instruments with the DARW GR (Table 7.1 shows the list of the overpass events and their corresponding TRMM orbit number). These non-TC events are from the 2011 and 2012 Australian summer/monsoon seasons that usually fall from

November to April. Unlike TC events, which are of synoptic scale, non-TC events could be of a relatively smaller size (some are less than 1 km, especially convective events). Thus,

TRMM overpass events that had at least 100 grid points within 100 km from the Darwin site are used for non-TCs. The events considered here encompass both stratiform and convective rainfall with some being highly stratiform and some being highly convective. As an example,

Figure 7.1c and d show the PPIs of widespread events that occurred on the 13th of January

2012 and on the 13th of March 2012 respectively. These two events are also frequently used in the latter sections of this paper as case studies for non-TC events. Their spatial coverage of reflectivity is large (somewhat similar in size to the two TC in the radar field-of-view) and their precipitation type is largely stratiform (similar to the 2 TC events) which makes them suitable to be used for a comparative analysis against the TC events especially for precipitation and terrain type separation.

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Table 7.1 TC (numbers 1 and 2) and non-TC (numbers 3 – 13) overpass events and

their corresponding TRMM orbit number

Number Event TRMM Orbit Number 1 14 February 2011 75484 2 17 February 2011 75523 3 9 November 2011 79651 4 17 November 2011 79773 5 20 November 2011 79819 6 13 January 2012 80667 7 17 January 2012 80728 8 18 January 2012 80750 9 21 January 2012 80789 10 25 January 2012 80850 11 27 February 2012 81369 12 10 March 2012 81559 13 13 March 2012 81598

7.1.2 Comparison of Reflectivity

Using the volume matching technique discussed in section 2, data are transformed onto a common 3-D coordinate system. Since the PIA is used both in the 2A25 and the COM, its analysis is also included at times to understand the differences (if there are any) between the latter two products. Figure 7.2 shows the matched PR-GR and COM-GR reflectivity PPIs of the two TC and the two non-TC case events (shown in Figure 7.1) for the 1.3º GR elevation sweep. A good spatial match of the PR and the COM with the GR is observed. Note that there are missing data in the PR near the GR origin point which is attributed to ground clutter in the

PR at low altitudes that has been accordingly filtered by the PR algorithm. The PR-GR spatial pairing is also missing at some coordinates due to the rejection of bins during averaging either in the PR or in the GR.

The data is stratified into two regions: altitudes less than 4 km and greater than 4 km, and the reflectivity comparison are performed for these two regions (the Do and the rainfall estimates are analysed only for the less than 4 km region). This altitude roughly divides the liquid and frozen hydrometer regions. Regions below the 0 ºC isotherm, which is located at

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about 5 km, are mostly dominated by liquid hydrometeors and we have chosen less than 4 km to minimise inclusion of frozen hydrometeors. At higher altitudes, frozen hydrometeors are more dominant. The melting layer is also at the 0 ºC isotherm which is usually seen as a bright band in the radar signature.

Figure 7.2 Matched reflectivity profiles (in dBZ) from the GR (left), PR (middle) and

COM (right) for the events shown in Figure 7.1 at the 1.3º GR elevation

sweep.

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The scatter plot in Figure 7.3 shows the distribution of the reflectivity in the PR and the

COM against the GR for the 2 TC and the 2 non-TC case events for elevations less than 4 km. There is a strong positive linear association between TRMM and the GR for the four case events. The scatter difference, however, could be both small (as in non-TC event 1) and large

(as in TC events 1 and 2 and in non-TC event 2).

Figure 7.3 Scatter plot of the matched reflectivity profiles (in dBZ) for altitude less

than 4 km from the PR (left) and the COM (right) against the GR for the

events shown in Figure 7.1.

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The statistics are presented next. Figure 7.4 shows the r, RMSE and bias for the four case events with rainfall of each event further separated into convective, stratiform, over the land and over the ocean. Considering separation into rainfall types, it is evident that there is a larger degree of disagreement between the satellite estimates and the GR during convective rainfall than during stratiform rainfall. For example, the correlation in convective rainfall is consistently weaker than that in stratiform rainfall and the RMSE and the bias are consistently larger for the convective than for the stratiform group. Note that the correlation and the bias difference between the convective and the stratiform group are much larger in TC event 1

(Figures 7.4a and c respectively) than in the other events. The more positive bias during convective rainfall shows a somewhat greater degree of overestimation by the satellite estimates during such rainfall. This could largely be due to the nature of convective type rainfall which can be highly variable within the PR footprint and rapidly changing with time.

Considering terrain separation (over the ocean and the land), a clear better performance of the PR over the ocean in comparison to that over the land is not evident. For example, events 1, 3 and 4 have a larger correlation and a smaller RMSE in the PR over the ocean than that over the land but for event 2 it is the opposite. Also, the bias for events 1 and 3 over the ocean is smaller than that over the land whereas for events 2 and 4 it is the opposite. While this could roughly point to a better performance over the ocean, a further computation shows that the terrain separation results are also dependant on the rainfall type over the area: for events 1, 3 and 4 there is a greater percentage of convective rainfall over the land than over the ocean whereas for event 2 it is the opposite. As discussed earlier, the performance is weaker when more convective rainfall is present.

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Figure 7.4 Statistics of r (left), RMSE (middle) and Bias (right) of the matched

reflectivity profiles for the events shown in Figure 7.1 for altitude less than

4 km. Events have been further separated into convective (Conv), stratiform

(Strat), over the land and over the ocean. The error bars show the 95 %

confidence interval.

Figure 7.5 shows the statistics for the matched reflectivity profiles of all the events (2

TC and 11 non-TC) for altitudes less than 4 km. The events are arranged in the order of increasing percentage of convective rainfall, the values of which are shown in Figure 7.5d.

The r (Figure 7.5a) for the majority of the events (11 out of 13 events for both the PR and

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COM) is in between 0.6 and 1 which shows a reasonable correlation between the space-borne instruments and the DARW GR. Also, for most of the events, there is marginal to no difference in the r between the PR, the COM and the PIA which shows that the different space-borne data have almost the same degree of linear association with the GR.

Figure 7.5 Statistics of (a) r, (b) RMSE and (c) Bias for the TC and non-TC events for

altitude less than 4 km. Panel (d) shows the percentage of convective

rainfall of each event. The TC events are marked as red (the first red point

from the left (event 5) is the 15 February 2011 event and the second red

point (event 7) is the 17 February 2011 event). The error bars show the 95

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% confidence interval.

The RMSE (Figure 7.5b) ranges from 1 to 7.56 dBZ (4.5 to 16 %) and for the majority of the events (11 out of 13) there is statistically no significant difference in the RMSE between the space-borne measurements. However, there is a systematic increase in the error with an increase in the percentage of convection in the rainfall events.

The bias (Figure 7.5c) is not that large; it ranges from ‒ 2.4 to 1.4 dBZ (‒ 5.75 to + 3.4

%) and the bias in the COM and the PIA is either statistically the same or smaller than in the

PR. Considering the degree of convective rainfall, the majority of the events (6 out of 8) below the 20 % level have a positive bias whereas all the events (5) above the 20 % level have a negative bias. This suggests that the space-borne instruments could be mostly biased high during highly stratiform rainfall (or overestimating the reflectivity when considering the

DARW GR as the reference) and they could be biased low during more convective rainfall

(or for the case of DARW GR as the reference, they underestimate the reflectivity). Placing the TC events into context, it is evident that the association of the PR and the COM with the

GR during the passage of TC Carlos is similar to that during the more stratiform rainfall events.

One of the factors that could lead to an error in the PR estimate is the non-uniform beam filling (NUBF), which is the presence of non-uniformity in the reflectivity within a radar field-of-view. NUBF is corrected for in the 2A25 V7 algorithm, but not in the COM and PIA algorithms. However, the NUBF correction requires an assumption of non- uniformity that can lead to overestimates if the assumed coefficient of variation is too high

(Iguchi et al., 2009). This can explain the overestimation of PR relative to the COM and the

PIA. It is also known that the PR suffers from significant attenuation, especially in convective rainfall, and an attenuation correction tends to perform quite well for convective rainfall but it slightly over-corrects for stratiform rainfall (Wang and Wolff, 2009). This further explains

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the positive bias in the space-borne instruments during highly stratiform rainfall and vice- versa for highly convective rainfall events. The overestimation of the COM and the PIA relative to the GR can possibly be explained by attenuation of the C-band reflectivity that is not fully corrected by the Bringi et al. (2001) method. This is evident in the outer range rings of Figure 7.2a, where a large positive difference between the PR (or the COM) reflectivity and the GR reflectivity exists at the 225° azimuth. Since this difference is present even outside the convective cores, there should not be a large error in the PR attenuation correction since there is not a significant attenuation along the PR line-of-sight in this situation.

However, there is significant attenuation along the GR line-of-sight in this situation and small underestimates in the attenuation correction can lead to these biases (Figure 7.6).

Figure 7.6 Reflectivity difference with respect to the GR at the 3 km altitude (a) for the

PR and (b) for the COM for TC 1 (20110214).

The statistics for reflectivities measured at altitudes greater than 4 km are also presented (shown in Figure 7.7). These are for 11 events as two events have a small sample

(less than 10) above the 4 km level. While the linear association (r) is almost the same as that for the less than 4 km group, there are some notable differences in the other statistics. Firstly, the error (RMSE) increases for the majority (9) of the events (the RMSE for the different space-borne measurements are almost the same). Secondly, the bias of the greater than 4 km

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group is less than that of the less than 4 km group for almost all of the events (the difference is in the range – 5.17 to 0.23 dBZ) and the difference is larger in the events with a larger percentage of stratiform rather than convective rainfall. The bias for the different space-borne measurements is the same for most of the events except for event 5 (which is TC event 1) and for event 6 where the bias in the COM and the PIA is larger than that in the PR.

Figure 7.7 Same as Figure 7.5 except for altitude greater than 4 km.

The results obtained here for the reflectivity comparison are consistent with most of the studies over other regions (Liao and Meneghini, 2009; Schwaller and Morris, 2011; Kim et al., 2014; Park et al., 2015). For example, Park et al. (2015) show that for elevations less than

4 km the bias for widespread events is small with slight overestimation by the PR (less than 1

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dBZ) whereas for convective cases the bias is negative (greater than – 4 dBZ) and the RMSE is larger than that in widespread cases, as also reported here. The usually negative bias for the more convective events suggests that weaker return signals from the space-borne instruments than the GR and the larger RMSE could be due to the nature of convective storms (a greater degree of small-scale spatial variability). Another contributing factor could be NUBF for small-scale events. Park et al. (2015) also show that for elevations greater than 4 km the bias becomes negative (1 – 3 dBZ smaller in the PR than in the GR) and the RSME increases in the widespread events whereas there is not much variation for convective events as reported here. Such differences are attributed to a mismatch in the bright band height and the scattering differences in the PR and the GR for mixed-phase hydrometeors in and above the melting layer (Park et al. (2015) and the references therein).

7.1.3 Comparison of Do

The consistency of the above results with other studies provides the impetus to examine the Do and the rainfall estimates. The Do estimates for the rainfall region (altitudes less than 4 km) are presented next. Figure 7.8 shows the corresponding scatter plots of Do for the 2 TC and the 2 non-TC case events (shown in Figure 7.1). A positive linear association between the PR (or the COM) and the GR is evident but the association is weak, particularly at smaller

Do values. Unlike the 2 TC events, the scatter for the 2 non-TC events is mostly above the line of perfect agreement. Also, the Do in the PR is greater than 1 mm whereas in the COM and in the GR there are values less than 1 mm.

Figure 7.9 shows the Do statistics for the 2 TC and the 2 non-TC case events with further separation into rainfall and terrain types. Similar to the reflectivity estimates, it is evident that there is a larger degree of disagreement between the satellite estimates and the

GR during convective rainfall than during stratiform rainfall. For the PR, the r of the convective group is weaker than that of the stratiform group (except for event 3) whereas the

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RMSE and the bias for the convective group are consistently larger than that for the stratiform group. For separation into terrain types, results are similar to that obtained for the reflectivity estimates whereby the PR has a larger deviation over the land for events 1, 3 and 4 in comparison to event 2.

Figure 7.8 Same as Figure 7.3.except for Do.

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Figure 7.9 Same as Figure 7.4 except for Do.

Figure 7.10 shows the statistics for the matched Do profiles of all the events (2 TC and

11 non-TC) in the rainfall region. The linear association (r, Figure 7.10a) between the space- borne instruments and the GR is generally not strong. Also, the RMSE (Figure 7.10b) is larger for the more convective events which show more variability between the space-borne and the

GR Do as events become more convective.

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Figure 7.10 Same as Figure 7.5 except for Do.

A similar trend is also observed in the bias (Figure 7.10c) where it increases with an increase in the convection; the bias ranges from – 0.08 to 0.57 mm (or – 6 to 58 %) in the PR.

Also, for the majority of the events, the bias is positive both in the PR and the COM which shows that TRMM tends to mostly overestimate the Do with respect to the DARW GR.

However, the bias in the COM appears to be smaller than that in the PR especially for the majority of the less convective events (i.e. events with less than 20 % convection). For the majority of the more convective events, there is statistically no significant difference between the PR and the COM. Moreover, it could be concluded that the association of the PR and the

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COM Do estimates with the GR during the passage of TC Carlos is similar to that during the more stratiform rainfall events (congruent with the results obtained for the reflectivity estimates).

The results obtained here for the PR and the COM Do are consistent with Bringi et al.

(2012) who found that the PR overestimates the Do with respect to the KWAJ GR for the two cases they examined (the bias ranged from 11.7 to 24.6 %). They also show that the bias in the COM is smaller than that in the PR (‒ 0.8 to 9.7 %). We note that in most cases in Figure

7.10c, the biases of PR and the PIA algorithm are similar to each other, but the COM algorithm can differ and is often closer to zero, particularly for cases with a low convective fraction. This suggests that the addition of measurements from TMI, specifically, the strong positive relationship between liquid water path and brightness temperature over water surfaces, is providing information that adjusts the DSD in rainfall over ocean that is not present in the radar-only algorithms, which rely on the default stratiform and convective DSD assumption in profiles without significant attenuation (Kozu et al., 2009).

7.1.4 Comparison of Rainfall Rate

Finally, we compare the rainfall rates estimated from the space-borne instruments and the GR. These are performed for altitudes less than 4 km. Figure 7.11 shows the scatter plots of the rainfall rate from the PR and the COM against the GR for the four case events. Both the PR and the COM have a positive linear relationship with the GR but the data points deviate considerably from the line of perfect agreement, especially for events 1, 2 and 4.

The statistics for the case events including separation into rainfall and terrain types are presented in Figure 7.12. It is evident that there is a larger degree of overestimation by the PR during convective rainfall than during stratiform rainfall for the 2 TC events (for the 2 non-

TC events the results are mixed). This follows the clear larger overestimation of reflectivity estimates during convective than during stratiform rainfall for the 2 TC events (Figure 7.4c

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and f). However, the COM consistently has a larger degree of overestimation for the convective group for both the TC and non-TC events. For separation into terrain types, a clear pattern is not evident.

Figure 7.11 Same as Figure 7.3 and Figure 7.8 except for rainfall rate.

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Figure 7.12 Same as Figure 7.4 and Figure 7.9 except for rainfall.

Figure 7.13 shows the statistics for the rainfall profiles of all the events (2 TC and 11 non-TC). The correlation (Figure 7.13a) of the PR and the COM with the GR for most of the events (11) is greater than 0.5 and it is the same for both the instruments. The correlation, nonetheless, decreases with an increase in the percentage of convection.

Consequently, the RMSE tends to increase with an increase in the percentage of convection which is more evident in the PR. For the greater stratiform events (below 20 % convection), the COM has a similar RMSE as the PR for events 1 to 3 (the RMSE for these events is also small) but for events 4 to 8 the COM generally has a larger RMSE than the PR.

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For the more convective events (greater than 20 % convection), a statistically significant difference in the error between the PR and the COM is not evident for most of the events.

Figure 7.13 Same as Figure 7.5 and Figure 7.10 except for rainfall rate.

The bias is shown in Figure 7.13c and some important conclusions are as follows. The bias decreases (becomes more negative) with an increase in the percentage of convection and this trend is prominent in both the PR and the COM. For the highly stratiform rainfall events, there is a mixture of a good match and overestimation with respect to the GR. For the highly convective events, the space-borne instruments generally underestimate the rainfall observed

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by the GR. Also, the bias the in COM is greater than that in the PR for more than 50 % of the events.

This is somewhat similar to the results obtained by Bringi et al. (2012) who report an increase in the bias in the COM rainfall with respect to the KWAJ GR. The biases they report are, however, negative in both the PR and the COM. The bias of the COM algorithm relative to the PIA and PR algorithms can also be explained in the context of the reflectivity and Do biases. In the events with significant positive bias, the reflectivity bias (relative to GR) is also positive but the Do bias, while positive, is less strongly positive than PR and PIA algorithms.

The combination of high reflectivity and smaller Do must result in a positive rainfall bias.

Furthermore, the rainfall statistics are dominated by the highest rates when compared to the dBZ and Do statistics (Figures 7.5 and 7.10), which are more normally distributed and thus have even contribution from light and moderate rates.

Comparing the results obtained here with similar cross-validation studies over other regions shows mixed results. Table 7.2 shows a list of some of these studies and the corresponding bias between the PR and GR. It is evident that there is a mixture of overestimation and underestimation of the rainfall by the PR over the different regions.

Nonetheless, the study here shows some clear pattern as discussed above. The next chapter summarises the key findings of this thesis and provides some recommendations for future work.

Table 7.2 PR and GR rainfall rate comparison from previous studies.

Region Study by Bias (% of mean) Rainfall/terrain Korea Kim et al. (2014) + 16 – 80 Stratiform + 26 – 150 Convective KWAJ Wolff et al. (2005) + 6 - Wolff and Fisher (2008) ‒ 13.7 Ocean MELB Wolff et al. (2005) ‒ 9.1 - Wolff and Fisher (2008) + 4.1 Ocean + 7 (+ 8) Land (coast) Liao and Meneghini (2009) +9 Stratiform ‒ 19 Convective

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8 Summary and Recommendations for Future Work

The aim of this research was twofold. First, it was to understand the accuracy and limitations of the Tropical Rainfall Measuring Mission (TRMM) derived rainfall products during the passage of tropical cyclones (TCs) over the south-west Pacific region. Second, it was to understand the rainfall drop size distribution (DSD) characteristics during the passage of TCs which have implications for remote sensing of rainfall (as those related to satellite- based estimation of precipitation) and microphysical parameterisations employed in

Numerical Weather Prediction models (which are another source of precipitation-related information during the passage of TCs). To achieve these objectives, this research commenced with the evaluation of the TRMM Multi-satellite Precipitation Analysis (TMPA)

3B42 precipitation estimates during the passage of TCs over New Caledonia and Fiji. It further compared the drop size distribution characteristics associated with TC and non-TC rainfall events over Darwin during the Australian summer-monsoon wet season. The implications of the differences in the TC and the non-TC DSDs on radar-rainfall estimation and cloud-modelling studies are ascertained. The study finally investigates the feasibility of using the TRMM precipitation radar (PR) and a combined PR and TRMM Microwave

Imager (TMI) algorithm (COM) to probe the DSD during the passage of TCs. The Darwin ground radar (GR) measurements are used as the reference dataset. This chapter summarises the key findings of this thesis and provides some recommendations for further work.

The evaluation over New Caledonia and Fiji gives some insight into the accuracy and limitations of the TMPA estimates. It is shown that TMPA has moderate skill in estimating rainfall associated with TCs over New Caledonia and Fiji. TMPA generally overestimates light rainfall events and underestimates heavy rainfall events. The skill of TMPA also varies

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under different conditions such as elevation, distance from the TC centre, and TC intensity.

The skill of TMPA decreases with increasing elevation, TMPA is in better agreement with the observations near the TC centre and TMPA has better skill for less intense TCs. The skill of TMPA varies from case to case but on average, TMPA is more skilful over TCs with heavy precipitation.

As an application for future TC related studies, the TMPA estimates could be blended with rain gauge data, which would take advantage of strengths and mitigate shortcomings of each data set, by producing blended gridded precipitation estimates for New Caledonia and

Fiji. Methods for such blending have been proposed by several studies, for example, Mitra et al. (2009), Vila et al. (2009), Li and Shao (2010) and Renzullo et al. (2011). In the near future, the Integrated Multi-satellite Retrievals for GPM (IMERG) precipitation product (Hou et al., 2014; Huffman et al., 2015) could also be incorporated but a prior thorough accuracy and error analysis of this data set would be required. Such a blended dataset is expected to provide a better precipitation estimate for New Caledonia and Fiji. Moreover, this could be extended to other Pacific Island countries like Samoa, Vanuatu and Solomon Islands.

The evaluation of the DSD characteristics shows that a statistically significant difference exists between the TC and the non-TC related DSDs with TCs comparatively having a smaller drop diameter at all rainfall rates. Moreover, it is shown that the TC DSD varies with distance from the TC centre whereby drops near the TC centre are statistically smaller than that further from the TC centre.

These differences have implications for radar rainfall estimation and cloud-modelling studies. It is shown that the radar parameters differ between TC and non-TC rainfall, under different rainfall types and with respect to the distance from the TC centre. Differences in the gamma DSD model parameters are also evident whereby TCs have larger slope and shape

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parameter values than non-TCs. With respect to distance from the TC centre, the slope and shape parameter values are larger near the TC centre than further from the TC centre.

As an application for future work, the differences in the Z-R relation parameters and the gamma DSD parameters suggest that a dynamic Z-R and gamma DSD relation should be utilised in radar rainfall retrievals and cloud microphysical parameterisations, based on the dynamical and microphysical context of the rainfall. For example, errors in the representation of the DSD together with the sensitivity to the hydro-meteorological related quantities have been attributed to some of the known biases in the PR and TMI algorithms (Iguchi et al.,

2009; Kozu et al., 2009). Incorporating a dynamic DSD in the retrieval algorithms could help in addressing some of these shortcomings and improve rainfall estimation.

Finally, the inter-comparison of the rainfall characteristics estimated from the PR, the

COM and the GR reveals that the correspondence of the space-borne instruments (i.e. the PR and the COM) with the DARW GR, taken as the reference, is largely dependent on the percentage of convection in the rainfall event. Moreover, putting the TC events into context, the association of the TRMM estimates with the GR for these events is similar to that observed for the highly stratiform non-TC events (there is no significant difference) but it differs largely from that observed for the majority of the highly convective non-TC events.

The PR and the COM mostly overestimate reflectivities of events with a greater percentage of stratiform rainfall and they mostly underestimate the reflectivities as events become more convective. The bias in the COM is either the same or smaller than that in the

PR and this could be a positive result of the blending. For the median volume diameter (Do) estimates, the linear association between the space-borne instruments and the GR is shown to be weak. The PR and the COM mostly overestimate the Do and the magnitude of overestimation increases as the events become more convective. Also, the bias in the COM is generally smaller than that in the PR for the highly stratiform events which shows that

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combining the TMI with the PR improves the DSD retrieval in the highly stratiform events where the PR is less reliable.

Considering the rainfall estimates, it is shown that the linear association and the bias between the space-borne instruments and the GR decreases as events become more convective. For the highly stratiform rainfall events, there is a mixture of a good match and overestimation with respect to the GR. For the same set of events, the COM tends to have a greater overestimation than the PR. For the highly convective events, the space-borne instruments generally underestimate the rainfall observed by the GR.

Following the above findings, it is concluded that the PR and the COM could be used to characterise the DSD of TC rainfall, however, its limitations need to be taken into consideration. For a more general conclusion, the study should be extended with more cases, especially during the passage of TCs, over a longer period of time and over different regions.

It would also be worthwhile to perform a similar cross-validation using the GPM based dual- frequency precipitation radar (DPR) with more TC rainfall events. In addition, GRs from the

Pacific Island countries could be cross-validated with the PR and the DPR and re-calibrated if inconsistencies are present.

In summary, this thesis provides a thorough understanding of (i) the accuracy and limitations of the TRMM-based estimates and (ii) the dynamical and microphysical aspects of precipitation formation that modify the DSD during the passage of TC and non-TC events over the south-west Pacific region and how these have implications for remote sensing of precipitation and cloud-modelling parameterizations. It furthermore adds valuable information to the scientific literature on precipitation characteristics and its estimation over the south-west Pacific region. On a regional level, the information presented here could be utilised to evaluate NWP forecasts and also improve rainfall retrieval algorithms. This would

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lead to a better forecasting and estimation of rainfall and the society will benefit from this in terms of disaster mitigation and preparedness.

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Minerva Access is the Institutional Repository of The University of Melbourne

Author/s: Deo, Anil

Title: Remote sensing tropical cyclone rainfall over the southwest Pacific region

Date: 2018

Persistent Link: http://hdl.handle.net/11343/217911

File Description: Completed Thesis: Remote sensing tropical cyclone rainfall over the southwest Pacific region

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