Influence of Hydrological, Geomorphological And

INFLUENCE OF HYDROLOGICAL, GEOMORPHOLOGICAL AND

CLIMATOLOGICAL CHARACTERISTICS

OF NATURAL CATCHMENTS ON

LAG PARAMETERS

A THESIS SUBMITTED IN FULFILMENT OF THE

REQUIREMENTS FOR THE AWARD OF THE DEGREE OF

DOCTOR OF PHILOSOPHY

FROM

THE UNIVERSITY OF WOLLONGONG

NANAYAKKARA DAYANANDA BODHINAYAKE BSc (Eng.) - University of Sri-Lanka Post Grad. Dip. Hyd. Eng. - International Institute for Hydraulic Engineering, Delft, The Netherlands Adv. Dip. Tech. Ed. - University of Manchester, United Kingdom Grad. Dip. Ed. - University of Technology Sydney, Australia

SCHOOL OF CIVIL, MINING AND ENVIRONMENTAL ENGINEERING

2004

THESIS CERTIFICATION

I, Nanayakkara Dayananda Bodhinayake, declare that this thesis, submitted in fulfilment of the requirements for the award of Doctor of Philosophy, in the School of Civil, Mining and Environmental Engineering, University of Wollongong, is wholly my own work unless otherwise referenced or acknowledged. The document has not been submitted for qualifications at any other academic institution.

N D Bodhinayake August 2004. iii

ABSTRACT

Catchment lag time is considered as a key factor in flood hydrograph modelling and design. The extensive literature investigation of this study revealed that most of the lag time equations that have been developed include various hydrological, geomorphological and climatological characteristics of the catchment. However, different studies use different combinations of these variables, and therefore, the appropriate context of the relation is not known with confidence.

The intention of this research is to determine to what extent the above mentioned catchment characteristics influence the lag parameter, which is directly related to the catchment’s lag time.

In order to assess the influence of catchment characteristics on the lag parameter, reliable and valid rainfall and flow data must be analysed.

Therefore, at the outset of this research, the reliability and validity of rainfall data of seventeen rural catchments in Queensland, Australia, were examined. These catchments belong to five river basins and they are, Mary, Haughton, Herbert, Don and Johnstone. A total of 254 storm events on these catchments were analysed.

To compute the lag parameters of the catchments, the computer based Watershed Bounded Network Model (WBNM) was selected due to its in-built non-linearity property as well as other capabilities. These include the ability to model spatially varying rainfall, the simplicity of data files and the requirement of a minimum amount of data. The constant- slope method was adopted to separate the base flow from the recorded total hydrograph in order to derive the ordinates of the surface runoff hydrograph, which is one of the essential components for the input file of WBNM. The time variation of the rainfall was examined by means of mass curves of rainfall and the spatial variability of the rainfall was studied with the help of isohyetal plots. Thereafter the rainfall and flow data, as well as the physical features of the catchments, were incorporated into WBNM to generate hydrographs for all iv

254 storm events. The lag parameter was altered until WBNM generated a hydrograph that closely resembled the recorded surface runoff hydrograph. This process was repeated for each storm event to obtain its lag parameter value. From this method, lag parameter values were derived for all 254 storm events on the seventeen catchments.

The next stage of the analysis involved testing to determine whether the lag parameter is related to a range of hydrological, geomorphological and climatological variables.

To carry out the analysis the necessary hydrological characteristics were extracted from the storm data. Other useful geomorphological and climatological characteristics were obtained from AUSLIG maps and the Bureau of Meteorology.

If the lag relations built into WBNM are sufficient to account for those variables, then no significant relation between the lag parameter and those variables should exist when the lag parameter is plotted against each variable.

The lag parameter (C) versus a range of hydrological, geomorphological and climatological characteristics of all seventeen catchments were plotted to examine their correlation. Two tailed statistical t-tests were carried out for each plot to find out whether the gradients of best-fit straight lines of those plots are significantly different from zero at 5% level of significance.

The results of this research have shown that there are no strong relationships between the lag parameter (C) and the range of catchment characteristics selected for this study. Therefore, the lag parameter can be considered as an independent factor applying to a wide range of catchments. While this research was carried out for the WBNM model, its essential findings, that the non-linearity power is near to 0.23, and that the dominant variable influencing catchment lag time is the catchment area, also apply to other flood hydrograph models.

ACKNOWLEDGEMENT

I wish to acknowledge the invaluable support, guidance and assistance contributed by Associate Professor Michael John Boyd during the term of my candidature. I would also like to thank Mr. Terry Malone of the Bureau of Meteorology, Brisbane, Australia, for providing the rainfall and flow data of five river basins to carry out this research study. Last but not least the encouragement and support given by my wife Chandrani and two sons Dinusha and Buddhi as well as my mother (Leelanganee Weraniyagoda Bodhinayake) are greatly appreciated.

TABLE OF CONTENTS

Title page i Thesis Certification ii Abstract iii Acknowledgement v Table of Contents vi List of Figures x List of Tables xxi Papers in preparation xxiii 1. INTRODUCTION 1 2. LITERATURE REVIEW ON RELATIONS BETWEEN LAG TIME AND HYDROLOGICAL, GEOMORPHOLOGICAL AND CLIMATOLOGICAL CHARATERISTICS OF CATCHMENTS 5 2.1 Introduction 5 2.2 Rational Method 7 2.3 Tangent Method 16 2.4 The Time-Area Method 16 2.5 The Unit Hydrograph Theory 17 2.6 Linear and Non-linear Models 30 2.7 Studies with RORB Model 48 2.8 Summary of Lag Relations 64 3. DESCRIPTION OF CATCHMENTS 73 3.1 Gympie, Moy Pocket, Bellbird, Cooran and Kandanga catchments of Mary River 74 3.2 Powerline and Mount Piccaninny catchments of Haughton River 86 3.3 Zattas, Nash’s Crossing, Gleneagle and Silver Valley catchments of Herbert River 88 3.4 Reeves, Mount Dangar, and Ida Creek catchments of Don River 92 3.5 Tung Oil, Nerada and Central Mill catchments of North and South Johnstone Rivers 95

vii

4. SELECTION OF AVAILABLE RAINFALL AND STREAM FLOW DATA 98 4.1 Introduction 98 4.2 Rainfall data of Mary River Basin 4.2.1 Temporal Patterns of Rainfall 98 4.2.2 Spatial variation of Rainfall 104 4.3 Rainfall data of Haughton River Basin 4.3.1 Temporal Patterns of Rainfall 110 4.3.2 Spatial variation of Rainfall 114 4.4 Rainfall data of Herbert River Basin 4.4.1 Temporal Patterns of Rainfall 120 4.4.2 Spatial variation of Rainfall 125 4.5 Rainfall data of Don River Basin 4.5.1 Temporal Patterns of Rainfall 131 4.5.2 Spatial variation of Rainfall 135 4.6 Rainfall data of Johnstone River Basin 4.6.1 Temporal Patterns of Rainfall 142 4.6.2 Spatial variation of Rainfall 147 4.7 STREAMFLOW DATA OF MARY RIVER BASIN 155 4.8 STREAMFLOW DATA OF HAUGHTON RIVER BASIN 159 4.9 STREAMFLOW DATA OF HERBERT RIVER BASIN 161 4.10 STREAMFLOW DATA OF DON RIVER BASIN 163 4.11 STREAMFLOW DATA OF JOHNSTONE RIVER BASIN 165 5. METHOD OF ANALYSIS 167 5.1 Introduction 167 5.2 Mary River Basin 168 5.3 Haughton River Basin 189 5.4 Herbert River Basin 199 5.5 Don River Basin 205 5.6 North Johnstone River Basin 217

viii

6. RELATIONSHIP BETWEEN LAG PARAMETER AND HYDROLOGICAL CHARACTERISTICS 246 6.1. Variation of Lag time with Discharge 246 6.2. Variation of Lag Parameter with Discharge 247

6.3. Relationship between Lag Parameter (C) and Peak Discharge (Qp) 249 6.4. Relationship between Lag Parameter (C) and Surface Runoff

Peak Discharge (Qs) 257

6.5. Relationship between Lag Parameter (C) and Total Rainfall Depth (DT) 264

6.6 Relationship between Lag Parameter (C) and Depth of Surface Runoff (DSRO) 271

6.7. Relationship between Lag Parameter (C) and Average Intensity (Iav) 278 6.8. Relationship between Lag Parameter (C) and the Ratio of Time to Peak Intensity

and Duration of Excess Rainfall (TpI/DURex) 285

6.9. Relationship between Lag Parameter (C) and Average Peak Intensity (AVPI) 292 6.10 Relationship between Lag Parameter (C) and the Ratio of Excess Depth and

Total Depth (Dex/DT) of Rainfall 298 6.11 Relationship between Lag Parameter (C) and the Ratio of Peak Intensity and

Average Intensity (Ip/Iav) of Rainfall 305 6.12 Relationship between Lag Parameter (C) and the Ratio of Rainfall Depths at

Centroids of Bottom and Top halves (DBC/DTC) of catchment 312 6.13 Summary of the findings of Chapter 6 320 7. RELATIONSHIP BETWEEN LAG PARAMETER AND GEOMORPHOLOGICAL & CLIMATOLOGICAL CHARACTERISTICS 323 7.1 Introduction 323 7.2 Relationship between Lag Parameter (C) and Catchment Area (A) 324

7.3 Relationship between Lag Parameter (C) and Equal Area Slope (Sc) 327 7.4 Relationship between Lag Parameter (C) and the Length of Main Stream (L) 331 7.5 Relationship between Lag Parameter (C) and Catchment Shape Factor (A/L2) 334 7.6 Relationship between Lag Parameter (C) and the Main Stream Length to the

Centroid from Catchment’s Outlet (Lc) 337 7.7 Relationship between Lag Parameter (C) and the Ratio of Main Stream

Length to the Centroid from Outlet and Main Stream Length (Lc/L) 340

7.8. Relationship between Lag Parameter (C) and the Number of Rain Days per Year (No.RD/year) 345 7.9 Relationship between Lag Parameter (C) and the Mean Annual Rainfall

(ARMean) 348 7.10 Relationship between Lag Parameter (C) and the 2-year ARI-72hr Rainfall 2 Intensity Pattern of AR&R ( I72) of catchment 351 7.11 Relationship between Lag Parameter (C) and the Mean Elevation of

Catchment (ELMean) 355 7.12 Relationship between Lag Parameter (C) and the Mean Elevation of the

Centroid of Catchment (ELCentroid) 358 7.13 Catchments with Large Lag Parameter Values 361 7.14 Summary of the findings of Chapter 7 367 8. CONCLUSION 371 REFERENCES 375 APPENDICES - in CD attached to thesis A - AUSLIG map data related to land use, developed areas, topsoil & subsoil properties and soil texture properties of four river basins (Haughton, Herbert, Don and Johnstone) B - Rainfall and flow data of five basins (Mary, Haughton, Herbert, Don and Johnstone) C - Actual & estimated rating curves of twelve catchment outlets and base flow separation & runoff hydrographs for selected storms of all seventeen catchments D - WBNM files of all 254 storm events E - Hyetographs, total hydrographs, surface runoff hydrographs and computer generated hydrographs of all seventeen catchments of five basins (Mary, Haughton, Herbert, Don and Johnstone)

LIST OF FIGURES

No. Description Page 3.1 Mary River and its contributing catchments 74 3.2 Stream elevations of Gympie catchment of Mary River 75 3.3 Stream elevations of Moy Pocket catchment of Mary River 75 3.4 Stream elevations of Bellbird catchment of Mary River 76 3.5 Stream elevations of Cooran catchment of Sixth Mile Creek (Tributary of Mary River) 76 3.6 Stream elevations of Kandanga catchment of Kandanga Creek (Tributary of Mary River) 77 3.7 Mary River at Gympie – Land Use Classification 79 3.8 Mary River at Gympie – Soil Texture of Topsoil 80 3.9 Mary River at Gympie – Soil Texture of Subsoil 81 3.10 Mary River at Gympie – Silt in Topsoil 82 3.11 Mary River at Gympie – Silt in Subsoil 83 3.12 Mary River at Gympie – Sand in Topsoil 84 3.13 Mary River at Gympie – Sand in Subsoil 85 3.14 Haughton River and its contributing catchments 86 3.15 Stream elevations of Powerline catchment of Haughton River 87 3.16 Stream elevations of Mount Piccaninny catchment of Haughton River 87 3.17 Herbert River and its contributing catchments 89 3.18 Stream elevations of Silver Valley catchment of Herbert River 90 3.19 Stream elevations of Gleneagle catchment of Herbert River 90 3.20 Stream elevations of Nash’s Crossing catchment of Herbert River 91 3.21 Stream elevations of Zattas catchment of Herbert River 91 3.22 Don River and its contributing catchments 92 3.23 Stream elevations of Reeves catchment of Don River 93 3.24 Stream elevations of Mount Dangar catchment of Don River 94 3.25 Stream elevations of Ida Creek catchment of Don River 94 3.26 North and South Johnstone Rivers and their contributing catchments 95 3.27 Stream elevations of Tung Oil catchment of North Johnstone River 96 3.28 Stream elevations of Nerada catchment of North Johnstone River 97 3.29 Stream elevations of Central Mill catchment of South Johnstone River 97 The figures 3.30 to 3.57 of remaining four basins are contained in Appendix A of the CD

4.1 Location of Rainfall Stations for Mary River 99 4.2 Mass Curve of Rainfall - Mary River (April 1989) 101 4.3 Mass Curve of Rainfall - Mary River (December 1991) 101 4.4 Mass Curve of Rainfall - Mary River (February 1992) 101 4.5 Mass Curve of Rainfall - Mary River (March 1992) 102 4.6 Mass Curve of Rainfall - Mary River (February 1995) 102 4.7 Mass Curve of Rainfall - Mary River (January 1996) 102 4.8 Mass Curve of Rainfall - Mary River (April 1996) 103

4.9 Mass Curve of Rainfall - Mary River (March 1997) 103 4.10 Rainfall Isohyets (mm) - Mary River (April 1989) 105 4.11 Rainfall Isohyets (mm) - Mary River (December 1991) 105 4.12 Rainfall Isohyets (mm) - Mary River (February 1992) 106 4.13 Rainfall Isohyets (mm) - Mary River (March 1992) 106 4.14 Rainfall Isohyets (mm) - Mary River (February 1995) 107 4.15 Rainfall Isohyets (mm) - Mary River (January 1996) 107 4.16 Rainfall Isohyets (mm) - Mary River (April 1996) 108 4.17 Rainfall Isohyets (mm) - Mary River (March 1997) 108 4.18 Location of Rainfall Stations of Haughton River 109 4.19 Mass Curve of Rainfall - Haughton River (January 1994) 112 4.20 Mass Curve of Rainfall - Haughton River (January 1996) 112 4.21 Mass Curve of Rainfall - Haughton River (February 1997) 112 4.22 Mass Curve of Rainfall - Haughton River (March 1997) 113 4.23 Mass Curve of Rainfall - Haughton River (February 2000) 113 4.24 Mass Curve of Rainfall - Haughton River (March 2000) 113 4.25 Mass Curve of Rainfall - Haughton River (April 2000) 114 4.26 Rainfall Isohyets (mm) - Haughton River (January 1994) 116 4.27 Rainfall Isohyets (mm) – Haughton River (January 1996) 116 4.28 Rainfall Isohyets (mm) – Haughton River (February 1997) 117 4.29 Rainfall Isohyets (mm) – Haughton River (March 1997) 117 4.30 Rainfall Isohyets (mm) – Haughton River (February 2000) 118 4.31 Rainfall Isohyets (mm) – Haughton River (March 2000) 118 4.32 Rainfall Isohyets (mm) – Haughton River (April 2000) 119 4.33 Location of Rainfall Stations of Herbert River 121 4.34 Mass Curve of Rainfall - Herbert River (January 1994) 122 4.35 Mass Curve of Rainfall - Herbert River (March 1996) 122 4.36 Mass Curve of Rainfall - Herbert River (March 1997) 122 4.37 Mass Curve of Rainfall - Herbert River (January 1998) 123 4.38 Mass Curve of Rainfall - Herbert River (December 1999) 123 4.39 Mass Curve of Rainfall - Herbert River (Early February 2000) 123 4.40 Mass Curve of Rainfall - Herbert River (Late February 2000) 124 4.41 Mass Curve of Rainfall - Herbert River (February 2001) 124 4.42 Rainfall Isohyets (mm) - Herbert River (January 1994) 126 4.43 Rainfall Isohyets (mm) - Herbert River (March 1996) 126 4.44 Rainfall Isohyets (mm) - Herbert River (March 1997) 127 4.45 Rainfall Isohyets (mm) - Herbert River (January 1998) 127 4.46 Rainfall Isohyets (mm) - Herbert River (December 1999) 128 4.47 Rainfall Isohyets (mm) - Herbert River (Early February 2000) 128 4.48 Rainfall Isohyets (mm) - Herbert River (Late February 2000) 129 4.49 Rainfall Isohyets (mm) - Herbert River (February 2001) 129 4.50 Location of Rainfall stations of Don River 131 4.51 Mass Curve of Rainfall -Don River (April 1989) 132 4.52 Mass Curve of Rainfall -Don River (December 1990) 132 4.53 Mass Curve of Rainfall -Don River (January 1991) 133 4.54 Mass Curve of Rainfall -Don River (February 1991) 133 4.55 Mass Curve of Rainfall -Don River (August 1998) 133

xii

4.56 Mass Curve of Rainfall -Don River (January 1999) 134 4.57 Mass Curve of Rainfall -Don River (December 1999) 134 4.58 Mass Curve of Rainfall -Don River (Early February 2000) 134 4.59 Mass Curve of Rainfall -Don River (Late February 2000) 135 4.60 Rainfall Isohyets (mm) - Don River (April 1989) 136 4.61 Rainfall Isohyets (mm) - Don River (December 1990) 136 4.62 Rainfall Isohyets (mm) - Don River (January 1991) 137 4.63 Rainfall Isohyets (mm) - Don River (February 1991) 137 4.64 Rainfall Isohyets (mm) - Don River (August 1998) 138 4.65 Rainfall Isohyets (mm) - Don River (January 1999) 138 4.66 Rainfall Isohyets (mm) - Don River (December 1999) 139 4.67 Rainfall Isohyets (mm) - Don River (Early February 2000) 139 4.68 Rainfall Isohyets (mm) - Don River (Late February 2000) 140 4.69 Locations of Rainfall stations of North and South Johnstone Rivers 142 4.70 Mass Curve of Rainfall - North & South Johnstone Rivers (March 1990) 143 4.71 Mass Curve of Rainfall - North & South Johnstone Rivers (January 1994) 144 4.72 Mass Curve of Rainfall - North & South Johnstone Rivers (March 1996) 144 4.73 Mass Curve of Rainfall - North & South Johnstone Rivers (March 1997) 144 4.74 Mass Curve of Rainfall - North & South Johnstone Rivers (December 1997) 145 4.75 Mass Curve of Rainfall - North & South Johnstone Rivers (January 1998) 145 4.76 Mass Curve of Rainfall - North & South Johnstone Rivers (March 1999) 145 4.77 Mass Curve of Rainfall - North & South Johnstone Rivers (December 1999) 146 4.78 Mass Curve of Rainfall - North & South Johnstone Rivers (February 2000) 146 4.79 Mass Curve of Rainfall - North & South Johnstone Rivers (April 2000) 146 4.80 Rainfall Isohyets (mm) - North & South Johnstone Rivers (March 1990) 148 4.81 Rainfall Isohyets (mm) - North & South Johnstone Rivers (January 1994) 148 4.82 Rainfall Isohyets (mm) - North & South Johnstone Rivers (March 1996) 149 4.83 Rainfall Isohyets (mm) - North & South Johnstone Rivers (March 1997) 149 4.84 Rainfall Isohyets (mm) - North & South Johnstone Rivers (December 1997) 150 4.85 Rainfall Isohyets (mm) - North & South Johnstone Rivers (January 1998) 150 4.86 Rainfall Isohyets (mm) - North & South Johnstone Rivers (March 1999) 151 4.87 Rainfall Isohyets (mm) - North & South Johnstone Rivers (December 1999) 151 4.88 Rainfall Isohyets (mm) - North & South Johnstone Rivers (February 2000) 152 4.89 Rainfall Isohyets (mm) - North & South Johnstone Rivers (April 2000) 152 4.90 Actual and Estimated rating curves for Mary River at Gympie 156 4.91 Total flood hydrograph for Mary River at Gympie (February 1995) 156 4.92 Recession curve of Mary River at Gympie (February 1995) 157 4.93 Base flow Separation of Mary River at Gympie (February 1995) 157 4.94 Surface runoff hydrograph of Mary River at Gympie (February 1995) 158 4.95 Actual and Estimated rating curves for Haughton River at Powerline 159 4.96 Recession curve of Haughton River at Powerline (February 1997) 159 4.97 Base flow separation of Haughton River at Powerline (February 1997) 160 4.98 Runoff hydrograph of Haughton River at Powerline (February 1997) 160 4.99 Actual and Estimated rating curves of Herbert River at Zattas 161 4.100 Recession curve of Herbert River at Zattas (December 1991) 161 4.101 Base flow separation of Herbert River at Zattas (December 1991) 162 4.102 Runoff hydrograph of Herbert River at Zattas (December 1991) 162

xiii

4.103 Actual and Estimated rating curves of Don River at Reeves 163 4.104 Recession curve of Don River at Reeves (April 1989) 163 4.105 Base flow separation of Don River at Reeves (April 1989) 164 4.106 Runoff hydrograph of Don River at Reeves (April 1989) 164 4.107 Actual and Estimated rating curves of North Johnstone River at Tung Oil 165 4.108 Recession curve of North Johnstone River at Tung Oil (March 1996) 165 4.109 Base flow separation of North Johnstone River at Tung Oil (March 1996) 166 4.110 Runoff hydrograph of North Johnstone River at Tung Oil (March 1996) 166 The Figures 4.111 to 4.384 are contained in Appendix C of the CD

5.1 Sub-areas of Mary River at Gympie 178 5.2 Hyetograph and hydrograph of Mary River at Gympie (April 1989) 180 5.3 Surface runoff and computer generated hydrographs of Mary River at Gympie (April 1989) 180 5.4 Hyetograph and Hydrograph of Mary River at Gympie (December 1991) 181 5.5 Surface runoff and computer generated hydrographs of Mary River at Gympie (December 1991) 181 5.6 Hyetograph and hydrograph of Mary River at Gympie (February 1992) 182 5.7 Surface runoff and computer generated hydrographs of Mary River at Gympie (February 1992) 182 5.8 Hyetograph and hydrograph of Mary River at Gympie (March 1992) 183 5.9 Surface runoff and computer generated hydrographs of Mary River at Gympie (March 1992) 183 5.10 Hyetograph and hydrograph of Mary River at Gympie (February 1995) 184 5.11 Surface runoff and computer generated hydrographs of Mary River at Gympie (February 1995) 184 5.12 Hyetograph and hydrograph of Mary River at Gympie (January 1996) 185 5.13 Surface runoff and computer generated hydrographs of Mary River at Gympie (January 1996) 185 5.14 Hyetograph and hydrograph of Mary River at Gympie (April 1996) 186 5.15 Surface runoff and computer generated hydrographs of Mary River at Gympie (April 1996) 186 5.16 Hyetograph and hydrograph of Mary River at Gympie (March 1997) 187 5.17 Surface runoff and computer generated hydrographs of Mary River at Gympie (March 1997) 187 The Figures 5.18 to 5.85 are contained in part 1 of Appendix E of the CD 5.86 Schematic of Haughton River at Powerline 189 5.87 Hyetograph and hydrograph of Haughton River at Powerline (January 1994) 190 5.88 Surface runoff and computer generated hydrographs of Haughton River at Powerline (January 1994) 190 5.89 Hyetograph, hydrograph and selected events of Haughton River at Powerline (January 1996) 191 5.90 Surface runoff and computer generated hydrographs of Haughton River at Powerline (January 1996) 191 5.91 Hyetograph and hydrograph of Haughton River at Powerline (February 1997) 192 5.92 Surface runoff and computer generated hydrographs of Haughton River at Powerline (February 1997) 192

xiv

5.93 Hyetograph and hydrograph of Haughton River at Powerline (March 1997) 193 5.94 Surface runoff and computer generated hydrographs of Haughton River at Powerline (March 1997) 193 5.95 Hyetograph, hydrograph and selected events of Haughton River at Powerline (August 1998) 194 5.96 Surface runoff and computer generated hydrographs of Haughton River at Powerline (August 1998) 194 5.97 Hyetograph, hydrograph and selected events of Haughton River at Powerline (February 2000) 195 5.98 Surface runoff and computer generated hydrographs of Haughton River at Powerline (February 2000) 195 5.99 Hyetograph and hydrograph of Haughton River at Powerline (March 2000) 196 5.100 Surface runoff and computer generated hydrographs of Haughton River at Powerline (March 2000) 196 5.101 Hyetograph and hydrograph of Haughton River at Powerline (April 2000) 197 5.102 Surface runoff and computer generated hydrographs of Haughton River at Powerline (April 2000) 197 The Figures 5.103 to 5.120 are contained in part 2 of Appendix E of the CD 5.121 Schematic of Herbert River at Zattas 199 5.122 Hyetograph, hydrograph and selected events of Herbert River at Zattas (February 1991) 200 5.123 Surface runoff and computer generated hydrographs of Herbert River at Zattas (February 1991) 200 5.124 Hyetograph, hydrograph and selected events of Herbert River at Zattas (Early February 2000) 201 5.125 Surface runoff and computer generated hydrographs of Herbert River at Zattas (Early February 2000) 201 5.126 Hyetograph and hydrograph of Herbert River at Zattas (Late February 2000) 202 5.127 Surface runoff and computer generated hydrographs of Herbert River at Zattas (Late February 2000) 202 5.128 Hyetograph, hydrograph and selected events of Herbert River at Zattas (February 2001) 203 5.129 Surface runoff and computer generated hydrographs of Herbert River at Zattas (February 2001) 203 The Figures 5.130 to 5.175 are contained in part 3 of Appendix E of the CD 5.176 Schematic of Don River at Reeves 205 5.177 Hyetograph and hydrograph of Don River at Reeves (April 1989) 206 5.178 Surface runoff and computer generated hydrographs of Don River at Reeves (April 1989) 206 5.179 Hyetograph and hydrograph and selected events of Don River at Reeves (December 1990) 207 5.180 Surface runoff and computer generated hydrographs of Don River at Reeves (December 1990) 207 5.181 Hyetograph and hydrograph of Don River at Reeves (January 1991) 208 5.182 Surface runoff and computer generated hydrographs of Don River at Reeves (January 1991) 208

5.183 Hyetograph and hydrograph and selected events of Don River at Reeves (February 1991) 209 5.184 Surface runoff and computer generated hydrographs of Don River at Reeves (February 1991) 209 5.185 Hyetograph and hydrograph of Don River at Reeves (August 1998) 210 5.186 Surface runoff and computer generated hydrographs of Don River at Reeves (August 1998) 210 5.187 Hyetograph and hydrograph of Don River at Reeves (January 1999) 211 5.188 Surface runoff and computer generated hydrographs of Don River at Reeves (January 1999) 211 5.189 Hyetograph and hydrograph of Don River at Reeves (February 1999) 212 5.190 Surface runoff and computer generated hydrographs of Don River at Reeves (February 1999) 212 5.191 Hyetograph and hydrograph of Don River at Reeves (December1999) 213 5.192 Surface runoff and computer generated hydrographs of Don River at Reeves (December 1999) 213 5.193 Hyetograph and hydrograph and selected events of Don River at Reeves (Early February 2000) 214 5.194 Surface runoff and computer generated hydrographs of Don River at Reeves (Early February 2000) 214 5.195 Hyetograph and hydrograph of Don River at Reeves (Late February 2000) 215 5.196 Surface runoff and computer generated hydrographs of Don River at Reeves (Late February 2000) 215 The Figures 5.197 to 5.230 are contained in part 4 of Appendix E of the CD 5.231 Schematic of North Johnstone River at Tung Oil 217 5.232 Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (March 1990) 218 5.233 Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (March 1990) 218 5.234 Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (January 1994) 219 5.235 Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (January 1994) 219 5.236 Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (March 1996) 220 5.237 Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (March 1996) 220 5.238 Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (March 1997) 221 5.239 Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (March 1997) 221 5.240 Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (December 1997) 222 5.241 Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (December 1997) 222 5.242 Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (January 1998) 223

xvi

5.243 Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (January 1998) 223 5.244 Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (March 1999) 224 5.245 Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (March 1999) 224 5.246 Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (December 1999) 225 5.247 Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (December 1999) 225 5.248 Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (February 2000) 226 5.249 Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (February 2000) 226 5.250 Hyetograph and hydrograph of North Johnstone River at Tung Oil (April 2000) 227 5.251 Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (April 2000) 227 The Figures 5.252to 5.289 are contained in part 5 of Appendix E of the CD

6.1 Lag time versus Discharge for different values of z 247 6.2 Calibrated Lag Parameter (C) for different values of z 248 6.3 C versus QP of Mary River at Gympie (8 values) 250 6.4 C versus QP of Mary River at Moy Pocket (10 values) 251 6.5 C versus QP of Mary River at Bellbird (10 values) 251 6.6 C versus QP of Mary River at Cooran (10 values) 252 6.7 C versus QP of Mary River at Kandanga (9 values) 252 6.8 C versus QP of Haughton River at Powerline (12 values) 252 6.9 C versus QP of Haughton River at Mt. Piccaninny (16 values) 253 6.10 C versus QP of Herbert River at Zattas (7 values) 253 6.11 C versus QP of Herbert River at Nash’s Crossing (17 values) 253 6.12 C versus QP of Herbert River at Gleneagle (9 values) 254 6.13 C versus QP of Herbert River at Silver Valley (17 values) 254 6.14 C versus QP of Don River at Reeves (20 values) 254 6.15 C versus QP of Don River at Mt. Dangar (10 values) 255 6.16 C versus QP of Don River at Ida Creek (20 values) 255 6.17 C versus QP of North Johnstone River at Tung Oil (34 values) 255 6.18 C versus QP of North Johnstone River at Nerada (24 values) 256 6.19 C versus QP of South Johnstone River at Central Mill (21 values) 256 6.20 C versus QP of all 17 catchments for 254 values 257 6.21 C versus QS of Mary River at Gympie (8 values) 258 6.22 C versus QS of Mary River at Moy Pocket (10 values) 259 6.23 C versus QS of Mary River at Bellbird (10 values) 259 6.24 C versus QS of Mary River at Cooran (10 values) 259 6.25 C versus QS of Mary River at Kandanga (9 values) 260 6.26 C versus QS of Haughton River at Powerline (12 Values) 260 6.27 C versus QS of Haughton River at Mt. Piccaninny (16 values) 260

xvii

6.28 C versus QS of Herbert River at Zattas (7 values) 261 6.29 C versus QS of Herbert River at Nash’s Crossing (17 values) 261 6.30 C versus QS of Herbert River at Gleneagle (9 values) 261 6.31 C versus QS of Herbert River at Silver Valley (17 values) 262 6.32 C versus QS of Don River at Reeves (20 values) 262 6.33 C versus QS of Don River at Mt. Dangar (10 values) 262 6.34 C versus QS of Don River at Ida Creek (20 values) 263 6.35 C versus QS of North Johnstone River at Tung Oil (34 values) 263 6.36 C versus QS of North Johnstone River at Nerada (24 values) 263 6.37 C versus QS of South Johnstone River at Central Mill (21 values) 264 6.38 C versus QS of all 17 catchments for 254 values 264 6.39 C versus DT of Mary River at Gympie (8 values) 265 6.40 C versus DT of Mary River at Moy Pocket (10 values) 265 6.41 C versus DT of Mary River at Bellbird (10 values) 266 6.42 C versus DT of Mary River at Cooran (10 values) 266 6.43 C versus DT of Mary River at Kandanga (9 values) 266 6.44 C versus DT of Haughton River at Powerline (12 values) 267 6.45 C versus DT of Haughton River at Mt. Piccaninny (16 values) 267 6.46 C versus DT of Herbert River at Zattas (7 values) 267 6.47 C versus DT of Herbert River at Nash’s Crossing (17 values) 268 6.48 C versus DT of Herbert River at Gleneagle (9 values) 268 6.49 C versus DT of Herbert River at Silver Valley (17 values) 268 6.50 C versus DT of Don River at Reeves (20 values) 269 6.51 C versus DT of Don River at Mt. Dangar (10 values) 269 6.52 C versus DT of Don River at Ida Creek (20 values) 269 6.53 C versus DT of North Johnstone River at Tung Oil (34 values) 270 6.54 C versus DT of North Johnstone River at Nerada (24 values) 270 6.55 C versus DT of South Johnstone River at Central Mill (21 values) 270 6.56 C versus DT of all 17 catchments for 254 values 271 6.57 C versus DT of all 17 catchments for 250 values 271 6.58 C versus DSRO of Mary River at Gympie (8 values) 272 6.59 C versus DSRO of Mary River at Moy Pocket (10 values) 272 6.60 C versus DSRO of Mary River at Bellbird (10 values) 273 6.61 C versus DSRO of Mary River at Cooran (10 values) 273 6.62 C versus DSRO of Mary River at Kandanga (9 values) 273 6.63 C versus DSRO of Haughton River at Powerline (12 values) 274 6.64 C versus DSRO of Haughton River at Mt. Piccaninny (16 values) 274 6.65 C versus DSRO of Herbert River at Zattas (7 values) 274 6.66 C versus DSRO of Herbert River at Nash’s Crossing (17 values) 275 6.67 C versus DSRO of Herbert River at Gleneagle (9 values) 275 6.68 C versus DSRO of Herbert River at Silver Valley (17 values) 275 6.69 C versus DSRO of Don River at Reeves (20 values) 276 6.70 C versus DSRO of Don River at Mt. Dangar (10 values) 276 6.71 C versus DSRO of Don River at Ida Creek (20 values) 276 6.72 C versus DSRO of North Johnstone River at Tung Oil (34 values) 277 6.73 C versus DSRO of North Johnstone River at Nerada (24 values) 277 6.74 C versus DSRO of South Johnstone River at Central Mill (21 values) 277

xviii

6.75 C versus DSRO of all 17 catchments for 254 values 278 6.76 C versus DSRO of all 17 catchments for 248 values 278 6.77 C versus Iav of Mary River at Gympie (8 values) 279 6.78 C versus Iav of Mary River at Moy Pocket (10 values) 279 6.79 C versus Iav of Mary River at Bellbird (10 values) 280 6.80 C versus Iav of Mary River at Cooran (10 values) 280 6.81 C versus Iav of Mary River at Kandanga (9 values) 280 6.82 C versus Iav of Haughton River at Powerline (12 values) 281 6.83 C versus Iav of Haughton River at Mt. Piccaninny (16 values) 281 6.84 C versus Iav of Herbert River at Zattas (7 values) 281 6.85 C versus Iav of Herbert River at Nash’s Crossing (17 values) 282 6.86 C versus Iav of Herbert River at Gleneagle (9 values) 282 6.87 C versus Iav of Herbert River at Silver Valley (17 values) 282 6.88 C versus Iav of Don River at Reeves (20 values) 283 6.89 C versus Iav of Don River at Mt. Dangar (10 values) 283 6.90 C versus Iav of Don River at Ida Creek (20 values) 283 6.91 C versus Iav of North Johnstone River at Tung Oil (34 values) 284 6.92 C versus Iav of North Johnstone River at Nerada (24 values) 284 6.93 C versus Iav of South Johnstone River at Central Mill (21 values) 284 6.94 C versus Iav of all 17 catchments for 254 values 285 6.95 C versus (TPI/DURex) of Mary River at Gympie (8 values) 286 6.96 C versus (TPI/DURex) of Mary River at Moy Pocket (10 values) 286 6.97 C versus (TPI/DURex) of Mary River at Bellbird (10 values) 286 6.98 C versus (TPI/DURex) of Mary River at Cooran (10 values) 287 6.99 C versus (TPI/DURex) of Mary River at Kandanga (9 values) 287 6.100 C versus (TPI/DURex) of Haughton River at Powerline (12 values) 287 6.101 C versus (TPI/DURex) of Haughton River at Mt. Piccaninny (16 values) 288 6.102 C versus (TPI/DURex) of Herbert River at Zattas (7 values) 288 6.103 C versus (TPI/DURex) of Herbert River at Nash’s Crossing (17 values) 288 6.104 C versus (TPI/DURex) of Herbert River at Gleneagle (9 values) 289 6.105 C versus (TPI/DURex) of Herbert River at Silver Valley (17 values) 289 6.106 C versus (TPI/DURex) of Don River at Reeves (20 values) 289 6.107 C versus (TPI/DURex) of Don River at Mt. Dangar (10 values) 290 6.108 C versus (TPI/DURex) of Don River at Ida Creek (20 values) 290 6.109 C versus (TPI/DURex) of North Johnstone River at Tung Oil (34 values) 290 6.110 C versus (TPI/DURex) of North Johnstone River at Nerada (24 values) 291 6.111 C versus (TPI/DURex) of South Johnstone River at Central Mill (21 values) 291 6.112 C versus (TPI/DURex) of all 17 catchments for 254 values 291 6.113 C versus (AvPI) of Mary River at Gympie (8 values) 292 6.114 C versus (AvPI) of Mary River at Moy Pocket (10 values) 293 6.115 C versus (AvPI) of Mary River at Bellbird (10 values) 293 6.116 C versus (AvPI) of Mary River at Cooran (10 values) 293 6.117 C versus (AvPI) of Mary River at Kandanga (9 values) 294 6.118 C versus (AvPI) of Haughton River at Powerline (12 values) 294 6.119 C versus (AvPI) of Haughton River at Mt. Piccaninny (16 values) 294 6.120 C versus (AvPI) of Herbert River at Zattas (7 values) 295 6.121 C versus (AvPI) of Herbert River at Nash’s Crossing (17 values) 295

xix

6.122 C versus (AvPI) of Herbert River at Gleneagle (9 values) 295 6.123 C versus (AvPI) of Herbert River at Silver Valley (17 values) 296 6.124 C versus (AvPI) of Don River at Reeves (20 values) 296 6.125 C versus (AvPI) of Don River at Mt. Dangar (10 values) 296 6.126 C versus (AvPI) of Don River at Ida Creek (20 values) 297 6.127 C versus (AvPI) of North Johnstone River at Tung Oil (34 values) 297 6.128 C versus (AvPI) of North Johnstone River at Nerada (24 values) 297 6.129 C versus (AvPI) of South Johnstone River at Central Mill (21 values) 298 6.130 C versus (AvPI) of all 17 catchments for 254 values 298 6.131 C versus (Dex/DT) of Mary River at Gympie (8 values) 299 6.132 C versus (Dex/DT) of Mary River at Moy Pocket (10 values) 299 6.133 C versus (Dex/DT) of Mary River at Bellbird (10 values) 300 6.134 C versus (Dex/DT) of Mary River at Cooran (10 values) 300 6.135 C versus (Dex/DT) of Mary River at Kandanga (9 values) 300 6.136 C versus (Dex/DT) of Haughton River at Powerline (12 values) 301 6.137 C versus (Dex/DT) of Haughton River at Mt. Piccaninny (16 values) 301 6.138 C versus (Dex/DT) of Herbert River at Zattas (7 values) 301 6.139 C versus (Dex/DT) of Herbert River at Nash’s Crossing (17 values) 302 6.140 C versus (Dex/DT) of Herbert River at Gleneagle (9 values) 302 6.141 C versus (Dex/DT) of Herbert River at Silver Valley (17 values) 302 6.142 C versus (Dex/DT) of Don River at Reeves (20 values) 303 6.143 C versus (Dex/DT) of Don River at Mt. Dangar (10 values) 303 6.144 C versus (Dex/DT) of Don River at Ida Creek (20 values) 303 6.145 C versus (Dex/DT) of North Johnstone River at Tung Oil (34 values) 304 6.146 C versus (Dex/DT) of North Johnstone River at Nerada (24 values) 304 6.147 C versus (Dex/DT) of South Johnstone River at Central Mill (21 values) 304 6.148 C versus (Dex/DT) of all 17 catchments for 254 values 305 6.149 C versus (IP/Iav) of Mary River at Gympie (8 values) 306 6.150 C versus (IP/Iav) of Mary River at Moy Pocket (10 values) 306 6.151 C versus (IP/Iav) of Mary River at Bellbird (10 values) 306 6.152 C versus (IP/Iav) of Mary River at Cooran (10 values) 307 6.153 C versus (IP/Iav) of Mary River at Kandanga (9 values) 307 6.154 C versus (IP/Iav) of Haughton River at Powerline (12 values) 307 6.155 C versus (IP/Iav) of Haughton River at Mt. Piccaninny (16 values) 308 6.156 C versus (IP/Iav) of Herbert River at Zattas (7 values) 308 6.157 C versus (IP/Iav) of Herbert River at Nash’s Crossing (17 values) 308 6.158 C versus (IP/Iav) of Herbert River at Gleneagle (9 values) 309 6.159 C versus (IP/Iav) of Herbert River at Silver Valley (17 values) 309 6.160 C versus (IP/Iav) of Don River at Reeves (20 values) 309 6.161 C versus (IP/Iav) of Don River at Mt. Dangar (10 values) 310 6.162 C versus (IP/Iav) of Don River at Ida Creek (20 values) 310 6.163 C versus (IP/Iav) of North Johnstone River at Tung Oil (34 values) 310 6.164 C versus (IP/Iav) of North Johnstone River at Nerada (24 values) 311 6.165 C versus (IP/Iav) of South Johnstone River at Central Mill (21 values) 311 6.166 C versus (IP/Iav) of all 17 catchments for 254 values 311 6.167 C versus (DBC/DTC) of Mary River at Gympie (8 values) 313 6.168 C versus (DBC/DTC) of Mary River at Moy Pocket (10 values) 313

6.169 C versus (DBC/DTC) of Mary River at Bellbird (10 values) 314 6.170 C versus (DBC/DTC) of Mary River at Cooran (10 values) 314 6.171 C versus (DBC/DTC) of Mary River at Kandanga (9 values) 314 6.172 C versus (DBC/DTC) of Haughton River at Powerline (12 values) 315 6.173 C versus (DBC/DTC) of Haughton River at Mt. Piccaninny (16 values) 315 6.174 C versus (DBC/DTC) of Herbert River at Zattas (7 values) 315 6.175 C versus (DBC/DTC) of Herbert River at Nash’s Crossing (17 values) 316 6.176 C versus (DBC/DTC) of Herbert River at Gleneagle (9 values) 316 6.177 C versus (DBC/DTC) of Herbert River at Silver Valley (17 values) 316 6.178 C versus (DBC/DTC) of Don River at Reeves (20 values) 317 6.179 C versus (DBC/DTC) of Don River at Mt.Dangar (10 values) 317 6.180 C versus (DBC/DTC) of Don River at Ida Creek (20 values) 317 6.181 C versus (DBC/DTC) of North Johnstone River at Tung Oil (34 values) 318 6.182 C versus (DBC/DTC) of North Johnstone River at Nerada (24 values) 318 6.183 C versus (DBC/DTC) of South Johnstone River at Central Mill (21values) 318 6.184 C versus (DBC/DTC) of all 17 catchments (254 values) 319 6.185 C versus (DBC/DTC) of 229 values (excluding C and DBC/DTC values larger than 2.5) 319

7.1 C versus A of all seventeen catchments 325 7.2 C versus A of twelve catchments 326 7.3 C versus Sc of all seventeen catchments 328 7.4 C versus Sc of fifteen catchments 329 7.5 C versus Sc of fourteen catchments 330 7.6 C versus L of all seventeen catchments 332 7.7 C versus L of fifteen catchments 333 7.8 C versus (A/L2) of all seventeen catchments 335 7.9 C versus (A/L2) of fifteen catchments 336 7.10 C versus Lc of all seventeen catchments 338 7.11 C versus Lc of fifteen catchments 339 7.12 C versus (Lc/L) of all seventeen catchments 342 7.13 C versus (Lc/L) of fifteen catchments 343 7.14 C versus (Lc/L) of fourteen catchments 344 7.15 C versus (No.RD/yr) of all seventeen catchments 346 7.16 C versus (No.RD/yr) of fifteen catchments 347 7.17 C versus (ARMean) of all seventeen catchments 349 7.18 C versus (ARMean) of fifteen catchments 350 2 7.19 C versus ( I72) of all seventeen catchments 352 2 7.20 C versus ( I72) of fifteen catchments 353 2 7.21 C versus ( I72) of fourteen catchments 354 7.22 C versus (ELMean) of all seventeen catchments 356 7.23 C versus (ELMean) of fifteen catchments 357 7.24 C versus (ELCentroid) of all seventeen catchments 359 7.25 C versus (ELCentroid) of fifteen catchments 360

xxi

LIST OF TABLES No. Description Page

2.1 Summary of equations of various researchers related to lag time 67 2.2 Summary of equations reduced to common forms of different physical and hydrological characteristics of catchments 70

3.1 List of Catchments 73

4.1 Summary of Rainfall for Mary River 99 4.2 Assessment Summary of Temporal Patterns of Rainfall – Mary Basin 103 4.3 Summary of Rainfall for Haughton River 111 4.4 Assessment Summary of Temporal Patterns of Rainfall – Haughton Basin 114 4.5 Summary of Rainfall for Herbert River 121 4.6 Assessment Summary of Temporal Patterns of Rainfall – Herbert Basin 124 4.7 Summary of Rainfall for Don River Basin 4.8 Assessment Summary of Temporal patterns of Rainfall – Don Basin 135 4.9 Summary of Rainfall for North and South Johnstone Rivers 143 4.10 Assessment Summary of Temporal Patterns of Rainfall – Johnstone Basin 147

5.1 Details of seventeen catchments selected for the study 170 5.2 Co-ordinates of centroids of sub-catchments of WBNM input file of Mary River at Gympie 171 5.3 Sub-areas and lag parameter of WBNM input file of Mary River at Gympie of 11th February 1995 Storm 172 5.4 Names of ten rainfall stations, co-ordinates and their respective rainfall depths of WBNM input file of Mary River at Gympie of 11th February 1995 Storm 173 5.5 Sub-areas and their loss rates of WBNM input file of Mary River at Gympie (11th February 1995 Storm) 177 5.6 Ordinates of surface runoff hydrograph of Mary River at Gympie of 11th February 1995 storm 178 5.7 Flow and runoff details and lag parameters of eight storms of Mary River at Gympie 188 5.8 Flow and runoff details and lag parameters of eight storms of Haughton River at Powerline 198 5.9 Flow and runoff details and lag parameters of four storms of Herbert River at Zattas 204 5.10 Flow & runoff details and lag parameters of ten storms of Don River at Reeves 216 5.11 Flow & runoff details and lag parameters of ten storms of North Johnstone River at Tung Oil 228 5.12 Summary of Storms of Mary River at Gympie 229 5.13 Summary of Storms of Mary River at Moy Pocket 230 5.14 Summary of Storms of Mary River at Bellbird 231 5.15 Summary of Storms of Sixth Mile Creek (Tributary of Mary River) at Cooran 232 5.16 Summary of Storms of Kandanga Creek (Tributary of Mary River) at Kandanga 233

xxii

5.17 Summary of Storms of Haughton River at Powerline 234 5.18 Summary of Storms of Haughton River at Mount Piccaninny 235 5.19 Summary of Storms of Herbert River at Zattas 236 5.20 Summary of Storms of Herbert River at Nash’s Crossing 237 5.21 Summary of Storms of Herbert River at Gleneagle 238 5.22 Summary of Storms of Herbert River at Silver Valley 239 5.23 Summary of Storms of Don River at Reeves 240 5.24 Summary of Storms of Don River at Mount Dangar 241 5.25 Summary of Storms of Don River at Ida Creek 242 5.26 Summary of Storms of North Johnstone River at Tung Oil 243 5.27 Summary of Storms of North Johnstone River at Nerada 244 5.28 Summary of Storms of South Johnstone River at Central Mill 245

6.1 t-test calculations of C versus Qp of Mary River at Gympie 250 6.2 t-test calculations of C versus QS of Mary River at Gympie 258 6.3 Signs of gradients and significance of plots of C versus Storm (Hydrological) characteristics 322

7.1 t-test calculations for C versus A of all seventeen catchments 325 7.2 t-test calculations for C versus A of twelve catchments 326 7.3 t-test calculations for C versus Sc of all seventeen catchment 328 7.4 t-test calculations for C versus Sc of fifteen catchments 329 7.5 t-test calculations for C versus Sc of fourteen catchments 330 7.6 t-test calculations for C versus L of all seventeen catchments 332 7.7 t-test calculations for C versus L of fifteen catchments 333 7.8 t-test calculations for C versus (A/L2) of all seventeen catchments 335 7.9 t-test calculations for C versus (A/L2) of fifteen catchments 336 7.10 t-test calculations for C versus Lc of all seventeen catchments 338 7.11 t-test calculations for C versus Lc of fifteen catchments 339 7.12 t-test calculations for C versus (Lc/L) of all seventeen catchments 342 7.13 t-test calculations for C versus (Lc/L) fifteen catchments 343 7.14 t-test calculations for C versus (Lc/L) fourteen catchments 344 7.15 t-test calculations for C versus (No. RD/yr) of all seventeen catchments 346 7.16 t-test calculations for C versus (No.RD/yr) of fifteen catchments 347 7.17 t-test calculations for C versus (ARMean) of all seventeen catchments 349 7.18 t-test calculations for C versus (ARMean) of fifteen catchments 350 2 7.19 t-test calculations for C versus ( I72) of all seventeen catchments 352 2 7.20 t-test calculations for C versus ( I72) of fifteen catchments 353 2 7.21 t-test calculations for C versus ( I72) of fourteen catchments 354 7.22 t-test calculations for C versus (ELMean) of all seventeen catchments 356 7.23 t-test calculations for C versus (ELMean) of fifteen catchments 357 7.24 t-test calculations for C versus (ELCentroid) of all seventeen catchments 359 7.25 t-test calculations for C versus (ELCentroid) of fifteen catchments 360 7.26 Statistical data of Mary River and the remaining basins selected for this study 361 7.27 Summary of Soil properties of five Major basins 366 7.28 Physical characteristics and details of all seventeen catchments 370

xxiii

PAPERS IN PREPARATION:

(1) Bodhinayake, N. D. and Boyd, M. J. “WBNM Lag Parameters for Queensland Rural Catchments”, 30th Hydrology and Water Resources Symposium, Institution of Engineers, Australia

(2) Boyd, M. J. and Bodhinayake, N. D. “WBNM Lag Parameters for Eastern Australia”, Australian Journal of Water Resources

CHAPTER 1

INTRODUCTION

1. INTRODUCTION

The rainfall and runoff process is a key feature in the study of hydrology. In this process rivers play a prominent role, since they are the primary means of transporting water from the land into the ocean. Rainfall as the source of rivers was discovered for the first time in the seventeenth century. In that period a French engineer, Mariotte, measured the rainfall and stream flow in the river Seine and proved that the rainfall provides sufficient amount of water to produce flow in the rivers. Since that time researchers, as well as engineering practitioners have been interested in finding a valid, reliable and accurate relationship between rainfall and runoff. In those studies the peak of the river flow became an important factor.

Associated with these relationships has been the time delay between the beginning of the rise of the flow due to excess rainfall and the peak flow (often expressed in terms of the lag time) of rivers. This has been considered as a vital issue for flood mitigation in rural and urban catchments. The lag time is intimately related to the prediction of the storm rainfall-runoff process, since many models of this process use a lag time or lag parameter. The majority of researchers have introduced a lag parameter (commonly called a scaling factor) into their equations of lag time, which consist of the physical and storm characteristics of catchments. Typical models which use lag time in this process are RORB and WBNM and their respective lag time equations are:

0.50 -0.25 tL = K A Q (1.1) 0.57 -0.23 tL = C A Q (1.2)

Where, tL is the lag time; K and C are lag parameters; A is the catchment area; and Q is the discharge in the main channel of catchment.

This research investigates the effect of hydrological, geomorphological and climatological characteristics of natural catchments (sizes range from 165km2 to 7292 km2) on the lag parameter. Rainfall and stream flow data for the last ten to fifteen years, collected from the Bureau of Meteorology, Queensland, Australia, for seventeen 2

catchments are used for this study. These catchments are from five major river basins, namely Mary, Haughton, Herbert, Don, and Johnstone.

Chapter 2 of this thesis reviews investigations carried out by various researchers from different countries of the world related to lag time. It has been observed from the equations derived by a majority of researchers, from the latter part of the 19th century onwards, that the hydrological and geomorphological characteristics have a substantial influence on lag time. It is important to note that the relationships related to lag time, found by many of the researchers are non-linear. This means that the lag time varies with the size of the flood.

Chapter 3 describes the physical properties of the five major river basins. These physical properties cover the land use, developed areas, topsoil and subsoil properties, climatic conditions and texture of soils of catchments. Most of this information is available in the National Resource Atlas of Australia, which can be found from the website http://audit.ea.gov.au/ANRA/atlas_home.cfm. The other physical properties such as the extent of mountainous terrains, valleys and elevations at various locations on catchments are found from the information provided by the AUSLIG maps of Australia.

Chapter 4, the validity and the reliability of the rainfall data of 42 storms on five major basins (shown in Tables 4.1, 4.3, 4.5, 4.7 and 4.9) are assessed by plotting the mass curves for all rainfall stations, in order to investigate temporal patterns. To examine the spatial variation of rainfall pattern within each basin, isohyets for all 42 storms are plotted for all five basins. Stream gauge rating data are used to derive equations for rating curves of all seventeen catchments. As described in the latter part of Chapter 4, flood discharge hydrographs for all seventeen catchment outlets are then derived by applying the rating curve equations to recorded river stage hydrographs.

In Chapter 5, the 42 storms are separated into individual bursts for analysis over the seventeen catchments. A total of 254 bursts (events) have been extracted through this process. The initial loss (the amount of rainfall which occurs before the beginning of surface runoff) is calculated for each selected storm of each catchment by examining its 3

rainfall hyetograph and the resulting flood discharge hydrograph, which are plotted on the same graph for easy reference. To calculate the ordinates of the surface runoff hydrographs, the base flow is subtracted by means of semi-log plots of recession limbs of the hydrographs.

All seventeen catchments are divided into their sub-catchments by examining their stream flow and the surface contour patterns, which are demarcated in the AUSLIG maps (scale 1:100000) of Australia. The objective of this activity is to make a meaningful sequential flow network to allow runoff from the sub-catchment to flow to the catchment outlet. The co-ordinates of the centroids of the sub-catchments and the locations of the rainfall stations, of all seventeen catchments, are measured from these maps.

The calculated and measured values of the storm and catchment features described in the two previous paragraphs are used to derive the lag parameter for each storm event by calibrating the WBNM computer model. This is described in Chapter 5.

Special attention is focussed on the reliability of equation 1.2, which is used for calculating the lag time in the flood hydrograph model WBNM by plotting curves of the lag parameter (C) with different exponents of discharge (Q) as well as different exponents of the catchment area (A). This is illustrated in the early parts of Chapters 6 and 7.

With the intention of finding out whether the catchment area (A) and the discharge (Q) are adequate to describe the lag time, or whether other hydrological, geomorphological or climatological characteristics of the catchment should be considered in the equations of lag time, a number of catchment characteristics are investigated, and their relationship with the lag parameter C is tested. This is explained in Chapters 6 and 7. Furthermore, visual investigations of plots of lag parameter versus catchment characteristics (storm and physical), as well as two tailed statistical significance tests, are carried out to determine whether the gradients of the best-fit straight lines of those plots are significantly different from zero. 4

Carefully assessing all the results obtained from this study, appropriate conclusions are made. Generally, the findings from the plots of lag parameter (C) versus the range of storm and physical characteristics revealed that none of them are strongly related to lag parameter. Therefore, the findings indicate that the lag time equation in WBNM is satisfactory for flood prediction in this part of Australia.

Most previous studies of catchment lag time have only considered a limited number of storm and catchment variables, and often used a limited set of data. This study used a large number of storms and catchments, and systematically examined the effect of a large number of storm variables, as well as a large number of catchment variables on the lag parameter. Therefore, this investigation provides considerable confidence on the relative effects of the various variables on the lag parameter.

CHAPTER 2

LITERATURE REVIEW

2. LITERATURE REVIEW ON RELATIONS BETWEEN LAG TIME AND HYDROLOGICAL, GEOMORPHOLOGICAL AND CLIMATOLOGICAL CHARACTERISTICS OF CATCHMENTS

2.1 Introduction A thorough investigation of hydrological, geomorphological and climatological characteristics of natural and urban catchments is necessary to make logical and acceptable recommendations related to the rainfall and runoff process. One of the factors that govern this process is the lag time. The lag time may be represented in many ways and some of them are: the time of concentration, time to peak flow, base length of a hydrograph, and as many researchers have considered, the distance from the centroid of excess rainfall hyetograph to that of the resulting hydrograph of the outflow.

Objectives of this literature review are to find out: • what types of empirical, graphical and analytical methods have been developed by various researchers to assess the lag time of catchments; • what types of relations between lag time and storm & physical characteristics of catchments have been found; • to what extent these methods have been applied in different parts of the world; and • the type of studies carried out by various researchers to verify the validity of the methods adopted to estimate the lag time in different catchments.

The following methods and techniques have been developed by various researchers from the beginning of the 20th Century to estimate the lag time of natural, semi-urban and urban catchments in different parts of the world: a) The Rational Method – Lloyd-Davis (1906) b) The Tangent Method – Reid (1927) & Norris (1946) c) The Time-area Method – Ross (1921) d) The Unit hydrograph Theory – Sherman (1932) (i) The S-curve Theory – Sherman (1932) (ii) The unit hydrograph as a percentage distribution of rainfall – Bernard (1935) (iii) The synthetic unit hydrograph – Snyder (1938) 6

(iv) The instantaneous unit hydrograph – Clark (1945) (v) The unit hydrograph from complex or multi-period storms – Linsley et al., (1946) e) Linear and non-linear models, including (i) Clark’s linear model (1945) (ii) Rockwood’s non-linear model (1958) (iii) Nash’s linear model (1960) (iv) Laurenson’s non-linear model (1964) (v) Pedersen’s single linear reservoir model (1978) (vi) RORB non-linear model – Mein et al., (1974); Laurenson and Mein (1985) (vii) RSWM or RAFTS non-linear model– Goyen and Aitken (1976) (viii) WBNM non-linear model – Boyd, Pilgrim and Cordery (1979) and Boyd, Rigby and Van Drie (2000)

The findings of the various studies, which are related to lag time in natural catchments, carried out by a number of researchers are discussed in detail in the next part of this chapter. All equations in this chapter have been expressed in metric units, for example L 2 (km), A (km ) and Sc (m/km). The list of references related to studies of various researchers is shown at the end of this thesis.

The following common symbols are applicable to most of the equations derived by various researchers described in this chapter: A = Catchment area (km2).

CR = Coefficient of runoff.

IR = Rainfall intensity (mm/hr). I = Inflow to channel (m3/sec).

Iex = Excess rainfall intensity (mm/hr). L = Length of main stream (km).

Lca = Length to centroid from outlet of catchment (km). n = Manning’s coefficient of roughness.

no = Overland roughness coefficient. OLS = Overland slope (m/km). 3 Qt = Outflow at time‘t’(m /sec). 7

Q = Main stream flow (m3/sec). S = Storage (m3).

Sc = Equal area slope of main stream (m/km).

tc = Time of concentration (hrs).

tL = Lag time (hrs). The other symbols used in the equations are defined under each study described in this chapter.

2.2 Rational Method According to “Australian Rainfall and Runoff (AR&R) 1997,” (Institution of Engineers, Australia) this method was introduced by T. J. Mulvaney in Ireland over 120 years ago. Although a considerable amount of assumptions have been made in the process of the development of this method, it became very popular due to its simplicity. This method allows the calculation of peak discharge, by considering the physical and hydrologic characteristics of rural and urban catchments. In this method the time of concentration is assumed to be equal to the duration of the rainfall. The Rational Method formula is given by:

Q = F CR IR A (2.1) Where, F is the unit conversion factor.

Using the Rational method, Kerby (1959) developed a nomograph to estimate the time of concentration after investigating the charts produced by Hathaway in 1945. He indicated in his paper that due to unavailability of a considerable amount of data, time of concentration had to be guessed by engineers during that time.

By incorporating the slope of the main stream of catchment and considering overland flow as a function of the product of ‘n’ and ‘L’, Kerby, introduced the following empirical formula to calculate the time of concentration: 0.47 0.47 -0.23 tc = 3.03 n L Sc (2.2)

Ragan and Duru (1972) used the Kinematic wave theory to develop a nomograph to estimate the time of concentration. They pointed out that, although Kerby has not considered the rainfall intensity in his nomograph, it has an influence on the time of concentration. The influence of the rainfall intensity on time of concentration has also 8

been demonstrated from the overland flow experiments conducted by Corps of Engineers (1954) and Izzard (1964), as mentioned by Ragan and Duru. They introduced the following equation: 0.6 -0.4 0.6 -0.3 tc = 57.8 n IR L Sc (2.3) Ragan and Duru evaluated their nomograph by comparing computed time of concentration with those obtained experimentally by Izzard (1964) and Corps of Engineers (1954). Although it is difficult to obtain a true time of concentration value from experimental data, the study gave them satisfactory results.

The reliability and validity of the Rational Method as a statistical design procedure have been verified with field data from 37 rural catchments (areas less than 250 km2 and situated in Central and South Eastern NSW, Australia), by French et al., (1974). They used the following formulae for their verification:

Name of Formula Formula for time of concentration 0.77 -0.385 Ramser-Kirpich tc = 0.94 L Sc (2.4) -0.1 -0.20 Bransby Williams tc = 0.97 L A Sc (2.5) 0.5 McIllwraith tc = 0.62 F A + 0.7 (2.6) 0.33 Bell tc = 0.73 B A (2.7) 0.40 Hoyt and Langbein tc = 0.68 B1 A (2.8) 0.47 0.47 -0.23 Bruce and Clark tc = 3.05 n L Sc (2.9) -1.0 -0.15 -0.1 -0.4 Friend tc = 52.7(ch) (CR Fy K s) L A Sc (2.10) -1.0 Distance/Velocity tc = 0.278 L V (2.11)

Where, F = Slope factor; B & B1 = Catchment cover factors; ch = Chezy coefficient;

Fy = Frequency factor; K = Rainfall factor and s = Shape factor.

French et al., indicated that, although the results of the study showed fairly poor correlation between the estimated time of concentration and the time of rise of observed hydrographs, the Rational Method can be used as a statistical design procedure.

The studies related to flood estimation in small rural catchments in NSW, Australia, were carried out by Pilgrim and McDermott (1982), and suggested that the Rational 9

Method is very effective for rural catchments with areas less than 250km2. They devised the following formula for time of concentration by studying 308 gauged rural catchments in NSW, Queensland and Victoria and a majority of them are in the Eastern NSW, Australia, as indicated in their paper: 0.38 tc = 0.76 A (2.12) The above equation has been recommended for NSW catchments by AR&R (1989 and 1998).

The Rational Method was tested for small and rural catchments in the Southwest of Western Australia by Flavell (1983). The available data was used to derive a design procedure for estimating design floods for catchments up to 250 km2.

At the beginning of the study 36 Jarrah forest catchments were considered and later that number was increased to 48. These catchments are covered with various types of vegetation. The best formula recommended by Flavell (1983) for time of concentration is: 0.54 tc = 2.31 A (2.13) Furthermore, this is one of the equations recommended by the AR&R (1998) to estimate the time of concentration particularly for the catchments in Western Australia.

Black et al., (1986) applied a Statistical Rational Method to verify its suitability for catchments larger than 250km2. Their study confined to the following four phases: (i) Relationships of catchment characteristics; (ii) Flood frequency analysis; (iii) Rainfall Intensity analysis; and (iv) Runoff coefficient analysis.

They used 20 catchments (areas ranging from 3.05km2 to 940km2) in Australia and five of them are in excess of 250km2, and also half of the catchments are above 100 km2. The following relationships were found from the major catchment parameters and they are similar to the relationships found by Gray (1961), Boyd (1978) and McDermott & Pilgrim (1982): L = 1.09 A0.67 (2.14) -0.61 Sc = 47.42 L (2.15) 10

-0.42 Sc = 47.80 A (2.16) The peak discharges were extracted for 2, 5, 10, 50 and 100 year ARIs, by fitting the partial duration flood series with a log Pearson Type III distribution. With the intention of calculating intensities for selected ARI values and durations (tc) by using the sixth order polynomial equation recommended by the “Australian Rainfall and Runoff (1977)” the following equations were derived to estimate the time of concentration: 0.65 tc = 0.487 A (2.17) 0.49 Tm = 1.00 A (2.18) 0.56 -1.0 tc = 4.752 L Sc (2.19) In the process of deriving these equations the suitability of Bransby-Williams formula as well as the relation of tc with the major catchment parameters were examined. After re-examining these formulae, the following formula was suggested for Adelaide Hills: 0.65 tc = 0.50 A (2.20) The runoff coefficients for all catchments, which were calculated by using the Rational Method with flow data, have shown no significant increase with increasing recurrence intervals. Therefore, there is no mathematical reason to make changes to the runoff coefficients for increasing ARI values. Further investigations, related to the variation of time of concentration with independent variables, revealed the following results: 0.58 -0.17 tc = 0.95 A L (2.21) -0.113 -0.215 1.015 tc = 1.02 A Sc L (2.22)

Although very high correlations between tc and catchment parameters A, L and Sc have been observed, they recommended the equation (2.20) for the Adelaide Hills environs, due to its simplicity. They also indicated that considerable caution is required in the application of the 50 and 100 year ARI design data.

Papadakis and Kazan (1987) evaluated eleven empirical and theoretical equations (derived by Kirpich, Izzard, Kerby/Hathaway, Carter, Eagleson, Kinematic Wave, Morgali & Linsley, Federal Aviation Agency (FAA), SCS Curve Number, SCS Velocity Chart, and the Singh’s Kinematic Wave & Chezy formulae). They used these equations to compute the time of concentration and then compared those equations with the equations derived by them. They emphasised the importance of the main channel discharge (related to the rainfall intensity and the storm duration for a given ARI) 11

especially for design purposes. They further indicated that the maximum discharge occurs when the duration of rainfall is equal to the time of concentration.

In the first phase of their study they were involved in an extensive literature search, which revealed that a larger amount of equations have been developed to compute the time of concentration. Most of those equations share the following general formula: a b -y -z tc = K L no Sc Iex (2.23) where, K is a constant. The data used for this study are:

• The measured length (L) and the average slope (Sc) of flow path of 84 natural

catchments of USA as well as the roughness coefficient (no), excess rainfall

intensity (Iex) and time of concentration (tc) of those catchments obtained from the US department of Agriculture;

• The L, Sc and applied rainfall intensity and measured time of equilibrium obtained from the tests carried out by Corps of Engineers from 1948 to 1952 at the Santa Monica Municipal Airport for 162 small watersheds. In these 162 watersheds, 89 were involved with simulated concrete surfaces and the remaining 73 were simulated with turf surfaces. The roughness coefficients of all surfaces were known;

• The values of L, Sc, no, Iex and tc were found from 93 experimental watersheds constructed at the Engineering Research Centre of Colorado State University; and • Another similar set of data is obtained from 36 laboratory tests carried out at the University of Illinois Urbana-Champaign. Papadakis and Kazan developed the following time of concentration equations: 0.52 0.50 -0.31 -0.38 tc = 0.25 no L Sc Iex (2.24) 0.52 0.52 -0.35 -0.35 tc = 0.16 no L Sc Iex (2.25) The data of 375 natural and simulated catchments (areas less than 2.02km2) specified previously were used to compare the results obtained from these two equations as well as the eleven equations developed by researchers and the research organisations described earlier. Their findings revealed the following:

• The exponents of L, Sc and Iex of equation (2.24) agree ±20%, ±25%, and ±15% with the respective parameters of the equations of Carter, Kinematic Wave, Morgali, FAA and Kerby; Izzard, FAA, Kerby, Carter, Kinematic Wave, Morgali and Singh; and Kinematic Wave, Morgali and Singh; and 12

• The equation (2.24) has more general applicability compared to the Kinematic wave equation (2.3) which is suitable to estimate time of concentration for very small watersheds where surface flow dominates.

As indicated by Weeks (1991) in his paper, the following researchers have tested the Rational Method for its accuracy on time of concentration and found satisfactory results: # Pilgrim and Mc Dermott (1982) - Over 300 catchments in NSW - areas less than 250km2 # Adams (1987) - Over 300 catchments in Victoria - no limit on catchment size # Flavell et al., (1987) - 48 catchments in Western Australia - areas less than 250km2. # Titmarsh et al., (1989) - 105 Agricultural catchments in Queensland - areas less than 700km2

Weeks used 47 rural catchments (areas ranging from 3km2 to 246km2) in Queensland to assess the reliability of the Bransby-Williams and Pilgrim & McDermott formulae.

Bransby-Williams formula allows the investigation of the relationships of three catchment characteristics, whereas the Pilgrim & McDermott formula is totally based on the catchment area, and it is more appropriate for catchments in NSW and Victoria as suggested by the Institution of Engineers, Australia. According to the findings of Weeks, Pilgrim & McDermott formula always produces a smaller time of concentration value than that of Bransby-Williams. Weeks recommended the Pilgrim & McDermott formula for rural catchments with areas less than 250km2 to estimate design floods, and that procedure adopted is simple, consistent and reasonably reliable he described.

Hughes (1993) carried out studies to estimate the travel time in mountain basins which consist of high gradient stream channels flowing bank full with large gravel, cobbles and random boulders. He used 42 catchments (areas less than 2.60 km2) in this study. He emphasised that especially for large catchments (more than 2.6km2 according to his assessment) the channel flow contributes significantly for travel time than the overland 13

flow. Hughes further stressed that although the high slopes of channels have the capacity to generate turbulent flow, the river bed with large gravel, cobbles and random boulders has the tendency to dissipate sufficient amount of kinetic energy to maintain fairly uniform flow conditions in the channel. For those reasons he indicated that the most suitable and accurate method that can be used to estimate travel time in large catchments is the Manning’s formula.

Considering the above indicated factors Hughes developed the following equation to estimate travel time in mountain basins with high gradient (slopes ≥ 0.002) natural channels lined with large gravel, cobbles and boulders: Travel time of channel, 0.1 Tv = 0.41 L Sc (2.26) In view of the above, when dealing with very complex flow conditions in natural high gradient rock lined channels, in large catchments, the simple empirical relationship given in equation (2.26) can be used to estimate channel travel time. Hughes concluded that these estimated values were fairly accurate.

McCuen and Spiess (1995) assessed the Kinematic Wave Time of Concentration, with the intention of predicting the travel times of sheet flow of catchments. The main purpose of their study was to establish a justifiable criterion to limit the length of the sheet flow in using the Kinematic Wave equation shown in (2.3).

Their investigations were based on the results of both a theoretical routing model and empirical analyses of measured data, and the following sequential issues were considered for their assessment: (i) Estimating sheet-flow travel times; (ii) Limits of applicability of kinematic wave equation (2.3); (iii) Routing model assessment; (iv) Empirical assessment; (v) Limits based on flow length; and (vi) Assessment of Manning’s n.

The IR of kinematic wave equation is estimated from the intensity-duration-frequency

(IFD) curves, by assuming a tc value. These calculations have been done for a couple of times until the assumed value of tc is equal to that of the calculated value. As indicated by McCuen and Spiess, due to considerable number of errors encountered by considering 0.5/[Dd (drainage density)], IRL and L (which can be described as reciprocal, product and single parameters respectively) when assessing the limits of applicability of Kinematic Wave equation, they selected the composite parameter 0.5 (nL/Sc ) since it incorporates the main properties of sheet flow. Furthermore, this composite parameter can differentiate between different flow conditions, such as 30.5m (100ft) flow length with a steep slope and a low Manning’s n, as well as a flow length of 30.5m with a flat slope and a high Manning’s n, as explained by them.

0.5 The Routing Model Studies revealed that when the value of (nL/Sc ) is less than 80, the relative detention-storage depth fell within the acceptable range.

The empirical assessment to determine suitable limit for kinematic wave equation was based on 59 field and Laboratory experiments. Performance of the three parameters L, 0.5 IRL and (nL/Sc ) were statistically analysed to determine the most reasonable and 0.5 accurate limit for sheet flow and found that (nL/Sc ) as the best option. The tests based on flow lengths revealed that using only L as the criterion is less accurate than using 0.5 (nL/Sc ), and its limit is found to be 100.

McCuen and Spiess produced curves for different ‘n’ values by plotting length (L) versus slope (Sc) and the maximum length applicable according to their study is about 152m (500 ft). They further insisted that the best criterion to assess the limiting value of 0.5 Kinematic Wave equation is (nL/Sc ), and that value should not exceed 100 when finding the limiting length of the sheet flow.

Wong (1996) derived a time of concentration (tc) formula by means of the kinematic wave equation for overland flow. In the development of the process of this formula he considered the following physical and hydrological characteristics of the catchment: • cascade of planes; • roughness of surfaces; 15

• different flow regimes; • different soil types; • infiltration rates resulting from different net intensities; • planes subject to different rainfall intensities; and • combining all these factors. Considering only one plane and combining the most significant factors from the above list, the following formula was suggested for time of concentration: 0.6 0.6 -0.3 -0.4 tc = 58.47 n L Sc IR (2.27) Wong further indicated that the equation (2.27) is applicable to turbulent or near turbulent flow regimes if Manning’s roughness values are used for n and this formula is consistent with the published formulae for a single plane.

Yang and Lee (1999) carried out studies to investigate the adequacy of the following time of concentration equations frequently used in Taiwan: • Kirpich’s given in equation (2.4) 0.22 -0.35 • Kadoya’s tc = 0.017 CR A Iex (2.28) 1.60 -0.6 • Rziha’s tc = 0.014 L H (2.29) Where, H is the difference in elevation between highest point of watershed and that of the outlet. • Taiwan Soil and Water Conservation Society (TSWCS) 0.5 -0.5 tc = 79.06 A (OLS) (2.30) In addition to these equations they derived the following two theoretical equations, using the kinematic wave theory, and adopting two conceptual models and they are: (i) Single Overland Plane Model

 n L  0.6 = o t 0.6 0.6 -0.30 -0.40 t c 0.23 0.5 0.67  = 0.23 no Lt (OLS) IR (2.31) (OLS) IR 

Where, Lt is the overland travel length. (ii) V-Shape Overland Plane Model, for Channel flow

0.6 W 2I n L L = × 2  R o  × 2 0.6 0.4 -0.4 0.6 -0.3 -0.40 t c 9.25 10 0.5 = 9.25 10 n W Lo L Sc IR (2.32) 2I R Lo  SC W 

Where, W is the width of channel of stream and Lo is the overland flow length.

A time of concentration equation for the V-Shape overland Plane Model (also known as V-KW equation) was derived by combining the equations (2.31) and (2.32). Three catchments (areas ranging from 0.114km2 to 0.344 km2) in Taiwan were used for their investigations and the numerical results revealed the following: • For channel flow dominated watersheds, Kirpich’s and Rziha’s formulae are suitable; • TSWCS equation is appropriate for practical application in Taiwan; and • The V-KW equation is capable of providing more realistic time of concentration, since it considers watershed geomorphological parameters as well as rainfall intensity.

2.3 Tangent Method According to the investigations carried out by Nash (1958) various researchers have discovered a number of inconsistencies in the Rational Method after applying it to practical situations. Nash further indicated that the coefficient of runoff ‘CR’ could change considerably from time to time. In other words ‘CR’ is assumed to vary with the antecedent conditions of the catchment at the time of occurrence of the storm. Furthermore, Reid (1927) and Norris (1946) put forward graphical methods to overcome the inconsistencies related to the Rational Method, for example producing greater discharge for a given frequency of rainfall for a part of a catchment rather than the whole. This graphical method is called the Tangent Method. Moreover, the discoveries of various researchers revealed that the physical characteristics of catchments, in particular, the slope, main stream length to centroid, width of main channel and total length of main stream, influence the lag time of the rainfall & runoff process. For these reasons, more and more researchers were inclined to find solutions to eliminate the shortcomings of the Rational Method.

2.4 The Time – Area Method The time–area method is basically a progressive algebraic analysis of rainfall from the top of a catchment to its outlet, through its sub-areas demarcated by means of the isochrones, to obtain the maximum flow. This method allows the elimination of one of the assumptions of the Rational Method, and that is the rainfall is uniformly distributed over the entire catchment for a given rainfall intensity. Ross (1921) became the first to introduce a graphical method with time contours to divide the catchment into sub-areas 17

to overcome that problem. Hence he had used the Hawken’s formula (2.33) to estimate the rainfall Intensity (IR) for different time periods (t) by considering 0.5hr time intervals for isochrones for the catchment. -0.5 IR = E t (2.33) The parameter E varies from region to region in Australia and for example, E for Brisbane is found to be 88.

Hawken (1921) argued that the rainfall intensities of a catchment vary more or less irregularly in actual practice. It is to say that, a short storm of high intensity may be followed by a lull and succeeded again by a moderate intensity then a high intensity and so on. Therefore, he was interested in developing a method to estimate the mean maximum intensity of rainfall. Although Hawken used the Ross’s time area method to divide the catchment into sub-areas, he used his own equation to produce rectangular hyperbolic intensity-duration curves. These curves and the extent of each sub-area (expressed as a percentage of the total catchment) were considered to estimate the mean maximum intensity (Im) for the entire catchment.

Hawken insisted the importance of always keeping the time intervals of isochrones as a constant, throughout the catchment in the analysis, and introduced the following formula to calculate the maximum outflow (QP):

QP = Im A (2.34) As described in his paper, Hawken believed that the nature and size of the sub-areas of equal time depend on the slope, roughness and porosity of the catchment. Thus the method he adopted allows the incorporation of the effects of these physical characteristics of catchments into Im.

2.5 The Unit Hydrograph Theory The unit hydrograph concept was introduced by Sherman (1932), as described by Nash (1958) and Wilson (1969), in the United States and gradually came into use for design flood analyses throughout the world. Although this linear method is replaced by runoff routing method in Australia, it is still widely used in the United States and elsewhere.

The unit hydrographs can generally be derived, subject to some degree of error, for any catchment for which a record of rainfall and stream flow is available, as explained by 18

Nash (1958) and Weeks & Stewart (1978). However, this theory became very popular and useful, because it helped engineers to derive hydrographs for the following situations: (a) Unit hydrographs for various durations; (b) Changing a long duration unitgraph to a shorter duration one, (S-Curve method); (c) Unit hydrograph as a percentage distribution of rainfall (Bernard, 1935); (d) Synthetic unit hydrographs (Snyder, 1938); (e) Instantaneous unit hydrographs (Clark, 1945); and (f) Unit hydrographs for complex or multi period storms (Collins 1939 and Linsley et al., 1943).

As described by Nash (1958) in his paper, experiments have been carried out by various researchers, using the unit hydrograph theory to find out relations between the characteristics of a catchment and its indicial response. The results can be summarised in the following manner:

• Bernard (1935) - Assumed that the peak flow (Qp) in inversely proportional to

time of concentration (tc),

∝ 1 i.e. Q p ; and t c

time of concentration (tc) is proportional to the length of longest channel of catchment divided by the square root of the equal area slope of the main stream,

∝ L i.e. t c (Sc)

The above assumptions have been accepted by studying 6 catchments in USA and their areas ranging from 1300 km2 to 15600 km2. • McCarthy (1935) - Selected 22, 6-hour unit hydrographs of catchments in USA (areas ranging from 192 km2 to 1854 km2) for the study and found satisfactory correlations between the catchment area, overland slope and stream pattern. However, his findings were not published.

• Snyder (1938) - Correlated the lag (tL), which is the time period between the centre of the area of the effective rainfall diagram and the peak of the storm

runoff hydrograph, against LLca and found some consistency in the lag for all cases considered. His equation is, 19

0.3 tL = 0.75(Cc)(LLca) (2.35)

In this equation the value of (Cc) varies from 1.8 to 2.2. • Linsley et al., (1958) - Found that the slope of a catchment reflects on the basin lag from their investigations, and they recommended the following general expression for basin lag (tp):   n = LLca t p 2.60(C t )   (2.36)  Sc 

Their studies revealed that the value of ‘n’ is equal to 0.38 and the value of (Ct) depends on the topographical features of the catchment, as shown below: For Foothill drainage area - 0.72; For Mountain drainage area - 1.20; and For Valley drainage area - 0.35. • Taylor and Schwartz (1952) - Carried out studies for 22 catchments in USA (areas ranging from 51.2 km2 to 4144 km2) and found the following relationships:

∝ 1 Peak of flow Qp Sc 0.30 Shape of unit hydrograph ∝ (LLca) • O’Kelly (1955) - obtained the instantaneous unit hydrograph by routing an isosceles triangular inflow with the correct volume and the base length C (hrs), through storage described by the equation, S = KQ. The relations found for C and K are: b Base length (C) of hydrograph = aSc and d Storage Factor (K) of Hydrograph = cSc Where, a, b, c and d are empirically derived constants. However, O’Kelly and Farrell, 1957, insisted that not much evidence is available to find an acceptable relationship between the catchment slope and base length of outflow hydrograph.

Nash (1960) used 90 British catchments (areas ranging from 12.4 km2 to 2225 km2) for his unit hydrograph study. He applied the method of moments to establish empirical correlations between the characteristics of the catchment and the distance from the centroid of excess rainfall to the centroid of the resulting hydrograph. 20

The equations devised by him are. 0.3 -0.3 tL = 10.39 A (OLS) (2.37) 0.3 -0.3 tL = 8.11 L Sc (2.38) The storms used to derive the above formulae are areally uniform with shorter duration as well as high intensity. Accurately gauged and continuously recorded catchments were used in this study and he has omitted the catchments in which the outflow is controlled by man-made features.

Gray (1961) carried out two different studies, one related to the interrelationships of physical characteristics of catchments and the other is to produce synthetic hydrographs from measurable topographic characteristics of un-gauged catchments. In the first study he used 47 small catchments in USA, and 42 catchments for the second, (areas ranging from 0.60 km2 to 84.5 km2 in all catchments). The relationships found from his studies are: (a) From the first study, L = 1.31 A0.57 (2.39) 0.96 Lca = 0.55 L (2.40) 0.55 Lca = 0.71 A (2.41) -0.662 Sc = 21.5 L (2.42) Combining the equations (2.39) and (2.42) gave the following relationship: -0.38 Sc = 17.98 A (2.43) Gray has also pointed out that the catchments selected for this study vary with different vegetative, soil, lithological, physiographic and climatic conditions. Furthermore, he found that the slope of the main stream (Sc) is inversely proportional to the parameters

L, Lca and A, through a simple power equation, provided that the regional influence is considered. (b) From the second study, he obtained several equations (for catchments in

different regions of the country) for period for rise (PR) of the flow

hydrographs. Gray also indicated that PR is approximately equal to tc, and tL and that can be observed from the equation (2.47). The formulae devised for various parts of the country are: Nebraska – Western Iowa:– 0.498 -0.249 PR = 0.17 γ’ L Sc (2.44)

Central Iowa – Missouri – Illinois – Wisconsin: – 0.562 -0.281 PR = 0.22 γ’ L Sc (2.45) 0.531 -0.266 Ohio:– PR = 0.27 γ’ L Sc (2.46)

The relationship between PR and tL is, 1.005 tL = tc = 1.017 PR (2.47) Where, γ’ is a dimensionless parameter.

Amorocho (1961) made constructive criticisms related to the unit hydrograph procedure, and some of his comments are: • The principle of superposition in unit hydrograph theory does not work effectively for every storm; • It is not possible to ascertain with any degree of assurance that a storm pattern that caused a flood hydrograph is actually measured; and • It is a well-known fact that the unitgraphs derived from large floods usually differ from those derived from minor floods. By deriving unit hydrographs, on the basis of floods produced by short storms (reasonably uniform) of different intensities, Amorocho produced the following expressions to show a relationship between maximum flow (qmax) and time to peak (tP) which is related to the lag time. • For unit response early in storm: = −1.6 t p 0.004q max (2.48) • For unit response late in storm: = −1.26 t p 0.013q max (2.49)

Morgan and Johnson (1962) carried out studies to determine the relative accuracy and reliability of some of the synthetic methods proposed, particularly by, Snyder, Soil Conservation Services (SCS), Common and Mitchell. The accuracy of the derived unitgraphs has been evaluated by comparing the actual flood hydrographs with the hydrographs produced from those methods.

They selected 12 catchments located in Illinois, USA, ranging in size from 26 km2 to 262km2. In addition to Snyder’s formulae these were tested for their accuracy: -1.0 SCS PR = 0.21A V QP (2.50) -1 Common PR = 4.96 A QP (2.51) 0.74 Mitchell tL = 0.30 A (2.52) 22

Where, PR is the period of rise of flow; Qp is the peak discharge and V is the runoff volume of the drainage area in millimetres.

Studies revealed that the term QP is the best indicator for the accuracy of each method, because of the nature of the relationships used in various synthetic methods.

Wu (1963) carried out extensive studies to design hydrographs for small catchments in Indiana, USA. The purpose of his study is to determine the relations between the shape of hydrograph and some identifiable and readily obtainable watershed characteristics.

He indicated that the shape of the hydrograph depends on the time to peak (tp) and storage coefficient (Kl). Those parameters depend upon the physical characteristics of the catchment such the as the area (A), main stream length (L) and slope of main stream

(Sc). He has also discussed the influence of shape factor (f), and valley shape factor (v) of catchments on tp and Kl.

Seventeen small watersheds distributed throughout the state of Indiana, were selected for his study and their areas ranging from 7.5 km2 to 260 km2. The Correlation Method was used to devise the following formulae:

• For hydrograph parameter tp: 1.085 -1.233 -0.668 tp = 4.32 A L Sc (2.53)

• For hydrograph parameter K1: 0.937 -1.474 -1.473 K1 = 21.7 A L Sc (2.54) Due to poor correlation, terms (f) and (v) have been omitted by Wu. It is interesting to note that the methodology developed in his study (to design a hydrograph) is semi- theoretical and semi-empirical.

The synthetic hydrograph methods proposed by various overseas researchers (Snyder, 1938, Taylor and Schwartz, 1952, Eaton, 1954, Nash, 1960 and Wu, 1963) were tested for their validity and reliability by Cordery (1968). He considered 12 rural catchments in Eastern New South Wales, Australia, ranging areas from 0.05 km2 to 642 km2. The purpose of his study was to devise formulae by correlating combined catchment characteristics with the base length of the time-area diagrams.

The two formulae representing lag time proposed by Cordery are: Base length (C) of time area diagram in hrs, 0.8 0.24 -0.40 C = 23.03 n (LLca) Sc (2.55) Catchment reservoir type storage (K) in hrs,  0.79  W + 0.5Ln  K = 5.50   (2.56)  (OLS) (Sc)  Where W is the average catchment width. Cordery found from his studies that the stream roughness (n) has a significant effect on the lag time, although most of the researchers have not incorporated that in their equations.

After analysing hydrologic data from higher intensity, short term storms in very small drainage areas using unit hydrograph theory, Viessman Jr (1968) insisted that the lag time has a varying effect on characteristics of catchments. Furthermore, not much correlation has been found between the lag time and the storm characteristics from his study. Six gauged small catchments selected for his study, and they vary in area from 6.7m2 to 3865m2 and located in USA. The formula related to the lag time proposed by Viessman jr, is: 0.66 0.66 -0.33 K = 1.78 n L Sc (2.57) Where, K is the catchment reservoir type storage in hrs.

Bell and Kar (1969) pointed out that the time of concentration, rise time, lag time, and time to equilibrium are essential features of a hydrograph and these time periods are governed by the storm and catchment characteristics.

The studies related to the rise time (Tm) and lag time (tL) have been carried out by them for 47 small catchments (less than 130 km2) located in many parts of USA and over 400 flood hydrographs were analysed. The following equations were proposed by Kar: • For Humid and Subhumid Catchments less than 103 km2 0.47 Tm = 0.92 Lca (2.58) • For Arid and Semiarid Catchments less than 103 km2

-0.14 -0.6 Tm = 3.20 L Sc (2.59) 24

0.77 -0.39 tL = 10.25 M L Sc (2.60)

As explained in their paper, Bell and Kar have attempted to obtain correlations of ‘M’ with several catchment characteristics, such as the slope, drainage density, catchment shape, vegetation cover, and precipitation factor. Only vegetation cover group showed strong relationship and different values proposed for ‘M’ for different conditions are:

Vegetation Cover group Mean ‘M’ Forest and good Woodland 2.05 Good pasture and poor to fair woodland. 1.50 Crops and poor to fair pasture. 1.15 Very poor pasture and desert vegetation 0.60

However, they concluded that no completely satisfactory method can be recommended to estimate any of those characteristic time periods by using physical factors of catchments. Furthermore, the existing formulae have failed to address some of the major factors, such as the roughness and magnitude of flood flows, as explained in their paper.

Askew (1970) has carried out extensive studies related to lag time of natural catchments. His views are very much similar to the comments made by Bell and Kar, as explained earlier.

Askew has described the lag time as an important hydrologic characteristic of the rainfall and runoff process. He further indicated that the analysis of hydrologic records is not possible without the lag time.

His findings on lag time are based on 5 natural catchments in NSW Australia, and their areas ranging from 0.4 km2 to 90 km2. The intention of his studies was to investigate the non-linearity response of catchment systems.

Askew emphasised the fact that the non-linearity of a catchment is clearly demonstrated by variation in lag time, and this variation in lag is highly correlated with the flood magnitude. He further indicated that the absolute magnitude of lag time is related to the catchment area (A) and overland slope (OLS). 25

Although Laurenson’s equation for storage delay time was available to relate lag time, Askew (1970) derived new lag-discharge equations for all rural catchments selected for his study. By observing the initial rise of direct runoff he separated the base flow for all single and multiple hydrographs. After measuring the time lag between the centre of mass of excess rainfall to centre of mass of direct runoff for all 240 storms, various characteristics of the areal and temporal distribution of excess rainfall were studied and the following equations were derived for lag time: = 0.57 −0.23 t L 2.12A q wm (2.61) = 0.54 −0.16 −0.23 t L 4.83A (OLS) q wm (2.62) = 0.80 −0.33 −0.23 t L 8.57 L (OLS) q wm (2.63)

Where qwm is the weighted mean discharge.

As described in Askew’s paper intercorrelations were found for 5 characteristics (tL, A, qwm, OLS and L) excluding the Manning’s Coefficient. Most of the relations are very similar to those given in Gray’s paper in 1961. Although the variation of lag time with A, L and A/L2 could not be regarded as statistically very significant, some correlation was found, Askew further explained.

Rastogi and Jones Jr (1971) carried out investigations to find out the behaviour of small drainage basins, by introducing unit hydrograph theory. Furthermore, various attempts have been made by them to promote and extend this theory to produce instantaneous unit hydrographs as well as synthetic unit hydrographs for ungauged catchments.

The following relations were developed from hydrologic characteristics of six small catchments in USA with areas ranging from 0.023 km2 to 0.554 km2. It was found from the study that in all catchments, as the excess rainfall intensity increases, the time to the peak decreases. That is because the increase in peak rate of flow is more than the increase in excess rainfall intensity.

Log tL = 2.328 + 0.1logD + 0.184logIex – 0.108logD (log Iex) (2.64) Where, D is the duration of excess rainfall. The results of this study showed that the base or time duration of a direct runoff hydrograph increased with an increase in rainfall excess intensity. 26

Cordery and Webb (1974) introduced a simple design method to derive synthetic hydrographs for ungauged catchments in Eastern NSW. As indicated in their paper this method is purely for design purposes and it is based on the general approach of the Clark– Johnstone synthetic unit hydrograph procedure. Furthermore, it is a storage routing model, in which two unit hydrograph parameters ‘C’ and ‘K’ have been introduced. The parameter ‘C’ represents the base length of the time-area diagram and the storage delay time of the catchment is related to the ‘K’ value. Moreover, both parameters represent the lag time of the rainfall–runoff process and the following relations have been found by Cordery and Webb after examining 21 catchments up to 250 km2, in the eastern NSW, Australia.  0.41  L  0.41 -0.41 C = 2.90  = 2.90 L Sc (2.65)  SC  K = 0.66 L0.57 (2.66) In 1976, Pilgrim used Tracer measurements of a small natural catchment known as Research Creek with an area of 250 km2. He obtained direct results for outflow hydrographs by adopting tracer injection technique and applying it to seven points of the watershed. Pilgrim further indicated that such results are not possible to find from conventional rainfall and runoff records.

His intention was to examine relationships of travel time (which is corresponding to the watershed lag) and average velocity with discharge. He strongly believed that, very little direct and quantitative information was available at that time. This information is related to the values and variations of travel times of actual flood runoff for use in research work related to hydrograph analyses. The following relationship was developed: -0.492 Tcm = 0.83qp (2.67) Where, Tcm is the time from injection to the centre of mass of the outflow hydrograph and qp is the peak discharge.

Baron et al., (1980) carried out extensive studies to review and investigate the following: (i) The processes and factors affecting the relationships between hydrological characteristics of small and large catchments; 27

(ii) To develop methodologies that can be applied to investigate those relationships; and (iii) To assess the possibility of transferring the results of small to large catchments.

The contents of their study may be categorised into the following four parts: • Effects of area on catchment runoff; • Annual rainfall-runoff relation; • Effects of area on flood hydrographs; and • Effects on catchment due to storm losses. They used 52 catchments ranging in size from 0.05 km2 to 15043 km2, from NSW, Queensland and Tasmania. Since the volume of water collected on the surface of a catchment for unit depth of excess runoff, represents the unit hydrograph, they insisted that the parameters of the unit hydrograph perfectly correlated with the catchment characteristics such as, the slope, surface roughness and shape.

The relationships between catchment characteristics and unit hydrograph parameters proposed by Cordery and Webb and the AR&R (1977) were tested for their reliability, by Baron et al., and found the following results: Cordery and Webb (1974) - Equations (2.65) and (2.66)

0.58  L  0.58 -0.29 AR&R (1977) - C = 1.50  = 1.50 L Sc (2.68)  Sc  - K = 0.08 L1.05 (2.69)

0.40  L  0.40 -0.40 Baron et al., (1980) - C = 3.00  = 3.00 L Sc (2.70)  Sc 

0.50  L  0.50 -0.25 - C = 1.70  = 1.70 L Sc (2.71)  Sc  - K = 0.70 L0.57 (2.72) - K = 1.00 L0.31 (2.73) Results revealed that the base flow length (C) of the hydrograph is slightly better related 0.5 to (L/Sc) than (L/Sc ), and therefore, it is suggested that the equation (2.70) be used. Baron et al., further indicated that the estimated K (storage delay time of catchment) values from equation (2.72) are only 6% different from those obtained from the 28

equation (2.66). Therefore, the equation (2.72) is a better option to consider, they emphasised.

The relationships of C and K of equations (2.70) and (2.72) have shown high correlation coefficients (> 0.92) and not much of scatter of data has found in the plot. They revealed from their other parts of the study that the strength of these relationships has improved due to the selection of L and Sc instead the catchment area (A), as the flood response directly proportional to those two factors.

It is interesting to note that Cordery et al., (1981) have made a joint study to assess the validity of the use of small catchment research results for the large basins. They carried out studies related to 52 catchments in Queensland, New South Wales and Tasmania in Australia, ranging their sizes from 0.05 km2 to 15000 km2. Some of the findings from their study are: (i) Rainfall losses increase with the size of the catchment; (ii) Rainfall-runoff and loss-area relations vary from region to region; (iii) Transferring of data between regions is not valid; (iv) Unit hydrograph parameters ‘C’ and ‘K’ vary consistently with the size of catchment; (v) The continuing loss rate is practically a constant for all storms on a catchment; and (vi) Initial loss increases as the catchment size increases. Out of all the relationships between catchment characteristics, the relationships given in equations (2.65) and (2.66) found to be valid and reliable. The findings of Baron et al., 1980, have supported these relationships as indicated by Cordery et al., in their paper.

Boyd (1978) carried out studies related to regional flood frequency data for NSW streams. The intention of his study was to relate flood estimates to hydrologic and topographic variables of NSW Catchments. Boyd used log Pearson Type 3 flood frequency distribution and fitted to the annual maximum flood series (q1.11 to q100) and found the following relations: -8 0.662 2.556 q1.11 = 1.274 x 10 A pe (2.74) -7 0.689 2.276 q2 = 3.609 x 10 A pe (2.75) -7 0.730 2.282 q5 = 6.396 x 10 A pe (2.76) 29

-7 0.758 2.331 q10 = 5.711 x 10 A pe (2.77) -7 0.792 2.416 q25 = 3.880 x 10 A pe (2.78) -7 0.814 2.473 q50 = 2.928 x 10 A pe (2.79) -7 0.835 2.537 q100 = 2.011 x 10 A pe (2.80)

Where, q1.11 to q100 are peak flows for different return periods and Pe is the depth of rainfall excess (mm).

As described by Boyd, 79 catchments were used for the study and 28 of them are located inland and the remainder is in the coastward of the Great Dividing Range. Catchment sizes vary from 9.0 to 22,500 km2 and nearly 40 years of data was available for the study. Boyd also indicated that the catchment slope was found to be least significant in the regressions and that was omitted in the estimation of flood frequencies. The following relationships were found for physical catchment characteristics: L = 1.813 A0.53 (2.81) -0.32 Sc = 51.07 A (2.82) Although the stream length is strongly correlated with the catchment area, the stream slope is less strongly correlated with the Area. Furthermore, relationships given in equations (2.81) and (2.82) agree with those found by Hack (1959), Gray (1961), Mueller (1973), and Boyd (1976).

Boughton and Collings (1982) carried out studies similar to those done by Boyd in 1978, related to regional variations in flood frequency characteristics.

The purpose of their study was to compare the calculated peak flows (for 2 year & 100 year ARI), with the flows estimated from the original data and also to assess the order of accuracy of the results. They also compared their regression equations with those of Boyd (1978). Four independent variables similar to what Boyd selected were chosen by Boughton and Collings to make the comparison easy. Although Boyd used median annual rainfall in his study, mean annual rainfall was used by them.

The 52 catchments in Queensland were used for the study and their sizes range from 31 km2 to 132100 km2. The main difference between the Queensland and NSW results is in the values of the coefficients in the regression equations as shown here, 30

0.565 0.911 QLD q100 = 0.54 A pe (2.83) -7 0.835 2.537 NSW q100 = 2.011 x 10 A pe (2.84) -5 0.580 1.583 QLD q2 = 7.047 x 10 A pe (2.85) -7 0.689 2.276 NSW q2 = 3.609 x 10 A pe (2.86)

Where, pe is the depth of rainfall excess (mm) It is important to note that both NSW and Queensland catchments have shown very little correlation with the length and slope as described by all these researchers.

2.6 Linear and Non-linear Models Various researchers have proposed linear and non-linear models to overcome difficulties related to unit hydrograph theory, for example limitations in estimating design floods for catchments with spatially varying rainfall.

Modelling is the process of representing the real system so that it can be used to solve problems, being in an office or laboratory. Physical or scale models can be built in a laboratory whereas a mathematical model is generally in the form of a computer program (eg. RORB, WBNM, etc.,). Mathematical models attempt to simulate what actually occurs in the real world, by introducing equations to describe the various processes.

In this section, the studies done by various researchers pertaining to modelling are discussed in detail.

Clark (1945) developed a linear model to calculate unit hydrographs by using flood routing techniques. As explained in his paper the purpose of his study was to clarify the inherent relationship between unit hydrograph and the method of flood routing. He has used four concepts to develop his model and they can be illustrated from the following equations: (i) Inflow (I), outflow (Q) and storage (S) relationship, dS = I - Q dt (2.87) (ii) Storage (S) as a non-linear function of stream flow (Q), S = K Qm (2.88) 31

Where, K is the basin storage coefficient related to the lag time and m is a positive exponent. (iii) Main stream storage (S) as weighted average value of the inflow (I) and outflow (Q), S = x I + (1-x) Q (2.89) Where, x is a coefficient which varies from 0.0 to 1.0. (iv) Storage (S) as a linear function of stream flow (Q), S = k Q (2.90) Where, k is a parameter related to the travel time in the reach. The intention of his study was to modify the runoff hydrograph by incorporating the effects of valley storage of the basin. This was done with the help of the above equations. In his method he suggested to alter the shape of the hydrograph to provide a sharper and earlier peaked unit hydrograph for high rates of runoff. The base length of the hydrograph was estimated by means of the number of intervals of the time-contour (isochrones) map of the catchment.

Four drainage basins in USA, Appomattox River at Petersburg (3458 km2), James River at Richmond (3546 km2), Smith River at Bassetts (686 km2) and Meherrin River at Emporia (1943 km2) were selected and Muskingum method of flood routing was adopted to derive the unit hydrographs. As indicated in his paper the number of advantages in his model is considerably more than its disadvantages.

Kull and Feldman (1998) carried out investigations to find out the possibility of introducing spatially distributed runoff onto the Clark’s Unitgraph method which consists of three parts, and they are, time of concentration (tc); the storage attenuation coefficient k; and time area histogram.

They further indicated that the Clark’s Model (presently known as new generation ModClark) became the driving force to generate different techniques to produce flood hydrographs by various researchers, during past 50 years. The ModClark is a methodology, and it has been developed by incorporating spatially distributed rainfall data and it has the capacity to produce suitable unit hydrographs to satisfy catchments with varying rainfall patterns. Furthermore, these capabilities were embedded into the 32

ModClark by using the advanced computer techniques and GIS facilities, as described by Kull and Feldman.

Calibrating the ModClark by means of the data of two basins, Salt River at lock and Dams 22 & 24 and Missouri at Mark Twain Lake (with drainage areas of 7304km2 and 6048km2 respectively, in USA), the following equation is derived for time of concentration:  0.28 = + −1.28  A  -1.28 0.28 -0.28 t c 8.29(1 0.03Iimp )   = 8.29 (1 + 0.03Iimp) A Sc (2.91)  SC 

Where, Iimp is the index of impervious cover.

Rookwood (1958) developed a non-linear model for stream-flow routing specifically for the Columbia Basin in USA, for a digital computer. In his model he routed excess rainfall through the sub-areas of the catchment to synthesise stream-flow up to the outlet.

In his paper he discussed the following three types of storage delays: (i) Delays within the tributaries of the main stream channel; (ii) Delays due to flows into the lakes of the catchment; and (iii) Delays due to main channel storages.

He used the general storage equation (2.88) for his routing method and considered the storage as a nonlinear function of outflow, and the lag time is incorporated to that function. The variation of storage time with outflow is considered by Rockwood, as one of the important features of the routing method for the basin and channel storage. He further explained that the time of travel of flood waves through channels may vary with discharge according to channel conditions.

He assumed that the storage time is inversely proportional to a power function of the outflow at time t and the following equation was developed. To obtain such a relationship he made use of the ability of the computer program to vary the storage time with discharge. -0.2 Ts = K Qt (2.92) 33

Where, Ts is the storage time; K is the basin storage coefficient; and Qt is the outflow at time t.

It has been observed from his studies related to Ts and Qt on Kootenay Lake, which is one of the major lakes in the Columbia Basin of USA that the storage time decreases markedly with increasing discharge.

Nash’s linear model was described in the earlier section under unit hydrograph theory. In his model the excess rainfall is routed through a series of equal linear storages. As explained by Macrae and Turner (1971); Boyd (1975&1976), the parameters K (basin storage coefficient) and N (parameter related to K and lag time) of the model have been found to vary from flood to flood on a given catchment. Furthermore, the hydrographs produced by the model do not totally match with the observed hydrographs, as described in AR&R 1998.

A reasonably satisfactory catchment storage non-linear model, based on a very general runoff-routing procedure, was developed by Laurenson (1964) to convert rainfall excess to surface runoff. He used this procedure to examine the lag time. In his study he selected the time-area diagram with isochrones to develop relations of storm and catchment characteristics. He carried out an in-depth literature survey related to runoff routing before developing his model.

The development and testing of the runoff routing procedure were carried out using the data of the South Creek catchment (with an area of 90.7 km2) near Sydney, NSW. The model equation developed is: -0.27 tL = 24.5qm (2.93)

Where, qm is the mean discharge at outlet.

Pedersen (1978) introduced a Single Linear Reservoir Model (SLRM), and Pedersen et al., (1980) tested this model by relating the model parameter ‘k’ with watershed characteristics as well as the intensity of effective rainfall.

For this investigation, Pedersen et al. selected the data from an experimental program conducted by the Los Angeles District, US Army Corps of Engineers and also the data 34

of three catchments (areas ranging from 0.34 km2 to 6 km2) from the engineering literature and the US Geological Survey.

SLRM is based on the concept that a watershed behaves as a reservoir in which storage ‘S’ is linearly related to outflow ‘Q’ as given in the equation (2.90). Pedersen used the kinematic wave theory to derive the equation (2.94) to estimate the value of ‘k’. 0.6 -0.4 -0.3 k = 28.9 (L n) IR Sc (2.94)

Pedersen et al., indicated that the value of ‘k’ has shown to be equal to the lag time (tL). The results of the study also indicated the following: • The effect on the calculated peak flow of underestimating or overestimating ‘k’ is dependent on the distribution of effective rainfall. • For a high intensity short duration storm, the effect of ‘k’ can be quite critical. • Variation in ‘k’ had little effect on a longer duration and less intense storm.

They also indicated that sufficient evidence exists to establish the variability of k (≈ tL) with rainfall characteristics, although traditional hydrograph theory believes that storm characteristics have no influence on time lag (tL).

Mein et al., (1974) developed a simple non-linear model for flood estimation. In their model the catchment is divided into number of sub-catchments (approximately equal in size) designated to the major tributaries. A single parameter ‘k’ (related to the travel time in the main stream) was evaluated in the study by fitting the recorded data of four catchments located in Victoria, Australia, into the following nonlinear storage formula. Three of these catchments are situated at the Thomson River Basin and the other is at the Yarra River Basin and their areas ranging from 339 km2 to 2300 km2.

S = k Qm (2.95) 5 0.6 0.4 -0.3 Parameter related to travel time (k) = 6.64 ×10 n W L Sc (2.96) Where W is the width of the main channel.

In their paper Mein et al., noted that the uncertainties that often arise in flood estimation, as a result of different unit hydrographs being derived from different floods, can be eliminated by using this model.

From the beginning of early sixties Laurenson engaged in studies individually as well as with other researchers, related to runoff routing methods and developed the runoff routing computer program RORB (Mein, Laurenon and McMahon 1974; Laurenson and Mein 1983).

In this model the storage is treated as a mathematical function that simulates the delay and attenuation of the hydrograph. The storage function is represented as indicated in equation (2.95), and its m value is between 0.6 and 1.0. Furthermore, the catchment is divided into sub-areas (generally between 10 and 20) along the watershed boundaries.

The rainfall excess at each upstream subarea is assumed to be in inflow hydrograph at the node of each subarea. All these hydrographs are routed downstream through the conceptual storage to the next node. At the next node, further rainfall may be added to another subarea, and the hydrograph is built up while moving downstream.

The parameter k is related to the conceptual storage, and it is formed as the product of two factors: k = kr kc (2.97)

Where, kr = relative delay time, calculated for each particular reach; and

kc = model parameter, applying to all storages in the catchment. This is also related to the lag time.

It has been found that kc is a function of the catchment area and therefore, the general formula for kc may be given as: x kc = a A (2.98) Where, x < 1.0, and a = scaling parameter which governs the lag time.

The respective general equations in RORB for kc and lag time (tL) are: 0.50 kc = 2.2 A (2.99) 0.50 -0.25 and tL = 2.2 A Q (2.100)

In addition to RORB, another model recommended by the AR&R, is the Regional Stormwater Model (RSWM) or RAFTS, jointly developed by Willing and Partners Pty Ltd., and the Snowy Mountains Engineering Corporation (Goyen and Aitken 1976; Black and Codner 1979). As for RORB, in RAFTS the catchment is divided into sub- catchments. 36

RSWM has the capacity to separate the impervious and pervious portions of a given sub-catchment and to route hydrographs of all sub-catchments to obtain the flow at the outlet. The selection and graphical presentation of isochrones for each sub-catchment is similar to that of RORB. The spacing of the isochrones in each sub-catchment is based 0.5 on the assumption that flow travel time is directly proportional to Σ(L/Sc ) as described by Laurenson, 1964.

The Storage-discharge relation shown in equation (2.95) is used in RAFTS and k is given by: k = B Q α (2.101) Where ‘α’ = -0.285 which gives a power of 0.715 for Q in the equation (2.95). A coefficient related to storage (B) is estimated by using the following equation, and it is developed by Aitken (1975): 0.52 -1.97 -.0.50 B = 0.285 A (1+U) Sc (2.102) Where, U is the fraction of catchment urbanised.

In addition to the other capabilities, RSWM has the following abilities, • Allows to introduce the infiltration, wetting and redistribution of rainfall, factors into a given catchment (application of these factors were tested by Boyd and Goodspeed 1979; Black and Aitken 1977 and found satisfactory results). • Estimates the rainfall excess and runoff frequency curves, by using the deterministic loss model embedded into it.

Reed et al., (1975) carried out a study related to variable lag time in the rainfall-runoff process. They introduced an additional parameter to the cascading reservoir model of that process and a semi-empirical relationship between lag time and storage is incorporated.

They mentioned that the studies done by Minshall (1960) and Rastogi & Jones (1969) have demonstrated that the lag time is related to intensity of rainfall excess. Reed et al., used the catchment (area of 19km2) of the Ray River at Grendon Underwood in Australia to find out the parameters a and b of the following equation, related to variation in lag: b tL=aqm (2.103) 37

and found these relationships, for linear variation: tL = 13.38 qm (2.104) -0.87 for non-linear variation: tL = 7.12 qm (2.105)

Where, qm is the mean total discharge.

Equation (2.105) revealed that the variation in lag is much more non-linear than the non-linearity suggested by Laurenson (1964) and Askew (1970). They also insisted that the parameter b, in particular, is related to the physical factors of the catchment and has the capacity to produce some effect on the variable lag.

Weeks and Stewart (1978) calibrated and tested the Clark-Johnstone Method (1949), and the Runoff Routing Model of Mein, Laurenson and McMahon (1974), to estimate the model parameters for Western Australia and Queensland catchments. They used physical characteristics of 27 ungauged catchments (6 from Western Australia and 21 from Queensland) and their areas ranging from 41km2 to 2331km2. Trial and error method was introduced to reproduce recorded hydrographs, and found the following formulae: • Clark-Johnstone Method parameters (K and C): WA K = 3.90 L0.71 (2.106)   0.94 L 0.94 -0.47 C = 1.70   = 1.70 L Sc (2.107) SC  QLD K = 0.09 L1.03 (2.108)   0.69 L 0.69 -0.35 C = 0.96   = 0.96 L Sc (2.109)  SC 

• Mein, Laurenson and McMahon Model parameters (k and m): WA k = 0.89 A0.91 (2.110)

m = 0.89 A-0.03 (2.111)

QLD k = 0.69 A0.63 (m = 0.73) (2.112) Although the Clark-Johnstone Method is based on the runoff routing concept, the disadvantages over the Runoff Routing Model were illustrated by Weeks and Stewart in the following manner: 38

• Model allows areal non-uniformity of rainfall and losses whereas the Method only considers uniformity; • Model considers non-linearity behaviour of catchments, however, the Method only accepts linearity; • although the Model has the capacity to derive hydrographs at various points of the mainstream, the Method could only be used to calculate hydrographs at gauging stations; and • Method could not produce post-construction hydrographs, whereas the Model has that capacity. However, both methodologies could produce satisfactory results, the Model showed better results, especially when the recorded peak discharges varied over a large range. They further described that although some of the regional formulae displayed similarities, there is a danger of using the formula assigned for one region to another.

Boyd (1978) carried out a study to overcome the difficulties related to synthetic hydrograph method. For example the synthetic hydrograph is not capable of specifying the relationships between the watershed hydrology and geomorphology of catchments. His study is based on storage-routing modelling and the purpose of the study was to find out relations between lag times, stream order and network magnitude for basins within a larger watershed. He extended the studies by testing the model with stream networks for a given channel magnitude.

Boyd has explained the advantages of studying lag time of catchments and has also indicated the important features of lag time in his paper in this manner: (i) The lag is the time between the centroid of excess rainfall pattern and the resulting runoff hydrograph; (ii) The lag time enables us to assess the travel time to peak, time of concentration, peak discharge or mean discharge; (iii) The lag time is precisely equal to the time parameter ‘K’ of the following equation, which describes the response of a storage element; dq  i - q = K   (2.113)  dt  39

Where, i is the inflow to storage at time t; q is the outflow from storage at time t; and K is the lag time of the storage element of catchment. (iv) The lag time is reasonably stable for a given drainage basin although it changes slightly due to non-linear effects; and (v) The lag time can be measured easily and may be calculated from recorded rainfall and stream flow data.

His study consists of four nested drainage basins in NSW Australia, and the catchment areas vary from 0.39 km2 to 39.8 km2. The following equations have been developed for the linear variation in lag: 0.38 For all NSW basins, KB = 2.51 A (2.114) 0.38 KI = 1.50 A (2.115)

Where, KB and KI are parameters related to lag time. Boyd also demonstrated that these models are able to reproduce variations of lag time which are observed on actual watersheds.

Boyd et al., (1979) developed a non-linear storage routing model known as Watershed Bounded Network Modelling (WBNM) to estimate the runoff hydrograph from rainfall excess. Although it is similar to RORB model there are considerable differences.

The continuing improvement of WBNM by various researchers in association with Boyd (Boyd, Bates, Pilgrim and Cordery 1987; Boyd, Rigby and Van Drie 1996; Rigby, Boyd and Van Drie 1999 and Boyd, Rigby, Van Drie and Schymitzek 2000) allowed the inclusion of more and more features into the model.

WBNM has been included in the 1987 and 1998 publications of the Australian Rainfall and Runoff (AR&R) of the Institution of Engineers, Australia, as well as the Water Resources Publications, LLC, USA. This model uses runoff routing procedures to calculate hydrographs, and it consists of storage elements which represents the sub- areas of the catchment. These sub-areas (stream and ordered) are connected systematically to make a meaningful stream network. This networking procedure has the capacity to handle the spatial variations in rainfall, losses and land use. This means 40

that, WBNM considers the storage characteristics and the storage delay time for each subarea of the catchment separately, in addition to its geomorphological relations.

Furthermore, this model calculates hydrographs for each sub-area and combines these hydrographs systematically and progressively, to obtain the hydrograph at the outlet of the catchment. In WBNM the storage function for each sub-area is represented by: dS For continuity, I − Q = (2.116) dt For storage-discharge relation, S = 3600 KQ (2.117)

Moreover, the non-linear response of the catchment has been introduced into the model. The non-linear behaviour, of the stream and overland flows of catchments, has been considered in Manning’s equation and the Kinematic wave equation respectively. Therefore, the flow rate Q is incorporated into the model, because that allows the model to recognise the continually varying flow velocities and lag time at every stage of the flood, as described by Boyd et al., (1987).

The following equations adopted in WBNM are similar to the findings of Askew (1970); and they are: • Transformation of excess rainfall to runoff, 0.57 -0.23 KB = C A Q (2.118)

• Transmission of upstream runoff through stream channel 0.57 -0.23 KI = 0.6 C A Q (2.119)

Where, KB and KI are parameters related to lag time. This model has been tested with 10 catchments with areas ranging from 0.39 km2 to 251 km2 in eastern NSW of Australia and found very satisfactory results.

The mean value of C (known as the lag parameter) is very close to 1.68 and it is somewhat lower than the coefficient of the equation derived by Askew (1970), shown in the equation (2.61). Furthermore, Boyd (1979) indicated in his paper that he found improved results after comparing WBNM with Nash (1960) and Laurenson (1964) model techniques as well as unit hydrograph theory. 41

WBNM is an event model not a continuous model and it has only one parameter ‘C’ to evaluate to calculate lag time for natural catchments. WBNM is easier to apply than RORB (Sobinoff 1983), because only sub-catchment areas have to be measured. Furthermore, the studies revealed that two models RORB and WBNM basically come out with similar results. (e.g. Bates and Pilgrim 1983, and Boyd 1983).

As indicated in the Australian Rainfall and Runoff Volume I (1998) and Water Resources Publications, LLC, USA, WBNM is a comprehensive flood hydrograph model and suitable for natural, urban and part-urban catchments. WBNM also has the capacity to produce detailed results of all calculations to its output file.

Bates and Pilgrim (1982) investigated the storage-discharge relations for river reaches and the runoff routing models.

The purpose of their investigation was to examine the performance of the power functions which describe the channel response. Since the majority of the storage of most catchments depends on their channel systems, as explained in their paper, they considered both runoff and flood routing techniques. They insisted that a constant value of ‘m’ in equation (2.95) does not satisfy the real behaviour of rivers, especially when the overbank or the floodplain flows are reached in the main stream. One of the major issues of their study is to re-examine the catchment lag relations developed by Askew (1968). They used the same catchment used by Askew for their analysis with 34 storm events and found the following relationship: -0.236 tL = 15.4 qwm (2.120)

Where, qwm is the weighted mean discharge.

As described by Bates and Pilgrim, although, Askew (1968) used smaller discharges in his study; his formula gave good results for large discharges as well.

Bates and Pilgrim (1983) introduced two distinct simple models for non-linear runoff routing and they are: (i) Piecewise-Linear Model (PLM); and (ii) Quasi-Linear Model (QLM) 42

These two models as well as RORB and WBMN models were tested by means of storm events of five catchments in Australia and their areas vary from 0.39km2 to 89.6km2.

Considering the following five characteristics, they developed an equation for lag time

(tL) by means of the PLM: • Catchment area (A);

• Rainfall excess (Pe);

• Duration of rainfall excess (De); • Antecedent catchment wetness; and • Spatial distribution of rainfall excess. Since the last two factors did not contribute significantly to the relationship, the following formula was introduced for the lag time: 0.46 -0.32 0.17 tL = 3.17 A Pe De (2.121)

For the QLM lag time found to be:

tL = K(Q) + T(Q) (2.122) Where, K (Q) and T (Q) are the storage delay and translation component of catchment lag respectively.

They suggested further testing of the models due to the following reasons: (i) All models tested namely PLM, QLM, RORB and WBMN failed to show that any one approach is significantly better than the other; (ii) All models were able to reproduce a range of recorded hydrographs and the non-linearity of response over this range with reasonable accuracy; (iii) PLM’s response at high discharges conforms better with the results of several investigations of flood response than those of power function type models.

McMahon and Muller (1983) calibrated the Non-linear Runoff Routing (NLRR) model described in the section 8.6 of the “Australian Rainfall & Runoff (1977)”. Purpose of their calibration exercise was to model the peak flood discharges, and also to match them with the observed values.

It is important to consider the following three sources, when assessing the true pattern of the excess rainfall by the user of the model: (i) the estimate of baseflow, which determines the quantity of surface runoff; (ii) the rainfall losses; and (iii) the degree to which the rainfall measured at the stations (within or near the catchment boundary) from the true rainfall, which represents the storm conditions over the entire catchment.

Furthermore, it is also important to see that the amount of excess rainfall resulting from the third source can be quite large. That is, sometimes more runoff is measured than the actual rainfall could supply.

McMahon and Muller have found the optimum values of m and k (parameters of equation of 2.95) for all sized storms by selecting the intersecting point of the plots of m vs k, as explained in their paper. They used a hypothetical mathematical catchment as well as the results found by Weeks for k and m values from his study, to carry out their studies.

The results revealed that the use of indifference curve or interaction curve techniques for calibration of NLRR model is very satisfactory. However, some limitations of this procedure are found, for example m and k values found for smaller floods may not be suitable for large floods. In view of the above, they further explained that sensitivity analysis is necessary to select appropriate m and k values for a given flood.

Sriwongsitanon et al., (1998) carried out studies to improve the storage-discharge relationships for river reaches and runoff-routing models. Furthermore, they reviewed the different regional values proposed by various researchers (Laurenson 1962; Askew 1968; Laurenson & Mein 1981; and Bates & Pilgrim 1983) for m and k of the storage- discharge equation (2.95), and suggested further investigations into the non-linear procedure which is currently used for runoff routing with certain degree of uncertainty. They claimed the constructive criticisms put forward by a number of researchers (Beven 1979; Brady & Johnson 1981; and Bates & Pilgrim 1983) related to the above issues. 44

Although Wong & Laurenson (1983); and Yu & Ford (1993), have attempted to improve the storage-discharge relationship, the results of their studies were unable to fulfil that requirement as indicated by Sriwongsitanon et al., in their paper. They further indicated that even though the hydrologic runoff-routing technique currently in use is a simple approach to flood estimation, it could not address the following natural phenomena: • compound channel behaviour in floods; • performance of channels with flat slopes due to flood waves; • different propagations of flow in floodplain and the main channels; and • effects due to backwater formation in streams

As described by Sriwongsitanon et al., the studies carried out by Myers; Wormleaton; Knight & Demetriou; and Baird & Ervine, revealed that the boundary shear stress around the channel periphery is much smaller compared to that made by the channel- floodplain interface. Therefore, the ratio of the width of channel floodplain to that of main channel is a vital parameter in the analysis of flows in compound channels. Moreover, major portion of the storage is contributed by the channel system in most of the catchments.

The following equation was proposed by Sriwongsitanon et al., for river reach and that relation changes as the river cross-section changes:

1 = + b S So k'L R Q (2.123)

Where So is the threshold storage; k' is related to the exponent (1/b) and it is equal to m; and LR is the reach length between two adjacent cross-sections.

They selected the Herbert River Basin in Queensland, Australia, with a catchment area of 9400m2 for their study as well as the river reach between Abergowrie and Ingham. As the first step, they re-derived the Clark model parameters and obtained the following results and their coefficients are different to those of Clark:

0.40  L  C = 0.28  (2.124)  SC  K = 0.77 L0.57 (2.125) 45

Secondly, four measured flood hydrographs in the 1970 to 1990 period were compared with the calculated hydrographs and a satisfactory agreement between them was found.

Finally storage-discharge relationship between two adjacent cross-sections was investigated. The results revealed the following: • geometric characteristics of the channel cross-sections are related to the flood hydrograph characteristics; • discharge and storage within the reach are related to the cross-sectional area of the downstream end of the reach; and • the above indicated relationships tend to change as the ratio between width and depth of flow of channel, changes. In view of the above factors, the following conclusions were made by Sriwongsitanon et al., • storage-discharge relationship used in the runoff-routing models depend on the cross-sectional properties of the flow than the magnitude of flood flows; and • considerable influence on the exponent of the storage-discharge relationship is evident when the overbank flow commences.

Therefore, they emphasised that using the same m (=0.8) for both small and large flood events to calibrate runoff routing models is questionable.

Zhang and Cordery (1999a) carried out studies to analyse the storage-discharge relationship given in the equation (2.95), to check whether the relationship is linear or non-linear.

The proposals made by various researchers (Bates & Pilgrim 1983; Wong Laurenson 1984; Bates & Pilgrim 1986; Wong 1989; Yu & Ford 1993; and Sriwongsitanon et al., 1998a & b) to demonstrate the calibration problem associated with the non-linear storage-discharge relationship were highlighted by Zhang and Cordery in their paper. They further indicated that the estimation of the optimum parameter value of k through

(using the values of kc and m) trial and error process is questionable.

Quoting the findings of Pilgrim (1986), that the runoff process is non-linear with low flows and linear with high flows, they insisted that finding meaningful answers to the following important questions, especially with regard to the practical application of runoff-routing models, is the main objective of their study: • Would it be possible to identify the real storage-discharge relationships by using the trial and error procedure? • Whether the non-linear routing approaches are suitable for design purposes?

• What is the physical significance of k or kc in the power function?

With the intention of identifying the storage-discharge relationship, they selected the recession cure of the flood hydrograph by using the continuity equation. They also insisted that the input rainfall is zero during the recession. Furthermore, a best-fit function was fitted onto the points of the recession curve and they regard that as the true storage-discharge relation of the catchment. Thus the parameters m and k were estimated.

Since different storm events produce different functions for recession curves, the necessity of fitting an appropriate power function, linear function or exponential function for each event has been emphasised by them.

The method explained above was tested on large flood events of six catchments in NSW, Australia, and their areas ranging from 40km2 to 261km2, and good quality long period of data was used. However, extrapolated rating curves were used to obtain high discharge values. Their results revealed the following: • for all selected catchments m is between 0.9 and 1.61, except for South Creek catchments, for the non-linear high flow fit; • the values of k obtained from global linear regression are quite different from the non-linear high flow piecewise regression;

The results obtained from the 5 floods of the Hacking River Catchment illustrated the following: 47

• k values vary quite considerably from event to event and found that they decrease as the peak discharge increases; • m values vary from 0.66 to 1.23 with a mean value of 1.06 and they are outside the range suggested by Laurenson & Mein (1995).

Zhang and Cordery suggested that a linear routing approach may be more appropriate when estimating large floods. Furthermore, they stated that it is necessary to analyse the recession curves of large events by fitting different functions to select the best-fit function and then it could be used to estimate floods.

Zhang and Cordery (1999b) investigated the travel time and storage-discharge relations (shown in equation 2.88) for flood estimation by means of a newly introduced volume law. This law has the capacity to illustrate the nature of storage distribution to th estimate the parameters K and ki, which is the storage delay time for the i sub- catchment.

Since there is no significant lateral flow into the river reach, the time difference between upstream and downstream flood peaks has been considered as K in their study, although a number of other methods, such as speed-discharge analysis, from measured data etc., are available to estimate the K value. The data of Brushy Creek, Texas, USA, and Wanshuri River, Hunan, China, found from studies done by Singh, V. P. (1988) and Zhang, Y. L. and Lin, S. Y. were used to find out the relations between travel time (K) and Discharge (Q).

In their second part of the investigation they introduced the volume law to the time invariant system and tested South Creek and Eastern Creek in NSW, Australia, using the Piecewise Linear Model (PLM) and WBNM model. A single value of K is adopted for the selected six events.

The results from the two parts of the investigations revealed the following: (i) For low discharges variation in K is quite significant, and for high flows K gave a constant value, for both Brushy and Wanshuri River flows. 48

(ii) The hydrographs produced by PLM and WBNM showed over-estimated rising limb with that of observed hydrograph. However, PLM made a complete match with the falling limb.

In view of the above findings Zhang and Cordery concluded the following; • For large floods constant travel time K is more appropriate;

• The ki of subcatchments can be interpolated by means of K; • The linear time invariant system could be used to achieve storage routing; and • There is no need to incorporate any trial and error procedure.

2.7 Studies with RORB Model.

Morris (1982) carried out extensive studies to estimate runoff routing model parameters for ungauged catchments. He used results from 86 catchments in all six states of Australia, to calibrate the RORB model. The value of ‘m’ (shown in equation 2.95) was kept as a constant and kc (shown in equation 2.97) was related to catchment area, for each case. The catchment areas used in Victoria, vary from 20 to 1924 km2, and areas in the other regions have not been indicated in his paper. The general formula applicable to Australian catchments, found from his study is: 0.48 kc = 2.00 A , m = 0.75 (2.126) The regional formulae are, 0.59 Victoria kc = 1.37 A , m = 0.75 (16 catchments) (2.127)

0.32 Tasmania kc = 4.86 A , m = 0.75 (17 catchments) (2.128) 0.47 Western Australia kc = 2.48 A , m = 0.80 (24 catchments) (2.129) 0.71 Queensland kc = 0.35 A , m = 0.75 (25 catchments) (2.130)

Morris recommended the equation (2.130) for all Queensland catchments. Hence for catchments less than 2000km2 the equation is: 0.85 kc = 0.15 A , m = 0.75 (2.131)

He indicated that there were insufficient data in the remaining states to derive formulae for kc. Morris considered, m = 0.75 to be the best value for ungauged catchments. 49

According to his findings it is interesting to note that the equation (2.126) has been derived by using 86 data pairs and the value of exponent is very close to 0.5. He further indicated that his findings are consistent with the results obtained by Askew (1970), and Laurenson et al., (1978). Therefore, the value of 0.5 as the exponent of ‘A’ can be regarded as a correct value, Morris emphasised.

Flavell et al., (1983) engaged in studies to estimate the model parameters of the runoff routing method of flood estimation (Mein, Laurenson and McMahon 1974) for ungauged rural catchments.

The purpose of the study was to develop regional formulae by using the data related to catchment characteristics in the four regions of Australia and the estimated kc parameter values of the model. These values were obtained from stream flow and pluviograph data, using the AR&R fitting procedure.

They published results for 52 gauged catchments with areas ranging from 5.46 km2 to 6526 km2 throughout the state of Western Australia (WA). They divided the state into four regions and developed formulae for each region. In all cases ‘m’ was set at 0.8 and

‘kc’ was related to the physical characteristics of catchments, and they are, the length of main stream, catchment area, and slope. They found the following relations: 0.93 South West kc = 1.45 L (2.132) 0.55 kc = 1.61 A (2.133)

0.71 -0.76 Wheat-belt kc = 3.00 L Sc (2.134) 0.43 -0.72 kc = 3.26 A Sc (2.135) 0.92 North West kc = 0.46 L (2.136) 0.51 kc = 0.58 A (2.137) 0.64 Kimberley kc = 0.34 A (2.138) 1.12 kc = 0.27 L (2.139) They compared these relations with those proposed by Weeks et al., (1979) for Queensland catchments and Morris (1982) for other regions of Australia. As described by Flavell et al., very similar relationships were found for all regions except for Tasmania, which does not appear to fit the general trend.

The relationships between kc and L for the four regions of WA shown in the above equations were plotted by Flavell et al., to compare the results. Similar results were found for Wheat-belt, North West and Kimberley regions and the following equations were found after combining the results of those three regions: 0.87 -0.46 kc = 1.06 L Sc (2.140) 0.46 -0.52 kc = 1.79 A Sc (2.141)

Furthermore, the plot of kc versus L of the three regions revealed that 30% of the kc values are in the lowest confidence category. After removing that 30% of the data by means of the regression analysis the following equation was found: 0.83 -0.48 kc=1.26L Sc (2.142)

They indicated that the equation (2.142) is very similar to the equation (2.140).

The similarities and the differences of the three major runoff routing models RORB, RSWM (RAFTS) and WBNM were examined by Sobinoff et al., (1983). Furthermore, the relationships between runoff routing parameter and the physical characteristics of Newcastle, Sydney and Wollongong catchments were explored and compared with the relationships given in the models.

They selected 26 rural catchments (areas ranging from 0.09 km2 to 4560 km2) and the following relationships were found for RORB model: 0.45 kc = 1.09 A (2.143) 0.79 kc = 0.73 L (2.144) 0.62 -0.31 kc = 2.38 L Sc (2.145)

As described by Sobinoff et al., in their paper the relationships obtained from the three models are fairly inconsistent. However, the most suitable and easy to apply model for rural catchments is WBNM, they further insisted.

Hairsine et al., (1983) evaluated the runoff routing parameters of the RORB model for small agricultural catchments to obtain regional parameters. The purpose of their study was to support the soil conservation schemes implemented by the private and the government organizations, to construct expensive drainage works on various catchments totally or partially. 51

They used four gauged agricultural catchments ranging in size from 2.5km2 to 50km2 with eight flood events. They indicated in their paper that the natural behaviour of these catchments (nested in the large catchment of Eastern Downs of Queensland, Australia) are disturbed in modeling by altering their lengths, slopes, stream patterns due to sub- division.

The relationship for kc of RORB model proposed by Weeks (1980) and Morris (1981), has been tested by this study and proposed the following equations:

0.62 • Hairsine et al., kc = 0.80 A (2.146) • Weeks, Morris and Hairsine et al., 0.61 kc = 0.68 A (2.147) The results revealed that the RORB model can be applied to small agricultural catchments and equation (2.146) is more appropriate for them. Furthermore, the equation (2.147) shows a better relationship for Queensland catchments.

Netchaef et al., (1985) calibrated the RORB model by using 8 catchments in the Pilbara Region in North Western Australia and their sizes ranging from 70km2 to 4456km2. Almost all of these catchments are relatively flat with an average slope less than 1%.

Furthermore, due to the unavailability of data for these catchments, flood data from nearby catchments were used for the calibration and that was done in two phases: (i) calibrated RORB by using data of various regional catchments; and (ii) correlated the recorded peak flows on the regional catchments to the catchment characteristics such as area, slope, etc.,

The results obtained from their study were compared with the results obtained by Flavell (1983) and Lipp (1983). Although the results found to be compatible, they indicated that more information related to this region is required. Thus light rains tend to make flooding in flat areas, and therefore, it is difficult to model with RORB in those circumstances.

Weeks (1986) applied the runoff routing model RORB to Queensland catchments to obtain model parameters for ungauged catchments. He selected 94 catchments (areas 52

ranging from 2.5 km2 to 16400 km2) from various parts of Queensland, Australia, for his study. Out of 94 catchments only 86 were used, due to the unsuitability of eight catchments, for the regional studies. The most suitable equation for the parameter ‘kc’ of RORB was found to be: 0.53 kc = 0.88 A (2.148) As suggested by Weeks equation (2.148) is very close to, 0.50 kc = 1.00 A (2.149) Weeks carried out two tests to improve the accuracy of this formula. First is to find out whether there is a considerable variation in kc for various regions. Second is to find out whether the stream slope has any significant effect on kc. Weeks further indicated that, no regional differences were found for kc and the area of the catchment is more effective than the slope on kc.

McMahon and Muller (1986) assessed the application of the peak flow Parameter Indifference Curve (PIC) technique with un-gauged catchments.

They insisted the importance of finding a proper value for ‘m’ rather using a value between 0.7 and 0.8. They also examined the studies done by Weeks (1980); Morris

(1982); and Flavell et al., (1983) related to lag time parameter kc of the NLRR model, described in AR&R (1977). McMahon and Muller (1986), found “m” values by plotting the indifference curves for the various storm events and extended their work by plotting k/dc versus m to investigate the sensitivity of peak flow to model parameter values.

They used 36 storm events of ten catchments (sizes are ranging from 37.3km2 to 1639 km2) in Queensland, Australia, to carry out indifference curve analyses at gauging stations on rivers and streams along the Eastern coast of Queensland. The results revealed that the PIC approach, in the calibration of NLRR model for un-gauged catchments, enables to assign satisfactory model parameter values for un-gauged catchments in Queensland.

Hansen et al., (1986) carried out studies to improve the existing expressions, combining kc value of RORB model with the physical and hydrological characteristics of catchments. They used the data of 40 ungauged Victorian catchments in Australia and their sizes ranging from 20km2 to 3910km2. 53

0.5 In addition to (L/Sc ) and (dav/L) the following characteristics of the catchment were considered for their studies: (i) Catchment area (A), (ii) Mainstream length (L),

(iii) Mainstream slope (Sc), (iv) Mean annual rainfall (R), and

(v) Average flow distance (dav),

They found the following relationships: 0.52 • Whole Victoria, kc = 1.30A (2.150) -6 0.95 1.18 kc = 3.00 × 10 L R (2.151)   0.38 = × −6  L  1.46 −0.50 × -6 0.38 1.46 -0.69 k c 9.58 10 R SC = 9.58 10 L R Sc (2.152)  SC 

• Region – Mean annual rainfall > 800mm 0.45 kc = 2.57 A (2.153)

0.88 kc = 1.40 L (2.154)   0.45 =  L  0.45 -0.225 k c 2.11 = 2.11 L Sc (2.155)  SC 

• Region – Mean annual rainfall < 800mm 0.65 kc = 0.49 A (2.156) 0.74 -0.49 kc = 0.09 L Sc (2.157)   0.80 =  L  0.80 -0.40 k c 0.12 = 0.12 L Sc (2.158)  SC  The following practical considerations have been highlighted by them: • a standard value of m = 0.8 applies to all catchments; • measurement of catchment characteristics, A and R, must be consistent with the method, adopted by them; and • the relationship only validly apply within the catchment localities and the parameters used to derive them.

Wong (1989) carried out studies related to non-linearity in catchment flood response and examined the basic assumptions in various runoff routing models, especially involved with the power function as shown in equation (2.95).

He used three catchments for his study, two from Victoria and one from Western Australia with sizes of 460, 4720 and 550 km2 respectively. Manning’s equation, rearranged into the form given below was applied to estimate the flow, 0.6 -0.3 0.4 0.6 S = L A = L n (Sf) P Q (2.159)

Where, L is the length of reach; A is the flow area; Sf friction slope; P is the wetted perimeter.

The power function lag time relationship considered was: b tL = aQ (2.160) Where, a = m k and b = (m-1). In his paper he described the general concept behind modelling of storage effects in catchments and the role of the storage- discharge relationships in runoff routing models, especially in the RORB model.

From his investigations he found that the lag time to peak flow showed a fair degree of scatter in the plots. Fitting a power function to five storm events gave a low degree of non-linearity with a poor correlation. Wong argued that the functional form of the equation (2.95) is inadequate to represent the nonlinear behaviour of the flood runoff process, especially for higher floods. Hence he proposed a new S-Q relation consisting of two primary functions to represent in-bank and out-bank flow conditions with a transition. He stressed that neither the power nor the linear function is suitable for the entire range of discharges investigated in his study. The power function that he found for lag time is given by: -0.07 tL = 15.4 Q (2.161)

Various researchers have carried out a number of investigations to calculate parameters acceptable to catchments located in different regions of Australia for lag time in runoff routing models.

Yu and Ford (1989) argued that the regional relationships developed for kc in RORB model are misleading since kc is proportional to dav, which is the distance from the catchment outlet to its centroid. They also indicated that the network layout of the catchment for routing could have a bearing on the storage discharge relationship.

Although they mentioned the three models, RORB, WBNM and RSWM (RAFTS), in their investigations they discussed the RORB model in detail because of its common use.

With the intention of using a regional relationship for un-gauged catchments, a great deal of information related to kc (parameter of RORB model usually expressed as a power function of catchment area) from 15 catchments throughout Australia was collected by Yu and Ford. They devised the following relationship between dav and catchment area after examining 31 catchments in Queensland and 30 in Victoria (Australia): 0.58 dav = 0.78 A (2.162) This equation is similar to the relationship found by Langbein et al., (1947) and Gray (1961) by studying 47 and 340 catchments respectively in USA and they are:

0.57 dav = 0.85 A and (2.163) 0.50 dav = 0.63 A (2.164)

Yu and Ford also defined a relationship between kc and dav and it is:

∗ k k = c (2.165) d av Where k* is the parameter of the power function which relates to the cross-sectional area of the natural stream channel.

They further indicated that the lag time is proportional to dav and that could be seen from the following relations developed by all researchers mentioned above: 0.58 Lag time (tL) ∝ 0.78 A 0.85 A0.57 and 0.63 A0.55 56

Yu and Ford insisted the importance of recognising and minimising the effect of network layout by selecting the appropriate amount of sub-catchments. They have also mentioned about the studies done by Boyd in 1985, to check the influence on runoff routing modelling due to sub-division of catchment in their paper. The findings of Boyd have been taken into consideration to make their comments.

Dyer et al., (1993) investigated the reliability of RORB model, in the estimation of the total hydrograph, by introducing the base flow into the model. They strongly recommended the inclusion of the base flow component into the routing process in the model, especially for streams where base flow forms a significant part of large events.

Although the parameter kr of RORB model (shown in equation 2.97) allows the inclusion of the base flow, it does not consider the lag time of base flow component to transfer its full effectiveness into the process to obtain reliable flows. Hence the peak of the calculated total hydrograph would be less than that of the real hydrograph for a given storm. These errors lead to incorrect and invalid kr values, as described by Dyer et al.,

Despite the fact that, there is no absolutely accurate method available to introduce base flow into the RORB model runoff routing procedure, RORB model can be used, but with caution due to the inherent problems associated with it, they further expressed.

Bates et al., (1993) carried out in-depth studies to examine the nonlinear behaviour of the flood runoff process by means of the model parameters of RORB model and NLFIT program suite. As mentioned by them, most of these models rely on the assumption that the power function (m) of the storage (S)–discharge (Q) relation represents the relationship between a measure of travel time and discharge. This is to say that the degree of nonlinearity is incorporated into the model by assigning a value for the model parameter m of the equation (2.95).

The methods adopted and equations produced by Leopold and Maddock (1953); Laurenson (1964); Askew (1970); and Pilgrim (1966, 1976, 1977 and 1982) related to spatial scales namely, the points, river reach, and catchment, were investigated.

Those equations are: Formula of Leopold and Maddock, Width of water surface w = a Qb (2.166) Mean depth of channel d = c Qf (2.167) Mean Velocity v = g Qh (2.168) Where, Q = discharge of channel and a, b, c, f, g, and h are parameters.

Formula of Laurenson, -0.27 Variation in lag tL=24.5Q (2.169) Equations of Askew and Pilgrim are (2.61) and (2.67) respectively.

Subsequently a case study, involving rainfall runoff data from five Australian catchments (three from Western Australia and two from NSW, and their areas ranging from 24.9 km2 to 114 km2), was conducted using the RORB model and NLFIT program suite to examine the following: • the variation of model parameter estimates with increasing event size; • the variation of the parameter estimates and their standard deviations between storm events; and • the utility of approaches to the flood estimation.

As described by Bates et al., the RORB model consists of a rainfall excess part and a catchment storage part which routs the computed rainfall excess hyetograph to produce a surface runoff hydrograph. The value of m in equation (2.95) was kept at 0.8 in their first trial run. Furthermore, a constant loss rate for NSW catchments and a constant runoff coefficient for the Western Australian catchments were considered in their analysis.

The results revealed that the model parameter estimates vary widely between storms. They indicated that the use of calibrated runoff routing models to collect further information pertaining to nonlinearity of flood runoff is questionable. These findings are similar to that found by Wong in 1989.

The reliability and validity of model predictions on nonlinearity rely mainly on the floods that consist of both channel bank and overbank flows. Therefore, the parameter estimates obtained from model calibration are subject to considerable uncertainty as explained by Bates, et al., in their paper.

Chapman (1993) further examined the work done by Bates et al., 1993, by comparing his results with theirs for Eastern Creek catchment in NSW, Australia.

He put forward his own nonlinear model by introducing an additional processing stage, just before the catchment discharge stage, named as “Common unitgraph derived from streamflow data sets” compared to RORB model. Furthermore, the “Distributed nonlinear routing-linked storages” of RORB model was replaced with a stage named as “Lumped nonlinear routing Single Storage” in his model. He believed that this replacement would enable researchers to illuminate the nature of nonlinearities in the rainfall runoff process.

Although Bates et al., divided the April 1963 event of the Eastern Creek catchment into three separate parts, Chapman treated it as a continuous event in his both studies related to runoff hydrograph and baseflow analyses. The value of m was found to be 0.47 for his model whereas the value obtained by Bates et al., from their study is 0.75, and Chapman considered this difference as a major issue. Furthermore, he insisted that his model has the capacity to relate the hydrological processes with the nonlinear storage, which is representing the processes of detention storage and overland or shallow subsurface flow to a stream channel. More importantly, as emphasised by Chapman, the common unitgraph of his model effectively identifies all the linear system elements in the rainfall runoff process, and also it concentrates on the nonlinearity as well.

Moreover, in his previous publications, he described the importance of inserting the nonlinear storage between the loss model and the common unitgraph stage. The purpose of this insertion is to prevent the production of erroneous unitgraphs, such as longer duration unitgraphs with shorter peaks as described by Chapman.

Although the actual runoff hydrograph of the January 1962 storm event match closely with that produced by his model, the April 1963 three peaked runoff hydrograph had not performed well. The reason given by him for this difference is the baseflow separation technique used for multi-peak hydrograph analysis.

The aim of the work done by Dyer et al., (1995) was to improve the accuracy of regional prediction equations for the RORB model parameter kc. This improvement is based on the catchment similarity with respect to the parameter for which the prediction equations are to be determined.

The data in the form of prepared RORB model data files were obtained for a total of 72 catchments located in the East coast of the Australian Mainland, Tasmania, the Adelaide hills, and the South West of Western Australia.

Moreover, the catchments have been formed into groups, which are considered to be similar with respect to the representation of the catchment using the RORB model. The grouping of the catchments involved the following three stages: (i) Determination of the relevant catchment parameters with which to assess catchment similarity; (ii) Use of cluster analysis to determine the initial groups of catchments; (iii) Refine the groups found in (ii) using the Andrews curves.

A new parameter for the RORB model has been introduced to replace kc with c1 which is defined by the following equation: k = c c1 (2.170) d av In their analysis two RORB catchment models were developed and the first one has 1/2 used L/S as the predictor of time delay while the second used L to determine dav in km, and the length of the reaches modelled in RORB model. These can then be used to determine the group to which the catchment belongs. From this analysis it is possible to predict c1(08) and hence kc(08) and they are the values of c1 and kc for m = 0.8 respectively.

The research revealed that a greater accuracy can be obtained in the prediction of the empirical parameter kc for the RORB model. The parameter c1 is a more fundamental parameter than kc but can be readily related to the parameter kc by the factor dav. Yu and Ford (1989) suggested similar relationship according to their equation (2.165). Moreover, initial loss-proportional, loss model was found to be a more accurate representation of the observed hydrograph in this analysis.

The prediction equations of the RORB model parameter c1 are based on groups of catchments that are considered to be hydrologically similar with respect to the RORB model, as distinct to previous methods that imposed artificial geographic limitations.

Although the validation of these prediction equations for catchments is not considered in this study, Dyer et al., urged that the regions underrepresented in this study would give even greater confidence in the application of these equations as a general method of estimating the RORB model parameter kc.

The effect of catchment sub-division on runoff routing models has been investigated by Boyd (1985). According to his paper the runoff routing models, Clark (1945); Rockwood (1958); Nash (1960); and Laurenson (1964), for flood hydrograph synthesis, and the runoff routing models (which represent the catchment stream water and sub- areas) RORB (Mein, Laurenson and McMahon 1974; Laurenson and Mein 1983), RSWM or RAFT (Goyen and Aitken 1976) and WBNM (Boyd, Pilgrim and Cordery 1979 a & b) have been considered for his investigations.

The linear runoff-routing models were evaluated by using the equations developed by Nash (1960) and they express the terms such as the distance from the centroid of excess rainfall hyetograph to the centroid of the outflow hydrograph (u1) and the variance (u2). Those variables are given in the following equations respectively

∝ ∫ u(t).t.dt = 0 u1 ∝ (2.171) ∫ u(t) dt 0

∝ 2 ∫ u(t)(t - u1 ) dt = 0 u2 ∝ (2.172) ∫ u(t) dt 0

Here ‘u1’ represents the lag time (tL) between rainfall and the outflow.

The properties of runoff routing models were studied by using the first order linear equation which represents the linear reservoir and it is given by: d k []q(t) + q (t) = i(t) (2.173) dt

Where, ‘k’ is equal to the lag time (tL) between inflow and outflow.

The lag time is then related to the catchment area, by reducing all equations developed by various researchers to a common form of: X Lag time (tL) = C A (2.174) Where, C is the lag parameter.

The catchment main stream slope (Sc) has been kept as a separate independent variable in his study due to its poor correlation. According to the findings from nearly 60 catchments in Australia with areas ranging from 0.2 km2 to 2200 km2, Boyd, suggested the following: (a) For linear models the lag parameter has the form of: K = C A x (2.175) (b) For non-linear models the lag parameter has the form of: K = C A0.57 q-0.23 (2.176)

It is revealed that there is an impact on lag parameter as the number of sub-areas (Z) increases. However, the number of sub-areas depends on the size of the catchment considered for the analysis. The minimum value of ‘Z’ varies from 4, 7 and 15 for catchment areas 0.1, 10 and 1000 km2 respectively. If the value of ‘Z’ is below its maximum value, then the outflow hydrograph properties could vary significantly. However, if the number of sub-areas in a catchment is fairly large then the model response approaches the case of pure translation in the outflow hydrograph, as described by Boyd, in his paper.

The estimated peak runoff was utilised to carry out risk-based assessment in small catchments by Jenkins et al., (2002). One of the intentions of their study was to formulate a methodology that has the capacity to include the natural phenomenon of the catchment in the rainfall runoff process.

The statistically based Rational Method and deterministically based models such as RORB, WBNM, and RAFTS (HECI) were examined, as their methods towards the peak flow estimation of the runoff routing process. The intention of this examination is to select either the method or one of the models as the methodology for their study.

However, due to a number of short comings in the Rational Method and the limitations in the Models, Jenkins et al., selected a more appropriate, as they defined, Statistical Modelling Approach (incorporated an advanced storm pattern) as their methodology for the study. In addition to the following capabilities, this methodology complies with the complex nature of the hydrologic process existent in the catchment during storm events: • The statistical Modelling Approach (SMA) procedure is much simpler and the peak runoff produced by SMA for a specific ARI is similar to that made by the deterministic approach for storm temporal patterns. • A statistical model for catchment response can be utilized with SMA and it uses a single simulation to produce peak runoff for any point in the catchment.

Jenkins et al., selected a storm pattern of type class 2 (known as a fully advanced storm pattern) for their methodology, and this pattern was defined by Pilgrim and Cordery (1975) which is similar to the Chicago Storm Pattern proposed by Keifer and Chu (1975). This pattern considers the following three most important characteristics: (i) the volume of water falling within the maximum period; (ii) the amount of antecedent rainfall; and (iii) the location of the peak rainfall intensity on the hyetograph.

Jenkins et al., indicated that this fully advanced storm pattern has the capacity to represent the intensity versus duration characteristics of the statistically based IFD data. Moreover, the surface infiltration, depression storage, surface detention and surface 63

runoff properties have been considered in the formulation of the advanced storm pattern as described by Keifer and Chu in their paper.

The WBNM model was adopted with fully advanced storm pattern by Jenkins et al., in their study. They further explained that the WBNM is similar in computational work, to other network based runoff routing models such as RORB and RAFTS.

They applied their methodology to two hypothetical catchments as trial tests and extended their assessment by using 47 catchments (areas ranging from 4km2 to 249km2) in Queensland, Australia, to determine the actual flood frequency characteristics at stream gauging stations. The WBNM model was calibrated in the following manner: • minimum lag parameter C value for 100 year ARI case; • maximum C value for 1 year ARI case; • keeping C constant for all ARI’s by varying the proportional loss. The results indicated the following: • significant variation in C with the variation of ARI of storms; • low proportional loss rates were shown by storms with a large ARI which means that storms have been preceded by some rainfalls which made the catchment fairly wet.

Similar results were found by McDermott and Pilgrim (1982) and Weeks (1991) when they used frequency factors to show that the increasing ARI tends to increase the runoff coefficients as explained by Jenkins et al., in their paper.

Some of the advantages of the methodology they used in their study are described in the following manner: • The network based WBNM model is capable of producing results to illustrate the variation of accurately estimated peak runoff and ARI, with little computational work; • By introducing the fully advanced storm pattern, the WBNM model allows the prediction of the peak runoff at all gauging stations throughout the catchment. 64

Since the annual exceedence probability (or ARI) governs the level of risk in any engineering practice, an effective assessment of that risk would not be possible without the assistance of an advanced storm pattern. Therefore, the rainfall-runoff models which are capable of predicting the deterministic processes taking place in catchments during storm events, could not produce satisfactory results for risk assessment without incorporating advanced storm patterns into the models, they further described.

2.8 Summary of Lag Relations The foregoing findings revealed that a considerable number of rainfall variables, basin physiographic characteristics, hydrographic factors and linear and non-linear model parameters have been selected in various investigations conducted by the researchers. The factors that have been used in most studies of lag time are: • Rainfall Intensity (average and excess), • Duration of rainfall, • The rise time of the outflow hydrograph, • Peak flow of the main stream, • Catchment area, • Slope of the main stream, • Main stream length, • Length to the centroid of catchment, • Shape factor of catchment, • Roughness of the main stream (Manning’s coefficient).

The equations found from the literature review are summarised in Table 2.1. Wherever possible these equations are reduced to common forms of physical and hydrological characteristics of catchments by using the relationships found by Gray (1961), shown in Equations 2.39 to 2.43. For example Equation 2.145 (found kc of RORB by Sobinoff et al., 1983) expresses kc in terms of L and Sc, 0.62 -0.31 kc = 2.38 L Sc Using equation 2.39 to replace L yields: 0.57 0.62 -0.31 kc = 2.38 (1.31 A ) Sc 0.35 -0.31 kc = 2.81 A Sc 65

As shown in equation 2.43, Sc is also related to A, and therefore, the above equation can be further reduced to contain A only, and it is: 0.35 -0.38 -0.31 kc = 2.81 A (17.98 A ) 0.47 kc = 1.15 A

The physical characteristics of the catchment, such as L, Sc and Lca, of all the equations described in this chapter are reduced to a common form of catchment area A as indicated in column 5 of Table 2.1.

Table 2.2 provides a similar summary, where the equations are reduced to consist only of A (column 2), or A & Sc (column 3) or Q (column 4) or A, Q & IR (column 5).

The majority of the findings have revealed that the lag time is directly proportional to a power function of the catchment area (A). Although the value of that exponent varies from 0.15 to 1.08, most of the values are between 0.32 and 0.75. The mean and median values of all the exponents of A shown in column 2 of Table 2.2 are 0.53 and 0.50 respectively. This median value fully agrees with the suggested value of 0.50 by Morris in 1982, after calibrating the RORB model. The mean value of the findings is also very close to 0.50. The mean and median values (0.53 and 0.50) are also very close to the exponent adopted in WBNM (0.57).

The results of some of the studies of the researchers have shown that the lag time is inversely proportional to a power function of the slope of the main stream (Sc) and the main channel outflow (Q) as shown in columns 3 and 4 of Table 2.2 respectively.

The mean and median values of the exponents of Sc of 48 equations shown in column 3 of Table 2.2 are -0.39 and -0.33 respectively. The range of these exponents is between - 0.10 and -1.47. Except for the one value (-1.47) the other exponents are between -0.10 and -0.76.

The mean and median values of the exponents of Q of 18 equations shown in column 4 of Table 2.2 are -0.54 and -0.26 respectively. The range of these exponents is between -0.07 and -1.60. It is important to note that thirteen values of these exponents are between -0.07 and -0.87 (which implies a lower reduction rate in lag time as Q 66

increases), whereas the remaining five values are equal or less than -1.0 (which indicates abrupt reduction in lag time for smaller Q values and a very low reduction rate in lag time for larger Q values). The median value of -0.26 of the exponent of Q found from the literature review is very close to the values suggested in the RORB model and Askew (1970) and they are -0.25 (m = 0.75) and -0.23 respectively. The median value (-0.26) is also very close to the value adopted in WBNM (-0.23).

Furthermore, a considerable number of studies has indicated that the rainfall intensity, mean annual rainfall intensity, duration of rainfall, duration of rainfall excess, porosity of soil, etc., of catchments are also influencing the lag time.

In view of the above, the intention of this research is to calculate lag parameters for natural catchments and also to find out to what extent the hydrological, geomorphological and climatological characteristics of catchments could influence the lag parameter. Seventeen gauged natural catchments of Queensland, Australia, with rainfall and flow data for 254 storm events, which have occurred during the past ten to fifteen years, have been selected for the study. The analysis of data is done by means of the WBNM computer program due to the following reasons:

(a) WBNM is very suitable for natural catchments (Sobinoff et at., 1983); (b) It is an event model; (c) It is easy to use because only one parameter ‘C’ has to be evaluated; (d) Geomorphological characteristics of catchments have been embedded into the model; (e) Spatial variability of land use, infiltration and rainfall have been considered in the model; and (f) Four rainfall loss methods are available in the program and it is user friendly.

Table 2.1 - Summary of equations of various researchers related to lag time

Catchment size Number of Developed equation (metric units) Reduced equation Source 2 w x y z x Country range (km ) Catchments Lag time = (Other factors) L A Sc Q Lag time = (Other factors)A

- -0.2 Rockwood (1958) 1 Ts = K Qt – USA - 0.47 0.47 -0.23 0.47 0.36 Kerby (1959) 1 tc = 3.03 L n Sc tc = 1.77 n A USA t = 10.39 A0.3 (OLS)-0.3 t = 4.37A0.41 UK Nash (1960) 12.4 - 2225 90 L L 0.3 -0.33 0.29 tL = 8.11 L Sc tL = 3.39 A UK t = 0.004 q -1.6 – USA Amorocho (1961) --p max -1..26 tp = 0.013 qmax – USA L = 1.31 A0.57 – USA L = 0.55 L0.96 – USA Gray (1961) 0.6 - 84.5 47 ca 0.55 Lca = 0.71 A – USA -0.662 SC = 21.5 L – USA 1.005 tL = tc = 1.017 PR – USA P = 0.17 γ’L0.498S -0.249 t = 0.09 γ’1.005A0.38 USA Gray (1961) 0.6 - 84.5 42 R c L 0.562 -0.281 1.005 0.43 PR = 0.22 γ’L Sc tL = 0.09 γ’ A USA 0.531 -0.266 1.005 0.41 PR = 0.27 γ’L Sc tL = 0.14 γ’ A USA Morgan and Johnson (1962) - Tested the equations of three researchers and SCS • 0.3 0.34 Snyder tL = 0.75(Cc)(LLca) tL = 0.73 Cc A USA • Soil Conservation Service (SCS) P = 0.21A V Q -1.0 P = 0.21 V Q -1.0 A1.0 USA 26 - 262 12 R P R P • -1 -1 1.0 Common PR = 4.96 A QP PR = 4.96 QP A USA • 0.74 0.74 Mitchell tL = 0.30 A tL = 0.30 A USA t = 4.32 A1.085 L-1.233 S -0.668 t = 0.45 A0.64 USA Wu (1963) 7.5 - 260 17 p c p 0.937 -1.474 -1.473 0.66 K1 = 21.7 A L Sc k1 = 0.21 A USA -0.27 Laurenson (1964) 90.7 1 tL = 24.5qm – Australia 0.24 -0.40 0.8 0.8 0.42 C = 23.03 (LLca) Sc n C= 7.12 n A Australia Cordery (1968) 0.05 - 642 12   0 . 79  W + 0 .5 Ln    K = 5.5  ( OLS ) ( Sc )  – Australia -6 -6 0.66 0.66 -0.33 0.66 0.50 Viessman Jr. (1968) 6.7x10 - 3865x10 6 tL = 1.78 n L Sc tL = 0.82 n A USA 0.47 0.26 Tm = 0.92 Lca Tm = 0.78 A USA -0.14 -0.6 0.15 Bell and Kar (1969) < 130 47 Tm = 3.20 L Sc Tm = 0.54 A USA 0.77 -0.39 0.59 tL = 10.25 M L Sc tL = 4.90 M A USA 0.57 -0.23 -0.23 0.57 tL = 2.12 A qwm tL = 2.12 qwm A Australia 0.54 -0.16 -0.23 -0.23 0.60 Askew (1970) 0.4 - 90 5 tL = 4.83 A (OLS) qwm tL = 3.0 qwm A Australia 0.80 -0.33 -0.23 -0.23 0.58 tL = 8.57 L (OLS) qwm tL = 4.10 qwm A Australia 0.6 0.6 -0.4 -0.3 0.6 -0.4 0.46 Ragan & Duru (1972) --tc = 57.8 L n IR Sc tc = 28.6 n IR A USA

French et al., (1974) - Tested the equations of seven researchers

• 0.77 -0.385 0.59 Ramser-Kirpich tc = 0.94 L Sc tc = 0.38 A USA • -0.1 -0.20 0.75 Bransby-Williams tc = 0.97 L A Sc tc = 0.71 A USA • 0.5 0.5 McIllwraith tc = 0.62 FA + 0.7 tc = 0.62 F A + 0.7 USA • 0.33 0.33 Bell < 250 37 tc = 0.73 B A tc = 0.73 B A USA • 0.40 0.40 Hoyt and Langbein tc = 0.68 B1 A tc = 0.68 B1 A USA • 0.47 0.47 -0.23 0.47 0.36 Bruce and Clark tc = 3.05 n L Sc tc = 1.78 n A USA • -1.0 -0.15 -0.1 -0.4 -1 -0.15 0.62 Friend tc = 52.7(ch) (CR Fy K s) L A Sc tc =21.7(ch) (CR Fy K s) A USA 0.41 -0.41 0.39 C = 2.90 L Sc C = 0.99 A Australia Cordery & Webb (1974) < 250 21 0.32 K = 0.66 L0.57 K = 0.77 A Australia 5 0.6 0.4 -0.3 5 0.6 0.4 0.68 Mein et al., (1974) 339 - 2300 4 k = 6.64 x10 n W L Sc k = 3.66 x 10 n W A Australia t = 13.38 q – Australia Reed et al., (1975) 19 1 L m -0.87 tL = 7.12 qm – Australia

Table 2.1 - Summary of equations of various researchers related to lag time (Contd.,)

Catchment size Number of Developed equation (metric units) Reduced equation Source 2 w x y z x Country range (km ) Catchments Lag time = (Other factors) L A Sc Q Lag time = (Other factors)A

-0.492 Pilgrim (1976) 250 1 Tcm = 0.83qp – Australia 0.6 -0.4 -0.3 0.6 -0.4 0.46 Pedersen et al., (1978) 0.34 - 6.00 3 tL = 28.9 (L n) IR Sc tL = 14.28 n IR A USA Weeks and Stewart (1978 ) - Tested two models of five researchers K = 3.90 L0.71 K = 4.72 A0.40 Australia C =1.70 L0.94 S -0.47 C = 0.56 A0.71 Australia • Clark-Johnstone c K = 0.09 L1.03 K = 0.12 A0.59 Australia 41 - 2331 27 0.69 -0.35 0.53 C = 0.96 L Sc C = 0.42 A Australia k = 0.89 A0.91 k = 0.89 A0.91 Australia • Mein, Laurenson & McMahon k = 0.69 A0.63 k = 0.69 A0.63 Australia L = 1.813 A0.53 – Australia Boyd (1978) 9 - 22500 79 -0.32 SC = 51.07 A – Australia 0.38 0.38 KB = 2.51 A KB = 2.51A Australia Boyd (1978) 0.39 - 39.8 4 0.38 0.38 KI = 1.50 A KI = 1.5 A Australia K = C A0.57 Q-0.23 K = C Q-0.23 A0.57 Australia Boyd (1979) 0.39 - 251 10 B B 0.5 -0.23 -0.23 0.50 KI = 0.6 C A Q KI = 0.6 C Q A Australia Baron et al., (1980) - Tested the equations of five researchers and the AR&R 0.41 -0.41 C = 0.99 A0.39 Australia • C = 2.90 L Sc Cordery and Webb 0.32 K = 0.66 L0.57 K = 0.77 A Australia C = 1.50 L0.58 S -0.29 C = 0.76 A0.44 Australia • AR&R c K = 0.08 L1.05 K = 0.12 A0.60 Australia 0.05 - 15043 52 0.40 -0.40 0.38 C = 3.00 L Sc C = 1.05 A Australia 0.50 -0.25 C = 0.94 A0.38 Australia • C = 1.70 L Sc Baron, Cordery and Pilgrim 0.32 K = 0.70 L0.57 K = 0.82 A Australia 0.18 K = 1.00 L0.31 K = 1.10 A Australia Bates and Pilgrim (1982) -0.236 --tL = 15.4 qwm – Australia 0.38 -0.15 0.48 Linsley et el.,(1982) --tp = 2.59 CC (LLca) SC tp = 0.63 A USA 0.38 0.38 Pilgrim & McDermott (1982) < 250 308 tc = 0.76A tc = 0.76 A Australia 0.48 0.48 kc = 2.00 A kc = 2.00 A Australia 0.59 0.59 kc = 1.37 A kc = 1.37 A Australia k = 4.86 A0.32 k = 4.86 A0.32 Australia Morris (1982) 20 - 1924 86 c c 0.47 0.47 kc = 2.48 A kc = 2.48 A Australia 0.71 0.71 kc = 0.35 A kc = 0.35 A Australia 0.85 0.85 kc = 0.15 A kc = 0.15 A Australia k = 2.2 A0.50 k = 2.2 A0.50 Australia Laurenson and Mein (1983) - - c c 0.50 -0.25 -0.25 0.50 tL = 2.2 A Q tL = 2.2 Q A Australia Bates and Pilgrim (1983) 0.46 -0.32 0.17 -0.32 0.17 0.46 0.39 - 89.60 5 tL = 3.17 A Pe De tL = 3.17 Pe De A Australia k = 0.80A0.62 k = 0.80A0.62 Australia Hairsine et al., (1983) 2.5 - 50 4 c c 0.61 0.61 kc = 0.68A kc = 0.68A Australia 0.54 0.54 Flavell (1983) < 250 48 tc = 2.31 A tc = 2.31A Australia 0.93 0.53 kc = 1.45 L kc = 1.86 A Australia 0.55 0.55 kc = 1.61 A kc =1.61 A Australia k = 3.00 L0.71 S -0.76 k = 0.40 A0.69 Australia Flavell (1983) 5.46 - 6526 52 c c c 0.43 -0.72 0.70 kc = 3.26 A Sc kc = 0.41 A Australia 0.92 0.52 kc = 0.46 L kc = 0.58 A Australia 0.51 0.51 kc = 0.58 A kc = 0.58 A Australia

Table 2.1 - Summary of equations of various researchers related to lag time (Contd.,)

Catchment size Number of Developed equation (metric units) Reduced equation Source 2 w x y z x Country range (km ) Catchments Lag time = (Other factors) L A Sc Q Lag time = (Other factors)A

0.64 0.64 kc = 0.34 A kc = 0.34 A Australia 1.12 0.64 kc = 0.27 L kc = 0.37 A Australia 5.46 - 6526 52 0.87 -0.46 0.67 Flavell (1983) - (Contd.,) kc = 1.06 L Sc kc = 0.35 A Australia 0.46 -0.52 0.66 kc = 1.79 A Sc kc = 0.40 A Australia 0.83 -0.48 0.66 kc = 1.26 L Sc kc = 0.39 A Australia 0.50 -0.32 -0.32 0.50 Laurenson (1983) --Kc = 2.2 A Q Kc = 2.2 Q A Australia 0.45 0.45 kc = 1.09 A kc = 1.09 A Australia 0.79 0.45 Sobinoff et al. (1983) 0.09 - 4560 26 kc = 0.73 L kc = 0.90 A Australia 0.62 -0.31 0.47 kc = 2.38 L Sc kc = 1.15 A Australia 0.53 0.53 Weeks (1986) 2.5 - 16400 94 kc = 0.88 A kc = 0.88 A Australia L = 1.09 A0.67 – Australia -0.61 Sc = 47.42 L – Australia -0.42 Sc = 47.80 A – Australia 0.65 0.65 tc = 0.487 A tc = 0.487 A Australia 0.49 0.49 Black et al., (1986) 3.05 - 940 20 Tm = 1.00 A Tm = 1.00 A Australia 0.56 -1.0 0.70 tc = 4.752 L Sc tc = 0.31 A Australia 0.65 0.65 tc = 0.50 A tc = 0.50 A Australia 0.58 -0.17 0.48 tc = 0.95 A L tc = 0.91A Australia -0.113 -0.215 1.015 0.55 tc = 1.02 A Sc L tc = 0.71A Australia 0.52 0.52 kc = 1.30 A kc = 1.30 A Australia -6 0.95 1.18 -6 1.18 0.54 kc = 3.00 x 10 L R kc = 3.88 x 10 R A Australia -6 0.38 1.46 -0.69 -4 1.46 0.48 kc = 9.58 x 10 L R Sc kc= 1.70 x 10 R A Australia 0.45 0.45 kc = 2.57 A kc = 2.57 A Australia 0.88 0.50 Hansen et al., (1986) 20 - 3910 40 kc = 1.40 L kc = 1.78 A Australia 0.45 -0.225 0.34 kc = 2.11 L Sc kc = 5.88 A Australia 0.65 0.65 kc = 0.49 A kc = 0.49 A Australia 0.74 -0.49 0.61 kc = 0.09 L Sc kc = 0.79 A Australia 0.80 -0.40 0.61 kc = 0.12 L Sc kc = 0.74 A Australia t = 0.25 n 0.52 L0.50 S -0.31 I -0.38 t = 0.12 n 0.52 I -0.38 A0.41 USA Papadakis & Kazan (1987) < 2.02 375 c o c ex c o ex 0.52 0.52 -0.35 -0.35 0.52 -0.35 0.43 tc = 0.16 no L Sc Iex tc = 0.07 no Iex A USA -0.07 Wong (1989) 460,550 and 4720 3 tL =15.4 Q – Australia 0.58 0.58 tL ∝0.78 A tL ∝0.78 A Australia 0.57 0.57 Yu & Ford (1989) - 15 tL ∝ 0.85 A tL ∝ 0.85 A Australia 0.50 0.50 tL ∝0.63 A tL ∝0.63 A Australia 0.1 0.53 Hughes (1993) < 2.60 42 Tv = 0.41 L Sc Tv = 0.72 A USA -- 0.6 0.6 -0.3 -0.4 0.6 -0.4 0.45 Wong (1996) tc = 58.47 n L Sc IR tc = 23.0 n IR A Singapore -1.28 0.28 -0.28 -1.28 0.39 Kull and Feldman (1998) 6048 and 7304 2 tc = 8.29 [1 + (0.03)Iimp] A Sc tc = 3.69 [1 + (0.03)Iimp] A USA Yang and Lee (1999) - Tested the equations of five researchers and the TSWCS • 0.77 -0.385 0.59 Kirpich tc = 0.94 L Sc tc = 0.38 A USA • 0.22 -0.35 -0.35 0.22 Kadoya tc = 0.017 CR A Iex tc = 0.017 CR Iex A Taiwan • Rziha t = 0.014 L 1.60 H-0.6 t = 0.02 H-0.60 A0.91 Taiwan 0.114 - 0.344 3 c c t =0.23 n 0.6 L0.6 (OLS)-0.30 I -0.40 t = 0.11 n 0.6 I -0.40 A0.45 Taiwan • Yang and Lee c o t R c o R 2 0.6 0.4 -0.4 0.6 -0.3 -0.40 2 0.6 0.4 -0.40 1.08 tc = 9.25× 10 n W Lo L Sc IR tc = 5.08x10 n W IR A Taiwan • 0.5 -0.5 0.69 TSWCS tc = 79.06 A (OLS) tc = 18.64 A Taiwan

Table 2.2 - Summary of equations reduced to common forms of different physical and hydrological characteristics of catchments

x ∝ x y z x z R Source Lag time ∝ A Lag time ∝ A Sc Lag time ∝ Q Lag time ∝ A Q I

-0.2 Rockwood (1958) ––Qt – 0.36 0.27 -0.23 Kerby (1959) A A Sc –– A0.41 A0.3 (OLS)-0.3 –– Nash (1960) 0.29 0.17 -0.33 A A Sc –– ––q -1.6 – Amorocho (1961) max -1.26 –– qmax – –––– –––– Gray (1961) –––– –––– ––––

0.38 0.28 -0.25 A A Sc –– Gray (1961) 0.43 0.32 -0.28 A A Sc –– 0.41 0.30 -0.27 A A Sc –– Morgan and Johnson (1962) - Tested the equations of three researchers and SCS • Snyder A 0.34 ––– • 1.0 -1.0 -1.0 Soil Conservation Service (SCS) A – QP A QP • 1.0 -1.0 -1.0 Common A – QP A QP • Mitchell A0.74 ––– A0.64 A0.38 S -0.67 –– Wu (1963) c 0.66 0.10 -1.47 A A Sc –– -0.27 Laurenson (1964) ––qm – A0.42 A0.27 S -0.40 –– Cordery (1968) c –––– 0.50 0.38 -0.33 Viessman Jr. (1968) A A Sc –– A0.26 ––– 0.15 0.09 -0.60 Bell and Kar (1969) A A Sc –– 0.59 0.44 -0.39 A A Sc –– 0.57 -0.23 0.57 -0.23 A qwm A qwm 0.60 0.54 -0.16 -0.23 0.54 -0.23 Askew (1970) A A (OLS) qwm A qwm 0.58 0.46 -0.33 -0.23 A A (OLS) qwm – 0.46 0.34 -0.30 Ragan & Duru (1972) A A Sc ––

French et al., (1974) - Tested the equations of seven researchers

• 0.59 0.44 -0.39 Ramser-Kirpich A A Sc –– • 0.75 0.47 -0.20 Bransby-Williams A A Sc –– • McIllwraith A0.5 ––– • Bell A0.33 ––– • Hoyt and Langbein A0.40 ––– • 0.36 0.27 -0.23 Bruce and Clark A A Sc –– • 0.62 0.47 -0.4 Friend A A Sc –– 0.39 A A0.23 S -0.41 –– Cordery & Webb (1974) c A0.32 ––– 0.68 0.57 -0.30 Mein et al., (1974) A A Sc –– ––q – Reed et al., (1975) m -0.87 –– qm –

Table 2.2 - Summary of equations reduced to common forms of different physical and hydrological characteristics of catchments (Contd.,)

x ∝ x y z x z R Source Lag time ∝ A Lag time ∝ A Sc Lag time ∝ Q Lag time ∝ A Q I

-0.492 Pilgrim (1976) ––qp – 0.46 0.34 -0.30 Pedersen et al., (1978) A A Sc ––

Weeks and Stewart (1978 ) - Tested two models of five researchers

A0.40 ––– A0.71 A0.54 S -0.47 –– • Clark-Johnstone c A0.59 ––– 0.53 0.39 -0.35 A A Sc –– A0.91 ––– • Mein, Laurenson & McMahon A0.63 ––– –––– Boyd (1978) –––– A0.38 ––– Boyd (1978) A0.38 ––– A0.57 – Q-0.23 – Boyd (1979) A0.50 – Q-0.23 – Baron et al., (1980) - Tested the equations of five researchers and the AR&R 0.39 A A0.23 S -0.41 –– • Cordery and Webb c A0.32 ––– A0.44 A0.33 S -0.29 –– • AR&R c A0.60 ––– 0.38 0.23 -0.40 A A Sc –– A0.38 A0.29 S -0.25 –– • Baron, Cordery and Pilgrim c A0.32 ––– A0.18 ––– Bates and Pilgrim (1982) -0.236 –– qwm – 0.48 0.43 -0.15 Linsley et el.,(1982) A A Sc –– Pilgrim & McDermott (1982) A0.38 ––– A0.48 ––– A0.59 ––– A0.32 ––– Morris (1982) A0.47 ––– A0.71 ––– A0.85 ––– A0.50 ––– Laurenson and Mein (1983) A0.50 – Q-0.25 A0.50 Q-0.25 Bates and Pilgrim (1983) 0.46 0.46 -0.32 0.17 A –– A Pe De A0.62 ––– Hairsine et al., (1983) A0.61 ––– Flavell (1983) A0.54 ––– A0.53 ––– A0.55 ––– A0.69 A0.40 S -0.76 –– Flavell (1983) c 0.70 0.43 -0.72 A A Sc –– A0.52 ––– A0.51 –––

Table 2.2 - Summary of equations reduced to common forms of different physical and hydrological characteristics of catchments (Contd.,)

x ∝ x y z x z R Source Lag time ∝ A Lag time ∝ A Sc Lag time ∝ Q Lag time ∝ A Q I

A0.64 ––– A0.64 ––– 0.67 0.50 -0.46 Flavell (1983) - (Contd.,) A A Sc –– 0.66 0.46 -0.52 A A Sc –– 0.66 0.47 -0.48 A A Sc –– Laurenson (1983) A0.50 – Q-0.32 A0.50 Q-0.32 A0.45 ––– Sobinoff et al. (1983) A0.45 ––– 0.47 0.35 -0.31 A A Sc –– Weeks (1986) A0.53 ––– –––– –––– –––– A0.65 ––– Black et al., (1986) A0.49 ––– 0.70 0.32 -0.10 A A Sc –– A0.65 ––– A0.48 ––– 0.55 0.47 -0.22 A A Sc –– A0.52 ––– A0.54 ––– 0.48 0.22 -0.69 A A Sc –– A0.45 ––– Hansen et al., (1986) A0.50 ––– 0.34 0.26 -0.23 A A Sc –– A0.65 ––– 0.61 0.42 -0.49 A A Sc –– 0.61 0.46 -0.40 A A Sc –– A0.41 A0.29 S -0.31 –– Papadakis & Kazan (1987) c 0.43 0.30 -0.35 A A Sc –– Wong (1989) –– Q-0.07 – A0.58 ––– Yu & Ford (1989) A0.57 ––– A0.50 ––– Hughes (1993) A0.53 ––– 0.45 0.34 -0.30 Wong (1996) A A Sc –– 0.39 0.28 -0.28 -1.28 0.28 Kull and Feldman (1998) A A Sc – Iimp A Yang and Lee (1999) - Tested the equations of five researchers and the TSWCS • 0.59 0.44 -0.39 Kirpich A A Sc – • 0.22 0.22 -0.35 Kadoya A –– A Iex • Rziha A0.91 ––– A0.45 ––– • Yang and Lee 1.08 0.34 -0.30 A A Sc –– • TSWCS A0.69 A0.5 (OLS)-0.5 ––

CHAPTER 3

DESCRIPTION OF CATCHMENTS

3. DESCRIPTION OF CATCHMENTS

Seventeen rural catchments from five coastal river basins in Queensland (specified in Table 3.1) have been selected for this study. Details of the physical properties of these catchments appear in the following sections.

Table 3.1 – List of Catchments

National Area of River or Creek Location of Gauging Stations Gauging Station Station Catchment of Catchment Number (km2) longitude latitude Mary River Gympie 138900 2920 152o 39’ 18’’ 26o 11’ 23’’ Mary River Moy Pocket 138111 830 152o 44’ 59” 26o 32’ 00” Mary River Bellbird 138110 480 152o 41’ 59” 26o 38’ 00” Six Mile Creek Cooran 138107 165 152o 49’ 23” 26o 19’ 24” Tributary of Mary River Kandanga Creek Kandanga 138113 176 152o 41’ 03” 26o 23’ 16” Tributary of Mary River Haughton River Powerline 119003 1735 147o 06’ 33” 19o 38’ 05” Haughton River Mount 119005 1140 146o 57’ 29” 19o 46’ 27” Piccaninny Herbert River Zattas 116905 7292 145o 49’ 43” 18o 27’ 09” Herbert River Nash’s Crossing Not 6842 145o 46’ 18” 18o 24’ 48” available Herbert River Gleneagle 116004 5370 145o 19’ 53” 18o 11’ 37” Herbert River Silver Valley 116014 586 145o 18’ 00” 17o 38’ 00” Don River Reeves 121003 1010 148o 08’ 35” 20o 09’ 05” Don River Mount Dangar 121903 808 148o 07’ 14” 20o 13’ 17” Don River Ida Creek 121902 620 148o 07’ 01” 20o 17’ 28” North Johnstone Tung Oil 112004 930 145o 55’ 59” 17o 33’ 00” River North Johnstone Nerada 112905 808 145o 50’ 44” 17o 31’58” River South Johnstone Central Mill 112903 390 145o 59’ 00” 17o 36’59” River

Information related to land use, developed areas, topsoil & subsoil properties, climatic conditions, and texture of soils of most of the catchments in Australia can be obtained from the Natural Resource Atlas of Australia and are available at the website http://audit.ea.gov.au/ANRA/atlas_home.cfm. As an example some of the information obtained from the website for the Gympie catchment of the Mary River basin is shown in the Figures 3.7 to 3.13. Similar information for the major catchments (Powerline, Zattas, Reeves, and Tung Oil) of the four remaining River basins (Haughton, Herbert, Don, and Johnstone) is contained in Appendix A of the CD. 74

3.1 Gympie, Moy Pocket, Bellbird, Cooran and Kandanga Catchments of Mary River

Mary River catchment at Gympie shown in Figure 3.1 covers nearly 2920 km2, which includes Six Mile and Kandanga Creeks, and is situated in the South-East coastal region of Queensland.

Gympie

Cooran

Kandanga

Moypocket

Bellbird

Figure 3.1 – Mary River and its contributing catchments

700

600

500

400

300 Elevation (m)

200 Profile of main stream

Equal area slope line 100

0 0 20000 40000 60000 80000 100000 120000 140000 Length (m)

Figure 3.2 - Stream elevations of Gympie catchment of Mary River

700

600

500

400

300 Elevation (m) Profile of main stream

200 Equal area slope line

100

0 0 10000 20000 30000 40000 50000 60000 70000 Length (m)

Figure 3.3 - Stream elevations of Moy Pocket catchment of Mary River

700

600

500

400 Profile of main stream

300 Elevation (m)

Equal area slope line 200

100

0 0 5000 10000 15000 20000 25000 30000 35000 40000 Length (m) Figure 3.4 - Stream elevations of Bellbird catchment of Mary River

160

140

120 Profile of main stream

100 Equal area slope line 80

Elevation (m) 60

0 0 5000 10000 15000 20000 25000 30000 35000 Length (m)

Figure 3.5 - Stream elevations of Cooran catchment of Sixth Mile Creek (Tributary of Mary River)

800

700

600

500

400 Profile of main stream Elevation (m) 300

200 Equal area slope line

100

0 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000 Length (m)

Figure 3.6 - Stream elevations of Kandanga catchment of Kandanga Creek (Tributary of Mary River)

Out of the seventeen catchments selected for this study, Gympie has the lowest equal area stream slope, 0.09%. The natural profile and the equal area slope line of the main stream are shown in Figure 3.2. The equal area slopes of the other catchments of Gympie, namely Cooran, Moy Pocket, Bellbird, and Kandanga are 0.12%, 0.22%, 0.48% and 0.51% respectively.

The Mary River begins in the Conondale Ranges at the Southern end of the catchment, at an altitude of about 600m above mean sea level. The river falls some 400m in the first 8km, and the grade of that part of the river is approximately 6%.

At the head of the river the mountains are rather high (600m). The valleys are also steep in this area and the river flows through deep gullies. In the upper region of the catchment the valley plain is very narrow. As the river levels out, the valleys become flatter and the mountainous terrains are with a gentle slope.

From the Figures 3.7 to 3.13 the following can be seen: • Open forests cover nearly 40% of the catchment, and that includes forestry. The remaining part is covered with vegetation and national parks. Grassland, isolated trees, sparse woodlands and closed forests, each cover between 10 to 15% of the Gympie catchment. A significant part of the catchment has been cleared of its natural vegetation due to grazing as well as agricultural needs and this has led to advanced erosion in some areas.

• The topsoil layer of the Gympie catchment is covered with clay and clay loams. Although sand and sandy loams patches are found in some parts of the catchment in its subsoil, most of the area is covered with light clay loams and loam. Therefore, the amount of water is not enough to sustain any irrigation needs. However, ground water is available in the alluvial plains. As a result of years of erosion and degradation, in conjunction with the flooding, much of the river system in the lower areas of the Gympie catchment has a considerable amount of silt deposits.

Mary River catchment at Gympie is sub-tropical with the Southern region being moist sub-tropical and the Northern region being dry sub-tropical. At Maleny the rainfall is around 2000mm and the mean monthly rainfall exceeds the evaporation. The Western parts of the catchment receive only about 880mm and the evaporation rate exceeds the mean monthly rainfall, therefore, this area relies on irrigation for the growing of crops. Because the area is sub-tropical the majority of the annual rainfall occurs during summer months, but there are still substantial falls throughout the year.

26.092 E 152.271

Legend

S 26.881 Map produced using the Australian Natural Resources Atlas E 153.060 from the National Land and Water Resources Audit, a Program of the Natural Heritage Trust

Citations AUSLIG (1998) MAPDATA TOPO-2.5M - State Borders AUSLIG (1998) MAPDATA TOPO-2.5M - Localities AUSLIG (1998) MAPDATA TOPO-2.5M - Drainage

NLWRA (2000) Land use 1996/1997

AUSLIG (1998) MAPDATA TOPO-2.5M - Coastline

Figure 3.7 – Mary River at Gympie – Land Use Classification

S 25.977 E 152.119

Legend

S 26.946 Map produced using the Australian Natural Resources Atlas E 153.087 from the National Land and Water Resources Audit, a Program of the Natural Heritage Trust

Citations AUSLIG (1998) MAPDATA TOPO-2.5M - State Borders AUSLIG (1998) MAPDATA TOPO-2.5M - Localities AUSLIG (1998) MAPDATA TOPO-2.5M - Drainage AUSLIG (1998) MAPDATA TOPO-2.5M - Waterbodies CSIRO (2001) Topsoil Soil Texture

AUSLIG (1998) MAPDATA TOPO-2.5M - Coastline

Figure 3.8 – Mary River at Gympie – Soil Texture of Topsoil

S 25.977 E 152.119

Legend

S 26.946 Map produced using the Australian Natural Resources Atlas E 153.087 from the National Land and Water Resources Audit, a Program of the Natural Heritage Trust

AUSLIG (1998) MAPDATA TOPO-2.5M - Coastline

Figure 3.9 – Mary River at Gympie – Soil Texture of Subsoil

S 25.848 E 151.906

Legend

S 27.079 Map produced using the Australian Natural Resources Atlas E 153.136 from the National Land and Water Resources Audit, a Program of the Natural Heritage Trust

AUSLIG (1998) MAPDATA TOPO-2.5M - Coastline

Figure 3.10 – Mary River at Gympie – Silt in Topsoil

S 25.848 E 151.906

Legend

S 27.079 Map produced using the Australian Natural Resources Atlas E 153.136 from the National Land and Water Resources Audit, a Program of the Natural Heritage Trust

AUSLIG (1998) MAPDATA TOPO-2.5M - Coastline

Figure 3.11 – Mary River at Gympie – Silt in Subsoil

S 25.848 E 151.906

Legend Use the Legend in next page

S 27.079 Map produced using the Australian Natural Resources Atlas E 153.136 from the National Land and Water Resources Audit, a Program of the Natural Heritage Trust

AUSLIG (1998) MAPDATA TOPO-2.5M - Coastline

Figure 3.12 – Mary River at Gympie – Sand in Topsoil

S 25.953 E 151.911

Legend

S 27.207 Map produced using the Australian Natural Resources Atlas E 153.165 from the National Land and Water Resources Audit, a Program of the Natural Heritage Trust

AUSLIG (1998) MAPDATA TOPO-2.5M - Coastline

Figure 3.13 – Mary River at Gympie – Sand in Subsoil

3.2 Powerline and Mount Piccaninny Catchments of Haughton River

Haughton River catchment at Powerline as shown in Figure 3.14 covers 1735 km2 and its major tributaries are Reid River and Major Creek. Comparing with other catchments selected for this study, Haughton River Basin is fairly small in size.

Powerline

Mt. Piccaninny

Figure 3.14 – Haughton River and its contributing catchments

The South-East part of the Powerline catchment is covered with rain forests, and the majority of the remainder is full of scattered vegetation, with some medium vegetation. The majority of the catchment is used for livestock grazing and the Haughton River basin has a mountainous terrain.

Powerline

Mt. Piccaninny

Figure 3.14 – Haughton River and its contributing catchments

700

600

500

400

300 Profile of main stream

Elevation (m)

200 Equal area slope line

100

0 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 Length (m)

Figure 3.15 - Stream elevations of Powerline catchment of Haughton River

700

600

500

400 Profile of main stream 300 Elevation (m) Elevation

200 Equal area slope line

100

0 0 10000 20000 30000 40000 50000 60000 70000 Length (m)

Figure 3.16 - Stream elevations of Mount Piccaninny catchment of Haughton River

The Training Centre of the Defence Department covers a significant part of the Powerline catchment and is situated in the North-Western part of the catchment. The sealed road runs across both catchments and they are very much circular in shape.

Although sand patches are found in some parts of the Haughton River basin, the majority of its topsoil and subsoil layers are covered with light clay loams and loam as shown in Figures 3.31 and 3.32 of Appendix A. Therefore, soil moisture in the topsoil and subsoil is fairly low.

The first half of the main stream of the Powerline catchment is nearly ten times steeper than that of the other half and their respective average slopes are approximately 1.26% and 0.123%. This variation in slope allows the sedimentation in the bottom part of the catchment and soil erosion at the top.

Out of the two catchments selected for the analysis from the Haughton River catchment, Mount Piccaninny has the highest equal area stream slope, and that is about 0.38%. The slope of the Powerline catchment is about 0.26%.

3.3 Zattas, Nash’s Crossing, Gleneagle, and Silver Valley Catchments of Herbert River

The Zattas catchment shown in Figure 3.17 is situated in the tropical coast to the North- West of Ingham and has an area of 7292 km2. It is the largest catchment selected for this study. Major flooding usually takes place during the wet season from January to March and minor flooding occurs in April and December.

Overall there is not much human activity in the Herbert River basin apart from logging, livestock, and tourism. The Herbert River flows through valleys and many gorges and some are covered with national parks and numerous unsealed roads. Natural vegetation dominates the catchment and some parts are covered with dense rain forests and the others are in medium rain forests. Low lying areas such as Abergowrie are utilised for cane sugar cultivation. Some waterfalls are present in the catchment due to the steep rocky outcrops and gullies. However, there are no large water bodies present.

As shown in Figure 3.38 of Appendix A, the Western part of the upstream of the Zattas catchment is covered with sandy loam and sand in its topsoil layer. The other parts are covered with clay loams and loam. Although there are some loam patches present in the upstream of the Zattas catchment, the remainder is covered with sandy loam as shown 90

in Figure 3.39 of Appendix A. Therefore, the water absorption in the Zattas catchment is fairly moderate and it has low moisture in its topsoil and subsoil layers.

A considerable fall of 520m in 92km (average slope of 0.57%) in the downstream region of the catchment can be observed from Figure 3.21. The average slope in the upstream region just before that fall is about 0.35%. These topographical features lead to sedimentation in the upper middle part of the catchment and soil erosion in the lower part, this occurs to a considerable extent.

Silver Valley

Gleneagle

Nash’s Crossing Zattas

Figure 3.17 - Herbert River and its contributing catchments

1100

1000

Equal area slope line 900

Profile of main stream 800

700 600

500

Elevation (m) 400

300

200

100

0 0 10000 20000 30000 40000 50000 60000 Length (m) Figure 3.18 - Stream elevations of Silver Valley catchment of Herbert River

1100 1000

900 Profile of main stream 800

700 Equal area slope line

600

500 Elevation (m) 400

300 200 100 0 0 20000 40000 60000 80000 100000 120000 140000 Length (m)

Figure 3.19 - Stream elevations of Gleneagle catchment of Herbert River

1100

1000

900 800 700

600 Profile of main stream 500 Elevation (m) Elevation 400 300 Equal area slope line 200

100

0 0 25000 50000 75000 100000 125000 150000 175000 200000 225000 Length (m) Figure 3.20 - Stream elevations of Nash’s Crossing catchment of Herbert River

1100

1000

900

800 700 600 Profile of main stream 500

Elevation (m) 400

300 Equal area slope line 200

100

0 0 25000 50000 75000 100000 125000 150000 175000 200000 225000 250000 Length (m)

Figure 3.21- Stream elevations of Zattas catchment of Herbert River

3.4 Reeves, Mount Dangar and Ida Creek Catchments of Don River

Total draining area of Don River basin at Reeves as shown in Figure 3.22 is 1010km2 and it is located in the tropical coast to the South of Bowen.

Reeves

Mt. Dangar

Ida Creek

Figure 3.22 – Don River and its contributing catchments

The entire Reeves catchment is covered with light clay loams and loam in its topsoil (as shown in Figure 3.45 of Appendix A), apart from an area near the upstream of the mainstream, which is covered with sand. The subsoil layer of the whole catchment is covered with sandy loam (as shown in Figure 3.46 of Appendix A), apart from an area near the upstream of the mainstream, which is covered with sand. Therefore, the subsoil layer of the catchment allows the water to percolate fairly quickly.

Since eighty percent of the catchment is covered with medium rain forests and the remainder with scattered forests, not much human activity is present other than livestock grazing. Apart from minor roads running through these catchments, not much development can be seen.

Although the equal area stream slope of Reeves catchment is about 0.33%, the total fall is about 530m for a stream length of 66.7km. As shown in Figure 3.23 the river falls about 320m in the first 7km of the upstream area and the grade of that part is approximately 4.5%. This steep slope contributes erosion in the upstream part of the catchment. The approximate average slope of the remaining part, with a length of 60km, of the Reeves catchment is 0.35%.

600

500

400

300 Profile of main stream Elevation (m)

200

Equal area slope line

100

0 0 10000 20000 30000 40000 50000 60000 70000 Length (m)

Figure 3.23 - Stream elevations of Reeves catchment of Don River

600

500

400

300 Profile of main stream

Elevation (m)

200 Equal area slope line

100

0 0 10000 20000 30000 40000 50000 60000 Length (m)

Figure 3.24 - Stream elevations of Mount Dangar catchment of Don River

600

500

400

300 Profile of main stream

Elevation (m)

200 Equal area slope line

100

0 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 Length (m)

Figure 3.25 - Stream elevations of Ida Creek catchment of Don River

3.5 Tung Oil, Nerada and Central Mill Catchments of North and South Johnstone Rivers

The combined area of North and South Johnstone River basins at the Tung Oil and Central Mill as shown in Figure 3.26 is 1320km2. These rivers rise in the tablelands of the North tropical coast and flow through steep narrow gorges to their outlets.

The middle parts of the catchments are mostly covered with natural forest and a significant part of the upstream of the Tung Oil catchment is used for livestock grazing. However, the upstream part of the Tung Oil catchment and downstream parts of both catchments (Tung Oil and Central Mill) are mainly utilised for dry agriculture. The majority of the downstream area of Central Mill catchment is rainforest.

Nerada Tung Oil

Central Mill

Figure 3.26 – North and South Johnstone Rivers and their contributing catchments

Both Tung Oil and Central Mill catchments are covered with clay and clay loams in their topsoil as shown in Figure 3.53 of Appendix A. The subsoil layers of the extreme 97

upstream parts of both catchments are covered with loam, and the remainder is with sandy loam, as shown in Figure 3.54 of Appendix A.

The equal area slope of the Tung Oil catchment is 0.76% and that of its sub-catchment, Nerada, is 0.87%. According to the profile of the main stream shown in Figure 3.27, the Tung Oil catchment illustrates fairly low slopes at the very top as well as at its very bottom parts and they are 0.46% and 0.24% respectively.

Although the low slope in the upstream region of the Tung Oil catchment has shown a considerable amount of sedimentation, it gradually reduces due to erosion as the flow approaches downstream of the catchment. A sudden drop of 580m within a length of 39.6km in the middle part of the catchment contributes this erosion.

800

700

600

Profile of main stream 500

400 Elevation (m) Elevation 300 Equal area slope line

200

100

0 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 Length (m)

Figure 3.27 - Stream elevations of Tung Oil catchment of North Johnstone River

Although the average slopes of the very top and bottom parts of the Central Mill catchment are 2.2% and 0.34%, its latter part of the main stream profile, shown in Figure 3.29, is very similar to that of the Tung Oil catchment. The equal area slopes of Central Mill and Tung Oil catchments are 0.88% and 0.76% respectively, and these values are very close to each other. Therefore, very similar behaviour patterns such as 98

turbulent flow and soil erosion can be found from both catchments especially in their downstream flow regions.

800 700

600

Profile of main stream 500

400

Elevation (m) 300 Equal area slope line

200

100

0 0 10000 20000 30000 40000 50000 60000 70000 80000 Length (m)

Figure 3.28 - Stream elevations of Nerada catchment of North Johnstone River

1000 900 800 700 600 Profile of main stream 500

Elevation (m) Elevation 400

300 Equal area slope line 200

100

0 0 10000 20000 30000 40000 50000 60000 70000 80000 Length (m)

Figure 3.29 - Stream elevations of Central Mill catchment of South Johnstone River

CHAPTER 4

SELECTION OF AVAILABLE RAINFALL AND STREAM FLOW DATA

4. SELECTION OF AVAILABLE RAINFALL AND STREAMFLOW DATA

4.1 Introduction

The first part of this chapter explains the methods used to check the accuracy and consistency of rainfall and streamflow data. The rainfall and flow data (supplied by the Queensland Bureau of Meteorology) are contained in Appendix B of the CD. As a first step the validity of the rainfall data has been assessed by means of rainfall mass curves and isohyets of the total rainfall depths. This assessment covers the examination of the similarities as well as the differences of rainfall mass curves at different rainfall stations resulting from all available storms on the catchments. The advantages of graphical examination using diagrams and maps are highlighted in this assessment.

Secondly, the methods used to produce surface runoff hydrographs, from the stage hydrographs and rating tables of catchments are discussed. The step by step analysis, which was employed to obtain the surface runoff hydrographs, is described in detail in section 4.7 of this chapter.

Since all seventeen catchments selected for this study are confined to five large river basins as mentioned in the previous chapter, the discussions in this chapter are also focused on those five river basins.

4.2 RAINFALL DATA OF MARY RIVER BASIN

4.2.1 Temporal Patterns of Rainfall Table 4.1 shows the total rainfall depths recorded for eight storms at ten stations (shown in Figure 4.1) of the Mary River basin. Although the rainfall data for all ten stations are not available for every storm, as shown in Table 4.1, the stations with data cover the Mary River basin fairly well. The maximum and minimum total rainfall depths recorded are 746 mm (Mapleton station in February 1992) and 27 mm (Maleny station in March 1997) respectively.

Gympie 1

Cooran 2 Pomona Kandanga 5 3 Cooroy 4 Imbil 6

Kenilworth 7 Mapleton 8 Jimna 9

10 Maleny

Figure 4.1– Location of Rainfall Stations for Mary River

Table 4.1- Summary of Rainfall for Mary River

Name of Rainfall Elevation Dates of eight storms and their total rainfall depths (mm) No Number Longitude Latitude Station in metres Apr-89 Dec-91 Feb-92 Mar-92 Feb-95 Jan-96 Apr-96 Mar-97 Not 1 0 ' '' 0 ' '' Gympie 7389 152 3918 26 1133 50 112 available 612 232 303 151 130 115 Not Not Not Not Not 2 0 ' '' 0 ' '' Cooran 7368 152 4923 26 1924 70 available available available available 443 124 163 available

3 Pomona 7105 152051'10'' 26021'59'' 100 241 151 611 237 501 136 196 297

4 Cooroy 7104 152054'36'' 26025'14'' 100 208 216 731 248 603 106 204 312

5 Kandanga 7106 152041'03'' 26023'16'' 75 161 180 620 151 374 149 138 247 Not 6 0 ' '' 0 ' '' 222 571 171 312 117 142 227 Imbil 7107 152 4045 26 2733 80 available

0 ' '' 0 ' '' 7 Kenilworth 7103 152 4357 26 3510 200 320 327 486 175 224 94 162 182 Not 8 0 ' '' 0 ' '' Mapleton 6447 152 5153 26 3828 300 385 351 746 306 564 98 available 236

9 Jimna 7360 152027'34'' 26038'56'' 480 223 207 302 198 161 80 103 85

0 ' '' 0 ' '' 10 Maleny 7101 152 5112 26 4517 320 383 486 745 395 498 130 416 27

100

Plots of rainfall mass curves for the eight storms at all ten stations are shown in Figures 4.2 to 4.9. Each figure has been studied to determine the variability of temporal patterns of storms. For example, for the April 1989 storm, the total storm duration (Figure 4.2) is 48hrs. Considering periods within this 48hrs, Figure 4.2 indicates that:

(a) The rainfall depth variations, in the first period of 24hrs at many rainfall stations, are fairly moderate with an approximate average rate of 2mm/hr, except for the stations Mapleton and Maleny (both lie almost on the same line), which have a rate of rainfall of approximately 6.7mm/hr; (b) In the next 11hrs (24 to 35hrs) the rainfall rates increased consistently for most of the stations. This means that the previous average rate of 2mm/hr has increased to 10mm/hr. However, the three stations namely Kenilworth, Mapleton and Maleny have reported fairly high rates and those rates are approximately 22.7mm/hr for Kenilworth and 13.6/mm/hr for both Mapleton and Maleny; (c) During the next 13hrs (35 to 48hrs) Cooroy, Mapleton and Maleny stations have shown considerable increments in their rates of rainfall and they are approximately 6.2mm/hr, 4.6mm/hr and 4.6mm/hr respectively; and (d) During the next 24 hrs (48 to 72hrs) zero rainfall was recorded at all stations.

The rainfall mass curves (Figures 4.2 to 4.9) at all stations have been examined and compared in order to check their consistencies. In Table 4.2 consistent rainfall temporal patterns are marked with a tick and inconsistent patterns marked with a cross. For example, in the first 24 hour period Mapleton and Maleny are given crosses, and in the next 11 hour period Kenilworth, Mapleton and Maleny are given crosses as well. It should be noted that the temporal patterns at these stations are not necessarily incorrect, only that they are somewhat different to the temporal patterns at the other stations.

While the total rainfall depths varied at different stations, the temporal patterns are reasonably consistent with one another in almost all of the eight storms.

As a further check on the data, the spatial variation of rainfall has been examined.

101

Mass curve of Rainfall

450 Gympie 400 Pomona 350 Cooroy 300

250 Kandanga

200 Kenilwort h

150 M apleton

100 Jimna 50 Maleny Cumulative(mm) Rainfall 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Time (hrs)

Figure 4.2 - Mary River -April 1989

Mass Curve of Rainfall

500 Pomona 450 400 Cooroy

350 Kandanga 300 Imbil 250 Kenilwo rt h 200 15 0 M apleton 10 0 Jimna 50 Maleny Cumulative Rainfall (mm) 0 0 5 10 15 20 25 30 35 40 45 50 55 Time (hrs)

Figure 4.3 - Mary River - December 1991

Mass Curve of Rainfall

800 750 Gympie 700 650 Pomona 600 Cooroy 550 500 Kandanga 450 400 Imbil 350 300 Kenilwo rt h 250 Mapleton 200 15 0 Jimna 10 0 50 Maleny Cumulative Rainfall (mm) 0 0 102030405060708090100110120130140150 Time (hrs)

Figure 4.4 - Mary River - February 1992

102

Mass Curve of Rainfall

450 Gympie 400 Pomona 350 Cooroy 300 Kandanga 250 imbil 200 Kenilwort h 150 M apleton 10 0 Jimna 50

Cumulative Rainfall (mm) Rainfall Cumulative Maleny 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 Time (hrs)

Figure 4.5 - Mary River - March 1992

Mass Curve of Rainfall

650 600 Gympie 550 Cooran 500 Pomona 450 Cooroy 400 350 Kandanga 300 Imbil 250 Kenilwo rt h 200 150 M apleton 10 0 Jimna 50 Cumulative Rainfall (mm) Maleny 0 0 102030405060708090100110 Time (hrs)

Figure 4.6 - Mary River - February 1995

Mass Curve of Rainfall

16 0 Gympie 14 0 Cooran 12 0 Pomona

10 0 Cooroy Kandanga 80 Imbil 60 Kenilwort h 40 M apleton Jimna 20

Cumulative Rainfall (mm) Rainfall Cumulative Maleny 0 0 102030405060 Time (hrs)

Figure 4.7 – Mary River – January 1996

103

Mass Curve of Rainfall

350 Gympie

300 Cooran

250 Pomona Cooroy 200 Kandanga 15 0 Imbil

10 0 Kenilwort h

Jimna 50 Maleny Cumulative Rainfall (mm) 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 Time (hrs)

Figure 4.8 - Mary River - April 1996

Mass Curve of Rainfall

320 300 Gympie 280 260 Pomona 240 Cooroy 220 200 Kandanga 18 0 16 0 Imbil 14 0 12 0 Kenilwo rt h 10 0 M apleton 80 60 Jimna 40 20

Cumulative Rainfall (mm) Rainfall Cumulative Maleny 0 0 5 10 15 20 25 30 Time (hrs)

Figure 4.9 - Mary River - March 1997

Table 4.2 - Assessment Summary of Temporal Patterns of Rainfall – Mary Basin

Dates of eight storms Apr-89 Dec-91 Feb-92 Mar-92 Feb-95 Jan-96 Apr-96 Mar-97 Name of Rainfall No Station Time periods of storms selected for the analysis 0 to 72 hrs 34 to 47 hrs 18 to 144 hrs16 to 52 hrs 71 to 92 hrs 10 to 49 hrs 41 to 72 hrs 15 to 27 hrs 24 11 13 24 27 6 6 8 38 12 65 29 21 18 7 6 21 28 9 5 18 9 19 3 42 5 13 12 13 14 6 3 hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs 1Gympie√√√√ not available xx√ xx√√√√√√√x √ x √√xx√ x √√√ 2 Cooran not available not available not available not available √√√√√√√√√√√√ not available √√x √√√x √√√√√√√√√√√√√√√√√√√√√√xx√ 3Pomona 4 Cooroy √√x √√xxx√√x √√√√√√√√√√√√√√x √√xxx√

5 Kandanga √√√√√√√√√√√√√x √√√√x √√√xx√√√√√x √√ not available √√√√√√√√√xx√√√x √√√√x √√√√√x √√ 6Imbil 7 Kenilworth √ x √√√√√√√√√√√xx√√√x √√√√√√√xx√ x √√ 8Mapletonxxx√ x √√√√√√xx√√√x √√xx√√√ not available xxx√ √√√√√√x √ xx√√√√√√√√x √ x √ x √√x √ xx√√√ 9Jimna 10 Maleny xxx√ xx√√√√√√x √√xx√√x √√√√√√xxxx√√ 104

4.2.2 Spatial variation of Rainfall

In the next few pages, maps of isohyets (Figures 4.10 to 4.17) for the eight storms (summarised in Table 4.1) are shown. The intentions of this mapping are to determine whether there are any similarities or differences in the spatial variation of total rainfall depths for each storm, and to find out the effect of spatial variation of rainfall on lag parameter.

April 1989 - Rainfall depth increases from the bottom to the top of the catchment, gradually from 150mm to 350 mm, as shown in Figure 4.10. The variation in rainfall depths is steadily decreasing from the top to bottom.

December 1991 - Rainfall depth decreases steadily in the top half of the catchment, from 400mm to 200 mm as shown in Figure 4.11. The average rainfall depth of the bottom half of the catchment is about 165mm.

February 1992 - Rainfall depth increases gradually from the Southwest to the Northeast of the catchment, from 300mm to 600mm as shown in Figure 4.12. However, a narrow area on the eastern edge of the catchment maintains a rainfall depth close to 700mm. The region close to the outlet has an approximate average rainfall depth of 614mm.

March 1992 - Rainfall depth decreases gradually from the top to the centre of the catchment. The direction of this variation is from the Southeast to the Northwest. The magnitude of this variation is from 375mm to 175 mm. However, there is very little variation in rainfall depth in the Western part of the catchment as shown in Figure 4.13. An average rainfall depth of 187mm may be considered for that part of the catchment.

February 1995 - Rainfall depth increases from the West of catchment to the East. This increase is from 200mm to 500mm. The spacing of the isohyets gradually decreases as the rainfall depths progress towards the Eastern part of catchment, as shown in Figure 4.14. Thus a consistent rainfall depth pattern persists within the entire catchment. 105

150

1 112 200

241 3 5 161 150 4 208 250 300 350 320 7 8 385 9 223 200 383 10 250 350 300

Figure 4.10 – Rainfall Isohyets (mm) – Mary River (April 1989)

151 200 5 180 3 4 216 222 6 300 7 327 8 351 200 9 207 400 486 10 300

400 Figure 4.11 – Rainfall Isohyets (mm) – Mary River (December 1991)

106

600 612 1

500

620 611 3 700 400 5 731 300 571 4 6

486 7 746 9 8 302

745 400 10 500 300 700 600

Figure 4.12 – Rainfall Isohyets (mm) – Mary River (February 1992)

1 225 232 175 175

3 237 151 5 248 4 171 6 275

175 7 8 306 198 9 325 375 395 225 10 275 325 375

Figure 4.13 – Rainfall Isohyets (mm) – Mary River (March 1992) 107

1 300 303 400

200 2 500 443 3 5 501 374 4 6 603 312 500 7 224 9 8 564 161

498 10 200 400

Figure 4.14 – Rainfall Isohyets (mm) – Mary River (February 1995)

150

140 1 151 130 140 130 124 130 148 2 130 5 136 3 120 120 106 4 6 117

110 94 7 100 8 98 9 80 100 90 110 130 10 90 100 110

120

Figure 4.15 – Rainfall Isohyets (mm) – Mary River (January 1996) 108

150 1 130

2 163 3 200 5 196 138 204 6 4 142 250

7 300 162 103 9 350 400 416 10

Figure 4.16 – Rainfall Isohyets (mm) – Mary River (April 1996)

1 115 200

100 150 250 3 300 297 247 5 4 312 227 6 300 250 7 182 8 9 236 85 200 150 10 100 27

Figure 4.17 – Rainfall Isohyets (mm) – Mary River (March 1997) 109

January 1996 - The isohyets of Figure 4.15 show an evenly developing pattern of rainfall depths throughout the catchment. However, the top part of the catchment indicates a slight increase in rainfall depth. The middle part of the catchment indicates a fairly steady variation in rainfall depth ranging from 100mm to 130mm.

April 1996 - The rainfall depth decreases gradually from 400mm to 150mm from the top to the centre of the catchment. The direction of this variation is from the Southeast to the Northwest. Rainfall is fairly uniform beyond the centre towards the Northwest region of the catchment, which covers its outlet as well. The approximate average rainfall depth in that region is 126mm.

March 1997 - Rainfall depth decreases from 300m to 100mm from the East to the West of the catchment and that variation is fairly steady as shown in Figure 4.17. However, an area extending from the Western boundary to the Southern boundary of the catchment, maintains an approximate average rainfall depth of 56mm.

The maps of the isohyets for eight storms have demonstrated some similarities in their patterns and they are grouped in the following manner:

The maps of the isohyets of the February 1992 & 1995 and March 1997 storms have shown some similarities in their rainfall depth variation patterns. Those variations are from the East to the West of the catchment. Moreover, the rainfall depths vary from 700mm to 300mm, 500mm to 200mm and 300mm to 100mm respectively in these three storms.

The spatial variation patterns of rainfall related to the April 1989, December 1991, March 1992 and April 1996 storms are fairly consistent particularly in the Southeast region of the catchment as shown in Figures 4.10, 4.11, 4.13, and 4.16.

The remaining maps have shown no similarities with each other.

110

Overall, the isohyetal maps show that the total rainfall depths at various stations are consistent. For the March 1997 storm, the mass curve of Figure 4.9 indicates that the total depth at Maleny is considerably lower than that at the other stations. However, the isohyets of Figure 4.17 show that the total depth at Maleny is not inconsistent with the spatial variation across the catchment. Therefore, the Maleny rainfall depth was included in the analysis.

Moreover, for the March 1997 storm, Table 4.2 shows some inconsistency in Cooroy and Mapleton rainfall patterns. In contrast Figure 4.17 shows no inconsistency in its isohyets, therefore the rainfall depths of Cooroy and Mapleton stations are included in the analysis.

After examination of all mass curves and isohyets for all storms, it was considered that no stations are sufficiently inconsistent to require deletion. Therefore, the data from all rainfall stations are included in the analysis.

A similar analysis to Mary River was carried out for the four remaining river basins. Summary figures and tables were prepared, and after examining these it was decided to include rainfall stations of all river basins in the analysis.

4.3 RAINFALL DATA OF HAUGHTON RIVER BASIN

4.3.1 Temporal Patterns of Rainfall Table 4.3 shows the total rainfall depths recorded for seven storms at eleven stations (shown in Figure 4.18) of the Haughton River basin. Although rainfall data is not available for some of the stations shown in Table 4.3, the localities of the remaining stations cover the Haughton River basin quite well. The highest total rainfall depth is 370mm (for the March 1997 storm) at Brabons station. The lowest is 3mm at Mingela station for the February 1997 storm.

The plots of rainfall mass curves of seven storms at eleven stations of the Haughton River basin are shown in Figures 4.19 to 4.25. After examining the temporal patterns of 111

the rainfall of seven storms at eleven stations of the Haughton River basin, their findings are tabulated in Table 4.4.

Cormacks 7 Brabons 9 McDonalds Giru 1 6 Nettlefield 8 Woodstock 5 Powerline 2

Upper Reid Cameron Hill 4 10 3 Mt Piccaninny

Mingela 11

Figure 4.18 – Location of Rainfall Stations of Haughton River

Table 4.3 – Summary of Rainfall for Haughton River

Dates of seven storms and their total rainfall Name of Rainfall Elevation No Number Longitude Latitude depths(mm) Station in metres Jan-94 Jan-96 Feb-97 Mar-97 Feb-00 Mar-00 Apr-00 Not Not Not Not Not Not 1 0 ' '' 0 ' '' 213 Giru 6330 147 0638 19 3050 20 available available available available available available

2 Powerline 6335 147006'33'' 19038'05'' 20 109 158 121 195 266 115 181

3 Mt.Piccaninny 6320 146057'29'' 19046'27'' 60 204 150 228 195 120 118 169 Not Not Not Not Not Not 4 0 ' '' 0 ' '' 141 Cameron Hills 6300 146 5131 19 4444 327 available available available available available available

5 Woodstock 6315 146050'21'' 19036'12'' 60 94 214 39 200 276 207 108 Not Not Not Not Not Not 6 0 ' '' 0 ' '' 275 Mc Donalds 2820 146 5051 19 3048 44 available available available available available available Not Not Not Not Not Not 7 0 ' '' 0 ' '' 172 Cormacks 2825 146 5048 19 2615 40 available available available available available available Not Not Not Not Not Not 8 0 ' '' 0 ' '' 197 Nettlefield 2810 146 4643 19 3510 80 available available available available available available Not Not Not Not Not Not 9 0 ' '' 0 ' '' 370 Brabons 2805 146 3750 19 2842 80 available available available available available available

10 Upper Reid 6310 146040'04'' 19043'55'' 140 83 149 17 166 184 185 284

0 ' '' 0 ' '' 11 Mingela 6305 146 3752 19 5250 280 110 64 3 158 99 140 113 112

Mass Curve of Rainfall

220 200 Powerline 18 0 16 0 M t .Piccaninny 14 0 12 0 Woodstock 10 0 80 Upper Reid 60 40 20 Mingela Cumulative Rainfall (mm) Rainfall Cumulative 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Time (hrs)

Figure 4.19 – Haughton River – January 1994

Mass Curve of Rainfall

220 200 Powerline 18 0

16 0 M t .Piccaninny 14 0 12 0 Woodstock 10 0 80 Upper Reid 60 40 20 Mingela Cumulative Rainfall (mm) Rainfall Cumulative 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Time (hrs)

Figure 4.20 - Haughton River – January 1996

Mass Curve of Rainfall

240 Powerline 220 200 180 M t.Piccaninny 160 140 Woodstock 120 100 80 Upper Reid 60 40 Mingela

Cumulative Rainfall (mm) 20 0 0 2 4 6 8 1012141618202224262830 Time (hrs)

Figure 4.21- Haughton River – February 1997

113

Mass Curve of Rainfall

400 375 Giru 350 Powerline 325 300 M t .Piccaninny 275 Cameron Hills 250 Woodstock 225 200 McDonalds 17 5 Cormacks 15 0 12 5 Nettlefield 10 0 Brabona 75 50 Upper Reid

Cumulative Rainfall (mm) 25 Mingela 0 0 102030405060708090100110 Time (hrs)

Figure 4.22 - Haughton River – March 1997

Mass Curve of Rainfall

150

Powerline

10 0 M t .Piccaninny

Woodstock 50

Mingela Cumulative Rainfall(mm) 0 0 5 10 15 20 25 30 35 40 45 Time (hrs)

Figure 4.23 - Haughton River – February 2000

Mass Curve of Rainfall

220 200 Powerline 18 0

16 0 M t .Piccaninny 14 0 12 0 Woodstock 10 0 80 Upper Reid 60 40 20 Mingela Cumulative Rainfall (mm) 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 Time (hrs)

Figure 4.24 - Haughton River – March 2000

114

Mass Curve of Rainfall

300 275 Powerline 250 225 M t.Piccaninny 200 17 5 15 0 Woodstock 12 5 10 0 Upper Reid 75 50 Mingela 25

Cumulative Rainfall (mm) 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Time (hrs)

Figure 4.25 - Haughton River – April 2000

Table 4.4 - Assessment Summary of Temporal Patterns of Rainfall – Haughton Basin

Dates of seven storms Jan-94 Jan-96 Feb-97 Mar-97 Feb-00 Mar-00 Apr-00 Name of Rainfall No Station Time periods of storms selected for the analysis 44 to 58hrs 37 to 70hrs 13 to 27hrs 80 to 106hrs 23 to 40hrs 41 to 59hrs 49 to 70hrs 27 07 21 03 31 07 20 12 11 07 03 06 65 25 10 06 16 09 04 11 41 09 07 02 42 13 11 04 hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs

1 Giru Not available Not available Not available √ xx√ Not available Not available Not available

2 Powerline √√xx√√√√√√√√√√x √√√√√√√√√√√x √

3 Mt.Piccaninny √√x √√√√√√x √√√√x √√√√√x √√√√√√√

4 Cameron Hills Not available Not available Not available √√√√ Not available Not available Not available

5 Woodstock x √√√x √√√√√√√√√√√x √√√√xx√√√x √

6 Mc Donalds Not available Not available Not available √ x √√ Not available Not available Not available

7 Cormacks Not available Not available Not available √√√√ Not available Not available Not available

8 Nettlefield Not available Not available Not available √√√√ Not available Not available Not available

9 Brabona Not available Not available Not availablexx√√ Not available Not available Not available

10 Upper Reid √√√√√√x √√√√√√√√√unreliable √xx√√√√√

11 Mingela √√√√√√x √√x √√√√√√x √√x √√√√xx√√

As shown in Table 4.3, out of the eleven rainfall stations, data is only available for five stations except for the March 1997 storm which has data for all stations. Although there are some inconsistencies in the temporal patterns at some stations, overall, the rainfall patterns are fairly consistent.

4.3.2 Spatial variation of Rainfall In the next few pages, the maps of isohyets for seven storms (summarised in Table 4.3) of the Haughton River basin are shown in Figures 4.26 to 4.32. The spatial variation of 115

rainfall for each storm has been studied and compared in order to check their similarities and differences.

January 1994 - Rainfall depth increases from 100mm to 200mm from the Northwest to Southeast of the catchment. The rainfall depth variation in the middle part of the catchment is fairly consistent as shown in Figure 4.26. A reasonable rainfall depth variation has not been observed in the remaining parts of the catchment. An average rainfall depth of 87mm may be considered for those parts of the catchment.

January 1996 - The rainfall depth increases from the Southwest to the Northeast of the catchment and that direction of variation is perpendicular to the direction of streamflow. Although the depths are increasing from 100mm to 200mm, the rainfall has been distributed fairly well to cover the entire catchment as shown in Figure 4.27.

February 1997 - Out of all the storms selected, this storm has produced fairly low rainfall depths in the catchment. They increase from 50mm to 200mm from the Northwest to the Southeast of the catchment. The distances between the isohyets are almost even and they indicate a steady variation in the rainfall depths at the lower part of the catchment. The top half of the catchment shows an approximate average depth of about 10.5mm according to Figure 4.28.

March 1997 - A gradual reduction in rainfall depths from 350mm to 175mm can be seen in the top part of the catchment down to its mid area. A consistent rainfall pattern (with an approximate average value of 150mm) has been maintained in the mid part of the catchment. An increment of 45mm (150mm to 195mm) from the centre to the bottom part of the catchment can be observed in Figure 4.29.

February 2000 - Rainfall depth increases from 100mm to 250mm from the South to the North of the catchment. The direction of this variation is perpendicular to the direction of the mainstream flow of the catchment. The distances between isohyets are almost equal and that produces a steadily varying rainfall depth pattern over the entire catchment as shown in Figure 4.30. 116

5 94 100 2 109 125 10 150 83 204 175 3 200

200 100 11 110 125 150

175

Figure 4.26 – Rainfall Isohyets (mm) – Haughton River (January 1994)

200

5 175 200 214 2 150 175 158

10 149 3 125 150 150 100 11 64 100 125

Figure 4.27 – Rainfall Isohyets (mm) – Haughton River (January 1996) 117

5 39 100 2 121

10 17 228 200 3

11 200 3 50 100 150

Figure 4.28 – Rainfall Isohyets (mm) – Haughton River (February 1997)

7 172 9 370 1 350 6 275 225 213 325 8 200 300 200 197 5 2 275 195 250 166 225 200 4 10 141 3 175 195

11 158 150 150 175

Figure 4.29 – Rainfall Isohyets (mm) – Haughton River (March 1997) 118

5 276 200 250 266 2 250

200 10 184 150 120 150 3

11 100 99 100

Figure 4.30 – Rainfall Isohyets (mm) – Haughton River (February 2000)

175 200 150 5 125 207 115 2 200

10 185 118 175 3

150 11 140 125

Figure 4.31 – Rainfall Isohyets (mm) – Haughton River (March 2000) 119

150

125

275 250 5 175 225 125 108 2 150 181 175 200

10 175 169 284 275 3 250 225 150 200 175 150 113 11 125

Figure 4.32 – Rainfall Isohyets (mm) – Haughton River (April 2000)

March 2000 - Rainfall depth increases from 125mm to 200mm from the Southeast to the Northwest of the catchment. A steady increase of rainfall depths can be seen in the middle part of the catchment as shown in Figure 4.31. The remaining parts (top and an area close to the eastern boundary) of the catchment have maintained fairly constant rainfall depths and their average values may be considered as 185mm and 118mm respectively.

April 2000 - Rainfall depth decreases gradually (from 275mm to 175mm) from the West to the East and this variation progresses down to the middle part of the catchment. The rainfall depth at the outlet is close to 175mm as shown in Figure 4.32. However, there is no significant rainfall depth variation in the remaining parts of the catchment.

Some similarities have been found from the figures of isohyets and those similarities can described in the following manner: 120

Maps of both January 1994 and February 1997 storms of the catchment have shown an increase in rainfall depths from the Northwest to the Southeast. A steady rainfall depth variation has also been noticed in the lower part of the catchment for these storms. Additionally the upstream end of the catchment has maintained a fairly constant rainfall depth as shown in Figures 4.26 and 4.28.

For the January 1996 storm the rainfall depth increases from the Southwest to the Northeast of the catchment. For the February 2000 storm that variation is from the South to the North. A steady rainfall depth variation can be seen in the middle part of catchment in both storms as shown in Figures 4.27 and 4.30. The remaining maps of isohyets have shown no similarities in their rainfall patterns.

4.4 RAINFALL DATA OF HERBERT RIVER BASIN

4.4.1 Temporal Patterns of Rainfall

Table 4.5 shows the total rainfall depths recorded for eight storms at eleven stations (shown in Figure 4.33) of the Herbert River basin. Although data for all storms is not available for all eleven stations, the locations of stations with data are able to cover the Herbert River basin fairly well. The maximum and minimum total rainfall depths are 777mm and 33mm at Revenshoe and Upper Rudd Creek stations respectively for March 1996 storm.

Since two rainfall stations (Zattas and Nash’s Crossing) are at close proximities to each other (shown in Figure 4.33) and the latter has rainfall data for six out of eight storms (Table 4.5), the Zattas station is excluded for this assessment as shown in Table 4.6.

Plots of the rainfall mass curves for eight storms at ten stations of the Herbert River basin are shown in Figures 4.34 to 4.41. After studying the variability of mass curves of rainfall for eight storms (for the selected number of time periods) the findings are tabulated in Table 4.6.

121

Herberton 11 10 McKell Road

9 Revenshoe Silver Valley 8 7 Mt. Garnet

6 Upper Rudd Creek

Kirrama 4 5 Gleneagle

2 Nash’s Crossing 1 Zattas Wallaman 3

Figure 4.33 – Location of Rainfall Stations of Herbert River

Table 4.5 – Summary of Rainfall for Herbert River

Dates of eight storms and their total rainfall depths (mm) Name of Rainfall Elevation in No Number Longitude Latitude Station metres Early Feb- Late Feb- Jan-94 Mar-96 Mar-97 Jan-98 Dec-99 Feb-01 00 00 Not Not Not 1 0 ' '' 0 ' '' 726 165 490 747 311 Zattas 6034 145 4943 18 2709 30 available available available Not Not 2 0 ' '' 0 ' '' 392 622 194 524 623 315 Nash's Crossing 6015 145 4618 18 2448 40 available available Not Not Not Not Not Not 3 0 ' '' 0 ' '' 285 488 Wallaman 6000 145 4415 18 2744 680 available available available available available available Not Not Not Not 4 0 ' '' 0 ' '' 313 346 73 237 Kirrama 6060 145 3632 18 0843 580 available available available available

5 Gleneagle 6052 145019'53'' 18011'37'' 560 81 129 168 209 153 107 265 98 Not 6 0 ' '' 0 ' '' 33 138 206 138 64 290 101 Upper Rudd Creek 6063 144 5206 18 0229 760 available Not 7 0 ' '' 0 ' '' 39 167 82 101 80 235 134 Mt. Garnet 6066 145 0842 17 4223 660 available Not Not 8 0 ' '' 0 ' '' 52 207 89 175 127 239 Silver valley 7183 145 1800 17 3800 640 available available Not 9 0 ' '' 0 ' '' 777 438 296 176 368 427 299 Revenshoe 6069 145 3143 17 3533 1100 available Not 10 0 ' '' 0 ' '' 174 232 331 139 262 466 256 McKell Road 2520 145 3029 17 2643 1000 available Not 11 0 ' '' 0 ' '' 121 272 119 126 134 407 214 Herberton 6072 145 2244 17 2243 900 available

122

Mass Curve of Rainfall

300 275 Wallaman 250 225 200 Gleneagle 17 5 15 0 12 5 Silver Valley 10 0 75 50 M cKell Road 25

Cumulative Rainfall (mm) 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Time (hrs)

Figure 4.34 - Herbert River – January 1994

Mass Curve of Rainfall

200 Wallaman

Kirrama 15 0 Gleneagle

Upper Rudd 10 0 Mt. Garnet

Revenshoe 50 M cKell Road

Herberton Cumulative Rainfall (mm) Rainfall Cumulative 0 0 10203040506070 Time (hrs)

Figure 4.35 - Herbert River – March 1996

Mass Curve of Rainfall

450 Nash's Crossing 400 Kirrama 350 Gleneagle 300 Upper Rudd 250 Mt.Garnet 200 Silver valley 150 R evenshoe 10 0 M cKell Road 50 Herbert o n

Cumulative(mm) Rainfall 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Time (hrs)

Figure 4.36 - Herbert River – March 1997

123

Mass Curve of Rainfall

500 450 Nash's Crossing

400 Gleneagle 350 Upper Rudd 300 250 Mt.Garnet 200 Silver Valley 150

10 0 Revenshoe

50 Herbert on Cumulative Rainfall (mm) 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 Time (hrs)

Figure 4.37 - Herbert River – January 1998

Mass Curve of Rainfall

200 Nash's Crossing 18 0 Kirrama 16 0 14 0 Gleneagle 12 0 Upper Rudd 10 0 Mt.Garnet 80 Silver valley

60 R evenshoe 40 M cKell Road 20 Herbert o n

Cumulative (mm) Rainfall 0 0 102030405060708090100110120 Time (hrs)

Figure 4.38 - Herbert River – December 1999

Mass Curve of Rainfall

550 500 Nash's Crossing 450 Gleneagle 400 350 Upper Rudd 300 Mt.Garnet 250 200 R evenshoe 15 0 M cKell Road 10 0 50 Herbert o n

Cumulative Rainfall (mm) 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 Time (hrs)

Figure 4.39 - Herbert River – Early February 2000

124

Mass Curve of Rainfall

400 Nash's Crossing 350 Gleneagle 300 Upper Rudd 250 Mt.Garnet 200

150 R evensho e

10 0 McKell Road 50 Herbert on Cumulative Rainfall (mm) 0 020406080100120140160180 Time (hrs)

Figure 4.40 - Herbert River – Late February 2000

Mass Curve of Rainfall

325 300 Nash's Crossing 275 250 225 Kirrama 200 17 5 Revenshoe 15 0 12 5 10 0 M cKell Road 75 50 Herb ert on 25 Cumulative(mm) Rainfall 0 0 102030405060708090100110120130140150160170180 Time (hrs)

Figure 4.41 - Herbert River – February 2001

Table 4.6 - Assessment Summary of Temporal Patterns of Rainfall – Herbert Basin

Dates of eight storms

Jan-94 Mar-96 Mar-97 Jan-98 Dec-99 Early Feb-00 Late Feb-00 Feb-01 Name of Rainfall No Station Time periods selected for the analysis 33 to 52hrs 49 to 69hrs 38 to 66hrs 33 to 83hrs 62 to 110hrs 66 to 231hrs 78 to 185hrs 47 to 171hrs 25 15 10 02 24 25 09 11 26 14 18 08 35 23 09 16 25 19 62 04 80 35 103 13 43 17 48 77 82 25 33 31 hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs

1 Nash's Crossing Not available Not available xxxx√ xxxxxx√ xx√√√√√√xx√√

2 Wallaman xx√ x √ x √√ Not available Not available Not available Not available Not available Not available

3 Kirrama Not available √ x √√√xx√√√Not available x √ Not available Not available x √√√

4 Glenagle √√√√√√√x √√x √ x √√√x √ x √ x √ x √√√√x Unreliable

5 Upper Rudd Creek Not available √√xx√√√√√√x √√√√x √√x √√√√x Unreliable

6 Mt. Garnet Not available √√√x √√√√√√√√√√√x √√x √√√√√ Unreliable

7 Silver valley √√x √Not available √√√√√√√√x √ xx Not available Not available Not available

8 Revenshoe Not available √√√√√√√√√√√√√√√√√√√√x √√√√√√√

9 McKell Road xx√ x √ xx√√√√√Not available √√√√√√√√x √√√√√x √

10 Herberton Not available √√x √√√√√√x √√√√√x √√√√√√x √√√x √ 125

4.4.2 Spatial variation of Rainfall In the next few pages, maps of isohyets for eight storms (summarised in Table 4.5) of the Herbert River basin are shown (Figures 4.42 to 4.49). The spatial variation of rainfall for each storm has been studied and compared in order to check their similarities and differences.

January 1994 - Rainfall depth increases from the middle of the catchment (from the West to the East) towards its outlet from 75 mm to 275 mm. In this variation a steady rate of change can be observed. The left half of the catchment has shown a reasonably uniform rainfall depth pattern with an average value of 52mm as shown in Figure 4.42.

March 1996 - A steady increase in rainfall depths in the right half of the catchment from 100 mm to 700 mm can be observed from Figure 4.43, and that variation begins from the middle of the catchment. Fairly uniform rainfall depth is present in the left half of the catchment with an approximate average value of 36mm.

March 1997 - Rainfall depth varies from 150 mm to 250 mm in the left half of the catchment. The direction of this variation is from the Southwest to the Northeast. In the other part of the catchment the rainfall depth increases from 300mm to 350mm from the West to the East as shown in Figure 4.44. A very small area on the eastern edge of the catchment has shown a higher rainfall depth.

January 1998 - Rainfall depth increases gradually from the Northwest to the outlet of the catchment. This variation is from 100 mm to 600 mm. It is a reasonably steady increase especially from the mid part of the catchment to its outlet, as shown in Figure 4.45. Fairly high rainfall depths are found at the bottom of the catchment.

December 1999 - There is no definite pattern of rainfall depth variation in the catchment for this storm. However, an increase in rainfall depths towards the top and the bottom parts of the catchment from its mid area can be observed in Figure 4.46. The rainfall is well distributed within the catchment and therefore, an average depth of 150mm may be considered for this storm. 126

150 125 100 75 10 174

8 52

175 200

225 250 5 275 81 75 100 125 1 150 3 285

Figure 4.42 – Rainfall Isohyets (mm) – Herbert River - January 1994

121 100 200 11 300 400 9 777 7 700 600 39 500

6 33 4 5 313 100 129

200 3 1 300 400 488

Figure 4.43 – Rainfall Isohyets (mm) – Herbert River - March 1996

127

272 300 250 11 331 10 350 400 207 9 438 7 8 200 167 400

150 6 138 4 150 5 346 168

200 2 250 300 1 350 392

Figure 4.44 – Rainfall Isohyets (mm) – Herbert River - March 1997

119 150

100 11 200

296 89 8 9 300 100 82 7 150

200 6 400 206 5 500 209

622 600 300 400 500 2 1 600 726

Figure 4.45 – Rainfall Isohyets (mm) – Herbert River - January 1998

128

126 11 10 139 150 125 176 175 8 175 9 7 175 101 150 125 125 6 100 138 5 4 73 100 153 125 150 150 2 175 194 165 1

175

Figure 4.46 – Rainfall Isohyets (mm) – Herbert River - December 1999

134 200 100 11 10 262 300 8 368 9 7 127 80

6 400 64 5 500 107

150 2 250 350 524 490 450 1

550

Figure 4.47 – Rainfall Isohyets (mm) – Herbert River - Early February 2000

129

400 407 350 10 300 11 250 466 427 239 8 9 235 250 7

450

290 550 5 265 300 623 650 400 500 2 1 747 600

Figure 4.48 – Rainfall Isohyets (mm) – Herbert River - Late February 2000

214 250 200 11 256 150 10

299 9 134 7

6 101 4 100 5 300 98 237

100 315 150 200 2 311 250 1

300

Figure 4.49 – Rainfall Isohyets (mm) – Herbert River - February 2001 130

Early February 2000 - Rainfall depth increases from 100 mm to 500 mm from the middle of the catchment towards its bottom part from the West to the East. Although the rate of rainfall variation is fairly steady, some uniformity in the rainfall depths can be seen on the left half of catchment with an approximate value of 72mm as shown in Figure 4.47.

Late February 2000 - Rainfall depth increases from the Northwest to the bottom of the catchment from 250 mm to 600 mm. A steady variation begins from the middle of the catchment as shown in Figure 4.48. Although higher rainfall depths are present at the bottom of the catchment, the left part has shown some uniformity with an approximate average value of 265mm.

February 2001 - A gradual increase in rainfall depth from the West to the East of the catchment can be seen in the Figure 4.49. The extreme left part of the catchment shows some uniformity in its rainfall depths with an approximate value of 111mm. Similarly the area close to the outlet has an average depth of 300mm.

The maps of isohyets of eight storms have illustrated some similarities in their patterns and they may be grouped in the following manner:

The maps of January 1994, January 1998 and early & late February 2000 storms have shown gradual increase in their rainfall depths from the middle to the bottom of the catchment. Moreover, a uniform rainfall depth pattern persists in the left part of the catchment.

The maps of isohyets of March 1996, March 1997 and February 2001 have shown somewhat steady increase in rainfall depths from the middle of the catchment to its Eastern side. The remaining parts have reported uniformity in their rainfall depths. The map dated December 1999 has shown no definite pattern, however, the rainfall depths are distributed fairly evenly to a considerable extent over the catchment.

131

4.5 RAINFALL DATA OF DON RIVER BASIN

4.5.1 Temporal Patterns of Rainfall Table 4.7 shows the total rainfall depths recorded for nine storms at eight stations as shown in Figure 4.50 of the Don River basin. Although some data is not available for Mount Dangar, Ida Creek, Roma Peak and Emu Creek stations for April 1989, December 1990, January 1991, and February 1991 storms respectively (shown in Table 4.7), all the stations with data have contributed to cover the Don River basin very well. According to Table 4.7 the highest rainfall depth is 1158mm, and it was found at the Reeves station in December 1990. The lowest rainfall depth is 30mm, which was found at the Upper Don station in January 1999.

Reeves 1

Mt Dangar 2

3 Moss Vale

Ida Creek 4 Roma Peak 5

Boundary Creek 6 Emu Creek 7

Upper Don 8

Figure 4.50 – Location of Rainfall stations of Don River

132

Table 4.7 – Summary of Rainfall for Don River Basin

Dates of nine storms and their total rainfall depths (mm) Name of Rainfall Elevation No Number Longitude Latitude Station in metres Feb-00 Feb-00 Apr-89 Dec-90 Jan-91 Feb-91 Aug-98 Jan-99 Dec-99 Early Late

1 Reeves 2630 148008'35'' 20009'05'' 40 187 1158 184 575 144 102 135 263 62 Not 2 0 ' '' 0 ' '' 792 145 297 121 98 148 192 45 Mt.Dangar 2625 148 07 14 20 13 17 120 available

3 Moss Vale 2600 148001'52'' 20014'22'' 80 231 552 183 412 155 77 123 156 38 Not Not 4 0 ' '' 0 ' '' Ida Creek 2620 148 07 01 20 17 28 80 available available 63 127 135 122 145 195 57 Not 5 0 ' '' 0 ' '' Roma Peak 2615 148 13 01 20 18 34 120 323 902 available 474 118 246 122 232 103 Not 6 0 ' '' 0 ' '' 546 184 469 188 45 131 268 64 Boundary Creek 2610 148 06 35 20 25 12 160 available Not Not Not Not 7 0 ' '' 0 ' '' 99 98 138 312 83 Emu Creek 2640 148 13 42 20 24 47 200 available available available available

0 ' '' 0 '' 8 Upper Don 2605 148 12 39 20 31'19 190 434 607 184 430 62 30 76 284 84

The plots of rainfall mass curves of nine storms at eight stations of the Don River basin are shown in Figures 4.51 to 4.59. The findings of the curves are tabulated in the Table 4.8.

Rainfall Mass Curve

450

400 Reeves 350 300 Moss vale 250 200 Roma Peak 150 10 0 50 Upper Don

Cumulative Rainfall (mm) 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Time (hrs)

Figure 4.51 – Don River – April 1989

Rainfall Mass Curve

500 450 Reeves 400 Mt.Dangar 350

300 M oss vale 250 200 Roma Peak 150 Boundary Creek 10 0

50 Upper Don

Cumulative(mm) Rainfall 0 0 5 10 15 20 25 30 35 40 45 50 55 Time(hrs)

Figure 4.52 – Don River – December 1990

133

Rainfall Mass Curve

200 18 0 Reeves 16 0 Mt.Dangar 14 0

12 0 M oss Vale 10 0 80 Ida Creek 60 Boundary Creek 40 20 Upper Don

Cumulative(mm) Rainfall 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Time (hrs)

Figure 4.53 – Don River – January 1991

Rainfall Mass Curve

500 450 Reeves 400 Mt.Dangar 350

300 Ida Creek 250 200 Roma Peak 150 Boundary Creek 10 0 50 Upper Don Cumulative Rainfall(mm) 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Time (hrs)

Figure 4.54 – Don River – February 1991

Rainfall Mass Curve

18 0 Reeves 16 0 Mt.Dangar 14 0 12 0 Moss vale 10 0 Ida Creek 80 Roma Peak

60 Boundary Creek

40 Emu Creek 20 Upper Don 0 Cumulative Rainfall(mm) 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Time (hrs)

Figure 4.55 – Don River – August 1998 134

Rainfall Mass Curve

260 240 Reeves 220 Mt.Dangar 200 18 0 M oss Vale 16 0 14 0 Ida Creek 12 0 Roma Peak 10 0 80 Boundary Creek 60 Emu Creek 40 20 Upper Don

Cumulative Rainfall (mm) 0 0 5 10 15 20 25 30 35 40 45 50 Time(hrs)

Figure 4.56 – Don River – January 1999

Rainfall Mass Curve

14 0 Reeves

12 0 Mt.Dangar

10 0 M oss Vale

80 Ida creek

Roma Peak 60 Boundary Creek 40 Emu Creek 20 Upper Don

Cumulative(mm) Rainfall 0 0 5 10 15 20 25 30 Time (hrs)

Figure 4.57 – Don River – December 1999

Rainfall Mass Curve

250 Reeves 225 200 Mt.Dangar

175 Moss Vale 15 0 Ida creek 12 5 Roma Peak 10 0 75 Boundary Creek 50 Emu Creek 25 Upper Don

Cumulative Rainfall (mm) (mm) Rainfall Cumulative 0 0 5 10 15 20 25 30 35 40 45 50 55 Time (hrs)

Figure 4.58 – Don River – Early February 2000 135

Rainfall Mass Curve

110 10 0 Reeves 90 Mt.Dangar 80 M oss Vale 70 60 Ida Creek

50 Roma Peak 40 Boundary Creek 30 20 Emu Creek 10 Cumulative Rainfall (mm) Rainfall Cumulative Upper Don 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 Time (hrs)

Figure 4.59 – Don River – Late February 2000

Table 4.8 – Assessment Summary of Temporal patterns of Rainfall – Don Basin

Dates of nine storms

Apr-89 Dec-90 Jan-91 Feb-91 Aug-98 Jan-99 Dec-99 Early Feb-00 Late Feb-00 Name of Rainfall No Station Time periods of storms selected for the analysis 45 to 73 hrs 25 to 50 hrs 34 to 55 hrs 11 to 54 hrs 29 to 35 hrs 26 to 43 hrs 21 to 26 hrs 42 to 52 hrs 53 to 78 hrs 25 20 10 18 09 06 10 25 24 06 15 10 18 08 08 22 11 07 11 08 11 04 17 11 06 07 05 08 14 11 06 21 25 28 13 12 hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs

1 Reeves √√xx√√√√x √√xx√√x √√√√√√√x √√√x √√√√√√√x

2 Mt.Dangar Not available √√√√√√√√x √√√√√√√√√√x √√√xx√√√√√√√

3 Moss Vale √√√√√√√√√√xx Not available √√√√√√√√√√√√x √√√√√√√

4 Ida Creek Not available Not available √√√√x √ xx√√x √√x √√x √√√xx√√√√√√

5 Roma Peak xx√√√√x Not available √√√√√√√x √ x √ x √ x √ x √√√x √ x √ x

6 Boundary Creek Not available √√√√√√xx√√√√√√√x √√x √√√√√√√√√√√√√

7 Emu Creek Not available Not available Not available Not available √√√√√√x √√xx√√√√√√√x √

8 Upper Don x √ x √√√√xx√ x √√√√√√√√√√√x √√xx√√xx√√√x √

4.5.2 Spatial variation of Rainfall In the next few pages, maps of isohyets for nine storms (summarised in Table 4.7) of the Don River basin are shown (Figures 4.60 to 4.68). The spatial variation of rainfall for each storm has been studied and compared in order to check their similarities and differences.

April 1989 - Rainfall depth decreases from 400mm to 200mm from the top to the bottom of the catchment and that variation is somewhat along the main stream of the catchment. The isohyets divide the catchment into fairly equal sections and this pattern of isohyets indicates a steady variation in rainfall depths as shown in Figure 4.60. 136

1 200

200 187

250 3 231 300

323 5 250 350

300 400

350 8 434

400

Figure 4.60 – Rainfall Isohyets (mm) – Don River (April 1989)

900 1 850 800 1158 750 700 600650 2 550 792 3 552

5 902 900 850 6 546 800

750 8 700 607 550 600 650

Figure 4.61 – Rainfall Isohyets (mm) – Don River (December 1990) 137

184 1

183 145 2 3 63 4 75

100

184 125 6 150 175 184 8

Figure 4.62 – Rainfall Isohyets (mm) – Don River (January 1991)

550 1 575

450 550 412 3

127 474 4 5 450

250

469 6 350 450 430 8

450

Figure 4.63 – Rainfall Isohyets (mm) – Don River (February 1991)

138

144

150 121 125 155 2 3 135 4 118 5

175

188 6 99 7 100

62 8 150 75 125 100 175 75

Figure 4.64 – Rainfall Isohyets (mm) – Don River (August 1998)

100 1 102 150 2 98 200 3 77 4 122 5 246 200

50 150 45 100 98 6 7

50 30 8

Figure 4.65 – Rainfall Isohyets (mm) – Don River (January 1999) 139

1 130 135 130 148 2 123 3

140 4 122 145 5

6 138 131 7

130 76 130 8 120 120 110 100 110

Figure 4.66 – Rainfall Isohyets (mm) – Don River (December 1999)

250 263 225 1 200 175 192 2 156 3 4 195 5 175 232 250 200 275 300 6 225 7 268 312 300 250 284 8

275

Figure 4.67 – Rainfall Isohyets (mm) – Don River (Early February 2000) 140

60 1 70 62 50 40 80 3 2 90 45 100 38 4 57 5 103 40 100 50 90 64 6 7 83 60

8 84 70 80

Figure 4.68 – Rainfall Isohyets (mm) – Don River (Late February 2000)

December 1990 - Rainfall depth increases from the Southwest to the Northeast of the catchment from 550mm to 900mm. A consistent rainfall depth variation can be observed in the mid area of the catchment to a considerable extent as shown in Figure 4.61.

January 1991 - Rainfall depth decreases from 175mm to 75mm from the boundary of the catchment towards its mid area. A fairly large area running along the boundary of the catchment (except for the region close to the outlet) maintains an approximate average rainfall depth of 184mm as shown in Figure 4.62.

February 1991 - Except for most of the areas close to the boundary of the catchment, the rainfall depth decreases from 400mm to 150mm from the outer edges of the middle part of the catchment towards its centre as shown in Figure 4.63. The approximate average rainfall depth near the outlet is about 550mm and that of the other areas close to the boundary is about 475mm. 141

August 1998 - Rainfall depth increases from the Southwest to the Northeast in the area close to the outlet of the catchment. The rainfall depth variation in the remaining part of the catchment is from the West to the East. This variation is from 175mm to 125mm as shown in Figure 4.64.

January 1999 - Rainfall depth increases from the Southwest to the Northeast of the catchment from 50mm to 200mm. The bottom part of the catchment maintains an approximate average rainfall depth of 125mm, whereas the top part is about 35mm as shown in Figure 4.65.

December 1999 - There is no definite pattern of rainfall depth variation, especially in the area close to the outlet of the catchment. The upstream part shows a rather slight increase in its rainfall depth variation and it is from 100mm to 120mm. There is not much of a difference in the average rainfall depths near the outlet and the Western part of the catchment. Average rainfall depths of 140mm and 136mm may be considered for these parts respectively.

Early February 2000 - Rainfall depth increases from the West to the East from 175mm to 225mm in the top half of the catchment, except for the area close to the outlet. The rainfall depth variation of the other half of the catchment is from the Northwest to the Southeast and it is from 250mm to 300mm as shown in Figure 4.67.

Late February 2000 - Rainfall depth increases from the West to the East of the top half of the catchment from 40mm to 100mm. The direction of rainfall depth variation in the bottom half of the catchment is from the Northwest to the Southeast. The spacing between isohyets in the downstream region close to outlet is fairly smaller than that of the other parts of the catchment.

The patterns of isohyets of January and February 1991 storms are very similar to each other. In both of these storms the rainfall depth decreases from the boundary of the catchment towards its mid area. The rainfall depths increase from the Southwest to the Northeast in the bottom part of the catchment as shown in Figures 4.61 and 4.65. Maps 142

of isohyets of early and late February 2000 storms have shown that the rainfall depth increases from the Northwest to the Southeast especially in the bottom part of the catchment. All the remaining maps of isohyets (April 1989, August 1998, and December 1999) have shown no similarities.

4.6 RAINFALL DATA OF NORTH JOHNSTONE RIVER BASIN

4.6.1 Temporal Patterns of Rainfall Table 4.9 shows the total rainfall depths recorded for ten storms at fifteen stations shown in Figure 4.69 of the North Johnstone River basin. Although the data is not available for a few stations at this basin, a sufficient amount of data is available to cover the basin as shown in Table 4.9. The maximum and minimum total depths reported are 1032mm (Topaz station in March 1999) and 41mm (Malanda station in 1997).

4 13 The Boulders Malanda

15 McKell Road Topaz 8

Millaa Millaa 11 Nerada 6 Tung Oil Bartle View 9 1 Greenhaven Revenshoe 12 Corsis Central Mill 14 3 2 7 Crawfords

Sutties Creek 10 5 Mena Vale

Figure 4.69 – Locations of Rainfall stations of North and South Johnstone Rivers

143

Table 4.9 – Summary of Rainfall for North and South Johnstone Rivers

Name of Rainfall Elevation in Dates of ten storms and their total rainfall depths (mm) No Number Longitude Latitude Station metres Mar-90 Jan-94 Mar-96 Mar-97 Dec-97 Jan-98 Mar-99 Dec-99 Feb-00 Apr-00

1 Tung oil 2565 145055'59'' 17033'00'' 40 394 575 485 412 571 563 752 438 399 325 Not 2 0 ' '' 0 ' '' 343 132 389 536 637 674 344 474 295 Central Mill 2555 145 59 00 17 36 59 20 available Not Not 3 0 ' '' 0 ' '' 417 710 679 371 625 606 782 344 Corsis 2550 145 53 59 17 36 00 100 available available Not Not Not Not Not Not Not 4 0 ' '' 0 ' '' 272 518 484 The Boulders 7344 145 52 00 17 21 00 80 available available available available available available available Not Not 5 0 ' '' 0 ' '' 498 573 634 403 628 645 596 271 Mena Vale 2545 145 53 11 17 40 57 240 available available Not 6 0 ' '' 0 ' '' 473 594 400 566 674 905 427 445 388 Nerada 2560 145 50 44 17 31 58 60 available Not 7 0 ' '' 0 ' '' 561 694 589 396 319 649 354 449 85 Crawfords 2540 145 48 00 17 37 02 340 available

8 Topaz 2515 145043'49'' 17028'15'' 660 494 412 572 622 239 449 1032 237 451 348 Not Not Not 9 0 ' '' 0 ' '' 513 434 567 843 218 443 279 Bartle View 2530 145 42 52 17 32 48 560 available available available

10 Sutties Creek 2535 145039'37'' 17040'49'' 680 443 318 412 345 138 486 368 263 327 135 Not 11 0 ' '' 0 ' '' 329 221 303 370 91 607 188 347 134 Millaa Millaa 2500 145 36 29 17 31 09 840 available

12 Greenhaven 2525 145035'56'' 17035'20'' 920 450 249 389 449 73 375 490 103 25 119

13 Malanda 2510 145035'29'' 17021'39" 720 359 206 212 284 41 180 605 155 207 96 Not Not Not Not Not Not 14 0 ' '' 0 ' '' 416 45 298 65 Revenshoe 6069 145 31 43 17 35 33 1100 available available available available available available Not Not 15 0 ' '' 0 ' '' 233 172 167 328 421 137 207 58 McKell Road 2520 145 30 29 17 26 43 1000 available available

The plots of rainfall mass curves of ten storms for fifteen rainfall stations of the North Johnstone River basin are shown in Figures 4.70 to 4.79. The findings of the curves are tabulated in Table 4.10.

Mass Curve of Rainfall

600 Tung Oil 550 500 Nerada 450 Crawfords 400 Topaz 350 300 Bartle View 250 M illaa M illaa 200 Greenhaven 15 0 10 0 Malanda 50 McKell Road Cumulative(mm) Rainfall 0 0 102030405060708090100110120130140150 Time (hrs)

Figure 4.70 – North and South Johnstone Rivers – March 1990

144

Mass Curve of Rainfall

300 Tung Oil

250 Nerada

Crawfords 200 Topaz

150 Bartle View

M illaa M illaa 10 0 Greenhaven

50 Malanda

Cumulative(mm) Rainfall M cKell Road 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Time (hrs)

Figure 4.71 – North and South Johnstone Rivers – January 1994

Mass Curve of Rainfall

550 50 0 Tung Oil 450 Crawfords 400 Topaz 350 300 Bartle View

250 M illaa M illaa 200 Greenhaven 150 10 0 Malanda

50 M cKell Road Cumulative Rainfall(mm) 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 Time (hrs)

Figure 4.72 – North and South Johnstone Rivers – March 1996

Mass Curve of Rainfall

650 600 T ung Oil 550 Nerada 50 0 450 Crawfords 400 350 Topaz 300 M illaa M illaa 250 200 Greenhaven 15 0 Malanda 10 0 50 M cKell Road Cumulative Rainfall (mm) 0 0 5 10 15 20 25 30 35 40 45 50 55 Time (hrs)

Figure 4.73 – North and South Johnstone Rivers – March 1997 145

Mass Curve of Rainfall

350 Tung Oil 300 Nerada 250 Crawfords

200 Topaz

15 0 M illaa M illaa Greenhaven 10 0 Malanda 50 M cKell Road Cumulative(mm) Rainfall 0 0 2 4 6 810121416182022 Time (hrs)

Figure 4.74 – North and South Johnstone Rivers – December 1997

Mass Curve of Rainfall

700 650 Tung Oil 600 550 Central M ill 500 Corsis 450 400 Mena Vale 350 300 Nerada 250 Topaz 200 150 Greenhaven 10 0 50 Malanda Cumulative Rainfall (mm) 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Time (hrs)

Figure 4.75 – North and South Johnstone Rivers – January 1998

Mass Curve of Rainfall

110 0 Tung Oil 10 0 0 900 Nerada 800 Crawfords

70 0 Topaz 600 Bartle View 50 0 400 M illaa M illaa 300 Greenhaven 200 Malanda 10 0 McKell Road

Cumulative Rainfall (mm) 0 0 102030405060708090100110120130140 Time (hrs)

Figure 4.76 – North and South Johnstone Rivers – March 1999

146

Mass Curve of Rainfall

400 Tung Oil 350 Nerada 300 Crawfords

250 Topaz

200 Bartle View

15 0 M illaa M illaa Greenhaven 10 0 Malanda 50

Cumulative Rainfall (mm) M cKell Road 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Time (hrs)

Figure 4.77 – North and South Johnstone Rivers – December 1999

Mass Curve of Rainfall

12 5 T ung Oil

Nerada 10 0 Crawfords

75 Topaz Bartle View

50 M illaa M illaa

Greenhaven 25 Malanda

Cumulative Rainfall(mm) M cKell Road 0 0 5 10 15 20 25 30 Time (hrs)

Figure 4.78 – North and South Johnstone Rivers – February 2000

Mass Curve of Rainfall

400 Tung Oil 350 Nerada

300 Crawfords

250 Topaz

200 Bartle View

150 M illaa M illaa Greenhaven 10 0 Malanda 50

Cumulative Rainfall (mm) M cKell Road 0 0 2 4 6 8 101214161820222426283032 Time (hrs)

Figure 4.79 – North and South Johnstone Rivers – April 2000

147

Table 4.10 – Assessment Summary of Temporal Patterns of Rainfall – Johnstone Basin

Dates of ten storms

Mar-90 Jan-94 Mar-96 Mar-97 Dec-97 Jan-98 Mar-99 Dec-99 Feb-00 Apr-00 Name of Rainfall No Station Time periods of storms selected for the analysis 24 to144 hrs43 to 72 hrs 22 to 60 hrs 25 to 49 hrs 14 to 21 hrs 21 to 69 hrs 08 to141 hrs 29 to 58 hrs 17 to 29 hrs 15 to 30 hrs 34 61 30 19 30 16 09 17 17 11 27 05 15 10 18 06 08 04 06 03 20 22 18 09 40 45 50 06 28 08 17 05 14 05 04 06 12 06 10 02 hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs hrs

1 Tung oil √ x √√√√√x √√x √√√√x √ xxx√√√√√√√√√xxxxx√ x √√x √

2 Central Mill Not selected Not selected Not available Not available Not available √√√x Not selected Not selected Not selected Not selected

3 Corsis Not selectedNot selected Not selected Not selected Not selected √√√√ Not selected Not available Not available Not available

4 Mena Vale Not selected Not selected Not selected Not selected Not selected √√√√ Not available Not available Not selected Not selected

5 Nerada √ x √√√√√√Not available √√xx√ xxx√√x √√√√√√x √ x √√√√√√x √

6 Crawfords √ x √√√x √√√√x √√√√xx√ xx Not available √√√√√√x √√x √ x √ xx√

7 Topaz √√x √√√xx√√√√√√√√√√x √ x √ x √√√x √√x √√√√√√x √√x

8 Bartle View √√√√√xx√√x √√Not available Not available Not available √√√√√√√√√√√√√√xx

9 Millaa Millaa √√√√√√√√√√√√√√√√√√√√Not available √√√√√√√√√√√√√√√√

10 Greenhaven √√√√√√√√√√√√√√√√√√√√√x √√√√√√x √ xx√ xx√√√√√

11 Malanda x √ x √ x √√√xx√ x √ xx√√√√√x √√x √√x √ x √ x √ xxxx√ x √√

12 McKell Road √√√√√√√√xx√√√√xx√√√√Not available √√√√x √√√√√x √ xx√√

4.6.2 Spatial variation of Rainfall In the next few pages, maps of isohyets (Figures 4.80 to 4.89) for ten storms (shown in Table 4.10) of North and South Johnstone River basins are shown.

March 1990 - Rainfall depth increases gradually from the Northwest to the Southeast of the catchment down to its centre from 250mm to 450mm. The rainfall depth variation from the centre of the catchment to its outlet is rather uneven. The part of the mid area close to the outlet of the catchment maintains a rainfall depth close to 525mm. However, that value reduces to 400mm at the outlet of the catchment as shown in Figure 4.80.

January 1994 - Rainfall depth gradually increases from 200 mm to 500 mm from the Northwest to the Southeast. However, that variation does not exist in the area close to the outlet as shown in Figure 4.81. Thus the bottom part of the catchment close to the outlet maintains an approximate average rainfall depth of 650mm.

148

350 400 359 300 13 450 250 233 15 494 450 8 250 400 329 473 300 513 394 11 6 • 350 500 1 9 450 417 343 561 • 12 3 2 400 7 400 450 550 498 450 443 10 5

Figure 4.80 – Rainfall Isohyets (mm) – North & South Johnstone Rivers (March 1990)

200 206 300 13

172 400 500 15 412

8 221 200 594 11 6 434 575 9 1 249 710 12 694 700 • 132 3 2 7

300 318 600 573 10 5 400 500 600

Figure 4.81 – Rainfall Isohyets (mm) – North & South Johnstone Rivers (January 1994) 149

200 300 212 13 400 167 500 15 572 200 8 303 500 11 567 300 485 389 9 1 500 12 600 589 679 3 400 7 412 10 634 600 5 500

Figure 4.82 – Rainfall Isohyets (mm) – North & South Johnstone Rivers (March 1996)

400 300

284 300 13 500 328 600 15 600 8 622 500 370 11 400 400 412 416 449 6 1 14 12 400 396 371 389 400 7 3 2 345 10 403 5

Figure 4.83 – Rainfall Isohyets (mm) – North & South Johnstone Rivers (March 1997) 150

100 41 13

200 15 239 300 8 400 91 500

11 566 45 6 571 73 1 14 12 319 625 3 536 100 7 2 138 600 10 500 600 400 200 300

Figure 4.84- Rainfall Isohyets (mm) - North & South Johnstone Rivers (December1997)

200 300 180 200 13

400 500 449 8 600 700

300 674 6 563 375 1 700 12 606 400 3 2 637 486 10 645 600 500 5

Figure 4.85 - Rainfall Isohyets (mm) - North & South Johnstone Rivers (January 1998) 151

600 605 700 13 500 800 421 900 15 1000 8 1000 1032 900 607 11 905 800 843 9 6 752 490 1 12 782 700 649 3 674 7 2

368 10 500 600

Figure 4.86 - Rainfall Isohyets (mm) - North & South Johnstone Rivers (March 1999)

200 250 272 150 155 4 300

13 350

137 400 237 15 8

188 427 218 6 438 11 1 9 103 344 354 2 14 12 7 150 200 250 263 10 350 300

Figure 4.87-Rainfall Isohyets (mm) - North & South Johnstone Rivers (December 1999) 152

300 400 518 207 4 13

207 15 451 8 200 347 445 400 11 6 399 443 400 9 1 100 12 474 298 25 2 14 449 300 7 500

596 327 5 10 400

Figure 4.88 - Rainfall Isohyets (mm) - North & South Johnstone Rivers (February 2000)

100

96 200 484 13 4 400 58 300

15 400 348 8 134 11 279 388

9 6 325 14 65 119 1 12 85 344 300 100 100 7 3 295 2 135 10 271 200 5

Figure 4.89 - Rainfall Isohyets (mm) - North & South Johnstone Rivers (April 2000) 153

March 1996 - Rainfall depth gradually increases from 200 mm to 500 mm from the Northwest to the Southeast down to the mid area of the catchment. The rainfall depths of the remaining part of the catchment have shown no real pattern according to Figure 4.82. However, the approximate average depth of 550mm may be considered for the bottom part of the catchment.

March 1997 - Rainfall depth decreases from 600mm to 400mm from the North to the South of the catchment. This variation covers a considerable part of the catchment as shown in Figure 4.83. Although the upstream half of the catchment shows no real pattern, an approximate average rainfall depth of 400mm may be considered for that part.

December 1997 - Rainfall depth increases from 100 mm to 500 mm in the middle part of the catchment from the West to the East as shown in Figure 4.84. However, a noticeable rainfall depth variation is not present in the extreme left and the bottom parts of the catchment. Approximate average rainfall depths of 62mm and 572mm may be considered for these parts respectively.

January 1998 - Rainfall depth increases from 200mm to 700mm from the top to the bottom of the catchment. The direction of this variation is very close to the direction of the main stream flow as shown in Figure 4.85. Furthermore, the pattern of rainfall is fairly consistent throughout the catchment.

March 1999 - Rainfall depth increases from 500 mm to 1000 mm from the Southwest to the Northeast of the catchment and the isohyets are somewhat semi-circular in shape as shown in Figure 4.86. A fairly consistent variation over the entire catchment can be seen from Figure 4.86. Approximate average rainfall depths of 736mm and 513mm may be considered for the areas close to the outlet and the top of the catchment respectively.

December 1999 - In the middle part of the catchment the rainfall depth variation is from 200mm to 350mm. This variation is from the West to the East of the catchment as shown in Figure 4.87. An approximate average rainfall depth of 146mm may be 154

considered for the top part of the catchment while a depth of 390mm may be considered for the bottom part.

February 2000 - No definite pattern of rainfall depth variation exists, especially in the extreme top and bottom parts of the catchment. However, there is a variation in rainfall depths (400mm to 200mm) in the middle part of the catchment as shown in Figure 4.88. This variation terminates at the lower upstream part of the catchment. An approximate rainfall depth of 100mm may be considered for that part of the catchment.

April 2000 - Rainfall depth gradually increases from 100mm to 300mm in the top half of catchment from the West to the East. Although the rainfall depth increases from the West to the East in the downstream part of the catchment, this increase is fairly inconsistent. The reason for this is that the left portion of the downstream half of catchment maintains an approximate average rainfall depth of 100mm as shown in Figure 4.89.

The maps of isohyets of January 1994, March 1996 and December 1999 storms have shown an increase in their rainfall depths from the Northwest to the Southeast of the catchment and those increments lead up to the middle part of the catchment. The bottom part of the catchment shows a fairly uniformly distributed rainfall depth pattern in all three cases.

The maps of isohyets of December 1997 and January 1998 storms have indicated an increase in rainfall depths from the top to the bottom of the catchment. This variation is fairly consistent in the mid part of the catchment for both storms as shown in Figures 4.84 and 4.85.

The maps of isohyets of March 1999 and April 2000 storms have shown an increase in rainfall depths from the West to the East of the catchment. However, that variation terminates at the mid part of the catchment. Thereafter the rainfall depth variation becomes fairly inconsistent. 155

The remaining maps of March 1990, March 1997 and February 2000 (shown in Figures 4.80, 4.83 and 4.88) have demonstrated no similarities in their patterns of isohyets.

4.7 STREAMFLOW DATA OF MARY RIVER BASIN

Streamflow data is collected from the Bureau of Meteorology of Queensland for the seventeen catchments of the five large drainage basins. This data is available as stage hydrographs as well as rating tables for each catchment. This section describes the methods used to convert this data to streamflow hydrographs, and to separate surface runoff from the underlying baseflow.

The ordinates of the surface runoff hydrographs of the seventeen catchments for various storms have been calculated from the data provided by the Bureau of Meteorology, by means of the following steps: (i) Plot the rating curves of river discharge (m3/s) versus stage (m); (ii) Introduce polynomials to fit the stage-discharge curves. Use several polynomials to cover various portions of the curves if it is difficult to fit a single polynomial to cover all points on the curve; and (iii) Use the equations of the polynomials derived in step (ii) to calculate the ordinates of the total flood hydrographs (m3/s) from the stage hydrographs.

The next task is to separate the surface runoff hydrograph from the total hydrograph. The steps in this procedure are: (i) Plot the semi-log curve of the recession part of the total flood hydrograph versus time, to find out the time at which the surface runoff terminates; and (v) Calculate the ordinates of the surface runoff flood hydrograph by separating the baseflow from the ordinates of the total flood hydrograph.

Figures 4.90 to 4.93 illustrate the procedures for Mary River at Gympie: (a) The points of Figure 4.90 indicate the relationship of recorded flow versus stage of stream flow; (b) Two fifth order polynomials (for stage intervals of 0.03 to 10.9m and 10.9m to 26.7m) have very closely fitted the points; and 156

(c) The ordinates of the total rainfall flood hydrograph for the February 1995 storm shown in Figure 4.91 have been calculated and plotted by using the equations of polynomials in Figure 4.90.

14000 • Actual points on rating curve 12000 Fitted polynomial

y = -0.0153x 5 + 1.3903x4 - 47.635x3 + 811.26x2 - 6694x + 21832 10000 (for 10.9m to 26.7m stages)

/s) 8000 3

6000 Flow (m Flow

4000

y = 0.0077x5 - 0.14x4 + 0.0649x3 + 13.528x 2 - 4.9579x - 1.2765 (for 0.03 to 10.9m stages) 2000

0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 Stage (m)

Figure 4.90 – Actual and Estimated rating curves for Mary River at Gympie

1200

1100

1000

900

800

700

600 /s) 3

500

Flow (m 400

300

200

100

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220

Time (hrs) Figure 4.91 – Total flood hydrograph for Mary River at Gympie (February 1995)

157

(d) The hydrograph recession is plotted on the semi-log scale with time on the linear scale, as shown in Figure 4.92

1000 /s)

3 End of surface runoff 100 Flow (m

10 124 126 128 130 132 134 136 138 140 142 144 146 148 150 152 154 156 158 160 162 164 166 168 170 172

Time (hrs) Figure 4.92 – Recession curve for Mary River at Gympie (February 1995)

1200

1100

1000

900

800

700 /s) 3

600 Flow (m Flow 500

400 Surface runoff

300 End of Surface runoff

200

100 Start of Rise of Hydrograph Base flow 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 Time (hrs)

Figure 4.93 – Base flow Separation for Mary River at Gympie (February 1995)

158

(e) A straight line, as shown in Figure 4.93, is used to separate the base flow from the total flow hydrograph. The resulting surface runoff hydrograph is shown on Figure 4.94.

1200

1100

1000

900

800

700

600 /s) 3

500

Flow (m 400

300

200

100

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220

Time (hrs) Figure 4.94 – Surface runoff hydrograph for Mary River at Gympie (February 1995)

Subsequently the rating curves, recession curves and total flood hydrographs are plotted for all storms selected for the remaining sixteen catchments, and the surface runoff hydrographs were derived by separating the base flow.

Note that for some of the storms, the plots of hydrograph recession do not clearly indicate the points, at which the surface runoff ends. For those cases the surface runoff termination points are found, based on the examination of all recession hydrographs for the catchments.

Typical results for the main drainage basins namely Haughton River at Powerline, Herbert River at Zattas, Don River at Reeves and North Johnstone River at Tung Oil are shown in the following pages. The actual and estimated rating curves (Figures 4.111 to 4.122) for the remaining catchments are contained in part 1 of Appendix C of the CD and the baseflow separation and surface runoff hydrographs (Figures 4.123 to 4.384) of all seventeen catchments are in part 2. 159

4.8 STREAMFLOW DATA OF HAUGHTON RIVER BASIN

5500 • Actual points on rating curve 5000 Fitted polynomial 4500

4000 y = 124.67x 3 - 3681.5x2 + 36807x - 121970 3500 (for 9.0m to 12.0m stages) /s) 3 3000

2500 Flow (m Flow 2000 y = 1.6458x4 - 41.245x 3 + 402.2x 2 - 1502.2x + 2182.9 (for 5.0m to 9.0m stages) 1500

1000

y = -0.3123x5 + 4.4347x4 - 24.546x3 + 88.52x2 - 70.573x + 12.477 500 (for 0.25m to 5.0m stages)

0 012345678910111213 Stage (m)

Figure 4.95 – Actual and Estimated rating curves for Haughton River at Powerline

1000

End of surface runoff /s) 3 100 Flow (m

10 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64

Time (hrs)

Figure 4.96 – Recession curve for Haughton River at Powerline (February 1997)

160

1200

1100

1000

900

800 /s) 3 700

600 Flow (m Flow

500

Surface Runoff 400

300

200 End of surface runoff

100 Start of Rise of Hydrograph Base flow 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 Time (hrs)

Figure 4.97 – Base flow separation for Haughton River at Powerline (February 1997)

1200

1100

1000

900

800 /s) 3 700

600 Flow (m Flow

500

400

300

200

100

0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 Time (hrs)

Figure 4.98 – Runoff hydrograph for Haughton River at Powerline (February 1997)

161

4.9 STREAMFLOW DATA OF HERBERT RIVER BASIN

4500 • Actual points on rating curve 4000 Fitted polynomial

3500

3000 y = 1.7688x4 - 32.756x3 + 217.69x2 - 277.18x + 442.41

/s) (for 1.9 to 9.7m stages)

3 2500

2000 Flow (m

1500

1000

500 y = -394.5x4 + 1346x3 - 1320.4x2 + 618.98x + 3E-09 (for 0 to 1.9m stages)

0 012345678910 Stage (m) Figure 4.99 – Actual and Estimated rating curves for Herbert River at Zattas

10000

End of surface runoff /s) 3 Flow (m Flow

100 120 130 140 150 160 170 180 190 200 210 220 230 240 Time (hrs)

Figure 4.100 – Recession curve for Herbert River at Zattas (December 1991)

162

5000

4500

4000

3500 /s) 3 3000 Flow (m 2500

2000

Start of rise of 1500 hydrograph Surface runoff End of surface runoff

1000 Base flow

500 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Time (hrs)

Figure 4.101– Base flow separation for Herbert River at Zattas (December 1991)

3500

3000

2500 /s) 3 2000 Flow (m

1500

1000

500

0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Time (hrs)

Figure 4.102 – Runoff hydrograph for Herbert River at Zattas (December 1991)

163

4.10 STREAMFLOW DATA OF DON RIVER BASIN

14000 • Actual points on rating curve Fitted polynomial 12000

10000

/s) 3 2

3 y = 473.33x - 11630x + 96197x - 263800 (for 8.0m to 10.5m stages)

8000

6000

Flow or Discharge (m Discharge or Flow 4000 y = 3E-11x3 - 5E-10x2 + 800x - 2600 (for 5.0m to 8.0m stages)

2000 y = -10.517x4 + 161.41x3 - 729.23x2 + 1398x - 962.08 (for 0 to 5.0m stages) 0 0123456789101112 Stage or depth (m) Figure 4.103 – Actual and Estimated rating curves for Don River at Reeves

10000

1000 /s) 3

Flow (m End of surface runoff

100

10 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 Time (hrs)

Figure 4.104 – Recession curve for Don River at Reeves (April 1989)

164

2750

2500

2250

2000

1750 /s) 3

1500 Flow (m 1250

1000

750

500

Start of rise of hydrograph End of surface runoff 250 Surface runoff

Base flow 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Time (hrs) Figure 4.105 – Base flow separation for Don River at Reeves (April 1989)

2750

2500

2250

2000

1750 /s) 3

1500 Flow (mFlow 1250

1000

750

500

250

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Time (hrs)

Figure 4.106 – Runoff hydrograph for Don River at Reeves (April 1989)

165

4.11 STREAMFLOW DATA OF JOHNSTONE RIVER BASIN

5500 • 5000 Actual points on rating curve Fitted polynomial 4500

4000 y = 0.1x5 - 4.2917x4 + 73.417x3 - 567.21x2 + 2436x - 4032 (for 6.0m to 11.0m stages) 3500 /s) 3 3000

2500 Flow (m 2000

1500

1000

y = 0.5292x5 - 6.4716x4 + 23.722x3 + 13.244x2 - 15.046x + 0.0032 500 (for 0 to 6.0m stages)

0 0123456789101112 Stage(m)

Figure 4.107- Actual and Estimated rating curves for North Johnstone River at Tung Oil

1000

End of surface runoff /s) 3

100 Flow (m

10 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 Time (hrs)

Figure 4.108 - Recession curve for North Johnstone River at Tung Oil (March 1996)

166

1200

1100

1000

900

800

700 /s) 3 600

Flow (m 500

400

300 Surface runoff Start of rise of End of surface runoff 200 hydrograph

100 Base flow

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Time (hrs) Figure 4.109- Base flow separation for North Johnstone River at Tung Oil (March 1996)

1100

1000

900

800

700 /s) 3

600 Flow (m Flow 500

400

300

200

100

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Time (hrs) Figure 4.110 - Runoff hydrograph for North Johnstone River at Tung Oil (March 1996)

Summary of rainfall and stream flow data of all 254 storm events of seventeen catchments is shown in Tables 5.12 to 5.28 of Chapter 5.

CHAPTER 5

METHOD OF ANALYSIS

167

5. METHOD OF ANALYSIS

5.1 Introduction

In this chapter, the method of analysis of data is discussed in detail and the results are illustrated graphically. The intention of the analysis is to derive the lag parameters and continuing losses for the selected storms that occurred during the past ten to fifteen years in the selected catchments. The lag parameters have been derived by calibrating the WBNM (Watershed Bounded Network Model) computer program (developed by Boyd et al., 2003) using the reliable hydrological data. The assessment of the reliability of data has already been discussed in the previous chapter.

All seventeen catchments described in the previous chapters are considered for the analysis. The most important information required to run WBNM successfully are: rainfall data, ordinates of runoff hydrographs, areas of sub-catchments, sequence of flow path through sub-catchments, and the co-ordinates of centroids of sub-catchments as well as the rainfall gauging stations. The ordinates of the runoff hydrographs have been calculated using the methods described in the previous chapter.

In the first part of the analysis, the initial losses of storms of all seventeen catchments are separated from their hyetographs by comparing them with their resulting hydrographs. These losses are illustrated as shaded areas in figures of this chapter, which consist of hyetographs (the hyetographs of the rainfall station closest to the outlet of the catchment are shown for illustration purposes) and hydrographs at outlets.

In the second part, the continuing loss rate of the WBNM program is adjusted until the excess rainfall depths match the recorded surface runoff depths. Thereafter, the lag parameter is adjusted until the calculated and recorded hydrographs match. The plotted hydrographs are visually inspected, with most emphasis being placed on matching the peak discharge.

After analysing the data successfully by means of the WBNM as explained in the two previous paragraphs, the lag parameters of all seventeen catchments and their respective continuing losses for various storms have been obtained from the WBNM output files.

168

5.2 Mary River Basin. The boundaries of the Gympie catchment as well as its sub-catchments have been demarcated on the AUSLIG map (with a scale of 1:100000), as demonstrated in Figure 5.1. These are transferred onto tracing paper. The tracing paper was placed on a grid containing 4mm x 4mm squares (each square represents 16ha for maps with scales of 1:100000) and the areas of sub-catchments have been calculated by counting the number of squares contained in each sub-catchment.

Outlet at Gympie

23 26 21 22 15 17 24 20 18 11

10 9 16 25 19

14 7 8 13

5 4 6

12 3

1 2

Figure 5.1- Sub-areas of Mary River at Gympie

The total catchment area of Gympie was calculated by adding the values of sub-areas together and that value of 292020ha was found to be very close to the value 292000ha 169

indicated in the Catalogue of “Stream Gauging Information Australia-1990,” published by the Australian Water Resources Council. Moreover, the values of the catchment areas were further checked by measuring them with a Planimeter. Therefore, it is revealed that the grid paper method has a high standard of accuracy and reliability.

This method is adopted to calculate the areas of all seventeen catchments (shown in Table 5.1) and these values are found to be very close to the respective values given in the catalogue.

The Eastern and Northern co-ordinates of the centroids of sub-areas as well as the locations of the rainfall stations of the Gympie catchment have been found from the co- ordinate system given in the AUSLIG maps.

As shown in Figures 5.2, 5.4, 5.6, 5.8, 5.10, 5.12, 5.14 and 5.16, the initial loss of various storms have been estimated. In this estimation process the patterns of the rainfall hyetographs were compared with their respective resulting total hydrographs to find out the time at which the flow begins to increase. This total time elapsed, between the start of the storm and at the time the flow begins to rise, is used to obtain the initial loss of storms.

The input file of WBNM is prepared by means of the rainfall, flow and topographical data of a given catchment. Some vital parts of the truncated input file of the 11th February 1995 storm of Mary River at Gympie are shown in Tables 5.2 to 5.6.

Subsequently the input file is used with WBNM for analysis. One of the purposes of this analysis is to find out the lag parameters related to all 254 storm events of all seventeen catchments. Since the storms with multiple events produce more than one lag parameter, this analysis had to be repeated several times to obtain the lag parameters. Considering one event at a time and examining the information provided by each output file of WBNM and making necessary adjustments to its respective input file in each submission, suitable lag parameters were obtained for all storm events, after satisfying the following conditions: • The value of continuous loss rate for every sub-area of the catchment is set to the same value; 170

• The depth of excess rainfall (derived by subtracting the continuing loss rate) is equal to the depth of surface runoff in the recorded hydrograph after separation of baseflow; • The peak flows of the recorded surface hydrograph and the WBNM generated hydrograph, are equal to each other; and • The ordinates of the WBNM generated hydrograph should match the ordinates of the actual runoff hydrograph (as illustrated in Figures 5.3, 5.5, 5.7, 5.9, 5.11, 5.13, 5.15 and 5.17 of Mary River at Gympie where the hydrographs with broken lines are produced by WBNM ).

The input and output files of WBNM used for this analysis provide useful information for this research study and therefore, this information is tabulated for each catchment. For example the information applicable to the Mary River at Gympie is tabulated in Table 5.7. The input and output files of WBNM, relating to all seventeen catchments (for selected storms), are contained in Appendix D of the CD.

The foregoing procedure has been adopted to obtain lag parameters and other features of storm events for the remaining sixteen catchments also considered for this study. The hyetographs, total hydrographs, surface runoff hydrographs and the WBNM computer generated hydrographs of the five major river basins are illustrated in the next part of this chapter. The essential information is summarised in the seventeen tables (Tables 5.12 to 5.28) shown in the last part of this chapter.

Table 5.1- Details of seventeen catchments selected for the study

Catchment Total Area Number of Number of Number Name (ha) subareas Rain Gauges 1 Gympie 292020 29 10 2 Moy Pocket 83023 34 6 3 Bellbird 47920 32 4 4 Cooran 16432 37 4 5 Kandanga 17568 25 3 6 Powerline 173456 119 5 7 Mt. Piccanniny 113893 84 6 8 Silver Valley 58624 15 5 9 Gleneagle 537016 91 8 10 Nash's Crossing 684152 119 8 11 Zattas 729200 140 8 12 Reeves 101032 96 6 13 Mt. Dangar 80784 77 7 14 Ida Creek 62008 53 5 15 Tung Oil 92936 56 9 16 Nerada 80792 46 8 17 Central Mill 38976 46 7

171

Table 5.2 - Co-ordinates of centroids of sub-catchments of WBNM input file of Mary River at Gympie

#####START_TOPOLOGY_BLOCK##########|###########|###########|###########| No. of sub catchments = 29 Eastern Co-ordinate Northern Co-ordinate Flow paths SUB1 47.30 70.38 -1.00 -1.00 SUB3 SUB2 47.70 70.44 -1.00 -1.00 SUB3 SUB3 47.60 70.48 -1.00 -1.00 SUB5 SUB4 46.00 70.54 -1.00 -1.00 SUB5 SUB5 47.35 70.55 -1.00 -1.00 SUB7 SUB6 48.42 70.47 -1.00 -1.00 SUB7 SUB7 47.55 70.64 -1.00 -1.00 SUB9 SUB8 48.30 70.70 -1.00 -1.00 SUB9 SUB9 47.25 70.74 -1.00 -1.00 SUB11 SUB10 48.22 70.76 -1.00 -1.00 SUB11 SUB11 47.58 70.78 -1.00 -1.00 SUB15 SUB12 44.75 70.58 -1.00 -1.00 SUB14 SUB13 44.34 70.71 -1.00 -1.00 SUB14 SUB14 46.40 70.68 -1.00 -1.00 SUB15 SUB15 47.50 70.81 -1.00 -1.00 SUB17 SUB16 48.20 70.81 -1.00 -1.00 SUB17 SUB17 47.22 70.84 -1.00 -1.00 SUB21 SUB18 44.52 70.78 -1.00 -1.00 SUB20 SUB19 45.55 70.75 -1.00 -1.00 SUB20 SUB20 46.35 70.79 -1.00 -1.00 SUB21 SUB21 47.50 70.86 -1.00 -1.00 SUB23 SUB22 45.80 70.84 -1.00 -1.00 SUB23 SUB23 47.10 70.94 -1.00 -1.00 SUB27 SUB24 49.20 70.79 -1.00 -1.00 SUB26 SUB25 48.68 70.84 -1.00 -1.00 SUB26 SUB26 48.00 70.93 -1.00 -1.00 SUB27 SUB27 46.58 70.96 -1.00 -1.00 SUB29 SUB28 47.12 71.80 -1.00 -1.00 SUB29 SUB29 46.65 71.20 -1.00 -1.00 SINK #####END_TOPOLOGY_BLOCK############|###########|###########|###########|

172

Table 5.3 - Sub-areas and lag parameter of WBNM input file of Mary River at Gympie of 11th February 1995 Storm

#####START_SURFACES_BLOCK##########|###########|###########|###########| 0.77 -99.90 Sub area (ha) Lag Parameter SUB1 12874.00 0.00 2.77 0.25 SUB2 4082.00 0.00 2.77 0.25 SUB3 13502.00 0.00 2.77 0.25 SUB4 18526.00 0.00 2.77 0.25 SUB5 4239.05 0.00 2.77 0.25 SUB6 20724.00 0.00 2.77 0.25 SUB7 12717.05 0.00 2.77 0.25 SUB8 13816.00 0.00 2.77 0.25 SUB9 2512.00 0.00 2.77 0.25 SUB10 2826.00 0.00 2.77 0.25 SUB11 1099.00 0.00 2.77 0.25 SUB12 30301.00 0.00 2.77 0.25 SUB13 14601.00 0.00 2.77 0.25 SUB14 28417.00 0.00 2.77 0.25 SUB15 3454.00 0.00 2.77 0.25 SUB16 6123.00 0.00 2.77 0.25 SUB17 942.00 0.00 2.77 0.25 SUB18 13816.00 0.00 2.77 0.25 SUB19 942.00 0.00 2.77 0.25 SUB20 10833.00 0.00 2.77 0.25 SUB21 3768.00 0.00 2.77 0.25 SUB22 14915.00 0.00 2.77 0.25 SUB23 5181.00 0.00 2.77 0.25 SUB24 12717.00 0.00 2.77 0.25 SUB25 1884.00 0.00 2.77 0.25 SUB26 15386.00 0.00 2.77 0.25 SUB27 4396.00 0.00 2.77 0.25 SUB28 16799.00 0.00 2.77 0.25 SUB29 628.00 0.00 2.77 0.25 #####END_SURFACES_BLOCK############|###########|###########|###########|

173

Table 5.4 - Names of ten rainfall stations, co-ordinates and their respective rainfall depths of WBNM input file of Mary River at Gympie of 11th February 1995 Storm

#####START_STORM_BLOCK#############|###########|###########|###########| 1 #####START_STORM#1 This rainfall has been recorded 60.00 60.00 #####START_RECORDED_RAIN 11/2/95 09:00 22 60.00 MM/PERIOD 10 Gympie 46.65 70.28 6.74 5.23 2.73 2.73 4.34 6.3 6.3 5.59 4.66 4.66 3.76 4.61 4.61 4.08 3.37 3.37 2.98 2.51 0.95 0.4 0 0 Cooran 48.22 70.87 10.4 7.68 3.4 3.4 6.24 9.69 9.69 9.69 9.69 9.26 8.18 9.88 9.88 12.72 16.5 16.5 9.22 174

0.63(Contd.,) 0.08 0 0 0 Mapleton 48.75 70.57 10.18 6.87 7.42 7.02 5.71 7.85 5 5.57 13.1 17.36 14.4 24.34 25.83 22.79 21.37 44.17 11.13 6.49 5.56 9.95 4.4 0 Maleny 48.50 70.41 5.11 4.69 3.8 3.8 3.59 3.32 3.32 6.39 10.8 10.8 11.68 12.77 12.77 14.82 17.97 17.97 14.23 9.56 9.56 9.96 10.53 10.39 Kenilworth 47.30 70.58 2.57 2.57 2.05 2.01 2.72 175

3.63(Contd.,) 3.63 4.08 4.73 4.73 5.25 5.89 5.89 5.58 5.09 5.09 3.71 1.98 1.98 1.34 0.42 0.41 Cooroy 49.15 70.79 12.76 10.3 4.87 4.87 7.94 11.87 11.87 12.81 14.19 14.19 16.91 20.31 20.31 22.98 27.12 27.12 16.73 3.63 3.63 2.66 1.26 1.22 Pomona 48.50 70.84 10.53 8.76 4.86 4.86 7.77 11.55 11.55 11.52 11.49 11.49 12.15 12.97 12.97 13.8 19.32 19.32 11.43 176

1.32(Contd.,) 1.32 0.79 0 0 Kandanga 46.78 70.91 9.9 7.35 1.74 1.74 3.23 5.16 5.16 5.28 6.05 6.05 5.29 3.74 3.74 4.39 5.42 5.42 3.62 1.32 1.32 0.78 0 0 Imbil 46.95 70.73 6.51 4.74 2.04 2.04 2.78 3.65 3.65 3.73 3.82 3.82 3.82 3.82 3.82 4.21 4.71 4.71 3 0.99 0.99 0.55 0 0 Jimna 44.70 70.49 1.21 1.24 1.47 1.47 1.51 177

1.58(Contd.,) 1.58 1.89 3.19 3.19 3.17 3.13 3.13 2.95 2.13 2.13 1.71 0.97 0.97 0.83 0.44 0.44 #####END_RECORDED_RAIN#####END_RECORDED_RAIN

Table 5.5 – Sub-areas and their loss rates of WBNM input file of Mary River at Gympie (11th February 1995 Storm)

#####START_LOSS_RATES SUB1 0.00 2.807 0.00 SUB2 0.00 2.807 0.00 SUB3 0.00 2.807 0.00 SUB4 0.00 2.807 0.00 SUB5 0.00 2.807 0.00 SUB6 0.00 2.807 0.00 SUB7 0.00 2.807 0.00 SUB8 0.00 2.807 0.00 SUB9 0.00 2.807 0.00 SUB10 0.00 2.807 0.00 SUB11 0.00 2.807 0.00 SUB12 0.00 2.807 0.00 SUB13 0.00 2.807 0.00 SUB14 0.00 2.807 0.00 SUB15 0.00 2.807 0.00 SUB16 0.00 2.807 0.00 SUB17 0.00 2.807 0.00 SUB18 0.00 2.807 0.00 SUB19 0.00 2.807 0.00 SUB20 0.00 2.807 0.00 SUB21 0.00 2.807 0.00 SUB22 0.00 2.807 0.00 SUB23 0.00 2.807 0.00 SUB24 0.00 2.807 0.00 SUB25 0.00 2.807 0.00 SUB26 0.00 2.807 0.00 SUB27 0.00 2.807 0.00 SUB28 0.00 2.807 0.00 SUB29 0.00 2.807 0.00 #####END_LOSS_RATES

178

Table 5.6 – Ordinates of surface runoff hydrograph of Mary River at Gympie of 11th February 1995 storm

#####START_RECORDED_HYDROGRAPHS 1 #####START_RECORDED_HYDROGRAPH#1 SUB29 BOTTOM 87 60.00 DISCHARGE 0.00 9.81 24.83 42.64 63.98 89.69 118.31 149.42 184.27 221.89 261.13 302.59 344.17 387.46 428.43 466.85 504.48 540.24 573.10 605.92 637.68 667.40 696.03 720.70 744.42 785.00 821.26 854.78 889.17 922.56 952.91 981.99 1009.73 1031.76 1054.21 1072.73 1084.88 1097.18 1105.11 1106.30 1109.77 1108.71 1103.12 1095.31 1087.53 1073.14 1058.89 1042.61 1022.24 179

1000.07(Contd.,) 976.19 950.69 923.66 895.21 863.53 832.52 800.32 763.46 729.11 696.82 673.91 650.91 626.86 598.89 570.83 539.80 505.80 471.78 436.82 400.02 363.38 327.94 292.83 258.14 225.82 196.76 167.41 141.32 117.57 95.27 75.22 57.32 40.00 26.82 16.76 6.96 0.00 #####END_RECORDED_HYDROGRAPH#1

180

4500 25

4000

20 3500 Hyetograph Total Hydrograph

3000

15 2500 /s) 3

2000 Flow (m 10 (mm) Rainfall

1500 No Initial Loss 1000 5

500

0 0 0 102030405060708090100110120130140 Time (hrs)

Figure 5.2 – Hyetograph and hydrograph of Mary River at Gympie (April 1989)

4500 Recorded Surface Runoff 4000 ---- WBNM

3500

3000

2500 /s) 3 Recorded and WBNM Hydrographs 2000 Flow (m

1500

1000

500

0 0 102030405060708090100110120130140 Time (hrs)

Figure 5.3 – Surface runoff and computer generated hydrographs of Mary River at Gympie (April 1989)

181

Hyetograph

Total Hydrograph Initial Loss (Shaded)

Figure 5.4 - Hyetograph and Hydrograph of Mary River at Gympie (December 1991)

800 Recorded Surface Runoff 700 ---- WBNM

600 Recorded and WBNM 500 Hydrographs /s) 3 400 Flow (m 300

200

100

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Time (hrs)

Figure 5.5 - Surface runoff and computer generated hydrographs of Mary River at Gympie (December 1991)

182

Total Hydrograph

Hyetograph

Initial Loss (Shaded)

Figure 5.6 - Hyetograph and hydrograph of Mary River at Gympie (February 1992)

7000 Recorded Surface Runoff WBNM 6000 ----

5000

4000 /s) 3 Recorded &WBNM Hydrographs 3000 Flow (m

2000

1000

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Time (hrs) Figure 5.7 – Surface runoff and computer generated hydrographs of Mary River at Gympie (February 1992)

183

Initial Loss (Shaded) Hyetograph

Total Hydrograph

Figure 5.8 - Hyetograph and hydrograph of Mary River at Gympie (March 1992)

2500 Recorded Surface Runoff 2250 ---- WBNM

2000

1750

1500 /s) 3 1250 Recorded & WBNM Hydrographs Flow (m 1000

750

500

250

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

Time (hrs) Figure 5.9 – Surface runoff and computer generated hydrographs of Mary River at Gympie (March 1992)

184

Hyetograph Total Hydrograph

Initial Loss (Shaded)

Figure 5.10 - Hyetograph and hydrograph of Mary River at Gympie (February 1995)

1200 Recorded Surface Runoff ---- WBNM 1000

800 /s) 3 600 Recorded &WBNM Hydrographs

Flow (m

400

200

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 Time (hrs) Figure 5.11 – Surface runoff and computer generated hydrographs of Mary River at Gympie (February 1995)

185

Initial Loss (Shaded)

Hyetograph

Total Hydrograph

Figure 5.12 - Hyetograph and hydrograph of Mary River at Gympie (January 1996)

800 Recorded Surface Runoff

700 ---- WBNM

600

500 /s) 3 Recorded & WBNM 400 Hydrographs Flow (mFlow

300

200

100

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time (hrs)

Figure 5.13 - Surface runoff and computer generated hydrographs of Mary River at Gympie (January 1996)

186

Total Hydrograph Hyetograph

Initial Loss (Shaded)

Figure 5.14 - Hyetograph and hydrograph of Mary River at Gympie (April 1996)

600 Recorded Surface Runoff ---- WBNM 500

400 /s) 3 300 Recorded & WBNM

Flow(m Hydrographs

200

100

0 0 102030405060708090100110120130140150160 Time (hrs)

Figure 5.15 – Surface runoff and computer generated hydrographs of Mary River at Gympie (April 1996)

187

Initial Loss (Shaded) Hyetograph

Total Hydrograph

Figure 5.16 - Hyetograph and hydrograph of Mary River at Gympie (March 1997)

800 Recorded Surface Runoff

700 ---- WBNM

600

500 /s)

3 Recorded &WBNM 400 Hydrographs Flow (mFlow

300

200

100

0 0 102030405060708090100110120 Time (hrs) Figure 5.17 – Surface runoff and computer generated hydrographs of Mary River at Gympie (March 1997)

188

The Figures 5.18 to 5.85 of Mary River at Moy Pocket, Bellbird, Cooran and Kandanga catchments are contained in part 1 of Appendix E of the CD.

Figure 5.7 - Flow and runoff details and lag parameters of eight storms of Mary River at Gympie

Peak Peak Surface Surface Number of Discharge Lag Date of Discharge Runoff Runoff Events Surface Parameter Storm Total Depth Duration Selected Runoff (C) (m3/s) (mm) (hrs) (m3/s) 1 Apr-89 4087 3613 164 71 2.75 2 Dec-91 731 696 39.8 14 2.63 3 Feb-92 6212 5862 310 127 3.20 4 Mar-92 2379 2327 132 37 2.89 5 Feb-95 1154 1110 62.4 22 2.77 6 Jan-96 666 628 31.3 40 1.94 7 Apr-96 568 538 26.3 32 1.84 8 Mar-97 713 695 32.4 13 2.36

189

5.3 Haughton River Basin.

53 57

59 63 43 45 46 48 50 52 56 58

61 62 65 64 42 44 47 49 51 55

27 54 60 68 67 66 54 21

29 28 34 69 71 74 73 72

22 23 30 77 76 75 31 35 39 70

24 32 33 36 37 38 40 41 78 84 85

25 26 17 80 82 83 86 88 79

19 18 16 81 89 90 91

13 14 1110 15 115 117 118 87 93 92 119 12 11 116 101 103 102 Outlet of Powerline 7 8 9

94 95 98 100 99 107 112 114 6 5

96 97 105 108 110 111 113 3 4

104 106 109 1 2

Figure 5.86 - Schematic of Haughton River at Powerline

190

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.87 – Hyetograph and hydrograph of Haughton River at Powerline (January 1994)

800 Recorded Surface Runoff 700 ---- WBNM

600

500 /s) 3 400 Recorded & WBNM Hydrographs Flow (mFlow 300

200

100

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Time (hrs)

Figure 5.88 – Surface runoff and computer generated hydrographs of Haughton River at Powerline (January 1994)

191

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.89 – Hyetograph, hydrograph and selected events of Haughton River at Powerline (January 1996)

800 Recorded Surface Runoff 700 ---- WBNM

600

500 Recorded & WBNM /s)

3 Hydrographs

400 Peak (2)

Flow (m Flow Recorded & WBNM Hydrographs 300 Peak (1)

200

100

0 0 102030405060708090100110120130140150 Time (hrs)

Figure 5.90 – Surface runoff and computer generated hydrographs of Haughton River at Powerline (January 1996)

192

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.91 – Hyetograph and hydrograph of Haughton River at Powerline (February 1997)

1200 Recorded Surface Runoff ---- WBNM 1000

800 /s) 3

600

Flow (m Recorded &WBNM Hydrographs 400

200

0 0 5 10 15 20 25 30 35 40 45 50 55 60 Time (hrs)

Figure 5.92 – Surface runoff and computer generated hydrographs of Haughton River at Powerline (February 1997)

193

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.93 – Hyetograph and hydrograph of Haughton River at Powerline (March 1997)

3000 Recorded Surface Runoff ---- WBNM 2500

2000 /s) 3 1500 Recorded &WBNM Hydrographs Flow (m

1000

500

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 Time (hrs)

Figure 5.94 – Surface runoff and computer generated hydrographs of Haughton River at Powerline (March 1997)

194

Hyetograph 2 Total Hydrograph

Initial Loss (Shaded)

Figure 5.95 - Hyetograph, hydrograph and selected events of Haughton River at Powerline (August 1998)

Recorded Surface Runoff ---- WBNM

Recorded and WBNM Hydrographs Peak (2)

Recorded and WBNM Hydrographs Peak (1)

Figure 5.96 - Surface runoff and computer generated hydrographs of Haughton River at Powerline (August 1998)

195

Hyetograph 1

Total Hydrograph

Initial Loss 2 3 (Shaded)

Figure 5.97 – Hyetograph, hydrograph and selected events of Haughton River at Powerline (February 2000)

1400 Recorded Surface Runoff

1200 ---- WBNM

1000

800 /s) 3

600 Flow (m

Recorded &WBNM 400 Hydrographs Recorded &WBNM Recorded &WBNM Peak (1) Hydrographs Hydrographs Peak (2) Peak (3) 200

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Time (hrs)

Figure 5.98 – Surface runoff and computer generated hydrographs of Haughton River at Powerline (February 2000)

196

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.99 – Hyetograph and hydrograph of Haughton River at Powerline (March 2000)

2000 Recorded Surface Runoff 1800 ---- WBNM

1600

1400

1200 Recorded &WBNM /s) 3 Hydrographs 1000 Flow (m 800

600

400

200

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 Time (hrs)

Figure 5.100 - Surface runoff and computer generated hydrographs of Haughton River at Powerline (March 2000)

197

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.101 – Hyetograph and hydrograph of Haughton River at Powerline (April 2000)

3500 Recorded Surface Runoff

3000 ---- WBNM

2500

2000 /s) 3

Recorded &WBNM Flow (mFlow 1500 Hydrographs

1000

500

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 Time (hrs)

Figure 5.102 – Surface runoff and computer generated hydrographs of Haughton River at Powerline (April 2000)

198

The Figures 5.103 to 5.120 of Haughton River at Mount Piccaninny catchment are contained in part 2 of Appendix E of the CD.

Table 5.8 - Flow and runoff details and lag parameters of eight storms of Haughton River at Powerline

Peak Selected Peak Surface Surface Number of Discharge Date of Number of Discharge Runoff Runoff Lag Events Surface Storm Peaks from Total Depth Duration Parameter Selected Runoff Each Storm (m3/s) (mm) (hrs) (m3/s) 1 Jan-94 Peak - 1 718 688 21.5 8.00 1.71 2 Jan-96 Peak - 1 449 338 9.45 7.50 0.95 3 Peak - 2 728 618 36.3 30.0 1.77 4 Feb-97 Peak - 1 1094 1054 32.1 13.5 1.92 5 Mar-97 Peak - 1 2529 2336 80.3 26.0 1.41 6 Aug-98 Peak - 1 267 258 11.2 6.00 1.81 7 Peak - 2 2064 1907 59.9 14.0 1.39 8 Feb-00 Peak - 1 1265 1178 50.2 16.5 1.84 9 Peak - 2 615 258 8.06 7.50 1.58 10 Peak - 3 594 434 15.9 6.00 1.30 11 Mar-00 Peak - 1 1941 1860 70.5 17.5 1.69 12 Apr-00 Peak - 1 3031 2878 92.9 20.5 1.44

199

5.4 Herbert River Basin.

29 28 47 48 50 52 64 62 58 41 31 30

43 49 51 53 59 65 63 33 32 42 25 60 44 68 67 66 61 57 34 35 69 26 56 39 45 72 71 54 55 70 37 36 27 40 46 73 81 87 89 91 92

38 21 80 79 85 86 88 90 94

24 23 22 93 77 78 83 84 95

14 15 11 20 19 74 76 82 96 97

13 12 18 17 75

98 99 8 9 10 16

100 101 6 7 126 127 125 124 102

104 105 4 5 130 129 128 123 103 106 107 1 3 2 131 122 121

108 109 110 Outlet of Zattas 140 120

119 117 115 114 111 132 135 136 139

118 116 112 113 133 134 137 138

Figure 5.121 - Schematic of Herbert River at Zattas

200

Hyetograph

Total Hydrograph 1

Initial Loss 2 (Shaded)

Figure 5.122 - Hyetograph, hydrograph and selected events of Herbert River at Zattas (February 1991)

Recorded Surface Runoff ---- WBNM

Recorded and WBNM Hydrographs Peak (1)

Recorded and WBNM Hydrographs Peak (2)

Figure 5.123 - Surface runoff and computer generated hydrographs of Herbert River at Zattas (February 1991)

201

Hyetograph

2 Total Hydrograph

Initial Loss (Shaded)

Figure 5.124 - Hyetograph, hydrograph and selected events of Herbert River at Zattas (Early February 2000)

Recorded Surface Runoff ---- WBNM

Recorded and WBNM Hydrographs Peak (1)

Recorded and WBNM Hydrographs Peak (2)

Figure 5.125 - Surface runoff and computer generated hydrographs of Herbert River at Zattas (Early February 2000)

202

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.126 – Hyetograph and hydrograph of Herbert River at Zattas (Late February 2000)

Recorded Surface Runoff ---- WBNM

Recorded and WBNM Hydrographs

Figure 5.127 – Surface runoff and computer generated hydrographs of Herbert River at Zattas (Late February 2000)

203

2 Total Hydrograph Hyetograph

Initial Loss 1 (Shaded)

Figure 5.128 – Hyetograph, hydrograph and selected events of Herbert River at Zattas (February 2001)

Recorded Surface Runoff ---- WBNM

Recorded and WBNM Recorded and Hydrographs WBNM Peak (1) Hydrographs Peak (2)

Figure 5.129 – Surface runoff and computer generated hydrographs of Herbert River at Zattas (February 2001)

204

The Figures 5.130 to 5.175 of Herbert River at Nash’s Crossing, Gleneagle and Silver Valley catchments are contained in part 3 of Appendix E of the CD.

Table 5.9 - Flow and runoff details and lag parameters of four storms of Herbert River at Zattas

Peak Selected Peak Surface Surface Number of Discharge Lag Date of Number of Discharge Runoff Runoff Events Surface Parameter Storm Peaks from Total Depth Duration Selected Runoff (C) Each Storm (m3/s) (mm) (hrs) (m3/s) 1Feb-91Peak - 1 4540 3398 37.3 20.0 1.08 2 Peak - 2 1836 792 6.91 55.0 1.02 3 Early Feb-00 Peak - 1 1296 1068 20.7 26.0 1.29 4 Peak - 2 889 407 10.2 34.0 1.09 5 Late Feb-00 Peak - 1 1866 1103 29.9 52.0 1.88 6Feb-01Peak - 1 721 388 7.66 9.0 1.08 7 Peak - 2 1132 576 10.1 9.0 1.04

205

5.5 Don River Basin.

18 17 16 34 36 37 39 38

19 20 35 41 40

42 21 22 23 49 50 48 45 43

54 26 25 24 32 51 47 46 44

33 55 27 31 52 56 75

30 53 14 15 28 29 58 60 76 77

9 12 13 74 57 59 61

70 11 10 71 72 73 69 6 7 8 68 64 62 63

5 4 Outlet of Reeves 96 65 67 66

1 3 2 89 95 78 80 83 85 86

94 93 79 82 84 87 88

81 90 92 91

Figure 5.176 - Schematic of Don River at Reeves

206

Hyetograph Total Hydrograph

Initial Loss (Shaded)

Figure 5.177 – Hyetograph and hydrograph of Don River at Reeves (April 1989)

3000

Recorded Surface Runoff

2500 ---- WBNM

2000

/s) Recorded &WBNM 3 1500 Hydrographs Flow (m

1000

500

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Time (hrs)

Figure 5.178 – Surface runoff and computer generated hydrographs of Don River at Reeves (April 1989)

207

Hyetograph

1 3

Total Hydrograph

Initial Loss (Shaded) 2 4

Figure 5.179 – Hyetograph and hydrograph and selected events of Don River at Reeves (December 1990)

2500 Recorded Surface Runoff 2250 ---- WBNM

2000

1750 Recorded &WBNM Hydrographs Recorded &WBNM 1500 Peak (1) Hydrographs /s) 3 Peak (3) 1250 Flow (m Flow 1000

750 Recorded Recorded &WBNM &WBNM 500 Hydrographs Hydrographs Peak (2) Peak (4) 250

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 Time (hrs)

Figure 5.180 – Surface runoff and computer generated hydrographs of Don River at Reeves (December 1990)

208

Hyetograph

Initial Loss (Shaded) Total Hydrograph

Figure 5.181 – Hyetograph and hydrograph of Don River at Reeves (January 1991)

2000

Recorded Surface Runoff 1750 ---- WBNM

1500

1250 /s) 3 Recorded &WBNM 1000 Hydrographs Flow (m Flow

750

500

250

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 Time (hrs)

Figure 5.182 – Surface runoff and computer generated hydrographs of Don River at Reeves (January 1991)

209

Hyetograph 2

4 3 Total Hydrograph

5 Initial Loss 1 (Shaded)

Figure 5.183 – Hyetograph and hydrograph and selected events of Don River at Reeves (February 1991)

4000 Recorded Surface Runoff 3500 ---- WBNM

Recorded &WBNM 3000 Hydrographs Peak (2)

2500 Recorded &WBNM

/s) Hydrographs 3 2000 Peak (4)

Flow (m Flow Recorded &WBNM 1500 Hydrographs Recorded Peak (1) &WBNM Hydrographs 1000 Peak (3) Recorded &WBNM Hydrographs Peak (5) 500

0 0 102030405060708090100

Time (hrs)

Figure 5.184 – Surface runoff and computer generated hydrographs of Don River at Reeves (February 1991)

210

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.185 – Hyetograph and hydrograph of Don River at Reeves (August 1998)

400 Recorded Surface Runoff 350 ---- WBNM

300

Recorded &WBNM 250 Hydrographs /s) 3 200 Flow (m Flow

150

100

0 0 102030405060708090 Time (hrs)

Figure 5.186 – Surface runoff and computer generated hydrographs of Don River at Reeves (August 1998)

211

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.187 – Hyetograph and hydrograph of Don River at Reeves (January 1999)

300 Recorded Surface Runoff ---- WBNM 250

200 Recorded &WBNM Hydrographs /s) 3 150 Flow (m Flow

100

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Time (hrs)

Figure 5.188 – Surface runoff and computer generated hydrographs of Don River at Reeves (January 1999)

212

Hyetograph Total Hydrograph

Initial Loss (Shaded)

Figure 5.189 – Hyetograph and hydrograph of Don River at Reeves (February 1999)

800 Recorded Surface Runoff 700 ---- WBNM Recorded &WBNM 600 Hydrographs

500 /s) 3

400 Flow (m

300

200

100

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Time (hrs)

Figure 5.190 – Surface runoff and computer generated hydrographs of Don River at Reeves (February 1999)

213

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.191 – Hyetograph and hydrograph of Don River at Reeves (December 1999)

900 Recorded Surface Runoff 800 ---- WBNM

700

600 /s) 3 500 Recorded &WBNM Hydrographs Flow (m 400

300

200

100

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

Time (hrs)

Figure 5.192 – Surface runoff and computer generated hydrographs of Don River at Reeves (December 1999)

214

Hyetograph 3

Total Hydrograph

Initial Loss 4 (Shaded)

Figure 5.193 – Hyetograph and hydrograph and selected events of Don River at Reeves (Early February 2000)

1200 Recorded Surface Runoff ---- WBNM 1000

Recorded &WBNM 800 Hydrographs Peak (3) Recorded &WBNM /s) 3 Hydrographs 600 Peak (2) Flow (m Recorded &WBNM 400 Hydrographs Peak (4)

200 Recorded &WBNM Hydrographs Peak (1)

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time (hrs)

Figure 5.194 – Surface runoff and computer generated hydrographs of Don River at Reeves (Early February 2000)

215

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.195 – Hyetograph and hydrograph of Don River at Reeves (Late February 2000)

800

Recorded Surface Runoff 700 ---- WBNM

600

500 Recorded &WBNM Hydrographs /s) 3 400 Flow (m Flow 300

200

100

0 0 102030405060708090100110120130

Time (hrs)

Figure 5.196 – Surface runoff and computer generated hydrographs of Don River at Reeves (Late February 2000)

216

The Figures 5.197 to 5.230 of Don River at Mount Dangar and Ida Creek catchments are contained in part 4 of Appendix E of the CD.

Table 5.10 - Flow & runoff details and lag parameters of ten storms of Don River at Reeves

16 Early Feb-00 Peak - 1 166 153 5.84 3.00 0.83 17 Peak - 2 864 773 18.4 8.50 0.65 18 Peak - 3 1057 947 19.7 5.00 0.68 19 Peak - 4 570 517 10.6 5.00 0.88

20 Late Feb-00 Peak - 1 782 703 17.2 8.00 0.70

217

5.6 North Johnstone River Basin.

32 33 31 30 29 42

36 43 34 35

44 37 38 40 45

46 25 26 28 39 41

24 27

47 23 22 21

49 48

19 20 16 12

50 51 18 17 15 14 13

54 11 10

53 55 8 52 56 9

6 7 Outlet of Tung Oil

5 4

3 2

Figure 5.231 – Schematic of North Johnstone River at Tung Oil

218

4 Total Hydrograph

Hyetograph

Initial Loss (Shaded) 2 1

Figure 5.232 – Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (March 1990)

2000 Recorded Surface Runoff 1800 ---- WBNM

1600

1400 /s)

3 1200

1000 Flow (m Recorded &WBNM

800 Hydrographs Recorded &WBNM Peak (4) Hydrographs 600 Peak (1) Recorded 400 &WBNM Recorded Hydrographs &WBNM 200 Peak (2) Hydrographs Peak (3) 0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 Time (hrs)

Figure 5.233 – Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (March 1990)

219

Total Hydrograph 2 Hyetograph

Initial Loss (Shaded)

Figure 5.234 – Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (January 1994)

4000 Recorded Surface Runoff 3500 ---- WBNM

3000 Recoded &WBNM Hydrographs Peak (2) 2500 /s) 3 2000 Flow (m

1500

1000 Recorded &WBNM

500 Hydrographs Peak (1)

0 0 102030405060708090100 Time (hrs)

Figure 5.235 – Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (January 1994)

220

Hyetograph 3 Total Hydrograph

Initial Loss (Shaded)

Figure 5.236 – Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (March 1996)

3000 Recorded Surface Runoff 2750 ---- WBNM 2500

2250

2000 Recorded & WBNM Hydrographs 1750

/s) (Peak3) 3 Recorded & 1500 WBNM Hydrographs Flow (m 1250 (Peak2)

1000

750 Recorded & WBNM 500 Hydrographs (Peak1) 250

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 Time (hrs)

Figure 5.237 – Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (March 1996)

221

Hyetograph 3 1 Total Hydrograph

Initial Loss (Shaded)

Figure 5.238 – Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (March 1997)

4000

WBNM 3500 Recorded Surface Runoff

3000 Recorded & WBNM Hydrographs 2500 (Peak 2) /s) 3

2000 Recorded & WBNM

Flow (m Hydrographs 1500 (Peak 1) Recorded & WBNM Hydrographs

1000 (Peak 3)

500

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Time (hrs)

Figure 5.239 – Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (March 1997)

222

1 Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.240 – Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (December 1997)

1200 Recorded Surface Runoff Recorded & WBNM ---- WBNM 1000 Hydrographs Peak (1)

800 /s) 3 600 Flow (m Flow Recorded & WBNM 400 Hydrographs Peak (2)

200

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 Time (hrs)

Figure 5.241 – Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (December 1997)

223

3 Hyetograph Total Hydrograph

1 Initial Loss (Shaded)

Figure 5.242 – Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (January 1998)

2500 Recorded Surface Runoff 2250 ---- WBNM Recorded &WBNM 2000 Hydrographs Peak (2) 1750 /s)

3 1500 Recorded &WBNM 1250 Flow (m Hydrographs Peak (3) 1000 Recorded &WBNM

750 Hydrographs Peak (1)

500

250

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 Time (hrs)

Figure 5.243 – Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (January 1998)

224

Initial Loss (Shaded) Total Hydrograph

Hyetograph 6

4 5 3 2 1

Figure 5.244 – Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (March 1999)

4000 Recorded Surface Runoff 3500 ---- WBNM

Recorded 3000 &WBNM Hydrographs Peak (6) 2500 /s) 3 2000

Flow (m Recorded Recorded 1500 &WBNM &WBNM Recorded &WBNM Hydrographs Hydrographs Peak (4) Peak (1) Hydrographs 1000 Peak (3) Recorded Recorded &WBNM &WBNM Hydrographs 500 Hydrographs Peak (5) Peak (2)

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 Time (hrs)

Figure 5.245 - Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (March 1999)

225

Hyetograph

3 6 Total Hydrograph Initial Loss 5 (Shaded) 1 2

Figure 5.246 - Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (December 1999)

Recorded Surface Runoff ---- WBNM

Recorded and WBNM Hydrographs Peak (4)

Recorded and WBNM Recorded and WBNM Hydrographs Hydrographs Peak (2) Recorded and WBNM Peak (5) Recorded and Hydrographs Recorded and WBNM Peak (3) WBNM Hydrographs Hydrographs Peak (1) Peak (6)

Figure 5.247 - Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (December 1999)

226

2 Total Hydrograph

Initial Loss (Shaded) Hyetograph 3

1 4

Figure 5.248 – Hyetograph, hydrograph and selected events of North Johnstone River at Tung Oil (February 2000)

1400

Recorded Surface Runoff 1200 ---- WBNM

1000 Recorded & WBNM Hydrographs Peak (2) /s) 3 800 Flow (m Recorded 600 Recorded &WBNM &WBNM Hydrographs Hydrographs Peak (1) Peak (3) 400 Recorded &WBNM 200 Hydrographs Peak (4)

0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 Time (hrs)

Figure 5.249 – Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (February 2000)

227

Hyetograph

Total Hydrograph

Initial Loss (Shaded)

Figure 5.250 – Hyetograph and hydrograph of North Johnstone River at Tung Oil (April 2000)

3000

2750 Recorded Surface Runoff

2500 ---- WBNM

2250

2000

1750 /s) 3

1500 Recorded &WBNM Hydrographs Flow (m 1250

1000

750

500

250

0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Time (hrs)

Figure 5.251 – Surface runoff and computer generated hydrographs of North Johnstone River at Tung Oil (April 2000)

The Figures 5.252 to 5.289 of North & South Johnstone Rivers at Nerada and Central Mill catchments respectively are contained in part 5 of Appendix E of the CD. 228

Table 5.11 – Flow & runoff details and lag parameters of ten storms of North Johnstone River at Tung Oil

Peak Selected Peak Surface Surface Number of Discharge Lag Date of Number of Discharge Runoff Runoff Events Surface Parameter Storm Peaks from Total Depth Duration Selected Runoff (C) Each Storm (m3/s) (mm) (hrs) (m3/s) 1Mar-90Peak - 1 685 639 38.9 5.50 1.38 2 Peak - 2 741 322 8.28 8.50 0.56 3 Peak - 3 530 373 11.9 6.00 0.77 4 Peak - 4 2093 1897 86 37.5 1.33 5Jan-94Peak - 1 889 826 41.0 15.0 1.49 6 Peak - 2 3910 3551 85.9 8.50 0.74 7Mar-96Peak - 1 1141 1012 39.5 21.0 1.04 8 Peak - 2 1767 1197 34.2 6.50 0.63 9 Peak - 3 2753 1763 35.4 3.00 0.56 10 Mar-97 Peak - 1 1104 1002 28.8 7.00 1.20 11 Peak - 2 836 384 9.61 3.50 0.61 12 Peak - 3 1913 1725 83.2 10.5 1.11 13 Dec-97 Peak - 1 3454 2642 87.6 7.00 0.81 14 Peak - 2 2212 1218 22.1 4.00 0.55 15 Jan-98 Peak - 1 1010 858 41.1 15.5 0.99 16 Peak - 2 2240 1957 88.3 23.5 1.47 17 Peak - 3 1913 1231 38.2 9.50 0.82 18 Mar-99 Peak - 1 1277 1146 63.0 22.0 1.25 19 Peak - 2 1196 817 56.1 11.0 1.57 20 Peak - 3 1376 801 49.9 6.00 1.38 21 Peak - 4 1743 1033 37.9 9.50 0.78 22 Peak - 5 1714 596 17.1 2.50 0.75 23 Peak - 6 3727 3202 110 14.0 0.99 24 Dec-99 Peak - 1 394 331 9.92 17.5 0.62 25 Peak - 2 282 114 4.63 6.00 0.72 26 Peak - 3 486 272 9.68 5.00 0.81 27 Peak - 4 1222 897 25.3 10.0 0.76 28 Peak - 5 426 284 14.2 3.50 1.18 29 Peak - 6 462 230 7.86 4.50 0.70 30 Feb-00 Peak - 1 775 694 23.4 11.5 0.88 31 Peak - 2 1217 1078 60.3 10.0 1.23 32 Peak - 3 916 354 12.3 7.50 0.67 33 Peak - 4 775 319 11.6 5.50 0.65 34 Apr-00 Peak - 1 2587 2403 70.8 15.5 0.64

229

at Gympie River of Mary Storms of Summary - Table 5.12

230

Pocket Moy at River of Mary Storms of Summary - Table 5.13

231

Bellbird at River Mary of Storms Summary of - Table 5.14

232

at CooranRiver) (Tributary Mary of Creek Storms Table Summary of Sixth Mile of - 5.15

233

at Kandanga (Tributary Creek River) of Mary of SummaryStorms Kandanga of Table - 5.16

234

of Powerline at SummaryRiver Storms Table of Haughton 5.17 -

235

Piccaninny River Mount at of - SummaryTableStorms Haughton 5.18 of

236

Zattas at Storms of Herbert River of TableSummary - 5.22

237

Table 5.21 - Summary of Storms of Herbert River at Nash’s at Crossing River Storms of Herbert of TableSummary - 5.21

238

Gleneagle at River Storms of Herbert Summary of Table - 5.20

239

at Silver Valley Storms of Herbert River of TableSummary - 5.19

240

Reeves at River Storms of Don Summary of Table - 5.23

241

Mount Dangar at River Storms Table Summary of Don of - 5.24

242

Ida Creek at of River SummaryStorms Table Don of - 5.25

243

Table 5.26 - Summary of Storms of North Johnstone River at Tung Oil at River of Johnstone Storms North of Summary - Table 5.26

244

at River Nerada Storms of North Johnstone of TableSummary - 5.27

245

Mill Central at River Johnstone of South Storms of Summary - Table 5.28

CHAPTER 6

RELATIONSHIP BETWEEN LAG PARAMETER AND HYDROLOGICAL CHARACTERISTICS

246

6. RELATIONSHIP BETWEEN LAG PARAMETER AND HYDROLOGICAL CHARACTERISTICS.

6.1 Variation of Lag Time with Discharge

In many situations, large floods in rural catchments demonstrate smaller lag times and small floods produce larger lag times. This non-linear behaviour is therefore, a very common phenomenon in rural catchments. The size of the flood can be expressed in several ways, for example, as the total rainfall depth, the excess depth, the rainfall intensity and the maximum flood discharge.

Eighteen out of the forty six studies shown in Table 2.1 have demonstrated that the lag time is inversely proportional to the discharge. This non-linear relationship of flow on catchments can be expressed as: -z Lag time (tL) = C Q (6.1) Where, C is a scaling factor. The majority of the values of z shown in Table 2.2 are between 0.07 and 0.87, and five of the values are greater than or equal to 1.0, with a maximum of 1.60. The calculated mean and median values of z, of the eighteen values, are 0.54 and 0.26 respectively.

To demonstrate the effect of the non-linear exponent ‘z’ on lag time, the curves shown in Figure 6.1 were calculated using equation 6.1, with C = 1.7. It is important to note that when z = 0 (linear response), the lag time is constant for all discharges. When the behaviour of the catchment is non-linear (z becomes greater than zero), the lag time decreases as the discharge (Q) increases. This variation becomes significantly higher when the catchment is more non-linear, and this is, when the z value is equal or greater than 0.5.

Figure 6.1 illustrates the following: • The shape of the curves, when z = 0.23 and 0.26, show a significant decrease in lag time with increasing discharge. Since the median value of z in Table 2.2 is 0.26, this variation reflects the behaviour of most of the natural catchments; 247

• As the z value gets closer to zero, the shape of the curve becomes more horizontal. For example, when z = 0.01 the variation of lag time is almost negligible. Note that such variation does not signify the behaviour of most of natural catchments; and • Although there is a considerable variation in lag time for the lower discharges (between 5 and 50m3/s), for higher discharges (Q > 50m3/s) the variation of lag time is relatively small.

As described in Chapter 2, equation (2.176) has been used in the development of WBNM by Boyd et al., 1978, and that equation demonstrates the non-linearity of the rainfall and runoff process with a z value of 0.23, which is very close to the median value z = 0.26, found from the studies described in the literature review.

1.8 Q-0.00 -0.01 1.6 Q

1.4

-0.07 1.2 Q ) - hrs L 1

0.8

Lag Time (t -0.23 0.6 Q Q-0.26 0.4

0.2 Q-0.54 Q-0.87 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 Discharge (Q) - m3/s

Figure 6.1- Lag time versus Discharge for different values of z

6.2 Variation of Lag Parameter with Discharge Equations similar to 6.1 have been adopted in many studies, as described in Chapter 2. For example, the following equation is used in WBNM: 0.57 -0.23 Lag time (tL) = C A Q (6.2) 248

Consider the case where WBNM is calibrated using a set of recorded flood data which satisfy the nonlinear relation in equation 6.1 with z = 0.23. Since in both situations the same exponent of 0.23 applied for nonlinearity, the same lag parameter (C) would apply to all calibrated events. Therefore, the plot of lag parameter (C) versus discharge (Q) would be a straight horizontal line. If however, the model used a value other than 0.23 for nonlinearity, and was calibrated on this recorded data, then the calculated value of Lag parameter (C) could vary considerably with discharge.

-0.54 7 Q

3 Lag Parameter (C)

-0.26 2 Q Q-0.23 1 Q-0.07 Q-0.01 0 0 102030405060708090100110 Discharge (Q) - m3/s

Figure 6.2 – Calibrated Lag Parameter (C) for different values of z Figure 6.2 shows how the lag parameter (C) would have to vary to maintain the correct value of the lag time (tL) if the recorded flood data had a nonlinearity exponent of 0.23, and the model had a range of values which are greater or less than 0.23 (for example, 0.54 and 0.07 respectively).

For various values of the nonlinearity exponent, the WBNM model would have produced different relationships for lag parameter (C) and discharge (Q) and these variations can be described in the following manner: • If the model adopted a nonlinearity exponent of 0.23, the same lag parameter applies to all discharges; 249

• If the model nonlinearity exponent is less than 0.23 (for example 0.07, that means the model is not sufficiently nonlinear) the calibrated lag parameter must decrease as Q increases; and • If the model nonlinearity exponent is greater than 0.23 (for example 0.54, which means the model is too nonlinear) the calibrated lag parameter must increase as Q increases.

Furthermore, Figure 6.2 illustrates the following: • For all discharges the lag parameter is a constant, when z = 0.23; • As the discharge increases the lag parameter decreases gradually for values of z less than 0.23, for example z = 0.07; • As the discharge increases the lag parameter increases very rapidly for values of z greater than 0.23, for example z = 0.54; and • For larger discharges, exceptionally high lag parameters were observed from the calculations especially when z > 0.50.

Therefore, a plot of calibrated lag parameter (C) against discharge (Q) is a good test to assess whether the model has the correct value of nonlinearity.

6.3 Relationship between Lag Parameter (C) and the Peak Discharge (QP) Figures 6.3 to 6.19 show the lag parameter (C) derived in Chapter 5, plotted against the peak discharge of the total flood hydrograph (Qp).

Those figures illustrate the following: • For all seventeen catchments the points show a significant amount of scatter; • For the six catchments Gympie, Cooran, Mt. Piccaninny, Nash’s crossing, Reeves and Ida Creek, the best-fit straight lines have positive gradients; • For eight of the catchments, namely Moy Pocket, Bellbird, Kandanga, Powerline, Silver Valley, Tung Oil, Nerada and Central Mill, the best-fit straight lines have negative gradients; and • Horizontal lines with zero gradients have been noticed in the plots of Zattas, Gleneagle and Mt.Dangar catchments. 250

For all seventeen catchments, two tailed significance t-tests have been carried out and it is found that, except for Mary River at Gympie (shown in Figure 6.3), the gradients of the best-fit straight lines are not significantly different from zero at 5% level of significance. Therefore, the variation between lag parameter and peak discharge of these sixteen catchments can be treated as being horizontal. Summary statistics of the t-tests and the equations of the best-fit straight lines are shown in Figures 6.3 to 6.19. Table 6.3 at the end of this chapter summarises these results.

Table 6.1 – t-test calculations of C versus Qp of Mary River at Gympie

Peak Discharge Lag Calculated 2 2 No. (Qp) Parameter (C) X Y XY Lag ( X ) ( Y ) Parameter (C)

1 4087 2.75 16700381.29 7.563 11238.178 2.89 731 2.63 534287.90 6.917 1922.399 2.32 2 3 6212 3.20 38588322.80 10.240 19878.240 3.25 4 2379 2.89 5657357.39 8.352 6873.923 2.60 5 1154 2.77 1332177.64 7.673 3197.134 2.39 6 666 1.94 443236.38 3.764 1291.574 2.31 7 568 1.84 322714.89 3.386 1045.267 2.29 8 713 2.36 508083.84 5.570 1682.208 2.32 Total 16508.87 20.38 64086562.13 53.4632 47128.922 20.38

Intercept of straight line (a) = 2.198790441 r2 = 0.554746301 Slope of straight line (b) = 1.68980E-04Standard error of estimate (Se) = 0.338620671 Correlation coefficient (r) =0.74481293 Estimated (t) = 2.734

3.5

3.0 y = 0.000169x + 2.1988

2.5

2.0 1.5 Lag Parameter(C)

1.0 t0.975 = 2.45

tCal = 2.73 0.5

0.0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.3 – C versus QP of Mary River at Gympie (8 values)

The catchments belonging to the same basin have shown no consistent variation in the gradients of their best-fit straight lines. For example, Mary River at Gympie and Cooran 251

have shown positive gradients whereas Moy Pocket, Bellbird and Kandanga have demonstrated negative gradients in their plots of C versus Qp as shown in Table 6.3. This indicates that overall there is no trend for the lag parameter to vary (either increasing for all cases or decreasing for all cases) as Qp varies. Note that the calculated two tailed t- statistic (for example -0.72 in Figure 6.4) should lie in the range -2.31 to +2.31. For simplicity throughout this thesis the plus (+) or minus (-) sign has been omitted from the t0.975 statistic.

2.4

2.0

y = -0.000074x + 1.7177 1.6

1.2

0.8 Lag Parameter (C) t0.975 = 2.31 0.4 tCal = -0.72

0.0 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.4 – C versus QP of Mary River at Moy Pocket (10 values)

1.8 1.6 1.4 y = -0.00024x + 1.3204 1.2 1.0

0.8

Lag Parameter (C) Parameter Lag 0.6

t = 2.31 0.4 0.975

tCal = -1.12 0.2

0.0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.5 – C versus QP of Mary River at Bellbird (10 values)

252

4.5 4.0

3.5

3.0 y = 0.001x + 2.6547 2.5 2.0

Lag Parameter (C) Parameter Lag 1.5 t0.975 = 2.31 t = 0.62 1.0 Cal 0.5 0.0 0 50 100 150 200 250 300 350 400 450 500 550 600 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.6 – C versus QP of Mary River at Cooran (10 values)

2.4

2.0

1.6

y = -0.00056x + 1.5814 1.2

Lag Parameter (C) 0.8 t0.975 = 2.36

tCal = -0.39 0.4

0.0 0 50 100 150 200 250 300 350 400 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.7 – C versus QP of Mary River at Kandanga (9 values)

2.4 2.0 y = -0.000033x + 1.6097 1.6

1.2

Lag Parameter(C) 0.8 t0.975 = 2.23 0.4 tCal = -0.34

0.0 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.8 – C versus QP of Haughton River at Powerline (12 values)

253

1.8

1.6

y = 0.00019x + 0.9222 1.4 1.2

1.0

0.8

Lag Parameter (C) 0.6 t = 2.14 0.4 0.975 tCal = 1.80 0.2

0.0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 Peak of Total Recorded Hydrograph (Q ) m3/s p Figure 6.9 – C versus QP of Haughton River at Mt. Piccaninny (16 values)

2.0 1.8

1.6

1.4 y = 0.00000044x + 1.2107 1.2 1.0 0.8

Lag Parameter (C) 0.6 t0.975 = 2.57 0.4 tCal = 0.004 0.2

0.0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.10 – C versus QP of Herbert River at Zattas (7 values)

2.0 1.8

1.6 1.4 y = 0.000064x + 0.9974 1.2 1.0 0.8

Lag Parameter(C) 0.6 t0.975 = 2.13

0.4 tCal = 0.75 0.2 0.0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.11– C versus QP of Herbert River at Nash’s Crossing (17 values)

254

3.2

2.8

2.4

2.0 y = 0.000011x + 2.014 1.6 1.2 Lag Parameter (C) t = 2.36 0.8 0.975 tCal = 0.08 0.4 0.0 0 500 1000 1500 2000 2500 3000 3500 4000 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.12 – C versus QP of Herbert River at Gleneagle (9 values)

3.2 2.8

2.4 2.0 1.6 y = -0.000398x + 1.7375

1.2 Lag Parameter (C) 0.8 t0.975 = 2.13 0.4 tCal = -1.56 0.0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400

3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.13 – C versus QP of Herbert River at Silver Valley (17 values)

1.6

1.4

1.2 y = 0.00007x + 0.7251 1.0

0.8

0.6 Lag Parameter (C) t0.975 = 2.10 0.4 tCal = 1.30 0.2

0.0 0 500 1000 1500 2000 2500 3000 3500 4000 Peak of Total Recorded Hydrograph (Q ) m3/s p

Figure 6.14 – C versus QP of Don River at Reeves (20 values)

255

1.2

1.0

0.8 y = 0.000016x + 0.7031

0.6

Lag Parameter (C) 0.4

t0.975 = 2.31 0.2 tCal = 0.18

0.0 0 250 500 750 1000 1250 1500 1750 2000 3 Peak of Total Recorded Hydrograph (Qp) m /s

. Figure 6.15 – C versus QP of Don River at Mt. Dangar (10 values)

1.6 1.4 1.2

y = 0.0001x + 0.679 1.0 0.8 0.6 Lag Parameter (C) 0.4 t0.975 = 2.10

t = 0.99 0.2 Cal 0.0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.16 – C versus QP of Don River at Ida Creek (20 values)

1.8 1.6

1.4

1.2

1.0 y = -0.00002x + 0.96 0.8

Lag Parameter (C) Parameter Lag 0.6

0.4 t0.975 = 2.04

tCal = -0.35 0.2 0.0 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.17 – C versus QP of North Johnstone River at Tung Oil (34 values) 256

2.4

2.0 1.6 1.2 y = -0.000049x + 1.1977

Lag Parameter (C) Parameter Lag 0.8

t0.975 = 2.07 0.4 tCal = -0.39 0.0 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.18 – C versus QP of North Johnstone River at Nerada (24 values)

2.4

2.0

1.6

1.2 y = -0.00016x + 1.5278

Parameter (C) Lag 0.8 t0.975 = 2.09

tCal = -1.14 0.4

0.0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 3 Peak of Total Recorded Hydrograph (Qp) m /s

Figure 6.19 – C versus QP of South Johnstone River at Central Mill (21 values)

Moreover, after investigating the plots for seventeen catchments individually, all 254 values of C and Qp were plotted in Figure 6.20, and it has been observed that the best-fit straight line is very close to horizontal. This finding further indicates that there is no real trend for C to vary as QP varies. Therefore, all these results indicate that, on average WBNM is correctly modelling the nonlinearity which is observed in real catchments.

257

4.0 3.5 3.0

2.5

2.0

1.5 y = -0.000014x + 1.2967 Lag Parameter (C) 1.0 t0.975 = 1.96 0.5 tCal = -0.33 0.0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 3 Peak of Total Recorded Hydrograph (Qp) m /s)

Figure 6.20 – C versus QP of all 17 catchments for 254 values

The correlation between lag parameter (C) and various other storm characteristics of the 17 catchments have been examined and their results are discussed in detail in the following sections of this chapter. As discussed previously the calculated and statistically obtained t-test values are shown on each plot.

6.4 Relationship between Lag Parameter (C) and the Surface Runoff Peak

Discharge (QS). Figures 6.21 to 6.37 show the lag parameter (C) derived in Chapter 5, plotted against the peak discharge of the surface runoff hydrograph (QS), which show the following: • The plots of seven catchments, Gympie, Cooran, Mt Piccaninny, Nash’s Crossing, Reeves, Ida Creek and Tung Oil have shown positive gradients; • The plots of six catchments, Moy Pocket, Bellbird, Kandanga, Silver valley, Nerada and Central Mill have indicated negative slopes; • Approximately horizontal lines have been found for the best-fit lines of four plots of catchments namely Powerline, Zattas, Gleneagle and Mt. Dangar catchments; • The gradients of the best-fit straight lines of the plots of Gympie and Reeves catchments are significantly different from zero according to the two tailed t-test 258

results. The other 15 catchments do not have gradients significantly different from zero; and • The best fit line of the plot containing all 254 values, as shown in Figure 6.38, is very close to a horizontal line.

It is important to note that the first two decimal places of the equations of all plots are equal to zero, and they demonstrate that the lag parameter varies only very slightly as

Qs varies. Therefore, the above indicated findings revealed that there is no significant variation in the lag parameter (C) with QS.

Table 6.2 – t-test calculations of C versus QS of Mary River at Gympie

Peak Lag Calculated 2 2 No. Discharge(QS) Parameter(C) X Y XY Lag ( X ) ( Y ) Parameter(C) 1 3613 2.75 13050951.01 7.563 9934.678 2.86 2 696 2.63 485084.39 6.917 1831.742 2.32 3 5862 3.20 34363981.93 10.240 18758.656 3.27 4 2327 2.89 5414882.46 8.352 6725.001 2.62 5 1110 2.77 1231589.45 7.673 3074.063 2.40 6 628 1.94 394032.40 3.764 1217.777 2.31 7 538 1.84 289831.49 3.386 990.582 2.29 2.36 482385.81 5.570 1639.114 2.32 8 695 Total 15468.55 20.38 55712738.94 53.4632 44171.614 20.38 Intercept of straight line (a) = 2.190397949 r2 = 0.569598645 Slope of straight line (b) = 1.84685E-04Standard error of estimate (Se) = 0.33292508 Correlation coefficient (r) =0.754717593 Estimated (t) = 2.818

3.5

3.0 y = 0.000185x + 2.1904 2.5

2.0

1.5 Lag Parameter (C) 1.0 t0.975 = 2.45 tCal = 2.82 0.5

0.0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000

3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.21 – C versus QS of Mary River at Gympie (8 values)

259

2.4

2.0

1.6 y = -0.000072x + 1.7108 1.2

0.8 Lag Parameter (C) t0.975 = 2.31

tCal = -0.65 0.4

0.0 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.22 – C versus QS of Mary River at Moy Pocket (10 values)

1.8

1.6

1.4 y = -0.00027x + 1.327 1.2 1.0 0.8

Lag Parameter (C) 0.6

t0.975 = 2.31 0.4 tCal = -1.25 0.2

0.0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 Peak of Surface Runoff Hydrograph (Q ) m3/s S

Figure 6.23 – C versus QS of Mary River at Bellbird (10 values)

4.5 4.0

3.5

3.0 y = 0.0011x + 2.6496 2.5 2.0

Lag Parameter (C) Parameter Lag 1.5

t0.975 = 2.31 1.0 tCal = 0.63 0.5 0.0 0 50 100 150 200 250 300 350 400 450 500 550 3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.24 – C versus QS of Mary River at Cooran (10 values)

260

2.4 2.0

1.6

1.2 y = -0.0005x + 1.5703

Lag Parameter (C) 0.8 t0.975 = 2.36 0.4 tCal = -0.34

0.0 0 50 100 150 200 250 300 350 400

3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.25 – C versus QS of Mary River at Kandanga (9 values)

2.4

2.0

y = -0.000022x + 1.5924 1.6

1.2

Lag Parameter (C) 0.8 t0.975 = 2.23

0.4 tCal = -0.22

0.0 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.26 – C versus QS of Haughton River at Powerline (12 values)

1.8 1.6 1.4 y = 0.00018x + 0.9471

1.2

1.0

0.8

Lag Parameter (C) 0.6 t0.975 = 2.14 0.4 tCal = 1.61

0.2

0.0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.27 – C versus QS of Haughton River at Mt. Piccaninny (16 values)

261

2.0 1.8 1.6 1.4 y = 0.0000036x + 1.2074 1.2

1.0

0.8 Lag Parameter(C) 0.6 t = 2.57 0.4 0.975

tCal = 0.03 0.2 0.0 0 500 1000 1500 2000 2500 3000 3500

3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.28 – C versus QS of Herbert River at Zattas (7 values)

2.0

1.8 1.6 1.4 y = 0.00006x + 1.0245 1.2 1.0

0.8 t = 2.13 Lag Parameter(C)Lag 0.975 0.6 tCal = 0.70 0.4 0.2 0.0 0 500 1000 1500 2000 2500 3000 3500 4000 4500

3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.29 – C versus QS of Herbert River at Nash’s Crossing (17 values)

3.2

2.8

2.4

2.0 y = 0.000035x + 1.9904 1.6

1.2 Lag Parameter (C) Parameter Lag

0.8 t0.975 = 2.36

0.4 t0.975 = 0.23

0.0 0 500 1000 1500 2000 2500 3000 3500 3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.30 – C versus QS of Herbert River at Gleneagle (9 values)

262

3.2

2.8

2.4 2.0

y = -0.0002x + 1.6268 1.6 1.2 Lag Parameter (C) 0.8 t0.975 = 2.13 0.4 tCal = -0.63 0.0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 3 Peak of Surface Runoff Hydrograph (QS) m /s Figure 6.31 – C versus QS of Herbert River at Silver Valley (17 values)

1.6

1.4

1.2

1.0 y = 0.00013x + 0.6719 0.8

0.6 Lag Parameter(C)

0.4 t0.975 = 2.10

tCal = 2.48 0.2

0.0 0 400 800 1200 1600 2000 2400 2800 3200 3600 3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.32 – C versus QS of Don River at Reeves (20 values)

1.2 1.0

0.8 y =0.000018x + 0.7021

0.6

Lag Parameter (C) Parameter Lag 0.4 t0.975 = 2.31 0.2 tCal = 0.20

0.0 0 250 500 750 1000 1250 1500 1750 2000 3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.33 – C versus QS of Don River at Mt. Dangar (10 values)

263

1.6 1.4

1.2 1.0 y = 0.0001x + 0.6844 0.8

0.6 Lag Parameter (C) Parameter Lag

0.4 t0.975 = 2.10

0.2 tCal = 0.95

0.0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400

3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.34 – C versus QS of Don River at Ida Creek (20 values)

1.8

1.6

1.4

1.2 y = 0.000028x + 0.8998 1.0 0.8

Lag Parameter (C) Parameter Lag 0.6

0.4 t0.975 = 2.04 tCal = 0.44 0.2

0.0 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.35 – C versus QS of North Johnstone River at Tung Oil (34 values)

2.4 2.0 1.6 y = -0.000082x + 1.2155 1.2

0.8 Lag Parameter (C)

0.4 t0.975 = 2.07 tCal = -0.55 0.0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.36 – C versus QS of North Johnstone River at Nerada (24 values)

264

2.4

2.0

1.6 1.2 y = -0.00018x + 1.5128

0.8 (C) Parameter Lag t0.975 = 2.09 0.4 tCal = -1.08

0.0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.37 – C versus QS of South Johnstone River at Central Mill (21 values)

4.5

4.0 3.5 3.0

2.5

2.0

y = 0.000027x + 1.2583

Lag Parameter (C) 1.5

1.0 t0.975 = 1.96 0.5 tCal = 0.57 0.0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 3 Peak of Surface Runoff Hydrograph (QS) m /s

Figure 6.38 – C versus QS of all 17 catchments for 254 values

6.5 Relationship between Lag Parameter (C) and Total Rainfall Depth (DT). Figures 6.39 to 6.55 show the lag parameter (C), derived in Chapter 5, plotted against the total rainfall depth (DT), which represents the size of the storm for various storms, and the results can be summarised as follows: • All plots have demonstrated a considerable amount of scatter; • Apart from Bellbird and Central Mill, all the remaining 15 catchments have shown positive gradients in their best-fit straight lines; • Two tailed t-test results have revealed that the gradients of the best-fit straight lines of the plots of Mary River at Gympie, Don River at Reeves and North Johnstone River at Ida Creek & Tung Oil are different from zero at 5% level of significance; 265

• It is important to note that the first two decimal places of the equations of the best- fit straight lines of all plots are zero; and • A positive gradient has been shown in the best-fit line of the plot in Figure 6.56 containing all 254 points. According to the results its gradient is significantly different from zero at 5% level of significance for a two tailed statistical t-test. However, most of the points are clustered onto the left side of Figure 6.56 and very few points are scattered around the right side of it.

Therefore, this relationship is further assessed by plotting Figure 6.57 by using 250 values, which are clustered as shown in Figure 6.56. The best-fit straight line of the plot containing 250 values has shown results similar to that in Figure 6.56, and the gradient of straight line of figure 6.57 is significantly different from zero as in the previous case. However, all the plots of catchments do not support a relationship between lag parameter C and DT.

3.5

3.0 y = 0.0024x + 2.164 2.5 2.0 1.5

Lag Parameter (C) Parameter Lag t0.975 = 2.45 1.0 tCal = 2.69

0.5

0.0 50 100 150 200 250 300 350 400 450 500 Total Rainfall Depth (DT) mm Figure 6.39 – C versus DT of Mary River at Gympie (8 values)

2.4

2.0

1.6 y = 0.0003x + 1.5814

1.2

Lag Parameter (C) 0.8

t0.975 = 2.31 t = 0.32 0.4 Cal

0.0 50 100 150 200 250 300 350 400 450 500 Total Rainfall Depth (DT) mm

Figure 6.40 – C versus DT of Mary River at Moy Pocket (10 values) 266

1.8

1.6

1.4 y = -0.000057x + 1.1613 1.2 1.0 0.8

0.4 t0.975 = 2.31

tCal = -0.04 0.2

0.0 25 50 75 100 125 150 175 200 225 250

Total Rainfall Depth (DT) mm

Figure 6.41 – C versus DT of Mary River at Bellbird (10 values)

4.5

4.0 3.5 3.0 y = 0.0013x + 2.6337 2.5 2.0

Lag Parameter(C) 1.5 t0.975 = 2.31 1.0 tCal = 0.72 0.5 0.0 0 50 100 150 200 250 300 350 400 450 500 550 600

Total Rainfall Depth (DT) mm

Figure 6.42 – C versus DT of Mary River at Cooran (10 values)

2.4

2.0 y = 0.0017x + 1.3711 1.6

1.2

Lag Parameter (C) 0.8 t0.975 = 2.36 tCal = 0.73 0.4

0.0 0 25 50 75 100 125 150 175 200 225 250

Total Rainfall Depth (DT) mm

Figure 6.43 – C versus DT of Mary River at Kandanga (9 values)

267

2.4

2.0 y = 0.001x + 1.505 1.6

1.2

Lag Parameter (C) 0.8 t0.975 = 2.23 0.4 tCal = 0.45

0.0 0 102030405060708090100110120130140 Total Rainfall Depth (DT) mm

Figure 6.44 – C versus DT of Haughton River at Powerline (12 values)

1.8

1.6

1.4

1.2

y = 0.003x + 0.9088 1.0 0.8

Lag Parameter (C) 0.6 t0.975 = 2.14 0.4 tCal = 2.09 0.2

0.0 0 20406080100120140160

Total Rainfall Depth (DT) mm

Figure 6.45 – C versus DT of Haughton River at Mt. Piccaninny (16 values)

2.0

1.8

1.6 y = 0.0081x + 0.8607 1.4 1.2 1.0

0.8 Lag Parameter (C) 0.6

t0.975 = 2.57 0.4 tCal = 1.89 0.2 0.0 0 1020304050607080 Total Rainfall Depth (DT) mm

Figure 6.46 – C versus DT of Herbert River at Zattas (7 values)

268

2.0

1.8

1.6 y = 0.0023x + 0.9907 1.4 1.2 1.0 0.8 Lag Parameter (C) 0.6 t0.975 = 2.13 0.4 tCal = 0.97 0.2

0.0 0 102030405060708090100110120130140150160 Total Rainfall Depth (DT) mm

Figure 6.47 – C versus DT of Herbert River at Nash’s Crossing (17 values)

3.2 2.8 2.4

2.0 y = 0.0027x + 1.8613 1.6

1.2 Lag Parameter (C) Parameter Lag t = 2.36 0.8 0.975 tCal = 0.73 0.4

0.0 0 102030405060708090100110120130140150 Total Rainfall Depth (DT) mm

Figure 6.48 – C versus DT of Herbert River at Gleneagle (9 values)

3.2

2.8

2.4

2.0 y = 0.0025x + 1.4084

1.6

1.2 Lag Parameter (C)

0.8 t0.975 = 2.13 0.4 tCal = 0.89

0.0 0 20406080100120140160 Total Rainfall Depth (DT) mm

Figure 6.49 – C versus DT of Herbert River at Silver Valley (17 values)

269

1.6

1.4

1.2 y = 0.0029x + 0.6448 1.0 0.8

0.6 Lag Parameter (C)

0.4 t0.975 = 2.10 t = 3.15 0.2 Cal

0.0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 Total Rainfall Depth (DT) mm

Figure 6.50 – C versus DT of Don River at Reeves (20 values)

1.2 1.0

0.8 y = 0.0019x + 0.6167

0.6

Lag Parameter (C) Parameter Lag 0.4 t0.975 = 2.31

0.2 tCal = 1.75

0.0 0 25 50 75 100 125 150 175 Total Rainfall Depth (DT) mm

Figure 6.51 – C versus DT of Don River at Mt. Dangar (10 values)

1.6

1.4 1.2 1.0 y = 0.0028x + 0.6055 0.8

0.6

Lag Parameter (C) t0.975 = 2.10 0.4

tCal = 2.67 0.2

0.0 0 20 40 60 80 100 120 140 160 180 200 220

Total Rainfall Depth (DT) mm

Figure 6.52 – C versus DT of Don River at Ida Creek (20 values)

270

1.8 1.6

1.4

1.2

1.0 y = 0.0037x + 0.6787 0.8

Lag Parameter (C) 0.6

t = 2.04 0.4 0.975 tCal = 3.39 0.2

0.0 0 20 40 60 80 100 120 140 160 180 Total Rainfall Depth (DT) mm

Figure 6.53 – C versus DT of North Johnstone River at Tung Oil (34 values)

2.4

2.0

1.6 y = 0.0029x + 0.9053

1.2

Lag Parameter (C) 0.8

t0.975 = 2.07 0.4 tCal = 1.54

0.0 20 40 60 80 100 120 140 160 180 200 Total Rainfall Depth (DT) mm

Figure 6.54 – C versus DT of North Johnstone River at Nerada (24 values)

2.4

2.0

y = -0.0002x + 1.4211 1.6 1.2

Lag Parameter (C) 0.8 t0.975 = 2.09 0.4 tCal = -0.16

0.0 25 50 75 100 125 150 175 200 225 250

Total Rainfall Depth (DT) mm

Figure 6.55 – C versus DT of South Johnstone River at Central Mill (21 values)

271

4.5

4.0 3.5 3.0 y = 0.0041x + 0.9488 2.5 2.0

Lag Parameter (C) 1.5

1.0 t0.975 = 1.96 tCal = 8.78 0.5

0.0 0 50 100 150 200 250 300 350 400 450 500 550 600 650 Total Rainfall Depth (DT) mm

Figure 6.56 – C versus DT of all 17 catchments for 254 values

4.5 4.0

3.5

3.0

2.5 y = 0.0041x + 0.9452 2.0

Lag Parameter (C) Parameter Lag 1.5

1.0 t0.975 = 1.96

0.5 tCal = 6.59

0.0 0 25 50 75 100 125 150 175 200 225 250 275 Total Rainfall Depth (DT) mm

Figure 6.57 – C versus DT of all 17 catchments for 250 values

6.6 Relationship between Lag Parameter (C) and Depth of Surface Runoff

(DSRO). Figures 6.58 to 6.74 show the lag parameter (C) plotted against the depth of surface runoff (DSRO) for various storms and those figures show the following:

• The majority of the plots have positive gradients in their best fit straight lines and only one plot (Mary River at Bellbird) demonstrates a negative gradient; • Significance tests have indicated that the gradients of the best-fit straight lines of the plots of the five catchments Gympie, Mt. Piccaninny, Reeves, Ida Creek and Tung Oil are significantly different from zero at 5% level for two tailed tests;

272

• The points of the plot containing 254 values (Figure 6.75) are scattered and most of them are clustered around the left side of the plot, and these points are clearly within the range of 0 to 175 mm for surface runoff depth; and • Although the gradients of the best-fit straight lines of Figure 6.75 (containing 254 values) and Figure 6.76 (only with 248 values clustered in the left side of Figure 6.75) are significantly different from zero according to their t-test results, the individual plots (as in the previous section) are not showing any consistency

in the variation of lag parameter C with DSRO.

Therefore, the above findings have shown that there is no real variation in lag parameter

3.5

3.0 y = 0.0037x + 2.1804 2.5

2.0

1.5

Lag Parameter (C) 1.0 t0.975 = 2.45 tCal = 3.03 0.5 0.0 0 50 100 150 200 250 300 350

Depth of Surface Runoff (DSRO) mm

Figure 6.58 – C versus DSRO of Mary River at Gympie (8 values)

2.4

2.0 y = 0.0003x + 1.605 1.6

1.2

Lag Parameter(C) 0.8 t0.975 = 2.31

tCal = 0.20

0.4

0.0 0 25 50 75 100 125 150 175 200 225 250 275 Depth of Surface Runoff (DSRO) mm

Figure 6.59 – C versus DSRO of Mary River at Moy Pocket (10 values)

273

1.8 1.6 1.4 y = -0.0006x + 1.1924 1.2

1.0

0.8

tCal = -0.28 0.2

0.0 0 102030405060708090100110120130 Depth of Surface Runoff (DSRO) mm

Figure 6.60 – C versus DSRO of Mary River at Bellbird (10 values)

4.5 4.0 3.5

3.0 y = 0.0022x + 2.6173

2.5

2.0

0.5

0.0 0 50 100 150 200 250 300 350 400

Depth of Surface Runoff (DSRO) mm

Figure 6.61 – C versus DSRO of Mary River at Cooran (10 values)

2.4 2.0 y = 0.0004x + 1.4944 1.6

1.2

Lag Parameter(C) 0.8 t0.975 = 2.36

tCal = 0.06

0.4

0.0 0 102030405060708090100 Depth of Surface Runoff (DSRO) mm

Figure 6.62 – C versus DSRO of Mary River at Kandanga (9 values)

274

2.4

2.0

y = 0.0002x + 1.5606 1.6

1.2

t0.975 = 2.23 0.4 tCal = 0.06

0.0 0 102030405060708090100

Depth of Surface Runoff (DSRO) mm

Figure 6.63 – C versus DSRO of Haughton River at Powerline (12 values)

1.8

1.6

1.4

1.2 y = 0.0057x + 0.9041 1.0

0.8

Lag Parameter(C) 0.6 0.4 t0.975 = 2.14

tCal = 2.42 0.2

0.0 0 1020304050607080 Depth of Surface Runoff (DSRO) mm

Figure 6.64 – C versus DSRO of Haughton River at Mt. Piccaninny (16 values)

2.0 1.8 1.6 y = 0.0131x + 0.9821 1.4 1.2

1.0

0.8

Lag Parameter (C) 0.6 0.4 t0.975 = 2.57 tCal = 1.33 0.2 0.0 5 10152025303540

Depth of Surface Runoff (DSRO) mm

Figure 6.65 – C versus DSRO of Herbert River at Zattas (7 values)

275

2.0

1.8 1.6 1.4

1.2 y = 0.0106x + 0.921 1.0 0.8 Lag Parameter (C) Parameter Lag 0.6 t0.975 = 2.13 0.4 tCal = 1.91 0.2

0.0 0 5 10 15 20 25 30 35 40 45 50 Depth of Surface Runoff (DSRO) mm

Figure 6.66 – C versus DSRO of Herbert River at Nash’s Crossing (17 values)

3.2

2.8 2.4 2.0 y = 0.0029x + 1.9343

1.6

1.2

Lag Parameter(C)

t0.975 = 2.36 0.8 tCal = 0.60 0.4

0.0 0 102030405060708090100110120 Depth of Surface Runoff (DSRO) mm

Figure 6.67 – C versus DSRO of Herbert River at Gleneagle (9 values)

3.2 2.8 2.4

2.0 y = -0.000077x + 1.5588 1.6

1.2 Lag Parameter(C)

0.8 t0.975 = 2.13 0.4 tCal = -0.02

0.0 0 102030405060708090100110120130140 Depth of Surface Runoff (DSRO) mm

Figure 6.68 – C versus DSRO of Herbert River at Silver Valley (17 values)

276

1.6

1.4 1.2 1.0 y = 0.0041x + 0.6811

0.8

0.6

Lag Parameter (C) 0.4 t0.975 = 2.10

tCal = 3.49 0.2

0.0 0 102030405060708090100110120130140

Depth of Surface Runoff (DSRO) mm

Figure 6.69 – C versus DSRO of Don River at Reeves (20 values)

1.2

1.0

0.8 y = 0.0026x + 0.6539

0.6

Lag Parameter(C) 0.4

t0.975 = 2.31 0.2 tCal = 1.09

0.0 0 1020304050607080 Depth of Surface Runoff (DSRO) mm

Figure 6.70 – C versus DSRO of Don River at Mt. Dangar (10 values)

1.6

1.4 1.2 y = 0.0048x + 0.6031 1.0

0.8

0.6

Lag Parameter (C) t = 2.10 0.4 0.975

tCal = 2.77 0.2

0.0 0 102030405060708090100110

Depth of Surface Runoff (DSRO) mm

Figure 6.71 – C versus DSRO of Don River at Ida Creek (20 values)

277

1.8 1.6 1.4 y = 0.0049x + 0.7348 1.2 1.0

0.8

Lag Parameter (C) 0.6 0.4 t0.975 = 2.04

0.2 tCal = 2.94

0.0 0 102030405060708090100110120 Depth of Surface Runoff (DSRO) mm

Figure 6.72 – C versus DSRO of North Johnstone River at Tung Oil (34 values)

2.4

2.0

1.6 y = 0.0052x + 0.8731

1.2

0.8 (C) Parameter Lag

t0.975 = 2.07 0.4 tCal = 1.92

0.0 10 20 30 40 50 60 70 80 90 100 110

Depth of Surface Runoff (DSRO) mm

Figure 6.73 – C versus DSRO of North Johnstone River at Nerada (24 values)

2.4 2.0

1.6 y = 0.0006x + 1.3484

1.2

Lag Parameter (C) 0.8 t0.975 = 2.09

tCal = 0.37 0.4

0.0 0 25 50 75 100 125 150 175 200 225 Depth of Surface Runoff (DSRO) mm

Figure 6.74 – C versus DSRO of South Johnstone River at Central Mill (21 values)

278

4.5 4.0 3.5

3.0

2.5 y = 0.0059x + 1.0001

2.0

Lag Parameter (C) 1.5 1.0 t0.975 = 1.96

tCal = 8.42 0.5

0.0 0 50 100 150 200 250 300 350 400 Depth of Surface Runoff (DSRO) mm

Figure 6.75 – C versus DSRO of all 17 catchments for 254 values

4.5

4.0 3.5 3.0

2.5 y = 0.0052x + 1.0154 2.0

1.0 t0.975 = 1.96

tCal = 5.58 0.5

0.0 0 25 50 75 100 125 150 175 Depth of Surface Runoff (D ) mm SRO

Figure 6.76 – C versus DSRO of all 17 catchments for 248 values

6.7 Relationship between Lag Parameter (C) and Average Intensity (Iav).

Figures 6.77 to 6.93 show the plots of lag parameter (C) versus average intensity (Iav) for seventeen catchments. These plots illustrate the following: • The plots of Gympie, Moy Pocket, Cooran, Mt. Piccaninny, Nash’s Crossing, Silver Valley, Reeves, Ida Creek and Nerada catchments from different basins show positive gradients; • The gradients of the plots of Bellbird, Kandanga, Zattas and Gleneagle catchments are negative; • Four plots out of the seventeen have shown straight horizontal lines for their best- fit lines with almost zero gradients; 279

• The two tailed hypothesis test results showed that the gradients of the best-fit straight lines of only two catchments (Mary River at Gympie and Don River at Reeves) are significantly different from zero at 5% level of significance; and • The best-fit line of the plot containing all 254 values, shown in Figure 6.94, is very close to a horizontal line and also the gradient of that line is not significantly different from zero according to the t-test results.

The foregoing findings revealed that there is no real trend for the lag parameter (C) to vary as Iav varies.

3.5 3.0

2.5 y = 0.3917x + 1.6617

2.0

1.5

Lag Parameter (C) 1.0 t0.975 = 2.45

tCal = 3.45 0.5

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Average Intensity (Iav) mm/hr

Figure 6.77 – C versus Iav of Mary River at Gympie (8 values)

2.4

2.0 y = 0.021x + 1.568

1.6

1.2

0.8 Lag Parameter(C) t0.975 = 2.31

tCal = 0.50 0.4

0.0 0123456789 Average Intensity (Iav) mm/hr

Figure 6.78 – C versus Iav of Mary River at Moy Pocket (10 values)

280

1.8

1.6

1.4 1.2 1.0

y = -0.0361x + 1.2812 0.8

0.6 Lag Parameter (C) Parameter Lag

0.4 t0.975 = 2.31

tCal = -1.14 0.2 0.0 012345678910 Average Intensity (Iav) mm/hr

Figure 6.79 – C versus Iav of Mary River at Bellbird (10 values)

4.5

4.0

3.5 y = 0.0527x + 2.6592 3.0

2.5 2.0

Lag Parameter (C) Parameter Lag 1.5 t0.975 = 2.31

1.0 tCal = 1.21

0.5

0.0 024681012141618202224 Average Intensity (Iav) mm/hr

Figure 6.80 – C versus Iav of Mary River at Cooran (10 values)

2.4

2.0

1.6

1.2 y = -0.1267x + 1.7301

Lag Parameter (C) 0.8 t0.975 = 2.36 tCal = -1.19 0.4

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Average Intensity (Iav) mm/hr

Figure 6.81 – C versus Iav of Mary River at Kandanga (9 values)

281

2.4

2.0

1.6 y = 0.0016x + 1.5596 1.2

Lag Parameter(C) 0.8 t0.975 = 2.23 0.4 t = 0.04 Cal

0.0 12345678910 Average Intensity (Iav) mm/hr

Figure 6.82 – C versus Iav of Haughton River at Powerline (12 values)

1.8 1.6

1.4

1.2 y = 0.0642x + 0.90 1.0 0.8

Lag Parameter (C) Parameter Lag 0.6

t0.975 = 2.14 0.4 tCal = 1.53 0.2 0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Average Intensity (Iav) mm/hr

Figure 6.83 – C versus Iav of Haughton River at Mt. Piccaninny (16 values)

2.0 1.8 1.6

1.4 y = -0.0816x + 1.2771 1.2

1.0

0.8

0.4 t0.975 = 2.57 0.2 tCal = -0.35

0.0 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Average Intensity (Iav) mm/hr

Figure 6.84 – C versus Iav of Herbert River at Zattas (7 values)

282

2.0

1.8

1.6

1.4 y = 0.1961x + 0.8906 1.2 1.0 0.8 Lag Parameter (C) 0.6 t0.975 = 2.13 0.4 tCal = 1.97 0.2 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Average Intensity (Iav) mm/hr

Figure 6.85 – C versus Iav of Herbert River at Nash’s Crossing (17 values)

3.2

2.8

2.4

2.0 y = -0.0783x + 2.1446

1.6

1.2 Lag Parameter (C)

0.8 t0.975 = 2.36 tCal = -1.16 0.4

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Average Intensity (Iav) mm/hr

Figure 6.86 – C versus Iav of Herbert River at Gleneagle (9 values)

3.2

2.8

2.4

2.0 y = 0.0305x + 1.5046 1.6

1.2 Lag Parameter (C)

0.8 t0.975 = 2.13

0.4 tCal = 0.39

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Average Intensity (Iav) mm/hr

Figure 6.87– C versus Iav of Herbert River at Silver Valley (17 values)

283

1.6

1.4

1.2

1.0 y = 0.0472x + 0.6615

0.8

0.6 Lag Parameter(C) t = 2.10 0.4 0.975 tCal = 2.48 0.2 0.0 01234567891011 Average Intensity (Iav) mm/hr

Figure 6.88 – C versus Iav of Don River at Reeves (20 values)

1.2

1.0

0.8 y = 0.0019x + 0.7115

0.6

Lag Parameter (C) 0.4

t = 2.31 0.2 0.975 tCal = 0.06

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Average Intensity (Iav) mm/hr

Figure 6.89 – C versus Iav of Don River at Mt. Dangar (10 values)

1.6

1.4

1.2 y = 0.0203x + 0.6881 1.0 0.8

0.6 Lag Parameter (C) 0.4 t0.975 = 2.10 0.2 tCal = 0.83

0.0 01234567891011 Average Intensity (Iav) mm/hr

Figure 6.90 – C versus Iav of Don River at Ida Creek (20 values) 284

1.8

1.6 1.4 1.2 y = 0.0081x + 0.8948 1.0

0.8

Lag Parameter (C) Parameter Lag 0.6

0.4 t0.975 = 2.04 t = 0.46 0.2 Cal

0.0 012345678910111213 Average Intensity (Iav) mm/hr

Figure 6.91 – C versus Iav of North Johnstone River at Tung Oil (34 values)

2.4

2.0

1.6

y = 0.0167x + 1.0573 1.2

Lag Parameter (C) 0.8

t0.975 = 2.07 0.4 tCal = 0.52

0.0 1234567891011 Average Intensity (Iav) mm/hr

Figure 6.92 – C versus Iav of North Johnstone River at Nerada (24 values)

2.4

2.0

1.6

1.2 y = 0.0038x + 1.3725

Lag Parameter(C) 0.8 t0.975 = 2.09 tCal = 0.17 0.4 0.0 0123456789101112131415

Average Intensity (Iav) mm/hr

Figure 6.93 – C versus Iav of South Johnstone River at Central Mill (21 values)

285

4.5

4.0

3.5

3.0 2.5

2.0 y = 0.0143x + 1.2357

Lag Parameter (C) 1.5 1.0 t0.975 = 1.96 0.5 tCal = 1.03 0.0 024681012141618202224 Average Intensity (I ) mm/hr av Figure 6.94 – C versus Iav of all 17 catchments for 254 values

6.8 Relationship between Lag Parameter (C) and Ratio of Time to Peak Intensity

and Excess Duration (TPI/DURex) Figures 6.95 to 6.111 show the lag parameter (C), plotted against the ratio of time to peak intensity and excess rainfall duration (TPI/DURex). This measure indicates whether the storm is peaking early or late. The figures illustrate the following: • The plots of nine catchments (Gympie, Moy Pocket, Cooran, Silver Valley, Reeves, Mt.Dangar, Tung Oil, Nerada and Central Mill) have illustrated positive gradients in their best-fit straight lines; • Seven catchments (Bellbird, Kandanga, Powerline, Mt. Piccaninny, Nash’s Crossing, Gleneagle and Ida Creek) have shown negative gradients in their best-fit straight lines; • The best-fit straight line of the plot of Zattas catchment is almost horizontal; • The two-tailed significance test revealed that the gradient of the best-fit straight line of the plot of Mary River at Kandanga is the only one significantly different from zero at 5% level of significance; and • The best-fit straight line of the plot containing all 254 values of all seventeen catchments, shown in Figure 6.112, is very close to a horizontal line and its gradient is not significantly different from zero according to the t-test results.

286

Overall the Figures (6.95 to 6.112) suggest that there is no significant variation of the lag parameter (C) with the ratio of time to peak intensity and excess duration

(TPI/DURex).

3.5 3.0

2.5 y = 0.1935x + 2.4987 2.0 1.5 Lag Parameter (C) (C) Parameter Lag 1.0 t = 2.45 0.975 0.5 tCal = 0.15

0.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex) Figure 6.95 – C versus (TPI/DURex) of Mary River at Gympie (8 values)

2.4

2.0

1.6 y = 0.2371x + 1.5658

1.2

Lag Parameter (C) Parameter Lag 0.8

t0.975 = 2.31 0.4 tCal = 0.31

0.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.96 – C versus (TPI/DURex) of Mary River at Moy Pocket (10 values)

1.8 1.6 1.4 1.2 1.0 y = -0.2206x + 1.2277

0.8

Lag Parameter(C) 0.6 0.4 t0.975 = 2.31 t = -0.49 0.2 Cal

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.97 – C versus (TPI/DURex) of Mary River at Bellbird (10 values) 287

4.5

4.0 y = 2.2872x + 2.1764 3.5 3.0 2.5

2.0

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.98 – C versus (TPI/DURex) of Mary River at Cooran (10 values)

2.4

2.0

1.6

1.2 y = -1.0224x + 1.8673

0.8 Lag Parameter(C)

t0.975 = 2.36 0.4 tCal = -2.39

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.99 – C versus (TPI/DURex) of Mary River at Kandanga (9 values)

2.4

2.0

1.6

y = -0.2644x + 1.6528 1.2

Lag Parameter (C) 0.8

t0.975 = 2.23 0.4 tCal = -0.51

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.100 – C versus (TPI/DURex) of Haughton River at Powerline (12 values)

288

1.8

1.6 1.4 1.2

1.0 y = -0.175x + 1.1521 0.8

Lag Parameter (C) Parameter Lag 0.6

0.4 t0.975 = 2.14

tCal = -0.44 0.2 0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.101 – C versus (TPI/DURex) of Haughton River at Mt. Piccaninny (16 values)

2.0 1.8 1.6

1.4 y = -0.0329x + 1.2227 1.2

1.0

0.8

0.4 t0.975 = 2.57 t = -0.05 0.2 Cal

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.102 – C versus (TPI/DURex) of Herbert River at Zattas (7 values)

2.0

1.8 1.6 1.4

1.2 y = -0.5233x + 1.352 1.0

0.8 Lag Parameter (C) 0.6

0.4 t0.975 = 2.13 0.2 tCal = -0.97 0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.103 – C versus (TPI/DURex) of Herbert River at Nash’s Crossing (17 values)

289

3.2

2.8 2.4 y = -0.8864x + 2.3345 2.0

1.6

1.2

0.8 t0.975 = 2.36 0.4 tCal = -1.03

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.104 – C versus (TPI/DURex) of Herbert River at Gleneagle (9 values)

3.2 2.8 2.4 2.0 y = 0.5977x + 1.3496 1.6 1.2 Lag Parameter (C)

0.8 t0.975 = 2.13 t = 0.84 0.4 Cal

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.105 – C versus (TPI/DURex) of Herbert River at Silver Valley (17 values)

1.6

1.4

1.2

1.0

0.8 y = 0.2928x + 0.7231

0.6 Lag Parameter (C)

0.4 t0.975 = 2.10 tCal = 0.98 0.2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.106 – C versus (TPI/DURex) of Don River at Reeves (20 values)

290

1.2

1.0

0.8

y = 0.163x + 0.666 0.6

Lag Parameter(C) 0.4

t0.975 = 2.31 0.2 tCal = 0.66

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.107 – C versus (TPI/DURex) of Don River at Mt. Dangar (10 values)

1.6

1.4

1.2 1.0 0.8 y = -0.4218x + 0.8707

0.6 Lag Parameter (C)

0.4 t0.975 = 2.10

0.2 tCal = -1.52

0.0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 Ratio of Time to Peak Intensity and Excess Duration (T /DUR ) PI ex

Figure 6.108 – C versus (TPI/DURex) of Don River at Ida Creek (20 values)

1.8

1.6 1.4 1.2

1.0 y = 0.1095x + 0.8848 0.8

Lag Parameter (C) Parameter Lag 0.6

t = 2.04 0.4 0.975 tCal = 0.35 0.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.109 – C versus (TPI/DURex) of North Johnstone River at Tung Oil (34 values)

291

2.4

2.0

1.6 y = 0.1829x + 1.0698

1.2

Lag Parameter (C) 0.8

t0.975 = 2.07 0.4 tCal = 0.41

0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.110 – C versus (TPI/DURex) of North Johnstone River at Nerada (24 values)

2.4

2.0

1.6 y = 0.1069x + 1.352

1.2

0.8 Parameter(C) Lag t0.975 = 2.09 0.4 tCal = 0.25

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.111 – C versus (TPI/DURex) of South Johnstone River at Central Mill (21 values)

4.5

4.0

t0.975 = 1.96 3.5 tCal = -1.11 3.0

2.5 2.0

Lag Parameter (C) 1.5 y = -0.2323x + 1.3649 1.0

0.5

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex)

Figure 6.112 – C versus (TPI/DURex) of all 17 catchments for 254 values

292

6.9 Relationship between Lag Parameter (C) and Average Peak Intensity (AVPI) Figures 6.113 to 6.129 show the lag parameter (C) plotted against the average peak intensity (AvPI). Average peak intensity is calculated by averaging the rainfall intensity over the main burst of the storm, considering all the rainfall stations designated for each catchment. The following can be observed from the figures:

• Out of the seventeen plots, eleven have shown positive gradients in their best-fit lines as shown in Figures 6.113, 6.116, 6.118 to 6.120, 6.121, 6.123, 6.124 and 6.126 to 6.128; • The best-fit straight lines of five plots (Figures 6.114, 6.115, 6.117, 6.122, and 6.129) contain negative gradients; • The gradients of the best-fit straight lines of the three plots shown in Figures 6.118, 6.123 and 6.124 are significantly different from zero at 5% level of significance for a two tailed test; and • Although the best-fit straight line of the plot containing all 254 values, shown in Figure 6.130 is with a negative gradient, its value is very close to zero. The t-test results show that the gradient of the best-fit line of the plot in Figure 6.130 is significantly different from zero. However, the individual plots of the seventeen catchments do not fully support this trend.

Therefore, the above findings do not demonstrate any significant variation of the lag parameter (C) with average peak intensity (AvPI).

3.5 3.0

2.5 y = 0.262x + 1.7611

2.0

1.5 Lag Parameter (C) 1.0 t0.975 = 2.45 0.5 tCal = 2.06

0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Average Peak Intensity (AvPI) mm/hr

Figure 6.113 – C versus (AvPI) of Mary River at Gympie (8 values)

293

2.4

2.0

1.6 y = -0.0791x + 1.8665

1.2

Lag Parameter (C) Parameter Lag 0.8

t0.975 = 2.31

tCal = -1.18 0.4

0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Average Peak Intensity (AvPI) mm/hr

Figure 6.114 – C versus (AvPI) of Mary River at Moy Pocket (10 values)

1.8 1.6 1.4 y = -0.0672x + 1.3842 1.2 1.0 0.8

Lag Parameter(C) 0.6

0.4 t0.975 = 2.31 0.2 tCal = -1.68

0.0 0.51.01.52.02.53.03.54.04.55.05.56.06.57.0 Average Peak Intensity (AvPI) mm/hr

Figure 6.115 – C versus (AvPI) of Mary River at Bellbird (10 values)

4.5

4.0 y = 0.2246x + 1.9953 3.5

3.0 2.5 2.0

t0.975 = 2.31 1.0 tCal = 1.42 0.5

0.0 1.01.52.02.53.03.54.04.55.05.56.06.57.07.5 Average Peak Intensity (AvPI) mm/hr

Figure 6.116 – C versus (AvPI) of Mary River at Cooran (10 values) 294

2.4

2.0

1.6 y = -0.1473x + 1.8593 1.2

Lag Parameter(C) 0.8 t0.975 = 2.36 tCal = -1.96 0.4

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 Average Peak Intensity (AvPI) mm/hr

Figure 6.117 – C versus (AvPI) of Mary River at Kandanga (9 values)

2.4 2.0

1.6 y = 0.0595x + 1.2302

1.2

Lag Parameter (C) 0.8 t0.975 = 2.23 t = 2.37 0.4 Cal

0.0 1234567891011 Average Peak Intensity (AvPI) mm/hr

Figure 6.118 – C versus (AvPI) of Haughton River at Powerline (12 values)

1.8 1.6

1.4 1.2 y = 0.0196x + 0.9608 1.0 0.8

Lag Parameter (C) 0.6

t0.975 = 2.14 0.4 tCal = 0.96 0.2

0.0 12345678910111213141516 Average Peak Intensity (A PI) mm/hr v

Figure 6.119 – C versus (AvPI) of Haughton River at Mt. Piccaninny (16 values)

295

2.0

1.8

1.6

1.4 y = 0.0435x + 1.1013 1.2 1.0 0.8 Lag Parameter (C) Parameter Lag 0.6

0.4 t0.975 = 2.57 tCal = 0.38 0.2

0.0 0.51.01.52.02.53.03.54.04.5 Average Peak Intensity (AvPI) mm/hr

Figure 6.120 – C versus (AvPI) of Herbert River at Zattas (7 values)

2.0 1.8 1.6

1.4 y = 0.0646x + 0.933

1.2

1.0

0.8 Lag Parameter (C) Parameter Lag 0.6 t0.975 = 2.13 0.4 tCal = 1.04 0.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Average Peak Intensity (AvPI) mm/hr

Figure 6.121 – C versus (AvPI) of Herbert River at Nash’s Crossing (17 values)

3.2 2.8 2.4

y = -0.0836x + 2.2544 2.0

1.6

1.2 Lag Parameter (C) t0.975 = 2.36 0.8

tCal = -0.69 0.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Average Peak Intensity (AvPI) mm/hr

Figure 6.122 – C versus (AvPI) of Herbert River at Gleneagle (9 values)

296

3.2 2.8 2.4 y = 0.1662x + 1.0846 2.0 1.6 1.2

Lag Parameter (C) 0.8 t0.975 = 2.13 tCal = 2.52 0.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 Average Peak Intensity (AvPI) mm/hr

Figure 6.123 – C versus (AvPI) of Herbert River at Silver Valley (17 values)

1.6

1.4

y = 0.0442x + 0.5105 1.2 1.0

0.8

0.6

Lag Parameter (C)

0.4 t0.975 = 2.10

tCal = 3.06 0.2

0.0 3 4 5 6 7 8 9 101112131415 Average Peak Intensity (A PI) mm/hr v

Figure 6.124 – C versus (AvPI) of Don River at Reeves (20 values)

1.2

1.0

0.8

0.6 y = 0.0006x + 0.7126

Lag Parameter (C) Parameter Lag 0.4

t0.975 = 2.31 0.2 tCal = 0.03

0.0 3456789101112 Average Peak Intensity (A PI) mm/hr v

Figure 6.125 – C versus (AvPI) of Don River at Mt. Dangar (10 values)

297

1.6

1.4

1.2 y = 0.0156x + 0.6442 1.0

0.8

0.6 Lag Parameter (C) Parameter Lag

0.4 t0.975 = 2.10 t = 0.98 0.2 Cal

0.0 0123456789101112131415 Average Peak Intensity (AvPI) mm/hr

Figure 6.126 – C versus (AvPI) of Don River at Ida Creek (20 values)

1.8

1.6 1.4 1.2 1.0 y = 0.0268x + 0.762 0.8

Lag Parameter (C) 0.6

t0.975 = 2.04 0.4 tCal = 0.92 0.2

0.0 234567891011 Average Peak Intensity (AvPI) mm/hr

Figure 6.127 – C versus (AvPI) of North Johnstone River at Tung Oil (34 values)

2.4

2.0

1.6 y = 0.0462x + 0.8339

1.2

t = 2.07 0.4 0.975 tCal = 1.00

0.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 Average Peak Intensity (AvPI) mm/hr

Figure 6.128 – C versus (AvPI) of North Johnstone River at Nerada (24 values) 298

2.4

2.0

1.6 y = -0.0391x + 1.7032 1.2

Lag Parameter (C) 0.8

t0.975 = 2.09 t = -1.61 0.4 Cal 0.0 3456789101112131415161718 Average Peak Intensity (AvPI) mm/hr

Figure 6.129 – C versus (AvPI) of South Johnstone River at Central Mill (21 values)

4.5 4.0

3.5 t0.975 = 1.96 3.0 tCal = -3.10 2.5 2.0

Lag Parameter (C) Parameter Lag 1.5

1.0 0.5 y = -0.0402x + 1.4917 0.0 024681012141618 Average Peak Intensity (AvPI) mm/hr

Figure 6.130 – C versus (AvPI) of all 17 catchments for 254 values

6.10 Relationship between Lag Parameter (C) and Ratio of Excess Depth and

Total Depth (Dex/DT) of Rainfall. Figures 6.131 to 6.147 show the lag parameter (C) derived in Chapter 5, plotted against the ratio of excess depth and total depth (Dex/DT) of rainfall for all seventeen catchments. This ratio reflects the proportion of the storm rainfall which becomes runoff, and hence it is a measure of the rainfall loss relative to the total storm depth. These plots illustrate the following: • Plots of the seven catchments shown in Figures 6.131, 6.134, 6.139 and 6.144 to 6.147 indicated positive gradients in their best-fit lines; • Best-fit lines with negative gradients have been found for the seven catchments shown in Figures 6.133, 6.135, 6.136, 6.138, 6.140, 6.141 and 6.143; 299

• The gradients of the best-fit straight lines of plots shown in Figures 6.131, 6.135 and 6.136 (Mary River at Gympie and Kandanga and Haughton River at Powerline) are significantly different from zero in their two tailed t-tests; and • The majority of the points in Figure 6.148 for all seventeen catchments containing 254 values illustrate an evenly distributed pattern. The best-fit line of this plot is horizontal and its gradient is not significantly different from zero at 5% level of significance according to the t-test results.

Therefore, the foregoing findings indicate that there is no real trend for the lag parameter to vary as (Dex/DT) varies.

3.5 3.0

2.5 y = 3.229x + 0.7054 2.0

1.5

(C) Parameter Lag 1.0 t0.975 = 2.45 0.5 tCal = 3.58 0.0 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.131 – C versus (Dex/DT) of Mary River at Gympie (8 values)

2.4

2.0

1.6 y = -0.0053x + 1.6327

1.2

Lag Parameter (C) 0.8 t0.975 = 2.31

tCal = -0.01 0.4

0.0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.132 – C versus (Dex/DT) of Mary River at Moy Pocket (10 values)

300

1.8 1.6 1.4

1.2

1.0 y = -0.1735x + 1.2502 0.8

Lag Parameter(C) 0.6

0.4 t0.975 = 2.31

tCal = -0.41 0.2

0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.133 – C versus (Dex/DT) of Mary River at Bellbird (10 values)

4.5

4.0

3.5

3.0 y = 0.5461x + 2.5981 2.5 2.0

0.5

0.0 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.134 – C versus (Dex/DT) of Mary River at Cooran (10 values)

2.4 2.0

1.6

y = -1.413x + 2.206

1.2

Lag Parameter (C) 0.8

t0.975 = 2.36 0.4 tCal = -2.56

0.0 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.135 – C versus (Dex/DT) of Mary River at Kandanga (9 values)

301

2.4

2.0

1.6 y = -0.962x + 2.1779

1.2

0.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.136 – C versus (Dex/DT) of Haughton River at Powerline (12 values)

1.8 1.6

1.4 1.2 1.0 y = 0.0232x + 1.0708 0.8

Lag Parameter (C) 0.6

0.4 t0.975 = 2.14

0.2 tCal = 0.08

0.0 0.20.30.40.50.60.70.80.91.0 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.137 – C versus (Dex/DT) of Haughton River at Mt. Piccaninny (16 values)

2.0

1.8

1.6

1.4 y = -0.1111x + 1.2613 1.2 1.0 0.8 Lag Parameter (C) 0.6

0.4 t0.975 = 2.57 t = -0.20 0.2 Cal 0.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.138 – C versus (Dex/DT) of Herbert River at Zattas (7 values)

302

2.0 1.8 1.6

1.4 y = 0.4481x + 0.8787 1.2

1.0

0.8

Lag Parameter (C) 0.6 t0.975 = 2.13 0.4 tCal = 1.34 0.2

0.0 0.00.10.20.30.40.50.60.70.80.91.0 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.139 – C versus (Dex/DT) of Herbert River at Nash’s Crossing (17 values)

3.2

2.8

2.4

2.0 y = -0.2306x + 2.1584 1.6

1.2 Lag Parameter (C) Parameter Lag t0.975 = 2.36 0.8 tCal = -0.44 0.4

0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.140 – C versus (Dex/DT) of Herbert River at Gleneagle (9 values)

3.2

2.8

2.4

2.0 y = -0.8062x + 2.0466 1.6

1.2 (C) Parameter Lag 0.8 0.4 t0.975 = 2.13

tCal = -1.87 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Ratio of Excess Depth and Total Depth (Dex/DT) Figure 6.141 – C versus (Dex/DT) of Herbert River at Silver Valley (17 values)

303

1.6

1.4

1.2

1.0 y = 0.0392x + 0.7997 0.8

0.6 (C) Parameter Lag 0.4 t0.975 = 2.10 t = 0.20 0.2 Cal

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.142 – C versus (Dex/DT) of Don River at Reeves (20 values)

1.2

1.0

0.8

0.6 y = -0.0722x + 0.7491

Lag Parameter (C) 0.4 t0.975 = 2.31 0.2 tCal = -0.33

0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.143 – C versus (Dex/DT) of Don River at Mt. Dangar (10 values)

1.6

1.4

1.2 1.0 0.8

y = 0.1669x + 0.6546 0.6 Lag Parameter (C) Parameter Lag

0.4 t0.975 = 2.10

0.2 tCal = 0.81

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.144 – C versus (Dex/DT) of Don River at Ida Creek (20 values)

304

1.8

1.6 1.4 1.2 y = 0.1816x + 0.8225 1.0 0.8

Lag Parameter (C) 0.6

0.4 t0.975 = 2.04

tCal = 0.83 0.2 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.145 – C versus (Dex/DT) of North Johnstone River at Tung Oil (34 values)

2.4

2.0

1.6 y = 0.3514x + 0.9131 1.2

Parameter(C) Lag 0.8

t = 2.07 0.4 0.975 tCal = 0.71

0.0 0.30.40.50.60.70.80.91.0

Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.146 – C versus (Dex/DT) of North Johnstone River at Nerada (24 values)

2.4 2.0

1.6 y = 0.2657x + 1.2231

1.2

Lag Parameter(C) 0.8

0.4 t0.975 = 2.09 tCal = 0.81

0.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.147 – C versus (Dex/DT) of South Johnstone River at Central Mill (21 values)

305

4.5

4.0 3.5 t0.975 = 1.96 tCal = 0.55 3.0

2.5 y = 0.0898x + 1.2306 2.0

Lag Parameter (C) Parameter Lag 1.5 1.0 0.5

0.0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Ratio of Excess Depth and Total Depth (Dex/DT)

Figure 6.148 – C versus (Dex/DT) of all 17 catchments for 254 values

6.11 Relationship between Lag Parameter (C) and Ratio of Peak Intensity and

Average Intensity (IP/Iav) of Rainfall. Figures 6.149 to 6.165 show the lag parameter (C), plotted against the ratio of peak intensity and average intensity (Ip/Iav). This measures the effect of the sharpness of the peak of storm rainfall. The findings from the figures can be summarised as: • Plots of five catchments Bellbird, Kandanga, Powerline, Reeves and Mt.Dangar have shown positive gradients in their best-fit straight lines; • Plots of nine catchments Gympie, Mt. Piccaninny, Zattas, Nash’s Crossing, Gleneagle, Ida Creek, Tung Oil, Nerada and Central Mill have shown negative gradients in their best-fit straight lines; • The majority of the equations of the plots show zero gradients up to their first decimal place; • The best-fit lines of the plots of three catchments (Moy Pocket, Cooran and Silver Valley) are nearly horizontal; and • Although Figure 6.166 shows a negative gradient in its best-fit straight line, most of the points are clustered towards the left side of the plot. It is also important to note that a small amount of scattered points are distributed along a horizontal band. The t-test results revealed that the gradient of the best-fit line of Figure 6.166 is not significantly different from zero at 5% level of significance.

In view of the above indicated findings, there is no significant trend for the lag parameter to vary as (Ip/Iav) varies. 306

3.5 3.0

y = -0.4022x + 3.1557 2.5

2.0

1.5 Lag Parameter (C) Parameter Lag 1.0 t0.975 = 2.45 0.5 tCal = -1.57

0.0 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75

Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.149 – C versus (IP/Iav) of Mary River at Gympie (8 values)

2.4

2.0 y = 0.0014x + 1.6252 1.6

1.2

Lag Parameter(C) 0.8 t0.975 = 2.31

tCal = 0.08 0.4

0.0 0 2 4 6 8 10121416182022 Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.150 – C versus (IP/Iav) of Mary River at Moy Pocket (10 values)

1.8 1.6 1.4 y = 0.048x + 1.0562 1.2 1.0

0.8

Lag Parameter (C) 0.6 0.4 t0.975 = 2.31

tCal = 2.27 0.2 0.0 0123456789101112 Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.151 – C versus (IP/Iav) of Mary River at Bellbird (10 values) 307

4.5

4.0

3.5 y = 0.0245x + 2.8862 3.0

2.5 2.0

Lag Parameter (C) Parameter Lag 1.5

t0.975 = 2.31 1.0 tCal = 0.07 0.5 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.152 – C versus (IP/Iav) of Mary River at Cooran (10 values)

2.4

2.0

1.6 y = 0.1383x + 1.2888

1.2

Lag Parameter (C) 0.8

t0.975 = 2.36 0.4 tCal = 0.80

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.153 – C versus (IP/Iav) of Mary River at Kandanga (9 values)

2.4

2.0

1.6 y = 0.1013x + 1.4112

1.2

0.8 Lag Parameter(C) t0.975 = 2.23 0.4 tCal = 1.71

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.154 – C versus (IP/Iav) of Haughton River at Powerline (12 values)

308

1.8

1.6

1.4

1.2

1.0 y = -0.0239x + 1.1464 0.8 Lag Parameter 0.6

0.4 t0.975 = 2.14

tCal = -0.52 0.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.155 – C versus (IP/Iav) of Haughton River at Mt. Piccaninny (16 values)

2.0 1.8 1.6

1.4 y = -0.0068x + 1.2497 1.2

1.0

0.8 Lag Parameter (C) 0.6 t = 2.57 0.4 0.975 tCal = -0.32 0.2

0.0 0 2 4 6 8 10121416182022

Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.156 – C versus (IP/Iav) of Herbert River at Zattas (7 values)

2.0 1.8 1.6

1.4

1.2

1.0 y = -0.0387x + 1.2342

0.8

Lag Parameter (C) 0.6 t = 2.13 0.4 0.975 tCal = -1.62 0.2

0.0 01234567891011121314 Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.157– C versus (IP/Iav) of Herbert River at Nash’s Crossing (17 values)

309

3.2 2.8 2.4 y = -0.0032x + 2.0466 2.0

1.6

Lag Parameter 1.2

t = 2.36 0.8 0.975 tCal = -0.18 0.4

0.0 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0

Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.158 – C versus (IP/Iav) of Herbert River at Gleneagle (9 values)

3.2

2.8

2.4

2.0 y = 0.0024x + 1.5482 1.6 1.2 (C) Parameter Lag 0.8 t0.975 = 2.13 tCal = 0.06 0.4

0.0 012345678910111213 Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.159 – C versus (IP/Iav) of Herbert River at Silver Valley (17 values)

1.6

1.4 1.2 1.0 y = 0.0195x + 0.7529

0.8

0.6

0.4 t0.975 = 2.10

0.2 tCal = 1.66

0.0 0 2 4 6 8 10121416182022

Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.160 – C versus (IP/Iav) of Don River at Reeves (20 values)

310

1.2

1.0

0.8 y = 0.0104x + 0.6523

0.6

Lag Parameter (C) Parameter Lag 0.4

t0.975 = 2.31 t = 1.74 0.2 Cal

0.0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.161– C versus (IP/Iav) of Don River at Mt. Dangar (10 values)

1.6

1.4

1.2

1.0

0.8 y = -0.0044x + 0.7689

0.6 Lag Parameter (C)

0.4 t0.975 = 2.10 0.2 tCal = -0.40

0.0 024681012141618202224 Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.162 – C versus (IP/Iav) of Don River at Ida Creek (20 values)

1.8

1.6 1.4 1.2

1.0 y = -0.0489x + 1.0356 0.8

Lag Parameter Parameter Lag (C) 0.6

0.4 t0.975 = 2.04

0.2 tCal = -1.42

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.163 – C versus (IP/Iav) of North Johnstone River at Tung Oil (34 values)

311

2.4

2.0

1.6

1.2 y = -0.1263x + 1.3491

Lag Parameter (C) 0.8

0.4 t0.975 = 2.07

tCal = -1.16

0.0 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.164 – C versus (IP/Iav) of North Johnstone River at Nerada (24 values)

2.4

2.0

1.6

y = -0.0794x + 1.5594 1.2

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0

Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.165 – C versus (IP/Iav) of South Johnstone River at Central Mill (21 values)

4.5 4.0

3.5 t0.975 = 1.96

tCal = -1.32 3.0 2.5 2.0

Lag Parameter (C) 1.5 y = -0.0135x + 1.3214 1.0 0.5

0.0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Ratio of Peak Intensity and Average Intensity (Ip/Iav)

Figure 6.166 – C versus (IP/Iav) of all 17 catchments for 254 values

312

6.12 Relationship between Lag Parameter (C) and Ratio of Rainfall Depths at

Centroids of Bottom and Top halves (DBC/DTC) of catchment. Figures 6.167 to 6.183 show the lag parameter (C), plotted against the ratio of rainfall depths at the centroids of the bottom and top halves (DBC/DTC) of the seventeen catchments. This ratio measures the effect of the spatial variation of rainfall depths on lag parameter.

It could be expected that spatially varying rainfall, where heavier rain occurs in the bottom part of the catchment and lighter rain in the top half, would lead to a more rapid rise in hydrograph and higher peak discharge, and this could result in lower lag parameters for these types of storms. However, WBNM does allow for spatial variation in rainfall (as mentioned in Chapter 2) and if it is properly accounted for, there may be no trend for lag parameter C to vary with spatial variations.

In this part of the study, each catchment is divided into two halves to represent its upstream and downstream segments. The rainfall depths at the centroids of these segments have been obtained from the isohyets of all storms, as shown in Chapter 4. From Figures 6.167 to 6.183, the following have been observed:

• Plots of seven catchments, Moy Pocket, Bellbird, Kandanga, Powerline, Zattas, Silver Valley and Reeves have shown positive gradients in their best-fit straight lines; • Plots of the remaining ten catchments Gympie, Cooran, Mt. Piccaninny, Nash’s Crossing, Gleneagle, Mt.Dangar, Ida Creek, Tung Oil, Nerada and Central Mill have shown negative gradients in their best-fit straight lines; and • Only two plots (Bellbird and Central Mill) have shown that the gradients of the best-fit lines are significantly different from zero at 5% level of significance of the two tailed t-test.

Although Figure 6.184 (plotted with all 254 values of the seventeen catchments) shows a negative gradient in its best-fit straight line, that gradient is not significantly different from zero at 5% level of significance of the two tailed test. 313

The relationship between C and (DBC/DTC) is investigated further by eliminating the values of C and DBC/DTC greater than 2.5, of Figure 6.184 and plotting it in Figure 6.185. Figure 6.185 has shown that the negative gradient of its best-fit straight line is also not significantly different from zero at 5% level of significance from the two tailed t-test results.

Therefore, all the above mentioned results have illustrated that no significant trend exists for the lag parameter to vary as (DBC/DTC) varies.

3.5

3.0

y = -0.1136x + 2.7055 2.5

Lag Parameter (C) Parameter Lag 2.0 t0.975 = 2.45

tCal = -0.33 1.5 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.167 – C versus (DBC/DTC) of Mary River at Gympie (8 values)

2.2

2.0

1.8

y = 0.022x + 1.6018 1.6

Lag Parameter (C) 1.4

1.2 t0.975 = 2.31 tCal = 0.36 1.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.168 – C versus (DBC/DTC) of Mary River at Moy Pocket (10 values)

314

1.80

1.60 y = 0.2109x + 0.8994 1.40 1.20

Lag Parameter (C) 1.00

0.80 t0.975 = 2.31

tCal = 2.66 0.60 0.40.81.21.62.02.42.83.23.64.0 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.169 – C versus (DBC/DTC) of Mary River at Bellbird (10 values)

4.5

4.0 3.5 3.0 y = -0.793x + 3.7205 2.5

2.0

t0.975 = 2.31 1.0 tCal = -0.51

0.5 0.65 0.75 0.85 0.95 1.05 1.15 1.25 1.35 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (D /D ) BC TC

Figure 6.170 – C versus (DBC/DTC) of Mary River at Cooran (10 values)

2.25 2.00

1.75

1.50 y = 0.1084x + 1.3803 1.25 Lag Parameter (C) 1.00 t0.975 = 2.36

0.75 tCal = 0.54

0.50 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.171 – C versus (DBC/DTC) of Mary River at Kandanga (9 values)

315

2.0

1.8 y = 0.1302x + 1.3695

1.6

1.4

Lag Parameter (C) 1.2

t0.975 = 2.23 1.0 tCal = 1.39 0.8 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.172 – C versus (DBC/DTC) of Haughton River at Powerline (12 values)

1.75

1.50

1.25

1.00 y = -0.1577x + 1.2678

Lag Parameter (C) 0.75

0.50 t0.975 = 2.14

tCal = -2.05

0.25 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.173 – C versus (DBC/DTC) of Haughton River at Mt. Piccaninny (16 values)

2.00

1.80

1.60

1.40 y = 0.0304x + 1.1443

Lag Parameter (C) 1.20

1.00 t0.975 = 2.57 tCal = 0.26 0.80 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC) Figure 6.174 – C versus (DBC/DTC) of Herbert River at Zattas (7 values)

316

2.00 1.75

1.50

1.25

y = -0.2155x + 1.3395 1.00 Lag Parameter (C) 0.75

t0.975 = 2.13 0.50 tCal = -0.74

0.25 0.75 1.00 1.25 1.50 1.75 2.00 2.25 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.175 – C versus (DBC/DTC) of Herbert River at Nash’s Crossing (17 values)

3.00

2.75

2.50

2.25

2.00 y = -1.7558x + 3.1312

1.75 (C) Parameter Lag 1.50 t0.975 = 2.36 1.25 tCal = -1.83 1.00 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC) Figure 6.176 – C versus (DBC/DTC) of Herbert River at Gleneagle (9 values)

3.0

2.5

2.0 y = 0.2827x + 1.3147 1.5

Lag Parameter (C) Parameter Lag 1.0

0.5 t0.975 = 2.13 tCal = 0.36

0.0 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.177 – C versus (DBC/DTC) of Herbert River at Silver Valley (17 values)

317

1.50

1.25

1.00 y = 0.1132x + 0.7177 0.75 Lag Parameter (C)

0.50 t0.975 = 2.10 tCal = 1.11

0.25 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (D /D ) BC TC

Figure 6.178 – C versus (DBC/DTC) of Don River at Reeves (20 values)

1.1

1.0

0.9

0.8 y = -0.0188x + 0.738 0.7 Lag Parameter (C) 0.6

0.5 t0.975 = 2.31 tCal = -0.16 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC) Figure 6.179 – C versus (DBC/DTC) of Don River at Mt.Dangar (10 values)

1.60

1.40 t0.975 = 2.10

tCal = -1.66 1.20 1.00

0.80 y = -0.2182x + 0.9979

Lag Parameter (C) 0.60

0.40

0.20 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.180 – C versus (DBC/DTC) of Don River at Ida Creek (20 values)

318

2.00

1.75 1.50 1.25 1.00 y = -0.0145x + 0.9562

0.75

Lag Parameter (C) 0.50

t0.975 = 2.04 0.25 tCal = -0.21

0.00 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.181 – C versus (DBC/DTC) of North Johnstone River at Tung Oil (34 values)

2.25

2.00 t0.975 = 2.07 tCal = -0.55 1.75 1.50

1.25 y = -0.1899x + 1.4617 Lag Parameter (C) Parameter Lag 1.00

0.75 0.50 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.182 – C versus (DBC/DTC) of North Johnstone River at Nerada (24 values)

2.2

2.0 t0.975 = 2.09 t = -2.35 1.8 Cal

1.6

1.4

y = -0.4218x + 2.0665 1.2 Lag Parameter (C) 1.0 0.8

0.6 0.81.01.21.41.61.82.02.22.42.6 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.183 - C versus (DBC/DTC) of South Johnstone River at Central Mill (21 values)

319

4.5

4.0 t0.975 = 1.96 3.5 tCal = -1.49

3.0

2.5

2.0

Lag Parameter (C) 1.5 1.0 0.5 y = -0.0814x + 1.3897

0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC)

Figure 6.184 – C versus (DBC/DTC) of all 17 catchments (254 values)

2.5

t0.975 = 1.96 2.0 tCal = -1.87

1.5 y = -0.1171x + 1.3059 1.0

0.5

0.0 0.25 0.75 1.25 1.75 2.25 2.75 Ratio of Rainfall Depths at the Centroids of Bottom and Top halves of Catchment (DBC/DTC) Figure 6.185 - C versus (DBC/DTC) of 229 values (excluding C and DBC/DTC values larger than 2.5)

320

6.13 Summary of the findings of Chapter 6. As explained previously the intention of this chapter is to investigate the relationship between lag parameter (C) and storm (hydrological) characteristics.

The description of storm characteristics, shown in Columns 4, 7, 9, 11, 13, 15, 16, 17, 18 and 19 of Tables 5.12 to 5.28 of Chapter 5, are shown in the first row of Table 6.3. The abbreviations designated for the storm characteristics are given in the second row of Table 6.3. The remaining rows show the findings of the relationships between the lag parameter and the storm characteristics of all seventeen catchments. The best-fit straight lines that have a positive gradient are given a positive sign (+), while negative sign (–) is given for a negative gradient, and a zero sign (0) for a zero gradient. If the gradient of the straight line is significantly different from zero at 5% level of significance for a two tailed t-test, then that result is shown with an (s) in Table 6.3.

Since the catchment’s discharge has been considered as one of the key variables in the lag time equation in WBNM as well as in the other computer based hydrological models, the initial investigation of this study was mainly directed towards the peak flows of recorded hydrographs (Qp) as well as the surface runoff hydrographs (QS) to examine their variation with the lag parameter (C). Thereafter this study was extended to examine the relationship between the lag parameter (C) and the following storm characteristics:

• Total Rainfall Depth (DT);

• Depth of Surface Runoff (DSRO);

• Average Intensity of Rainfall (Iav);

• Ratio of Time to Peak Intensity and Excess Duration (TPI/DURex);

• Average Peak Intensity (AvPI);

• Ratio of Excess Depth and Total Depth of Rainfall (Dex/DT);

• Ratio of Peak Intensity and Average Intensity (Ip/Iav); and

• Ratio of Rainfall Depths at Centroids of Bottom and Top halves (DBC/DTC) of catchment.

321

Some of the attributes in this list are directly related to the rainfall patterns of storms of catchments while the others are related indirectly. Moreover, these items cover a significant amount of storm characteristics.

The results of the investigations relating to Qp and QS have revealed that there is no sufficient amount of evidence to suggest that the lag parameter (C) varies with Qp and

QS. Therefore, the findings described in sections 6.3 and 6.4 of this chapter support the validity of WBNM to model the nonlinear behaviour of natural catchments.

Apart from the total depth (DT) and the depth of surface runoff (DSRO), the storm characteristics selected for this study have clearly shown from the results discussed in sections 6.7 to 6.12, that there is no real trend in variation with the lag parameter (C).

Although the trends are not very strong for DT and DSRO, the results in sections 6.5 and 6.6 show some evidence that the lag parameter is larger for larger rainfall depths. This scenario may suggest that WBNM is perhaps not modelling nonlinearity as well as it could. Furthermore, this could imply that WBNM is too nonlinear for very large floods and they could possibly be modeled with linear models.

While the lag parameter increases with DT and DSRO (particularly for larger floods) the same data shows no trend with discharge. It is important to note that the discharge is represented by QP and QS, and also that the discharge is directly proportional to DT and

DSRO. There are thus some contradictions in the results, in that the lag parameter C varies with rainfall depths (DT and DSRO) but not with discharge (QP and QS) even though QP and QS are themselves dependent on DT and DSRO.

Overall, while the lag parameter does appear to increase with DT and DSRO (most of the gradients of the best-fit straight lines of the plots in sections 6.5 and 6.6 are positive), a similar variation could not be found with QP and QS, and consequently WBNM can be considered to model nonlinearity satisfactorily.

322

Ratio of Ratio of Time Peak of Total Peak of Ratio of Ratio of Peak Rainfall Depths Total Rainfall Depth of Average to Peak Average Peak Recorded Surface Runoff Excess Depth Intensity and at Centroids of Depth Surface Runoff Intensity Intensity and Intensity Hydrograph Hydrograph and Total Average Bottom and Catchment (mm) (mm) (mm/hr) Excess (mm/hr) (m3/s) (m3/s) Depth Intensity Top halves of Duration No catchment

Qp QS DT DSRO Iav TPI/DURex AvPI Dex/DT Ip/Iav DBC/DTC

Columns Selected from Tables 5.12 to 5.28 of 18 19 4 7 9 13 15 16 17 11 Chapter 5

1 Gympie +s+s+s+s+s+x+x+s-x-x

2 Moy Pocket-x-x+x0x+x+x-x0x0x+x

3 Bellbird-x-x0x-x-x-x-x-x+x+s

4 Cooran +x+x+x+x+x+x+x+x0x-x

5 Kandanga-x-x+x0x-x-s-x-s+x+x

6 Powerline-x0x+x0x0x-x+s-s+x+x

7 Mt. Piccaninny+x+x+x+s+x-x+x0x-x-x

8 Zattas 0x0x+x+x-x0x+x-x-x+x

9 Nash's Crossing+x+x+x+x+x-x+x+x-x-x

10 Gleneagle0x0x+x+x-x-x-x-x-x-x

11 Silver Valley-x-x+x0x+x+x+s-x0x+x

12 Reeves +x+s+s+s+s+x+s0x+x+x

13 Mt.Dangar0x0x+x+x0x+x0x-x+x-x

14 Ida Creek+x+x+s+s+x- x+x+x -x -x

15 Tung Oil - x + x + s + s 0 x + x + x + x - x - x

16 Nerada -x-x+x+x+x+x+x+x-x-x

17 Central Mill-x-x-x+x0x+x-x+x-x-s characteristics Storm plots of versus (Hydrological) of C significance and gradients Table Signs of – 6.3 Most dominant sign None None + + None None NoneNone None None

CHAPTER 7

RELATIONSHIP BETWEEN LAG PARAMETER AND GEOMORPHOLOGICAL AND CLIMATOLOGICAL CHARACTERISTICS

323

7. RELATIONSHIP BETWEEN LAG PARAMETER AND GEOMORPHOLOGICAL AND CLIMATOLOGICAL CHARACTERISTICS.

7.1 Introduction

Generally catchments with larger areas produce larger lag times and those with smaller areas demonstrate smaller lag times. Therefore, the catchment area (A) is considered to be one of the key physical (geomorphological) characteristics which could influence the lag time. Some of the other physical characteristics of catchments that may control the lag time are, slope and length of main stream, distance to centroid from outlet of catchment along the main stream, elevation at centroid and catchment shape.

The majority of the studies carried out by various researchers described in Chapter 2, have developed relations in which the lag time is directly proportional to the catchment area (A), and the length of the main stream (L), and also inversely proportional to the slope of the main stream (Sc). These relationships can be combined and expressed in a common equation: W X -Y Lag time (tL) = C L A Sc (7.1) Several studies have also included a measure of the size of the flood in a nonlinear relation of the form: W X -Y -Z Lag time (tL) = C L A Sc Q (7.2) As shown in equation (2.176) in Chapter 2, WBNM has adopted the following formula 0.57 -0.23 for lag time: Lag time (tL) = C A Q (7.3) Where C is the scaling factor known as the lag parameter. WBNM therefore, calculates the lag time using catchment size only, disregarding the other physical factors. A key question therefore, is whether the area (A) alone is sufficient to describe the lag time, or whether the other physical characteristics of a catchment should be considered.

The equations relating to lag time devised by various researchers as indicated in Table 2.1, have been transferred to a common form of the catchment area (A) as described in Chapter 2, and shown in Table 2.2. The mean and median values of the exponent x of A of the equations of Table 2.2 are found to be 0.53 and 0.50 respectively, and they are close to the value of 0.57 adopted in WBNM.

324

One of the objectives of this chapter is to assess the validity and the reliability of equation (7.3). This assessment can be carried out by studying the variation of the lag parameter with a range of physical characteristics of catchments. The average values of the lag parameters of all seventeen catchments, as well as the list of geomorphological and climatological characteristics shown at the end of this chapter in Table 7.28 are selected for this study, and the results are discussed in detail. The significance t-tests were carried out separately for all the plots shown in this chapter and their results are tabulated and shown under each figure.

7.2 Relationship between Lag Parameter (C) and Catchment Area (A). Figure 7.1 illustrates the plot of lag parameter (C) versus catchment area (A) for all seventeen catchments selected for this study. The following features were found: • The catchments cover a wide range of areas (A); • Results of twelve catchments are clustered together, while the remaining five are scattered. Four catchments (Gympie, Zattas, Nash’s Crossing and Gleneagle), out of those five, have considerably larger areas; • Except for Gympie, Cooran and Gleneagle, the remaining fourteen catchments have reasonably similar lag parameter values; • The gradient of the best-fit straight line is almost equal to zero; and • The results of the two tailed t-test shown in Table 7.1 reveals that the gradient is not significantly different from zero at 5% level of significance.

To make the analysis more meaningful the twelve catchments within the clustered area of Figure 7.1 were examined further by plotting the values of C and A of those catchments as shown in Figure 7.2: • Points of all twelve catchments show a significant amount of scatter; • The gradient of the best-fit straight line is slightly less than that of the plot containing all seventeen catchments as shown in Figure 7.1; and • The results of the two tailed test, shown in Table 7.2, show that the gradient is not significantly different from zero at 5% level of significance.

The above findings demonstrate that there is no clear trend for the lag parameter (C) to vary as catchment area (A) varies. This indicates that the exponent of area (A), x = 0.57

325

in equation 7.3, is quite satisfactory for these catchments. The remainder of this chapter examines any possible relationship between C and a range of catchment physical characteristics.

3.0 Cooran

Gympie 2.5

Gleneagle 2.0

Moy Pocket y = 0.000000102x + 1.3949 Silver Valley Powerline 1.5 Kandanga Central Mill Nerada Zattas Bellbird Mt.Piccaninny Nash's Crossing

Lag Parameter (C) 1.0 Tung OIl Reeves Ida Creek Mt.Dangar 0.5 t0.975 = 2.13

tCal = 0.15 0.0 0 100000 200000 300000 400000 500000 600000 700000 800000 Catchment Area (A) - ha

Figure 7.1 – C versus A of all seventeen catchments

Table 7.1 – t-test calculations for C versus A of all seventeen catchments

Catchment Lag Calculated No Catchment Name Area (A) in ha Parameter (C) X2 Y2 XY Lag (X) ( Y ) Parameter (C)

1 Gympie 292020 2.55 85275680400.00 6.5025 744651 1.42 2 Moy Pocket 83023 1.63 6892818529.00 2.6569 135327.49 1.40 3 Bellbird 47920 1.16 2296326400.00 1.3456 55587.2 1.40 4 Cooran 16432 2.92 270010624.00 8.5264 47981.44 1.40 5 Kandanga 17568 1.51 308634624.00 2.2801 26527.68 1.40 6 Powerline 173456 1.56 30086983936.00 2.4336 270591.36 1.41 7 Mt. Piccaninny 113893 1.08 12971501556.25 1.1664 123003.9 1.41 8 Silver Valley 58624 1.56 3436773376.00 2.4336 91453.44 1.40 9 Gleneagle 537016 2.03 288386184256.00 4.1209 1090142.48 1.45 10 Nash's Crossing 684152 1.08 468063959104.00 1.1664 738884.16 1.46 11 Zattas 729200 1.21 531732640000.00 1.4641 882332 1.47 12 Reeves 101032 0.82 10207465024.00 0.6724 82846.24 1.41 13 Mt.Dangar 80784 0.72 6526054656.00 0.5184 58164.48 1.40 14 Ida Creek 62008 0.75 3844992064.00 0.5625 46506 1.40 15 Tung Oil 92936 0.93 8637100096.00 0.8649 86430.48 1.40 16 Nerada 80792 1.14 6527347264.00 1.2996 92102.88 1.40 17 Central Mill 38976 1.39 1519128576.00 1.9321 54176.64 1.40 Total 3209831.50 24.04 1466983600485.25 39.9464 4626708.87 24.04 Intercept of straight line (a) = 1.394899169 r2 = 0.001498805 Slope of straight line (b) = 1.01785E-07Standard error of estimate (Se) = 0.629396132 Correlation coefficient (r) = 0.038714406Estimated (t) = 0.150

326

1.8

1.6 Moy Pocket Silver Valley Powerline Kandanga 1.4 Central Mill y = -0.00000037x + 1.2168 1.2 Bellbird Nerada Mt.Piccaninny 1.0 Tung Oil Reeves 0.8 Ida Creek Mt.Dangar

Lag Parameter (C) Parameter Lag 0.6

0.4

t0.975 = 2.23 0.2 tCal = -0.14

0.0 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000 Catchment Area (A) - ha Figure 7.2 – C versus A of twelve catchments

Table 7.2 – t-test calculations for C versus A of twelve catchments

Catchment Lag Calculated No Catchment Name Area (A) in ha Parameter (C) X2 Y2 XY Lag (X) ( Y ) Parameter (C) 1 Moy Pocket 83023 1.63 6892818529.00 2.6569 135327.49 1.19 2 Bellbird 47920 1.16 2296326400.00 1.3456 55587.2 1.20 3 Kandanga 17568 1.51 308634624.00 2.2801 26527.68 1.21 4 Powerline 173456 1.56 30086983936.00 2.4336 270591.36 1.15 5 Mt. Piccaninny 113893 1.08 12971501556.25 1.1664 123003.9 1.17 6 Silver Valley 58624 1.56 3436773376.00 2.4336 91453.44 1.20 7 Reeves 101032 0.82 10207465024.00 0.6724 82846.24 1.18

8 Mt.Dangar 80784 0.72 6526054656.00 0.5184 58164.48 1.19 9 Ida Creek 62008 0.75 3844992064.00 0.5625 46506 1.19 10 Tung Oil 92936 0.93 8637100096.00 0.8649 86430.48 1.18

11 Nerada 80792 1.14 6527347264.00 1.2996 92102.88 1.19 12 Central Mill 38976 1.39 1519128576.00 1.9321 54176.64 1.20 Total 951011.50 14.25 93255126101.25 18.1661 1122717.79 14.25

Intercept of straight line (a) = 1.21678006 r2 = 0.001962287 Slope of straight line (b) = -3.69460E-07Standard error of estimate (Se) = 0.352389482 Correlation coefficient (r) = -0.044297714Estimated (t) = -0.140

327

7.3 Relationship between Lag Parameter (C) and Equal Area Slope (Sc) Figure 7.3 shows the plot of the lag parameter (C) versus the equal area slope of the main stream (Sc) for all seventeen catchments and it illustrates the following: • All points are fairly scattered in the plot; • The best-fit straight line shows a negative gradient of 0.1341; • Except for points of Gympie, Cooran and Gleneagle catchments, others are inside a horizontal thick band of the plot as shown in Figure 7.3; and • The results of the statistical analysis of a two tailed t-test shown in Table 7.3 have indicated that the gradient is significantly different from zero at 5% level of significance.

It is worth noting that Gympie, Cooran, and to a lesser extent, Gleneagle, have larger C values, and flatter stream slopes. This could indicate a relation between C and Sc. However, to test the possibility that Gympie and Cooran are outliers, the analysis was repeated, omitting these two catchments. Figure 7.4 for those fifteen catchments show that: • All points are significantly scattered; • Although the slope of the best-fit straight line is negative, the value of the gradient in the equation of the straight line shown in Figure 7.4 is close to zero; and • The results of the two tailed t-test, shown in Table 7.4, show that the gradient in Figure 7.4 is not significantly different from zero at 5% level of significance.

The plot of Figure 7.5 is made by eliminating catchments with lag parameters greater than 2.0 (Gympie, Cooran and Gleneagle) and that plot, containing fourteen catchments, illustrates the following: • The points are scattered and they cover the plot area reasonably well; • The best-fit straight line is horizontal and the gradient is very close to zero; and • The results of the statistical analysis of the two tailed t-test shown in Table 7.5 indicate that the gradient in Figure 7.5 is not significantly different from zero at 5% level of significance.

The foregoing findings indicate that there is a trend for the lag parameter (C) to decrease as the equal area slope of the main stream of the catchment (Sc) increases, but

328

this result is dependent on the large C values for two of the catchments (Gympie and Cooran).

3.0 Cooran

Gympie 2.5

2.0 Gleneagle y = -0.1341x + 1.9882 Moy Pocket Silver Valley 1.5 Powerline Kandanga Central Mill Zattas Bellbird Nerada Mt.Piccaninny Nash's Crossing

Lag Parameter (C) 1.0 Reeves Tung Oil Mt.Dangar Ida Creek

0.5 t0.975 = 2.13

tCal = -2.36

0.0 0123456789

Equal Area Slope of main Stream of Catchment (Sc) - m/km

Figure 7.3 – C versus Sc of all seventeen catchments

Table 7.3 – t-test calculations for C versus Sc of all seventeen catchment

Equal area Slope of Lag Calculated 2 2 No Catchment Name Main Stream (Sc) Parameter (C) X Y XY Lag (m/km) (X) ( Y ) Parameter (C)

1 Gympie 0.90 2.55 0.81 6.5025 2.295 1.87 2 Moy Pocket 2.20 1.63 4.84 2.6569 3.586 1.69 3 Bellbird 4.80 1.16 23.04 1.3456 5.568 1.34 4 Cooran 1.20 2.92 1.44 8.5264 3.504 1.83 5 Kandanga 5.10 1.51 26.01 2.2801 7.701 1.30 6 Powerline 2.50 1.56 6.25 2.4336 3.9 1.65 7 Mt. Piccaninny 3.80 1.08 14.44 1.1664 4.104 1.48 8 Silver Valley 5.80 1.56 33.64 2.4336 9.048 1.21 9 Gleneagle 2.00 2.03 4.00 4.1209 4.06 1.72 10 Nash's Crossing 4.30 1.08 18.49 1.1664 4.644 1.41 11 Zattas 4.00 1.21 16.00 1.4641 4.84 1.45 12 Reeves 3.30 0.82 10.89 0.6724 2.706 1.55 13 Mt.Dangar 3.50 0.72 12.25 0.5184 2.52 1.52 Ida Creek 4.30 14 0.75 18.49 0.5625 3.225 1.41 15 Tung Oil 7.60 0.93 57.76 0.8649 7.068 0.97 16 Nerada 8.70 1.14 75.69 1.2996 9.918 0.82 17 Central Mill 8.80 1.39 77.44 1.9321 12.232 0.81 Total 72.80 24.04 401.48 39.9464 90.9190 24.04 Intercept of straight line (a) = 1.988222799 r2 = 0.270981228 Slope of straight line (b) = -1.34063E-01Standard error of estimate (Se) = 0.537797935 Correlation coefficient (r) = -0.520558574Estimated (t) = -2.361

329

2.5

2.0 Gleneagle

Moy Pocket Powerline Silver Valley 1.5 Kandanga Central Mill y = -0.0365x + 1.4099 Zattas Bellbird Nerada Mt.Piccaninny 1.0 Nash's Crossing Tung Oil Reeves Lag Parameter(C) Ida Creek Mt.Dangar

0.5 t0.975 = 2.16

tCal =-0.79

0.0 123456789

Equal Area Slope of Main Stream of Catchment (Sc) - m/km

Figure 7.4 – C versus Sc of fifteen catchments

Table 7.4 – t-test calculations for C versus Sc of fifteen catchments

Equal area Slope of Lag Calculated Main Stream (Sc) No Catchment Name Parameter (C) X2 Y2 XY Lag (m/km) ( Y ) Parameter (C) (X) 1 Moy Pocket 2.20 1.63 4.84 2.6569 3.586 1.33 2 Bellbird 4.80 1.16 23.04 1.3456 5.568 1.23 Kandanga 5.10 3 1.51 26.01 2.2801 7.701 1.22 4 Powerline 2.50 1.56 6.25 2.4336 3.9 1.32 5 Mt. Piccaninny 3.80 1.08 14.44 1.1664 4.104 1.27 6 Silver Valley 5.80 1.56 33.64 2.4336 9.048 1.20 7 Gleneagle 2.00 2.03 4.00 4.1209 4.06 1.34 8 Nash's Crossing 4.30 1.08 18.49 1.1664 4.644 1.25 9 Zattas 4.00 1.21 16.00 1.4641 4.84 1.26 10 Reeves 3.30 0.82 10.89 0.6724 2.706 1.29 11 Mt.Dangar 3.50 0.72 12.25 0.5184 2.52 1.28 12 Ida Creek 4.30 0.75 18.49 0.5625 3.225 1.25 13 Tung Oil 7.60 0.93 57.76 0.8649 7.068 1.13 14 Nerada 8.70 1.14 75.69 1.2996 9.918 1.09 15 Central Mill 8.80 1.39 77.44 1.9321 12.232 1.09 Total 70.70 18.57 399.23 24.9175 85.12 18.57 Intercept of straight line (a) = 1.409872217 r2 = 0.04552 Slope of straight line (b) = -3.64651E-02Standard error of estimate (Se) = 0.37622 Correlation coefficient (r) = -0.213356179Estimated (t) = -0.787

330

1.8

Moy Pocket 1.6 Powerline Silver Valley Kandanga 1.4 Central Mill

Zattas y = -0.0018x + 1.1902 1.2 Bellbird Mt.Piccaninny Nerada Nash's Crossing 1.0 Tung Oil 0.8 Reeves Ida Creek Mt.Dangar

Lag Parameter (C) 0.6

0.4 t0.975 = 2.18 0.2 tCal =-0.04

0.0 23456789

Equal Area Slope of Main Stream of Catchment (Sc) - m/km

Figure 7.5 – C versus Sc of fourteen catchments

Table 7.5 – t-test calculations for C versus Sc of fourteen catchments

Equal area Slope of Lag Calculated Main Stream (S ) No Catchment Name c Parameter (C) X2 Y2 XY Lag (m/km) ( Y ) Parameter (C) (X)

1 Moy Pocket 2.2 1.63 4.84 2.6569 3.586 1.19 2 Bellbird 4.8 1.16 23.04 1.3456 5.568 1.18 3 Kandanga 5.1 1.51 26.01 2.2801 7.701 1.18 4 Powerline 2.5 1.56 6.25 2.4336 3.9 1.19 5 Mt. Piccaninny 3.8 1.08 14.44 1.1664 4.104 1.18 6 Silver Valley 5.8 1.56 33.64 2.4336 9.048 1.18 7 Nash's Crossing 4.3 1.08 18.49 1.1664 4.644 1.18 8 Zattas 4.0 1.21 16.00 1.4641 4.84 1.18 9 Reeves 3.3 0.82 10.89 0.6724 2.706 1.18 10 Mt.Dangar 3.5 0.72 12.25 0.5184 2.52 1.18 11 Ida Creek 4.3 0.75 18.49 0.5625 3.225 1.18 12 Tung Oil 7.6 0.93 57.76 0.8649 7.068 1.18 13 Nerada 8.7 1.14 75.69 1.2996 9.918 1.17 14 Central Mill 8.8 1.39 77.44 1.9321 12.232 1.17 Total 68.70 16.54 395.23 20.7966 81.06 16.54 Intercept of straight line (a) = 1.190223102 r2 = 0.00015 Slope of straight line (b) = -1.79219E-03Standard error of estimate (Se) = 0.32347 Correlation coefficient (r) = -0.012191339Estimated (t) = -0.042

331

7.4 Relationship between Lag Parameter (C) and Length of Main Stream (L). The plot of the lag parameter (C) versus the length of main stream of the catchment (L) for all seventeen catchments shown in Figure 7.6 indicates the following: • Points are scattered but the majority of them are in the left side of the plot; • The best-fit straight line is almost horizontal and its gradient, shown in the equation in Figure 7.6, is found to be equal to zero up to its 3rd decimal place; and • The results of the two tailed significance test shown in Table 7.6 have indicated that the gradient of the best-fit straight line is not significantly different from zero at 5% level of significance.

With the intention of studying the relationship between the lag parameter (C) and the main stream length (L) of the fifteen catchments by omitting two catchments with larger C values (Gympie and Cooran), Figure 7.7 was plotted. The findings from Figure 7.7 can be summarised as: • The points are scattered and once again most of the points are in the left part of the plot; • The gradient of the best-fit straight line is equal to zero up to its 3rd decimal place; and • The results of the two tailed t-test indicated in Table 7.7 clearly show that the gradient of the best-fit straight line on Figure 7.7 is not significantly different from zero at 5% level of significance.

The general trend would be to have a higher lag time for a long stream and a smaller lag time for a shorter stream and that concept has been illustrated to a certain extent by the plot in Figure 7.7 with a positive slope. However, not much support has been found from the other results, shown in the Figure 7.6 as well as Table 7.6, to agree with that concept.

Therefore, it is not possible to accept that the lag parameter (C) would increase as the length of the main stream (L) increases. This result indicates that the effect of stream length (L), which is highly correlated with A, is properly accounted for in equation 7.3.

332

3.0 Cooran

Gympie 2.5

2.0 Gleneagle

Moy Pocket Powerline y = -0.0002x + 1.4277 1.5 Kandanga Silver Valley Central Mill Zattas Bellbird Nerada Mt.Piccaninny Nash's Crossing

Lag Parameter (C) Parameter Lag 1.0 Tung Oil Reeves Ida Creek Mt.Dangar

0.5 t0.975 = 2.13

tCal = -0.05

0.0 20 40 60 80 100 120 140 160 180 200 220 240 Length of Main Stream of Catchment (L) - km

Figure 7.6 – C versus L of all seventeen catchments

Table 7.6 – t-test calculations for C versus L of all seventeen catchments

Length of Main Lag Calculated Stream (L) No Catchment Name Parameter (C) X2 Y2 XY Lag (km) ( Y ) Parameter (C) (X) 1 Gympie 131.10 2.55 17187.21 6.5025 334.305 1.41 2 Moy Pocket 69.05 1.63 4767.90 2.6569 112.5515 1.42 3 Bellbird 46.35 1.16 2148.32 1.3456 53.766 1.42 4 Cooran 31.60 2.92 998.56 8.5264 92.272 1.42 5 Kandanga 52.45 1.51 2751.00 2.2801 79.1995 1.42 6 Powerline 94.50 1.56 8930.25 2.4336 147.42 1.41 7 Mt. Piccaninny 68.10 1.08 4637.61 1.1664 73.548 1.42 8 Silver Valley 55.80 1.56 3113.64 2.4336 87.048 1.42 9 Gleneagle 127.90 2.03 16358.41 4.1209 259.637 1.41 10 Nash's Crossing 214.40 1.08 45967.36 1.1664 231.552 1.40 11 Zattas 225.90 1.21 51030.81 1.4641 273.339 1.39 12 Reeves 66.70 0.82 4448.89 0.6724 54.694 1.42 13 Mt.Dangar 55.60 0.72 3091.36 0.5184 40.032 1.42 14 Ida Creek 46.30 0.75 2143.69 0.5625 34.725 1.42 15 Tung Oil 85.80 0.93 7361.64 0.8649 79.794 1.41 16 Nerada 73.20 1.14 5358.24 1.2996 83.448 1.42 17 Central Mill 78.20 1.39 6115.24 1.9321 108.698 1.42 Total 1522.95 24.04 186410.14 39.9464 2146.029 24.04 Intercept of straight line (a) = 1.427743729 r2 = 0.000194286 Slope of straight line (b) = -1.52102E-04Standard error of estimate (Se) = 0.629807143 Correlation coefficient (r) = -0.013938644Estimated (t) = -0.054

333

2.5

2.0 Gleneagle

Moy Pocket y = 0.00079x + 1.1663 1.5 Silver Valley Powerline Kandanga Central Mill Zattas Nerada Bellbird Mt.Piccaninny 1.0 Nash's Crossing Tung Oil Ida Creek Lag Parameter (C) Reeves Mt.Dangar

0.5 t0.975 = 2.16 tCal = 0.44 0.0 40 60 80 100 120 140 160 180 200 220 240 Length of Main Stream of Catchment (L) - km Figure 7.7 – C versus L of fifteen catchments

Table 7.7 – t-test calculations for C versus L of fifteen catchments

Length of Main Lag Calculated Stream (L) No Catchment Name Parameter (C) X2 Y2 XY Lag (km) ( Y ) Parameter (C) (X) 1 Moy Pocket 69.05 1.63 4767.90 2.6569 112.5515 1.22 2 Bellbird 46.35 1.16 2148.32 1.3456 53.766 1.20 3 Kandanga 52.45 1.51 2751.00 2.2801 79.1995 1.21 4 Powerline 94.50 1.56 8930.25 2.4336 147.42 1.24 5 Mt. Piccaninny 68.10 1.08 4637.61 1.1664 73.548 1.22 6 Silver Valley 55.80 1.56 3113.64 2.4336 87.048 1.21 Gleneagle 127.90 7 2.03 16358.41 4.1209 259.637 1.27 8 Nash's Crossing 214.40 1.08 45967.36 1.1664 231.552 1.34 9 Zattas 225.90 1.21 51030.81 1.4641 273.339 1.34 10 Reeves 66.70 0.82 4448.89 0.6724 54.694 1.22 11 Mt.Dangar 55.60 0.72 3091.36 0.5184 40.032 1.21 12 Ida Creek 46.30 0.75 2143.69 0.5625 34.725 1.20 13 Tung Oil 85.80 0.93 7361.64 0.8649 79.794 1.23 14 Nerada 73.20 1.14 5358.24 1.2996 83.448 1.22 15 Central Mill 78.20 1.39 6115.24 1.9321 108.698 1.23 Total 1360.25 18.57 168224.37 24.9175 1719.452 18.57 Intercept of straight line (a) = 1.166333222 r2 = 0.014537468 Slope of straight line (b) = 7.90297E-04Standard error of estimate (Se) = 0.382282023 Correlation coefficient (r) = 0.120571422Estimated (t) = 0.438

334

7.5 Relationship between Lag Parameter (C) and the Catchment Shape Factor (A/L2). As described in Chapter 2, a reasonable number of researchers have considered A, L and a combination of A & L in their studies. The ratio of A and L2 represents the catchment shape factor. A low shape factor indicates that the catchment is long and narrow, whereas a high shape factor is for catchments that are rounded in shape. Therefore, it could be expected that lag times would be larger for long narrow catchments, so that the lag parameter C might increase as the shape factor of a catchment decreases.

Figure 7.8 shows the plot of lag parameter (C) versus the catchment shape factor (A/L2) for all seventeen values and the following information was found from the plot: • Although the points are scattered, except for Gympie and Cooran catchments which demonstrate larger C values, the remaining points are situated within a horizontal band in which C varies from 0.72 to 2.03 as shown in Figure 7.8; • The gradient of the best-fit straight line is just above unity with a negative slope; and • The results of the two tailed t-test shown in Table 7.8 have indicated that the gradient is not significantly different from zero at 5% level of significance.

To assess the behaviour of (A/L2) with C for fifteen catchments, excluding Gympie and Cooran, the Figure 7.9 was plotted and the following was found from it: • The points are scattered and their positions are along a thick horizontal band; • The gradient of the equation of the best-fit straight line is close to zero and it is almost horizontal; and • The gradient of that straight line is not significantly different from zero at 5% level of significance according to the results of a two tailed t-test as shown in Table 7.9.

While there is a slight trend for C to increase as the shape factor decreases, as might be expected, these findings revealed that the trend is not significant. Therefore, there is no substantial evidence to prove that the lag parameter (C) varies as the shape factor (A/L2) varies.

335

3.0 Cooran

2.5 Gympie

2.0 Gleneagle

Kandanga Moy Pocket Powerline 1.5 Silver Valley y = -1.0669x + 1.6126 Central Mill Zattas Nerada Bellbird Nash's Crossing Mt.Piccaninny

Lag Parameter (C) Parameter Lag 1.0 Tung Oil Reeves Mt.Dangar Ida Creek

0.5 t0.975 = 2.13

tCal = -0.49

0.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Rato of Catchment Area and Second Power of Length of Main Stream (A/L2)

Figure 7.8 – C versus (A/L2) of all seventeen catchments

Table 7.8 – t-test calculations for C versus (A/L2) of all seventeen catchments

Rato of Catchment Area and Second Lag Calculated No Catchment Name Power of Length Parameter (C) X2 Y2 XY Lag of Main Stream ( Y ) Parameter (C) (A/L2) (X)

1 Gympie 0.17 2.55 0.03 6.5025 0.433258801 1.43 2 Moy Pocket 0.17 1.63 0.03 2.6569 0.283830238 1.43 3 Bellbird 0.22 1.16 0.05 1.3456 0.258746999 1.37 4 Cooran 0.16 2.92 0.03 8.5264 0.480506329 1.44 5 Kandanga 0.06 1.51 0.00 2.2801 0.096429138 1.54 6 Powerline 0.19 1.56 0.04 2.4336 0.303005358 1.41 7 Mt. Piccaninny 0.25 1.08 0.06 1.1664 0.265231229 1.35 8 Silver Valley 0.19 1.56 0.04 2.4336 0.293718734 1.41 9 Gleneagle 0.33 2.03 0.11 4.1209 0.666411026 1.26 10 Nash's Crossing 0.15 1.08 0.02 1.1664 0.160741048 1.45 11 Zattas 0.14 1.21 0.02 1.4641 0.172901821 1.46 12 Reeves 0.23 0.82 0.05 0.6724 0.186217776 1.37 13 Mt.Dangar 0.26 0.72 0.07 0.5184 0.188151752 1.33 14 Ida Creek 0.29 0.75 0.08 0.5625 0.216943681 1.30 15 Tung Oil 0.13 0.93 0.02 0.8649 0.117406556 1.48 16 Nerada 0.15 1.14 0.02 1.2996 0.171890173 1.45 17 Central Mill 0.06 1.39 0.00 1.9321 0.088592827 1.54 Total 3.16 24.04 0.67 39.9464 4.384 24.04

2 Intercept of straight line (a) = 1.612570642 r = 0.015693504 Slope of straight line (b) = -1.06693E+00Standard error of estimate (Se) = 0.624906368 Correlation coefficient (r) = -0.125273716Estimated (t) = -0.489

336

2.5

2.0 Gleneagle

Moy Pocket

1.5 Kandanga Silver Valley Powerline Central Mill y = -0.3735x + 1.3084

Zattas Nerada Bellbird Mt.Piccaninny 1.0 Nash's Crossing Tung Oil

Lag Parameter (C) Parameter Lag Reeves Ida Creek Mt.Dangar

0.5 t0.975 = 2.16

tCal = -0.28

0.0 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Rato of Catchment Area and Second Power of Length of Main Stream (A/L2)

Figure 7.9 – C versus (A/L2) of fifteen catchments

Table 7.9 – t-test calculations for C versus (A/L2) of fifteen catchments

Rato of Catchment Area and Second Lag Calculated No Catchment Name Power of Length Parameter (C) X2 Y2 XY Lag of Main Stream ( Y ) Parameter (C) (A/L2) (X) 1 Moy Pocket 0.17 1.63 0.03 2.6569 0.283830238 1.24 2 Bellbird 0.22 1.16 0.05 1.3456 0.258746999 1.23 3 Kandanga 0.06 1.51 0.00 2.2801 0.096429138 1.28 4 Powerline 0.19 1.56 0.04 2.4336 0.303005358 1.24 5 Mt. Piccaninny 0.25 1.08 0.06 1.1664 0.265231229 1.22 6 Silver Valley 0.19 1.56 0.04 2.4336 0.293718734 1.24 7 Gleneagle 0.33 2.03 0.11 4.1209 0.666411026 1.19 8 Nash's Crossing 0.15 1.08 0.02 1.1664 0.160741048 1.25 9 Zattas 0.14 1.21 0.02 1.4641 0.172901821 1.26 10 Reeves 0.23 0.82 0.05 0.6724 0.186217776 1.22 11 Mt.Dangar 0.26 0.72 0.07 0.5184 0.188151752 1.21 12 Ida Creek 0.29 0.75 0.08 0.5625 0.216943681 1.20 13 Tung Oil 0.13 0.93 0.02 0.8649 0.117406556 1.26 14 Nerada 0.15 1.14 0.02 1.2996 0.171890173 1.25 15 Central Mill 0.06 1.39 0.00 1.9321 0.088592827 1.28 Total 2.83 18.57 0.61 24.9175 3.470 18.57 Intercept of straight line (a) = 1.308410443 r2 = 0.005878453 Slope of straight line (b) = -3.73518E-01Standard error of estimate (Se) = 0.383957859 Correlation coefficient (r) = -0.076671068Estimated (t) = -0.277

337

7.6 Relationship between Lag Parameter (C) and the Main Stream Length to the

Centroid from the Catchment’s Outlet (Lc).

As described in Chapter 2, some researchers have used the value of Lc as one of the variables in their studies of lag time. Therefore, Lc was selected for this study to investigate its influence on the lag parameter.

Figure 7.10 shows the plot of lag parameter (C) versus the main stream length to the centroid from the catchment’s outlet (Lc) for all seventeen values and the findings from Figure 7.10 can be illustrated in the following manner: • The equation of the best-fit straight line indicates a negative slope and the value of the gradient is equal to zero up to its 3rd decimal place; and • The gradient of the best-fit line in Figure 7.10 is not significantly different from zero at 5% level of significance according to the t-test results shown in Table 7.10.

With the intention of analysing the relationship between the lag parameter (C) and the main stream length to the centroid from the catchment’s outlet (Lc) for the fifteen catchments (disregarding two catchments with larger C values, Gympie and Cooran) the Figure 7.11 was plotted and the following were found: • The points are scattered and however, most of the points are in the left part of plot; • The gradient of the equation of the best-fit straight line is equal to zero up to its 3rd decimal place as in the previous case; and • The results of the two tailed t-test indicated in Table 7.11 clearly show that the gradient of the straight line in Figure 7.11 is not significantly different from zero at 5% level of significance.

The best-fit straight line in Figure 7.11 consisting of a slightly positive slope shows that the larger the Lc the higher the lag time and the shorter the Lc the shorter the lag time. This relationship agrees with the behaviour of natural catchments. However, the two tailed significance test results shown in Table 7.11 have clearly shown that the gradient of the best-fit line is not significantly different from zero and also the value of that gradient is equal to zero up to its 3rd decimal place. According to the findings from Figure 7.11, there is not enough evidence to insist that the lag parameter (C) increases as the length of the main stream (Lc) increases.

338

Figure 7.10 – C versus Lc of all seventeen catchments

3.0 Cooran

2.5 Gympie

2.0 Gleneagle

Moy Pocket y = -0.0006x + 1.4408 1.5 Kandanga Silver Valley Powerline Central Mill Zattas Bellbird Nerada Nash's Crossing Mt.Piccaninny

Lag Parameter (C) 1.0 Tung Oil Ida Creek Reeves Mt.Dangar

0.5 t0.975 = 2.13

tCal = -0.14

0.0 0 25 50 75 100 125 150

Main Stream Length to the Centroid of Catchment from Outlet (Lc) - km

Table 7.10 – t-test calculations for C versus Lc of all seventeen catchments

Main Stream Length to the Centroid of Lag Calculated No Catchment Name Catchment from Outlet Parameter (C) X2 Y2 XY Lag (LC) (km) ( Y ) Parameter (C) (X) 1 Gympie 59.50 2.55 3540.25 6.5025 151.725 1.41 2 Moy Pocket 37.40 1.63 1398.76 2.6569 60.962 1.42 3 Bellbird 16.20 1.16 262.44 1.3456 18.792 1.43 4 Cooran 18.40 2.92 338.56 8.5264 53.728 1.43 5 Kandanga 21.70 1.51 470.89 2.2801 32.767 1.43 6 Powerline 43.70 1.56 1909.69 2.4336 68.172 1.42 7 Mt. Piccaninny 27.40 1.08 750.76 1.1664 29.592 1.42 8 Silver Valley 22.70 1.56 515.29 2.4336 35.412 1.43 9 Gleneagle 65.70 2.03 4316.49 4.1209 133.371 1.40 10 Nash's Crossing 133.10 1.08 17715.61 1.1664 143.748 1.36 11 Zattas 139.50 1.21 19460.25 1.4641 168.795 1.36 12 Reeves 31.80 0.82 1011.24 0.6724 26.076 1.42 13 Mt.Dangar 24.80 0.72 615.04 0.5184 17.856 1.43 14 Ida Creek 21.30 0.75 453.69 0.5625 15.975 1.43 15 Tung Oil 44.50 0.93 1980.25 0.8649 41.385 1.41 16 Nerada 33.80 1.14 1142.44 1.2996 38.532 1.42 17 Central Mill 37.10 1.39 1376.41 1.9321 51.569 1.42 Total 778.60 24.04 57258.06 39.9464 1088.457 24.04 Intercept of straight line (a) = 1.440783551 r2 = 0.001230291 Slope of straight line (b) = -5.82225E-04Standard error of estimate (Se) = 0.629480754 Correlation coefficient (r) = -0.035075511Estimated (t) = -0.136

339

2.5

2.0 Gleneagle

Moy Pocket Silver Valley Powerline 1.5 Kandanga y = 0.00075x + 1.2028 Central Mill

Zattas Bellbird Nerada 1.0 Mt.Piccaninny Nash's Crossing Tung Oil

Lag Parameter (C) Parameter Lag Reeves Ida Creek Mt.Dangar

0.5 t0.975 = 2.16

tCal = 0.28

0.0 0 25 50 75 100 125 150

Main Stream Length to the Centroid of Catchment from Outlet (Lc) - km

Figure 7.11 – C versus Lc of fifteen catchments

Table 7.11 – t-test calculations for C versus Lc of fifteen catchments

Main Stream Length to the Centroid of Lag Calculated No Catchment Name Catchment from Outlet Parameter (C) X2 Y2 XY Lag (LC) (km) ( Y ) Parameter (C) (X) 1 Moy Pocket 37.40 1.63 1398.76 2.6569 60.962 1.23 2 Bellbird 16.20 1.16 262.44 1.3456 18.792 1.22 3 Kandanga 21.70 1.51 470.89 2.2801 32.767 1.22 4 Powerline 43.70 1.56 1909.69 2.4336 68.172 1.24 5 Mt. Piccaninny 27.40 1.08 750.76 1.1664 29.592 1.22 6 Silver Valley 22.70 1.56 515.29 2.4336 35.412 1.22 7 Gleneagle 65.70 2.03 4316.49 4.1209 133.371 1.25 8 Nash's Crossing 133.10 1.08 17715.61 1.1664 143.748 1.30 9 Zattas 139.50 1.21 19460.25 1.4641 168.795 1.31 10 Reeves 31.80 0.82 1011.24 0.6724 26.076 1.23 11 Mt.Dangar 24.80 0.72 615.04 0.5184 17.856 1.22 12 Ida Creek 21.30 0.75 453.69 0.5625 15.975 1.22 13 Tung Oil 44.50 0.93 1980.25 0.8649 41.385 1.24 14 Nerada 33.80 1.14 1142.44 1.2996 38.532 1.23 15 Central Mill 37.10 1.39 1376.41 1.9321 51.569 1.23 Total 700.70 18.57 53379.25 24.9175 883.004 18.57 Intercept of straight line (a) = 1.202847382 r2 = 0.006064907 Slope of straight line (b) = 7.52518E-04Standard error of estimate (Se) = 0.38392185 Correlation coefficient (r) = 0.077877516Estimated (t) = 0.282

340

7.7 Relationship between Lag Parameter (C) and the Ratio of Main Stream

Length to Centroid and Main Stream Length (Lc/L).

The shape of the catchment is represented by the ratio of (Lc/L). It means that for a larger (Lc/L) most of the catchment’s area is located near the headwaters. It could be expected that catchments with large (Lc/L) will have a larger lag parameter C.

Figure 7.12 shows the plot of lag parameter (C) versus the ratio of main stream length to centroid and main stream length (Lc/L) and the following were observed from it: • All points are scattered significantly; • The best-fit straight line shows a positive gradient with a value of 1.6213; • It is interesting to note that the majority of the points in Figure 7.12 are within a horizontal band except for the points of Gympie and Cooran catchments; and • The results of the two tailed t-test shown in Table 7.12 have indicated that the gradient of the best-fit straight line is not significantly different from zero at 5% level of significance.

To test the effect of (Lc/L) on C for fifteen catchments (excluding two catchments Cooran and Gympie with larger C values) Figure 7.13 was plotted and it illustrates the following: • All the points are scattered and distributed within the plot area quite well; • Except for the Gleneagle catchment, all the other points are located on a horizontal band; • Although the slope of the best-fit straight line is positive its gradient is much less than that in Figure 7.12 and is closer to zero; and • Once again the gradient of the best-fit line is not significantly different from zero at 5% level of significance.

The plot in Figure 7.14 is made by eliminating the catchment with a lag parameter of 2.03 (Gleneagle) and the findings from it are listed below: • The points are distributed well enough to cover the entire plot area; • The best-fit straight line is close to a horizontal line and its gradient is -0.16. This value shows a considerable reduction in the gradient compared to the value obtained for all seventeen catchments in Figure 7.12; and

341

• Even for this plot, the gradient of the best-fit line is not significantly different from zero at 5% level of significance, according to the two tailed t-test results shown in Table 7.14.

For all seventeen catchments, there is a slight trend for C to increase as (Lc/L) increases, as expected. However, the result depends on the inclusion of the Gympie and Cooran catchments and the gradient of the fitted straight line is not significantly different from zero. This lack of significance is confined when Gympie and Cooran are omitted from the analysis.

The foregoing findings indicate that there is no real trend for the lag parameter (C) to vary as (Lc/L) varies.

342

3.0 Cooran

2.5 Gympie

2.0 Gleneagle y = 1.6213x + 0.6319 Moy Pocket Silver Valley Powerline 1.5 Kandanga Central Mill Zattas Nerada Nash's Crossing Bellbird Mt.Piccaninny

Lag Parameter (C) Parameter Lag 1.0 Tung Oil Reeves Mt.Dangar Ida Creek

0.5 t0.975 = 2.13

tCal = 0.79

0.0 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

Ratio of Main Stream Length to the Centroid and Main Stream Length (Lc/L)

Figure 7.12 – C versus (Lc/L) of all seventeen catchments

Table 7.12 – t-test calculations for C versus (Lc/L) of all seventeen catchments

Ratio of Main Stream Length to Lag Calculated the Centroid and No Catchment Name Parameter (C) 2 2 XY Lag Main Stream X Y ( Y ) Parameter (C) Length (Lc/L) (X)

1 Gympie 0.45 2.55 0.21 6.5025 1.157322654 1.37 2 Moy Pocket 0.54 1.63 0.29 2.6569 0.882867487 1.51 3 Bellbird 0.35 1.16 0.12 1.3456 0.405436893 1.20 4 Cooran 0.58 2.92 0.34 8.5264 1.700253165 1.58 5 Kandanga 0.41 1.51 0.17 2.2801 0.624728313 1.30 6 Powerline 0.46 1.56 0.21 2.4336 0.721396825 1.38 7 Mt. Piccaninny 0.40 1.08 0.16 1.1664 0.434537445 1.28 8 Silver Valley 0.41 1.56 0.17 2.4336 0.634623656 1.29 9 Gleneagle 0.51 2.03 0.26 4.1209 1.042775606 1.46 10 Nash's Crossing 0.62 1.08 0.39 1.1664 0.670466418 1.64 11 Zattas 0.62 1.21 0.38 1.4641 0.747211155 1.63 12 Reeves 0.48 0.82 0.23 0.6724 0.390944528 1.40 13 Mt.Dangar 0.45 0.72 0.20 0.5184 0.321151079 1.36 14 Ida Creek 0.46 0.75 0.21 0.5625 0.345032397 1.38 15 Tung Oil 0.52 0.93 0.27 0.8649 0.482342657 1.47 16 Nerada 0.46 1.14 0.21 1.2996 0.526393443 1.38 17 Central Mill 0.47 1.39 0.23 1.9321 0.659450128 1.40 Total 8.20 24.04 4.05 39.9464 11.747 24.04 Intercept of straight line (a) = 0.631864616 r2 = 0.040303706 Slope of straight line (b) = 1.62129E+00Standard error of estimate (Se) = 0.617044782 Correlation coefficient (r) = 0.200757829Estimated (t) = 0.794

343

2.3

2.0 Gleneagle

1.8 Moy Pocket Silver Valley Powerline 1.5 Kandanga Central Mill y = 0.2204x + 1.1327 1.3 Zattas Bellbird Nerada Mt.Piccaninny Nash's Crossing 1.0 Tung Oil Reeves

Lag Parameter (C) 0.8 Ida Creek Mt.Dangar 0.5

t0.975 = 2.16 0.3 tCal = 0.16

0.0 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

Ratio of Main Stream Length to the Centroid and Main Stream Length (Lc/L)

Figure 7.13 – C versus (Lc/L) of fifteen catchments

Table 7.13 – t-test calculations for C versus (Lc/L) fifteen catchments

Ratio of Main Stream Length to Lag Calculated the Centroid and No Catchment Name Parameter (C) 2 2 XY Lag Main Stream X Y ( Y ) Parameter (C) Length (Lc/L) (X) 1 Moy Pocket 0.54 1.63 0.29 2.6569 0.882867487 1.25 2 Bellbird 0.35 1.16 0.12 1.3456 0.405436893 1.21 3 Kandanga 0.41 1.51 0.17 2.2801 0.624728313 1.22 4 Powerline 0.46 1.56 0.21 2.4336 0.721396825 1.23 5 Mt. Piccaninny 0.40 1.08 0.16 1.1664 0.434537445 1.22 6 Silver Valley 0.41 1.56 0.17 2.4336 0.634623656 1.22 7 Gleneagle 0.51 2.03 0.26 4.1209 1.042775606 1.25 8 Nash's Crossing 0.62 1.08 0.39 1.1664 0.670466418 1.27 9 Zattas 0.62 1.21 0.38 1.4641 0.747211155 1.27 10 Reeves 0.48 0.82 0.23 0.6724 0.390944528 1.24 11 Mt.Dangar 0.45 0.72 0.20 0.5184 0.321151079 1.23 12 Ida Creek 0.46 0.75 0.21 0.5625 0.345032397 1.23 13 Tung Oil 0.52 0.93 0.27 0.8649 0.482342657 1.25 14 Nerada 0.46 1.14 0.21 1.2996 0.526393443 1.23 15 Central Mill 0.47 1.39 0.23 1.9321 0.659450128 1.24 Total 7.17 18.57 3.50 24.9175 8.889 18.57 Intercept of straight line (a) = 1.132725347 r2 = 0.002018284 Slope of straight line (b) = 2.20358E-01Standard error of estimate (Se) = 0.384702589 Correlation coefficient (r) = 0.04492532Estimated (t) = 0.162

344

1.8

Silver Valley Moy Pocket Powerline 1.5 Kandanga

Central Mill 1.3 y = -0.163x + 1.2589 Zattas Bellbird Nerada Mt.Piccaninny Nash's Crossing 1.0 Tung Oil Reeves 0.8 Mt.Dangar Ida Creek Lag Parameter (C) 0.5

t = 2.18 0.3 0.975 tCal = -0.14

0.0 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

Ratio of Main Stream Length to the Centroid and Main Stream Length (Lc/L)

Figure 7.14 – C versus (Lc/L) of fourteen catchments

Table 7.14 – t-test calculations for C versus (Lc/L) fourteen catchments

Ratio of Main Stream Length to Lag Calculated the Centroid and No Catchment Name Parameter (C) 2 2 XY Lag Main Stream X Y ( Y ) Parameter (C) Length (Lc/L) (X) 1 Moy Pocket 0.54 1.63 0.29 2.6569 0.882867487 1.17 2 Bellbird 0.35 1.16 0.12 1.3456 0.405436893 1.20 3 Kandanga 0.41 1.51 0.17 2.2801 0.624728313 1.19 4 Powerline 0.46 1.56 0.21 2.4336 0.721396825 1.18 5 Mt. Piccaninny 0.40 1.08 0.16 1.1664 0.434537445 1.19 6 Silver Valley 0.41 1.56 0.17 2.4336 0.634623656 1.19 7 Nash's Crossing 0.62 1.08 0.39 1.1664 0.670466418 1.16 8 Zattas 0.62 1.21 0.38 1.4641 0.747211155 1.16 9 Reeves 0.48 0.82 0.23 0.6724 0.390944528 1.18 10 Mt.Dangar 0.45 0.72 0.20 0.5184 0.321151079 1.19 11 Ida Creek 0.46 0.75 0.21 0.5625 0.345032397 1.18 12 Tung Oil 0.52 0.93 0.27 0.8649 0.482342657 1.17 13 Nerada 0.46 1.14 0.21 1.2996 0.526393443 1.18 14 Central Mill 0.47 1.39 0.23 1.9321 0.659450128 1.18 Total 6.65 16.54 3.24 20.7966 7.847 16.54 Intercept of straight line (a) = 1.258904921 r2 = 0.001667045 Slope of straight line (b) = -1.63047E-01Standard error of estimate (Se) = 0.323223091 Correlation coefficient (r) = -0.040829464Estimated (t) = -0.142

345

7.8 Relationship between Lag Parameter (C) and the Number of Rain Days per Year (No. RD/Year). The real effect of the climate of the catchment on the lag parameter is not possible to be measured directly. However, the climate of the catchment might be expected to have an effect on the lag parameter. For example, a wetter climate could lead to greater vegetation growth, possibly reducing flow velocities and increasing lag times. Conversely, the wetter soil might lead to more rapid runoff and that could cause smaller lag times. Several measures of climate have been used in this study, as described in the following sections.

The Figure 7.15 shows the plot of lag parameter (C) versus the number of rain days per year (No.RD/Year of all seventeen catchments and the finding of the plot can be described in the following manner: • The plot demonstrates considerable scatter; • Although the slope of the best-fit straight line is positive, the value of its gradient as shown in the equation of Figure 7.15, is almost zero; and • The significant t-test results of Table 7.15 demonstrate that the gradient of the best-fit straight line is not significantly different from zero at 5% level of significance.

To find out the effect of the number of rain days per year (No.RD/year) on the lag parameter of the fifteen catchments other than Gympie and Cooran which show higher C values, the Figure 7.16 was plotted and its findings can be summarised as: • The points are very well scattered and cover the entire plot area; • Although the slope of the best-fit straight line is negative, the value of the gradient is almost zero, as in the previous case, as shown in Figure 7.16; and • The values of the significant two tailed t-test results shown in Table 7.16 reveal that the gradient of the best-fit straight line is not significantly different from zero at 5% level of significance.

Therefore, all the above described findings revealed that there is no real trend for lag parameter (C) to vary as the number of rain days per year (No.RD/Year) varies.

346

3.0 Cooran

2.5 Gympie

2.0 Gleneagle

Moy Pocket y = 0.0011x + 1.2963 Powerline Silver Valley 1.5 Kandanga Central Mill Zattas Bellbird Nerada Mt.Piccaninny

Lag Parameter (C) 1.0 Nash's Crossing Tung Oil Reeves Ida Creek Mt.Dangar

0.5 t0.975 = 2.13

tCal = 0.33

0.0 40 60 80 100 120 140 160 180 200 220 Number of Rain Days per Year (No.RD/Year)

Figure 7.15 – C versus (No.RD/yr) of all seventeen catchments

Table 7.15 – t-test calculations for C versus (No. RD/yr) of all seventeen catchments

Number of Rain Lag Calculated Days per Year No Catchment Name Parameter (C) X2 Y2 XY Lag (No.RD/Year) ( Y ) Parameter (C) (X) 1 Gympie 117 2.55 13689.00 6.5025 298.35 1.42 2 Moy Pocket 118 1.63 13924.00 2.6569 192.34 1.43 3 Bellbird 116 1.16 13456.00 1.3456 134.56 1.42 4 Cooran 129 2.92 16641.00 8.5264 376.68 1.44 5 Kandanga 100 1.51 10000.00 2.2801 151.00 1.41 6 Powerline 62 1.56 3844.00 2.4336 96.72 1.36 7 Mt. Piccaninny 76 1.08 5776.00 1.1664 82.08 1.38 8 Silver Valley 65 1.56 4225.00 2.4336 101.4 1.37 9 Gleneagle 70 2.03 4900.00 4.1209 142.1 1.37 10 Nash's Crossing 114 1.08 12996.00 1.1664 123.12 1.42 11 Zattas 114 1.21 12996.00 1.4641 137.94 1.42 12 Reeves 43 0.82 1849.00 0.6724 35.26 1.34 13 Mt.Dangar 68 0.72 4624.00 0.5184 48.96 1.37 14 Ida Creek 68 0.75 4624.00 0.5625 51.00 1.37 15 Tung Oil 183 0.93 33489.00 0.8649 170.19 1.50 16 Nerada 209 1.14 43681.00 1.2996 238.26 1.52 17 Central Mill 183 1.39 33489.00 1.9321 254.37 1.50 Total 1835.00 24.04 234203.00 39.9464 2634.330 24.04 Intercept of straight line (a) = 1.296338107 r2 = 0.007228595 Slope of straight line (b) = 1.09115E-03Standard error of estimate (Se) = 0.627587673 Correlation coefficient (r) = 0.085021143Estimated (t) = 0.330

347

2.5

2.0 Gleneagle

Moy Pocket 1.5 Powerline Silver Valley Kandanga y = -0.0002x + 1.2615 Central Mill

Zattas Bellbird Nerada 1.0 Mt.Piccaninny Nash's Crossing Tung Oil

Lag Parameter (C) Reeves Ida Creek Mt.Dangar 0.5 t0.975 = 2.16

tCal = -0.11

0.0 40 60 80 100 120 140 160 180 200 220 Number of Rain Days per Year (No.RD/Year)

Figure 7.16 – C versus (No.RD/yr) of fifteen catchments

Table 7.16 – t-test calculations for C versus (No.RD/yr) of fifteen catchments

Number of Rain Lag Calculated Days per Year No Catchment Name Parameter (C) X2 Y2 XY Lag (No.RD/Year) ( Y ) Parameter (C) (X) 1 Moy Pocket 118 1.63 13924.00 2.6569 192.34 1.24 2 Bellbird 116 1.16 13456.00 1.3456 134.56 1.24 3 Kandanga 100 1.51 10000.00 2.2801 151.00 1.24 4 Powerline 62 1.56 3844.00 2.4336 96.72 1.25 5 Mt. Piccaninny 76 1.08 5776.00 1.1664 82.08 1.24 6 Silver Valley 65 1.56 4225.00 2.4336 101.4 1.25 7 Gleneagle 70 2.03 4900.00 4.1209 142.1 1.25 8 Nash's Crossing 114 1.08 12996.00 1.1664 123.12 1.24 9 Zattas 114 1.21 12996.00 1.4641 137.94 1.24 10 Reeves 43 0.82 1849.00 0.6724 35.26 1.25 11 Mt.Dangar 68 0.72 4624.00 0.5184 48.96 1.25 Ida Creek 68 12 0.75 4624.00 0.5625 51.00 1.25 13 Tung Oil 183 0.93 33489.00 0.8649 170.19 1.22 14 Nerada 209 1.14 43681.00 1.2996 238.26 1.22 15 Central Mill 183 1.39 33489.00 1.9321 254.37 1.22 Total 1589.00 18.57 203873.00 24.9175 1959.300 18.57 Intercept of straight line (a) = 1.261490452 r2 = 0.000906618 Slope of straight line (b) = -2.21747E-04Standard error of estimate (Se) = 0.384916793 Correlation coefficient (r) = -0.030110092Estimated (t) = -0.109

348

7.9 Relationship between Lag Parameter (C) and the Mean Annual Rainfall

(ARMean). Since the amount of rainfall depends on many factors of a catchment, such as its location, topographical features, temperature, etc., the mean annual rainfall can be treated as a unique characteristic, which is purely designated to a particular catchment area. Therefore, mean annual rainfall has been considered as a physical characteristic of catchments and it is selected in this study.

Figure 7.17 shows the plot of lag parameter (C) versus the mean annual rainfall

(ARMean) for all seventeen catchments and its findings can be summarised as follows: • Although the points are fairly scattered, the two points for Gympie and Cooran catchments are well away from the remaining points because they contain larger lag parameters; • Although the slope of the best-fit straight line is negative, the value of its gradient, as shown in the equation of Figure 7.17, is equal to zero up to its 4th decimal place; and • According to the two tailed t-test results shown in Table 7.17 the gradient of the best-fit straight line is not significantly different from zero at 5% level of significance.

The behaviour of the fifteen catchments (disregarding Gympie and Cooran) is examined by plotting Figure 7.18 and its findings are: • The points are very well scattered to cover most parts of the plot area; • Although the slope of the best-fit straight line is negative as in the previous case, the value of the gradient is equal to zero up to its 4th decimal place as well; and • The results of the two tailed t-test revealed that the gradient of the best-fit straight line is not significantly different from zero at 5% level of significance.

Therefore, all the findings from the plots of Figures 7.17 and 7.18 as well as the Tables 7.17 and 7.18 explicitly describe that there is no real variation of the lag parameter with variation of the mean annual rainfall.

349

3.0 Cooran

2.5 Gympie

2.0 Gleneagle

Silver Valley Powerline Moy Pocket y = -0.000088x + 1.5554 1.5 Kandanga Central Mill Zattas Bellbird Mt.Piccaninny Nash's Crossing Nerada

Lag Parameter (C) 1.0 Tung Oil Reeves Ida Creek Mt.Dangar 0.5 t0.975 = 2.13

tCal = -0.61

0.0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400 4800

Mean Annual Rainfall (ARMean) - mm

Figure 7.17 – C versus (ARMean) of all seventeen catchments

Table 7.17 – t-test calculations for C versus (ARMean) of all seventeen catchments

Mean Annual Lag Calculated Rainfall (ARMean) No Catchment Name Parameter (C) X2 Y2 XY Lag (mm) ( Y ) Parameter (C) (X) 1 Gympie 1132 2.55 1282329.76 6.5025 2887.62 1.46 2 Moy Pocket 1359 1.63 1847696.49 2.6569 2215.659 1.44 3 Bellbird 1240 1.16 1538344.09 1.3456 1438.748 1.45 4 Cooran 1354 2.92 1831962.25 8.5264 3952.22 1.44 5 Kandanga 1186 1.51 1406121.64 2.2801 1790.56 1.45 6 Powerline 1173 1.56 1375459.84 2.4336 1829.568 1.45 7 Mt. Piccaninny 877 1.08 769479.84 1.1664 947.376 1.48 8 Silver Valley 875 1.56 765800.01 2.4336 1365.156 1.48 9 Gleneagle 823 2.03 677822.89 4.1209 1671.299 1.48 10 Nash's Crossing 1842 1.08 3392227.24 1.1664 1989.144 1.39 11 Zattas 1842 1.21 3392227.24 1.4641 2228.578 1.39 12 Reeves 812 0.82 659993.76 0.6724 666.168 1.48 13 Mt.Dangar 862 0.72 743733.76 0.5184 620.928 1.48 14 Ida Creek 862 0.75 743733.76 0.5625 646.80 1.48 15 Tung Oil 3326 0.93 11061610.81 0.8649 3093.087 1.26 16 Nerada 4518 1.14 20410516.84 1.2996 5150.292 1.16 17 Central Mill 3326 1.39 11061610.81 1.9321 4623.001 1.26 Total 27410.10 24.04 62960671.03 39.9464 37116.202 24.04 Intercept of straight line (a) = 1.555448265 r2 = 0.024228378 Slope of straight line (b) = -8.76546E-05Standard error of estimate (Se) = 0.622191203 Correlation coefficient (r) = -0.155654675Estimated (t) = -0.610

350

2.5

2.0 Gleneagle

Powerline Moy Pocket Silver Valley 1.5 Kandanga Central Mill Zattas Nerada Mt.Piccaninny Bellbird Nash's Crossing 1.0 y = -0.000032x + 1.2903 Tung Oil Reeves Lag Parameter (C) Ida Creek Mt.Dangar 0.5 t = 2.16 0.975 tCal = -0.35

0.0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400 4800

Mean Annual Rainfall (ARMean) - mm

Figure 7.18 – C versus (ARMean) of fifteen catchments

Table 7.18 – t-test calculations for C versus (ARMean) of fifteen catchments

Mean Annual Lag Calculated Rainfall (AR ) No Catchment Name Mean Parameter (C) X2 Y2 XY Lag (mm) ( Y ) Parameter (C) (X)

1 Moy Pocket 1359 1.63 1847696.49 2.6569 2215.659 1.25 2 Bellbird 1240 1.16 1538344.09 1.3456 1438.748 1.25 3 Kandanga 1186 1.51 1406121.64 2.2801 1790.56 1.25 4 Powerline 1173 1.56 1375459.84 2.4336 1829.568 1.25 5 Mt. Piccaninny 877 1.08 769479.84 1.1664 947.376 1.26 Silver Valley 6 875 1.56 765800.01 2.4336 1365.156 1.26 7 Gleneagle 823 2.03 677822.89 4.1209 1671.299 1.26 8 Nash's Crossing 1842 1.08 3392227.24 1.1664 1989.144 1.23 9 Zattas 1842 1.21 3392227.24 1.4641 2228.578 1.23 10 Reeves 812 0.82 659993.76 0.6724 666.168 1.26 11 Mt.Dangar 862 0.72 743733.76 0.5184 620.928 1.26 12 Ida Creek 862 0.75 743733.76 0.5625 646.80 1.26 13 Tung Oil 3326 0.93 11061610.81 0.8649 3093.087 1.19 14 Nerada 4518 1.14 20410516.84 1.2996 5150.292 1.15 15 Central Mill 3326 1.39 11061610.81 1.9321 4623.001 1.19 Total 24924.20 18.57 59846379.02 24.9175 30276.362 18.57 Intercept of straight line (a) = 1.290267775 r2 = 0.009460399 Slope of straight line (b) = -3.14560E-05Standard error of estimate (Se) = 0.38326551 Correlation coefficient (r) = -0.097264585Estimated (t) = -0.352

351

7.10 Relationship between Lag Parameter (C) and the 2Year-72hour Rainfall 2 Intensity Pattern of AR&R ( I72). As described in the previous section, the 2year-ARI, 72-hour rainfall intensity pattern can be treated as a physical characteristic confined to a particular catchment according to the Australian Rainfall and Runoff publication. Figure 7.19 shows the plot of lag 2 parameter (C) versus the 2year-72hour rainfall intensity pattern of AR&R ( I72) and it illustrates the following: • All points are scattered significantly. Apart from the points of Gympie and Cooran, the positions of the other catchments are distributed within a horizontal band of the plot area; • The best-fit straight line has shown a negative gradient with a value of 0.1106 as shown in Figure 7.19 and it is reasonably greater than zero; and • The results of a two-tailed t-test, shown in Table 7.19 indicated that the gradient of the best-fit straight line is not significantly different from zero at 5% level of significance.

2 To test the effect of ( I72) on C for fifteen catchments, whose points are within a horizontal band, Figure 7.20 was plotted and its findings are listed as: • All the points are scattered and distributed within the plot area fairly well. Apart from Gleneagle catchment, other points are located on a horizontal band; • Although the slope of the best-fit straight line is negative its gradient is much less than that shown in Figure 7.19 and also it is very close to zero; and • The results of the two tailed t-test, shown in Table 7.20, indicate that the gradient of the best-fit straight line is not significantly different from zero at 5% level of significance.

The plot in Figure 7.21 was made by eliminating the Gleneagle catchment in Figure 7.20 to study the behaviour of the remaining catchments and its findings can be given as: • The points are distributed fairly well to cover the entire plot area; • Although the slope of the best-fit straight line is negative, its value is much less than the values for other two cases; and

352

• Once again the gradient of the best-fit straight is not significantly different from zero at 5% level of significance, according to the t-test results shown in Table 7.21. The discussions related to the findings from Figures and Tables 7.19, 7.20 and 7.21 2 have indicated that there is no real trend for the lag parameter (C) to vary as ( I72) varies.

3.0 Cooran

2.5 Gympie

2.0 Gleneagle

Silver Valley Moy Pocket 1.5 Powerline Kandanga y = -0.1106x + 1.8391 Central Mill Zattas Bellbird Nerada Mt.Piccaninny Nash's Crossing

Lag Parameter (C) 1.0 Tung Oil Reeves Ida Creek Mt.Dangar 0.5 t0.975 = 2.13

tCal = -1.16

0.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 2 2 year 72 Hour Rainfall Intensity Pattern of AR&R ( I72hr) - mm/hr

2 Figure 7.19 – C versus ( I72) of all seventeen catchments

2 Table 7.19 – t-test calculations for C versus ( I72) of all seventeen catchments

2 year 72 Hour Rainfall Intensity Lag Calculated Pattern of AR&R No Catchment Name Parameter (C) X2 Y2 XY Lag (2I ) 72hr ( Y ) Parameter (C) (mm/hr) (X) 1 Gympie 2.88 2.55 8.29 6.5025 7.344 1.52 2 Moy Pocket 3.00 1.63 9.00 2.6569 4.89 1.51 3 Bellbird 3.00 1.16 9.00 1.3456 3.48 1.51 4 Cooran 3.38 2.92 11.42 8.5264 9.8696 1.47 5 Kandanga 2.70 1.51 7.29 2.2801 4.08 1.54 6 Powerline 3.38 1.56 11.42 2.4336 5.2728 1.47 7 Mt. Piccaninny 2.88 1.08 8.29 1.1664 3.1104 1.52 8 Silver Valley 2.45 1.56 6.00 2.4336 3.822 1.57 9 Gleneagle 2.30 2.03 5.29 4.1209 4.669 1.58 10 Nash's Crossing 4.25 1.08 18.06 1.1664 4.59 1.37 11 Zattas 4.55 1.21 20.70 1.4641 5.5055 1.34 12 Reeves 3.00 0.82 9.00 0.6724 2.46 1.51 13 Mt.Dangar 3.38 0.72 11.42 0.5184 2.4336 1.47 14 Ida Creek 3.45 0.75 11.90 0.5625 2.59 1.46 15 Tung Oil 6.70 0.93 44.89 0.8649 6.231 1.10 16 Nerada 7.50 1.14 56.25 1.2996 8.55 1.01 17 Central Mill 6.55 1.39 42.90 1.9321 9.1045 1.11 Total 65.35 24.04 291.15 39.9464 87.997 24.04 Intercept of straight line (a) = 1.839100749 r2 = 0.082031865 Slope of straight line (b) = -1.10554E-01Standard error of estimate (Se) = 0.603480967 Correlation coefficient (r) = -0.286412055Estimated (t) = -1.158

353

2.3

2.0 Gleneagle

1.8 Silver Valley Moy Pocket Powerline 1.5 Kandanga Central Mill 1.3 Zattas y = -0.0613x + 1.4795 Bellbird Nerada Nash's Crossing Mt.Piccaninny 1.0 Tung Oil Reeves Ida Creek

Lag Parameter (C) 0.8 Mt.Dangar

0.5

t0.975 = 2.16 0.3 tCal = -1.03

0.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 2 2 year 72 Hour Rainfall Intensity Pattern of AR&R ( I72hr) - mm/hr

2 Figure 7.20 – C versus ( I72) of fifteen catchments

2 Table 7.20 – t-test calculations for C versus ( I72) of fifteen catchments

2 year 72 Hour Rainfall Intensity Lag Calculated Pattern of AR&R No Catchment Name Parameter (C) X2 Y2 XY Lag (2I ) 72hr ( Y ) Parameter (C) (mm/hr) (X) 1 Moy Pocket 3.00 1.63 9.00 2.6569 4.89 1.30 2 Bellbird 3.00 1.16 9.00 1.3456 3.48 1.30 3 Kandanga 2.70 1.51 7.29 2.2801 4.077 1.31 4 Powerline 3.38 1.56 11.42 2.4336 5.2728 1.27 5 Mt. Piccaninny 2.88 1.08 8.29 1.1664 3.1104 1.30 6 Silver Valley 2.45 1.56 6.00 2.4336 3.822 1.33 7 Gleneagle 2.30 2.03 5.29 4.1209 4.669 1.34 8 Nash's Crossing 4.25 1.08 18.06 1.1664 4.59 1.22 9 Zattas 4.55 1.21 20.70 1.4641 5.5055 1.20 10 Reeves 3.00 0.82 9.00 0.6724 2.46 1.30 11 Mt.Dangar 3.38 0.72 11.42 0.5184 2.4336 1.27 12 Ida Creek 3.45 0.75 11.90 0.5625 2.5875 1.27 13 Tung Oil 6.70 0.93 44.89 0.8649 6.231 1.07 14 Nerada 7.50 1.14 56.25 1.2996 8.55 1.02 15 Central Mill 6.55 1.39 42.90 1.9321 9.1045 1.08 Total 59.09 18.57 271.44 24.9175 70.783 18.57 Intercept of straight line (a) = 1.479504749 r2 = 0.075370655 Slope of straight line (b) = -6.13060E-02Standard error of estimate (Se) = 0.370294834 Correlation coefficient (r) = -0.274537166Estimated (t) = -1.029

354

1.8

Moy Pocket Silver Valley 1.6 Powerline Kandanga 1.4 Central Mill

Zattas 1.2 y = -0.0274x + 1.2924 Bellbird Nerada Mt.Piccaninny Nash's Crossing 1.0 Tung OIl

0.8 Reeves Ida Creek Mt.Dangar

Lag ParameterLag (C) 0.6

0.4

t0.975 = 2.18 0.2 tCal = -0.51

0.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 2 2 year 72 Hour Rainfall Intensity Pattern of AR&R ( I72hr) - mm/hr

2 Figure 7.21 – C versus ( I72) of fourteen catchments

2 Table 7.21 – t-test calculations for C versus ( I72) of fourteen catchments

2 year 72 Hour Rainfall Intensity Lag Calculated Pattern of AR&R No Catchment Name Parameter (C) X2 Y2 XY Lag (2I ) 72hr ( Y ) Parameter (C) (mm/hr) (X) 1 Moy Pocket 3.00 1.63 9.00 2.6569 4.89 1.21 2 Bellbird 3.00 1.16 9.00 1.3456 3.48 1.21 3 Kandanga 2.70 1.51 7.29 2.2801 4.077 1.22 4 Powerline 3.38 1.56 11.42 2.4336 5.2728 1.20 5 Mt. Piccaninny 2.88 1.08 8.29 1.1664 3.1104 1.21 6 Silver Valley 2.45 1.56 6.00 2.4336 3.822 1.23 7 Nash's Crossing 4.25 1.08 18.06 1.1664 4.59 1.18 8 Zattas 4.55 1.21 20.70 1.4641 5.5055 1.17 9 Reeves 3.00 0.82 9.00 0.6724 2.46 1.21 10 Mt.Dangar 3.38 0.72 11.42 0.5184 2.4336 1.20 11 Ida Creek 3.45 0.75 11.90 0.5625 2.5875 1.20 12 Tung Oil 6.70 0.93 44.89 0.8649 6.231 1.11 13 Nerada 7.50 1.14 56.25 1.2996 8.55 1.09 14 Central Mill 6.55 1.39 42.90 1.9321 9.1045 1.11 Total 56.79 16.54 266.15 20.7966 66.114 16.54

2 Intercept of straight line (a) = 1.292418929 r = 0.021331735 Slope of straight line (b) = -2.73616E-02Standard error of estimate (Se) = 0.320023911 Correlation coefficient (r) = -0.146053878Estimated (t) = -0.511

355

7.11 Relationship between Lag Parameter (C) and the Mean Elevation (ElMean). The elevations at different positions as well as the mean elevation of catchments vary from catchment to catchment. In this section the effect of the mean elevation (mean of the highest and lowest elevations) on lag parameter has been assessed for the seventeen catchments selected in this study.

Figure 7.22 illustrates the plot of lag parameter (C) versus the mean elevation (ElMean) of seventeen catchments and its findings are discussed as follows: • The points are fairly scattered. However, the points of Gympie and Cooran are away from the other points due to their high C values; • Although the slope of the best-fit straight line is negative, its equation in Figure 7.22 clearly demonstrates that the gradient is equal to zero up to its 3rd decimal place; and • It has been noticed from the results of the two tailed t-test that the gradient of the best-fit straight line is not significantly different from zero at 5% level of significance.

To find out the effect of the mean elevation on lag parameter for the fifteen catchments neglecting Gympie and Cooran, Figure 7.23 was plotted and its findings are given below: • The points illustrate a significant amount of scatter although most of the points are on the left side of the plot; • Although the slope of the best-fit straight line is positive, its gradient is equal to zero up to its 2nd decimal place; and • The results of the two tailed t-test, shown in Table 7.23, show that the gradient of the best-fit straight line is significantly different from zero at 5% level of significance.

Although the gradient of the second plot shows a significant deviation from zero, the other findings do not support a real trend for the lag parameter (C) to vary as the mean elevation of catchments vary.

356

3.0 Cooran

2.5 Gympie

2.0 Gleneagle

Moy Pocket Powerline Kandanga Silver Valley 1.5 Central Mill

Bellbird Zattas Nerada y = -0.0002x + 1.5078 Mt.Piccaninny Nash's Crossing

Lag Parameter (C) Parameter Lag 1.0 Tung Oil Reeves Ida Creek Mt.Dangar 0.5 t0.975 = 2.13

tCal = -0.25

0.0 50 150 250 350 450 550 650 750 850

Mean Elevation of Catchment (ELMean) - m

Figure 7.22 – C versus (ELMean) of all seventeen catchments

Table 7.22 – t-test calculations for C versus (ELMean) of all seventeen catchments

Mean Elevation of Lag Calculated Catchment No Catchment Name Parameter (C) X2 Y2 XY Lag (EL ) Mean ( Y ) Parameter (C) (m) (X)

1 Gympie 325 2.55 105625.00 6.5025 828.75 1.43 2 Moy Pocket 340 1.63 115600.00 2.6569 554.2 1.43 3 Bellbird 350 1.16 122500.00 1.3456 406 1.43 4 Cooran 105 2.92 11025.00 8.5264 306.6 1.48 5 Kandanga 383 1.51 146306.25 2.2801 577.575 1.42 6 Powerline 329 1.56 108241.00 2.4336 513.24 1.43 7 Mt. Piccaninny 345 1.08 119025.00 1.1664 372.6 1.43 8 Silver Valley 820 1.56 672400.00 2.4336 1279.2 1.32 9 Gleneagle 778 2.03 605284.00 4.1209 1579.34 1.33 10 Nash's Crossing 520 1.08 270400.00 1.1664 561.6 1.39 11 Zattas 512 1.21 262144.00 1.4641 619.52 1.39 12 Reeves 295 0.82 87025.00 0.6724 241.9 1.44 13 Mt.Dangar 310 0.72 96100.00 0.5184 223.2 1.44 14 Ida Creek 318 0.75 101124.00 0.5625 238.5 1.44 15 Tung Oil 390 0.93 152100.00 0.8649 362.7 1.42 16 Nerada 400 1.14 160000.00 1.2996 456 1.42 17 Central Mill 475 1.39 225625.00 1.9321 660.25 1.40 Total 6994.50 24.04 3360524.25 39.9464 9781.175 24.04 Intercept of straight line (a) = 1.507768992 r2 = 0.004202407 Slope of straight line (b) = -2.27618E-04Standard error of estimate (Se) = 0.628543459 Correlation coefficient (r) = -0.064825972Estimated (t) = -0.252

357

2.5

2.0 Gleneagle

Moy Pocket

1.5 Powerline Kandanga Silver Valley Central Mill

Bellbird Zattas y = 0.0014x + 0.6259 Nerada Mt.Piccaninny Nash's Crossing 1.0 Tung Oil Reeves Lag Parameter (C) Parameter Lag Ida Creek Mt.Dangar 0.5 t0.975 = 2.16

tCal = 2.80

0.0 250 300 350 400 450 500 550 600 650 700 750 800 850

Mean Elevation of Catchment (ELMean) - m

Figure 7.23 – C versus (ELMean) of fifteen catchments

Table 7.23 – t-test calculations for C versus (ELMean) of fifteen catchments

Mean Elevation of Lag Calculated Catchment No Catchment Name Parameter (C) X2 Y2 XY Lag (EL ) Mean ( Y ) Parameter (C) (m) (X)

1 Moy Pocket 340 1.63 115600.00 2.6569 554.2 1.10 2 Bellbird 350 1.16 122500.00 1.3456 406 1.12 3 Kandanga 383 1.51 146306.25 2.2801 577.575 1.16 4 Powerline 329 1.56 108241.00 2.4336 513.24 1.09 5 Mt. Piccaninny 345 1.08 119025.00 1.1664 372.6 1.11 6 Silver Valley 820 1.56 672400.00 2.4336 1279.2 1.77 7 Gleneagle 778 2.03 605284.00 4.1209 1579.34 1.71 8 Nash's Crossing 520 1.08 270400.00 1.1664 561.6 1.35 9 Zattas 512 1.21 262144.00 1.4641 619.52 1.34 10 Reeves 295 0.82 87025.00 0.6724 241.9 1.04 11 Mt.Dangar 310 0.72 96100.00 0.5184 223.2 1.06 12 Ida Creek 318 0.75 101124.00 0.5625 238.5 1.07 13 Tung Oil 390 0.93 152100.00 0.8649 362.7 1.17 14 Nerada 400 1.14 160000.00 1.2996 456 1.19 15 Central Mill 475 1.39 225625.00 1.9321 660.25 1.29 Total 6564.50 18.57 3243874.25 24.9175 8645.825 18.57 Intercept of straight line (a) = 0.625865729 r2 = 0.376539824 Slope of straight line (b) = 1.39874E-03Standard error of estimate (Se) = 0.304066221 Correlation coefficient (r) = 0.613628409Estimated (t) = 2.802

358

7.12 Relationship between Lag Parameter (C) and the Elevation of the Centroid

(ElCentroid). The topography of a catchment could be represented by the elevation of its centroid. Therefore, the study of the relationship between the lag parameter and the elevation of the centroid of a catchment enables the assessment of the influence of the topography on the lag parameter. Thus the elevation of the centroid is considered for this study.

The plot of lag parameter (C) versus the elevation of the centroid of the catchment

(ElCentroid) is shown in Figure 7.24 and it demonstrates the following: • A fair amount of scatter can be observed from the plot; • The best-fit straight line of the plot in Figure 7.24 has a negative slope, but the value of the gradient is equal to zero up to its 4th decimal place; and • The statistical analysis results from the two tailed significance test indicate that the gradient of the best-fit straight line is not significantly different from zero at 5% level of significance as shown in Table 7.24.

Neglecting the two catchments (Gympie and Cooran) from the plot shown in Figure 7.24, Figure 7.25 is made for the remaining fifteen catchments, and the findings from it can be described in the following manner: • The points of the plot are scattered; • Although the best-fit straight line indicates a positive slope, the gradient of the equation in Figure 7.25 is almost zero; and • It has been noticed from the results of the two tailed t-test shown in Table 7.25 that the gradient of the best-fit straight line is not significantly different from zero at 5% level of significance.

As in Section 7.11, it is clear that the lag parameter (C) does not vary considerably as the elevation of centroid of the catchment (ElCentroid) varies, according to the findings described above.

359

3.0 Cooran

2.5 Gympie

2.0 Gleneagle

Moy Pocket Powerline Kandanga Silver Valley 1.5 Central Mill

Bellbird Zattas y = -0.000081x + 1.4377 Nerada Mt.Piccaninny Nash's Crossing

Lag Parameter (C) Parameter Lag 1.0 Tung Oil Reeves Ida Creek Mt.Dangar 0.5 t0.975 = 2.13

tCal = -0.12

0.0 50 150 250 350 450 550 650 750 850

Elevation at Centroid of Catchment (ELCentroid) - m

Figure 7.24 – C versus (ELCentroid) of all seventeen catchments

Table 7.24 – t-test calculations for C versus (ELCentroid) of all seventeen catchments

Elevation at Centroid of Lag Calculated Catchment No Catchment Name Parameter (C) 2 2 XY Lag (EL ) X Y Centroid ( Y ) Parameter (C) (m) (X)

1 Gympie 78 2.55 6084.00 6.5025 198.9 1.43 2 Moy Pocket 100 1.63 10000.00 2.6569 163 1.43 3 Bellbird 140 1.16 19600.00 1.3456 162.4 1.43 4 Cooran 118 2.92 13924.00 8.5264 344.56 1.43 5 Kandanga 160 1.51 25600.00 2.2801 241.6 1.42 6 Powerline 80 1.56 6400.00 2.4336 124.8 1.43 7 Mt. Piccaninny 150 1.08 22500.00 1.1664 162 1.43 8 Silver Valley 838 1.56 702244.00 2.4336 1307.28 1.37 9 Gleneagle 630 2.03 396900.00 4.1209 1278.9 1.39 10 Nash's Crossing 550 1.08 302500.00 1.1664 594 1.39 11 Zattas 440 1.21 193600.00 1.4641 532.4 1.40 12 Reeves 115 0.82 13225.00 0.6724 94.3 1.43 13 Mt.Dangar 130 0.72 16900.00 0.5184 93.6 1.43 14 Ida Creek 150 0.75 22500.00 0.5625 112.5 1.43 15 Tung Oil 300 0.93 90000.00 0.8649 279 1.41 16 Nerada 440 1.14 193600.00 1.2996 501.6 1.40 17 Central Mill 500 1.39 250000.00 1.9321 695 1.40 Total 4919.00 24.04 2285577.00 39.9464 6885.840 24.04 Intercept of straight line (a) = 1.437676871 r2 = 0.000960525 Slope of straight line (b) = -8.14204E-05Standard error of estimate (Se) = 0.629565759 Correlation coefficient (r) = -0.030992331Estimated (t) = -0.120

360

3.0

2.5

2.0 Gleneagle

Moy Pocket Silver Valley Central Mill 1.5 Powerline Kandanga y = 0.0006x + 1.0377 Bellbird Zattas Nerada Mt.Piccaninny Nash's Crossing

Lag Parameter (C) Parameter Lag 1.0 Reeves Tung Oil Ida Creek Mt.Dangar 0.5 t0.975 = 2.16

tCal = 1.59

0.0 50 150 250 350 450 550 650 750 850

Elevation at Centroid of Catchment (ELCentroid) - m

Figure 7.25 – C versus (ELCentroid) of fifteen catchments

Table 7.25 – t-test calculations for C versus (ELCentroid) of fifteen catchments

Elevation at Centroid of Lag Calculated Catchment No Catchment Name Parameter (C) X2 Y2 XY Lag (EL ) Centroid ( Y ) Parameter (C) (m) (X) 1 Moy Pocket 100 1.63 10000.00 2.6569 163 1.10 2 Bellbird 140 1.16 19600.00 1.3456 162.4 1.13 3 Kandanga 160 1.51 25600.00 2.2801 241.6 1.14 4 Powerline 80 1.56 6400.00 2.4336 124.8 1.09 5 Mt. Piccaninny 150 1.08 22500.00 1.1664 162 1.13 6 Silver Valley 838 1.56 702244.00 2.4336 1307.28 1.57 7 Gleneagle 630 2.03 396900.00 4.1209 1278.9 1.44 8 Nash's Crossing 550 1.08 302500.00 1.1664 594 1.39 9 Zattas 440 1.21 193600.00 1.4641 532.4 1.32 10 Reeves 115 0.82 13225.00 0.6724 94.3 1.11 11 Mt.Dangar 130 0.72 16900.00 0.5184 93.6 1.12 12 Ida Creek 150 0.75 22500.00 0.5625 112.5 1.13 13 Tung Oil 300 0.93 90000.00 0.8649 279 1.23 14 Nerada 440 1.14 193600.00 1.2996 501.6 1.32 15 Central Mill 500 1.39 250000.00 1.9321 695 1.36 Total 4723.00 18.57 2265569.00 24.9175 6342.380 18.57 Intercept of straight line (a) = 1.037660092 r2 = 0.163472003 Slope of straight line (b) = 6.36269E-04Standard error of estimate (Se) = 0.352211926 Correlation coefficient (r) = 0.404316712Estimated (t) = 1.594

361

7.13 Catchments with large Lag Parameter Values Two catchments of Mary River basin, Gympie and Cooran, have demonstrated considerable influence on the results of this study due to their large lag parameter values. Therefore, it is useful to examine some possible reasons as to why they produce such large lag parameter values.

It was first decided to carry out hypothesis tests to examine the difference of the mean lag parameters, of 8 storm events of Gympie versus the remaining 15 catchments (excluding Cooran) and 10 storm events of Cooran versus the remaining 15 catchments (excluding Gympie). However, the small number of lag parameter values (< 30) in both catchments did not permit hypothesis z-tests to be carried out.

Therefore, the whole Mary River basin (with 47 lag parameter values) consisting of five catchments, Gympie, Moy Pocket, Bellbird, Cooran, and Kandanga, versus the remaining 12 catchments (with 207 lag parameter values) were considered for hypothesis testing. The mean and standard deviation values of 47 and 207 respectively are shown in Table 7.26. The testing procedure is described in the next two pages.

Table 7.26 - Statistical data of Mary River and the remaining basins selected for this study

Mary River Basin Remaining four River Basins (Haughton, Herbert, Don and Johnstone)

Number of lag parameter values = 47 (nx) Number of lag parameter values = 207 (ny) Mean of lag parameter values = 1.937 ( x) Mean of lag parameter values = 1.133 ( y ) Standard deviation of lag parameter values Standard deviation of lag parameter values

= 0.832 (Sx) = 0.458 (Sy)

362

From the theory of statistics, the equation applicable for testing the hypothesis about the equality of the means of two independent populations (with more than 30 values) is given by Gosling (1995) as:

x - y z = ; (7.4) s2 s 2 x + y n x n y By substituting the values in Table 7.26 into equation (7.4), the z statistic can be found and is equal to: 1.937 -1.133 = 6.41 ()2 ()2 0.832 + 0.458 47 207

Since the z-statistic 6.41 > 1.96 (z0.95 of chart), this result indicates that the difference of the means of the lag parameter values of Mary River basin (containing the catchments Gympie and Cooran) and the remaining four basins (containing 12 catchments) is significantly different from zero.

In an attempt to determine reasons for these large values a range of physical properties of Gympie and Cooran catchments have been investigated. Some of the findings are:

• Catchment Size or Catchment area (A) While the Cooran catchment bears the smallest area (164 km2) out of all catchments, Gympie (2920km2) is in the mid range of the rest of the fifteen catchments as shown in Table 5.1 of Chapter 5. Therefore, the Gympie and Cooran are not greatly different in size compared to the remaining catchments.

• Equal Area Slope of Main Stream (Sc) As shown in Table 7.3 of this chapter, out of all seventeen catchments Gympie and

Cooran have the two smallest values of Sc, 0.9(m/km) and 1.2(m/km) respectively.

The range of Sc values for the remaining catchments is between 2.0(m/km) and

8.8(m/km). These values clearly show that the Sc values of Gympie and Cooran

catchments are lower than the Sc values of the remaining fifteen catchments. Apart from the very extreme upstream region, the Gympie catchment demonstrates a flat

363

bed slope in its main stream as shown in Figure 3.2 of Chapter 3. Although the equal area slope of the main stream of the Cooran catchment is 1.2, which is larger than that of Gympie, it demonstrates a fairly flat bed slope throughout the entire length of its main stream as shown in Figure 3.5 of Chapter 3.

• Catchment Shape Factor (A/L2) The (A/L2) values of Gympie and Cooran catchments are 0.17 and 0.16 respectively as shown in Table 7.8. The range of (A/L2) values for the remaining fifteen catchments is between 0.06 and 0.33. Both values for Gympie and Cooran are well within that range. Therefore, Gympie and Cooran catchments are not showing considerable differences in their (A/L2) values compared to the remaining catchments.

• Catchment Shape (Lc/L) The range of this ratio for fifteen catchments (excluding Gympie and Cooran) is

between 0.35 and 0.62 as shown in Table 7.12. The values of (Lc/L) of Gympie and Cooran are 0.45 and 0.58 respectively. They are at the mid range of the values of the remaining 15 catchments. Therefore, the values of Gympie and Cooran are not indicating substantial difference in their shapes compared to the other fifteen catchments.

• Stream Profile As shown in Figures 3.2, 3.3 and 3.4 of Chapter 3, the three catchments of Mary River basin, Gympie, Moy Pocket and Bellbird, demonstrate fairly similar shapes for their stream profiles. These profiles illustrate sharp falls in the far upstream parts of the catchments. Considerably flat slopes can be observed for Cooran, Silver Valley and Gleneagle catchments as shown in Figures 3.5, 3.18 and 3.19. The stream profiles for Powerline and Mount Piccaninny catchments (shown in Figures 3.15 and 3.16) illustrate reduction in levels at fairly regular intervals along the entire length of their streams. Profiles somewhat similar to Powerline and Mount Piccaninny can be observed from Reeves, Mount Dangar and Ida Creek catchments (shown in figures 3.23, 3.24 and 3.25), although sharp changes can be seen at only two positions of their profiles. The upstream part of the stream profile for Kandanga catchment (shown in Figure 3.6) demonstrates a steep slope and the downstream

364

part with a gradually declining slope. The other remaining catchments, Nash’s Crossing, Zattas, Tung Oil, Nerada and Central Mill (shown in Figures 3.20, 3.21 and 3.27 to 3.29 of Chapter 3) are showing irregular shapes in their profiles. Therefore, these findings have indicated that the shapes of the main stream profiles of Gympie and Cooran have not shown noticeable differences when compared with the remaining fifteen catchments.

• Soil Type Three different types of properties of soil (texture, percentage of silt and sand in topsoil and subsoil layers) of five river basins (Mary, Haughton, Herbert, Don and Johnstone) have been investigated and the findings are compiled in Chapter 3 and Appendix A of the CD. The information provided by the Australian Natural Land and Water Resources audit, is used to carry out this investigation. A summary of the findings is shown in Table 7.27.

The majority of the Mary River basin is covered with clay and clay loam, in its topsoil layer. Similar soil texture in topsoil has been demonstrated by the four remaining basins although, some parts of the three basins, Haughton, Herbert and Don, have shown sandy patches.

The majority of the subsoil layers of the Mary and Haughton River basins are covered with light clay loam and loam. Almost all parts of the subsoil layers of the remaining three basins consist of sandy loam, apart from the extreme upstream part of the Johnstone basin, which is covered with loam.

The percentage of silt in the topsoil of all five basins is similar to each other, and that is between 0 and 40%. The percentage of silt in the subsoil layer in most parts of all five basins is between 0 and 20%.

The percentage of sand in the topsoil varies from 20 to 60% in all five basins apart from some small parts of Haughton and Johnstone River basins. The percentage of sand in most parts of the subsoil layers of Mary and Haughton River basins varies from 20 to 60%. This variation in the percentage of sand in the remaining three basins is 0 to 20% in some parts and 20 to 40% in the other.

365

The studies relating to soil properties of five basins (shown in Table 7.27) have revealed that the Mary River basin (containing Gympie and Cooran catchments) has not shown a considerable difference in its soil properties compared with the other four remaining basins.

Therefore, according to the findings of Section 7.13, it is not possible to indicate with confidence that the physical properties investigated in this section, other than the equal area slope, may have contributed to large lag parameter values for Gympie and Cooran catchments.

366

Soil Texture Percentage of Silt in Soil Percentage of Sand in Soil Basin Topsoil Subsoil Topsoil Subsoil Topsoil Subsoil

Although sand and sandy Although the data is not Although the data is not The majority of the basin is loam patches are found in The majority of the basin has Nearly 40% of the basin has available for some parts of the available for about 30% of the Mary River covered with clay and clay some parts of the basin, most 20 to 40%.The remainder has 20 to 60%. The remainder has basin, the majority of the basin, the other 60% has loam. of the basin is covered with 0 to 20% 0 to 20% basin has 0 to 20%. 20 to 60%. light clay loam and loam.

Although a small portion near Although sand patches are The majority of the area has Very small areas near the At some areas near the the Southern boundary of the Very small parts of the basin found in some parts of the 0 to 20%.The areas close to Northern boundary of the Northern and Southern basin is covered with sand, upstream have 20 to 60%. Haughton River basin, all the other parts of the the Northern and South basin have 20 to 40%. The boundaries of the basin have the remaining parts are The remainder has basin are covered with light Eastern boundaries of the remainder of the basin has 0 to 20%. Other parts have covered with light clay loam 0 to 20%. clay loam and loam. basin have 20 to 40%. 0 to 20%. 20 to 60%. and loam.

Although the Western part of Some loam patches are the basin is covered with Although some parts of the Most of the downstream Although the extreme present in the upstream part sandy loam and sand, the Western region of the basin middle area of the basin has The majority of the basin has upstream part of the basin has Herbert River of the basin.The remaining remainder of the basin is have 20 to 40%, the majority 20 to 40%. All the other areas 20 to 60%. 20 to 40%, the majority of the parts of the basin are covered covered with clay loam and of the basin has 0 to 20%. have 0 to 20%. basin has 0 to 20%. in sandy loam. loam.

The entire basin is covered The entire basin is covered with light clay loam and loam, with sandy loam, apart from The middle part of the basin Some parts near the middle of The middle part of the basin

Table 7.27 – Summary of Soil properties basins Major Table properties of five – Soil Summary of 7.27 The entire basin has 0 to Don River apart from an area near the an area near the upstream of has 20 to 40%. The remainder the basin have 20 to 60%. has 20 to 40%. The remainder 20%. upstream of the mainstream, the mainstream, which is has 0 to 20%. Other parts have 20 to 40% has 0 to 20%. which is covered with sand. covered with sand.

Although some parts close to Although some parts close to The extreme upstream part of Nearly half of the basin has the Northern and Southern Some parts of the basin the Northern and Southern The entire basin is covered the basin is covered with loam Johnstone River 0 to 20% and the other half boundaries of the basin have upstream have 20 to 40%. boundaries of the basin have with clay and clay loam. and the remainder is covered has 20 to 40%. 20 to 40%, the majority of the The remainder has 0 to 20%. 0 to 20%, majority of the basin with sandy loam. basin has 0 to 20%. has 20 to 40%.

367

7.14 Summary of the Findings of Chapter 7 The purpose of this chapter is to examine the relationship between lag parameter (C) and the geomorphological and climatological characteristics of catchments. The details of physical characteristics and the mean values of lag parameters for each catchment are summarised in Table 7.28 at the end of this chapter.

The catchment area (A) is often adopted as the first major element of the lag time formula (as shown in equation 7.3) of WBNM, as well as in other hydrological models developed by the majority of researchers described in Chapter 2 and indicated in Table 2.1. Therefore, the catchment area has been selected as the first physical characteristic to examine its relationship with lag parameter (in all seventeen catchments) in this study.

In addition to the catchment area (A), the relationship between lag parameter and the following ten physical (geomorphological) and climatological characteristics have also been investigated individually in this study as explained in the previous sections:

• Equal Area Slope of Main Stream of Catchment (Sc); • Length of Main Stream of Catchment (L); • Ratio of Catchment Area and the Second Power of Length of Main Stream (A/L2);

• Main Stream Length to the Centroid from Catchment’s Outlet (Lc);

• Ratio of Main Stream Length to Centroid and Main Stream Length (Lc/L); • Number of Rain Days per Year (No.RD/Year);

• Mean Annual Rainfall (ARMean); 2 • 2Year-72Hour Rainfall Intensity Pattern of AR&R ( I72);

• Mean Elevation of Catchment (ElMean);

• Elevation of the Centroid of Catchment (ElCentroid); and

Many of these physical characteristics have been used by various researchers in their lag time equations as described in Chapter 2, for example Sc, L and Lc. Therefore, the effectiveness of such relationships has been assessed with all seventeen catchments in this study. Some items in the above list are directly related to the catchment physical characteristics, whereas the others (climatic) are indirectly related to them.

368

The results of the lag parameter versus equal area slope have shown that C decreases as

Sc increases. However, this result is dependent on the two catchments, Gympie and Cooran, which have larger C values. A range of physical properties of these two catchments were investigated to find out the reasons for high lag parameter values and the findings are described in Section 7.13 of this chapter. However, apart from slope, the findings of this investigation do not indicate any reasons for these two catchments to have large lag parameter values.

Although the t-test showed that the effect of slope (Sc) is significant (Figure 7.3), the calculated t static (-2.36) only just exceeds the tabulated value (-2.13). Additionally, there is considerable scatter in the plot, with the r2 value (Table 7.3) being as low as 0.27. Therefore, there is no really strong evidence to indicate that slope has a strong effect on the lag parameter.

The values of all seventeen catchments have shown that there is no real trend for the lag parameter to vary with the catchment area. Furthermore, the similarities of plots of lag parameter versus catchment area (A) and L as well as Lc have highlighted that both L and Lc are well represented by the catchment area. The relationships developed by Gray 0.57 0.55 (L = 1.31 A and Lc = 0.71 A as described in Chapter 2) illustrate the strong correlation between L, Lc and A.

2 A slight trend with A/L and Lc/L can be observed from the plots, but no significant variations are there to accept that trend.

2 The plots of lag parameter versus No.RD/year, ARMean and I72 have shown some similarities. The general trend of larger travel time and higher lag parameters, for high rainfall areas with more vegetation growth and possibly lower flow velocities, are not shown from these plots. Moreover, sometimes increasing and sometimes deceasing lag parameters have been found from the plots.

Although plots of ELMean and ELCentroid have shown similarities, the gradients of their best-fit straight lines are inconsistent (negative in some plots and positive in others). Therefore, this inconsistency is not supporting a real trend between the elevations and the lag parameter.

369

Therefore, there is no adequate amount of evidence to introduce any other physical characteristics into the lag time equation of WBNM other than catchment area (A) and the main channel discharge (Q), according to the results found from the investigations carried out in relation to lag parameter and the geomorphological and climatological characteristics discussed in this chapter. The results further illustrate that WBNM is modelling the behaviour of natural catchments satisfactorily.

370

1 2 3456789101112131415

Ratio of Number of Equal Area Length to Ratio of 2Yr 72hr Length of Catchment Mean Elevation at Storms Catchment Slope of Main Centroid of Length to Number of Mean Annual Rainfall Average of Main Stream Area and 2nd Elevation of Centroid of Selected for Area Stream of Catchment Centroid and Rain days per Rainfall Intensity Lag Parameter of Catchment power of Catchment Catchment No. Catchment Name Each (ha) Catchment from Outlet Length of year (mm) AR&R (km) Length of (m) (m) Catchment (m/km) (km) Main Stream (mm/hr) Main Stream

2 2 NS CMean A SC L A/L LC LC/L RD/Year ARMean I72 ELMean ELCentroid

1 Gympie 8 2.55 292020 0.9 131.10 0.17 59.5 0.454 117 1132.4 2.88 325 78

2 Moy Pocket 10 1.63 83023 2.2 69.05 0.17 37.4 0.542 118 1359.3 3.00 340 100

3 Bellbird 10 1.16 47920 4.8 46.35 0.22 16.2 0.350 116 1240.3 3.00 350 140

4 Cooran 10 2.92 16432 1.2 31.60 0.16 18.4 0.582 129 1353.5 3.38 105 118

5 Kandanga 9 1.51 17568 5.1 52.45 0.06 21.7 0.414 100 1185.8 2.70 383 160

6 Powerline 12 1.56 173456 2.5 94.50 0.19 43.7 0.462 62 1172.8 3.38 329 80

7 Mt. Piccaninny 16 1.08 113893 3.8 68.10 0.25 27.4 0.402 76 877.2 2.88 345 150

8 Zattas 7 1.21 729200 4.0 225.90 0.14 139.5 0.618 114 1841.8 4.55 512 440

9 Nash's Crossing 17 1.08 684152 4.3 214.40 0.15 133.1 0.621 114 1841.8 4.25 520 550

10 Gleneagle 9 2.03 537016 2.0 127.90 0.33 65.7 0.514 70 823.3 2.30 778 630

11 Silver Valley 17 1.56 58624 5.8 55.80 0.19 22.7 0.407 65 875.1 2.45 820 838

12 Reeves 20 0.82 101032 3.3 66.70 0.23 31.8 0.477 43 812.4 3.00 295 115

13 Mt.Dangar 10 0.72 80784 3.5 55.60 0.26 24.8 0.446 68 862.4 3.38 310 130

14 Ida Creek 20 0.75 62008 4.3 46.30 0.29 21.3 0.460 68 862.4 3.45 318 150 Table 7.28 – Physical characteristics and details of all seventeencatchments 15 Tung Oil 34 0.93 92936 7.6 85.80 0.13 44.5 0.519 183 3325.9 6.70 390 300

16 Nerada 24 1.14 80792 8.7 73.20 0.15 33.8 0.462 209 4517.8 7.50 400 440

17 Central Mill 21 1.39 38976 8.8 78.20 0.06 37.1 0.474 183 3325.9 6.55 475 500

Total Number of Storms = 254 24.04

Average of all lag parameters = 1.41

CHAPTER 8

CONCLUSION

371

8. CONCLUSION

The objective of this study has been to investigate whether the lag parameter of runoff routing models is affected by the hydrological, geomorphological and climatological characteristics of natural catchments. The lag parameter is generally incorporated into the lag time equations adopted in computer models. For example RORB and WBNM models use equations 1.1 and 1.2 respectively. Selection of the lag parameter enables the prediction of catchment lag time, which is an indicator of flow travel time of rural catchments. This then allows prediction of flood hydrographs from storm rainfall, using runoff routing models. This valuable information can be used for emergency services as well as design of hydraulic structures such as dams, culverts and bridges. Thus the prediction of floods by means of computer models would be much improved if default lag parameter values can be designated for each catchment or for a particular region.

The extensive literature review described in Chapter 2, has demonstrated that the lag time is directly proportional to the catchment size (A) and inversely proportional to the peak flow (Qp) of the main stream, according to most of the lag time equations developed by various researchers. Some of the other characteristics highlighted in their equations are slope of main stream (Sc), length of main stream (L), main stream length from outlet to the centroid (Lc) and rainfall intensity (I) of catchments.

While catchment area A and flow peak Qp appear in many of the published lag relations, the other catchment and storm characteristics are generally less significant.

It is advantageous therefore, to use a runoff routing model which has a minimum number of catchment characteristics with a relatively simple relation. In view of the foregoing reasons, the Watershed Bounded Network Model (WBNM) was selected due to its inherent capabilities, outlined in the latter part of section 2.8 of Chapter 2, to estimate lag parameter values of seventeen gauged catchments for 254 storm events.

WBNM was calibrated using recorded rainfall and stream flow data, and the accuracy of the results was then assessed, as explained in the next paragraph.

372

As described in Chapter 5, all seventeen catchments were delineated on topographical maps. Thereafter these catchments were divided into a number of subcatchments according to their size. The areas and coordinates of centroids of these subcatchments, as well as rainfall stations assigned for each catchment were inserted into the data file of the program. The constant-slope method was adopted to separate the baseflow to obtain surface runoff hydrographs from recorded total hydrographs, and that surface runoff flow data was also included in the data file of the program. Following this, several simulations using WBNM were carried out for each storm event by adjusting the continuing loss rate and lag parameter values until the computer generated hydrograph matched the recorded surface runoff hydrograph.

The lag parameters of all storm events were compared with hydrological characteristics (listed in section 6.13 of Chapter 6), geomorphological and climatological characteristics (listed in section 7.14 of Chapter 7) of all seventeen catchments. In this comparison the validity of the lag time equation of WBNM (equation 1.2) was assessed by examining the plots of lag parameter versus peak discharge of total runoff (Qp), peak discharge of surface runoff (Qs) and catchment size (A). This examination included statistical t-test analyses to ascertain whether the relationships were statistically significant or not.

The plots of lag parameter versus catchment area and peak flow were examined using statistical t-test of the gradients of best-fit straight lines. The results of these investigations revealed that there is no significant variation of lag parameter with catchment area A or peak flow Q. This indicates that the lag relation built into WBNM (equation 1.2) properly accounts for these variables.

Of the other hydrological variables tested, only two, the total rainfall depth in the storm and the depth of surface runoff, showed a significant variation of C. All the other hydrological variables were found to be not significant.

The plots in sections 6.5 and 6.6 do show that the lag parameter is higher for storms with large rainfall depths. This could indicate that the lag parameter depends on the size of the storm. However, this result is not supported by plots of C versus peak discharge

Qp (section 6.3) and Qs (section 6.4), which show no relation between C and the size of 373

the flood. Therefore, this contradiction in the results indicates that there is no strong evidence for any trend for the lag parameter to vary with either size of storm or its runoff.

The geomorphological and climatological characteristics listed in section 7.14 of Chapter 7 represent the equal area slope of main stream, length of mainstream, broadness or narrowness, length of main stream from the outlet to the centroid, distribution of area either towards the headwater or outlet, degree of wetness of subsoil during the year, distribution of rainfall over the year, intensity-frequency-distribution of rainfall, mean sea level of topography and the elevation at the centroid of catchments.

The plots of lag parameter (C) versus length of main stream (L) as well as the length of main stream from outlet to centroid (Lca) of seventeen catchments have demonstrated results similar to the plots of lag parameter (C) versus catchment area (A). That is, parameter C does not vary with these variables. This can be expected since the stream lengths are strongly related to catchment area (Gray, 1961).

Although the equal area slope (Sc) has demonstrated some effect on the lag parameter, that trend is mainly due to two catchments (Gympie and Cooran) which have larger lag parameters and flatter slopes. However, a similar trend has not been observed from the results of the remaining fifteen catchments with moderate lag parameter values. 2 Moreover, fairly low correlation between C and Sc (r = 0.27) is found from the results in Table 7.3, and also this relationship is only just significant according to the calculated t static and the tabulated values shown in Figure 7.3.

The other geomorphological and climatological characteristics selected for this research 2 2 (L, Lca, A/L , Lca/L, No.RD/year, ARmean, I72, ElMean and ElCentroid) have shown no meaningful relationships, indicating that those do not have a strong effect on the value of C.

All the findings of this study have clearly demonstrated that there is no strong evidence to include characteristics other than catchment area and stream discharge into the lag time equation of WBNM. Therefore, WBNM has been found to model the behaviour of natural catchments effectively and efficiently. The mean lag parameter value found for 374

Queensland catchments from this study is near to 1.40, somewhat less than the default value of 1.70 suggested in the model for New South Wales.

Although this study has shown that the lag parameter C is generally independent of the hydrological, geomorphological and climatological variables of catchments, some variables such as total rainfall depth (DT), surface runoff depth (DSRO), slope (Sc), length of main stream (L) and ratio of main stream length to centroid and main stream length

(Lc/L) and the mean elevation (ElMean) have been shown, in some instances, to be weakly related to lag parameter C. Therefore, further research on those variables may be worthwhile to determine whether such relations actually do exist.

REFERENCES

375

REFERENCES

1. Alexander, G.N. (1972) Effect of Catchment Area on Flood Magnitude. Jour. Hydrol., Vol. 16, pp.225-239.

2. Amorocho, J. (1961) Predicting Storm Runoff on Small Experimental Watershed. Journal of the Hydraulics Division, Proc. ASCE., Vol. 87, No.HY2, pp.185-191.

3. Askew, A.J. (1970) Derivation of Formulae for Variable Lag Time. Jour. Hydrol., Vol. 10, pp.225-242.

4. Askew, A.J. (1970) Variation in Lag Time for Natural Catchments. Journal of the Hydraulics Division, Proc. ASCE., Vol. 96, No.HY2, pp.317-329.

5. Bates, B.C. and Pilgrim, D.H. (1982) Investigation of Storage-Discharge Relations for River Reaches and Runoff Routing Models. Hydrology and Water Resources Symposium, Melbourne. I.E. Aust. National Conference, Publ.82/3, pp. 120-126.

6. Bates, B.C, and Pilgrim, D.H. (1983) Simple Model for Nonlinear Runoff Routing. Hydrology and Water Resources Symposium, Hobart. I.E. Aust. National Conference, Publ.83/13, pp. 141-147.

7. Bates, B.C., Summer, N.R. and Boyd, M.J. (1993) Nonlinearity of Flood Runoff: What Can Be Gleaned From Calibrated Runoff Routing Models? Civ. Engg.Trans.Inst.Engrs.Aust., Vol. CE35, No.2, pp.151-164.

8. Baron, B.C., Pilgrim, D.H. and Cordery, I. (1980) Hydrological relationships between small and large catchments. Dept. of Nat. Develop. and Energy, Aust. Water Res. Council Tech. paper No.54.

9. Bell, F.C. and Kar, O.M.S. (1969) Characteristics Response Times in Design Flood Estimation. Jour. Hydrol., Vol. 8, pp.173-196.

10. Black, R.E. and Clifford, P.J. (1977) A Runoff Prediction Method for Western Australian Catchments – Part1, Civ. Engg.Trans.Inst.Engrs.Aust., Vol. CE19, No.2, pp.196-203.

11. Black, R.E., Pivovaroff, J.M, Maguire, J.C. and MacDonald, P.M. (1986) The Statistical Rational Method Applied to Adelaide Catchments. Hydrology and Water Resources Symposium, Griffith University, Brisbane. I.E. Aust. National Conference, Publ.86/13, pp. 21-26.

12. Boughton, W.C. and Collings, A.S. (1982) Regional Variations in Flood Frequency Characteristics in Queensland. Civ. Engg.Trans., Inst.Engrs.Aust., Vol.CE24, pp.127-134.

13. Boughton, W.C. (1986) Hydrograph Analysis as a Basis for Rainfall–Runoff Modelling. Hydrology and Water Resources Symposium, Griffith University, Brisbane. I.E. Aust. National Conference, Publ.86/13, pp. 79-83.

376

14. Boyd, M.J. (1978) A storage routing model relating drainage basin hydrology and geomorphology. Water Resour. Res., Vol. 14, No.5, pp.921-928.

15. Boyd, M.J. (1978a) Regional Flood Frequency Data for NSW Streams. Civ. Eng.Trans.I.E.Aust., Vol. CE 20, No.1, pp.88-95.

16. Boyd, M.J. (1978b) A Storage Routing Model Resisting Drainage Basin Hydrology and Geomorphology. Water Resour. Res., Vol. 14, No.5, pp.921-928.

17. Boyd, M.J., Pilgrim, D.H. and Cordery, I. (1979a) A Storage Routing Model Based on Catchment Geomorphology. Jour. Hydrol., Vol. 42, pp.209-230.

18. Boyd, M.J. (1985) Effect of catchment sub-division on runoff routing models. Instn. Eng. Aust., Civ. Engrs. Trans., Vol. CE 27, No.4, pp.403-410.

19. Boyd, M.J., Bates, B. C., Pilgrim, D.H. and Cordery, I. (1987a) WBNM: a general runoff routing model. 4th National Local Govt Engg Conference. Inst Engrs Aust., Batl Conf. Publ. No. 87/9, pp. 137-141.

20. Boyd, M.J., Bates, B. C., Pilgrim, D.H. and Cordery, I. (1987b) WBNM: a general runoff routing model – Programs and user manual. Univ. of New South Wales. Water Res. Lab. Report No. 170.

21. Boyd, M.J. and Bufill, M.C., (1989) Determining runoff routing model parameters without rainfall data. Jour. Hydrol., Vol. 108, pp.281-294.

22. Boyd, M.J., Rigby, E.H. and Van Drie, R. (1996) WBNM – a comprehensive flood model for natural and urban catchments. 7th International Conference on Urban Storm Drainage, Hannover Germany, pp.329-334.

23. Boyd, M.J., Rigby, T, Drie, R.V. and Schymitzek, I. (2002) Mathematics Models of Small Watershed Hydrology and Applications, Ch.8, Water Resources Publications, LLC, ISBN1887201351.

24. Chapman, T.G. (1993) Nonlinearity of Flood Runoff: What Can Be Gleaned From Calibrated Runoff Models? Aust., Civ. Engg. Trans., Vol. CE35, No.2, pp.151-164.

25. Chow, V.T. (1959) “Open Channel Hydraulics”. McGraw-Hill, New York.

26. Chowdhury, M.S.K. and Bell, F.C. (1980) New Routing Model for continuous runoff Simulation, Journal of the Hydraulics Division, ASCE., Vol. 106, No.HY4, pp.489-500.

27. Clark, C.O. (1945) Storage and the unit hydrograph. Proc. Amer. Soc. Civ. Eng., Vol. 69, pp.1333-1360.

28. Cordery, I. (1968) Synthetic unit graphs for Small Catchments in Eastern New South Wales. Civ. Engg.Trans., Inst.Engrs.Aust., Vol. CE 10, pp.47-57.

377

29. Cordery, I. and Webb, S.N. (1974) Flood Estimating in Eastern NSW – A Design Method. Civ. Eng.Trans.I.E.Aust., Vol. CE16, No.1, pp.87-93.

30. Cordery, I., Pilgrim, D.H. and Baron, B.C. (1981) Validity of use of small catchment research results for large basins. Civil Eng. Trans., Inst Engrs Aust., Vol. CE23, No.2, pp.131-137.

31. Dyer, B.G., Nathan, R.J., McMahon, T.A. and O’Neil, I.C. (1993) A Cautionary Note on the Modelling of Baseflow in RORB. Civ. Engg.Trans., Vol. CE35, No.4, pp.337-340.

32. Dyer, B.G., Nathan, R.J., McMahon, T.A. and O’Neil, I.C. (1995) Prediction Equations for RORB Parameter kc Based on Catchment Charateristics. Australian Journal of Water Resources., Vol. 1, No.1, pp29-38.

33. French, R., Pilgrim, D.H. and Laurenson, E.M. (1974). Experimental examination of the Rational Method for small rural catchments. Civ. Eng. Trans. Inst. Engrs. Aust., Vol. CE16, No.2, 95-102.

34. Flavell, D.J. (1983) The Rational Method applied to small rural catchments in the South West of Western Australia. Civ. Engg. Trans., Inst. Engrs. Aust., Vol. CE25, pp. 121-127.

35. Flavell, D.J., Belstead, B.S, Chivers, B. and Walker, M.C. (1983) “Runoff Routing Model Parameters for Catchments in Western Australia. Hydrology and Water Resources Symposium, Hobart, IE Aust. National Conference, Publ.83/13, pp. 22- 27.

36. Gray, D. M.. (1961) Interrelationships of watershed characteristics. Jour. Geophys. Res., Vol. 66, pp.1215-1223.

37. Gray, D.M. (1961) Synthetic unit Hydrographs for Small Watersheds. Journal of the Hydraulics Division, Proc. ASCE., Vol. 87, No.HY4, pp.33-53.

38. Gosling, J. (1995) Introductory Statistics - A Comprehensive Self-paced Step-by step Statistics Course for Tertiary Students, Pascal Press.

39. Hairsine, P.B., Ciesiolka, C.A.A, Marshall, J.P. and Smith, R.J. (1983) Runoff Routing Parameter Evaluation for Small Agricultural Catchments. Hydrology and Water Resources Symposium, Hobart. I.E. Aust. National Conference, Publ.83/13, pp. 33-37.

40. Hansen, W.R., Reed, G.A. and Weinmann, P.E. (1986) Runoff Routing Parameters for Victorian Catchments. Hydrology and Water Resources Symposium, Griffith University, Brisbane. I.E. Aust. National Conference, Publ.86/13, pp. 192-197.

41. Hawken, W.H. (1921) An Analysis of Maximum Runoff and Rainfall Intensity. Trans. Instn Engrs Aust., Vol. 2, pp. 193-215.

378

42. Hughes, W. (1993) Travel time in mountain basins. Symposium on Engineering Hydrology, San Francisco. ASCE Conference, Publ. Pp. 192-197.

43. Jenkins, G. A., Goonetilleke, A. and Black, R.G. (2002) Estimating Peak Runoff for Risk-Assessment in Small Catchments. I.E.Aust. Australian Journal of Water Resources., Vol. 5, No.2, pp.177-193.

44. Keifer, C.L. and Chu, H.H.(1957) Synthetic Storm pattern for drainage design. Jour. Hydraulics Division, ASCE, HY4: 1332-1-25.

45. Kerby, W.S. (1959) “Times of Concentration for Overland flow”. Civil Engineering, Vol. 29, No.3, p.60.

46. Klaassen, B. and Pilgrim, D.H. (1975) Hydrograph Recession Constants for New South Wales Streams. Civ. Engg.Trans., Inst.Engrs.Aust., Vol.CE17, pp.43-49.

47. Kull, D.W. and Feldman, A. D. (1998) Evolution of Clark’s Unit Graph Method to Spatially Distributed Runoff. Journal of Hydrologic Eng., Vol. 3, No.1, pp. 9-19.

48. Laurenson, E.M. and Pilgrim, D.H. (1963) “Loss Rates for Australian Catchments and their Significance”. Jour. Inst. Eng. Aust., Vol. 35, No., 1-2, pp.9-24.

49. Laurenson, E.M. (1964) A catchment storage model for runoff routing. Jour. Hydrol., Vol. 2, pp.141-163.

50. Laurenson, E.M. and Mein, R.G. (1985) RORB-Version 3 Runoff routing program – User Manual Second Edition, Revised March 1985. Dept. of Civil Eng. Monash University.

51. Linsley, R.K., Kohler, M.A. and Paulhus, J.L.H. (1975) Hydrology for Engineers. 3rd Ed. New York, McGraw-Hill.

52. Linsley, R.K., Kohler, M.A. and Paulus, J.L.H. (1982), Applied Hydrology, McGraw-Hill, New York.

53. McCuen, R.H. and Spiess, J. M. (1995) Assessment of Kinematic Wave Time of Concentration. Journal of Hydraulic Eng., Proc. ASCE., Vol. 121, No.3, pp.256- 266.

54. McMahon, G.M. and Muller, D.K. (1983) Calibration Strategies for Non-linear Runoff-routing Models. Hydrology and Water Resources Symposium, Hobart. I.E. Aust. National Conference, Publ.83/13, pp. 129-134.

55. McMahon, G.M. and Muller, D.K. (1986) The Statistical Rational Method Applied to Adelaide Catchments. Hydrology and Water Resources Symposium, Griffith University, Brisbane. I.E. Aust. National Conference, Publ.86/13, pp. 186-191.

56. Mein, R.G., Laurenson, E.M. and McMahon, T.A. (1964) Simple nonlinear model for flood estimation. Jour. Hydrol., Vol. 2, pp.141-163.

379

57. Morgan, P.E. and Johnson, S.M. (1962) Analysis of Synthetic Unit-graph Methods. Journal of the Hydraulics Division, Proc. ASCE., Vol. 88, No.HY5, pp.199-220.

58. Morris, W.A. (1982) Runoff Routing Model Parameter Evaluation for Ungauged Catchments. Hydrology and Water Resources Symposium, Melbourne. I.E. Aust. National Conference, Publ.82/3, pp. 110-114.

59. Nash, J.E. (1958) Determining Runoff from Rainfall. Proc. I.C.E., Vol. 10, pp.163- 184.

60. Nash, J.E. (1960) A Unit Hydrograph Study with Particular Reference to British Catchments. Proc. I.C.E., Vol. 17, pp.249-282.

61. Netchaef, P., Wood, B. and Franklin, R. (1985) RORB Parameters for Beat Fit – Catchments in Pilbara Region. Hydrology and Water Resources Symposium, Sydney. I.E. Aust. National Conference, Publ.85/2, pp. 53-57.

62. Overton, D.E. (1970) Route or Convolute? Water Resour. Res., Vol. 6, No.1, pp.43- 52.

63. Papadakis, C. N. and Kazan, M.N. (1987) Time of Concentration in Small Rural Watersheds. Engineering Hydrology Symposium, Williamsburg, VA. ASCE National Conference, Publ. pp. 633-638.

64. Pedersen, J.T., Peters, J.C. and Helweg, O.J. (1980) Hydrographs by Single Linear Reservoir Model. Journal of the Hydraulics Division, Proc. ASCE., Vol. 106, No.HY5, pp.837-851.

65. Pilgrim, D.H. and Cordery, I. (1975) Rainfall temporal patterns for design floods. Jour. Hydraulics Davison, ASCE, Vol. 101, HY4: 91-95.

66. Pilgrim, D.H. (1976) “Travel Times and Nonlinearity of Flood Runoff from Tracer measurements on a Small Watershed”. Water Resour. Res., Vol. 12, No.3, pp.487- 496.

67. Pilgrim, D.H. (1977) “Isochrones of Travel Time and Distribution of Flood Storage from a Tracer Study on a Small Watershed”. Water Resour. Res., Vol. 13, No.3, 1977, pp.587-595

68. Pilgrim, D.H. (1982) Characteristics of Nonlinearity and Spatial Variations of Flood Runoff form Two Tracing Studies. Civ. Engg.Trans., Inst.Engrs.Aust., Vol.CE24, pp.121-126.

69. Pilgrim, D.H. and McDermott, G.E. (1982) Design floods for small rural catchments in eastern New South Wales. Civ. Engg. Trans., Inst. Engrs. Aust., Vol. CE24, pp. 226-234.

70. Ragan, R.M. and Duro. J.O (1972) Kinematic wave nomograph for times of concentration. Proc.ASCE., Vol. 98, No.HY10, pp.1765-1771.

380

71. Rastogi, R.A. and Jones, B.A. (1971) Non-linear response of a small drainage basin model. Jour. Hydrol., Vol. 14, pp.29-42.

72. Reed, D.W., Johnson, P. and Firth, J.M (1975) A Non-Linear Rainfall-Runoff Model. Providing for variable lag time. Jour. Hydrol., Vol. 25, pp.295-305.

73. Rockwood, D.M. (1958) Columbia Basin Streamflow Routing by Computer. Proc. ASCE., Vol. 84, No.WW5, paper No. 1874.

74. Ross, C.N. (1921) The calculation of flood discharges by the use of a time contour plan. Trans. Instn. Engrs. Aust., Vol. 2, p.85.

75. Seelye, E.E.(1968) Design-Data Book for Civil Engineers. Vol.1, John Wiley and Sons, New York, N.Y., pp. 01-18.

76. Sobinoff, P., Pola, J.P. and O’Loughlin, G.G. (1983) “Runoff Routing Parameters for the Newcastle-Sydney-Wollongong Region”. Hydrol. and Water Resour. Symp., Hobart, IE Aust. Nat. Conf. Publ. 83/13, pp.22-27.

77. Sriwongsitanon, N., Cordery, I. and Ball, J.E. (1998b) Improvement of Storage- Discharge relationships for River Reaches and Runoff –Routing Models. Australian Journal of Water Resources., Vol. 2, No.2, pp77-88.

78. Stewart, B.J. (1983) The Effects of Storages on Runoff Routing parameters. Hydrology and Water Resources Symposium, Hobart. I.E. Aust. National Conference, Publ.83/13, pp. 136-140.

79. The Institution of Engineers, Australia Australian Rainfall and Runoff (1977), Flood Analysis and Design, Canberra.

80. The Institution of Engineers, Australia Australian Rainfall and Runoff (1989), A Guide to Flood Estimation, 2 Volumes, Canberra.

81. The Institution of Engineers, Australia Australian Rainfall and Runoff (1998), A Guide to Flood Estimation, 2 Volumes, ISBN1858256886.

82. Viessman, Jr.W. (1968) Runoff Estimation for very Small Drainage Areas. Water Resour. Res., Vol. 4, No.1, pp.87-93.

83. Weeks, W.D. and Stewart, B.J. (1978) “Linear and Non-Linear Runoff Routing for ungauged Catchments”. Hydrology Symposium, Canberra, I.E. Aust., National Conference publication No.78/9, pp. 124-128.

84. Weeks, W.D. (1986) Flood Estimation by Runoff Routing – Model Applications in Queensland. Civ. Engg. Trans. Inst. Engrs. Aust., Vol. CE28, No.2, pp.159-165.

85. Weeks, W.D. and Boughton, W.C. (1987) A Simple ARMA Hydrologic Model for Ungauged Catchments in Queensland. Civ. Engg.Trans., Inst.Engrs.Aust., Vol.CE29, No.2, pp.85-94.

381

86. Weeks, W.D. (1991) Design Floods for Small Rural Catchments in Queensland. Civ. Engg. Trans., Inst. Engrs. Aust., Vol. CE33, pp.249-260.

87. Wilson, E.M. (1969) Engineering Hydrology. 4th Ed. London, MacMillan.

88. Wong, T.H.F. and Laurenson, E.M. (1983) “Wave Speed-Discharge Relations in Natural Catchments”. Water Resour. Res., Vol. 19, No.3, pp.701-706.

89. Wong, T.H.F. (1989) Nonlinearity in Catchment Flood Response. Civ. Engg.Trans., Inst.Engrs.Aust., Vol. CE31, pp.30-37.

90. Wong, T.S.W. (1996) Time of Concentration and Peak Discharge Formulas for Planes in Series. Journal of Irrigation and Drainage Engineering, Proc.A.S.C.E., Vol. 122, No.4, pp.256-258.

91. Wu, I.P. (1963) Design Hydrographs for Small Watersheds on Indiana. Proc.A.S.C.E., Vol. 89, No.HY6, pp.35-66.

92. Yu, B. and Ford, B.R. (1989) “Salt-Consistency in Runoff Routing Models”. Civ. Engg.Trans., Inst.Engrs.Aust., Vol. CE31, pp.47-52.

93. Yang, M.S. and Lee, K.T. (1999) The Evaluation of Time of Concentration Equations in Taiwan. 25th Hydrology & Water Resources Symposium, Brisbane, I.E. Aust., 2nd International Conference on Water Resources & Environment Research, Vol. 1, pp. 483-488.

94. Zhang, S. and Cordery, I. (1999a) The Catchment Storage-discharge Relationship: Non-Linear or Linear? Australian Journal of Water Resources., Vol. 3, No.1, pp.155-165.

95. Zang, S. and Cordery, I. (1999b) Travel time and Storage-discharge relations for flood estimation. 25th Hydrology & Water Resources Symposium, Brisbane, I.E. Aust., 2nd International Conference on Water Resources & Environment Research, Vol. 1, pp. 483-488.