Enhanced Joint Probability Approach for Flood Modelling
Wilfredo Llacer Caballero (Hons 1) Student ID 99199278
A thesis submitted for fulfilment for the degree of Doctor of Philosophy in Civil Engineering
Supervisory Panel: Dr Ataur Rahman Prof Kenny Kwok A/Prof Surendra Shrestha
School of Computing, Engineering and Mathematics University of Western Sydney, Australia December 2013
Enhanced Joint Probability Approach Caballero
ABSTRACT
Flood is one of the worst natural disasters that cause on average $400 million annual damage in Australia in addition to loss of human lives. During 2010-11 periods, the flood damage in Australia exceeded $20 billion. Design flood estimates are needed for various water resources management tasks including design of bridge, culvert, weir, spill way, detention basin, flood control levee and floodplain modelling, flood insurance and environmental and ecological studies. Flood frequency analysis is the most direct method of design flood estimation, which needs a longer period of recorded streamflow data at the site of interest. There are many catchments in Australia which are ungauged; the estimation of design floods in these catchments appears to be a difficult task. Methods commonly adopted for design flood estimation in ungauged catchments include Index Flood Method, Probabilistic Rational Method and Quantile Regression Technique. However, these types of approximate methods are limited to flood peak estimation only and are not particularly useful when the estimation of complete streamflow hydrograph is required. Also, the regionalised rainfall runoff modelling is associated with a large degree of uncertainty.
To estimate complete design flood hydrograph, rainfall runoff modelling is preferred in which the rainfall-based Design Event Approach (DEA) is the currently recommended method in Australian Rainfall and Runoff (ARR). In this approach, the probabilistic nature of rainfall depth is considered in the rainfall runoff modelling; however, this ignores the probabilistic behaviour of other model inputs and parameters such as rainfall temporal patterns and losses. To overcome the limitations associated with the DEA, a more holistic approach such as Joint Probability Approach (JPA)/ Monte Carlo Simulation Technique (MCST) has received notable attention in recent years in Australia. The National Committee on Water Engineering is going to recommend MCST for general application in Australia in the upcoming ARR.
A considerable research has been undertaken on the development and application of the JPA/MCST in design flood estimation problem. However, JPA/MCST has not been popular in routine hydrologic applications due to lack of readily available design data. It is thus
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Enhanced Joint Probability Approach Caballero necessary to derive design data by regionalisation so that stochastic inputs are available for practical application of the JPA/MCST. These regional design data include stochastic rainfall duration, temporal pattern and losses which are largely unavailable in Australian states. The application of JPA/MCST to ungauged catchments in Australia has not been well- investigated with a large data set. Hence, this thesis undertakes the regionalisation of the JPA/MCST considering a large number of pluviograph and stream gauging stations for eastern New South Wales (NSW) in Australia.
This thesis develops a regionalised Enhanced Monte Carlo Simulation Technique (EMCST) for eastern NSW as this part of NSW has adequate pluviograph and stream gauging stations of acceptable quantity and quality to develop and test a regional EMCST. This thesis uses data from 86 pluviograph stations and 12 catchments to derive regional distributions of various stochastic model inputs and parameters that are needed to apply a runoff routing model, i.e. rainfall complete storm duration (DCS), rainfall inter-event duration (IED), rainfall depth (intensity-frequency-duration, IFD), rainfall temporal pattern (TP), initial loss (IL), continuing loss (CL) and runoff routing model’s storage delay parameter (k). Two different probability distributions (exponential and gamma) are tested to fit the observed data of DCS, IED, IL, CL and k by applying three goodness-of-fit tests (Chi-Squared, Kolmogorov- Smirnov and Anderson-Darling) at 5% level of significance. A spatial proximity method has been adopted to regionalise the model inputs and parameters. An Inverse Distance Weighted
Averaging (IDWA) method has been used to regionalise the DCS, IED and IFD data. These regionalised stochastic inputs/parameters are then used with the EMCST to obtain derived flood frequency curve (DFFC) at a number of selected catchments in NSW. A sensitivity analysis has been undertaken to assess the impacts of possible uncertainty in these inputs/parameter values on the DFFCs. Model validation is carried out by comparing the results of the EMCST with those of the DEA, Australian Rainfall and Runoff Regional Flood Frequency Estimates (ARR-RFFE) 2012 model (test version) and ARR 1987-PRM.
Based on the three goodness-of-fit tests, it has been found that the regional distributions of the DCS, IED, IL and k data can be approximated by two-parameter gamma distribution and the CL data by one-parameter exponential distribution. Based on IDWA method adopted, the
DCS, IED and IFD data can be regionalised by using DCS, IED and IFD data from three to five
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Enhanced Joint Probability Approach Caballero nearby pluviograph stations (whenever it is available, otherwise one pluviograph station is found to be adequate) within 30 km radius from the approximate centre of the catchment of interest. The TP data from 15 nearby pluviograph stations can be pooled to form regional TP data for application at any arbitrary location in eastern NSW. The sensitivities of the input variables and storage delay parameter have been found to be in the following order (the most sensitive to the least sensitive one): k (-30% to 95%), IED (-29% to 60%), DCS (-30% to 50%), IL (-40% to 40%), IFD (10% to 24%), TP (9% to 15%) and CL (-10% to 14%). In addition, it has been shown that up to about 10% variations in the stochastic model inputs/parameters do not make any notable effects on the DFFCs.
The independent testing to six catchments shows that the EMCST generally out-performs the DEA, ARR-RFFE 2012 model (test version) and the ARR-PRM. The developed EMCST can be applied at any arbitrary location in eastern NSW. Although the method and design data developed here are primarily applicable to eastern NSW, the method can be adapted to other Australian states and other countries. The developed EMCST will assist in making a shift from the application of the DEA to MCST in Australia as per the recommendations of the upcoming new edition of ARR.
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STATEMENT OF AUTHENTICY
'I certify that all materials presented in this thesis are of my own creation, and that any work adopted from other sources is duly cited and referenced as such.’ This thesis contains no material that has been submitted for any award or degree in other university or institution.
Wilfredo Llacer Caballero
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ACKNOWLEDGMENTS
I gratefully acknowledge the contribution of my supervisor Dr Ataur Rahman for providing me direction, advice and encouragement throughout the study. I really appreciate his help and support.
I also appreciate the friendship of other academics and colleagues in research in the School of Computing, Engineering and Mathematics at UWS. In particular, thanks to Professor Kenny Kwok and Associate Professor Surendra Shrestha for their advice and support.
I would also like to acknowledge the Australian Bureau of Meteorology and NSW Office of Water for providing the pluviograph and streamflow data for NSW, respectively.
Thanks to my fellow PhD students for all your help, fun times and support. Special thanks to Dr Khaled Haddad, Kashif Aziz, Melanie Loveridge and to the late Md Ashrafuz Zaman for their friendship, help and support.
Thanks to my family in overseas, relatives and friends (Sister Salve and Sister Annaliza) for their prayers. A special thanks to my wife, Asuncion, and my kids, Philip and Reina for being supportive, patient and loving throughout my study. Thanks to Auntie Remy and Uncle John for their encouragement and support.
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PUBLICATIONS MADE (UNTIL 16TH DECEMBER 2013) FROM THIS PhD STUDY
Caballero, W.L., Haque, M.M. and Rahman, A. (2013). Flood risk assessment in Australia: Application of an holistic approach. In: Flooding: Risk factors, Preventive Measures and Environmental Impacts, Editor: M. R. Motsholapheko, Nova Publishers (Accepted on 12 September 2013).
Caballero, W.L. and Rahman, A. (2013). Development of regionalised Joint Probability Approach to flood estimation: A case study for Eastern New South Wales, Australia, Hydrological Processes, Published online in Wiley Online Library (wileyonlinelibrary.com), 10 pp.
Caballero, W.L. and Rahman, A. (2014). Application of Monte Carlo simulation technique for flood estimation for two catchments in New South Wales, Australia. Natural Hazards, (accepted on 18 May 2014).
Caballero, W.L. and Rahman, A. (2013). Variability in rainfall temporal patterns: A case study for New South Wales, Australia. Journal of Hydrology and Environment Research, 1(1), pp. 10-17.
Caballero, W.L. and Rahman, A. (2013). Sensitivity of the regionalised inputs in the Monte Carlo Simulation Technique in design flood estimation for New South Wales. 35th Hydrology and Water Resources Symposium, Engineers Australia, 24-27 February 2012, Perth, Australia. 8 pp. (Submitted 7th October 2013)
Caballero, W.L. and Rahman, A. (2013). Application of Monte Carlo Simulation Technique to design flood estimation: A case study for the Orara River catchment in New South Wales. The 20th International Congress on Modelling and Simulation (MODSIM 2013), 1-6 December 2013, Adelaide, 7 pp.
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Caballero, W., Rahman, A. and Shrestha, S. (2012). Regionalisation of rainfall temporal patterns in New South Wales for application with the Monte Carlo Simulation Technique to design flood estimation, 34th Hydrology and Water Resources Symposium, Engineers Australia, 19-22 November 2012, Sydney, Australia. pp. 17-24.
Caballero, W.L., Taylor, M., Rahman, A. and Shrestha, S. (2011). Regionalisation of intensity-frequency-duration data: A case study for New South Wales. 19th International Congress on Modelling and Simulation, 12-16 December 2011, Perth, pp. 3775-3781.
Caballero, W. and Rahman, A. (2011). Regionalisation of rainfall duration for NSW. 34th IAHR World Congress and 33rd Hydrology and Water Resources Symposium, 26 June - 1 July 2011, Brisbane, pp. 74-81.
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TABLE OF CONTENTS
ABSTRACT…………………………………………………………………………………..ii STATEMENT OF AUTHENTICITY………………………………………………………v ACKNOWLEDGMENTS…………………………………………………………………..vi PUBLICATIONS MADE (UNTIL 16TH DECEMBER 2013) FROM THIS PhD STUDY...... vii TABLE OF CONTENTS……………………………………………………………………ix LIST OF FIGURES ………………………………………………………………………..xv LIST OF TABLES…………………………………………………………………………xxi LIST OF SYMBOLS……………………………………………………………………xxviii LIST OF ABBREVIATIONS…………………………………………………………….xxxi
CHAPTER 1 ...... 2
INTRODUCTION ...... 2 1.1 GENERAL ...... 2 1.2 BACKGROUND ...... 2 1.3 NEED FOR THIS RESEARCH ...... 7 1.4 RESEARCH QUESTIONS ...... 9 1.5 SUMMARY OF RESEARCH UNDERTAKEN IN THIS THESIS ...... 9 1.6 OUTLINE OF THE THESIS ...... 11
CHAPTER 2 ...... 16
LITERATURE REVIEW ...... 16 2.1 GENERAL ...... 16 2.2 DESIGN FLOOD ESTIMATION METHODS ...... 16 2.2.1 Streamflow-based flood estimation methods ...... 16 2.2.2 Rainfall-based flood estimation methods ...... 18 2.3 REVIEW OF PREVIOUS STUDIES ON JOINT PROBABILITY APPROACH TO FLOOD ESTIMATION ...... 26 2.3.1 Analytical methods ...... 27 2.3.2 Approximate methods ...... 33 2.4 RUNOFF ROUTING MODEL ADOPTED IN THE PREVIOUS STUDIES ON JPA/MCST ...... 44 2.5 LOSS MODELS ...... 45
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2.6 INPUT VARIABLES IN RAINFALL RUNOFF MODELLING ...... 47 2.6.1 Rainfall characteristics ...... 47 2.6.2 Loss variables ...... 49 2.6.3 Runoff routing model parameters and baseflow ...... 50 2.7 REGIONALISATION METHODS ...... 51 2.8 SUMMARY OF CHAPTER 2 ...... 52
CHAPTER 3 ...... 55
DESCRIPTION OF THE METHODS ADOPTED IN THE DEVELOPMENT OF THE ENHANCED MONTE CARLO
SIMULATION TECHNIQUE ...... 55 3.1 INTRODUCTION ...... 55 3.2 SELECTION OF RAINFALL EVENTS ...... 56 3.3 SELECTED RUNOFF ROUTING MODEL ...... 58 3.4 SELECTED INPUT VARIABLES FOR STOCHASTIC REPRESENTATION ...... 58 3.5 FORMULATION OF RUNOFF ROUTING MODEL ...... 59 3.5.1 Selection of concurrent rainfall and streamflow events ...... 59 3.5.2 Criteria for baseflow separation ...... 60 3.5.3 Estimation of losses ...... 60 3.5.4 Calibration of the runoff routing model ...... 61 3.6 IDENTIFICATION OF MARGINAL PROBABILITY DISTRIBUTION FOR AN INPUT VARIABLE ...... 62 3.6.1 Fitting of a distribution to the observed data of an input variable ...... 64 3.6.2 Goodness-of-fit tests ...... 65 3.7 SPECIFICATION OF THE DISTRIBUTION OF RAINFALL DEPTH (IFD DATA) ...... 66 3.7.1 Correlation between rainfall intensity and durations ...... 67 3.7.2 Development of at-site IFD curves ...... 68 3.8 DERIVATION OF THE DIMENSIONLESS COMPLETE STORM TEMPORAL PATTERNS ...... 71 3.9 REGIONALISATION METHOD ADOPTED IN THIS STUDY ...... 72 3.10 IMPLEMENTATION OF THE ENHANCED MONTE CARLO SIMULATION TECHNIQUE (EMCST) ...... 74 3.11 FORMATION OF ANNUAL MAXIMUM FLOOD SERIES FROM GENERATED PARTIAL DURATION SERIES FLOOD PEAK DATA ...... 78 3.12 SENSITIVITY ANALYSIS ...... 80 3.13 VALIDATION OF THE ENHANCED MONTE CARLO SIMULATION TECHNIQUE (EMCST) ...... 81 3.13.1 Collation of the observed annual maximum flood series at the selected test catchments ...... 82 3.13.2 Design Event Approach ...... 82 Specification of rainfall intensity-frequency-duration (IFD) data ...... 83 Specification of design IL, CL, k, m and BF values ...... 86 Specification of rainfall TP data...... 86 3.13.3 Australian Rainfall and Runoff Regional Flood Frequency Estimation 2012 Model (Test version) 88
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3.13.4 Australian Rainfall and Runoff (1987) Probabilistic Rational Method (PRM) ...... 89 3.13.5 Model evaluation statistics ...... 91 3.14 SUMMARY OF CHAPTER 3 ...... 92
CHAPTER 4 ...... 95
DESCRIPTION OF STUDY AREA AND DATA ...... 95 4.1 INTRODUCTION ...... 95 4.2 SELECTION OF STUDY REGION ...... 95 4.3 COLLATION OF RAINFALL AND STREAMFLOW DATA ...... 96 4.3.1 Selection of pluviograph stations ...... 97 4.3.2 Selection of study catchments ...... 98 4.4 EXTRACTIONS OF PLUVIOGRAPH AND STREAMFLOW DATA ...... 112 4.4.1 Extraction of pluviograph data...... 112 4.4.2 Extraction of streamflow data ...... 113 4.5 SUMMARY OF CHAPTER 4 ...... 113
CHAPTER 5 ...... 115
REGIONALISATION OF INPUT VARIABLES ...... 115 5.1 INTRODUCTION ...... 115 5.2 SELECTED RAINFALL EVENTS FOR REGIONALISATION ...... 115 5.3 SELECTED CONCURRENT RAINFALL AND STREAMFLOW EVENTS FOR DERIVATION OF IL, CL AND K VALUES ...... 116 5.3.1 Selected concurrent rainfall and streamflow events ...... 117 5.3.2 Results of baseflow separation...... 121 5.3.3 Estimated losses and calibrated runoff routing model ...... 122
5.4 REGIONALISATION OF RAINFALL COMPLETE STORM DURATION (DCS) DATA ...... 124 5.5 REGIONALISATION OF RAINFALL INTER-EVENT DURATION (IED) DATA ...... 129 5.6 REGIONALISATION OF INTENSITY-FREQUENCY-DURATION (IFD) DATA ...... 134 5.6.1 Regionalisation of the IFD curves ...... 136 5.6.2 Finding the optimum number of stations to regionalise IFD curves at the location of interest .. 136 5.6.3 Summary of IFD data regionalisation ...... 143 5.7 REGIONALISATION OF TEMPORAL PATTERNS (TP) DATA ...... 144 5.8 REGIONALISATION OF THE INITIAL LOSS (IL) DATA ...... 144 5.8.1 Fitting of probability distributions to the at-site IL data ...... 144 5.8.2 Fitting of a probability distribution to the regional IL data ...... 145 5.8.3 Summary of IL data regionalisation ...... 145 5.9 REGIONALISATION OF CONTINUING LOSS (CL) DATA ...... 146 5.9.1 Fitting of probability distribution to the at-site CL data ...... 146
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5.9.2 Fitting of probability distribution to regional CL data ...... 147 5.9.3 Summary of CL data regionalisation ...... 147 5.10 REGIONALISATION OF STORAGE DELAY PARAMETER (K) ...... 147 5.10.1 Fitting distributions to the at-site k data ...... 148 5.10.2 Fitting distributions to the at-site standardised k data ...... 149 5.10.3 Fitting distribution to regional standardised k data ...... 150 5.11 CORRELATIONS AMONG THE INPUT VARIABLES AND PARAMETERS ...... 150 5.12 SUMMARY OF THE REGIONALISATION OF THE INPUT VARIABLES AND PARAMETERS ...... 150
CHAPTER 6 ...... 153
SENSITIVITY OF THE REGIONALISED DISTRIBUTIONS IN THE APPLICATION OF THE ENHANCED MONTE CARLO
SIMULATION TECHNIQUE ...... 153 6.1 INTRODUCTION ...... 153 6.2 SELECTION OF TEST CATCHMENTS FOR SENSITIVITY ANALYSIS ...... 153
6.3 SENSITIVITY ANALYSIS FOR RAINFALL COMPLETE STORM DURATION (DCS) ...... 154
6.3.1 Sensitivity analysis: Complete storm duration (DCS) ...... 154
6.3.2 Derived flood frequency curves using the adjusted DCS values ...... 155
6.3.3 Results of the sensitivity analysis for rainfall DCS ...... 156
6.3.4 Summary of the sensitivity analysis for rainfall DCS ...... 161 6.4 SENSITIVITY ANALYSIS FOR RAINFALL INTER-EVENT DURATION (IED) ...... 161 6.4.1 Sensitivity analysis: inter-event duration (IED) ...... 161 6.4.2 Derived flood frequency curves (DFFC) based on the adjusted IED values ...... 162 6.4.3 Results of the sensitivity analysis for rainfall IED ...... 162 6.4.4 Summary of the sensitivity analysis for rainfall IED ...... 166 6.5 SENSITIVITY ANALYSIS FOR RAINFALL INTENSITY-FREQUENCY-DURATION (IFD) DATA ...... 167 6.5.1 Sensitivity analysis: intensity-frequency-duration (IFD) ...... 167 6.5.2 Derived flood frequency curves using different IFD data ...... 168 6.5.3 Results of the sensitivity analysis for rainfall IFD data ...... 168 6.5.4 Summary of the sensitivity analysis for intensity-frequency-duration (IFD) data ...... 172 6.6 SENSITIVITY ANALYSIS FOR TEMPORAL PATTERNS (TP) DATA ...... 172 6.6.1 Sensitivity analysis: temporal patterns (TP) ...... 173 6.6.2 Derived flood frequency curves using different sets of TP data ...... 173 6.6.3 Results of the sensitivity analysis for temporal patterns (TP) ...... 173 6.6.4 Summary of the sensitivity analysis for temporal pattern (TP) data ...... 175 6.7 SENSITIVITY ANALYSIS FOR INITIAL LOSS (IL) DATA ...... 175 6.7.1 Sensitivity analysis: initial loss (IL)...... 175 6.7.2 Derived flood frequency curves using the adjusted IL values ...... 176 6.7.3 Results of the sensitivity analysis for IL ...... 176
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6.7.4 Summary of the sensitivity analysis for initial loss (IL) data ...... 180 6.8 SENSITIVITY ANALYSIS FOR CONTINUING LOSS (CL) DATA ...... 180 6.8.1 Sensitivity analysis: continuing loss (CL) ...... 181 6.8.2 Derived flood frequency curves using the adjusted CL values ...... 181 6.8.3 Results of the sensitivity analysis for continuing loss ...... 182 6.8.4 Summary of the sensitivity analysis for continuing loss ...... 184 6.9 SENSITIVITY ANALYSIS FOR STORAGE DELAY PARAMETER (K) ...... 184 6.9.1 Sensitivity analysis: Storage delay parameter (k) ...... 184 6.9.2 Derived flood frequency curves using the adjusted k values ...... 185 6.9.3 Results of the sensitivity analysis for storage delay parameter ...... 185 6.9.4 Summary of the sensitivity analysis for storage delay parameter (k) data ...... 189 6.10 SUMMARY OF CHAPTER 6 ...... 190
CHAPTER 7 ...... 192
VALIDATION OF THE DEVELOPED ENHANCED MONTE CARLO SIMULATION TECHNIQUE ...... 192 7.1 INTRODUCTION ...... 192 7.2 SELECTION OF TEST CATCHMENTS FOR VALIDATION ...... 193 7.3 DERIVATION OF THE FLOOD FREQUENCY CURVES USING AT-SITE FLOOD FREQUENCY ANALYSIS (FFA) ...... 194 7.4 DERIVATION OF FLOOD QUANTILES USING DESIGN EVENT APPROACH (DEA) ...... 197 7.5 DERIVED FLOOD FREQUENCY CURVE (DFFC) USING EMCST...... 200 7.6 FLOOD QUANTILE ESTIMATES USING ARR RFFE 2012 MODEL (TEST VERSION) ...... 205 7.7 FLOOD QUANTILE ESTIMATES USING THE PROBABILISTIC RATIONAL METHOD ...... 208 7.8 SUMMARY OF CHAPTER 7 ...... 212
CHAPTER 8 ...... 214
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS...... 214 8.1 GENERAL ...... 214 8.2 SUMMARY OF THE RESEARCH UNDERTAKEN IN THIS THESIS ...... 214 8.3 CONCLUSIONS ...... 219 8.4 RECOMMENDATIONS FOR FURTHER STUDY ...... 221
REFERENCES ...... 225
APPENDIX A ...... 243
A.1 EAGLESON’S JOINT PROBABILITY APPROACH BASED ON KINEMATIC RUNOFF MODEL ...... 243 A.2 TOTAL PROBABILITY THEOREM ...... 245
APPENDIX B ...... 247
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APPENDIX C ...... 298
APPENDIX D ...... 317
D.1 FORTRAN PROGRAM FOR SELECTING COMPLETE STORM EVENTS ...... 317 D.2 MATLAB PROGRAM FOR INVERSE DISTANCE WEIGHTED AVERAGING METHOD TO REGIONALISE INTENSITY-FREQUENCY-DURATION DATA ...... 319 D.3 FORTRAN PROGRAMS FOR INITIAL LOSS ANALYSIS ...... 341 D.4 FORTRAN PROGRAM FOR SIMULATION OF STREAMFLOW HYDROGRAPH ...... 344 D.5 FORTRAN PROGRAM FOR DESIGN EVENT APPROACH ...... 345
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LIST OF FIGURES
FIGURE 1.1: FLOOD WATERS AT KEMPSEY, THE PACIFIC HIGHWAY SOUTHBOUND FROM FREDERICKTON TO
KEMPSEY…………………………………………………………………………………………….3
FIGURE 1.2: AERIAL SHOT OF THE FLOODED SOUTHERN QUEENSLAND TOWN OF THEODORE ON JANUARY 1, 2011………………………………………………………………...... 4
FIGURE 1.3: ILLUSTRATION OF MAJOR STEPS IN THIS RESEARCH STUDY .……………………...... 11
FIGURE 2.1: VARIOUS DESIGN FLOOD ESTIMATION METHODS………………………………...... 17
FIGURE 2.2: PHYSICAL PROCESSES WHICH CONTRIBUTE TO RAINFALL LOSS……………………………………..46
FIGURE 2.3: INITIAL LOSS-CONTINUING LOSS MODEL………………………………………...... 47
FIGURE 3.1: RAINFALL EVENTS: COMPLETE STORM AND STORM-CORE…………………………………………..56
FIGURE 3.2: EXAMPLE OF A HISTOGRAM OF DCS FOR PLUVIOGRAPH STATION (ID 48027)……………………….63
FIGURE 3.3: RELATIONSHIP BETWEEN RAINFALL INTENSITY AND DURATION AT PLUVIOGRAPH STATION 48027……………………………………………………………………………………………….68
FIGURE 3.4: RELATIONSHIP BETWEEN RAINFALL INTENSITY AND DURATION AT PLUVIOGRAPH STATION 48031……………………………………………………………………………………………….68
FIGURE 3.5: EXAMPLE OF IFD CURVES DEVELOPED FROM COMPLETE STORM DATA………………………….….71
FIGURE 3.6: SAMPLE OF AT-SITE DIMENSIONLESS TEMPORAL PATTERNS (TP) FOR THE OXLEY RIVER
CATCHMENT………………………………………………………………………………………...72
FIGURE 3.7: ILLUSTRATION OF IDWA METHOD………………………………………………………………….73
FIGURE 3.8: SCHEMATIC DIAGRAM OF THE DEVELOPED EMCST………………………………………………...77
FIGURE 3.9: INTENSITY-FREQUENCY-DURATION CHART FOR THE OXLEY RIVER CATCHMENT (USED WITH THE DEA)……………………………………………………………………………………………….84
FIGURE 3.10: INTENSITY-FREQUENCY-DURATION DATA FOR THE OXLEY RIVER CATCHMENT (USED WITH THE DEA)……………………………………………………………………………………………….84
FIGURE 3.11: AUS-IFD VERSION 2.0 INTERFACE SHOWING HOW TO CONVERT LOG NORMAL VALUES TO LP3
ONES………………………………………………………………………………………………..85
FIGURE 3.12: EXAMPLE ARRANGEMENT OF INITIAL LOSS (IL) DATA FOR THE OXLEY RIVER CATCHMENT (FOR
RUNNING THE DEA FORTRAN PROGRAM)………………………………………………………...86
FIGURE 3.13: ZONE FOR TPS IN AUSTRALIA (EXTRACTED FROM VOLUME 2 OF ARR 1987)……………………..87
FIGURE 3.14: EXTRACTED TEMPORAL PATTERN PERCENTAGES PER PERIOD FOR THE OXLEY RIVER CATCHMENT
(FOR THE DEA APPLICATION)………………………………………………………………………88
FIGURE 3.15: STORM DURATIONS GROUPS BASED ON THEIR PERIODS……………………………………………88
FIGURE 4.1: HISTOGRAM OF RECORD LENGTHS FOR THE SELECTED 86 PLUVIOGRAPH STATIONS IN NSW……….97
FIGURE 4.2: SELECTED 86 PLUVIOGRAPH STATIONS AND 12 STUDY CATCHMENTS IN NSW……………………..98
FIGURE 4.3: OXLEY RIVER CATCHMENT (STATION ID 201001)………………………………………………...103
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FIGURE 4.4: SITE - OXLEY RIVER CATCHMENT…………………………………………………………………104
FIGURE 4.5: WILSONS RIVER CATCHMENT (STATION ID 203014)………………………………………………105
FIGURE 4.6: SITE - WILSONS RIVER CATCHMENT……………………………………………………………….106
FIGURE 4.7: BIELSDOWN CREEK CATCHMENT (STATION ID 203017)…………………………………………...107
FIGURE 4.8: DOWNSTREAM - BIELSDOWN CREEK CATCHMENT………………………………………………...107
FIGURE 4.9: ORARA RIVER CATCHMENT (STATION ID 204025)………………………………………………...108
FIGURE 4.10: SITE - ORARA RIVER CATCHMENT………………………………………………………………..109
FIGURE 4.11: WEST BROOK RIVER CATCHMENT (STATION ID 210080)………………………………………...110
FIGURE 4.12: SITE - WEST BROOK RIVER CATCHMENT ………………………………...... 110
FIGURE 4.13: BELAR CREEK CATCHMENT (STATION ID 420003)……………………………………………….111
FIGURE 4.14: SITE - BELAR CREEK CATCHMENT………………………………………………………………..112
FIGURE 5.1: AVERAGE NUMBER OF COMPLETE STORM EVENTS SELECTED PER YEAR FROM THE SELECTED 86
PLUVIOGRAPH STATIONS IN EASTERN NSW……………………………………………………….116
FIGURE 5.2: EXAMPLE OF BASEFLOW SEPARATION FOR AN EVENT……………………………………………...121
FIGURE 5.3: EXAMPLE OF BASEFLOW SEPARATION FOR AN EVENT WITH BIG GAP………………………………122
FIGURE 5.4: FREQUENCIES OF COMPLETE STORM DURATION (DCS) DATA FOR PLUVIOGRAPH STATION 56202….125
FIGURE 5.5: SPATIAL DISTRIBUTION OF THE STATIONS SATISFYING EXPONENTIAL AND GAMMA DISTRIBUTIONS
BASED ON THE KOLMOGOROV-SMIRNOV TEST (“NO DISTRIBUTION” INDICATES NEITHER GAMMA OR
EXPONENTIAL)…………………………………………………………………………………….126
FIGURE 5.6: SPATIAL DISTRIBUTION OF THE STATIONS SATISFYING EXPONENTIAL AND GAMMA DISTRIBUTIONS
BASED ON THE ANDERSON-DARLING TEST (“NO DISTRIBUTION” INDICATES NEITHER GAMMA OR
EXPONENTIAL)…………………………………………………………………………………….128
FIGURE 5.7: FREQUENCIES OF RAINFALL IED DATA FOR PLUVIOGRAPH STATION 67035……………………….130
FIGURE 5.8: FREQUENCIES OF THE TRIMMED RAINFALL IED DATA FOR PLUVIOGRAPH STATION 67035………..131
FIGURE 5.9: SPATIAL DISTRIBUTION OF THE STATIONS SATISFYING EXPONENTIAL AND GAMMA DISTRIBUTIONS
BASED ON THE KOLMOGOROV-SMIRNOV TEST. HERE “NO DISTRIBUTION” INDICATES NEITHER
GAMMA OR EXPONENTIAL IS ACCEPTABLE………………………………………………………...132
FIGURE 5.10: SPATIAL DISTRIBUTION OF THE STATIONS SATISFYING EXPONENTIAL AND GAMMA DISTRIBUTIONS
BASED ON THE ANDERSON-DARLING TEST. HERE “NO DISTRIBUTION” INDICATES NEITHER GAMMA
OR EXPONENTIAL IS ACCEPTABLE…………………………………………………………………133
FIGURE 5.11: DERIVED IFD CURVES FOR STATION 48027 ……………………………………………………...135
FIGURE 5.12: DERIVED IFD CURVES FOR STATION 48031………………………………………………………135
FIGURE 5.13: WEIGHTED AVERAGE IFD CURVES FOR OXLEY RIVER CATCHMENT……………………………..137
FIGURE 5.14: IFD CURVES FOR STATION ID 58109 FOR OXLEY RIVER CATCHMENT…………………………...137
FIGURE 5.15: IFD CURVES FOR STATION ID 58129……………………………………………………………..138
FIGURE 5.16: IFD CURVES FOR STATION ID 58113……………………………………………………………..138
FIGURE 5.17: IFD CURVES FOR STATION ID 58158……………………………………………………………..139
FIGURE 5.18: IFD CURVES FOR STATION ID 58044……………………………………………………………..140
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FIGURE 5.19: WEIGHTED AVERAGE IFD CURVES FOR ORARA RIVER CATCHMENT…………………………….141
FIGURE 5.20: IFD CURVES FOR STATION 59026 FOR CATCHMENT 204025…………………………………….142
FIGURE 5.21: IFD CURVES FOR STATION ID 59040……………………………………………………………..142
FIGURE 5.22: IFD CURVES FOR STATION ID 59067……………………………………………………………..143
FIGURE 6.1: DFFCS BASED ON THE ADOPTED DIFFERENT DCS MEAN VALUES FOR THE OXLEY RIVER CATCHMENT ...... 156
FIGURE 6.2: DFFCS BASED ON THE ADOPTED DIFFERENT DCS MEAN VALUES FOR BIELSDOWN CREEK CATCHMENT ...... 157
FIGURE 6.3: DFFCS BASED ON THE ADOPTED DIFFERENT DCS MEAN VALUE FOR THE BELAR CREEK CATCHMENT ...... 157
FIGURE 6.4: DFFCS BASED ON THE ADOPTED DIFFERENT DCS STANDARD DEVIATION VALUES FOR THE OXLEY
RIVER CATCHMENT...... 159
FIGURE 6.5: DFFCS BASED ON THE ADOPTED DIFFERENT DCS STANDARD DEVIATION VALUES FOR BIELSDOWN
CREEK CATCHMENT...... 159
FIGURE 6.6: DFFCS BASED ON THE ADOPTED DIFFERENT DCS STANDARD DEVIATION VALUES FOR THE BELAR
CREEK CATCHMENT...... 160
FIGURE 6.7: DFFCS BASED ON THE ADOPTED DIFFERENT IED MEAN VALUES FOR THE OXLEY RIVER CATCHMENT ...... 163
FIGURE 6.8: DFFCS BASED ON THE ADOPTED DIFFERENT IED MEAN VALUES FOR THE BIELSDOWN CREEK
CATCHMENT...... 163
FIGURE 6.9: DFFCS BASED ON THE ADOPTED DIFFERENT IED MEAN VALUES FOR THE BELAR CREEK CATCHMENT ...... 164
FIGURE 6.10: DFFCS BASED ON THE ADOPTED DIFFERENT STANDARD DEVIATION VALUES OF IED FOR THE OXLEY
RIVER CATCHMENT...... 165
FIGURE 6.11: DFFCS BASED ON THE ADOPTED DIFFERENT STANDARD DEVIATION VALUES OF IED FOR THE
BIELSDOWN CREEK CATCHMENT...... 165
FIGURE 6.12: DFFCS BASED ON THE ADOPTED DIFFERENT STANDARD DEVIATION VALUES OF IED FOR THE BELAR
CREEK CATCHMENT...... 166
FIGURE 6.13: DFFCS BASED ON THE ADOPTED DIFFERENT IFD DATA COMBINATIONS FOR THE OXLEY RIVER
CATCHMENT...... 169
FIGURE 6.14: DFFCS BASED ON THE ADOPTED DIFFERENT IFD DATA COMBINATIONS FOR THE BIELSDOWN CREEK
CATCHMENT...... 169
FIGURE 6.15: DFFCS BASED ON THE ADOPTED DIFFERENT IFD DATA COMBINATIONS FOR THE BIELSDOWN CREEK
CATCHMENT...... 170
FIGURE 6.16: DFFCS BASED ON THE ADOPTED IFD DATA FROM EACH SET OF PLUVIOGRAPH STATIONS FOR THE
OXLEY RIVER CATCHMENT...... 171
FIGURE 6.17: DFFCS BASED ON THE ADOPTED IFD DATA FROM EACH SET OF PLUVIOGRAPH STATIONS FOR THE
BIELSDOWN CREEK CATCHMENT...... 171
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Enhanced Joint Probability Approach Caballero
FIGURE 6.18: DFFCS BASED ON THE ADOPTED IFD DATA FROM EACH SET OF PLUVIOGRAPH STATIONS FOR THE
BELAR CREEK CATCHMENT...... 172
FIGURE 6.19: DFFCS BASED ON THE ADOPTED DIFFERENT SETS OF POOLED TP DATA FOR THE OXLEY RIVER
CATCHMENT...... 174
FIGURE 6.20: DFFCS BASED ON THE ADOPTED DIFFERENT POOLED TP DATA FOR THE BIELSDOWN CREEK
CATCHMENT...... 174
FIGURE 6.21: DFFCS BASED ON THE ADOPTED DIFFERENT SETS OF POOLED TP DATA FOR THE BELAR CREEK
CATCHMENT...... 175
FIGURE 6.22: DFFCS BASED ON THE ADOPTED DIFFERENT IL MEAN VALUES FOR THE OXLEY RIVER CATCHMENT ...... 177
FIGURE 6.23: DFFCS BASED ON THE ADOPTED DIFFERENT IL MEAN VALUES FOR THE BIELSDOWN CREEK
CATCHMENT...... 177
FIGURE 6.24: DFFCS BASED ON THE ADOPTED DIFFERENT IL MEAN VALUES FOR THE BELAR CREEK CATCHMENT ...... 178
FIGURE 6.25: DFFCS BASED ON THE ADOPTED DIFFERENT IL STANDARD DEVIATION VALUES FOR THE OXLEY
RIVER CATCHMENT...... 179
FIGURE 6.26: DFFCS BASED ON THE ADOPTED DIFFERENT IL STANDARD DEVIATION VALUES FOR THE BIELSDOWN
CREEK CATCHMENT...... 179
FIGURE 6.27: DFFCS BASED ON THE ADOPTED DIFFERENT IL STANDARD DEVIATION VALUES FOR THE BELAR
CREEK CATCHMENT...... 180
FIGURE 6.28: DFFCS BASED ON THE ADOPTED DIFFERENT CL MEAN VALUES FOR THE OXLEY RIVER CATCHMENT ...... 182
FIGURE 6.29: DFFCS BASE ON THE ADOPTED DIFFERENT CL MEAN VALUES FOR THE BIELSDOWN CREEK
CATCHMENT...... 183
FIGURE 6.30: DFFCS BASE ON THE ADOPTED DIFFERENT CL MEAN VALUES FOR THE BELAR CREEK CATCHMENT ...... 183
FIGURE 6.31: DFFCS BASED ON THE ADOPTED DIFFERENT K MEAN VALUES FOR THE OXLEY RIVER CATCHMENT ...... 186
FIGURE 6.32: DFFCS BASED ON THE ADOPTED DIFFERENT K MEAN VALUES FOR THE BIELSDOWN CREEK
CATCHMENT...... 186
FIGURE 6.33: DFFCS BASED ON THE ADOPTED DIFFERENT K MEAN VALUES FOR THE BELAR CREEK
CATCHMENT...... 187
FIGURE 6.34: DFFCS BASED ON THE ADOPTED DIFFERENT K STDEV VALUES FOR THE OXLEY RIVER
CATCHMENT...... 188
FIGURE 6.35: DFFCS BASED ON THE ADOPTED DIFFERENT K STDEV VALUES FOR THE BIELSDOWN CREEK
CATCHMENT...... 189
FIGURE 6.36: DFFCS BASED ON THE ADOPTED DIFFERENT K STDEV VALUES FOR THE BELAR CREEK CATCHMENT ...... 189
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FIGURE 7.1: AT-SITE FFA ESTIMATES FOR THE OXLEY RIVER CATCHMENT...... 196
FIGURE 7.2: OBSERVED FLOOD PEAKS AND FLOOD QUANTILES (USING FLIKE AND THE DEA) FOR THE SIX TEST
CATCHMENTS...... 199
FIGURE 7.3: OBSERVED ANNUAL FLOOD PEAKS, FLOOD QUANTILES (USING FLIKE AND THE DEA) AND DFFC
(USING EMCST) FOR THE SELECTED TEST CATCHMENT ...... 202
FIGURE 7.4: FLOOD QUANTILE ESTIMATES USING THE ARR RFFE 2012 MODEL AND OBSERVED ANNUAL
MAXIMUM FLOOD SERIES FOR THE SIX SELECTED TEST CATCHMENTS...... 207
FIGURE 7.5: OBSERVED FLOOD PEAKS, FLOOD QUANTILES (USING ARR RFFE 2012 MODEL (TEST VERSION) AND
THE ARR1987 PROBABILISTIC RATIONAL METHOD) AND DFFC (USING EMCST) FOR THE SELECTED
TEST CATCHMENTS...... 209
FIGURE C.3.1: CONVERTED RAINFALL INTENSITIES IN TABULATED FORM FOR THE OXLEY RIVER CATCHMENT .298
FIGURE C.3.2: TEMPORAL PATTERN HYETOGRAPHS FOR ZONE 1...... 299
FIGURE C.3.3: TEMPORAL PATTERN HYETOGRAPHS FOR ZONE 2...... 300
FIGURE C.3.4: TEMPORAL PATTERN HYETOGRAPHS FOR ZONE 3...... 301
FIGURE C.3.5: TEMPORAL PATTERN PERCENTAGES PER PERIOD FOR ZONE 1...... 302
FIGURE C.3.6: TEMPORAL PATTERN PERCENTAGES PER PERIOD FOR ZONE 2...... 303
FIGURE C.3.7: TEMPORAL PATTERN PERCENTAGES PER PERIOD FOR ZONE 3...... 304
FIGURE C.7.1: AT-SITE FFA ESTIMATES AND 90% CONFIDENCE LIMITS FOR THE WILSONS RIVER CATCHMENT ...... 305
FIGURE C.7.2: AT-SITE FFA ESTIMATES AND 90% CONFIDENCE LIMITS FOR THE BIELSDOWN CREEK CATCHMENT ...... 305
FIGURE C.7.3: AT-SITE FFA ESTIMATES AND 90% CONFIDENCE LIMITS FOR THE ORARA RIVER CATCHMENT ...306
FIGURE C.7.4: AT-SITE FFA ESTIMATES AND 90% CONFIDENCE LIMITS FOR THE WEST BROOK RIVER
CATCHMENT...... 306
FIGURE C.7.5: AT-SITE FFA ESTIMATES AND 90% CONFIDENCE LIMITS FOR THE BELAR CREEK CATCHMENT ...307
FIGURE C.7.6: FLOOD QUANTILE ESTIMATES USING THE DEA AND FLIKE, OBSERVED ANNUAL PEAKS AND DFFC
USING EMCST FOR THE OXLEY RIVER CATCHMENT...... 307
FIGURE C.7.7: FLOOD QUANTILE ESTIMATES USING THE DEA AND FLIKE, OBSERVED ANNUAL PEAKS AND DFFC
USING EMCST FOR THE WILSONS RIVER CATCHMENT...... 308
FIGURE C.7.8: FLOOD QUANTILE ESTIMATES USING THE DEA AND FLIKE, OBSERVED ANNUAL PEAKS AND DFFC
USING EMCST FOR THE BIELSDOWN CREEK CATCHMENT...... 308
FIGURE C.7.9: FLOOD QUANTILE ESTIMATES USING THE DEA AND FLIKE, OBSERVED ANNUAL PEAKS AND DFFC
USING EMCST FOR THE ORARA RIVER CATCHMENT...... 309
FIGURE C.7.10: FLOOD QUANTILE ESTIMATES USING THE DEA AND FLIKE, OBSERVED ANNUAL PEAKS AND
DFFC USING EMCST FOR THE WEST BROOK RIVER CATCHMENT...... 309
FIGURE C.7.11: FLOOD QUANTILE ESTIMATES USING THE DEA AND FLIKE, OBSERVED ANNUAL PEAKS AND
DFFC USING EMCST FOR THE BELAR CREEK CATCHMENT...... 310
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Enhanced Joint Probability Approach Caballero
FIGURE C.7.12: FLOOD QUANTILE ESTIMATES USING THE BGLS-ROI AND OBSERVED STREAMFLOW DATA FOR
THE OXLEY RIVER CATCHMENT...... 310
FIGURE C.7.13: FLOOD QUANTILE ESTIMATES USING THE BGLS-ROI AND OBSERVED STREAMFLOW DATA FOR
THE WILSONS RIVER CATCHMENT...... 311
FIGURE C.7.14: FLOOD QUANTILE ESTIMATES USING THE BGLS-ROI AND OBSERVED STREAMFLOW DATA FOR
THE BIELSDOWN CREEK CATCHMENT...... 311
FIGURE C.7.15: FLOOD QUANTILE ESTIMATES USING THE BGLS-ROI AND OBSERVED STREAMFLOW DATA FOR
THE ORARA RIVER CATCHMENT...... 312
FIGURE C.7.16: FLOOD QUANTILE ESTIMATES USING THE BGLS-ROI AND OBSERVED STREAMFLOW DATA FOR
THE WEST BROOK RIVER CATCHMENT...... 312
FIGURE C.7.17: FLOOD QUANTILE ESTIMATES USING THE BGLS-ROI AND OBSERVED STREAMFLOW DATA FOR
THE BELAR CREEK CATCHMENT...... 313
FIGURE C.7.18: FLOOD QUANTILE ESTIMATES USING THE PRM AND ARR RFFE 2012, OBSERVED ANNUAL PEAKS
AND DFFC USING EMCST FOR THE OXLEY RIVER CATCHMENT...... 313
FIGURE C.7.19: FLOOD QUANTILE ESTIMATES USING THE PRM AND ARR RFFE 2012, OBSERVED ANNUAL PEAKS
AND DFFC USING EMCST FOR THE WILSONS RIVER CATCHMENT...... 314
FIGURE C.7.20: FLOOD QUANTILE ESTIMATES USING THE PRM AND ARR RFFE 2012, OBSERVED ANNUAL PEAKS
AND DFFC USING EMCST FOR THE BIELSDOWN CREEK CATCHMENT...... 314
FIGURE C.7.21: FLOOD QUANTILE ESTIMATES USING THE PRM AND ARR RFFE 2012, OBSERVED ANNUAL PEAKS
AND DFFC USING EMCST FOR THE BIELSDOWN CREEK CATCHMENT...... 315
FIGURE C.7.22: FLOOD QUANTILE ESTIMATES USING THE PRM AND ARR RFFE 2012, OBSERVED ANNUAL PEAKS
AND DFFC USING EMCST FOR THE OXLEY RIVER CATCHMENT...... 315
FIGURE C.7.23: FLOOD QUANTILE ESTIMATES USING THE PRM AND ARR RFFE 2012, OBSERVED ANNUAL PEAKS
AND DFFC USING EMCST FOR THE OXLEY RIVER CATCHMENT...... 316
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LIST OF TABLES
TABLE 2.1: EXAMPLE OF COMPUTED FLOOD PEAKS BY DESIGN EVENT APPROACH FOR DURATIONS 1H TO 72H
(HERE Q2 MEANS FLOOD PEAK DISCHARGE HAVING ARI OF 2 YEARS) ...... 21
TABLE 3.1: AN EXAMPLE OF CLASS INTERVALS AND REPRESENTATIVE POINTS FOR COMPLETE STORM DURATION
(DCS) FOR DEVELOPING IFD CURVES ...... 69
TABLE 3.2: EXAMPLE OF AN IFD TABLE DEVELOPED FROM COMPLETE STORM DATA ...... 70
TABLE 3.3: EXAMPLE SEQUENCES OF GENERATED RAINFALL EVENTS AND CONSTRUCTION OF AM FLOOD PEAK
EVENTS ……………………………………………………………………………………………..80
TABLE 3.4: SUMMARISED RAINFALL INTENSITIES FOR THE OXLEY RIVER CATCHMENT (FOR THE DEA) ………. 85
TABLE 4.1: SELECTED CATCHMENTS FOR REGIONALISATION OF LOSSES AND RUNOFF ROUTING MODEL
PARAMETER………………………………………………………………………………………...99
TABLE 4.2: PLUVIOGRAPH STATIONS FOR THE SELECTED SIX CATCHMENTS SHOWN IN TABLE 4.1 …………….100
TABLE 4.3: SELECTED CATCHMENTS FOR TESTING THE APPLICABILITY OF THE REGIONALISED EMCST ………102
TABLE 4.4: PLUVIOGRAPH STATIONS FOR THE SELECTED THREE TEST CATCHMENTS SHOWN IN TABLE 4.3 ……102
TABLE 5.1: SUMMARY OF SELECTED EVENTS IN INITIAL CALIBRATION OF THE RUNOFF ROUTING MODEL (F1 = 0.8
AND F2 = 0.9) ……………………………………………………………………………………...118
TABLE 5.2: SELECTED EVENTS FOR CALIBRATION OF THE ADOPTED RUNOFF ROUTING MODEL (REDUCTION
FACTORS F1 = 0.8 AND F2 = 0.9) …………………………………………………………………..120
TABLE 5.3: RETAINED EVENTS IN THE INITIAL CALIBRATION …………………………………………………..123
TABLE 5.4: RETAINED EVENTS IN THE FINAL CALIBRATION OF THE ADOPTED RUNOFF ROUTING MODEL
(REDUCTION FACTORS F1 = 0.6 AND F2 = 0.7) ……………………………………………………..124
TABLE 5.5: SUMMARY OF THE CALIBRATED VALUES OF IL, CL AND K FOR COOPERS CREEK CATCHMENT
(STATION ID 203002) ……………………………………………………………………………..124
TABLE 5.6: SUMMARY OF THE GOODNESS-OF-FIT TEST (STATIONS SHOWING THE ACCEPTED DISTRIBUTIONS) FOR
COMPLETE STORM DURATIONS (DCS) DATA (“NUMBER OF STATIONS” INDICATES THE NUMBER OF
STATIONS SATISFYING THE HYPOTHESISED DISTRIBUTION.) ………………………………………126
TABLE 5.7: SUMMARY OF THE GOODNESS-OF-FIT TEST FOR THE STATIONS SATISFYING BOTH EXPONENTIAL AND
GAMMA DISTRIBUTIONS FOR COMPLETE STORM DURATIONS (DCS) DATA (“NUMBER OF STATIONS”
INDICATES THE NUMBER OF STATIONS SATISFYING THE HYPOTHESISED DISTRIBUTION.) …………127
TABLE 5.8: EXAMPLE OF INVERSE DISTANCE WEIGHTED AVERAGING FOR RAINFALL DCS DATA FOR OXLEY RIVER
CATCHMENT ………………………………………………………………………………………128
TABLE 5.9: SUMMARY OF THE GOODNESS-OF-FIT TEST FOR RAINFALL IED DATA – 1ST SET (“NUMBER OF
STATIONS” INDICATES THE NUMBER OF STATIONS SATISFYING THE HYPOTHESISED DISTRIBUTION.). …………………………………………………………………………………………………….130
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Enhanced Joint Probability Approach Caballero
TABLE 5.10: SUMMARY OF THE GOODNESS-OF-FIT TEST FOR TRIMMED RAINFALL IED DATA – 2ND SET (“NUMBER
OF STATIONS” INDICATES THE NUMBER OF STATIONS SATISFYING THE HYPOTHESISED DISTRIBUTION.) …………………………………………………………………………………………………….131
TABLE 5.11: SUMMARY OF THE GOODNESS-OF-FIT TEST FOR THE STATIONS SATISFYING BOTH EXPONENTIAL AND
GAMMA DISTRIBUTIONS FOR INTER-EVENT DURATIONS (IED) DATA ……………………………..132
TABLE 5.12: EXAMPLE OF INVERSE DISTANCE WEIGHTED AVERAGING FOR RAINFALL IED DATA ……………..133
TABLE 5.13: DESIGN IFD DATA FOR PLUVIOGRAPH STATION 48027 …………………………………………...134
TABLE 5.14: DESIGN IFD DATA FOR PLUVIOGRAPH STATION 48031 …………………………………………...134
TABLE 5.15: WEIGHTED AVERAGE IFD DATA FOR OXLEY RIVER CATCHMENT (STATION ID 201001) ………...139
TABLE 5.16: SUMMARY OF THE WEIGHTS IN OBTAINING THE WEIGHTED AVERAGE IFD DATA FOR OXLEY RIVER
CATCHMENT ………………………………………………………………………………………140
TABLE 5.17: SUMMARY OF WEIGHTS IN OBTAINING THE WEIGHTED AVERAGE IFD DATA FOR ORARA RIVER
CATCHMENT ………………………………………………………………………………………141
TABLE 5.18: GOODNESS-OF-FIT TESTS SUMMARY FOR THE INITIAL LOSS DATA FOR THE SIX CATCHMENTS. HERE,
THE CODE ZERO (0) AND ONE (1) STANDS FOR ‘DO NOT REJECT’ AND ‘REJECT’ THE HYPOTHESIS,
RESPECTIVELY. EXPONENTIAL DISTRIBUTION = ED AND GAMMA DISTRIBUTION = GD …………..145
TABLE 5.19: SUMMARY OF GOODNESS-OF-FIT TESTS FOR INITIAL LOSS (IL) DATA. HERE, PERCENTAGE (%)
IMPLIES THE % OF STATIONS SATISFYING A HYPOTHESISED DISTRIBUTION ……………………….146
TABLE 5.20: GOODNESS-OF-FIT TEST SUMMARY FOR THE CONTINUING LOSS (CL) DATA FOR THE SIX
CATCHMENTS. IN THIS TABLE, THE CODE ZERO (0) AND ONE (1) STANDS FOR ‘DO NOT REJECT’ AND
‘REJECT’ THE NULL HYPOTHESIS, RESPECTIVELY. EXPONENTIAL DISTRIBUTION = ED AND GAMMA
DISTRIBUTION = GD ………………………………………………………………………………146
TABLE 5.21: SUMMARY OF GOODNESS-OF-FIT TESTS FOR CONTINUING LOSS (CL) DATA. HERE, PERCENTAGE (%)
IMPLIES THE % OF STATIONS SATISFYING A HYPOTHESISED DISTRIBUTION ……………………….147
TABLE 5.22: GOODNESS-OF-FIT TESTS SUMMARY FOR THE STORAGE DELAY PARAMETER DATA FOR THE SIX
CATCHMENTS. IN THIS TABLE, THE CODE ZERO (0) AND ONE (1) STANDS FOR ‘DO NOT REJECT’ AND
‘REJECT’ THE HYPOTHESIS, RESPECTIVELY. EXPONENTIAL DISTRIBUTION = ED AND GAMMA
DISTRIBUTION = GD ………………………………………………………………………………148
TABLE 5.23: SUMMARY OF GOODNESS-OF-FIT TESTS FOR STORAGE DELAY PARAMETER DATA. HERE, PERCENTAGE
(%) IMPLIES THE % OF STATIONS SATISFYING A HYPOTHESISED DISTRIBUTION …………………..148
TABLE 5.24: GOODNESS-OF-FIT TESTS FOR THE STANDARDISED STORAGE DELAY PARAMETER DATA FOR THE SIX
CATCHMENTS. IN THIS TABLE, THE CODE ZERO (0) AND ONE (1) STANDS FOR ‘DO NOT REJECT’ AND
‘REJECT’ THE HYPOTHESIS, RESPECTIVELY. EXPONENTIAL DISTRIBUTION = ED AND GAMMA
DISTRIBUTION = GD ………………………………………………………………………………149
TABLE 5.25: SUMMARY OF GOODNESS-OF-FIT TESTS FOR STANDARDISED STORAGE DELAY PARAMETER DATA FOR
THE SIX CATCHMENTS. HERE, PERCENTAGE (%) IMPLIES THE % OF STATIONS SATISFYING A
HYPOTHESISED DISTRIBUTION …………………………………………………………………….150
TABLE 5.26: REGIONALISED MODEL INPUTS AND THEIR PROBABILITY DISTRIBUTIONS FOR EASTERN NSW …...151
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Enhanced Joint Probability Approach Caballero
TABLE 6.1: MODEL INPUTS FOR THE THREE TEST CATCHMENTS ………………………………………………..154
TABLE 6.2: ADJUSTED DCS MEAN AND STANDARD DEVIATION VALUES FOR THE OXLEY RIVER CATCHMENT ....155
TABLE 6.3: ADJUSTED DCS MEAN AND STANDARD DEVIATION VALUES FOR THE BIELSDOWN CREEK CATCHMENT …………………………………………………………………………………………………….155
TABLE 6.4: ADJUSTED DCS MEAN AND STANDARD DEVIATION VALUES FOR THE BELAR CREEK CATCHMENT.....155
TABLE 6.5: ADJUSTED IED MEAN AND STANDARD DEVIATION VALUES FOR THE OXLEY RIVER CATCHMENT …161
TABLE 6.6: ADJUSTED IED MEAN AND STANDARD DEVIATION VALUES FOR THE BIELSDOWN CREEK CATCHMENT …………………………………………………………………………………………………….162
TABLE 6.7: ADJUSTED IED MEAN AND STANDARD DEVIATION VALUES FOR THE BELAR CREEK CATCHMENT ...162
TABLE 6.8: PLUVIOGRAPH STATION NUMBERS AND DISTANCES FOR THE OXLEY RIVER CATCHMENT …………167
TABLE 6.9: PLUVIOGRAPH STATION NUMBERS AND DISTANCES FOR THE BIELSDOWN CREEK CATCHMENT …...167
TABLE 6.10: PLUVIOGRAPH STATION NUMBERS AND DISTANCES FOR THE BELAR CREEK CATCHMENT (ID 420003) …………………………………………………………………………………………………….168
TABLE 6.11: ADJUSTED IL MEAN AND STANDARD DEVIATION VALUES FOR THE OXLEY RIVER CATCHMENT ….176
TABLE 6.12: ADJUSTED IL MEAN AND STANDARD DEVIATION VALUES FOR THE BIELSDOWN CREEK CATCHMENT …………………………………………………………………………………………………….176
TABLE 6.13: ADJUSTED IL MEAN AND STANDARD DEVIATION VALUES FOR THE BELAR CREEK CATCHMENT ...176
TABLE 6.14: ADJUSTED VALUES OF CL MEAN FOR THE OXLEY RIVER CATCHMENT …………………………...181
TABLE 6.15: ADJUSTED VALUES OF CL MEAN FOR THE BIELSDOWN CREEK CATCHMENT ……………………..181
TABLE 6.16: ADJUSTED VALUES OF CL MEAN FOR THE BELAR CREEK CATCHMENT …………………………..181
TABLE 6.17: ADJUSTED K MEAN AND STANDARD DEVIATION VALUES FOR THE OXLEY RIVER CATCHMENT …..184
TABLE 6.18: ADJUSTED K MEAN AND STANDARD DEVIATION VALUES FOR THE BIELSDOWN CREEK CATCHMENT …………………………………………………………………………………………………….185
TABLE 6.19: ADJUSTED K MEAN AND STANDARD DEVIATION VALUES FOR THE BELAR CREEK CATCHMENT …..185
TABLE 7.1: MODEL INPUTS AND PARAMETERS FOR THE APPLICATION OF THE NEW EMCST FOR THE SIX TEST
CATCHMENTS ……………………………………………………………………………………..194
TABLE 7.2: ANNUAL MAXIMUM FLOW DATA FOR THE OXLEY RIVER CATCHMENT …………………………….195
TABLE 7.3: AT-SITE FFA ESTIMATES AND 90% CONFIDENCE LIMITS FOR THE OXLEY RIVER CATCHMENT ……196
TABLE 7.4: FLOOD QUANTILES (M3/S) SUMMARY FOR THE OXLEY RIVER CATCHMENT USING DEA…………...197
TABLE 7.5: CATCHMENT DATA AND TIME OF CONCENTRATION (TC) VALUES FOR THE SIX TEST CATCHMENTS …198
TABLE 7.6: PARAMETER VALUES FOR THE SIX SELECTED TEST CATCHMENT TO APPLY EMCST ……………….201
TABLE 7.7: SUMMARY OF RELATIVE ERROR (RE) FOR THE SELECTED TEST CATCHMENTS USING EMCST AND
DEA ………………………………………………………………………………………………203
TABLE 7.8: SUMMARY OF RATIO (R) FOR THE SELECTED TEST CATCHMENTS USING EMCST AND DEA……….203
TABLE 7.9: SUMMARY OF RELATIVE MEAN BIAS (BIAS) FOR THE SELECTED TEST CATCHMENTS USING EMCST
AND DEA………………………………………………………………………………………….204
TABLE 7.10: SUMMARY OF RELATIVE ROOT MEAN SQUARE ERROR (RMSE) FOR THE SELECTED TEST
CATCHMENTS USING EMCST AND DEA…………………………………………………………..204
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Enhanced Joint Probability Approach Caballero
TABLE 7.11: INPUTS FOR THE SELECTED TEST CATCHMENTS FOR USING ARR RFFE 2012 MODEL (TEST VERSION) …………………………………………………………………………………………………….206
TABLE 7.12: FLOOD QUANTILE ESTIMATES USING ARR RFFE 2012 MODEL FOR THE OXLEY RIVER CATCHMENT …………………………………………………………………………………………………….206
TABLE 7.13: FLOOD QUANTILE ESTIMATES USING PROBABILISTIC RATIONAL METHOD FOR THE SELECTED TEST
CATCHMENTS ……………………………………………………………………………………..208
TABLE 7.14: SUMMARY OF RELATIVE ERROR (RE) FOR THE SELECTED TEST CATCHMENTS USING EMCST, ARR
RFFE 2012 MODEL (TEST VERSION) AND DEA …………………………………………………...210
TABLE 7.15: SUMMARY OF RATIO (R) FOR THE SELECTED TEST CATCHMENTS USING EMCST, ARR RFFE 2012
MODEL (TEST VERSION) AND DEA ………………………………………………………………..211
TABLE 7.16: SUMMARY OF RELATIVE MEAN BIAS (BIAS) FOR THE SELECTED TEST CATCHMENTS USING EMCST,
ARR RFFE 2012 MODEL (TEST VERSION) AND DEA ……………………………………………..211
TABLE 7.17: SUMMARY OF RELATIVE ROOT MEAN SQUARE ERROR (RMSE) FOR THE SELECTED TEST CATCHMENTS
USING EMCST, ARR RFFE 2012 MODEL (TEST VERSION) AND DEA ……………………………211
TABLE 7.18: RANKING OF THE FOUR METHODS BASED ON THE MODEL EVALUATION STATISTICS FOR THE SELECTED
TEST CATCHMENTS ………………………………………………………………………………..212
TABLE 8.1: STOCHASTIC MODEL INPUTS/PARAMETER VALUES FOR EASTERN NSW AND TYPICAL PARAMETER
VALUES OF THE RESPECTIVE MARGINAL DISTRIBUTIONS ………………………………………….218
TABLE B.4.1: PLUVIOGRAPH STATIONS AND SELECTED EVENTS FROM NSW …………………………………..247
TABLE B.4.2: COMPLETE STORM DURATION DATA STATISTICS…………………………………………………250
TABLE B.5.1: SUMMARY OF CALIBRATION RESULTS FOR THE BYRON CREEK CATCHMENT ……………………254
TABLE B.5.2: SUMMARY OF CALIBRATION RESULTS FOR THE POKOLBIN CREEK CATCHMENT…………………255
TABLE B.5.3: SUMMARY OF CALIBRATION RESULTS FOR THE ANTIENE CREEK CATCHMENT ………………….255
TABLE B.5.4: SUMMARY OF CALIBRATION RESULTS FOR TOONGABBIE CREEK CATCHMENT………………...... 256
TABLE B.5.5: SUMMARY OF CALIBRATION RESULTS FOR THE MILL POST CREEK CATCHMENT ………………..256
TABLE B.5.6: GOODNESS-OF-FIT TEST RESULTS FOR DCS DATA ……………………………………………….. 257
TABLE B.5.7: RAINFALL INTER-EVENT DURATION (ORIGINAL DATA) DATA STATISTICS ……………………..259
TABLE B.5.8: GOODNESS-OF-FIT TEST RESULTS FOR IED DATA (1ST SET)………………………………………262
TABLE B.5.9: RAINFALL INTER-EVENT DURATION (TRIMMED DATA) DATA STATISTICS ……………………..265
TABLE B.5.10: GOODNESS-OF-FIT TEST RESULTS FOR IED DATA (2ND SET)……………………………………..268
TABLE B.6.1: DIFFERENCES IN DFFCS WHEN INCREASING AND DECREASING DCS MEAN VALUES FOR THE OXLEY
RIVER CATCHMENT ……………………………………………………………………………….271
TABLE B.6.2: DIFFERENCES IN DFFCS WHEN INCREASING AND DECREASING DCS MEAN VALUES FOR THE
BIELSDOWN CREEK CATCHMENT………………………………………………………………….271
TABLE B.6.3: DIFFERENCES IN DFFCS WHEN INCREASING AND DECREASING DCS MEAN VALUES FOR THE BELAR
CREEK CATCHMENT……………………………………………………………………………….272
TABLE B.6.4: DIFFERENCES IN DFFCS WHEN INCREASING AND DECREASING DCS STANDARD DEVIATION VALUES
FOR THE OXLEY RIVER CATCHMENT ……………………………………………………………...272
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Enhanced Joint Probability Approach Caballero
TABLE B.6.5: DIFFERENCES IN DFFCS WHEN INCREASING AND DECREASING DCS STANDARD DEVIATION VALUES
FOR THE BIELSDOWN CREEK CATCHMENT ………………………………………………………..273
TABLE B.6.6: DIFFERENCES IN DFFCS WHEN INCREASING AND DECREASING DCS STANDARD DEVIATION VALUES
FOR THE BELAR CREEK CATCHMENT ……………………………………………………………..273
TABLE B.6.7: DIFFERENCE IN DFFC WHEN INCREASING AND DECREASING IED MEAN VALUES FOR THE OXLEY
RIVER CATCHMENT………………………………………………………………………………..274
TABLE B.6.8: DIFFERENCES IN DFFCS WHEN INCREASING AND DECREASING IED MEAN VALUES FOR THE
BIELSDOWN CREEK CATCHMENT………………………………………………………………….274
TABLE B.6.9: DIFFERENCES IN DFFCS WHEN INCREASING AND DECREASING IED MEAN VALUES FOR THE BELAR
CREEK CATCHMENT……………………………………………………………………………….275
TABLE B.6.10: DIFFERENCE IN DFFCS WHEN INCREASING AND DECREASING IED STANDARD DEVIATION VALUES
FOR THE OXLEY RIVER CATCHMENT………………………………………………………………275
TABLE B.6.11: DIFFERENCES IN DFFCS WHEN INCREASING AND DECREASING IED STANDARD DEVIATION VALUES
FOR THE BIELSDOWN CREEK CATCHMENT………………………………………………………...276
TABLE B.6.12: DIFFERENCES IN DFFCS WHEN INCREASING AND DECREASING IED STANDARD DEVIATION VALUES
FOR THE BELAR CREEK CATCHMENT……………………………………………………………...276
TABLE B.6.13: DIFFERENCES IN DFFCS WHEN CHANGING STATION COMBINATIONS (ONE TO NINE STATIONS,
EXCEPT FIVE STATIONS) FOR THE OXLEY RIVER CATCHMENT…………………………………….277
TABLE B.6.14: DIFFERENCES IN DFFCS WHEN CHANGING STATION COMBINATIONS (ONE STATION AND THREE TO
NINE STATIONS) FOR THE BIELSDOWN CREEK CATCHMENT……………………………………….277
TABLE B.6.15: DIFFERENCES IN DFFCS WHEN CHANGING STATION COMBINATIONS (TWO TO NINE STATIONS) FOR
THE BELAR CREEK CATCHMENT…………………………………………………………………..278
TABLE B.6.16: DIFFERENCES IN DFFCS WHEN USING DIFFERENT PLUVIOGRAPH STATIONS (1ST TO 8TH STATION)
FOR THE OXLEY RIVER CATCHMENT ……………………………………………………………...278
TABLE B.6.17: DIFFERENCES IN DFFCS WHEN USING DIFFERENT PLUVIOGRAPH STATIONS (1ST TO 8TH STATION)
FOR THE BIELSDOWN CREEK CATCHMENT………………………………………………………...279
TABLE B.6.18: DIFFERENCES IN DFFCS WHEN USING DIFFERENT PLUVIOGRAPH STATIONS (2ND TO 9TH STATION)
FOR THE BELAR CREEK CATCHMENT……………………………………………………………...279
TABLE B.6.19: DIFFERENCES IN DFFCS WHEN USING COMBINATIONS OF POOLED TP DATA FROM DIFFERENT
PLUVIOGRAPH STATIONS (TWO TO NINE STATION COMBINATIONS) FOR THE OXLEY RIVER
CATCHMENT……………………………………………………………………………………….280
TABLE B.6.20: DIFFERENCES IN DFFCS WHEN USING COMBINATIONS OF POOLED TP DATA FROM DIFFERENT
PLUVIOGRAPH STATIONS (TWO TO NINE STATION COMBINATIONS) FOR THE BIELSDOWN CREEK
CATCHMENT ………………………………………………………………………………………280
TABLE B.6.21: DIFFERENCES IN DFFCS WHEN USING COMBINATIONS OF POOLED TP DATA FROM DIFFERENT
PLUVIOGRAPH STATIONS (TWO TO NINE STATION COMBINATIONS) FOR THE BELAR CREEK
CATCHMENT ………………………………………………………………………………………281
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Enhanced Joint Probability Approach Caballero
TABLE B.6.22: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF IL MEAN FOR THE OXLEY RIVER
CATCHMENT……………………………………………………………………………………….281
TABLE B.6.23: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF IL MEAN FOR THE BIELSDOWN CREEK
CATCHMENT……………………………………………………………………………………….282
TABLE B.6.24: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF IL MEAN FOR THE BELAR CREEK
CATCHMENT ………………………………………………………………………………………282
TABLE B.6.25: DIFFERENCE IN DFFC WHEN CHANGING THE VALUES OF IL STANDARD DEVIATION FOR THE
OXLEY RIVER CATCHMENT………………………………………………………………………..283
TABLE B.6.26: DIFFERENCE IN DFFC WHEN CHANGING THE VALUES OF IL STANDARD DEVIATION FOR THE
BIELSDOWN CREEK CATCHMENT …………………………………………………………………283
TABLE B.6.27: DIFFERENCE IN DFFC WHEN CHANGING THE VALUES OF IL STANDARD DEVIATION FOR THE
BELAR CREEK CATCHMENT……………………………………………………………………….284
TABLE B.6.28: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF CL MEAN FOR THE OXLEY RIVER
CATCHMENT ………………………………………………………………………………………284
TABLE B.6.29: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF CL MEAN FOR THE BIELSDOWN CREEK
CATCHMENT ………………………………………………………………………………………285
TABLE B.6.30: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF CL MEAN FOR THE BELAR CREEK
CATCHMENT ………………………………………………………………………………………285
TABLE B.6.31: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF K MEAN FOR THE OXLEY RIVER
CATCHMENT……………………………………………………………………………………….286
TABLE B.6.32: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF K MEAN FOR THE BIELSDOWN CREEK
CATCHMENT……………………………………………………………………………………….286
TABLE B.6.33: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF K MEAN FOR THE BELAR CREEK
CATCHMENT……………………………………………………………………………………….287
TABLE B.6.34: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF K STANDARD DEVIATION FOR THE
OXLEY RIVER CATCHMENT………………………………………………………………………..287
TABLE B.6.35: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF K STANDARD DEVIATION FOR THE
BIELSDOWN CREEK CATCHMENT………………………………………………………………….288
TABLE B.6.36: DIFFERENCES IN DFFCS WHEN CHANGING THE VALUES OF K STANDARD DEVIATION FOR THE
BELAR CREEK CATCHMENT ………………………………………………………………………288
TABLE B.7.1: ANNUAL MAXIMUM FLOW DATA FOR THE WILSONS RIVER CATCHMENT ………………………..289
TABLE B.7.2: ANNUAL MAXIMUM FLOW DATA FOR THE BIELSDOWN CREEK CATCHMENT …………………….289
TABLE B.7.3: ANNUAL MAXIMUM FLOW DATA FOR THE ORARA RIVER CATCHMENT…………………………..290
TABLE B.7.4: ANNUAL MAXIMUM FLOW DATA FOR THE WEST BROOK RIVER CATCHMENT …………………...290
TABLE B.7.5: ANNUAL MAXIMUM FLOW DATA FOR THE BELAR CREEK CATCHMENT…………………………..291
TABLE B.7.6: AT-SITE FFA ESTIMATES AND 90% CONFIDENCE LIMITS FOR THE WILSONS RIVER CATCHMENT..291
TABLE B.7.7: AT-SITE FFA ESTIMATES AND 90% CONFIDENCE LIMITS FOR THE BIELSDOWN CREEK CATCHMENT …………………………………………………………………………………………………….292
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TABLE B.7.8: AT-SITE FFA ESTIMATES AND 90% CONFIDENCE LIMITS FOR THE ORARA RIVER CATCHMENT….292
TABLE B.7.9: AT-SITE FFA ESTIMATES AND 90% CONFIDENCE LIMITS FOR THE WEST BROOK RIVER
CATCHMENT……………………………………………………………………………………….293
TABLE B.7.10: AT-SITE FFA ESTIMATES AND 90% CONFIDENCE LIMITS FOR THE BELAR CREEK CATCHMENT...293
TABLE B.7.11: FLOOD QUANTILES (M3/S) SUMMARY FOR THE WILSONS RIVER CATCHMENT USING DEA……..294
TABLE B.7.12: FLOOD QUANTILES (M3/S) SUMMARY FOR THE BIELSDOWN CREEK CATCHMENT USING DEA….294
TABLE B.7.13: FLOOD QUANTILES (M3/S) SUMMARY FOR THE ORARA RIVER CATCHMENT USING DEA……….294
TABLE B.7.14: FLOOD QUANTILES (M3/S) SUMMARY FOR THE WEST BROOK RIVER CATCHMENT USING DEA...295
TABLE B.7.15: FLOOD QUANTILES (M3/S) SUMMARY FOR THE BELAR CREEK CATCHMENT USING DEA……….295
TABLE B.7.16: FLOOD QUANTILE ESTIMATES USING RFFE 2012 MODEL FOR THE WILSONS RIVER CATCHMENT …………………………………………………………………………………………………….295
TABLE B.7.17: FLOOD QUANTILE ESTIMATES USING RFFE 2012 MODEL FOR THE BIELSDOWN CREEK
CATCHMENT……………………………………………………………………………………….296
TABLE B.7.18: FLOOD QUANTILE ESTIMATES USING RFFE 2012 MODEL FOR THE ORARA RIVER CATCHMENT..296
TABLE B.7.19: FLOOD QUANTILE ESTIMATES USING RFFE 2012 MODEL FOR THE WEST BROOK RIVER
CATCHMENT……………………………………………………………………………………….296
TABLE B.7.20: FLOOD QUANTILE ESTIMATES USING RFFE 2012 MODEL FOR THE BELAR CREEK CATCHMENT..297
TABLE D.1: EXAMPLE INPUT FILES TO PROGRAM MCSA5CS1.FOR FOR SELECTING COMPLETE STORM EVENTS ...317
TABLE D.2: EXAMPLE OUTPUT FILES FROM PROGRAM MCSA5CS1.FOR FOR SELECTING COMPLETE STORM EVENTS …………………………………………………………………………………………………….318
TABLE D.3: EXAMPLE INPUT FILES TO PROGRAM DISTANCE_COMPUTATION_1M.M FOR INVERSE DISTANCE
WEIGHTED AVERAGING METHOD …………………………...... 339
TABLE D.4: EXAMPLE OUTPUT FILES FROM PROGRAM DISTANCE_COMPUTATION_1M.M FOR INVERSE DISTANCE
WEIGHTED AVERAGING METHOD ……………………...... 340
TABLE D.5: EXAMPLE INPUT FILES TO PROGRAM MCSA5CS1.FOR FOR LOSS ANALYSIS…………………………341
TABLE D.6: EXAMPLE OUTPUT FILES FROM PROGRAM MCSA5CS1.FOR FOR LOSS ANALYSIS……………………341
TABLE D.7: EXAMPLE INPUT FILES TO LOSSSCA.FOR FOR LOSS ANALYSIS……………………………………...342
TABLE D.8: EXAMPLE OUTPUT FILES FROM PROGRAM LOSSSCA.FOR FOR LOSS ANALYSIS……………………...342
TABLE D.9: EXAMPLE INPUT FILES TO CALI2.FOR FOR LOSS ANALYSIS…………………………………………343
TABLE D.10: EXAMPLE OUTPUT FILE FROM PROGRAM CALI2.FOR FOR LOSS ANALYSIS………………………...343
TABLE D.11: EXAMPLE OUTPUT FILES FROM PROGRAM MCDFFC4ID3.FOR……………………………………...344
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LIST OF SYMBOLS
2 ID 2-year ARI intensity for the selected storm duration D 2 Id 2-year ARI intensity for the selected sub-storm duration d A Catchment area A2 Anderson and Darling test statistics C Runoff coefficient
C1 Complete storm threshold 1
C2 Complete storm threshold 2
C10 Dimensionless runoff coefficient for ARI of 10 years
CY Dimensionless runoff coefficient for ARI of Y years d Sub-storm duration d c Mean value of storm-core duration at the station or in the region D Storm duration D1, D2 … Sequence of design storm durations
Dc Storm-core duration
Di Random value of generated complete storm duration
DCS Complete storm duration
DCS1 Simulated complete storm duration of event 1
Ei Expected frequencies
F1 Reduction factor 1
F2 Reduction factor 2 F2 and F50 Geographical factors
FFY Frequency factor for Y ARI with the PRM
Fn(x) Observed cumulative distribution function
F0(x) Expected cumulative distribution function G Average regional skewness I Rainfall intensity
Ii Value of generated rainfall intensity during simulation
ICS Rainfall intensity for complete storm
I tc,Y Average rainfall intensity for a time of concentration and ARI of Y years
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Enhanced Joint Probability Approach Caballero
xn, Critical values (e.g. Dn,0.05) k Storage delay parameter and number of parameters estimated ki Random value of storage delay parameter l Total number of classes m Assigned rank and non-linearity parameter (0.80) M Number of data points in a class n Number of samples and points N Number of data points NG Number of data points to be generated in simulation NY Number of years of data generated in simulation
Oi Observed frequencies p ( ) Probability density Q Flood peak estimate and rate of outflow
Q2 Flood peak discharge for 2 years ARI
Qi Peak discharge of generated streamflow hydrograph in simulation
Qobs Observed flood quantile
Qpred Predicted flood quantile
QY Peak flow rate for an ARI of Y years R2 Coefficient of determination
RFId Sub-storm duration
RFID Storm duration for duration D S Maximum water abstraction and catchment storage
S e Equal area slope of the main stream projected to the catchment divide
SF1 Total streamflow at step 1
SFi Total streamflow at step i t1 Time elapsed between the start of surface runoff and end of the rainfall event tc Time of concentration T Return period (average recurrence interval)
TPi Random temporal pattern generated in simulation TPG30 Temporal pattern greater than 30 hours duration TPL30 Temporal pattern less than 30 hours duration
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Enhanced Joint Probability Approach Caballero
xmaxabs Absolute maximum difference x Mean of observed value of a random variable X2 Chi-squared statistics v Degrees of freedom Fraction of surface runoff in baseflow separation Average number of storm events per year Philip infiltration model index µ Mean value of population of a random variable 2 Variance of a random variable
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LIST OF ABBREVIATIONS
2D Two dimensional A-D Anderson-Darling AEP Annual exceedance probability AM Annual maximum AMC Antecedent soil moisture ARI(s) Average recurrence interval(s) ARR Australian Rainfall and Runoff ARR-IFD Australian Rainfall and Runoff - Intensity-frequency-duration BF Baseflow BGLS Bayesian Generalised Least Square BGLS-ROI Bayesian Generalised Least Square - Region-of-influence BITRE Bureau of Infrastructure, Transport and Regional Economics BOM Australian Bureau of Meteorology C-S Chi-Squared CD Compact disc cdf Cumulative distribution function CL Continuing loss CM Continuous monitoring DEA Design Event Approach DEA-IFD Design Event Approach - Intensity-frequency-duration DFFC(s) Derived flood frequency curve(s) DOW Department of Water EMCST Enhanced Monte Carlo Simulation Technique FFA Flood frequency analysis FLIKE Flood frequency analysis software developed by Prof George Kuczera FORTRAN IBM Mathematical FORmula TRANslating System GB Grubbs and Beck GEV Generalised extreme value GLUE Generalised Likelihood Uncertainty Estimation
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GOF Goodness-of-fit GPU Graphic processing unit GR4J Genie Rural, 4 parameters, Journalier GUH Geomorphologic unit hydrograph IDWA Inverse distance weighted averaging I. E. Australia Institution of Engineers Australia IL Initial loss IL-CL Initial loss - continuing loss IFD Intensity-frequency-duration or design rainfall depth JPA Joint Probability Approach JPA-IFD Joint Probability Approach - Intensity-frequency-duration K-S Kolmogorov-Smirnov LN Log Normal LP3 Log Pearson Type 3 MATLAB MATrix LABoratory MCST Monte Carlo Simulation Technique NCWE National Committee on Water Engineering NSW New South Wales pdf Probability density function PRM Probabilistic Rational Method PRT Parameter Regression Technique QF Quickflow R Ratio RE Relative error RFFA Regional flood frequency analysis RFFE Regional Flood Frequency Estimation RMC Rational Monte Carlo RMSE Relative root mean square error ROI Region-of-influence RORB Runoff routing software developed by Monash University RR(s) Rating ratio(s) SCS Soil Conservation Service SCS-CN Soil Conservation Service - Curve Number
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SFT Total streamflow TCEV Two components extreme value TP(s) Temporal pattern(s) TOPMO Altered TOPMODEL TOPMODEL TOPography based hydrological MODEL UK United Kingdom URBS Unified River Basin Simulator developed by Don Carroll UMCST URBS Monte Carlo Simulation Technique USDA United States Department of Agriculture USDA-SCS United States Department of Agriculture - Soil Conservation Service USGS United States’ Geological Survey WBNM Watershed Bounded Network Model
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University of Western Sydney Page 1
Enhanced Joint Probability Approach Caballero CHAPTER 1 Introduction
1.1 General
This thesis focuses on rainfall-based flood estimation by applying Joint Probability Approach (JPA)/Monte Carlo Simulation Technique (MCST). The method is a holistic approach of design flood estimation that allows consideration of the probabilistic nature and the interaction of the input variables and model parameters that are deemed to be important in rainfall runoff modelling. More specifically, JPA/MCST considers probability distributed model inputs and parameters to simulate rainfall events, which are then fed into a calibrated rainfall runoff model to simulate runoff hydrographs. The peak of these simulated runoff hydrographs are used to construct a derived flood frequency curve (DFFC). This thesis aims to enhance the JPA/MCST so that this method can be applied to ungauged or poorly gauged catchments. Thus, the key emphasis of this thesis is to regionalise the distributions of the model inputs and parameters from a selected reliable observed dataset, and use the regionalised distributions to generate inputs for the rainfall runoff models, which eventually generates runoff hydrographs for a catchment of interest. In the JPA/MCST, thousands of runoff hydrographs are simulated from the possible combinations of the model inputs/parameters. The flood characteristics of interest (e.g. peak flow, time to peak and runoff volume) are then subject to a frequency analysis to obtain derived distributions. This chapter of the thesis begins by presenting a background to this study, need for this research, research questions, research tasks and an outline of this thesis.
1.2 Background
Flood is one of the worst natural disasters that cause millions of dollars’ worth of damage each year which includes loss of human lives, livestock and crops, damage to properties, roads and other infrastructures, disruption to communication and insurance liability. During 2010-11 periods, the flood damage in Australia exceeded $20 billion (FM Global, 2011).
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Flood can cause community isolations e.g. the recent flooding in New South Wales (NSW) (February 2013), the flood waters at Kempsey cover part of the Pacific Highway, southbound from Frederickton to Kempsey (as shown in Figure 1.1) thus restricting movement of traffic on the Pacific Highway. In Australia, the average annual cost of flood damage is estimated to be around $377 million (BITRE, 2008). The state of NSW alone has an average annual cost of flood damage of over $172 million, which is almost 46% of the average annual cost for Australia. The state of Queensland is second largest in terms of flood damage, with an average annual cost of $125 million. Importantly, the December 2010 - January 2011 devastating flood caused Queensland State more than $5 billion estimated for flood restoration and reconstruction costs (Queensland Reconstruction Authority, 2011). Figure 1.2 shows the flood inundation of Queensland during 2010-11 devastating flood.
Figure 1.1: Flooding at Kempsey, the Pacific Highway southbound from Frederickton to Kempsey (The Australian, 2013)
Floods may result from prolonged or very heavy rainfall, severe thunderstorms, monsoonal (wet season) rains in the tropics, or tropical cyclones along with wet catchment condition. The flash flooding results from relatively short intense bursts of rainfall, commonly from University of Western Sydney Page 3
Enhanced Joint Probability Approach Caballero thunderstorms; this can occur in any part of Australia. It is a serious problem in urban areas (for smaller catchments having shorter response time) where drainage system may not be able to cope with excessive flood runoff. Due to these reasons, water infrastructure (which requires design flood estimation) should be designed based on a more reliable flood estimate. This can make the water infrastructure safer during floods. Furthermore, this would reduce overall flood damage and thereby results in savings of millions of dollars annually in Australia.
Figure 1.2: Aerial view of the flooded central Queensland town of Theodore on January 1, 2011 (ABC News, 2011)
Variety of water resources management tasks that need design flood estimation include design of bridge, culvert, weir, spill way, detention basin, and floodplain modelling, flood insurance studies and flood damage assessment tasks. The estimation of design flood in ungauged catchments is probably the most common design problem in flood estimation as many catchments in Australia (also in many other countries) are ungauged or poorly gauged (Zaman et al., 2012). Several methods are commonly adopted for ungauged catchment flood
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Enhanced Joint Probability Approach Caballero estimation including Index Flood Method (Dalrymple, 1960; Hosking and Wallis, 1993; Parida et al., 1998; Javelle et al., 2002), the Probabilistic Rational Method (I. E. Australia, 1987; Pilgrim, 1989; Wong, 2002; Young, et al., 2009; Rahman et al., 2011) and the Quantile Regression Technique (Benson, 1962; Tasker and Stedinger, 1989; Rahman, 2005; Griffis and Stedinger, 2007; Haddad and Rahman, 2011a, Haddad et al., 2012). However, these types of approximate methods are limited to flood peak estimation only and are not particularly useful when the estimation of complete streamflow hydrograph is required. A complete streamflow hydrograph is needed for hydraulic modelling i.e. to prepare flood plan maps and also to design volume-sensitive hydrologic systems.
The rainfall-based Design Event Approach (DEA) is currently recommended by Australian Rainfall and Runoff (ARR 1987) to estimate complete design flood hydrograph in Australia (I. E. Australia, 1987). In this approach, the probabilistic nature of rainfall depth is considered in the rainfall runoff modelling; however, this ignores the probabilistic behaviour of other model inputs and parameters such as rainfall temporal patterns and losses. The key assumption involved in the DEA is that the representative design inputs and parameters in the modelling can be defined in such a way that these are annual exceedance probability (AEP) neutral, i.e. the resulting flood output has the same AEP as the rainfall depth input (Rahman et al., 2002a). This assumption is hardly satisfied in many practical situations (Hill and Mein 1996), and the arbitrary treatment of various flood producing variables can lead to inconsistencies and significant bias in flood estimates for a given AEP. This might lead to either over-estimation or under-estimation of the design floods (which might result in too large or too small water infrastructure projects), both with considerable financial cost.
To overcome the limitations associated with the DEA, two methods have often been proposed: JPA/MCST (e.g. Eagleson, 1972; Rahman et al., 2002a; Aronica and Candela, 2007; Muncaster and Bishop, 2009; Kjeldsen et al, 2010) and continuous simulation approach (e.g. Cameron et al., 1999; Boughton and Droop, 2003; Blazkova and Beven, 2009; Grimaldi et al., 2012). Rahman et al. (1998) prepared a detailed review of the JPA to design flood estimation problem. They examined the earlier studies such as Eagleson (1972), Beran (1973), Russell et al. (1979), Diaz-Granados et al. (1984) and Sivapalan et al. (1990). Majority of these applications were found to be restricted to theoretical studies to
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Enhanced Joint Probability Approach Caballero experimental types of catchments. In addition, mathematical complexity, difficulties in parameter estimation and limited flexibility usually prevent the application of these JPA- based methods under practical situations (Rahman et al., 1998).
A considerable research has been undertaken on the development and application of the JPA/MCST in design flood estimation problem (e.g. Muzik, 1993; Heneker et al., 2002; Rahman et al., 2002a; Charalambous et al., 2003; Kuczera et al., 2003; Aronica and Candela, 2004; Aronica and Candela, 2007; Kjeldsen et al., 2010; Aronica et al., 2012; Charalambous et al., 2013; Mirfenderesk et al., 2013; Svensson et al., 2013). Muzik (1993), Rahman et al. (2002a) and Aronica and Candela (2007) developed and applied successfully a simplified MCST based on the principles of joint probability. Most of these studies were applied to gauged catchments. The JPA developed by Aronica and Candela (2007) targeted the ungauged or partially gauged catchments. This method was shown to reproduce the observed flood frequency curves with reasonable accuracy over a wide range of return periods using a simple and parsimonious hydrologic model, limited data input and without any calibration of the adopted hydrologic model. The application of JPA/MCST to ungauged catchments in Australia has not been well-researched with a large data set.
More recently, the JPA has been adopted in flood risk assessment/hydrologic modelling in a number of international studies. For example, Gioia et al. (2008) proposed a two-component derived distribution based on two runoff thresholds characterized by different scaling behaviour. Haberlandt et al. (2008) introduced Monte Carlo simulation of meteorological inputs coupled with lumped, distributed or semi-distributed hydrological models in flood modelling. Viglione and Bloschl (2009) investigated the role of critical storm duration in the framework of the JPA. Gioia et al. (2011) applied JPA to investigate the spatial variability of the coefficient of skewness and its impacts on flood peak estimation. Iacobellis et al. (2011) tested the JPA in the context of regional analysis by means of an objective jack knife procedure. Kalyanapu et al. (2012) presented a Monte Carlo-based flood inundation modelling framework for estimating probability weighted flood risk using a computationally efficient graphic processing unit (GPU) and hydraulic model. The most recent is the work by Svensson et al. (2013) where they adopted a MCST to estimate frequencies of flood peak and
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Enhanced Joint Probability Approach Caballero total event flow volume. All these studies have demonstrated that the JPA provided more accurate and realistic flood estimates than the typical DEA.
One of the most simplified MCST methods developed by Rahman et al. (2002a) uses a non- linear runoff routing model to simulate streamflow hydrographs. This is particularly suited to Australia as non-linear runoff routing models are widely adopted here e.g. RORB model Version 6.14 (Mein and Nathan, 2010), URBS Version 4.00 (Carroll, 2004) and WBNM (Boyd et al., 1996). Rahman et al. (2002a) found that the applications of JPA with non-linear runoff routing models with Victoria and Queensland data (e.g. Carroll and Rahman, 2004) produced quite accurate DFFCs and could overcome some of the limitations associated with the current DEA. The above studies on MCST require large volume of observed pluviograph and streamflow data to derive stochastic model inputs in the runoff routing modelling; however, for practical applications, the design engineers ideally need the required model input data to be readily available. This is regarded as the most critical issue as far as the practical application of the MCST is concerned.
It should be noted here that MCST has been the recent focus by the National Committee on Water Engineering (NCWE) in Australia. In this regard, NCWE’s ARR Revision Committee prepared a position paper (Leonard, 2009), which strongly advocates to replace the DEA with JPA/MCST for flood estimation in Australia. Recently, Nathan and Weinmann (2013) presented a discussion paper which also supports JPA/MCST. They emphasised the previous recommendation by Kuczera et al. (2003) where they argued that the JPA/MCST should replace the DEA in Australia. To achieve this objective, i.e. to adopt JPA/MCST in practice instead of the DEA, regionalisation of the stochastic model inputs (regarded as random variables) in the JPA/MCST are needed. Hence, this thesis undertakes the regionalisation of the JPA/MCST considering a large number of pluviograph and stream gauging stations for the State of NSW in Australia.
1.3 Need for this research
Australia is the sixth largest country in the world in terms of area and considered to be the earth’s biggest island with an unlimited number of natural streams. Most of these streams are ungauged or poorly gauged as monitoring of such a large number of streams would be too
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Enhanced Joint Probability Approach Caballero expensive. The design flood estimation in small to medium sized ungauged catchments is of great economic significance (Pilgrim and Cordery, 1993). In Book IV of Australian Rainfall and Runoff (1998), the small catchments are defined having an upper limit of 25 km2, whereas medium sized catchments up to 1000 km2; this is however a guide only. The need for flood estimation on ungauged catchments is one of the most important aspects in hydrologic practice as it covers a large number of catchments where hundreds of infrastructures are built each year in Australia. The accuracy of the flood estimation for ungauged catchments is important as an over-estimation would result in higher construction cost and under-estimation would increase flood damage.
The common opinion amongst researchers in hydrology is that the currently recommended rainfall-based DEA is not based upon hydrologically meaningful rationale and should be replaced by a more holistic approach. As a result, further research is necessary to find more appropriate methods to overcome the limitations associated with the DEA. More recently, NCWE in Australia has resolved that DEA should be replaced, as mentioned above, with more holistic approaches such as the MCST (Leonard, 2009). It appears that the MCST by Rahman (2002a) has enough flexibility and offers scope of further development for routine application, which has prompted further research and the subsequent endorsement of the MCST by the NCWE in Australia. However, MCST cannot be applied in routine design practice unless it is regionalised. Once MCST is regionalised, the necessary input data to apply the technique will be readily available. Hence this thesis aims to regionalise the MCST, which is referred to as regional MCST (EMCST).
In view of the fact that ARR came out in 1987 (3rd edition), there have been both advancements in flood frequency analysis and the availability of more than 24 years’ worth of rainfall and streamflow data at many locations since 1987. In this thesis, these additional rainfall and streamflow data (data up to 2011) have been used to develop and test a regional MCST for the State of NSW. The outcome of this research is expected to pave the way in applying the MCST in routine hydrological practice. Currently, the NCWE and the ARR Revision Team are in the stage of finalising the revision of the ARR (4th edition). Through positive results, this research could support the revision of the ARR in relation to the application of the MCST in practice. This research would thus contribute towards the
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Enhanced Joint Probability Approach Caballero replacement of the DEA with the regional MCST (EMCST) - a long desire in hydrologic practice in Australia as stated in ARR 1987 (I. E. Australia, 1987). In this regard, the new regional MCST developed in this thesis, is henceforth called ‘Enhanced MCST’ (EMCST).
1.4 Research questions
This thesis is devoted to answer the following research hypotheses/questions in relation to the development and testing of the regional MCST (EMCST):
Whether complete storms can be used in the EMCST instead of storm-cores in combination with inter-event duration?
Whether the incorporation of inter-event duration in the EMCST can enable the construction of annual maximum flood series from the generated partial duration flood series in the EMCST?
How possible uncertainty/error in various input variables data can affect the derived flood frequency curves (DFFCs) and what is the degree of sensitivity of these input variables on the DFFCs?
Whether various input variables can be regionalised to facilitate ‘easy application’ of the EMCST? In this regard, whether a regional database can be developed for the State of NSW to promote the application of the EMCST?
How does the regional EMCST perform as compared to other established methods in flood quantile estimation for ungauged catchments?
1.5 Summary of research undertaken in this thesis
The research tasks undertaken in this thesis to answer the research questions posed in Section 1.4 are outlined below and illustrated in Figure 1.3.
Perform a literature review on the various methods of rainfall based flood estimation techniques and examine their advantages and disadvantages, limitations and assumptions, with a particular emphasis on JPA/MCST to flood estimation. Based on
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the literature review, identify the gaps and further research opportunity on the JPA/MCST to flood estimation.
Formulate the research questions/hypotheses and identify data requirements for the proposed research to develop the EMCST.
Select a set of suitable study catchments (with adequate data in terms of quantity and quality) from the state of NSW and collate rainfall, streamflow and relevant catchment characteristics data for the proposed research. Select catchments covering a wide range of hydrologic and catchment characteristics as far as possible within the scope and time of this research.
Develop the EMCST by (a) adopting complete storm rather than storm-core, (b) including inter-event duration as a new random variable in the simulation, and (c) regionalising various input variables.
Obtain the distributions of the input variables i.e. rainfall complete storm duration, inter-event duration, intensity-frequency-duration (rainfall depth), temporal patterns, initial loss, continuing loss and runoff routing model parameter (storage delay parameter) based on the observed rainfall and streamflow data from the selected stations/events across the state of NSW. Regionalise these distributions for the state of NSW so that these can be used in the practical application of the MCST in this State.
Conduct a sensitivity analysis to identify which of the input variables are more important in the simulation to achieve satisfactory results as far as practical application of EMCST is concerned. The primary objective of this task is to identify how much tolerance/variability in each of these variables is acceptable in obtaining DFFCs using the EMCST.
Validate the EMCST; for this, compare the results of the EMCST with other established methods of design flood estimation such as at-site flood frequency analysis (FFA), DEA, ARR 1987 Probabilistic Rational Method (PRM) and ARR Regional Flood Frequency Estimation 2012 model (ARR-RFFE 2012) (test version).
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Introduce the research/thesis Conduct a critical literature review: Design Event Approach (DEA), Joint Provide background Probability Approach (JPA) and Monte Carlo Simulation (MCST)
Identify the need for this research Ascertain current state of knowledge on the research field and find gaps in the current knowledge base Formulate research questions Formulate research questions to create new knowledge to close the current Identify research tasks gaps in the application of the MCST in design flood estimation
Establish/illustrate methodology to answer the research questions/hypothesis Select study area, catchments and pluviograph stations that satisfy the adopted Describe: DEA, JPA/MCST, EMCST, FFA, PRM, ARR RFFE Model criteria of quantity, quality and representativeness for the purpose of this thesis 2012 (test version) Collate pluviograph and streamflow data: check for data accuracy, fill the gaps Develop codes/programs for data analysis and modelling in relation to the in the data and conduct exploratory analysis development and testing of the new EMCST
Regionalise input variables/model parameters Carry out sensitivity analysis to assess the impacts of possible uncertainty in distributional parameters of the input variables on the DFFCs Select complete storm events (to derive values of DCS, IED, IFD and TP)
Select concurrent rainfall and streamflow events (to derive IL, CL and k) Change parameters of exponential and gamma distribution by an arbitrary range e.g. ± 5%, ± 10%, ± 20%, ± 50% , and assess their impacts on DFFCs Fit an appropriate distribution to each of the input variables/ model parameters Rank the input variables/model parameters in order of the most to least Regiolalise input distributions sensitive ones
Validate the new EMCST Summarise the research and draw conclusions Compare EMCST with at-site FFA (ARR-FLIKE), DEA, PRM and ARR RFFE 2012 (test version) Recommend further research tasks/aspects to improve the new EMCST. Evaluate the EMCST and other methods using a suite of evaluation statictics
Figure1.3: Illustration of major steps in this research study
1.6 Outline of the thesis
The research undertaken in this study is presented in this thesis consisting of eight chapters and four appendices, as outlined below.
Chapter 1 presents a brief introduction to the proposed research, including the background and need for this research, emphasising the limitations of the current DEA and advantages of the JPA/MCST. The research questions/hypotheses that are to be investigated and the research tasks to be undertaken to answer the identified research questions are also presented in this chapter. It also provides an overview of the adopted research methodology.
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Chapter 2 presents a literature review on various flood estimation methods, in particular the rainfall-based ones. Research studies on JPA/MCST are reviewed with a greater emphasis on the assessment of their relative strengths and limitations. In addition, the runoff routing models adopted in the previous studies in the application of JPA/MCST are discussed. Further, this chapter presents a brief review of the loss models and input variables that are deemed to be important in rainfall runoff modelling. Review of various regionalisation methods is presented to select an appropriate method to be adopted in this study. At the end, this chapter summarises the advantages and disadvantages of the previous methods on JPA/MCST, identify gaps in the current state of the knowledge on the MCST and formulate the research problems that are to be resolved in this thesis.
Chapter 3 presents the methodology adopted in this thesis. This begins with discussion of the selection of rainfall events. The consideration of the selected runoff routing model is then presented. This is followed by the examination of the selected input variables for stochastic simulation. In addition, this chapter discusses the procedure of the identification of an appropriate probability distribution to approximate the observed data of an input variable/model parameter. This is followed by the discussion of the development of rainfall depth (IFD curves) for application with the EMCST. The derivation of the dimensionless complete storm temporal patterns is then investigated. The regionalisation method for an input variable, i.e. how an input variable can be estimated at an ungauged location from the gauged data is presented. The formation of annual maximum flood series considering the inter-event duration data from the simulated hydrograph peaks is then examined. The sensitivity analysis of the developed regional EMCST is also outlined, which essentially examines how a variation in an input variable could influence the DFFCs, and also which of the input variables are relatively more sensitive in determining the DFFCs. Finally, the validation/testing procedure of the new EMCST is presented.
Chapter 4 presents the selection of study area and data. The chapter starts with discussion of the selection of study region, which is followed by the selection of pluviograph and stream gauging stations and data collation. This also presents a quantitative summary of the data used in this thesis.
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Chapter 5 presents the regionalisation of the various input distributions. The chapter commences with description of the selection of rainfall events from the selected pluviograph stations. This is followed by the selection of the concurrent rainfall and streamflow events for the calibration of the adopted runoff routing model and estimation of losses. The chapter then presents the regionalisation of various input variables and model parameters: rainfall complete storm duration, inter-event duration, intensity-frequency-duration (rainfall intensity), temporal pattern, initial loss, continuing loss and runoff routing model (storage delay parameter, k) data for the selected study region.
Chapter 6 presents the sensitivity of the regionalised distributions in the application of the developed EMCST. This covers all the selected stochastic variables i.e. rainfall complete storm duration, inter-event duration, intensity-frequency-duration, temporal pattern, initial loss, continuing loss and runoff routing model (storage delay parameter k). The impacts of varying a distributional parameter (by an arbitrary selected range e.g. 10%, 20% and 30%) on the DFFCs are examined.
Chapter 7 presents the validation/testing of the EMCST. This presents a comparison of the results from the new EMCST with the observed flood quantiles (obtained from at-site flood frequency analysis), DEA and the new ARR-RFFE 2012 model (test version) and the ARR 1987 PRM.
Chapter 8 presents the summary of the research undertaken in this thesis, conclusions and recommendations for further research.
Appendix A presents major steps in Eagleson’s kinematic runoff routing model (as it is the very first attempt of establishing JPA in flood estimation by Eagleson (1972)) and a summary of the Total Probability Theorem (as this is the fundamental equation underpinning the JPA/MCST).
Appendix B presents some additional tables from Chapters 4, 5, 7 and 7 to supplement the discussion and results presented in the main body of the thesis.
Appendix C presents some additional figures from Chapters 3 and 7 to enhance the discussion in these chapters.
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Appendix D presents a list of the programs/codes developed/adapted in this thesis to carry out the necessary analyses to answer the identified research questions.
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Enhanced Joint Probability Approach Caballero CHAPTER 2 Literature Review
2.1 General
Chapter 1 has presented the background, the need for this research and the research questions to be investigated. This chapter provides a review of design flood estimation methods with a particular emphasis on the rainfall-based design flood estimation techniques. A detailed review of the design flood estimation methods based on the Joint Probability Approach (JPA) is presented to ascertain the current state of knowledge, to identify gaps in the current research and to formulate the research questions examined in this study. In addition, this chapter presents a brief review on the runoff routing and loss models adopted in the previous studies. This chapter also discusses the commonly used input variables and parameters in the rainfall runoff modelling, and which should be treated as random variables in the Enhanced Monte Carlo Simulation Technique (EMCST).
2.2 Design flood estimation methods
Different methods can be used to estimate a design flood with a specified annual exceedance probability (AEP) or average recurrence interval (ARI) or return period (T). The selection of the type of flood estimation method for a given application largely depends on the data availability and the purpose of the flood estimates (Hoang, 2001). Lumb and James (1976), Feldman (1979), James and Robinson (1986) and Australian Rainfall and Runoff (ARR) (I. E. Australia, 1987) broadly classified design flood estimation methods into two main categories: streamflow-based methods and rainfall-based methods. These are discussed below and illustrated in Figure 2.1.
2.2.1 Streamflow-based flood estimation methods
Streamflow-based flood estimation methods base their analyses mainly on recorded data from stream-gauging station in question and are applicable to ‘gauged catchments’, having a University of Western Sydney Page 16
Enhanced Joint Probability Approach Caballero considerably long streamflow record length. In these methods, the design flood for a given AEP is estimated by undertaking a flood frequency analysis (FFA) of the observed streamflow data. A gauged catchment indicates that streamflow records exist for flood height and flood flow over a considerable period of time, normally 20 years or longer at one location so that the parameters of the assumed probability distribution can be estimated with a high degree of confidence. The gauging locations are generally found within a given large catchment and located at the points of interests such as the convergence of two major creeks or the outlet of the catchment. FFA and regional flood frequency analysis (RFFA) are the most common streamflow-based methods and these are discussed below. It should be noted that RFFA methods generally consider catchment characteristics in the estimation; however, FFA is solely dependent on gauged streamflow records.
Figure 2.1: Various design flood estimation methods (modified from Rahman et al., 1998)
Flood frequency analysis
Flood frequency analysis (FFA) is a procedure of analysing the recorded flood data by statistical analysis. The main objective of this method is to develop a relationship between the magnitude of extreme flood events and their frequency of occurrence through the use of
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Enhanced Joint Probability Approach Caballero probability distributions (Chow et al., 1988; Rao and Hamed, 2000). This deals mainly with direct frequency analysis, where a record of floods at or near the design site is available. In addition, the application of these methods is primarily made to flood peaks. These may sometimes be applied to flood volumes or even monthly maximum floods; however, little evidence is available on appropriate types of probability distributions in these cases (I. E. Australia, 1998).
Regional flood frequency analysis
Regional flood frequency analysis (RFFA) is a means of transferring flood frequency information from gauged catchments to another site on the basis of similarity in catchment characteristics (I. E. Australia, 1998). This procedure is important for estimating design floods at ungauged sites as this can stabilise site estimates using the regional relationships, particularly for parameters such as skew, which is more prone to small-sample errors and data extremes. In addition, regional relationship can mitigate the effects of outliers and can lead to more reliable extrapolation of flood frequency curve to rarer frequencies. RFFA also enhances the design flood estimates at gauged sites where data may be limited and where direct FFA is not feasible. These regional procedures are discussed in more detail in Chapter 5.
2.2.2 Rainfall-based flood estimation methods
Rainfall-based flood estimation methods calculate design floods by utilising rainfall data. In hydrologic practice, these methods are quite common due to the large availability of rainfall data which can be converted into flood flows. In general, the procedure involves the use of a rainfall-runoff model or unit hydrograph to convert net rainfall (gross rainfall minus loss) into a flood hydrograph. In the conversion of rainfall to runoff, a number of events of concurrent observed rainfall and streamflow data are generally calibrated to the rainfall-runoff model and representative value(s) of the model parameter(s) are selected for a given catchment.
Important aspects considered in these methods are: (i) usually rainfall records are longer than streamflow ones and the use of these rainfall records in conjunction with a rainfall-runoff model generally results in a more accurate flood estimates as compared to those obtained
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Enhanced Joint Probability Approach Caballero from streamflow records alone, in particular, at sites with limited streamflow data; (ii) due to land use change, conditions of catchment may also change with time; thus, portion of the streamflow data may become irrelevant, whereas climatic conditions remain rather stable over time (this has become questionable due to the impacts of climate change) and thus, long series of rainfall data can be used to obtain more accurate flood estimates; (iii) areal extrapolation of rainfall data is relatively easy as compared to that of the streamflow data; and (iv) rainfall-runoff models facilitate extreme flood estimation by incorporating catchment physical features in the rainfall-runoff modelling. These features of rainfall-based methods make them suitable for catchments with little recorded streamflow data, or in sites where catchment conditions have changed considerably over a period of record, and for extreme flood estimation.
The discussion of various rainfall-based flood estimation methods is presented below. This discussion is based on the three broad categories: empirical methods, event-based methods and continuous methods.
Event-based methods
In Australia, event-based flood estimation methods make use of design rainfall, which is based on the intensity-frequency-duration (IFD) data given in the ARR (I. E. Australia, 1987). The IFD data in the ARR are derived from a fitted surface through observed rainfall sites, which is quality-checked using meteorological knowledge. All event-based methods use a calibrated runoff-routing model and are probabilistic in nature. Generally, the assumptions or constraints associated with event-based methods include (i) the use of the IFD data assumes that skew is independent of duration and ARI, which is questionable; (ii) the IFD estimates in areas of high rainfall gradient have caused concern such as the Wollongong escarpment and Gold Coast hinterland; and (iii) the IFD data over large areas are problematic in terms of consistency and application with a rainfall runoff model.
Three event-based methods are discussed below: the Design Event Approach (DEA) and the ‘Improved’ DEA, which simulates a single event and the Joint Probability Approach (JPA) which simulates multiple events. These methods are explained in detail below.
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Design Event Approach
The ARR currently recommends DEA for the estimation of a design flood hydrograph with the runoff routing models (I. E. Australia, 1987). The procedure involves the estimation of design rainfall input with the rainfall loss and the rainfall excess routing through the catchment outlet to produce the flood hydrograph. The following are the steps associated with this approach as outlined in the ARR (I. E. Australia, 1958, 1977, 1987), Beran (1973) and Ahern and Weinmann (1982).
Select a number of design storm durations D1, D2, ... . For each of these, obtain a streamflow hydrograph following the steps, given below.
Obtain an average rainfall depth from the IFD curve, given the design location, specified AEP and duration.
Obtain average catchment rainfall using an empirical areal reduction factor.
Select a design rainfall temporal pattern.
Compute gross rainfall hyetograph.
Select loss parameters and compute rainfall excess hyetograph.
Formulate catchment response model.
Select catchment response parameters.
Select design baseflow.
Compute streamflow hydrograph and add the baseflow to the calculated hydrograph.
Repeat the above procedure from (b) to (j) for the selected durations D1, D2, ...
To determine the critical duration and the corresponding design flood, the computed flood peaks for different durations are tabulated (see Table 2.1) to find the duration giving the maximum flood peak. This duration is taken as critical duration and the respective flood peak
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Enhanced Joint Probability Approach Caballero is taken as the design flood of the specified AEP. In this example in Table 2.1, the 12-hour duration (in bold font) has the maximum flood peak.
Table 2.1: Example of computed flood peaks (using hypothetical data) by Design Event Approach for durations 1h to 72h (Here Q2 means flood peak discharge having ARI of 2 years) Flood peaks 1h 2h 3h 6h 12h 24h 48h 72h (m3/s)
Q2 528.70 699.75 762.16 799.77 855.24 773.17 507.06 498.71
Q5 756.82 1002.60 1074.83 1138.92 1247.07 1141.63 738.66 720.55
Q10 901.53 1183.55 1262.34 1340.19 1488.48 1374.25 886.10 863.61
Q20 1114.23 1417.27 1520.55 1615.52 1807.17 1686.60 1078.39 1049.51
Q50 1380.77 1786.01 1873.07 1929.64 2080.45 1891.14 1243.00 1241.80
Q100 1583.90 2050.66 2146.48 2210.59 2405.19 2198.33 1432.32 1435.71
The ARR 1987 recommends the DEA for adoption with the runoff routing models (I. E. Australia, 1987) to estimate design flood hydrograph. Runoff routing model is frequently adopted as the preferred method of rainfall-runoff modelling over the unit hydrograph approach in Australia. The DEA considers the probabilistic nature of rainfall intensity but largely ignores the probabilistic behaviour of other input variables in the rainfall runoff modelling such as initial loss and temporal patterns. In this method, the key assumption involved is that the representative design values of the inputs/parameters can be defined in such a way that these are ‘AEP neutral’. This means that the flood output has the same AEP as that of the rainfall input. The success of the DEA is crucially dependent on how well this assumption is satisfied.
There are no specific guidelines on how the selections of appropriate values of input variables/parameters is to be made to convert a rainfall depth of a particular AEP to the design flood of the same AEP. There are various methods to determine an input value, the choice of which is largely dependent on various assumptions and preferences of the individual designer. A designer is usually in a situation to select an input value such as the median value from a sample of inputs or fitted parameter values from a number of observed data values. As an example, an input variable such as initial loss shows a wide variability (Rahman et al., 2002a; Loveridge et al., 2013) and it is not easy to select a representative value of a particular input variable that show such a wide variability to maintain the AEP neutrality.
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It is generally not possible to know a priori how a representative value for an input should be selected to preserve the AEP due to the non-linearity of the transformation process involved. Muzik (1994), Heneker et al. (2002), Rahman et al. (2002a), Kuczera et al. (2003), Nathan and Weinmann (2004), Kuczera et al. (2006), Gioia et al. (2008), Kjeldsen et al. (2010) and Svensson et al. (2013) widely criticised the DEA and noted that this method can lead to inconsistencies and significant bias in flood estimates for a given AEP. Working on improvements to specific components of the DEA, other researchers have noted that their efforts were largely unsuccessful by the interactions among various input variables, which the existing method could not deal with satisfactorily.
‘Improved’ Design Event Approach
The ‘Improved’ DEA, as alternative to the conventional DEA, uses the same flood estimation procedure as of traditional DEA but with better estimates of input and parameter values. In doing this, the improved method is expected to overcome some of the limitations associated with the current DEA as mentioned above as these limitations arise partly from the uncertainties involved in the selections of input and parameter values in design applications.
In line with this, a number of research studies have been undertaken. For example, the uncertain behaviour of maximum water abstraction (S) was characterised by Haan and Schulze (1987) using a probability distribution. These substituted different values of S into the rainfall-runoff model to find the corresponding values of flood peak estimates Q. Edwards and Haan (1989) proposed a rigorous method to analyse parameter uncertainties using the Bayesian theorem and a Monte Carlo method for deriving flood frequency curves using the Soil Conservation Service (SCS) unit hydrograph method (SCS, 1972).
The application of this method permits integration of new information with previous probability assessments to yield new probabilities of events of interests (Haan, 1977). An optimisation technique was applied by Overney et al. (1995) in calibrating optimal parameter values for a unit hydrograph model. The curve number values were expressed by a probability distribution obtained from observed data using the SCS abstraction method to simulate runoff. Thereafter flows were generated from combinations of the generated
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Enhanced Joint Probability Approach Caballero stochastic rainfall, unit hydrograph model parameters and curve number values using Monte Carlo simulation.
Even though the above methods overcome the limitations to certain degree in the selection of input and parameter values by recommending different ways to allow for uncertainty in the estimates of individual parameters in the design process, these are still subject to a common basic limitation as with the current DEA, which is ‘the AEP of the resulting flood peak is still assumed to be equal to that of the rainfall depth input’.
Empirical methods
Empirical methods are intended to convert rainfall into runoff to derive one or several coefficients to be incorporated into an equation representing the rainfall-runoff relationship. The coefficients of this equation are established from rainfall and flood events of the same probability which are achieved from frequency analyses of observed rainfall and runoff data (Hoang et al., 1999). The most common examples of these methods are Probabilistic Rational Method (PRM) (I. E. Australia, 1987) and United States’ Geological Survey (USGS) Quantile Regression Technique (Benson, 1962, Rahman, 2005) and Parameter Regression Technique (PRT) (Haddad and Rahman, 2012). These methods may be regarded as a ‘black- box’ type of models, that is, these do not incorporate any hydrologic knowledge in the system but are simply a means of converting a known rainfall of a certain ARI input into a design flood output through the use of lumped rainfall input and other climatic catchment characteristics data.
The advantages of empirical methods are that these are quite simple to apply in practice; these can overcome to some extent the limitations of more accepted approaches such as the DEA because the flood of a selected probability is directly linked with rainfall of the same probability (James and Robinson, 1986, I. E. Australia, 1987); and by doing this, effects of other flood variables are automatically considered as these are part of the black-box transformation process.
The main disadvantage of the empirical methods is that these have a limited scope of application because these shares the principal limitation of the black-box type methods i.e.
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Enhanced Joint Probability Approach Caballero the physical processes cannot be incorporated in the estimation methods. In addition, these have limited range of applications as these only generate peak flow estimates, and not the full streamflow hydrograph. Further, their direct application is limited to within the range of conditions these have been calibrated to (James and Robinson, 1986; I. E. Australia, 1987) and as a result extrapolation must be done with extreme caution, if needed.
Joint Probability Approach
The JPA is a more holistic approach to design flood estimation. This method incorporates the randomness of flood producing variables like rainfall event duration, intensity, temporal pattern and their interrelationship to determine a derived distribution of flood characteristics such as flood peak or flood volume. The basic idea underlying this method is that the design flood characteristic could result from a variety of combinations of flood producing factors, rather than from a single combination, as done in the DEA. As a result, this method attempts to eliminate bias in selecting input values in design by using the same input values as the current DEA but treating inputs and parameters values as random variables.
In Australia, the JPA has been investigated by Rahman et al. (1998, 2001, 2002a, 2002b, 2002c), Weinmann et al. (2002), Kuczera et al. (2003), Nathan et al. (2003), Nathan and Weinmann (2004), Rahman and Carroll (2004), Haddad and Rahman (2005), Muncaster and Bishop (2009), Charalambous et al. (2013) and Mirfenderesk et al. (2013). The methods of Rahman et al. (2002a), Nathan et al. (2003) and Haddad and Rahman (2005) adopted a Monte Carlo Simulation technique, which is flexible and based on common design data and models readily available in Australia. This method can be conceived as a combination of deterministic and probabilistic hydrological modelling techniques, and was pioneered by Eagleson (1972), and has been further advanced for more than four decades. This method is discussed in more details in Section 2.3.
Continuous simulation methods
Continuous simulation for design flood estimation is another alternative method to the DEA. This method requires simulation of a sufficiently long period of streamflow from which the needed flood statistics can be extracted. One important characteristic of this method is the
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Enhanced Joint Probability Approach Caballero continuous use of a water balance model for the catchment so that continuous antecedent conditions to each storm event are known. Continuous simulation of water balance eliminates the need for arbitrary assumptions about losses.
Cameron et al. (1999) demonstrated the use of a continuous simulation methodology for the purpose of flood frequency estimation. It utilised the rainfall-runoff model known as TOPMODEL (Beven, 1997), together with stochastic rainstorm generator, in order to produce estimates of flood events of relatively higher ARIs. Good reproduction of the observed hourly annual maximum flood peaks was demonstrated by this study. Reasonable estimates were also obtained for higher return period floods such as 100 years ARI. In addition, this method demonstrated a consistency between the parameterisation of TOPMODEL for both hourly annual maximum peaks and continuous hourly hydrograph simulation.
Boughton and Droop (2003) developed a method of continuous simulation of streamflow time series in Australia. Faulkner and Wass (2005) applied the same method in the Don catchment in South Yorkshire, United Kingdom. Blazkova and Beven (2009) applied similar method in the Skalka catchment in Czeck Republic. Grimaldi et al. (2012) used the same method to Tiber River located in central Italy. However, only few studies have compared continuous simulation with other methods of design flood estimation, and no significant studies have been undertaken comparing different continuous simulation methods. Most of the available methods use recorded streamflow data for calibration and there is little information available for the use of continuous simulation methods on ungauged catchments.
Rahman et al. (1998) stated the advantages of continuous simulation methods over the DEA as summarised below.
It eliminates the need for the use of synthetic storms as it uses actual storm records (Russell, 1977); It eliminates bias in selecting antecedent conditions for the land surface since a water balance is accounted for in each time step of the simulation and thus automatically logs antecedent moisture conditions (James and Robinson, 1986);
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It handles antecedent conditions correctly because the continuous time series of flows include all effects of antecedent conditions (Huber et al., 1986); It overcomes the problem of critical storm duration as it simulates the resultant flows for all the storms (Lumb and James, 1976); and It undertakes a frequency analysis of the variable of interest (e.g. peak discharges, flow volumes and pollutant wash-off) by statistically analysing the time series of model outputs as opposed to assuming equal probability of floods and causative rainfall (Huber et al., 1986).
Lumb and James (1976), Ahern and Weinmann (1982), James and Robinson (1982), and ARR (I. E. Australia, 1987) stated the problems associated with the application of continuous simulation which are:
The use of relatively long time steps can miss sharp events; The gathering of data needed for simulation of long continuous sequences requires significant amount of time and effort; The management of huge amount of time series output; and The expertise needed in estimation of the parameter values which best reproduce historical hydrographs.
2.3 Review of previous studies on Joint Probability Approach to flood estimation
The JPA incorporates the randomness of flood producing variables and their correlations to determine a derived distribution of flood characteristics such as flood peak or flood volume. As a result, this method attempts to minimise the bias in selecting input values. In this method, a design flood characteristic could result from a variety of combination of flood producing factors, rather than from a single combination. The method of combining probability distributed inputs to form a probability distributed output is known as the derived distribution approach (Eagleson, 1972).
According to Weinmann (1994) and Rahman et al. (1998), using the rules of probability, the derived probability distribution can be computed by (i) analytical methods; or (ii) approximate methods. Generally, the choice of the method in computing a derived University of Western Sydney Page 26
Enhanced Joint Probability Approach Caballero distribution is influenced mainly by the level of analytical skills and the computer resources available for the task (Weinmann, 1994). However, the computer time for these types of simulation is not a problem nowadays.
2.3.1 Analytical methods
Analytical derivation of the distribution and the reduction of the need for model calibration require the use of simplistic rainfall and catchment models. While these models may not be able to predict streamflow as good as complex models, it may be argued that the use of simple models is justified for poorly gauged regions (Moughamian et al., 1987). Several examples where an analytical method has been used for deriving flood frequency distributions were presented by Bates (1994), Sivapalan et al. (1996), and Rahman et al. (1998). Earlier works on the analytical methods are presented below depending on the runoff routing method adopted.
Methods based on Eagleson’s kinematic runoff model
Eagleson (1972) pioneered the analytical derivation of flood frequency distribution based on kinematic wave representation of the surface runoff process. There are three major steps used in this method: (i) rainfall model, (ii) runoff model, and (iii) transformation from rainfall to runoff. The steps and the corresponding equations associated with this method are presented in Appendix A1 (see Appendix A). In this method, rainfall intensity and duration are random variables with an exponential joint probability density function. In addition, it was assumed that the area contributing to direct runoff is a narrow band symmetrical about the centre of the stream and that the infiltration can be represented by a simple Horton model with constant infiltration capacity.
Wood (1976) adopted the analytical method developed by Eagleson (1972). In his method, he considered dividing the parameters into two categories: first category consisted of unknown fixed parameters such as stream length or slope; and second category consisted of parameters that vary from storm event to storm event such as infiltration, and its behaviour over time was assumed to be stochastic. In contrast, Eagleson (1972) considered the infiltration rate as a constant.
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Another example of the analytical method is the study by Cadavid et al. (1991) who derived flood frequency distribution incorporating the method of Eagleson (1972), Philip’s (1957) infiltration equation and kinematic wave representation of the surface runoff process. The method was applied to two urban catchments, where overland flow is the predominant runoff mechanism. It was found that the method estimated the frequency of low flows better than the frequency of the higher flood flows.
Furthermore, Muzik (1994) adopted analytical solution of the kinematic wave equations of overland flow from an impervious runoff plane resulting from uniformly distributed rainfall. In his study, he illustrated how the physical laws applicable to runoff affected the probability distribution of peak flows. The study found that the effect of the physical parameters of the runoff plane on the distribution of the peak flows approaches the parent distribution as the physical parameters of the runoff plane increases.
The practical application of the analytical methods in the derivation of flood probability distribution has limitations due to mathematical complexity, difficulties in the estimation of parameters, and the assumptions needed to simplify the problem which usually results in poor performance (Loukas, 2002).
Methods based on geomorphologic unit hydrograph
The geomorphologic unit hydrograph (GUH) is an instantaneous unit hydrograph derived from measurable drainage network and catchment properties. GUH is a simple function of measurable physical parameters applied by Rodriguez-Iturbe and Valdes (1979), Rodriguez- Iturbe et al. (1979), Valdes and Rodriguez-Iturbe (1979), Gupta et al. (1980) and Wang et al. (1981) in their studies. Hebson and Wood (1982) incorporated the runoff routing models based on GUH in deriving the cumulative distribution function of the peak streamflow analytically by using a similar rainfall model as proposed by Eagleson (1972). It should be noted that Diaz-Granados et al. (1984) adopted the GUH proposed by Rodriguez-Iturbe et al. (1982a, 1982b) in similar studies. The application of the two methods was made to real catchments and these appeared to give reasonable results when compared to the observed data.
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In addition, Moughamian et al. (1987) examined the performance of Hebson and Wood (1982) and Diaz-Granados et al. (1984) methods in the derivation of flood frequency curves. They selected three catchments having over forty years of streamflow data and applied these methods. The flood frequency curves obtained from each method were compared with the observed flood frequency curves for each catchment and it was found that the two methods performed poorly. Based on this, they concluded that the derived distribution methods needed improvement before these could be applied in routine practice.
Further, Sivapalan et al. (1990) developed a method of obtaining derived flood frequency distribution that included runoff generation on partial areas by both infiltration excess and saturation excess. This method presented the integration of partial area runoff generation model with the generalised GUH-based runoff routing model. In this method, the initial moisture conditions were allowed to vary between storms in contrast to the earlier works in that the initial moisture state were assumed to be constant for all the storms. The resulting flood frequency distributions were presented in a dimensionless framework where issues such as catchment scale and similarity could easily be dealt with. In line with this, Troch et al. (1994) adopted the basic ideas of the partial area runoff generation model used by Sivapalan et al. (1990). The distributed runoff production model was modified to take into account a more general formulation of soil hydraulic properties in the basin. The channel routing model was expressed in terms of the catchment’s ‘width function’. The method was applied to catchments in the province of eastern Pennsylvania, and it was found that the modified model produced a much closer fit between observed and simulated runoff volume for all the selected flood events.
Furthermore, Goel et al. (2000) presented a physically based derived flood frequency distribution method by adopting the GUH introduced by Rodriguez-Iturbe et al. (1982a) as the rainfall-runoff model. The study examined the assumption of both independent or negatively correlated rainfall duration and intensity. They found that when a positive correlation in rainfall duration and intensity existed, the resulting derived flood frequency curve (DFFC) under-estimated the observed floods. The results from four Indian catchments and one catchment in the United States indicated that the cross correlation of rainfall duration and intensity has an important impact on the estimated floods.
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Methods based on U.S. Soil Conservation Service’s Curve Number method
Soil Conservation Service Curve Number (SCS-CN) method was developed by the United States Department of Agriculture (USDA) (SCS, 1972) and has been widely used for the estimation of direct runoff from a given rainfall event on small agricultural catchments. This method is evaluated by the use of tables and nomograms (also called nomograph, a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a function). This method requires subjective interpretation of graphical output. Due to its low input data requirements and its simplicity, many catchments models use this method to determine runoff.
Haan and Edwards (1988) extended the work of Haan and Schulze (1987) by deriving the joint probability density function of runoff and maximum water abstraction. They adopted SCS-CN method in estimating the runoff and the Extreme Value type I distribution in describing the rainfall event. However, the method is only applicable to SCS-CN method, and in situations where a more complex transformation between rainfall runoff is required, the derivation procedure becomes much more complicated (Rahman et al., 1998).
In addition, Raines and Valdes (1993) developed another method of obtaining derived flood frequency distribution using the SCS-CN method which substituted Philip’s (1957) infiltration equation in the method adopted by Diaz-Granados et al. (1984) in estimating runoff. The method was applied to four catchments in Texas. They found that the accuracy of determining rainfall parameters, especially the mean rainfall intensity, were the most important aspect that affects the final DFFC (Cadavid et al., 1991).
Further, Becciu et al. (1993) presented a method to determine derived flood frequency distribution for ungauged catchments. The method adopted a two component extreme value distribution in deriving the regional growth function and a derived distribution method in estimating the index flood. Here, the point rainfall was described by a Poisson distribution and the intensity and duration of rainfall were assumed to be independent random variables with an exponential distribution, and the spatial reduction of precipitation over the basin area was accounted for by means of an areal reduction factor. To model the surface runoff, they applied the SCS-CN method and linear reservoir cascade theory. The method was applied to
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Enhanced Joint Probability Approach Caballero catchments in Northern Italy and it was found that this method could reproduce the frequency distribution of the observed flood data quite well.
Furthermore, Kurothe (1995) applied kinematic wave based derived flood frequency distribution models to a number of central Indian catchments. The probability density function of the effective rainfall intensity and duration was derived using index, the Philip infiltration model and the SCS-CN method. He found that the method based on SCS-CN performed the best.
Moreover, De Michele and Salvatori (2002) presented an analytical expression of the derived distribution of flood peak using simple assumptions on rainfall dynamics and catchment response. They adopted the SCS-CN method to transform the rainfall depth to rainfall excess. The derived distribution method was applied to three catchments located in Thyrrhenian Liguria, North-Western Italy. The derived distribution method presented showed a fairly good agreement with the observed flood data for small return period (T) (say, T ≤ 100 years).
Aronica and Candela (2007) applied the SCS-CN method to model the catchment response in semi-distributed form for the transformation of total rainfall to effective rainfall for six Sicilian catchments in Italy. This method was also employed in the studies by Brocca et al. (2009a, 2009b, 2011) for estimation of losses to catchments in central Italy. Further, Tramblay et al (2010) adopted this method in the modelling approach to simulate the flood events in a small headwater catchment in the Cevennes region in France.
Methods based on other types of rainfall-runoff models
Previous works by Beven (1986, 1987), Blazkova and Beven (1997, 2002), Lamb (1999) and Cameron et al. (1999, 2000a, 2000b) were applied by Blazkova and Beven (2004) for a large catchment in Czech Republic. The method was based on Eagleson’s (1972) work in combination with TOPMODEL (a TOPography based hydrological MODEL). In addition, this method adopted a Generalised Likelihood Uncertainty Estimation (GLUE) framework under a continuous simulation. The continuous simulation method presented had a sufficient range of functionality to reproduce the observed flood frequency characteristics of the
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Enhanced Joint Probability Approach Caballero catchments. However, they found that there were remarkable uncertainties with the flood estimates of higher return periods.
Haan and Wilson (1987) developed a derived distribution approach using two runoff variables (runoff volumes and peak flows) to compute runoff frequencies from the rainfall probabilistic behaviour and other factors affecting runoff. Their method in determining derived distribution of flood peaks was based on the Rational Method of the following form:
Q CIA (2.1)
The study found that runoff coefficient C is a random variable reflecting many hydrologic factors which include antecedent conditions and can be calculated from several observed storm events using equation (2.1). Their method used numerical integration to determine derived distribution under the assumption of the independence of C and I in which their probability distributions can be approximated by Beta and Extreme Value Type I distributions, respectively. In the method presented, consideration of runoff coefficient as a random variable provided larger flood peaks than that obtained assuming C as constant, particularly at higher return periods. Their method also demonstrated the suitability of the JPA but did not make any clear recommendation on the use of this approach, and suggested further study before ‘any sweeping conclusion can be made’ as noted by Rahman et al. (1998).
Sivapalan et al. (1996) developed a derived flood frequency methodology largely based on the use of the intensity-frequency-duration (IFD) curves in examining the connection between process controls and flood frequency. They used IFD curves for the probabilistic description of rainfall inputs and specified the joint distribution of rainfall intensity and duration by multiplying IFD curves with marginal distributions of duration. The adopted method introduced the use of IFD curves in the derived distribution method that would aid to unify theoretical research on derived flood frequency with traditional design practice since IFD data is generally used in design flood estimation using rainfall runoff models.
Furthermore, Bloschl and Sivapalan (1997) adopted the method developed by Sivapalan et al. (1996). They used IFD curves for the rainfall model in examining the effects of various flood
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Enhanced Joint Probability Approach Caballero producing factors such as runoff coefficients, antecedent conditions, storm durations and temporal pattern on flood frequency curve in a derived distribution framework. Their study found that non-linear runoff generation, random antecedent soil moisture, and non-linear routing, all translate into steeper flood frequency curves than in the linear case. The study also found storm temporal pattern to be of critical importance for the flood frequency behaviour and the assumption of equal return periods of the input rainfall depth and output flood associated with the current DEA “is always grossly in error”, a finding which has very important implication in design practice. For the two study catchments in Austria, the DEA under-estimated flood return periods by a factor of at least two but “this factor may be as large as ten” (Rahman et al., 1998).
Further, Iacobellis and Fiorentino (2000) proposed an analytical derivation of flood frequency distribution giving importance to the effects of climate on flood generation process at catchment scale. They selected eight gauged catchments in Basilicata, southern Italy with areas ranging from 40 to 1,600 km2. Their results showed strong connection between climatic factors and derived flood frequency distributions.
Recently, Brodie (2013) developed a Rational Monte Carlo (RMC) method to independently check the ARI estimates based on January 2011 flash flood at Toowoomba, Australia. This method is a simple derived distribution approach where the Rational equation was linked with the observed rainfall intensity at a reference pluviograph to the flood peak flow. The flood estimated by RMC was 475-515 years ARI which is comparable with the log-Pearson 3 method (450-year ARI).
2.3.2 Approximate methods
In most practical cases of non-linear transformation where analytical solution would be quite complex, a more practical approach would be the use of approximate methods (Weinmann, 1994). In hydrology, approximate methods are often used in determining derived frequency distribution. Rahman et al. (1998) categorised these into two groups: (i) discrete methods and (ii) simulation techniques, which are described below.
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Discrete methods
In discrete methods, the continuous distributions of hydrologic variables such as rainfall duration are discretized and the Total Probability Theorem is generally adopted in obtaining derived distribution. Examples of these include studies by Beran (1973), Laurenson (1974), Russell et al. (1979) and Fontaine and Potter (1993). In these methods, all hydrologic variables such as rainfall duration and antecedent soil moisture condition are treated as discrete even though they are continuous ones. The accuracy of these methods depends on the degree of discretization. The Total Probability Theorem are summarised in Appendix A.2 (see Appendix A) as this is the foundation of any JPA/MCST-based flood modelling.
This theorem represents the expansion of the probability of an event in terms of its conditional probabilities, conditioned on a set of mutually exclusive and collectively exhaustive events (Rahman et al., 1998). It is often a useful expansion in problems where it is desired to compute the probability of an event, since the terms in the sum may be more readily obtainable than the probability of the event itself (Benjamin and Cornell, 1970). It is considered as one of the workhorses in probability applications (Kuczera, 1994).
Lerlerc and Schaake (1972) numerically solved Eagleson’s (1972) kinematic wave equations using a finite difference scheme. Conceptually, this numerical approach can be used for more complex natural catchments that are mathematically intractable from an analytic point of view (Hebson and Wood, 1982).
Beran (1973) presented an approximate method of determining the derived distribution where he considered all the possible ways in which a rainfall event of a particular AEP can cause floods and derived their joint probability distributions. The continuous distributions of variables such as rainfall duration were discretized in order that each variable assumed only one of a finite number of possible values to each of which a probability weight was attached. The method made assumption of independence to rainfall variables throughout the simulation. Due to the assumption of independence made, discretizing allowed considerable simplification in the simulation. In addition, Laurenson (1974) developed the most general application of the Total Probability Theorem described by the ‘transformation matrix’
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Enhanced Joint Probability Approach Caballero method. This method considered only a single step in the transformation of stochastic input into a stochastic output in which the output from this step becomes the input to the next step.
Russell et al. (1979) adopted a quite different method for computing design floods under the joint probabilistic framework. This method is believed to be the simplest yet most reasonably realistic rainfall runoff model represented by three parameters such as infiltration rate, I, time of concentration, T, and storage constant, R. The method used actual storm records and assumed constant infiltration rate. In this method, the resulting flood peaks were estimated using 60 largest storms recorded with 120 different combinations of I, T, R. Then the estimated flood peaks were plotted on Gumbel probability paper and from these, AEPs of 50 specified flood peaks were estimated. The AEPs were stored in a large matrix with 50 rows (one for each of the specified flood peak values) and 120 columns (one for each combination of parameters, I, T, R). Using these stored data, AEPs of the stored floods in any particular catchment can be calculated if probability distributions of the parameters are given.
Shen et al. (1990) developed simple expressions to describe the time of concentration, time to peak, and flood peaks as function of catchment and rainfall characteristics for small catchments. These simple expressions are based on results obtained from a specially derived kinematic wave rainfall-runoff model. The kinematic wave numerical model used in this study was based on Eagleson’s (1972) method. The models were found to have reasonably wider applications.
Fontaine and Potter (1993) developed the joint probability distribution of rainfall and antecedent conditions using rainfall runoff model to simulate floods resulting from various combinations of rainfall and antecedent conditions. In this method, for a given flood, the exceedance probability is expressed as the sum of three terms, each being the joint probability of extreme rainfall and antecedent soil moisture. To demonstrate, this method is applied to the Big Eau Pleine River near Stratford, Wisconsin, USA. They found that it can be used to evaluate flood hazards at an existing structure on a regional or national basis, identifying the sites in a region with the highest risk and resulting in the maximum reduction of risk per dollar spent on flood protection.
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Simulation methods
In the simulation methods, random sampling is conducted from the distributions of input variables/marginal distributions which are then used to simulate thousands of streamflow hydrographs using a calibrated rainfall runoff model. The following is a brief review of the simulation methods.
Beran (1973) presented a simulation technique where sampling was conducted across combination of rainfall depth and duration. Through the sampling procedure, it was found that small changes in catchment wetness index had a marked effect on the resulting flood. The study also found that the generalised simulation produced lower flood values having smaller ARIs as compared with the expected flood following rainfall events of that same ARI. Although the method appeared to be a promising tool in assessing the sensitivity of design floods for small ARIs, the method was not doing well in reproducing the observed flood frequency curve in higher ARIs.
Tavakkoli (1985) adopted a simulation technique to derive flood frequency curves for an Austrian catchment as reported in Sivapalan et al. (1996). In his technique, he considered the dependence of rainfall intensity and duration, multiple events, within-storm time patterns (temporal patterns) and variable runoff coefficients. Slight over-estimation of flood peaks was resulted in the simulation approach which he mainly attributed to the runoff generation model.
Muzik and Beersing (1989) examined the transformation process of probability density function of rainfall intensity into the probability density functions of flood peak resulting from an elemental rainfall runoff process. Here, the elemental rainfall runoff process was defined as the runoff from an impervious uniformly sloping plane. To obtain probability density functions of flood peak, the three density functions such as normal, two-parameter gamma and exponential distributions of rainfall intensity were used in a Monte Carlo simulation. Then, the flood peak was computed by using the kinematic wave and experimentally derived relations. Based on the study, it was found that the runoff planes having flat slopes and large hydraulic resistance generally produced more skewed distributions of flood peak and lower values of the mean as compared to runoff planes having
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Enhanced Joint Probability Approach Caballero steeper and hydraulically more efficient planes subject to the same rainfall inputs. This method was not tested on real catchments, and only carried out in laboratory conditions at a basic level of an experimental rainfall runoff process.
Muzik (1993) developed a physically based stochastic method to rainfall-runoff modelling. The method adopted modified SCS-CN method in Monte Carlo simulation in obtaining a derived distribution of flood peak. With the aid of a hydrologically oriented GIS, the method was tested in the study region along the eastern slopes of Rocky Mountains (Alberta, Canada). The following conclusions were made based on the results of the study: (i) the use of standard SCS-CN method resulted under-estimation of the direct runoff amount in Alberta foothills; (ii) the use of modified SCS-CN method improved runoff predictions due to the superior relationships of potential maximum retention and initial abstraction derived from local data; and (iii) even if the true distribution of rainfall input, maximum potential retention, initial abstraction, etc. were not exactly known, effects of their variation within physically reasonable limits can be assessed, and considered in water resources planning and design by using Monte Carlo simulation. He further noted that by applying stochastic input and deterministic modelling, Monte Carlo simulation provides an excellent approach to study flood probabilities.
Durrans (1995) applied a simulation technique to determine the DFFC for regulated sites such as downstream of dams. The process in this technique involves thousands of random sampling of unregulated annual flood peak and unregulated flood volume, a dimensionless initial reservoir depth and dimensionless gate opening area, and routing the inflow hydrograph through the reservoir. This technique has been described as an integrated deterministic-stochastic approach to flood frequency analysis as noted by Rahman et al. (1998). The method presented can also be useful to a wide ranging condition other than outflows from reservoirs.
Loukas et al. (1996) presented a physically based stochastic-deterministic method for flood frequency estimation for ungauged catchments. The method used the numerical derivation of the flood probability and incorporated the findings from the previous studies on spatial and temporal distribution of the rainfall including the catchment response of the region. They used Monte Carlo simulation to generate 5000 random values of the various parameter values
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Enhanced Joint Probability Approach Caballero and to simulate the hydrograph flood peaks. This method was applied to eight coastal British Columbia catchments in Canada and it was found that the results compared well with the observed data and with the observed flood frequency curves. In addition, this method can be applied to the coastal Pacific Northwest of Canada due to similarity of the catchment climatic and hydrologic characteristics to those of British Columbia (Loukas, 2002). However, the method was not tested for the estimation of floods with return periods larger than 100 years due to high uncertainty in the estimation of the extreme events. Thus, it should not be used for more extreme flood range (Loukas, 2002).
Bloschl and Sivapalan (1997) developed a Monte Carlo simulation technique for mapping rainfall return period to runoff return period. The process in this method involved random sampling from continuous distributions of input variables and parameters, and the use of rainfall-runoff model in obtaining the flood hydrograph. In addition, the method required N simulations (N in the order of thousands), and the N different values of the output variables were then used to determine the derived distribution. The generated flood peaks were ranked allowing assignment of a return period to each event. The simulation method presented was relatively simple and it appeared to be a potential method for practical application (Rahman et al., 1998).
Hoang et al. (1999) applied the simulation method adopted by Bloschl and Sivapalan (1997) using rainfall records from 19 pluviograph stations in South-eastern Victoria. In this study, they concentrated on the storm rainfall characteristics such as rainfall duration and intensity, and the within-event temporal pattern, which were influential in defining the flood frequency distribution. This method demonstrated that it was quite feasible to describe a joint probability of design rainfall using a new storm definition that can produce random rainfall event duration and intensity.
In line with the study by Hoang et al. (1999), a Monte Carlo simulation technique (MCST) to determine a derived flood frequency distribution based on the JPA was developed by Rahman et al. (2002a). This method considered probability distributed inputs and model parameters, and their correlations, to determine probability distributed outputs. In this method, four input variables/parameters, rainfall duration, intensity, temporal pattern, and initial loss, were treated as random input variables. The method focused on the distributions of storm-core,
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Enhanced Joint Probability Approach Caballero which was taken as the intense part of a complete storm. The method involved generation of a large set of data from the four marginal distributions representing rainfall duration, intensity, temporal pattern and initial loss. They found that the storm-core rainfall duration can be approximated using exponential distribution which is expressed by:
1 p(D ) eDc (2.2) c
where p ( ) is the probability density, Dc is the storm-core duration, β which can be taken as the mean of the observed storm-core duration values, is the parameter of the exponential distribution. In their adopted MCST, the IFD curves for storm-core rainfall intensity were also developed which involved fitting of exponential distribution to the partial series rainfall intensities, Ii (i 1,...,M ) , where M is the number of data points in a class. Rainfall quantiles were then obtained from the following equation:
I(T) I0 ln(T) (2.3)
Where I 0 is the smallest value in the series; Ii M I0 ; M / N ; N is the number of years of data; and T is the average recurrence interval (ARI) in years.
Rahman et al. (2002a) also found that the initial loss, IL, can be approximated by a Beta distribution, which is expressed by:
IL1 (1 IL) 1 p(IL;, ) (2.4) B(, ) where B(α,β) is a Beta function (α and β are parameters).
Thousands of events were simulated from the distributions of rainfall duration, intensity and observed pool of non-dimensional temporal patterns and initial loss, which were then run through the calibrated runoff routing model to simulate streamflow hydrographs. Using the appropriate probability plotting position formula, the peaks of all the simulated hydrographs were then used to determine a DFFC. The determination of the DFFC for the ARI ranging
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Enhanced Joint Probability Approach Caballero from 1 to 100 years, generation of 2000 years of data was found to be adequate and the number of data points to be generated (NG) was obtained from the equation as expressed by the following equation:
NG (NY ) (2.5) where λ is the average number of storm-core events per year and NY is the number of years of data to be generated.
The set of NG simulated flood peaks were used in the construction of a DFFC. Here, the NG simulated flood peaks were arranged in decreasing order of magnitude and was assigned rank (m). From the ranked floods, the computation of ARI was done by using the following equation:
NG 0.2 1 NY .02 ARI (2.6) m 0.4 m 0.4
A DFFC was constructed by plotting the flood peaks versus ARI.
The above method was applied to three catchments in Victoria: the Tarwin River, Boggy Creek and Avoca River. They found that the obtained DFFCs compared very well with the observed flood frequency curves over a wide range of flood frequencies. However, they stated that the approach should be tested on additional catchments representing a wider range of hydrologic conditions before it can be recommended for general application (Rahman et al., 2001; 2002a).
Further, Rahman et al. (2002b) tested the previous works by Rahman et al. (2001, 2002a) in the MCST by integrating it with the distributed non-linear runoff routing model URBS. The new method was applied to the Tarwin River catchment in Victoria, one of the catchments used by Rahman et al. (2001, 2002a). The DFFCs of the method compared very well over a wide range of frequencies resulted from flood frequency analyses of the flood series data available at the site.
Rahman and Weinmann (2002) also examined the MCST using a number of Northern Australian catchments (the Bremer River, Running Creek and Teviot Brook) in Queensland.
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The selected catchments were mainly unregulated and rural with no major land-use changes occurring over their periods of streamflow records. The DFFCs of the adopted method under- estimated the observed floods at smaller ARIs for both the Running Creek and Teviot Brook catchments. However, the overall results compared quite well similar to Rahman et al. (2002b).
Rahman et al. (2002c) investigated the use of probability distributed initial losses in design flood estimation using data from ten Victorian catchments in Australia. A four-parameter Beta distribution was used to fit the initial loss data. To determine the DFFCs, the stochastic losses were applied in the MCST with stochastically generated design rainfall events. They found that the DFFCs were reasonably sensitive to details of the adopted loss modelling method in the range of relatively frequent floods, but relatively insensitive to higher ARIs.
In contrast, Heneker et al. (2002) adopted a method for design flood estimation using continuous simulation in producing links between rainfall and rainfall excess, therefore, eliminating the need in the assumption of initial loss. The method used the KinDog kinematic runoff-routing catchment model developed by Kuczera et al. (2000) to route the rainfall to the catchment outlet. They applied the method to the Boggy Creek catchment in Victoria and found that the DFFCs resulted from the simplified rainfall excess frequency duration (REFD) method showed a good relationship to the fitted distribution between an ARI of 10 to 100 years.
Charalambous et al. (2003) extended the previously developed MCST method by Rahman et al. (2002a, 2002b, 2002c); Rahman and Weinmann (2002); and Weinmann et al. (2002) to large gauged catchments. The method was applied with the industry-based flood estimation model URBS (Carroll, 2001) and was called URBS-MCST (UMCST) (Rahman et al., 2002b). The result of the study concluded that UMCST can be applied to large catchments with multiple rainfall and stream gauging stations, and also it was feasible to vary the initial loss and storm duration across sub-catchments. However, they noted that the UMCST required extensive data to develop the input distributions for application in the MCST.
Kader and Rahman (2004) presented how the rainfall intensity distribution can be regionalised in the State of Victoria in Australia for application with the MCST. This method
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Enhanced Joint Probability Approach Caballero used 23 pluviograph stations data from South-east Victoria to develop the regional relationships between JPA-IFD data and the currently available ARR 1987 IFD data (DEA- IFD data). The developed regional prediction equation for JPA-IFD was tested to the Tarwin River East Branch catchment in Victoria. They found that the regional approach could be applied to obtain IFD data for application with the MCST for design flood estimation in South-east Victoria. However, the results were not very satisfactory and hence, this was not recommended for practical application.
In another study, Rauf and Rahman (2004) investigated the design rainfall estimates provided by the ARR 1987 and JPA methods using rainfall data from Victoria in Australia. The study examined the sampling properties of rainfall events using the two methods and found that for 91 stations in Victoria; about 50% storm burst events shared common rainfall spells in ARR 1987 method, which indicated that many data points across various durations were not independent. Overall, the ARR-IFD curves were higher as compared to that of the JPA-IFD. However, they could not establish any general relationship between the two different types of IFD curves.
Carroll and Rahman (2004) considered the application of MCST to sub-tropical areas of Australia along with the URBS model. They applied the model to 13 stations from sub- tropical areas (South-east Queensland) and 29 stations from Victoria. In South-east Queensland, they found that the complete storm durations could be approximated by an exponential distribution but the storm-core durations by gamma distribution (Rahman et al., 2001; Weinmann et al., 2002). The gamma distribution can be expressed by the following equation:
d 1edc p(d ;, ) c for d 0 (2.7) c (r) c where α and β are parameters and can obtained from
2 d c (2.8) 2
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2 (2.9) dc
where d c is the mean value of storm-core duration at the station or in the region and 2 is the variance of d c values at the station or in the region.
Aronica and Candela (2004) presented a MCST to determine derived flood frequency distributions of extreme discharge using regional data. The adopted method was based on two modules: (i) stochastic rainfall generator module; and (ii) catchment response module. In this method, the maximum rainfall depth for a fixed duration was assumed to follow the two components extreme value (TCEV) distribution (Rossi et al., 1984). In addition, the SCS-CN method adopted by USDA-SCS (1986) was used to transform storm depth to effective rainfall depth with the Generalised Likelihood Uncertainty Estimation (GLUE) method to explore the estimation of the uncertain knowledge of antecedent soil moisture (AMC) affecting the derivation of flood frequency curve. Their method was applied to the Oreto River located in the north-western part of Sicily (Italy) to derive the flood frequency curves with return period ranging from 1 to 500 years by 10,000 Monte Carlo runs. They found that the developed method could reproduce the observed flood frequency curves with reasonable accuracy over a wide range of return periods using a simple and parsimonious approach.
Aronica and Candela (2007) extended their previous work (Aronica and Candela, 2004) using a semi-distributed stochastic rainfall-runoff model suited for ungauged or partially gauged catchments to determine the derived flood frequency distributions. The method was based on three modules: (i) stochastic rainfall generator module; (ii) hydrologic loss module; and (iii) flood routing module. This method was applied to six Sicilian catchments in Italy to derive the flood frequency curves by simulating 5000 flood events combining 5000 values of total rainfall depth for the storm duration and antecedent moisture conditions. They found that it could reproduce the observed flood frequency curves with reasonable accuracy over a wide range of return periods using a simple and parsimonious approach (similar to Aronica and Candela, 2004), limited data input and without any calibration of the rainfall-runoff model. This method could be applied for ungauged catchment in routine application.
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More recently, the JPA has been adopted in flood risk assessment in a number of international studies. For instance, Gioia et al. (2008) applied a two-component derived distribution based on two runoff thresholds characterised by different scaling behaviour. Haberlandt et al. (2008) presented Monte Carlo simulation of meteorological inputs coupled with lumped distributed or semi-distributed hydrological models in flood modelling. Viglione and Bloschl (2009) considered the role of critical storm duration in the JPA framework. Gioia et al. (2011) proposed JPA to examine the spatial variability of the coefficient of skewness and its impacts on flood peak estimation. Iacobellis et al. (2011) tested the JPA in the context of regional analysis by means of an objective jack knife procedure. All these studies proved that the JPA could provide more accurate and realistic flood estimates.
The most recent work by Svensson et al. (2013) adopted a MCST to estimate frequencies of flood peak and total event flow volume for UK catchments. Their method allows all the input variables to take on values across the full range of their individual distributions which are brought together in all possible combinations as input to an event-based rainfall-runoff model in a Monte Carlo simulation framework. Using the adopted method, they found that the DFFC did not reproduce the upper bound as suggested by the generalised extreme value (GEV) distribution fitted to the observed annual maximum flood series. This might be because of the shortness of the observed series that may not reflect the true distribution.
2.4 Runoff routing model adopted in the previous studies on JPA/MCST
Rahman et al. (1998) reviewed the runoff routing models that are generally adopted with the JPA/MCST. They found that the semi-distributed and non-linear type of catchment routing models, e.g. RORB (Laurenson and Mein, 1995, 1997), URBS (Carroll, 1994, 2004) and WBNM (Boyd et al., 1996) referred to as runoff routing models, were the commonly used models in Australian flood design practice. Being distributed in nature, these types of models can account for the areal variation of rainfall and losses to a good extent.
Based on the studies by Rahman et al. (1998) and Weinmann et al. (1998), a simple conceptual runoff routing model with a single concentrated storage at the catchment outlet was adopted by Rahman et al. (2001), referred to a single non-linear storage model. This modelling approach used in determining a DFFC had three main components: (i) the
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Enhanced Joint Probability Approach Caballero hydrologic modelling framework to simulate the flood formation process; (ii) the key inputs and parameters or the model variables with their probability distributions; and (iii) the stochastic modelling framework to synthesise the derived flood distribution from the distributions of inputs and parameters. The use of this model, with its joint probability framework, provided an indication of what the semi-distributed model like URBS (Carroll, 1994, 2004) could achieve for catchments in the order of 500 km2. Thus, it is adopted in this thesis.
2.5 Loss models
The estimation of losses is considered to be one of the important steps in the rainfall runoff modelling where design flood hydrograph is needed. The losses (as shown in Figure 2.2) are part of rainfall that does not appear as direct runoff after the rainfall event. These include evaporation, interception by trees or vegetation, loss through the stream bed and banks (transmission loss), retention on the surface or surface detention (depression storage) and infiltration which have been conceptualised in simple forms (Nandakumar et al., 1994). Due to their complexity in representation, these losses are not directly accounted for in many loss models, and simply treated as infiltration into the soil (Hill et al., 1996). These infiltration models include Horton model (Horton, 1935), the Philip model (Philip, 1969) and the modified Green-Ampt model (Mein and Larson, 1971). Horton infiltration models were used by Wood (1976) and Hebson and Wood (1982) whilst the Philip infiltration models were applied by Diaz-Granados et al. (1984) and Shen et al. (1990) in their joint probability studies.
In practical flood estimation problems, the simplified conceptual lumped loss models are more preferred than the infiltration models due to their simplicity and ability to approximate catchment runoff behaviour (Nandakumar et at., 1994). Thus, this conceptual lumped loss model is adopted in this thesis. The models are lumped as these do not consider the spatial variability of the rainfall losses and estimate their model parameters by using the observed rainfall runoff events data. Frequently used methods for lumped losses include the constant loss rate, SCS-CN, initial loss-continuing loss and initial loss-proportion loss models. Flavell and Belstead (1986) used the constant loss rate model in the Kimberly region of Western
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Australia and in the previous joint probability studies in design flood estimation by Eagleson (1972). The SCS-CN method (USDA-SCS, 1985) were adopted by Haan and Edward (1988), Raines and Valdes (1993) and the recent study by Aronica and Candela (2007).
Figure 2.2: Physical processes which contribute to rainfall loss (modified from Wordpress, 2012).
The initial loss-continuing loss (IL-CL) model, as shown in Figure 2.3, is the most commonly used conceptual lumped loss model in Australia (I. E. Australia, 1987; Hill et al., 1996; Hill et al., 2012). This method was adopted by Hoang et al. (1999), Rahman et al. (2001, 2002a) and Tularam and Ilahee (2007) in their JPA/MCST. In this method, the initial loss is defined as the rainfall that is lost at the beginning of the storm before the commencement of the surface runoff. The continuing loss is the average rate of loss throughout the remainder of the storm. This model can be applied to compute the average loss of rainfall at the catchment or sub-catchment scale (Hoang, 2001).
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Figure 2.3: Initial loss-continuing loss model (based on Hill et al., 1996)
2.6 Input variables in rainfall runoff modelling
The currently recommended DEA in design flood estimation ignores the probabilistic behaviour of input variables in the rainfall runoff modelling except for the rainfall intensity (I. E. Australia, 1987). In contrast, the JPA/MCST by Hoang et al. (1999) and Rahman et al. (2001, 2002a) and Rahman and Carroll (2004) considered four input variables (rainfall intensity, duration, temporal pattern and initial loss) for probabilistic representation. The uses of four random inputs were found to significantly reduce the bias and uncertainties associated with the design flood estimates obtained from a DEA.
The commonly used random input variables and the other fixed input variables in the rainfall runoff modelling are discussed in the following sections within the categories of rainfall characteristics, loss variables, runoff routing model parameters and baseflow.
2.6.1 Rainfall characteristics
The observed rainfall events vary significantly with respect to rainfall intensity, rainfall duration, temporal pattern and the spatial distribution of rainfall at the catchment scale (Hoang, 2001). This variability leads to the inclusion of the following rainfall variables in the
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The durations of rainfall events that have the potential to produce floods, vary considerably for the observed rainfall events. Aside from the joint probability studies by Rahman et al. (1998), Weinmann et al. (1998), Hoang et al. (1999) and Rahman et al. (2001, 2002a), this was also considered as a random variable in the earlier works by Eagleson (1972), Beran (1973), Russel et al. (1979), Muzik (1993) and Bloschl and Sivapalan (1997). Hence, this is taken as a random variable in this thesis.
The temporal pattern is a very important input that needs to be considered as a random variable aside from rainfall depth and duration as this can have a major effect on the flood outcome (Book II, Section 2, ARR, 1998). In the studies presented by Askew (1975), Milston (1979), Brown (1982), Wood and Alvarez (1982), Cordery el al. (1984), Rahman et al. (2006), Varga et al. (2009), Ball and Aboura (2010) and Akbari et al. (2011), the assumption of different temporal patterns may cause up to 50 percent variation in flood peaks. In addition, the adopted extreme temporal patterns may cause resulting flood peaks to vary up to 2.5 times for every heavy rainfall (I. E. Australia, 1987). Furthermore, Viessman et al. (1989) described that the shape and peak magnitude of flood hydrographs are significantly affected by rainfall temporal patterns. Therefore, the temporal pattern is another rainfall variable that needs to be treated as a random variable.
The inter-event duration is a variable that can be used in the MCST to account for the arrival time of a storm event. This is defined by Hoang et al. (1999) as separation time, with a minimum value of 6 hours, in their rainfall event definition. Previous works in the JPA by Hoang et al. (1999) and Rahman et al. (2001, 2002a) only considered the inter-event duration to identify significant rainfall events. The recent study by Kjeldsen et al. (2010) considered the inter-event duration as a random variable. This thesis started before Kjeldsen et al. (2010) and decided that inter-event duration should be used as a random variable in the JPA/MCST.
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The modelling of rainfall areal pattern variability is considered to be less important, in particular for smaller catchments, as compared to rainfall intensity, duration and temporal pattern. Frequently, the derivation of its probability distribution is problematic due to limited availability of pluviograph data at sub-catchment scale. Due to these reasons, the randomness of the rainfall areal pattern is not considered in this study. However, the variability consideration of rainfall areal pattern in larger catchments with a higher rainfall gradient over the catchment is worth allowing for. In contrast, for smaller catchments, it may be assumed that rainfall areal pattern is constant. For simplicity and since this thesis focuses on smaller catchments, it is assumed that areal rainfall is constant. However, in this thesis the average catchment rainfall is obtained from point design rainfall using an areal reduction factor (Siriwardena and Weinmann, 1996).
2.6.2 Loss variables
In the runoff generation process, loss is an important variable. According to Beran (1973), the correct choice of loss rate is the most important in examining sensitivity of the design flood to alterations of the assumed values of variables. This is represented by a loss model with one or two variables (Hoang, 2001). The application of constant loss rate instead of a probability distribution under-estimates the exceedance probability for a given flood peak (Wood, 1976).
In line with this, the sensitivity analysis conducted by Hoang (1997) for the Gungoandra Creek catchment in New South Wales showed that design flood estimates are very sensitive to values of losses adopted in the design. She found that the assumption of an initial loss lower than the median value may increase by up to 120% in the flood peak. In addition, the studies by Lumb and James (1976), James and Robinson (1986), Haan and Schulze (1987), and I. E. Australia (1987) stated that the strong influence of loss values on design flood estimates is based on the fact that a given rainfall occurring on a dry watershed produces significantly less runoff than the same rainfall occurring on a wet catchment. As a result, Rahman et al. (1998) concluded that loss is the most important factor and thus, treated initial loss as a random variable in their joint probability study (Rahman et al., 2001, 2002a). Hence, this study is adopted initial loss as a random variable.
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In most of the previous applications of the JPA/MCST in Australia continuing loss was treated as a constant (e.g. Hoang et al. (1999), Hoang (2001) and Rahman et al. (2001, 2002a)). The continuing loss is not as variable as the initial loss (Hoang, 2001), but still a variable worth considering as a random input in the analysis as done in the earlier works by Ilahee and Rahman (2003) and Ilahee (2005). The recent investigation by Ilahee and Imteaz (2009) showed that the median values of continuing loss from the 48 selected catchments in the State of Queensland range from 0.71-5.8 mm/hr. Similarly, the analysis conducted by El- Kafagee and Rahman (2011) using five selected catchments in the State of New South Wales showed a notable variability in the median values of continuing loss (which was: 0.53-1.56 mm/hr). Given the wide variability of continuing loss values in these previous studies, it appears that it is not easy to select a representative value of continuing loss in flood modelling. Thus, continuing loss is considered to be a random variable in this thesis.
2.6.3 Runoff routing model parameters and baseflow
The factors affecting hydrograph formation are catchment response parameters which consist of model type, model structure and model parameters, and the design baseflow. Most of the hydrologic studies focused on the hydrograph formation process, although it is renowned that the most important problem in the design flood estimation is the determination of ‘what to route’ not the problem in ‘how to route’ (Sivapalan et al., 1990). This implies that the variability of runoff routing model parameters and baseflow on flood estimates is of secondary importance compared with that of the runoff generation process (Rahman et al., 1998). The consideration of runoff routing model parameters and baseflow as random variables on flood estimates is considered to be less important (Hoang, 2001).
Though the runoff routing model parameters is of secondary importance and only refinement to the current JPA/MCST, Patel and Rahman (2010) treated the storage delay parameter (one of the runoff routing model parameters) as a random variable in their recent study. They found that storage delay parameter values showed a moderate degree of variability and resulted in quite different flood peak estimates if different possible representative values are adopted in the design. Thus, this thesis considers storage delay parameter as a random variable in the rainfall runoff modelling. It should be noted that the non-linearity parameter of the adopted runoff routing model is assumed to be 0.8 (a constant) in this thesis. University of Western Sydney Page 50
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The design baseflow generally accounts for only a very small portion of the surface runoff for most typical catchments except for a very small flood (Hoang et al., 1999). Even though any streamflow hydrograph has a random baseflow component, in reality, the variability in baseflow magnitude is mainly seasonal, and regarded as having a small effect on design flood estimates. As a result, baseflow is treated as fixed input in this study similar to the previous JPA/MCST.
2.7 Regionalisation methods
In hydrology, regionalisation is referred to the method of transferring information from donor gauged catchment to the target ungauged catchment or catchment of interest (Bloschl and Sivapalan, 1995). Commonly adopted regionalisation methods are physical similarity (catchment characteristics similarity), spatial proximity and regression-type (statistical regression) methods (Vaze et al., 2011). The physical similarity method is based on the assumption that optimised input parameters from a physically similar catchment with the same catchment characteristics are applicable to the other (Deckers et al, 2010, Vaze et al, 2011). The spatial proximity method transfers the calibrated input parameters from the geographically closest catchments (Vaze et al., 2011). The regression-type method involves estimation of a relationship among the values of input parameter calibrated from gauged catchments and climatic and physical characteristics of the catchments. The derived relationships are then used to estimate input parameter values for the ungauged catchment of interest.
Of these three methods, the regression-type method is widely used in the regionalisation studies (Young, 2006; Deckers et al., 2010); however, it has been strongly criticised by Bardossy (2007) and Oudin et al. (2008) as the cross-correlation between parameters are seldom taken into account. In addition, model calibration can produce vastly different sets of parameter values that give similar model performance i.e. the equifinality problem (Beven and Freer, 2001). The spatial proximity and physical similarity methods have been more popular and used in several recent regionalisation studies (Merz and Bloschl, 2004; Parajka et al., 2005; Bardossy, 2007; Oudin et al., 2008; Vaze and Teng, 2011).
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For example, three regionalisation methods were compared using 308 and 320 Austrian catchments by Merz and Bloschl (2004) and Parajka et al. (2005), respectively, using an 11- parameter HBV model. In the comparison, the spatial proximity method showed that it performed the best followed by the physical similarity method. The regression-type method performed the worst (Vaze et al., 2011). Similar conclusion was reached by Oudin et al. (2008) using the GR4J and TOPMO (two rainfall-runoff models) in 913 French catchments. They mentioned that the spatial proximity method did not totally outperform the physical similarity method and hence, they suggested that combining the two methods in selecting a donor gauged catchment might improve the modelling results. This thesis has adopted the spatial proximity with the aid of inverse distance weighted averaging in regionalising various input variables/model parameters (as discussed in Section 3.9).
2.8 Summary of Chapter 2
This chapter has discussed various rainfall-based design flood estimation methods with a particular emphasis on Design Event Approach (DEA) and Joint Probability Approach (JPA)/Monte Carlo Simulation Technique (MCST). It has been found that the DEA has serious limitations in selecting the input variables in the design where it ignores the probabilistic nature of the input variables except for the rainfall depth. To overcome the limitations associated with the DEA, alternative methods can be applied such as continuous simulation, ‘Improved’ DEA, the JPA and the runoff files approach. It has been found that only continuous simulation and the JPA have the potential to fully overcome the limitations associated with the currently recommended DEA. Continuous simulation generates flood runoff sequences from rainfall time series and other climatic characteristics and loss parameters using a continuous simulation water balance model and a flood routing model. While the JPA estimates design floods using the same rainfall runoff modelling input variables as the DEA; it treats input variables and the flood output as random variables and accounts for their correlations. Thus, the JPA has the potential to offer considerable improvements in rainfall-based design flood estimation as it is theoretically superior as it can consider the probabilistic nature of the input variables in the runoff routing model. A number of research studies as mentioned in this chapter have demonstrated that the JPA can overcome the major limitations associated with the DEA.
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It has been found from the literatures that the analytical methods in the JPA are quite complicated due to its mathematical complexity and cannot be used in practical situations for flood modelling in real catchments. In contrast, the approximate form of the JPA such as MCST has enough flexibility for practical application as demonstrated by some previous studies. Using the MCST, the stochastic nature of rainfall characteristics (e.g. rainfall duration, intensity and temporal patterns) and catchment antecedent wetness condition to a rainfall event or rainfall losses can be considered and converted into a flood frequency distribution without much complications. Although the JPA/MCST has shown significant promise to become a practical tool of flood modelling by replacing the DEA, no development and testing of the JPA/MCST over a large region has been made to-date. To achieve this objective, it needs regionalisation of the model inputs and parameters considering data from a large number of pluviograph/rainfall stations and catchments. This thesis thus proposes to enhance the MCST by regionalising the inputs/parameters for state of New South Wales in Australia so that the new Enhanced Monte Carlo Simulation Technique (EMCST) can be applied to ungauged or poorly gauged catchments.
The proposed EMCST is based on complete storm rather than storm-core as it is easier to define. In addition, difficulty in estimating losses can be reduced for complete storms as compared to storm-cores. The proposed study also adopts inter-event duration as a random variable in the MCST in addition to rainfall duration, intensity, temporal pattern, initial loss, continuing loss and storage delay parameter of the runoff routing model. The inter-event duration can be used to formulate annual maximum flood series from the generated partial series in the EMCST.
It has also been found that a spatial proximity method is the preferred method to regionalise the parameters of the input distributions for application with the EMCST.
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Enhanced Joint Probability Approach Caballero CHAPTER 3 Description of the Methods Adopted in the Development of the Enhanced Monte Carlo Simulation Technique
3.1 Introduction
Chapter 2 has presented a literature review on design flood estimation methods particularly on the rainfall-based methods that employ Joint Probability Approach (JPA)/Monte Carlo Simulation Technique (MCST). In addition, the runoff routing models adopted in the previous studies, the loss models and the commonly used input variables and parameters used in the JPA/MCST have been discussed briefly in Chapter 2. This chapter discusses the methodology adopted in this thesis to develop the Enhanced MCST (EMCST) so that it can be applied in design flood hydrograph estimation for ungauged or poorly gauged catchments with relative ease.
For the development of the EMCST, the following major steps are involved: (i) Selection of rainfall events; (ii) Selection of runoff routing model; (iii) Selection of input variables for stochastic simulation; (iv) Formulation of runoff routing model; (v) Identification of marginal probability distribution for each of the selected input variables; (vi) Specification of the distribution of rainfall depth i.e. intensity-frequency-duration (IFD) curves; (vii) Derivation of a dimensionless complete storm temporal pattern; (viii) Regionalisation method adopted in the study; (ix) Implementation of the proposed EMCST; and (x) Formation of annual maximum flood series from generated partial duration series flood peak data to obtain the derived flood frequency curve (DFFC). This chapter discusses all of these steps and the other relevant methods adopted in this thesis.
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3.2 Selection of rainfall events
The proposed EMCST is based on the definition of a random ‘rainfall event’. Thus, the first and foremost step in the EMCST is identification of rainfall events. This study applied the rainfall event definition introduced by Hoang et al. (1999) and Rahman et al. (2002a) which incorporated the random nature of the three rainfall characteristics (rainfall duration, intensity and temporal pattern). Unlike previous studies by Hoang et al. (1999) and Rahman et al. (2002a), the inter-event duration is also used in this thesis as a new random variable, which is the time elapsed between the two successive selected rainfall events. From JPA perspective, a ‘complete storm’ and a ‘storm-core’ are defined as below.
A complete storm, as shown in Figure 3.1, is defined in three steps as described by Hoang et al. (1999) in their study.
Figure 3.1: Rainfall events: complete storm and storm-core (based on Hoang et al., 1999)
Step 1: A ‘gross’ storm is a period of rain starting and ending by a non-dry hour (i.e. hourly rainfall > C1 mm/h), preceded and followed by at least six dry hours.
Step 2: Any ‘insignificant rainfall’ periods at the beginning or end of a gross storm (referred to as ‘dry period’) are then excluded from the gross storm, the remaining part of the storm
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Enhanced Joint Probability Approach Caballero being called as ‘net’ storm. A period is defined as ‘dry’ if all hourly rainfalls in the period are
≤ C2 (mm), and the average rainfall intensity during the period ≤ C1 (mm/h).
Step 3: The net storms, from now on is referred to as ‘complete storms’, which are then assessed in terms of their potential to produce a significant runoff. This is performed by comparing their average intensities with arbitrarily selected threshold intensities. A net storm is only selected for further analysis if the average rainfall intensity during the entire storm duration (RFID) or during a sub-storm duration (RFId), satisfies one of the following two conditions:
2 RFID ≥ F1 × ID (3.1)
2 RFId ≥ F2 × Id (3.2)
2 2 where ID is the 2-year ARI intensity for the selected storm duration D and Id is the 2 corresponding intensity for the sub-storm duration d, contained within D. The values of ID 2 and Id are estimated from the design rainfall data (e.g. from Australian Rainfall and Runoff, ARR 87) (I. E. Australia, 1987).
The use of appropriate reduction factors F1 and F2, as defined above, enables the selection of only the events that have the potential to produce significant runoff/flood. The adoption of smaller values of F1 and F2 captures relatively large number of events; many of these events may not be relevant in design flood analysis; therefore, appropriate values of F1 and F2 need to be selected so that events of very small average intensities are excluded. In this study, the following parameter values have been adopted: F1 = 0.4, F2 = 0.5, C1 = 0.25 mm/hr and C2 = 1.2 mm/hr (similar to Hoang et al., 1999 and Rahman et al., 2002a). This typically resulted in 2 to 8 complete storm rainfall events (on average) being selected per year from each pluviograph station selected in the study. These selected complete storm rainfall events are analysed in Chapter 5 to derive marginal distributions of various rainfall event characteristics.
For each of the selected complete storms, a storm-core can be identified, which is defined as “the most intense part of a complete storm”. The storm-core is found by calculating the 2 average intensities of all possible storm bursts and the ratio with the threshold intensity Id for the relevant sub-duration d, then selecting the burst of that sub-duration which produces the
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Enhanced Joint Probability Approach Caballero highest ratio. Rahman et al. (2002a), in their MCST, focused on storm-cores; however, this study (EMCST) focuses on complete storms. It is believed that complete storms are easier to identify and moreover, the rainfall temporal patterns and losses can be analysed more explicitly for a complete storm as compared to a storm-core.
3.3 Selected runoff routing model
The simple conceptual runoff routing model adopted by Rahman et al. (2001, 2002a), referred to as a single non-linear storage model, was adopted in this study in determining DFFC due to its simplicity, as this does not require sub-division of a catchments into smaller units and hence applicable to smaller catchments. The storage-discharge relationship of this model is expressed by the following equation:
S = kQm (3.3) where S is catchment storage in m3, k is the storage delay parameter in hour, Q is the rate of outflow in m3/s and m is the non-linearity parameter assumed to be 0.8 in this study. This value of m is generally used in Australian flood hydrology practice (e.g. Laurenson and Mein, 1995). It should be noted that in the adopted runoff routing model Equation 3.3 and the basic water balance equation (inflow - outflow = rate of change of discharge) need to be solved.
It should be noted here that Charalambous et al. (2013) adopted a multi-storage non-linear model URBS with the MCST as opposed to Rahman et al. (2002a) who adopted a single non- linear storage model. The catchment size used in this study (13 to 223 km2, as shown in Tables 4.1 and 4.3) is well within the application of the single non-linear storage model and moreover these are rural catchments; for developed urban catchments, multi-storages models are preferable. The reason for adopting single non-linear storage model in this thesis is to reduce the time of simulation run. The regional EMCST developed in this thesis can easily be adapted to multi-storages non-linear model like URBS and RORB.
3.4 Selected input variables for stochastic representation
For practical reasons, the initial investigation by Rahman et al. (1998), Weinmann et al. (1998), Hoang et al. (1999) and Rahman et al. (2001, 2002a) considered four input variables
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Enhanced Joint Probability Approach Caballero in their JPA for probabilistic representation. Each of these inputs variables has a distribution of possible values and the probability of the computed flood peak should theoretically account for the effect of the combined probabilities. In this study, the development and application of the EMCST considered seven input variables/parameter as random variables as it was noted by previous researchers that these variables are essentially random in nature (e.g. CL) (Rahman et al., 2002a; Ilahee, 2005; Charalambous et al., 2013). These variables are complete storm duration (DCS), inter-event duration (IED); rainfall intensity expressed in the form of intensity-frequency-duration (IFD) data, temporal pattern (TP), initial loss (IL), continuing loss (CL), and runoff routing model storage delay parameter (k). The addition of three new random variables (i.e. continuing loss, runoff routing model storage delay parameter and inter-event duration) would provide an enhancement to the MCST developed by Rahman et al. (2002a). The rainfall areal pattern, baseflow and non-linearity parameter (m) are considered to be ‘fixed’ inputs in the new EMCST. This is because this study focuses on relatively smaller catchments where areal rainfall can be assumed to be ‘fixed’. Baseflow is a smaller proportion of total flood flow in most of the Australian catchments and hence it is kept ‘fixed’. Finally, m is generally kept ‘fixed’ in Australian flood hydrology practice and hence it is kept ‘fixed’ in the new EMCST.
3.5 Formulation of runoff routing model
In order to estimate the losses and to calibrate the adopted runoff routing model, concurrent rainfall and streamflow events data are required. This section begins with the selection of rainfall and streamflow events, separation of baseflow, estimation of losses and calibration of the runoff routing model. All of these are needed to set up the runoff routing model.
3.5.1 Selection of concurrent rainfall and streamflow events
The selection of concurrent rainfall and streamflow events starts with the selection of study catchments (which is presented in Chapter 4). The selected catchments for the development and testing of the EMCST must have nearby pluviograph station(s) (preferably within maximum of 30 km from catchment centre). In addition, the catchments to be selected must have at least 10 years of concurrent rainfall and streamflow data. After the identification of the pluviograph station(s), the selections of rainfall events that have the potential to produce University of Western Sydney Page 59
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significant runoff are selected. This is achieved by using appropriate reduction factors F1 and
F2 (as mentioned in Section 3.2) and by modifying the FORTRAN program by Rahman (1999) so that the complete storm events and other relevant storm characteristics as well as IED are abstracted and saved for subsequent analyses. For each of the selected complete storm events, corresponding streamflow events are selected by comparing the start and end times of complete storms with the relevant hourly streamflow data. In doing so, the complete storm events which do not produce any runoff are excluded for further investigation.
3.5.2 Criteria for baseflow separation
Before estimating the CL and k values from complete streamflow hydrographs, baseflow needs to be separated from the total streamflow. This study adopts the method proposed by Boughton (1988) for baseflow separation. The method considers that the rate of increase in the baseflow depends on a fraction of the surface runoff (). Thus, the baseflow rate at any 3 time step i (BFi) in (m /s), can be expressed as the sum of the baseflow in the previous time
3 step (BFi-1) in (m /s) and times of the difference of the total streamflow at step i (SFi) in 3 (m /s) and the baseflow at step i-1 (BFi-1). This is expressed by the equation below:
BFi = BFi-1 + (SFi – BFi-1) (3.4)
In the application, the baseflow is assumed to be equal to the streamflow (BF1 = SF1) at the beginning of surface runoff (to define the initial condition). In order to apply equation 3.4 for a given catchment, the parameter needs to be estimated from the selected streamflow events and a design value needs to be selected, which provides an ‘acceptable’ baseflow separation for all the selected events for a given catchment. Once the baseflow separation is made, the CL values can be estimated as presented below.
3.5.3 Estimation of losses
Once the concurrent rainfall and streamflow events are selected, the IL and CL are estimated. The method adopted for this loss estimation has been discussed in Section 2.5. In this study, to estimate the IL, a surface runoff threshold value equal to 0.01 mm/h has been adopted (similar to Hill et al., 1996); while, the estimation of CL has been achieved using a water
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R = IL + CL*t1 + QF (3.5) where R is the total gross rainfall of an event over the catchment, expressed in depth of rainfall (mm), IL (mm), CL (mm/h) and t1 is the time elapsed between the start of surface runoff and end of the rainfall event (h) and QF is the quickflow (mm), resulting from the rainfall. Since QF is the total streamflow (SFT) minus baseflow (BF), equation 3.5 may be written as below:
R = IL + CL*t1 + SFT - BF (3.6)
To estimate CL from equation 3.6, it may be expressed as:
CL = (R – IL – QF)/t1 (3.7)
In order to estimate QF using equation 3.7, the separation of baseflow (Section 3.5.2) from total streamflow is required as discussed above. For each of the selected rainfall and streamflow events (Section 3.5.1), the runoff routing model is calibrated (to estimate k) as discussed in Section 3.5.4.
3.5.4 Calibration of the runoff routing model
The main objective of the runoff routing model calibration is to determine a value of k that results in a reasonable fit between the observed and model estimated runoff from a range of recorded rainfall and runoff events at the catchment outlet. The calibration of the adopted runoff routing model (equation 3.3) is similar to the technique adopted in the calibration of the other common runoff routing models (e.g. RORB). The following are the general steps in the calibration of a runoff routing model as suggested by Rahman et al. (2001), which have also been adopted in this study:
Select a number of concurrent rainfall and runoff events from the observed data at the catchment outlet. Check the data for completeness, consistency and for any other gross errors.
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From the selected rainfall and runoff events, calibrate the runoff routing model i.e. select an appropriate value of k. A good technique is to fix IL and change CL value to match the rising limb of the computed and observed hydrographs and to obtain a volume balance (i.e. the computed runoff volume matches the observed streamflow volume). In this study, a lower limit of 0.00 and upper limit of 20 mm/h are set for the CL (similar to Hill et al., 1996), events having CL values outside of this range are excluded from further analysis as they are most likely to be affected by data error. When these are achieved, provisionally fix the IL and CL values but change the k value to match the peak. An increase in k reduces the peak flood and vice versa. Finally, the adopted IL, CL and k values should give a volume balance, and good matches in the rising limbs and peaks. Events with volumes and peaks that cannot be balanced in a reasonable fashion are excluded for further analysis.
In the application of DEA, the values of IL, CL and k obtained above, select a global IL, CL and k values for all the selected events (e.g. a median or a mean value) giving appropriate weight to the values from individual events depending on data quality and purpose of modelling. For the application of the DEA, a median value is used in this study. However, for the EMCST, the values of mean and or standard deviation are used depending on the distribution used to approximate the observed k data (e.g. mean for exponential distribution, and mean and standard deviation for gamma distribution).
Finally, use the selected IL, CL and k values and the fitted probability distributions with the EMCST to determine DFFC.
A FORTRAN program developed by Rahman (1999) has been used to calibrate the adopted runoff routing model interactively (see the details in Appendix D).
3.6 Identification of marginal probability distribution for an input variable
The EMCST developed in this study considers seven input variables/parameter as stochastic variables as mentioned in Section 3.4. The probability distributions of five of these variables,
DCS, IED, IL, CL and k are identified using the procedure as discussed below. The other two
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Enhanced Joint Probability Approach Caballero variables (IFD and TP) are not described by a probability distribution as such. That is, IFD is obtained at each pluviograph station by fitting an appropriate probability distribution to the intensity and duration data as described in Section 3.7. The TP are selected randomly from the pool of observed non-dimensional patterns of the selected pluviograph stations as described in Section 3.8.
For each of the input variables (except the IED and TP), a histogram is prepared based on the observed data, which indicates the general shape of the possible marginal distributions.
Typical example of a histogram of DCS is shown in Figure 3.2.
Figure 3.2: Example of a histogram of DCS for pluviograph station (ID 48027)
In the regionalisation study of rainfall duration by Haddad and Rahman (2011b) for the State of Victoria, the storm-core durations were approximated by an exponential distribution. However, in the application of MCST by Carroll and Rahman (2004), the complete storm durations were approximated by the exponential distribution for South-east Queensland while the storm-core durations by gamma distribution. From the shape of the histograms of the observed DCS, it appeared that two candidate distributions: one-parameter exponential distribution and two-parameter gamma distribution may be considered. These are similar to
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3.6.1 Fitting of a distribution to the observed data of an input variable
To assess the applicability of exponential or gamma distributions to the observed input variable data, a goodness-of-fit (GOF) test was applied to test the statistical hypothesis that the input variable data in a particular station follows the hypothesised distribution. These two distributions are discussed below.
The probability density function (pdf) of the exponential distribution can be expressed by:
ex/ f (x) (3.8)
where x is input variable (e.g. DCS) and µ is the mean value of x.
The cumulative distribution function (cdf) of the exponential distribution can be expressed by (Kottegoda and Rosso, 1997):
x/ F(x) 1 e (3.9)
Similarly, the pdf of the gamma distribution can be expressed by (Kottegoda and Rosso, 1997):
x1ex/ f (x;;) x 0 (3.10) () where and β are parameters of the gamma distribution and can be obtained from:
2 / x (3.11)
2 x / 2 (3.12) where x is the mean and 2 is the variance of input variable data.
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3.6.2 Goodness-of-fit tests
After the initial selection of the distribution, three goodness-of-fit tests are applied at 5% level of significance to test the statistical hypothesis that an input variable data follow a given distribution. These are Chi-Squared (C-S), Kolmogorov-Smirnov (K-S) and Anderson- Darling (A-D) tests.
Chi-Squared (C-S) test is a test of significance based on the Chi-squared statistics which is related to the sum of squared differences between the observed and theoretical frequencies. The test statistic is expressed by the following equation as per Kottegoda and Rosso (1997):
l (O E )2 X 2 i i (3.13) i1 Ei
where Oi and Ei are observed and expected frequencies, respectively, for each class i out of a total of l classes into which an ordered sample of n observations is placed. A hypothesised theoretical distribution gives the expected frequencies. A large value of this statistic indicates a poor fit; hence one needs to know what values are acceptable. The sampling distribution of
2 2 X tends, as n approaches infinity, to a v distribution, where v = l – 1 – k represents the degrees of freedom where k is the number of parameters estimated from the same data used for the test. The test is applicable to discrete and continuous variates, with a minimum of 5 values in each class.
The Kolmogorov-Smirnov (K-S) test is a nonparametric test that relates to the cumulative distribution function (cdf) rather than the probability density function (pdf) of a continuous variable. It is not applicable to discrete variates. This test is based on the absolute maximum difference (xmaxabs) between the observed cdf Fn(x) and expected cdf F0(x). The xmaxabs can be expressed by (Kottegoda and Rosso, 1997):
xmax abs Fn (x) F0 (x) (3.14)
Then the absolute maximum difference between the two sets of data is compared to critical values xn, for large samples, say n > 40. In this study, most stations have over 40 selected events (n), and hence the following equations are used to compute the critical values:
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Dn,0.05 1.3581/ n (3.15)
Dn,0.01 1.6276 / n (3.16)
To pass the test, the absolute maximum difference must be smaller than the critical value.
The Anderson-Darling (A-D) test is devised to give heavier weighting to the tails of a distribution where unexpectedly high or low values, called outliers are located (Kottegoda and Rosso, 1997). The test statistics is expressed by:
2 2 1 A Fn (x) F0 (x) f0 (x)dx (3.17) F0 (x)1 F0 (x)
where f0(x) is the hypothetical pdf. Anderson and Darling (1954) showed that this is equivalent to:
n (2i 1)ln F (x ) ln1 F (x ) A2 n 0 (i) 0 (ni1) (3.18) i1 n
where x(1), x(2), ... , x(n) are the observations ordered in increasing order. For large values of 2 test statistics A , the null hypothesis that Fn(x) and F0(x) have the same distribution is
2 rejected. For large samples, the 5% and 1% values of the statistics are A0.05 2.492 and
2 A0.01 3.857 , respectively. These critical values of the test statistics are sufficiently accurate for n greater than 10. In this study, number of data points for an input variable is always greater than 10.
3.7 Specification of the distribution of rainfall depth (IFD data)
The design rainfall intensity, commonly known as intensity-frequency-duration (IFD) data, is considered to be one of the most important input variables in flood estimation. In Chapter 2 of ARR, the estimates of IFD are derived as a set of IFD curves readily available for any design location in Australia (I. E. Australia, 1987). These IFD curves were developed for intense rainfall bursts of pre-determined durations. These design IFD curves presented in ARR (1987) are regarded as accurate and consistent as these curves were derived from a
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The JPA is based on a different event definition in contrast to the definition of burst adopted by the I. E. Australia (1987) for deriving the design IFD curves in the ARR. The ARR events are of fixed durations (e.g. 6 hours and 24 hours) and the longer durations generally contain shorter duration bursts as a part of the longer duration events (Rauf and Rahman, 2004). Thus, the IFD curves from ARR cannot be applied directly in the present study; as a result, new IFD curves must be generated based on the adopted rainfall event definition (as described in Section 3.2).
The development of the JPA-based IFD curves in this thesis is described below. This begins with the consideration of strong relationship between rainfall duration and average rainfall intensity for the observed rainfall events at the specified pluviograph station. It is followed by the development of the at-site IFD data. Finally, the developed at-site IFD data are regionalised for the application in ungauged catchments, which involves estimation of IFD data at an ungauged location from the IFD data of nearby gauged stations.
3.7.1 Correlation between rainfall intensity and durations
Figures 3.3 and 3.4 show example plots of average rainfall intensities against the corresponding rainfall durations of the observed events at pluviograph stations 48027 and 48031. This is needed to determine the degree of correlation between rainfall intensity and duration. The fitted regression line to the plotted data points was used to estimate the coefficient of determination (R2). The two example plots indicate that there are strong relationships between the rainfall intensity and rainfall duration for stations 48027 and 48031. As illustrated in these plots, the relationship between rainfall intensity and duration are in the form of a power function in which these are generally approximated by straight lines on a log-log plot.
In Figures 3.3 and 3.4, the coefficient of determination values (R2) which are 0.6543 and 0.7429, show that 65.43% and 74.29%, respectively, of the variations in rainfall intensity data
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Figure 3.3: Relationship between rainfall intensity and duration at pluviograph station 48027
Figure 3.4: Relationship between rainfall intensity and duration at pluviograph station 48031
3.7.2 Development of at-site IFD curves
In the development of IFD curves, the methodology proposed by Hoang et al. (1999) and Rahman et al. (2001, 2002a) is adopted; however, here the complete storms are considered
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With the modified procedure for developing the at-site IFD data, the rainfall intensities for rainfall events in predefined duration intervals are pooled for frequency analysis. This analysis involves the compilation of series of rainfall intensities for some representative duration, the fitting of a distribution to each intensity series, the checking of the goodness-of- fit of the fitted distributions, and the interpolation and extrapolation of the intensity- frequency curves to other durations and ARIs to derive the complete set of IFD curves. The modified procedure is comprised of five steps, as described below.
The range of DCS is divided into a number of class intervals (with a mid-point or representative point for each class). Table 3.1 shows an example of this.
Table 3.1: An example of class intervals and representative points for complete storm duration (DCS) for developing IFD curves
Class interval Representative (hours) point (hours) 1 1 2 - 3 2 4 - 12 6 13 - 36 24 37 - 60 48 61 - 84 72 greater than 85 100
For the data in each class interval (except the 1h class), a linear regression line is
fitted between log(DCS) and log(ICS). The slope of the fitted regression line is used to adjust the intensities for other nearby durations to the representative point. It should be noted here that rainfall events can have any duration. Initially all the events from a pluviograph station are selected with many different durations, which are then scaled to some fixed rounded duration (as representative point in Table 3.1) to develop the
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IFD data which is the standard procedure in developing the IFD data for the application of MCST as explained in Rahman et al. (2002a) and Charalambous et al. (2013).
For each class, an exponential distribution is fitted to the adjusted data series, Ii (i = 1, …, M), where M is the number of data points in a class. The rainfall quantiles (for a given duration) are obtained from the following equation:
I(T) = I0 + βln(λT) (3.19)
where I0 is the smallest value in the series; β = ∑Ii/M – I0; λ = M/N; N is the number of years of data and T is the ARI in years. Adopting this procedure, design rainfall
intensity values ICS(T) are computed for ARIs of 2, 5, 10, 20, 50 and 100 years.
The computed ICS(T) values for each duration range are used to fit a second degree
polynomial (Equation 3.19) between log(DCS) and log(ICS) for a selected ARI to obtain rainfall quantile estimates for any duration:
2 log(ICS) = a[log(DCS)) + b(log(DCS)] + c (3.20)
where ICS is the rainfall intensity for complete storm, a, b and c are regression coefficients estimated from the observed data. Equations 3.19 and 3.20 are used to construct an IFD table/curves for each station. Table 3.2 and Figure 3.5 provide typical examples of IFD tables and IFD curves, respectively, developed in this study.
Table 3.2: Example of an IFD table developed from complete storm data (rainfall intensity values in the table are in mm/h)
48027 ARI (year) Durations 0.1 1 1.11 1.25 2 5 10 20 50 100 500 1000 106 (h) mm/h mm/h mm/h mm/h mm/h mm/h mm/h mm/h mm/h mm/h mm/h mm/h mm/h 1 4.23 4.94 5.78 6.73 10.52 18.01 23.72 29.44 37.03 42.77 56.12 61.88 119.29 2 4.59 5.08 5.61 6.21 8.56 13.03 16.36 19.68 24.06 27.36 35.02 38.31 71.09 6 3.23 3.45 3.69 3.96 5.01 7.01 8.50 9.99 11.95 13.43 16.86 18.33 33.02 24 0.89 1.00 1.14 1.28 1.78 2.67 3.31 3.96 4.80 5.43 6.89 7.52 13.78 48 0.33 0.40 0.48 0.57 0.91 1.52 1.97 2.42 3.00 3.44 4.46 4.90 9.26 72 0.16 0.21 0.27 0.33 0.59 1.07 1.43 1.80 2.27 2.64 3.47 3.83 7.43 100 0.09 0.12 0.16 0.21 0.40 0.79 1.10 1.40 1.81 2.12 2.84 3.15 6.25
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Figure 3.5: Example of IFD curves developed from complete storm data
3.8 Derivation of the dimensionless complete storm temporal patterns
The application of runoff routing model to generate flood hydrograph with the DEA and MCST requires rainfall temporal patterns (TP) data. The rainfall TP is a dimensionless representation of rainfall intensity over the sub-durations of a rainfall event. The derivation of TP uses pluviograph data of some arbitrary durations of short length such as five minutes, one hour, two hours and six hours. The design TP data are obtained from recorded pluviograph data by using techniques such as method of average variability (Pilgrim and Cordery, 1975; Rahman et al., 2006). In most cases, design TPs are characterised by a dimensionless mass curve, i.e., a plot of dimensionless cumulative rainfall depth versus dimensionless storm time with 10 equal time increments (as shown in Figure 3.6). Figure 3.6 shows an example how at-site dimensionless TP vary from each other to illustrate that selection of a representative TP as done with the currently recommended DEA is quite difficult. In the application of the MCST, using pluviograph data from Victoria, Rahman et al. (2001) found that the dimensionless TPs from different seasons and for different rainfall depths can be pooled together as these do not depend on season and total rainfall depth. Here, “pooling” means putting it in a bin without any modification to the observed dimensionless TP data from the selected pluviograph stations. However, the TPs were found to be
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Figure 3.6: Sample of at-site dimensionless temporal patterns (TP) for the Oxley River catchment
The development and application of the TP database in the proposed EMCST could follow the ‘multiplicative cascade model’ (Hoang, 2001) or historic TP (Rahman et al., 2001). The historic TPs are the observed TPs in a dimensionless form that can be drawn randomly during the simulation from the observed samples corresponding to the generated DCS values. This study uses the historic TPs similar to Rahman et al. (2001) to develop TP database based on the selected pluviograph stations from New South Wales (NSW). Rahman et al. (2001) developed the TPs database for MCST using a minimum of 4 hours rainfall duration, the rainfall event with less than 4-hour durations were assumed to have the same TPs as the observed 4 to 12 hour rainfall events. This assumption seems to be reasonable and is applied in this thesis, too.
3.9 Regionalisation method adopted in this study
After the identification of the marginal (probability) distributions of the input variables based on the observed rainfall and streamflow data, regionalisation of these distributions needs to be achieved so that the EMCST can be applied to any arbitrary gauged/ungauged location in
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State of NSW. The spatial proximity method (one of the regionalisation methods discussed in Section 2.7) is adapted in this study with the aid of an Inverse Distance Weighted Averaging
(IDWA) method (Shephard, 1968) to regionalise the input variables (i.e. DCS, IED and IFD). This method assigns weight from surrounding stations as an inverse function of distance from the point of interest (where regional estimate is needed) as illustrated in Figure 3.7.
Station n
w n
Station 1
w 1 x n
w T x 1
Station 2 w 2 x 2
x x 3 Outlet
w 3 Station 3
Figure 3.7: Illustration of IDWA method
The assigned weights to the selected nearby pluviograph stations are calculated using the equations below:
w1 = (x2x3…xn)/[(x2x3…xn) + (x1x3…xn) + (x1x2…xn) + … + (x1x2x3…xn-1)] (3.21)
w2 = (x1x3…xn)/[(x2x3…xn) + (x1x3…xn) + (x1x2…xn) + … + (x1x2x3…xn-1)] (3.22)
w3 = (x1x2…xn)/[(x2x3…xn) + (x1x3…xn) + (x1x2…xn) + … + (x1x2x3…xn-1)] (3.23)
wn = (x1x2x3…xn-1)/[(x2x3…xn) + (x1x3…xn) + (x1x2…xn) + … + (x1x2x3…xn-1)] (3.24)
where w1, w2, w3, …, wn are the weights, x1, x2, x3, …, xn are the distances from the point of interest to the respective pluviograph station and n is the number of points selected for the averaging. The weighted average (WA) at the location of interest can be obtained from:
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WA = w1W1 + w2W2 + w3W3 +... + wnWn (3.25)
where W1, W2, W3, ..., Wn are corresponding values of an input variable (i.e. IFD value) considered from surrounding points (1, 2, 3, ..., n).
An example can be seen in Table 5.15 (Section 5.6.1) that illustrates how the IDWA method was applied to obtain regional IFD data.
The regionalisation of the DCS, IED and IFD is done through the use of spatial proximity method based on IDWA (Equation 3.25) using nearby pluviograph stations’ data within 30 km radius from the catchment of interest.
For the TP, a regional database for the catchment of interest is built based on the at-site dimensionless TP data from the pluviograph station(s) situated within a maximum of 200 km radius around the catchment of interest, but a maximum of 20 pluviograph stations. For the case of IL, CL and k data, the at-site values (from the selected catchments) of the rainfall and runoff events selected for calibration are used to fit a distribution. These fitted distributions are used to generate random values of IL, CL and k during simulation.
3.10 Implementation of the Enhanced Monte Carlo simulation technique (EMCST)
The distribution of the flood outputs can be directly determined by simulating the possible combinations of model inputs and parameter values (Rahman et al., 2001), which is the fundamental idea in the modelling framework underpinning the MCST. Two stochastic modelling frameworks can be applied: the deterministic simulation approach and the stochastic or Monte Carlo simulation approach (Rahman et al., 1998; Weinmann et al., 1998). The deterministic simulation approach employs a discrete representation of continuous probability distributions, and completes enumeration of all possible event combinations. The latter approach is more flexible and can be applied to both independent and correlated random variables (Hoang et al., 1999). In addition, a computer program is readily available for computing the probability distribution of floods from statistical distributions of flood producing factors (Rahman, 1999). Thus, Monte Carlo simulation is adopted and enhanced in this thesis by adding three additional random variables (i.e. IED, CL and k). The adopted procedure is briefly described below. Further details can be found in Rahman et al. (2001). University of Western Sydney Page 74
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For each run of the loss and runoff routing model combination, a specific set of input and model parameter values is randomly selected by drawing values from their respective distributions. Using the principle of conditional probability distribution, any significant correlation between the variables is explicitly allowed for. As an example, the strong correlation between rainfall duration and intensity is allowed for by first drawing a value of duration and then a value of intensity from the conditional distribution of rainfall intensity for that duration interval. The flood peaks resulted from the runs are stored and the Monte Carlo simulation procedure is repeated a sufficiently large number of times to fully reflect the expected range of variation of input and parameter values in the generated flood peak output. The simulated flood peak values, which are partial series, are then used to constitute an equivalent annual maximum flood series by incorporating the generated IED as mentioned in the following section. The method is also illustrated in Figure 3.8. The overall EMCST is stepped out below.
Draw a random value of rainfall inter-event duration IEDi from the conditional regional distribution of inter-event duration;
Draw a random value of duration Di from the identified regional marginal distribution of rainfall duration;
Given the duration Di, and a randomly selected ARI, draw a value of rainfall intensity
Ii(Di) from the regional conditional distribution of rainfall intensity i.e. the IFD table/curves;
Given the duration Di, draw a random temporal pattern TPi(Di) from the derived regional database of the temporal pattern;
Draw a random value of initial loss ILi from the conditional distribution of IL derived based on the observed IL data of the concurrent rainfall and runoff events at the selected gauged catchment;
Draw a random value of initial loss CLi from the conditional distribution of CL derived based on the observed CL data of the concurrent rainfall and runoff events at the selected gauged catchment;
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Draw a random value of runoff routing model storage delay parameter ki from the conditional distribution of k derived based on the observed k data of the concurrent rainfall and runoff events at the selected gauged catchment;
Use the randomly generated values of Di, Ii, TPi, ILi, CLi and ki to construct the runoff hyetograph and then to generate streamflow hydrograph from the adopted runoff routing model;
Add the baseflow to the simulated flood hydrograph and note the peak Qi of the generated streamflow hydrograph;
Repeat the above steps N times (N in the order of thousands, i.e. i = 1, 2, ..., N);
From the N simulated flood peaks determine the annual maximum flood peaks following the approach described in Section 3.11; and
Use the constructed annual maximum flood peak series to determine the DFFC using rank-order statistics (i.e. using a non-parametric distribution method as described in Section 3.11.
The developed FORTRAN programs (given in Appendix D) have in-built facility to generate data randomly from a specified distribution. For example, in the case of Gamma distribution, it starts by generating a uniform random deviate, which is then transformed using the FORTRAN codes into a random Gamma deviate based on the specified regional mean and standard deviation of the variable.
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Figure 3.8: Schematic diagram of the developed EMCST
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3.11 Formation of annual maximum flood series from generated partial duration series flood peak data
The simulated flood peaks from the MCST essentially form a partial duration flood peak series since these are based on partial series rainfall events. Generally, 5 to 8 partial series rainfall events are selected from each pluviograph station, which are analysed to establish distributions of rainfall duration, intensity and temporal patterns, which are randomly sampled in the MCST to produce runoff hyetographs. These are then routed through the calibrated runoff routing model to generate partial duration series flood peak events. These partial duration series flood peak events can be used to construct an equivalent annual maximum flood peak series by using the generated IED data. The method is outlined below.
Let us consider sequence of simulated stochastic rainfall events: DCS1, IED1, DCS2, IED2,
DCS3, IED3, and so on. Here, DCS1 is the simulated complete storm duration of event 1, IED1 is the first simulated inter-event duration, and subscript 2 indicates 2nd simulated event and so on. These series are added up until an equivalent year i.e. 365 days is achieved.
sum1 = DCS1 + IED1 + DCS2 + IED2 + DCS3 + IED3 + ... (3.26)
In Equation 3.26, sum1 corresponds to Year 1 AM flood peaks which needs to be checked whether it has just exceeded or equal to 365 days, i.e. when sum1 365 (first occurrence). Maximum of the Year 1 simulated flood peaks is taken as the AM flood peak of Year 1, which is expressed by AM1. Similarly, AM of Year 2 (denoted by AM2) is selected and so on. The procedure eventually gives the AM flood peak series from the generated partial series flood hydrograph peaks: AM1, AM2, AM3, and so on.
Table 3.3 presents an example for the construction of AM flood series from the simulated partial series flood data. The simulated rainfall events with their DCS, IED and the corresponding generated hydrograph flood peaks are shown in this table. For Year 1, the DCS and IED values of Events 1 to 5 are added to get the sum of the sequences equal to 270.54 days which is still smaller than 365 days. Event 6 is now added, which gives 446.46 days that exceeds the 365 day limit. Here, the maximum of the first 6 generated hydrograph peaks (shown in the 6th column of Table 3.3) is taken as AM1, which is 285.12 m3/s. In a similar manner, the AM2 (i.e. AM for Year 2) is computed by subtracting the 365 day limit from the University of Western Sydney Page 78
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Thereafter, Cunnane’s (1978) plotting position formula is used to compute ARIs from the constituted AM flood series AM1, AM2, AM3, …,. Here, the AM1, AM2, AM3, … flood series data are ranked in descending order for applying Equation 3.27.
ARI = (n + 0.2) / (i - 0.40) (3.27) where n is total number of constituted AM data points and i is the rank of the ordered AM data points, where i =1 for the largest value of constituted AM data points, i = 2 for the second largest event and so on.
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Table 3.3: Example sequences of generated rainfall events and construction of AM flood peak events
Sum of Generated Generated Generated Generated sequences of hydrograph Annual Event DCS (in DCS (in IED (days) DCS and IED flood peaks maximum hours) days) events (days) (m3/s) Event 1 19 0.79 4 4.79 285.12 AM1 Event 2 1 0.04 12 16.83 6.59
Event 3 48 2.00 38 56.83 1.68
Event 4 6 0.25 139 196.08 91.11
Event 5 11 0.46 74 270.54 196.48
Event 6 22 0.92 175 446.46 68.55
Sum/tally 446.46 - 365 = 81.46
Event 7 11 0.46 42 123.92 1.68
Event 8 85 3.54 40 167.46 211.23 AM2 Event 9 8 0.33 62 229.79 37.02
Event 10 4 0.17 70 299.96 39.95
Event 11 63 2.63 4 306.58 145.82
Event 12 19 0.79 43 350.38 5.93
Event 13 16 0.67 199 550.04 1.68
Sum/tally 550.04 - 365 = 185.04
Event 14 1 0.04 153 338.08 24.01
Event 15 14 0.58 12 350.67 15.66
Event 16 31 1.29 157 508.96 711.59 AM3 Sum/tally 508.96 - 365 = 143.96
Event 17 47 1.96 11 156.92 1.68
Event 18 27 1.13 79 237.04 80.12
Event 19 15 0.63 26 263.67 28.79
Event 20 50 2.08 10 275.75 62.52
Event 21 48 2.00 29 306.75 61.37
… … ......
3.12 Sensitivity Analysis
To check the sensitivity of the obtained DFFC to the likely uncertainty in the regionalised stochastic input variables, a detailed sensitivity analysis is undertaken. This involves changing a parameter value within an expected margin of variability of the selected distribution for a given input variable. The following input variables are considered for sensitivity analysis: DCS, IED, IL, CL and k. The variation is achieved by making an arbitrary
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3.13 Validation of the Enhanced Monte Carlo Simulation Technique (EMCST)
To assess the relative accuracy of the proposed EMCST, a number of methods are adopted. Firstly, the DFFC is compared with the observed annual maximum flood series data at the selected gauged test catchments. Here, at-site flood frequency analysis (FFA) is conducted using ARR FLIKE software (Kuczera, 1999), which implements a Bayesian-Log-Pearson Type III (LP3) distribution among number of other methods. Based on the findings by other studies (e.g. Haddad and Rahman, 2012); Bayesian LP3 procedure is adopted, which provides the best results for at-site FFA generally for eastern Australian catchments.
Secondly, the DFFC is compared with the flood quantiles estimated by the currently recommended DEA (I.E. Australia, 1987). Thirdly, the DFFC is compared with the flood quantile estimates obtained from the ARR Regional Flood Frequency Estimation (RFFE) model (test version), referred to as "ARR RFFE 2012" (ARR Project 5 Stage 1 and 2 reports, Rahman et el., 2009; 2012). Lastly, the DFFC is compared with the flood quantile estimates by the Probabilistic Rational Method (PRM) (I. E. Australia, 1987). These adopted methods for comparison are discussed briefly in the following sections. Detail description of these methods can be found in the above cited references.
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3.13.1 Collation of the observed annual maximum flood series at the selected test catchments
The AM flood data in a selected test station is extracted from the PINNEENA CM Version 10.1 (2012), which is the NSW Government official surface water data archive. The AM flood series data are first checked for any missing data in the series. The missing data in the AM flood series is the year where data are not available. To fill up the missing data or gaps in the series, two methods are used as suggested by Haddad et al. (2010b): (i) careful examination of the monthly and daily maximum flood series to ascertain whether a gap is located during the ‘dry’ period; and (ii) by using regression analysis where the gap is filled by developing a regression equation between the mean daily and instantaneous maximum flow at the same station. The monthly and daily maximum flood series streamflow data are extracted from PINNEENA CM Version 10.1 (2012).
For at-site FFA, Bayesian-LP3 distribution is used. In this method, the observed AM flood series data discussed in Section 3.13.1 are first checked for outliers by using the Grubbs and Beck (GB) method developed for GB statistic to detect outlier (Rao and Hamed, 2000). After checking for the outliers, the Bayesian-LP3 distribution is fitted to the AM flood data using FLIKE software (a computer program developed by Professor George Kuczera of the University of Newcastle (Kuczera, 1999)) which facilitates Bayesian analysis. FLIKE also allows deriving the 90% confidence limits of the at-site FFA estimates, which are used in this study to assess the overall error, bound of the at-site FFA.
3.13.2 Design Event Approach
The currently recommended DEA, as discussed in Section 2.2.2, is also applied to obtain flood quantiles, which are then compared with the DFFC obtained for the test catchments. In the DEA, the IFD values from ARR 1987 have been adopted (I. E. Australia, 1987). The adopted IL, CL, k and BF values are taken as the median values from the calibration of the selected events. Here, a fixed value of m (which is 0.80) in the adopted runoff routing model is used. The design TP data are selected from ARR 1987. The derivations of these model inputs and parameters for the DEA are further discussed below.
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Specification of rainfall intensity-frequency-duration (IFD) data
The average rainfall intensity and the corresponding temporal patterns are determined for each ARI of interest for a number of trial durations. For design flood estimation by the DEA, the ARI of the flood output is assumed to be equal to that of the rainfall depth input. As the design floods of interest in this study are in the ARI range of 2 to 100 years, the design rainfall input ARIs’ are adopted to be of 2, 5, 10, 20, 50 and 100 years.
To determine the appropriate range of durations of storm bursts to be used in the design, it is necessary to obtain a preliminary estimate of the critical storm duration of each of the study catchments. This duration can be roughly determined as the time of concentration (tc) of the catchment, which is defined as the travel time from the most remote point on the catchment 2 to the catchment outlet. The tc can be estimated using the catchment area, A (km ), from equation 3.28 (I. E. Australia, 1987). However, other equations could have been used to estimate tc.
0.38 tc = 0.76 A (3.28)
The average design rainfall intensity for a specified ARI and storm burst duration at the point of interest is determined from the Australian Bureau of Meteorology website (as mentioned in Section 3.13.3). From the website, the Log Normal (LN) rainfall intensities, average regional skewness (G) and the geographical factors (F2 and F50) values for the point of interest are obtained by using its latitude and longitude. As an example, for the Oxley River catchment, the representative point of interest for estimating catchment rainfalls is taken as the location of the centre (-28.357o latitude, 153.189o longitude) of the catchment. Using these latitude and longitude, IFD chart and table are generated as shown in Figures 3.9 and 3.10. Either the IFD chart or IFD table is used to find the six LN rainfall intensities (raw data, located at the bottom left of the chart and table) as inputs to calculate the design average rainfall intensities. In this method, a LP3 distribution is used to characterise design rainfalls at any location in Australia based on mapped skew values (I. E. Australia, 1987).
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Figure 3.9: Intensity-frequency-duration chart for the Oxley River catchment (used with the DEA)
Figure 3.10: Intensity-frequency-duration data for the Oxley River catchment (used with the DEA)
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For a point of interest, the LP3 based design rainfall intensity is estimated from the six basic rainfall intensities based on a LN distribution, one G, one F2 and one F50 values. As an example, for the Oxley River catchment, the six LN rainfall intensities (i.e. 48.75, 11.49, 3.75, 87.47, 24.14 and 8.43 mm/h), the G (0.09), F2 (4.4) and F50 (17.02) values are used as inputs to the AUS-IFD Version 2.0 (Jenkins et al., 2001) as shown in Figure 3.11 to get the LP3 based intensities. Examples of the final rainfall intensities are shown in Table 3.4 (see Figure C.3.1 in Appendix C for further details).
Figure 3.11: AUS-IFD Version 2.0 (Jenkins et al., 2001) interface showing how to convert Log Normal values to LP3 ones
Table 3.4: Summarised rainfall intensities for the Oxley River catchment (for the DEA)
ARI Rainfall intensities in mm/hr for durations (years) 1-hr 2-hr 3-hr 6-hr 12-hr 24-hr 48-hr 72-hr 2 48.50 32.60 25.70 17.10 11.400 7.58 4.92 3.72 5 60.00 41.40 33.00 22.40 15.200 10.20 6.68 5.09 10 67.00 46.50 37.30 25.50 17.500 11.80 7.79 5.96 20 77.00 53.00 43.00 29.70 20.500 13.90 9.23 7.08 50 89.00 63.00 51.00 35.30 24.600 16.80 11.20 8.62 100 98.00 70.00 57.00 39.60 27.800 19.00 12.70 9.83
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Specification of design IL, CL, k, m and BF values
Other model inputs (i.e. IL, CL, k and BF) are also required for DEA. The representative IL, CL, k and BF values are obtained from the values obtained during calibration of the runoff routing model as discussed in Section 5.3. These are the median values of the model inputs for the six catchments which are listed in Table 7.1. As an example, for the Oxley River catchment, the median IL value is 14.94 mm, the median CL value is 0.81 mm/h, the median k value is 10.84 hours and the median BF value is 1.64 m3/s. The fixed value of m = 0.8 is adopted. The median IL value for this analysis is arranged in a number of forms as illustrated in Figure 3.11 based on their intervals which is discussed further in the next section, in the specification of TP data.
Figure 3.12: Example arrangement of initial loss (IL) data for the Oxley River catchment (for running the DEA FORTRAN program)
Specification of rainfall TP data
The rainfall TP data in the DEA are selected from Volume 2 of ARR 1987 based on the location of the catchment of interest. Here, the TPs are divided into eight zones for Australia as shown in Figure 3.13. The State of NSW comprises of three zones, which are Zones 1, 2 and 3. Each zone has TP hyetographs (see Figure C.3.2 to C.3.4 in Appendix C) which are converted to TP percentages per period (see Figure C.3.5 to C.3.7 in Appendix C) as per ARR1987.
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Figure 3.13: Zone for TPs in Australia (extracted from Volume 2 of ARR 1987)
From these TP percentages per period, the TP data are extracted for the DEA analysis. As an example, the TP percentages per period extracted for the Oxley River catchment are shown in Figure 3.14. These TP percentages per period are grouped into two sub-groups (i.e. TP data with rainfall duration up to 30 hours and TP data with rainfall durations greater than 30 hours) which are shown in Figure 3.14 with labels TPL30 (for TP less than 30 hours) and TPG30 (for TP greater than 30 hours). These are further grouped based on their periods (i.e. 12 periods of 30 minutes, 24 periods of one hour and 18 periods of one hour) as displayed in Figure 3.15. The 1-hour, 3-hour and 6-hour storm durations are grouped into 12 periods; 2- hour, 12-hour, 24-hour and 48-hour storm duration are in 24 periods and 72-hour storm
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Figure 3.14: Extracted temporal pattern percentages per period for the Oxley River catchment (for the DEA application)
Figure 3.15: Storm durations groups based on their periods
3.13.3 Australian Rainfall and Runoff Regional Flood Frequency Estimation 2012 Model (Test version)
The ARR Project 5 has developed a beta version of regional flood estimation model (Rahman et al., 2012). This uses the Bayesian Generalised Least Squares (BGLS) regression in a region-of-influence (ROI) framework (Haddad and Rahman, 2012). The BGLS-ROI is University of Western Sydney Page 88
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3.13.4 Australian Rainfall and Runoff (1987) Probabilistic Rational Method (PRM)
The Rational Method has been commonly regarded as a deterministic method for estimating the peak flood from an individual storm. In ARR 1987, this method was presented as a probabilistic method, referred to as Probabilistic Rational Method (PRM) in estimating design flood peaks (I.E. Australia, 1987). The Rational Method has often been recommended for application to only small catchments below some arbitrary limit such as 25 km2. However, in the revised PRM in ARR 1987 for eastern NSW, this method can be applied to catchments up to 250 km2 in area (ARR 1987). The revised PRM used flood data from 308 gauged catchments (Mittelstadt et al., 1987). In this method, the physical considerations have less importance to the probabilistic interpretation of the PRM, thus, their effects were incorporated in the recorded floods, and hence in the flood frequency statistics and the derived values of the runoff coefficient CY . As reported in ARR 1987, the PRM derived from observed data should be valid for catchment areas and ARIs up to and somewhat beyond the maximum areas and record lengths used in their derivation (I.E. Australia, 1987). In ARR 1987, the PRM is represented by:
QY 0.278CY AI tc,Y (3.29)
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3 where QY is the peak flow rate (m /s) for an ARI of Y years; CY is the dimensionless runoff coefficient for ARI of Y years; I tc,Y is the average rainfall intensity (mm/h) for a time of
2 concentration tc (hours) and ARI of Y years; and A is the catchment area (km ). From Equation 3.29, the value of the runoff coefficient is given by:
QY CY (3.30) 0.278Itc,Y A
In which, the values of QY for a station can be obtained from at-site flood frequency analysis, where it is subject to the availability of reasonably long streamflow records. Values for I tc,Y at a given location can be found from Book II Section 1 of ARR. In here, the catchment and rainfall characteristics and conditions affecting the relation between QY, A and IY are incorporated in CY, but not necessarily in a physically realistic fashion.
For the probabilistic interpretation of the Rational Method, as in the PRM, these physical measures are not that important. However, Equation 3.30 shows that the value of CY depends on the duration of rainfall, and some design duration related to catchment characteristics that must be specified as part of the overall procedure. A typical response time of flood runoff is appropriate, and the ‘time of concentration’ is a convenient measure. In this context, its accuracy regarding travel time is much less important than the consistency and reproducibility of derived CY values. In addition, values of CY cannot be compared unless consistent estimates of tc are used in their derivation. The tc (equation 3.28) is described earlier in Section 3.13.2. Alternatively, the Bransby William formula (I. E. Australia, 1987) can be used to estimate the tc. The equation is given below:
58L tc 0.1 0.2 (3.31) A Se
where tc is in minutes; L is the mainstream length measured to the catchment divide (km); A
2 is the catchment area (km ) and S e is the equal area slope of the main stream projected to the catchment divide (m/km). This is the slope of a straight line drawn on a profile of a stream
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In ARR 1987, Equation 3.28 was adopted with the PRM for eastern NSW and Victoria. Weeks (1991) also adopted this similar equation in an attempt to develop the PRM for Queensland. In this current study, Equation 3.28 is adopted as it is easier to use. In the development of the PRM for a region, the C10 value for each individual catchment is estimated using Equation 3.30. The value of frequency factor for ARI of Y year, FFY, is estimated for each of the model catchments using Equations 3.30 and 3.32; the average or median FFY value is then used in the design.
CY FFY (3.32) C10
In this thesis, the CY and FFY values are obtained from ARR 1987 Volume 2.
3.13.5 Model evaluation statistics
The performance of the EMCST is compared with DEA, ARR RFFE 2012 model (test version) and PRM of ARR 1987 by using a number of evaluation statistics: the relative error (RE), ratio (R, dimensionless), relative mean bias (BIAS, dimensionless) and relative root mean square error (RMSE, dimensionless). These statistics are computed from the following equations:
Q Q RE pred obs 100 (3.33) Qobs Q R pred (3.34) Qobs
n 1 Qpred Qobs BIAS (3.35) n i1 Qobs
2 n 1 Qpred Qobs RMSE (3.36) n i1 Qobs
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Where Qpred is the predicted flood quantile using the EMCST, DEA, ARR RFFE 2012 model
(test version) and PRM, Qobs is the observed flood quantile obtained from at-site FFA using FLIKE (Kuczera, 1999) and n is the number of flood quantiles for the specified ARIs (2, 5, 10, 20, 50 and 100-years), i.e. n = 6 here.
The R provides an indication of the degree of bias (i.e. systematic over- and under- estimation), where a value of 1 indicates perfect agreement between Qpred and Qobs. Here, R values smaller than 0.5 and greater than 2 may be used to identify cases showing gross under- estimation and over-estimation, respectively (Rahman et al., 2011). The BIAS provides an indication of whether the model is over or under predicting overall compared to the observed values. Positive and negative values of BIAS occur when the regional estimates are higher and lower than the observed values, respectively (Haddad and Rahman, 2012). The RMSE provide an indication of the overall accuracy of a model.
3.14 Summary of Chapter 3
This chapter has discussed various methods associated with the development and validation of the proposed EMCST. In the development of EMCST, the rainfall events are selected based on complete storms. A single non-linear storage model is selected for runoff routing modelling. Seven input variables are selected for stochastic representation which are: complete storm duration (DCS), inter-event duration (IED), rainfall intensity in terms of intensity-frequency-duration (IFD), temporal pattern (TP), initial loss (IL), continuing loss (CL), and runoff routing model storage delay parameter (k). Concurrent rainfall and streamflow events are adopted to estimate the losses and calibrate the runoff routing model. Marginal probability distribution of an input variable is identified by fitting two probability distributions. These are the one-parameter exponential distribution and two-parameter gamma distribution, which are assessed using three goodness-of-fit tests (Chi-Squared, Kolmogorov- Smirnov and Anderson-Darling) at 5% level of significance to test the statistical hypothesis that an input variable data follow a hypothesised distribution. The development of JPA-based IFD curves considered the strong relationship between rainfall duration and average rainfall intensity for the observed rainfall events at the specified pluviograph station. The development and application of TP database are based on historic TPs which can be drawn
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randomly during the MCST from the observed samples corresponding to the generated DCS values.
The marginal probability distributions of the input variables are regionalised so that the regional EMCST can be applied to any arbitrary ungauged location in NSW. The DCS, IED and IFD data are regionalised using the spatial proximity method with the aid of Inverse Distance Weighted Averaging (IDWA) method. The EMCST is implemented by simulating the possible combinations of the model inputs and parameter values to generate runoff hydrograph. The annual maximum flood series are formed from generated partial duration series flood peak data resulted from the simulations which are then used to construct the derived flood frequency curve (DFFC) using a non-parametric frequency approach.
In the validation of EMCST, the DFFC is compared with: (i) at-site flood frequency analysis (FFA) results conducted using ARR FLIKE software; (ii) flood quantiles estimated by the currently recommended Design Event Approach (DEA) in ARR 1987; (iii) flood quantile estimates obtained from the ARR Regional Flood Frequency Estimation (RFFE) Model 2012 (test version); and (iv) the flood quantile estimates by the Probabilistic Rational Method (PRM) from ARR 1987.
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Enhanced Joint Probability Approach Caballero CHAPTER 4 Description of Study Area and Data
4.1 Introduction
Chapter 3 has discussed the methodology adopted for the development of the proposed Enhanced Monte Carlo Simulation Technique (EMCST) for estimation of design floods. This chapter describes the study area and data used for the development and testing of the proposed EMCST. In particular, this chapter discusses the selection of the study region and the data collation procedure adopted in this study. This research needs rainfall and streamflow data plus other catchment characteristics as discussed in this chapter.
4.2 Selection of study region
The previous studies by Hoang et al. (1999), Rahman et al. (2002a) and Charalambous et al. (2013) on the rainfall-based Joint Probability Approach (JPA)/Monte Carlo Simulation Technique (MCST) for design flood estimation demonstrated enough flexibility with this new method so that this can be applied in practice. However, there has been limited development and testing of the MCST over a large region, which would involve regionalisation of the input variables and parameter for the wider application of the MCST (as mentioned in Section 3.1). Most of the applications of MCST were concentrated to the States of Victoria and Queensland. Examples of these applications are found in Hoang et al. (1999), Heneker et al. (2002), Rahman et al. (2002a) and Charalambous et al. (2013). Rahman et al. (2002a) used three catchments (Avoca River, Boggy Creek and Tarwin River) in Victoria. In addition, Kader and Rahman (2004) and Rauf and Rahman (2004) adapted the MCST using the data from Victoria.
Rahman and Weinmann (2002) also tested the MCST to the three Northern Australian catchments (Bremer River, Running Creek and Teviot Brook) in Queensland. Furthermore, Carroll and Rahman (2004) considered the application of MCST to sub-tropical areas of
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Australia. Their method was integrated with URBS model (Carroll, 2013) and they used the model to 13 rainfall stations from sub-tropical areas (South-east Queensland) and 29 stations from Victoria. The MCST by Patel (2010) incorporated the randomness of storage delay parameter and tested it to five catchments in New South Wales (NSW). Charalambous et al. (2013) applied the MCST and hydrologic model URBS to a large catchment (North Johnstone River) in North Queensland with multiple pluviograph and stream gauging stations.
In this study, the EMCST to the design flood estimation is applied to the State of NSW with a focus on the regionalisation of input variables and parameter values so that MCST can be applied at any arbitrary location in NSW. The reason for selecting NSW is that it is considered to be large enough to regionalise the MCST and moreover it has readily available rainfall and streamflow data of adequate quantity and quality to regionalise MCST. The data used from NSW in this study are described in details in the following sections of this chapter.
4.3 Collation of rainfall and streamflow data
The proposed EMCST to the design flood estimation requires two basic data: rainfall and streamflow. The rainfall data are extracted from the observed rainfall records at the selected pluviograph and daily rainfall stations. The pluviograph stations are rainfall gauging stations with continuous reading from where this can be extracted in the desired time step e.g. 1-hour. The daily rainfall stations are rainfalls recorded on a daily basis in which the accumulated rainfall in a 24-hour period is read at 9 am every day (as practiced in Australia). In this study, the observed pluviograph data are extracted at hourly interval (from pluviograph station), based on these data the probability distributions of rainfall characteristics (e.g. duration, inter- event duration, intensity and temporal patterns) at a given pluviograph station are developed.
In addition to pluviograph data, the selection of catchments with stream gauging stations having a good record length is needed. From these stream gauging stations, the observed streamflow data are extracted in the desired time step (similar to rainfall data), which is hourly time step in this study. The extracted streamflow and pluviograph data are then used to select concurrent events, which are then used to estimate losses and to calibrate the adopted runoff routing model. The observed annual maximum (AM) flood peaks are also extracted
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4.3.1 Selection of pluviograph stations
In this study, the selection of pluviograph stations is based on a minimum threshold record length of 30 years. It is assumed that a threshold of 30 years would deliver a good number of events from a given pluviograph station so that a meaningful statistical test can be undertaken to specify the probability distribution of the rainfall characteristics at a given station. The State of NSW has 272 pluviograph stations based on 2011 Bureau of Meteorology (BOM) rainfall database. However, only 86 pluviograph stations were selected in this study based on the above criterion of 30 years minimum record length. The details of these pluviograph stations are provided in Table B.4.1 in Appendix B. The rainfall record lengths of the selected pluviograph stations range from 30 years to 101 years with an average record length of 45 years. A histogram of record lengths is provided in Figure 4.1, which shows that the majority of stations have record lengths in between 40 to 50 years. The selected 86 pluviograph stations present a good spatial distribution over the eastern NSW (as can be seen in Figure 4.2); however, there is no station selected from the far western NSW as there is no pluviograph station in this region with enough record length of good quality data. Hence, the proposed EMCST may not be applicable to far western NSW.
Figure 4.1: Histogram of record lengths for the selected 86 pluviograph stations in NSW
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Figure 4.2: Selected 86 pluviograph stations and 12 study catchments in NSW
4.3.2 Selection of study catchments
In the selection of catchments for the application of the proposed EMCST, the considerations of catchment type, size and data availability are deemed to be important. The selected catchments should be rural and have no significant artificial storage and major regulation. In addition, these should be small to medium-sized (up to 500 km2 in mountainous regions, or 1,000 km2 in flat areas). According to Australian Rainfall and Runoff (ARR) (I. E. Aust., 1987), small and medium sized catchments have an upper limit of 25 km2 and 1000 km2, respectively. These should have also readily obtainable rainfall (the rainfall gauging station is inside or near the catchment, within 30 km radius) and streamflow data of good quality and quantity. Here, 30 km is an arbitrary distance, which seems to be appropriate as there are many catchments in Australia which do not have a pluviograph station within the catchment, and 30 km is a reasonable distance to represent rainfall over a catchment. Further, the selection of catchments is based on a minimum threshold streamflow record length of 20 years in order to have at least 10 years of concurrent rainfall and streamflow data for the
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In this study, two sets of catchments are selected: (i) catchments needed in the calibration of runoff routing model and estimation of losses and (ii) catchments to test the applicability of the proposed EMCST.
Selection of catchments for calibration of runoff routing model and estimation of losses
For the selection of catchments for calibration of runoff routing model, 13 small catchments are selected initially based on the criteria described in Section 4.3.2. However, after checking the availability of the pluviograph stations within 30 km radius, only six catchments (as listed in Table 4.1 and shown in Figure 4.2 in brown circles) are left. As indicated in Table 4.1, the Coopers Creek catchment has the highest mean rainfall and the Byron Creek catchment has the highest evaporation. In contrast, the Mill Post catchment has the lowest mean annual rainfall and evaporation. The selected catchments have relatively long records of streamflow data (at least 26 years), which is necessary for accurate at-site flood frequency analysis. In addition, the catchments selected have concurrent record length (for streamflow and pluviograph) of more than 10 years as shown in Table 4.2. From this table, it can be seen that the streamflow data record length ranges from 21 to 47 years, with an average of 27 years.
Table 4.1: Selected catchments for regionalisation of losses and runoff routing model parameter
Mean Mean annual Streamflow Streamflow Station Area annual potential Station name period of record length ID (km2) rainfall evaporation record (years) (mm) (mm) Coopers Creek at 203002 62 1976 - 2009 33 1953 1518 Repentance Byron Creek at Binna 203012 39 1977 - 2009 32 1820 1543 Burra Pokolbin Creek at 210068 25 1963 - 2009 46 968 1377 Pokolbin Site 3 Antiene Creek at 210076 13 1968 - 2010 42 864 1346 Liddell Toongabbie Creek at 213005 70 1979 - 2009 30 1110 1185 Brien Road Mill Post Creek at 411001 16 1959 - 1985 26 808 1096 Bungendore
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Table 4.2: Pluviograph stations for the selected six catchments shown in Table 4.1
Pluviograph Concurrent Streamflow Pluviograph Catchment Pluviograph Station record record period of period of station ID station ID name length length record record (years) (years) Federal Post 203002 58072 1976 - 2009 1965 - 1998 33 22 Office Federal Post 203012 58072 1977 - 2009 1965 - 1998 33 21 Office Pokolbin 210068 61238 1963 - 2009 1962 - 2011 49 46 (Somerset) Liddell 210076 61212 (Power 1968 - 2010 1964 - 1995 31 27 Station) Liverpool 213005 67035 (Whitlam 1979 - 2009 1965 - 2001 37 22 Centre) Canberra 411001 70014 Airport 1959 - 1985 1937 - 2010 73 26 Comparison
The sizes of the selected six catchments for the derivation of the statistical distribution of the initial loss, continuing loss and the calibration of runoff routing model parameters range from 13 to 70 km2. All the catchments selected are rural and unregulated. Other features of these catchments are described below.
The first catchment is the Coopers Creek at Repentance. The gauged is located at 28.64° latitude and 153.41° longitude in south-eastern NSW. The catchment area is 62 km2 and the mean annual rainfall is 1953.23 mm. The length of the Coopers Creek (the main stream of the catchment) is 18.50 km. The elevation at gauge is 42.938 m. The catchment has three pluviograph stations nearby; the closest one is station 58072 (as listed in Table 4.2). The pluviograph data of this gauging station has a record length of 33 years.
The second catchment is the Byron Creek at Binna Burra. The catchment outlet is located at 28.71° latitude and 153.50° longitude in south-eastern NSW. The catchment area is 39 km2 and the mean annual rainfall is 1819.79 mm. The length of the Byron Creek (the main stream of the catchment) is 17.50 km. The elevation at gauge is 32.040 m. The catchment has three pluviograph stations nearby, the closest one being station 58072.
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The third catchment is the Pokolbin Creek at Pokolbin Site 3. The catchment outlet is located at 32.80° latitude and 151.33° longitude in south-eastern NSW. The catchment area is 25 km2 and the mean annual rainfall is 967.88 mm. The length of the Pokolbin Creek (the main stream of the catchment) is 17.50 km. The elevation at gauge is 60.00 m. The catchment has one pluviograph station nearby, which is station 61238. The pluviograph data of this gauging station has a record length of 50 years.
The fourth catchment is the Antiene Creek at Liddell. The catchment outlet is located at 32.34° latitude and 150.98° longitude in south-eastern NSW. The catchment area is 13 km2 and the mean annual rainfall is 864.24 mm. The length of the Antiene Creek (the main stream of the catchment) is 6.50 km. The elevation at gauge is 132.034 m. The catchment has one pluviograph station nearby (station 61212). The rainfall data of this gauging station has record length of 31 years.
The fifth catchment is the Toongabbie Creek at Brien Road. The catchment outlet is located at 33.80° latitude and 150.98° longitude in south-eastern NSW. The catchment area is 70 km2 and the mean annual rainfall is 1110.22 mm. The length of the Toongabbie Creek (the main stream of the catchment) is 11.50 km. The elevation at gauge is 9.518 m. The catchment has three pluviograph stations nearby; the closest one is station 67035. The pluviograph data of this gauging station has a record length of 38 years.
The sixth catchment is the Mill Post Creek at Bungendore. The catchment outlet is located at 35.28° latitude and 149.39° longitude in south-eastern NSW. The catchment area is 16 km2 and the mean annual rainfall is 808.36 mm. The length of the Mill Post Creek (the main stream of the catchment) is 4.42 km. The elevation at gauge is 760.00 m. The catchment has two pluviograph stations nearby; the closest one is station 70014. The pluviograph data of this gauging station has record length of 74 years.
Selection of catchments for testing and validation of the proposed EMCST
For testing and validation, two small (less than 100 km2) and four medium catchments (greater than 100 km2 but less than 300 km2) are selected as listed in Table 4.3 (and shown in Figure 4.2 in red circles). It should be noted that these limits of small and medium catchments
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The sizes of the selected validation catchment set range 76 to 223 km2. All the catchments selected are rural and unregulated. The catchments characteristics of these validation catchments are described below.
Table 4.3: Selected catchments for testing the applicability of the regionalised EMCST
Streamflow Mean Mean annual Streamflow Catchment Area record annual potential Station name period of station ID (km2) length rainfall evaporation record (years) (mm) (mm) 201001 Oxley River at Eungella 213 1957 - 2011 55 1857 1301 203014 Wilsons River at Eltham 223 1957 - 2010 53 2461 1498 Bielsdown Creek at 204017 76 1969 - 2011 32 1862 1383 Dorrigo No. 2 and No. 3 204025 Orara River at Karangi 135 1970 - 2011 41 1711 1438 West Brook River at 210080 Upper Stream Glendon 80 1970 - 2011 41 985 1373 Brook 420003 Belar Creek at Warkton 133 1976 - 2005 30 690 1296
Table 4.4: Pluviograph stations for the selected three test catchments shown in Table 4.3
Pluviograph Concurrent Streamflow Pluviograph Catchment Pluviograph record record Station name period of period of station ID station ID length length record record (years) (years) Tyalgum 201001 58109 1957 - 2011 1965 - 1996 33 32 (Kerrs Lane) Federal Post 203014 58072 1957 - 2010 1965 - 1998 33 33 Office Dorrigo 204017 59067 1969 - 2011 1954 - 1999 49 31 (Myrtle Street) Upper Orara 204025 59026 1970 - 2011 1970 - 2010 41 41 (Aurania) Dorrigo 210080 59067 1970 - 2011 1954 - 1999 49 29 (Myrtle Street) Coonabarabran 420003 64046 1976 - 2005 1971 - 2011 40 30 (Westmount)
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The Oxley River catchment at Eungella (as shown in Figure 4.3) is considered to be a medium catchment with an area of 213 km2 and mean annual rainfall of 1857 mm. The main stream length of the Oxley River is 25.0 km. The elevation at gauge is 13.29 m. The catchments’ centre is located at 28.357° latitude and 153.190° longitude in south-eastern NSW. Figure 4.4 shows location of outlet of the catchment. The red dots identified as 006 and 007 in Figure 4.3 are gauging locations for sub-catchments where streamflow are recorded. The catchment has five pluviograph stations nearby; the closest one is the pluviograph station 58109. The rainfall data of this station has record length of 32 years.
Figure 4.3: Oxley River catchment (station ID 201001) (DOW NSW, 2013)
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Figure 4.4: Site - Oxley River catchment (DOW NSW, 2013)
The Wilsons River catchment at Eltham (as shown in Figure 4.5) is considered to be a medium catchment with an area of 223 km2 and mean annual rainfall of 2461 mm. The main stream length of the Wilsons River is 131.00 km. The elevation at gauge is 7.46 m. The catchments’ centre is located at 28.688° latitude and 153.468° longitude in south-eastern NSW. Figure 4.6 shows location of outlet of the catchment. The red dots identified as 001, 013 and 038 in Figure 4.5 are gauging locations for sub-catchments where streamflow are recorded. The catchment has three pluviograph stations nearby, the closest one is station 58072. The pluviograph data of this gauging station has record length of 33 years.
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Figure 4.5: Wilsons River catchment (station ID 203014) (DOW NSW, 2013)
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Figure 4.6: Site - Wilsons River catchment (DOW NSW, 2013)
The Bielsdown Creek catchment at Dorrigo No. 2 and No. 3 (as shown in Figure 4.7) is considered to be a small catchment with an area of 76 km2 and mean annual rainfall of 1862 mm. The main stream length of the Bielsdown Creek is 38 km. The elevation at gauge is 628.13 m. The catchments’ centre is located at 30.353° latitude and 152.698° longitude in south-eastern NSW. Figure 4.8 shows downstream of outlet of the catchment. The red dots identified as 010 in Figure 4.7 is gauging location for sub-catchment where streamflow is recorded. The catchment has two pluviograph stations nearby, the closest one is station 59067. The rainfall data of this station has record length of 46 years.
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Figure 4.7: Bielsdown Creek catchment (station ID 204017) (DOW NSW, 2013)
Figure 4.8: Downstream - Bielsdown Creek catchment (DOW NSW, 2013)
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The Orara River catchment at Karangi (as shown in Figure 4.9) is considered to be a medium size catchment with an area of 135 km2 and mean annual rainfall of 1711 mm. The main stream length of the Orara River is 20.0 km. The elevation at gauge is 98.86 m. The catchments’ centre is located at 30.286° latitude and 152.980° longitude in south-eastern NSW. Figure 4.10 shows downstream of outlet of the catchment. The catchment has three pluviograph stations nearby, the closest one is station 59026. The rainfall data of this station has a record length of 41 years.
Figure 4.9: Orara River catchment (station ID 204025) (DOW NSW, 2013)
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Figure 4.10: Site - Orara River catchment (DOW NSW, 2013)
The West Brook River catchment at Upper Stream Glendon Brook (as shown in Figure 4.11) is considered to be a small size catchment with an area of 80 km2 and mean annual rainfall of 986 mm. The main stream length of the West Brook River is 15.5 km. The elevation at gauge is 68.53 m. The catchments’ centre is located at 32.421° latitude and 151.276° longitude in south-eastern NSW. Figure 4.12 shows location of gauge of the catchments. The catchment has two pluviograph stations nearby; the closest one is station 61158. The rainfall data of this station has record length of 48 years.
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Figure 4.11: West Brook River catchment (station ID 210080) (DOW NSW, 2013)
Figure 4.12: Site - West Brook River catchment (DOW NSW, 2013)
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The Belar Creek catchment at Warkton (as shown in Figure 4.13) is considered to be a medium sized catchment with an area of 133 km2 and mean annual rainfall of 691 mm. The main stream length of the Belar Creek is 21.0 km. The elevation at gauge is 11.44 m. The catchments’ centre is located at 31.361° latitude and 149.128° longitude in south-eastern NSW. Figure 4.14 shows location of gauge of the catchment. The catchment has only one pluviograph station nearby (station 64046). The rainfall data of this station has record length of 41 years.
Figure 4.13: Belar Creek catchment (station ID 420003) (DOW NSW, 2013)
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Figure 4.14: Site - Belar Creek catchment (DOW NSW, 2013)
4.4 Extractions of pluviograph and streamflow data
After the selection of the pluviograph and stream gauging stations, extraction of pluviograph and streamflow data are needed. The basic pluviograph data are obtained from BOM. Based on this data, hourly rainfall depth are extracted using HYDSTRA program (HYDSTRA, 2011) and PINNEENA CM Version 10.1 (NSW Office of Water, 2012) for hourly streamflow data. In this study, a one-hour time step is considered to be reasonable since the catchment is not too small. In contrast, the use of finer time steps would produce a very large data file as rainfall and streamflow data are available for over many years at the stations used in this study. The extractions of rainfall and streamflow data are discussed below.
4.4.1 Extraction of pluviograph data
The availability of the data for the selected 86 pluviograph stations is summarised in Table B.4.2 in Appendix B. The station identification number (station ID), station names, start and end dates of data, and length of records are listed in this table. In this study, in order to ensure the quality of outputs, only periods with good continuous records are included, whereas
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Enhanced Joint Probability Approach Caballero periods with missing or accumulated data, gaps, or errors in data transcription are not used. The accumulated data are discarded because these are considered of very little use, especially in the analysis of rainfall temporal patterns. In addition, most of the pluviograph stations used have concurrent data of 21 years to 46 years as shown in Tables 4.2 and 4.4. The longest pluviograph record is from 1937 to 2010; however, only 26 years of concurrent record length have been used due to short streamflow record at the corresponding station.
4.4.2 Extraction of streamflow data
Similar to the observed pluviograph data, observed streamflow data are stored on the HYDSTRA database in PINNEENA CD. The availability of streamflow data are summarised in Table 4.1. It can be seen from this table that recorded flow data are available for 33 years (from 1977 to 2009) for the Coopers Creek catchment, 32 years (from 1977 to 2009) for the Byron Creek catchment, 46 years (from 1963 to 2009) for the Pokolbin Creek catchment, 42 years (from 1968 to 2010) for the Antiene Creek catchment, 30 years (from 1979 to 2009) for the Toongabbie Creek catchment and 26 years (from 1959 to 1985) for the Mill Post Creek catchment.
4.5 Summary of Chapter 4
For this research, the State of New South Wales (NSW) has been selected as the study region. The selection of catchments and pluviograph stations and collations of the pluviograph and streamflow data have been discussed. The criteria for the selection of pluviograph stations and study catchments have been presented. Based on the adopted criteria, 86 pluviograph stations and 12 catchments are selected. From the selected catchments, six catchments are used in the calibration of the adopted runoff routing model while the other six catchments are used for the application and validation of the Enhanced Monte Carlo Simulation Technique (EMCST) to design flood estimation.
The basic pluviograph data are obtained from BOM and then extracted using the HYDSTRA program while streamflow data are extracted using the HYDSTRA program which are in- built in PINNEENA CD of NSW Department of Water. The extracted data are analysed in Chapter 5 for regionalisation of the various input variables and subsequent analyses.
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Enhanced Joint Probability Approach Caballero CHAPTER 5 Regionalisation of Input Variables
5.1 Introduction
Chapter 4 has selected the study area and data for the development of the proposed Enhanced Monte Carlo Simulation Technique (EMCST) to design flood estimation. This chapter describes the regionalisation of the distributions of various input variables and model parameters: rainfall complete storm duration (DCS), rainfall inter-event duration (IED), rainfall intensity-frequency-duration (IFD) data, rainfall temporal pattern (TP), initial loss (IL), continuing loss (CL), and storage delay parameter (k) of the adopted runoff routing model. This regionalisation is the core thrust of this thesis since the regionalised EMCST can be used at any arbitrary location in eastern NSW for estimation of derived flood frequency curves. For each of the selected pluviograph stations, the complete storm events are selected and DCS, IED, IFD and TP data are obtained. These data over all the selected pluviograph stations are used to regionalise their marginal distributions. For IL, CL and k values, the concurrent rainfall and streamflow events are selected from the selected study catchments, which are then analysed to obtain IL, CL and k values for each of the selected events. These data over all the selected catchments form the basis of their regionalisation.
5.2 Selected rainfall events for regionalisation
The rainfall events are selected using the steps presented in Section 3.2. The selected events use hourly time step rainfall data with a minimum of six hours separation time adopted between successive rainfall events as mentioned in Section 3.2. In addition, an appropriate reduction factors F1 and F2 values (see details in Section 3.2) are applied in this study (similar to Hoang et al., 1999 and Rahman et al., 2002a) to select the potential rainfall events that are likely to produce significant flood runoff. A FORTRAN program originally developed by Rahman (1999) is upgraded to select the complete storm events for this thesis including the inter-event durations.
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A total of 19,718 rainfall events are selected from 86 pluviograph stations. The rainfall events being selected from each pluviograph station range from 65 to 622 events, with an average of 229 events per pluviograph station. This represents two to eight events per year, with an average of five rainfall events per year. The distribution of the number of events selected per year from each of the 86 pluviograph stations is shown in Figure 5.1. The number of events selected from each pluviograph station are also summarised in Table B.4.1 (see Appendix B).
From these rainfall events selected, the corresponding DCS, IED and IFD data are analysed as discussed in Sections 5.4, 5.5 and 5.6, respectively.
Figure 5.1: Average number of complete storm events selected per year from the selected 86 pluviograph stations in eastern NSW
5.3 Selected concurrent rainfall and streamflow events for derivation of IL, CL and k values
The estimation of losses and the calibration of the runoff routing model require two types of basic data: the continuous rainfall and streamflow data. The continuous readings of rainfall data are obtained from a pluviograph station whereas the streamflow data from a stream gauging station (as explained in Section 4.3). From these readings, concurrent rainfall and streamflow events are selected to estimate the losses and to calibrate the adopted runoff routing model, as discussed below. University of Western Sydney Page 116
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5.3.1 Selected concurrent rainfall and streamflow events
The selected catchments (as listed in Table 4.1) have nearby pluviograph station(s) (within 30 km) and with record length of at least 20 years as discussed in Section 4.3.2. From these selected catchments and pluviograph stations, the concurrent complete storm events are identified which are based on significant rainfall over the complete storm duration as discussed in Section 3.2. Some of these events (although having higher overall rainfall intensity) do not produce any runoff (due to higher losses); thus, it is not appropriate to include these events in the calibration, as losses are unrealistic for these events i.e. too high. It should be noted that in rainfall runoff modelling conceptual loss is the difference between the catchment rainfall and measured streamflow data at catchment outlet. Since the catchment rainfall is never known (due to inadequate number of pluviometers on the catchment), the estimated input catchment rainfall may not represent the true catchment rainfall, for example, the pluviometer may show rainfall at a particular point, which does not mean that the other parts of the catchments get the rainfall at the same time. This is due to the problem of conversion from point data to spatially averaged data. Due to this problem the “computed loss values”, in some cases become negative or too high, as noted by Hill et al. (2013).
In the event selection process, the end of the streamflow event is considered to be the time when the quickflow almost ceases or it is between the end of the falling limb in the streamflow of the previous event and the start of the rise in the streamflow of the next event. In addition, the streamflow events with surface runoff values never exceeding the threshold value, as discussed in Section 3.5.2, are excluded from further analysis.
Based on the criteria as mentioned above, a total of 172 concurrent rainfall and streamflow events are selected from the six study catchments as summarised in Table 5.1. The selected concurrent events range from 15 to 64 events per catchment (with an average of 29 events per catchment), which represents 1 to 2 events per year on average per catchment.
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Table 5.1: Summary of selected events in initial calibration of the runoff routing model (F1 = 0.8 and F2 = 0.9)
Catchment Concurrent record Total events station ID length (years) for calibration 203002 22 16 203012 21 16 210068 46 64 210076 27 22 213005 22 15 411001 26 39 Total 164 172 Average 27 29
From the events selected for each catchment, the events with no streamflow, gross error in data and multi-events which cannot be explicitly analysed in the baseflow separation step are not included for further analysis (as illustrated in Table 5.2). In addition, the selected events with too high IL are eliminated, as these do not have quickflow greater than the threshold value. This implies that IL value is too high to produce quickflow. In some cases, quickflow which starts after the cessation of the rainfall are also removed as these do not satisfy the assumption of the definition of the IL-CL loss model. Furthermore, successive rainfall events which are separated by a short period of time are excluded from the analysis as the surface runoff produced by this individual event cannot be clearly identified.
Furthermore, from these concurrent events selected, only periods with good continuous records are included in the analysis in order to guarantee the quality of outputs. Periods with missing data or gaps, accumulated data, or errors in data are not considered. Furthermore, the accumulated data are not included as these are considered to be of limited use, especially in the analysis of rainfall TP as noted by Hoang (2001). In addition, this study discards periods with no direct streamflow i.e. no rise in the streamflow hydrograph.
Based on the above considerations, a total of 14, 14, 32, 20, 14 and 21 events are retained for further analysis from the Coopers Creek, Byron Creek, Pokolbin Creek, Antiene Creek, Toongabbie Creek and Mill Post Creek catchments, respectively. The final outcomes of this events selection are summarised in Table 5.2.
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The baseflow separation is carried out as discussed next, and the losses and k values are estimated.
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Table 5.2: Selected events for calibration of the adopted runoff routing model (reduction factors F1 = 0.8 and F2 = 0.9)
Selected events Too high IL No streamflow Multi-event Error in data Catchment Total station ID events Number Percent- Number Percentage Number Percentage Number Percentage Number Percentage of stations age (%) of stations (%) of stations (%) of stations (%) of stations (%) 203002 16 14 88 1 6 0 0 0 0 1 6 203012 16 14 88 2 13 0 0 0 0 0 0 210068 64 32 50 16 25 15 23 0 0 1 2 210076 22 20 91 2 9 0 0 0 0 0 0 213005 15 14 93 1 7 0 0 0 0 0 0 411001 39 21 53.8 16 41 0 0 1 2.6 1 2.6 Total 172 115 38 15 1 3
Average 29 19 6 3 0 1
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5.3.2 Results of baseflow separation
In the implemented baseflow separation procedure (as discussed in Section 3.5.2), the values of best fit range from 0.001 to 0.01. It should be noted here that Boughton (1988) baseflow separation method (as described in Section 3.5.2) is adopted in this study, which is an industry standard for the baseflow separation (Ilahee, 2005). The baseflow separation procedure is executed by plotting the streamflow and baseflow of each event in an excel spreadsheet where the value can be changed interactively to achieve an acceptable baseflow separation. For the six study catchments calibrated, a value of equals to an average of 0.002 to 0.004 provides a reasonable baseflow separation. As an example, Figure 5.2 shows that baseflow 1 using value of 0.002 achieves the best fit. In this example, baseflow 2 is not considered to be acceptable.
Figure 5.2: Example of baseflow separation for an event
While the use of either baseflow 1 or 3 in the analysis are acceptable; this study prefers the application of lower value in the analysis. However, when the value is not high enough to separate the baseflow from the hydrograph, a higher value needs to be used to separate the events. In addition, once the maximum value of 0.01 is reached and the gap is still present, the event is not considered in the calibration process and subsequent analysis as this
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Figure 5.3: Example of baseflow separation for an event with big gap
5.3.3 Estimated losses and calibrated runoff routing model
Using a surface runoff threshold value equal to 0.01 mm/h similar to Hill et al. (1996) and the water balance equations (Equations 3.5 to 3.7) (Section 3.5.3), the IL and CL values are estimated. The estimation is done using the runoff routing model, S = kQm, discussed in Section 3.4. The runoff routing model is applied to selected six catchments using the FORTRAN program developed by Rahman (1999). A total of 172 selected events are calibrated. However, after the proper quality control and hydrological consistency assessment, only 64 events are retained as listed in Table 5.3. Some of these events are excluded due to unusually high CL values (e.g. more than 20 mm/h).
Considering the selected events in each station, in some cases, numbers of retained events are less than 10. A sample of less than 10 is not significant enough to fit a distribution. Thus, in order to increase the number of calibrated events, it is decided to reduce the values of the
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reduction factors (see Section 3.2) to F1 = 0.6 and F2 = 0.7 so that a greater number of events can be selected from a station. It should be noted that these values of F1 and F2 are arbitrary thresholds to facilitate selection of sufficient number of rainfall events which are likely to generate a streamflow event in the order of magnitude of annual maximum flow. Previous studies such as Rahman et al. (2002) and Charalambous et al. (2013) showed that F1 = 0.4 to
0.6 and F2 = 0.5 to 0.7 are adequate for the purpose of MCST for deriving flood frequency curves in Australian condition.
Table 5.3: Retained events in the initial calibration
Catchment Concurrent record Total events Retained events station ID length (years) for calibration after calibration 203002 22 16 9 203012 21 16 9 210068 46 64 23 210076 27 22 6 213005 22 15 5 411001 26 39 12 Total 164 172 64 Average 27 29 11
Application of these new values of F1 and F2, results in the selection of 2 rainfall events on average per station per year (as shown in Table 5.4). The selected events now increase from a total of 172 to 346 events (as shown in Tables 5.3 and 5.4), i.e. about 100% increase in the total number of the selected events. In addition, these produce more calibrated events for each catchment; a total increase by 44 events. Accordingly, the use of the new F1 = 0.6 and F2 = 0.7 values are adopted in the selection of concurrent rainfall and streamflow for all the six catchments. The results of the new calibration are summarised in Table 5.5 (as an example table) and Tables B.5.1 to B.5.5 are presented in appendix (see Appendix B). These calibration results are the basis of the regionalisation of the IL, CL and k data for eastern NSW which are discussed in Sections 5.8, 5.9 and 5.10, respectively. Next section discusses the regionalisation of DCS data.
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Table 5.4: Retained events in the final calibration of the adopted runoff routing model (reduction factors F1 = 0.6 and F2 = 0.7)
Catchment Concurrent record Total events Retained events station ID length (years) for calibration after calibration 203002 22 25 13 203012 21 25 18 210068 46 140 29 210076 27 41 10 213005 22 37 16 411001 26 78 22 Total 164 346 108 Average 27 58 18
Table 5.5: Summary of the calibrated values of IL, CL and k for Coopers Creek catchment (station ID 203002)
Initial loss Alpha Continuing Storage delay Standardised Selected Year (mm) values loss (mm/hr) parameter (k) k events 1978 33.34 0.005 0.883 2.12 0.03 Event 1 1979 36.65 0.002 1.281 27.04 0.44 Event 2 1979 17.76 0.005 15.368 19.10 0.31 Event 3 1979 23.87 0.003 3.995 15.15 0.24 Event 5 1983 13.67 0.010 1.085 3.66 0.06 Event 9 1984 38.27 0.009 6.727 7.82 0.13 Event 11 1984 3.68 0.001 0.787 17.49 0.28 Event 12 1984 24.19 0.002 3.248 18.95 0.31 Event 13 1988 30.96 0.006 3.140 3.40 0.05 Event 19 1990 26.65 0.007 6.051 12.62 0.20 Event 22 1990 27.56 0.010 2.300 2.05 0.03 Event 23 1994 31.68 0.005 2.107 16.95 0.27 Event 24
5.4 Regionalisation of rainfall complete storm duration (DCS) data
From the selected complete storm events as shown in Table B.4.2 (see Appendix B), the lower and upper limits of the averages of the selected DCS data for the selected pluviograph station are 1 hour (range: 1 to 2 hours) and 116 hours (range: 53 to 220 hours), respectively.
The regional average values of the mean and standard deviation of the DCS data are 26 hours
(range: 14 to 55 hours) and 22 hours (range: 11 to 42 hours), respectively. Histograms of DCS values for each of the 86 pluviograph stations are plotted at 10 hours class interval (as
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Enhanced Joint Probability Approach Caballero suggested by Sturges, 1926). An example of this histogram is shown in Figure 5.4. For visual assessment of the goodness-of-fit test of a distribution, plots of the cumulative frequency distributions are prepared for the observed and fitted exponential and gamma distributions. It should be emphasised here that gamma and exponential distributions are adopted as candidates to specify the DCS distribution based on the findings of the previous studies on MCST (Rahman et al., 2002a; Haddad and Rahman, 2011b). It can be seen from Figure 5.4 that both the exponential and gamma distributions demonstrate quite a good fit to the DCS data.
Figure 5.4: Frequencies of complete storm duration (DCS) data for pluviograph station 56202
However, based on the three goodness-of-fit tests (at 5% level of significance), the gamma distribution shows a better fit than the exponential distribution for the majority of the selected 86 stations as indicated in Table B.5.6 (see Appendix B) and summarised in Table 5.6. With the Chi-Squared (C-S) test, 15% and 28% of the stations fit the exponential and gamma distributions, respectively. The Kolmogorov-Smirnov (K-S) test fits the exponential and gamma distributions for the 50% and 76% of the stations, respectively. The Anderson- Darling (A-D) test fits the exponential and gamma distributions for the 51% and 79% of the stations, respectively.
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Table 5.6: Summary of the goodness-of-fit test (stations showing the accepted distributions) for complete storm durations (DCS) data (“Number of stations” indicates the number of stations satisfying the hypothesised distribution.)
C-S test K-S test A-D test Distributions Number Percentage Number Percentage Number Percentage of stations (%) of stations (%) of stations (%) Exponential 13 15 43 50 44 51 Gamma 24 28 65 76 68 79
In addition, the spatial distributions of stations satisfying the exponential and gamma distributions based on K-S and A-D tests are shown in Figures 5.5 and 5.6. In these figures, no regional pattern is detected; however, the gamma distribution provides a denser and wider network than the exponential distribution. In Table 5.7, the goodness-of-fit test results also show that 38% and 40% of the stations fit both the exponential and gamma distributions based on the K-S and A-D tests, respectively (at 5% level of significance). Overall, the gamma distribution provides a better fit based on the three goodness-of-tests conducted here.
Figure 5.5: Spatial distribution of the stations satisfying exponential and gamma distributions based on the Kolmogorov-Smirnov test (“No distribution” indicates neither gamma or exponential)
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Table 5.7: Summary of the goodness-of-fit test for the stations satisfying both exponential and gamma distributions for complete storm durations (DCS) data (“Number of stations” indicates the number of stations satisfying the hypothesised distribution.)
C-S test K-S test A-D test Distributions Number Percentage Number Percentage Number Percentage of stations (%) of stations (%) of stations (%) Exponential 11 13% 32 38% 34 40% and gamma
Based on the three tests, it appears that the C-S test results are remarkably different than those of the K-S and A-D tests. The C-S test rejects about 72% of the stations, which seems to be unreasonable when compared to the two other test results, and hence the C-S test results are ignored. It may be stated that the objective here is to find a distribution, which provides overall fit to the observed data of rainfall duration and hence the test based on cumulative distribution such as Kolmogorov-Smirnov (K-S) and Anderson-Darling (A-D) tests are more relevant than the Chi-squared test, which is based on discrete variable; for some class interval, the difference between the observed and expected frequency might be too high to make the result too sensitive for the Chi-squared test. The results from the K-S and A-D tests are more relevant here and hence adopted. In this study, the rainfall DCS data can be represented by the gamma distribution for about 80% of the selected stations. Thus, the gamma distribution is adopted in this thesis to regionalise the rainfall DCS data. The Inverse Distance Weighted Averaging (IDWA) method is adopted to obtain the DCS value at the location of interest based on a set of nearby gauged catchments’ DCS data.
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Figure 5.6: Spatial distribution of the stations satisfying exponential and gamma distributions based on the Anderson-Darling test (“No distribution” indicates neither gamma or exponential)
The application of the regionalisation procedure of the DCS data is illustrated in Table 5.8 for the Oxley River catchment. The weighted average values are calculated by multiplying the assigned weights with values of the at-site mean and standard deviation of the rainfall DCS values of the corresponding station listed in Table B.4.2 (see Appendix B) and then adding their products. The estimated weighted average values are then used to generate rainfall DCS data in the EMCST. Next section discusses the regionalisation of rainfall inter-event duration data.
Table 5.8: Example of inverse distance weighted averaging for rainfall DCS data for Oxley River catchment
Surrounding pluviograph stations ID Parameter inputs Weighted average 58109 58129 58113 58158 58044
mean DCS (hour) 38.163 35.967 34.916 36.341 38.711 37.536
stdev DCS (hour) 33.212 33.269 33.946 29.521 34.909 33.093 Assign weights 0.676 0.104 0.089 0.077 0.054
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5.5 Regionalisation of rainfall inter-event duration (IED) data
In a similar manner to the regionalisation of rainfall DCS data (as discussed above in Section 5.4), the rainfall IED data are analysed to derive its regional distribution. In this analysis, two sets of tests are conducted: for original IED data and for trimmed IED data. The original IED data are the data obtained from the selected complete storm events data without any modification; while the trimmed IED data is constructed after removing IED values greater than 730 days (2-years period). The 730-day is the assumed maximum number of days of no significant rain that is acceptable as in Australia long drought is not uncommon. Therefore, two sets of tests are conducted for this analysis.
For the first set, the averages of the rainfall IED data range from 44 to 171 days as presented in Table B.5.7 (see Appendix B) with regional average values of the mean and standard deviation of 79 days and 153 days, respectively. Histograms of the IED values for each of the 86 pluviograph stations are also plotted at 25 days class interval (as per suggestion by Freedman and Diaconis, 1981). An example of this histogram is shown in Figure 5.7. In addition, plots of the cumulative frequency distributions for the fitted exponential and gamma distributions are examined for visual assessment of the goodness-of-fit test. As shown in Figure 5.7, the two hypothesised distributions approximately fit the IED data reasonably well. The three goodness-of-fit tests are then applied (at 5% level of significance) to the exponential and gamma distributions: the C-S, K-S and A-D tests to test their applicability; however, only the K-S and A-D test results are accepted as C-S test results are found to be inconsistent.
Based on the two goodness-of-fit tests, the gamma distribution shows a relatively better fit than the exponential distribution for the majority of the selected 86 stations as indicated in Table B.5.8 (see Appendix B). These results are also summarised in Table 5.9, with the K-S test fitting the exponential and gamma distributions for the 15% and 43% of the stations, respectively. The A-D test fits the exponential and gamma distributions for the 14% and 37% of the stations, respectively. Though the results for the two tests show a better fit for gamma distribution, this cannot be used to approximate a rainfall IED data in the simulation due to its low percentage of acceptance in the test. Thus, this study decides to run another set of test for the IED data with 730-day upper limit as mentioned above. University of Western Sydney Page 129
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Figure 5.7: Frequencies of rainfall IED data for pluviograph station 67035
Table 5.9: Summary of the goodness-of-fit test for rainfall IED data – 1st set (“Number of stations” indicates the number of stations satisfying the hypothesised distribution.).
K-S test A-D test Distributions Number of Percentage Number of Percentage stations (%) stations (%) Exponential 13 15% 12 14% Gamma 37 43% 32 37%
For the second set, the average values of the trimmed IED data result in the range of 42 to 148 days as presented in Table B.5.9 (see Appendix B) after discarding the IED values greater than 730 days. In addition, the regional average values of the mean and standard deviation of the trimmed IED data are found to be 70 days and 83 days, respectively. As indicated in the histogram of the trimmed IED data (an example is shown in Figure 5.8), the plots of the cumulative frequency distributions for the exponential and gamma distributions fit the trimmed IED data better as compared to the results in Figure 5.7.
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Figure 5.8: Frequencies of the trimmed rainfall IED data for pluviograph station 67035
For this trimmed IED data set, the three goodness-of-fit tests (C-S, K-S and A-D tests) are used to test the applicability of the two hypothesised distributions. From the performed test, gamma distribution shows superiority over the exponential distribution by showing more stations not rejecting the hypothesis as shown in Table B.5.10 (see Appendix B). As summarised in Table 5.10, the K-S and A-D tests demonstrate that gamma distribution fits 80% and 78% of the selected stations’ using trimmed IED data, respectively, as indicated. The test results based on the C-S test are ignored as these are surprisingly different to those of the K-S and A-D tests result. The C-S test rejects about 72% of the stations which seems to be unreasonable when compared with the two other test results. Finally, this thesis adopts the gamma distribution to specify the distribution of the regionalised rainfall IED data with the aid of IDWA method in the application of the proposed EMCST.
Table 5.10: Summary of the goodness-of-fit test for trimmed rainfall IED data – 2nd set (“Number of stations” indicates the number of stations satisfying the hypothesised distribution.)
C-S test K-S test A-D test Distributions Number Percentage Number Percentage Number Percentage of stations (%) of stations (%) of stations (%) Exponential 22 26 30 35 25 29 Gamma 24 28 69 80 67 78
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Additionally, for the trimmed rainfall IED data, the spatial distributions of stations satisfying the exponential and gamma distributions based on K-S and A-D tests are shown in Figures
5.9 and 5.10. In these figures, similar to DCS data, no regional pattern is detected; however, the gamma distribution provides a denser and wider network than the exponential distribution. Figures 5.9 and 5.10 show that the stations satisfying both the exponential and gamma distributions (brown circles) are also the stations satisfying the exponential distributions plus the two stations in red circles. In Table 5.11, the goodness-of-fit test results also show that 33% and 27% of the stations fit both the exponential and gamma distributions based on the K-S and A-D tests (at 5% level of significance), respectively. Overall, the gamma distribution provides a better fit based on the three goodness-of-tests conducted here.
Table 5.11: Summary of the goodness-of-fit test for the stations satisfying both exponential and gamma distributions for inter-event durations (IED) data
C-S test K-S test A-D test Distributions Number Percentage Number Percentage Number Percentage of stations (%) of stations (%) of stations (%) Exponential 16 19% 28 33% 23 27% and gamma
Figure 5.9: Spatial distribution of the stations satisfying exponential and gamma distributions based on the Kolmogorov-Smirnov test. Here “No distribution” indicates neither gamma or exponential is acceptable.
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Figure 5.10: Spatial distribution of the stations satisfying exponential and gamma distributions based on the Anderson-Darling test. Here “No distribution” indicates neither gamma or exponential is acceptable.
Similar to rainfall DCS, the application of the regionalisation procedure for rainfall IED data is presented in Table 5.12 for the Oxley River catchment. The weighted average values are also computed by multiplying the assigned weights with values of the at-site mean and standard deviation of the rainfall IED of the corresponding station listed in Table B.5.10 in Appendix B and then adding their products (see Equation 3.25). The estimated weighted average values are then used to generate rainfall IED data for the application of the proposed EMCST. Next section discusses the regionalisation of rainfall intensity-frequency-duration data.
Table 5.12: Example of inverse distance weighted averaging for rainfall IED data
Surrounding pluviograph stations ID Parameter Inputs Weighted average 58109 58129 58113 58158 58044 mean IED (day) 103.060 125.404 76.695 78.634 119.460 102.056 stdev IED (day) 128.934 129.564 86.610 96.728 153.575 124.101 Assign weights 0.676 0.104 0.089 0.077 0.054
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5.6 Regionalisation of intensity-frequency-duration (IFD) data
Using the procedure described in Section 3.7, the design IFD data were obtained for each of the selected 86 pluviograph stations. Examples of these IFD estimates, called IFD table, are presented in Tables 5.13 and 5.14. Plot of these estimates, called the IFD curves, look consistent with no kinks in the curves as presented in Figures 5.11 and 5.12. It can be seen from these tables and figures that the average design rainfall intensity of frequent storms decreases with increasing event duration as expected. However, for ARIs 0.1 and 1 year with 2 hours duration, the average rainfall intensity (red colour font) increases although the event duration increases; however this should not create a major issue in the MCST. These IFD tables can be used to obtain a value of rainfall intensity ICS for any duration DCS for a selected ARI in the MCST.
Table 5.13: Design IFD data for pluviograph station 48027
48027 ARI (year) Durations 0.1 1 1.11 1.25 2 5 10 20 50 100 500 1000 106 (h) 1 4.23 4.94 5.78 6.73 10.52 18.01 23.72 29.44 37.03 42.77 56.12 61.88 119.29 2 4.59 5.08 5.61 6.21 8.56 13.03 16.36 19.68 24.06 27.36 35.02 38.31 71.09 6 3.23 3.45 3.69 3.96 5.01 7.01 8.50 9.99 11.95 13.43 16.86 18.33 33.02 24 0.89 1.00 1.14 1.28 1.78 2.67 3.31 3.96 4.80 5.43 6.89 7.52 13.78 48 0.33 0.40 0.48 0.57 0.91 1.52 1.97 2.42 3.00 3.44 4.46 4.90 9.26 72 0.16 0.21 0.27 0.33 0.59 1.07 1.43 1.80 2.27 2.64 3.47 3.83 7.43 100 0.09 0.12 0.16 0.21 0.40 0.79 1.10 1.40 1.81 2.12 2.84 3.15 6.25
Table 5.14: Design IFD data for pluviograph station 48031
48031 ARI (year) Durations 0.1 1 1.11 1.25 2 5 10 20 50 100 500 1000 106 (h) 1 8.75 9.52 10.36 11.31 15.10 22.49 28.09 33.69 41.10 46.70 59.72 65.33 121.22 2 7.19 7.69 8.22 8.82 11.19 15.78 19.25 22.71 27.29 30.74 38.77 42.22 76.63 6 4.15 4.39 4.64 4.92 6.03 8.20 9.84 11.47 13.64 15.27 19.06 20.70 36.97 24 1.37 1.47 1.57 1.69 2.16 3.05 3.72 4.38 5.26 5.92 7.45 8.11 14.68 48 0.66 0.72 0.79 0.87 1.16 1.74 2.17 2.59 3.16 3.58 4.57 5.00 9.23 72 0.41 0.45 0.50 0.56 0.79 1.22 1.55 1.88 2.32 2.65 3.42 3.75 7.04 100 0.27 0.30 0.34 0.39 0.56 0.91 1.18 1.44 1.80 2.07 2.69 2.96 5.64
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Figure 5.11: Derived IFD curves for station 48027
Figure 5.12: Derived IFD curves for station 48031
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5.6.1 Regionalisation of the IFD curves
The developed set of IFD curves/tables from the selected 86 pluviograph stations forms the basis of regionalisation of the IFD data in eastern NSW. In order to apply it for an arbitrary location, the IDWA method discussed in Section 3.9 is applied to obtain IFD estimate using the IFD data from a number of nearby stations. In this study, it is assumed that stations located beyond 30 km distance from the point of interest should not be included in obtaining the weighted average IFD value as it may not give meaningful IFD value at the location of interest. It should be noted that the closer the pluviograph stations from the catchment of interest the better the estimated average IFD, and 30 km distance here is only an arbitrary limit, which is found to be satisfactory for eastern NSW. This is further discussed in the following section.
5.6.2 Finding the optimum number of stations to regionalise IFD curves at the location of interest
Initially, a limit of 30 km radius from the centre of a catchment of interest is set to find the optimum number of stations needed to regionalise IFD data at the location of interest. In order to test this approach, this study selects six catchments (stations ID 201001, 203014, 204017, 204025, 210080 and 420003). For the Oxley River catchment (station ID 201001), as an example, the IFD data is obtained using the developed IFD curves of nearby pluviograph stations by applying the IDWA method. These nearby pluviographs are stations 58109 (located within the catchment), 58129, 58113, 58158 and 58044 with distances of 2.36 km, 14.08 km, 16.51 km, 18.81 km and 26.87 km from the approximate centre of the Oxley River catchment, respectively. It can be seen from Figure 5.13 that the resulting IFD curves for the Oxley River catchment is very similar to the IFD curves of the first three nearby pluviograph stations (in Figures 5.14, 5.15 and 5.16) as the IFD curves of these stations look very similar. This weighted average IFD data is shown in Table 5.15.
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Figure 5.13: Weighted average IFD curves for Oxley River catchment
Figure 5.14: IFD curves for station ID 58109 for Oxley River catchment
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Figure 5.15: IFD curves for station ID 58129
Figure 5.16: IFD curves for station ID 58113
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Table 5.15: Weighted average IFD data for Oxley River catchment (station ID 201001)
201001 ARI (years) Durations (h) 0.1 1 1.11 1.25 2 5 10 20 50 100 500 1 13.350 14.262 15.238 16.355 20.792 29.463 36.026 42.591 51.270 57.836 73.082 2 8.727 9.341 9.999 10.746 13.698 19.447 23.794 28.141 33.887 38.234 48.326 6 4.745 5.089 5.459 5.879 7.534 10.750 13.179 15.608 18.818 21.246 26.883 24 2.412 2.595 2.794 3.020 3.909 5.634 6.938 8.240 9.962 11.264 14.287 48 1.782 1.923 2.076 2.249 2.932 4.259 5.261 6.263 7.587 8.589 10.914 72 1.510 1.632 1.765 1.916 2.512 3.670 4.545 5.419 6.575 7.450 9.479 100 1.329 1.439 1.559 1.695 2.234 3.282 4.074 4.866 5.913 6.705 8.544
Though the IFD curves of the other two pluviograph stations in Figures 5.17 and 5.18 look slightly different, these do not affect the resulting IFD curves as much as the first three pluviograph stations having 6.64%, 11.00% and 9.38% of the weighted average (as listed in Table 5.16). As expected, the IFD curves of pluviograph station 58109 have significant influence on the resulting IFD curves as this is the closest station and having the highest weight.
Figure 5.17: IFD curves for station ID 58158
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Figure 5.18: IFD curves for station ID 58044
Table 5.16: Summary of the weights in obtaining the weighted average IFD data for Oxley River catchment
Station ID Distances (km) Weights Percentage (%) 58109 2.36 0.656 65.6 58129 14.08 0.110 11.0 58113 16.51 0.094 9.4 58158 18.81 0.082 8.2 58044 26.87 0.058 5.8
Similarly, the IFD curves for the Orara River catchment (station ID 204025) are obtained based on pluviograph stations 59026 (located within the catchment), 59040 and 59067, with distances of 3.46 km, 13.67 km and 25.68 km, respectively. In this analysis, only three pluviograph stations are used as most of the stations are located beyond the adopted 30 km limit. The resulting IFD curves are again found to be very similar to the IFD curves of the nearest station, indicating no gross error with the adopted weighting method. The consistency in the resulting IFD curves for the catchment (Figure 5.19) and the IFD curves of pluviograph station 59026 (which is the closest station, Figure 5.20) can be noticed.
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In this weighted averaging method, the IFD curves that match with the resulting IFD curves can be seen for 5 years ARI of station 59040 in Figure 5.21 and for 2-year ARI of station 59067 in Figure 5.22. This means that the closest pluviograph station (ID 59026) has the highest weight (72.07%) as indicated in Table 5.17 on the resulting IFD curves as compared to the two other nearby pluviograph stations (ID 59040 and ID 59067) with weights of 18.23% and 9.70%, respectively.
Table 5.17: Summary of weights in obtaining the weighted average IFD data for Orara River catchment
Station ID Distances (km) Weights Percentage (%) 59026 3.458 0.721 72.1 59040 13.671 0.182 18.2 59067 25.681 0.097 9.7
Figure 5.19: Weighted Average IFD Curves for Orara River catchment
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Figure 5.20: IFD Curves for Station 59026 for Catchment 204025
Figure 5.21: IFD curves for station ID 59040
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Figure 5.22: IFD curves for station ID 59067
5.6.3 Summary of IFD data regionalisation
In this section, the adopted regionalisation procedure of IFD data is summarised. A total of 86 at-site IFD tables have been developed, which forms the basis of obtaining regional IFD data at any arbitrary location in eastern NSW based on a number of nearby stations’ IFD data. Based on the IFD data regionalisation procedure, it has been found that the closest station has the most significant influence on the resulting regional IFD data (as per Equation 3.25). It is found that the use of the IFD data from the stations which are located within the 30 km radius of the centre of the catchment of interest would suffice to derive the regional IFD data at the location of the catchment of interest. The regional IFD data for the six selected test catchments (stations 201001, 203014, 204017, 204025, 210080 and 420003) have been derived, which present a consistent set of IFD data and hence can be used in the EMCST. The regionalisation of temporal patterns is discussed next.
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5.7 Regionalisation of temporal patterns (TP) data
Using 86 pluviograph stations from eastern NSW, a total of 19,718 complete storms’ TPs are obtained in dimensionless form following the procedure described in Section 3.8. To form the regional TP database for eastern NSW, the dimensionless TPs from these individual stations are pooled irrespective of the season and total rainfall depth. However, the TPs are grouped based on rainfall durations, one group with durations up to 12 hours and other group greater than 12 hours. The TPs of nearby pluviograph stations within arbitrary distances of 30 km, 50 km, 100 km, and up to 200 km from centre of the catchment of interest or up to a maximum of 20 nearby pluviograph stations are considered in the regionalisation procedure. The regionalisation of TPs data are described further in Chapter 6. The next section discusses the regionalisation of losses and storage delay parameter (k).
5.8 Regionalisation of the initial loss (IL) data
In the calibration of the runoff routing model for the selected six catchments, the IL data listed in Table 5.5 and Tables B.5.1 to B.5.5 in Appendix B are obtained, which are regionalised using the procedure described in Section 3.9. Here, the K-S and A-D tests are applied to conduct the goodness-of-fit test. These tests are applied to the selected at-site IL data of each catchment (Section 5.8.1) and then to the combined IL data set for the selected six catchments (Section 5.8.2) as discussed in the following sections.
5.8.1 Fitting of probability distributions to the at-site IL data
Using the K-S test, two distributions (exponential and gamma) are applied to the IL data of each of the six catchments. From the conducted test, overall, gamma distribution shows superiority over exponential distribution as shown in Table 5.18. The test using the A-D test gives very similar results as with the K-S test as can be seen in Table 5.18. This shows that for the entire stations gamma shows an acceptable fit.
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Table 5.18: Goodness-of-fit tests summary for the initial loss data for the six catchments. Here, the code zero (0) and one (1) stands for ‘do not reject’ and ‘reject’ the hypothesis, respectively. Exponential distribution = ED and gamma distribution = GD
Catchment K-S test A-D test station ID ED GD ED GD 203002 0 0 0 0 203012 0 0 0 0 210068 0 0 0 0 210076 0 0 0 0 213005 0 0 0 0 411001 1 0 1 0 Combined 1 0 1 0 all stations
5.8.2 Fitting of a probability distribution to the regional IL data
In a similar manner as mentioned in Section 5.8.1, using the K-S and A-D tests, the two distributions (exponential and gamma) are tested to the combined IL data from all the six catchments. From the two tests implemented, gamma distribution is found to show a better fit to the combined IL data than the exponential distribution as can be seen in Table 5.18.
5.8.3 Summary of IL data regionalisation
In the regionalisation of IL data, two distributions are applied to the at-site IL data and the combined IL data using the K-S and A-D tests at 5% level of significance. Based on the two tests, either exponential distribution or gamma distribution can be adopted to describe the at- site IL data with the result of about 83% and 100% stations satisfying the hypothesised distribution as shown in Table 5.19, respectively. For the two tests applied using the combined IL data, gamma distribution presents a better fit as compared to the exponential distribution. Thus, gamma distribution is used to approximate the IL data in the application of the EMCST for eastern NSW. Next section discusses the regionalisation of CL data.
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Table 5.19: Summary of goodness-of-fit tests for initial loss (IL) data. Here, percentage (%) implies the % of stations satisfying a hypothesised distribution K-S test A-D test Distributions Number of Percentage Number of Percentage catchment (%) catchment (%) Exponential 5 83 5 83 Gamma 6 100 6 100
5.9 Regionalisation of continuing loss (CL) data
The CL data given in Table 5.5 and Tables B.5.2 to B.5.6 in Appendix B are regionalised using the two distributions: exponential and gamma. The applicability of regional exponential or gamma distribution is assessed by applying two tests, similar to the IL data discussed in Section 5.8.2. This procedure is discussed below.
5.9.1 Fitting of probability distribution to the at-site CL data
The two distributions (exponential and gamma) are applied to the CL data of each of the six catchments using the K-S test initially. The test results show (with no station rejecting the null hypothesis) that the CL data can be approximated by either exponential distribution or gamma distribution as shown in Table 5.20. Similarly, the A-D test shows similar results with five catchments not rejecting the hypothesised distribution and one catchment (station ID 210076) rejecting the null hypothesis.
Table 5.20: Goodness-of-fit test summary for the continuing loss (CL) data for the six catchments. In this table, the code zero (0) and one (1) stands for ‘do not reject’ and ‘reject’ the null hypothesis, respectively. Exponential distribution = ED and gamma distribution = GD
Catchment K-S test A-D test station ID ED GD ED GD 203002 0 0 0 0 203012 0 0 0 0 210068 0 0 0 0 210076 0 0 1 1 213005 0 0 0 0 411001 0 0 0 0 Combined 0 0 0 0 all stations
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5.9.2 Fitting of probability distribution to regional CL data
The two distributions (exponential and gamma) are also applied to the combined CL data using the K-S test and A-D test. In this case, the CL data of the six catchments are combined to form a regional CL database. The two tests show identical results with either exponential or gamma distribution can be used to describe the CL data as presented in Table 5.20. These means that the regional CL data can be approximated using either the exponential or gamma distribution.
5.9.3 Summary of CL data regionalisation
Based on the K-S test, either exponential distribution or gamma distribution can be used to estimate the at-site CL data with the result of 100% stations being satisfied for both the distributions as shown in Table 5.21. Whereas, the A-D test results in about 83% for both the distributions, in which it is not as good as the K-S test result. On the other hand, using the two tests for the combined CL data, the exponential and gamma distributions demonstrate a similar fit. This means that either exponential or gamma distribution can be used to approximate the at-site or regional CL data. However, the exponential distribution is preferable as this has only one parameter as compared to two-parameter gamma distribution, and hence exponential distribution is adopted as the regional distribution of CL from eastern NSW. The regionalisation of the storage delay parameter data is discussed next.
Table 5.21: Summary of goodness-of-fit tests for continuing loss (CL) data. Here, percentage (%) implies the % of stations satisfying a hypothesised distribution K-S test A-D test Distributions Number of Percentage Number of Percentage catchment (%) catchment (%) Exponential 6 100 5 83 Gamma 6 100 5 83
5.10 Regionalisation of storage delay parameter (k)
Employing the procedure described in Sections 3.6, the k data given in Table 5.5 and Tables B.5.1 to B.5.5 in Appendix B are regionalised. To assess the applicability of regional exponential and gamma distribution, the two goodness-of-fit tests (the K-S and the A-D tests)
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5.10.1 Fitting distributions to the at-site k data
For the at-site k data of each of the six catchments, the two distributions are applied using the K-S test initially. The test for the two distributions results no rejection of the null hypothesis as shown in Table 5.22. This means that the at-site k data can be approximated by either exponential or gamma distributions. However, A-D test shows different results with only three catchments not rejecting the null hypothesis for exponential distribution and for the other three catchments, a rejection of the null hypothesis. In contrast, with the test for gamma distribution, there is no rejection to any of the six catchments. Based on the two tests, gamma distribution shows superiority over exponential distribution for the at-site k data with 100% no rejection as presented in Table 5.23. Thus, the at-site k data can be approximated using the gamma distribution.
Table 5.22: Goodness-of-fit tests summary for the storage delay parameter data for the six catchments. In this table, the code zero (0) and one (1) stands for ‘do not reject’ and ‘reject’ the hypothesis, respectively. Exponential distribution = ED and gamma distribution = GD
Catchment K-S test A-D test station ID ED GD ED GD 203002 0 0 0 0 203012 0 0 1 0 210068 0 0 1 0 210076 0 0 0 0 213005 0 0 1 0 411001 0 0 0 0
Table 5.23: Summary of goodness-of-fit tests for storage delay parameter data. Here, percentage (%) implies the % of stations satisfying a hypothesised distribution K-S test A-D test Distributions Number of Percentage Number of Percentage catchment (%) catchment (%) Exponential 6 100 3 50 Gamma 6 100 6 100
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5.10.2 Fitting distributions to the at-site standardised k data
The at-site k data of the six catchments are standardised as these catchments have different catchment areas as listed in Table 4.1. Generally, the larger the catchment, the higher the k value is. The standardisation is done by dividing the k data of a catchment by its corresponding catchment area. Here, a linear assumption is made in standardising the k value, which is unlikely to affect the results of the analysis since k mainly depends on catchment area. A non-linear transformation is unlikely to improve the results and hence was not adopted. After the standardisation, the same tests as presented in Section 5.10.1 are applied to test the applicability of the exponential and gamma distributions. The K-S test results to five catchments with no rejection of the hypothesised distribution for both the exponential and gamma distribution as presented in Table 5.24. Whereas, in the A-D test, three catchments result to no rejection of null hypothesis for exponential distribution and for five catchments, no rejection for the gamma distribution.
Hence, the gamma distribution fits the standardised k data better than the exponential distribution with about 83% no rejection to the hypothesis for both the tests as presented in Table 5.25. Thus, the gamma distribution is used to approximate the standardised k data.
Table 5.24: Goodness-of-fit tests for the standardised storage delay parameter data for the six catchments. In this table, the code zero (0) and one (1) stands for ‘do not reject’ and ‘reject’ the hypothesis, respectively. Exponential distribution = ED and gamma distribution = GD
Catchment K-S test A-D test station ID ED GD ED GD 203002 0 0 0 0 203012 0 0 1 0 210068 1 1 1 1 210076 0 0 0 0 213005 0 0 1 0 411001 0 0 0 0 Combined 1 0 1 0 all stations
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Table 5.25: Summary of goodness-of-fit tests for standardised storage delay parameter data for the six catchments. Here, percentage (%) implies the % of stations satisfying a hypothesised distribution K-S test A-D test Distributions Number of Percentage Number of Percentage catchment (%) catchment (%) Exponential 5 83 3 50 Gamma 5 83 5 83
5.10.3 Fitting distribution to regional standardised k data
The combined standardised k data from the six catchments are tested by applying the two distributions. Both the K-S and A-D tests show no rejection to gamma distribution as indicated in Table 5.24, and hence, the combined standardised k data is approximated by gamma distribution.
5.11 Correlations among the input variables and parameters
In this study, the following seven input variables/model parameters have been considered: (i) Rainfall duration; (ii) Rainfall inter-event duration; (iii) Rainfall intensity; (iv) Rainfall temporal patterns; (v) Initial loss; (vi) Continuing loss; and (vii) Storage delay parameter of the runoff routing model. The correlation between the rainfall intensity and duration (as described in Section 3.7.1) was found to be high (R2 in the range of 0.65 to 0.75). This correlation was considered in the modelling by expressing the depth of rainfall as a conditional distribution of rainfall duration in the form of intensity-frequency-duration (IFD) curve (for example see Figure 3.5 and Table 3.2). The second most important correlation was between rainfall duration and temporal pattern, which was accounted for by expressing temporal patterns as a function of rainfall duration (see Section 3.8). There was no notable correlation among other variables, which was similar to the findings in previous studies on MCST such as Rahman et al. (2002a) and Aronica and Candela (2007).
5.12 Summary of the regionalisation of the input variables and parameters
This chapter has investigated the regionalisation of the distributions of input variables and storage delay parameter data in eastern NSW for application with the proposed EMCST to design flood estimation. The rainfall events data from the selected 86 pluviograph stations are
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Enhanced Joint Probability Approach Caballero extracted. In addition, the concurrent rainfall and streamflow events data have been selected for the analysis of losses and storage delay parameter from the six selected catchments. The regionalisation of the following six input variables and parameter have been completed: rainfall duration, rainfall inter-event duration, rainfall intensity-frequency-duration, initial loss, continuing loss and storage delay parameter while the regionalisation of the temporal pattern is further detailed in Chapter 6.
From the results of this chapter, the following conclusions can be made: rainfall duration, inter-event duration, initial loss and storage delay parameter data can be approximated by gamma distribution while the continuing loss data by exponential distribution. These results are summarised in Table 5.26. The intensity-frequency-duration data can be regionalised by using the intensity-frequency-duration data of the nearby stations within 30 km radius of the approximate catchment centre and by applying the IDAW method. For TP, the dimensionless TP data of nearby 20 pluviograph stations can be used to form a TP database for a location of interest that can be used for random sampling during simulation.
Table 5.26: Regionalised model inputs and their probability distributions for eastern NSW
Model inputs Probability distributions
Rainfall complete storm duration (DCS) Gamma Rainfall inter-event duration (IED) Gamma Initial loss (IL) Gamma Continuing loss (CL) Exponential Storage delay parameter (k) Gamma Adopt IDWA method to obtain IFD data set at a location of interest from the nearby IFD data of pluviograph stations Rainfall depth (IFD) located within 30 km radius from the approximate centre of the catchment of interest Use dimensionless TP data of nearby 20 stations to form TP Temporal pattern (TP) database at a location of interest
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Enhanced Joint Probability Approach Caballero CHAPTER 6 Sensitivity of the Regionalised Distributions in the Application of the Enhanced Monte Carlo Simulation Technique
6.1 Introduction
Chapter 5 has discussed the regionalisation of the input variables for eastern New South Wales (NSW). This chapter presents the results of the sensitivity analysis of the regionalised distributions in the new EMCST to assess how a possible variation in an input variable could affect the final derived flood frequency curves (DFFCs). The chapter begins with the selection of the catchments in Sections 6.2, which is followed by the discussion on the sensitivity analyses of the input variables and model parameters in Sections 6.3 to 6.9.
6.2 Selection of test catchments for sensitivity analysis
In order to check the sensitivity of the regionalised distributions in the new EMCST, the catchments in Table 4.3 are used, which represent two ranges of catchment sizes. The Bielsdown Creek (76 km2), the Belar Creek (133 km2) and the Oxley River (213 km2) catchments represent small to medium catchments. These three catchments are considered as these capture a good variability in catchment size which provides an opportunity to check the sensitivity on DFFCs for catchment of different sizes. In addition, these catchments are selected because of their relatively long streamflow records (at least 30 years of data). In particular, the concurrent rainfall and streamflow record lengths are also relatively long, minimum of 30 years (as shown in Table 4.4). Further, base values of the model input are already established for these three catchments (as given in Table 6.1).
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Table 6.1: Model inputs for the three test catchments
Parameter Inputs Oxley River Bielsdown Creek Belar Creek mean IED (day) 104.05 79.13 41.96 stdev IED (day) 126.39 97.44 48.77
mean DCS (hour) 38.27 40.73 22.06
stdev DCS (hour) 33.75 41.52 19.99 mean IL (mm) 7.24 13.61 36.90 stdev IL (mm) 4.68 5.92 19.25 mean CL (mm/h) 0.85 0.57 5.64 mean k (h) 11.47 5.83 26.99 stdev k (h) 1.04 2.82 6.33 median BF (m3/s) 1.64 1.68 0.22
6.3 Sensitivity analysis for rainfall complete storm duration (DCS)
The distributional parameters of the DCS data for each of the three catchments are considered to examine the effects of sampling variability/uncertainties in the DCS on the resulting derived flood frequency curves (DFCCs). It is found that DCS data of the study pluviograph stations can be approximated by a two-parameter gamma distribution (as detailed in Section 5.4). Here, the gamma distribution has two parameters (location and scale), which are estimated from the weighted mean and standard deviation values of the DCS data from the selected nearby pluviograph stations. In the adopted sensitivity analysis, the mean and standard deviation values of the DCS data for each of these catchments are varied within an arbitrary margin of variability to assess their impacts on DFFCs, as presented below.
6.3.1 Sensitivity analysis: Complete storm duration (DCS)
To achieve a reasonable variation in the DCS value, an increase and decrease of 5%, 10%, 20% and 50% are applied to the base value of the mean and standard deviation of the weighted DCS data. As an example, the base value of the weighted mean DCS for the Oxley
River is 38.27 hours; by adding 5% to this base value, the new DCS becomes 40.18 hours. In a similar manner, the reduction of 5% results in a DCS value of 36.35 hours. The adjusted weighted mean DCS values resulted from 5%, 10%, 20% and 50% variations for each of the three catchments (the Oxley River, the Bielsdown Creek and the Belar Creek) are presented
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in Tables 6.2, 6.3 and 6.4. These adjusted values of DCS are then used in the simulation to obtain a DFFC as described in the following section.
Table 6.2: Adjusted DCS mean and standard deviation values for the Oxley River catchment
Base Percentage (%) increase Percentage (%) decrease Input parameter value 5 10 20 50 5 10 20 50
mean DCS (hour) 38.27 40.18 42.09 45.92 57.40 36.35 34.44 30.61 19.13 stdev DCS (hour) 33.75 35.44 37.12 40.50 50.62 32.06 30.37 27.00 16.87
Table 6.3: Adjusted DCS mean and standard deviation values for the Bielsdown Creek catchment
Base Percentage (%) increase Percentage (%) decrease Input parameter value 5 10 20 50 5 10 20 50
mean DCS (hour) 40.73 42.77 44.80 48.88 61.10 38.69 36.66 32.58 20.37 stdev DCS (hour) 41.52 43.60 45.67 49.82 62.28 39.44 37.37 33.22 20.76
Table 6.4: Adjusted DCS mean and standard deviation values for the Belar Creek catchment
Base Percentage (%) increase Percentage (%) decrease Input parameter value 5 10 20 50 5 10 20 50
mean DCS (hour) 22.06 23.17 24.27 26.48 33.10 20.96 19.86 17.65 11.03
stdev DCS (hour) 19.99 20.99 21.99 23.99 29.98 18.99 17.99 15.99 9.99
6.3.2 Derived flood frequency curves using the adjusted DCS values
For the Oxley River catchment, all the base values of the parameter inputs in Table 6.1 are used in the first run of the simulation. The weighted mean value of DCS (38.27 hours) i.e. the base value is then replaced with the adjusted DCS mean value (e.g. 40.18 hours) in each of the succeeding simulation runs; while the other model inputs (i.e. IED, IFD, TP, IL, CL and k) are kept constant in this particular simulation. This procedure is also applied using the weighted standard deviation value of DCS. The procedure is then repeated to the two other test catchments (i.e. the Bielsdown Creek and the Belar Creek).
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6.3.3 Results of the sensitivity analysis for rainfall DCS
The DFFCs using the adopted different mean values of DCS for the Oxley River, Bielsdown Creek and Belar Creek catchments show a relatively small to moderate variability as can be seen in Figures 6.1, 6.2 and 6.3. The increase and decrease in DCS mean value for the Oxley River by up to 20% results in about 10% differences in the flood quantile estimates as shown in Table B.6.1 (see Appendix B). In this table, the change of ± 20% results in over-estimation by up to 2% and under-estimation by up to 8% in flood quantile estimates. Similar results are found for the Bielsdown Creek catchment. The flood quantile estimates show an over- estimation by up to 7% and under-estimation by up to 8% as shown Table B.6.2 (see Appendix B). For the Belar Creek catchment, the flood quantile estimates show an over- estimation by up to 14% and under-estimation by up to 16% as can be seen in Table B.6.3 (see Appendix B).
Figure 6.1: DFFCs based on the adopted different DCS mean values for the Oxley River catchment
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Figure 6.2: DFFCs based on the adopted different DCS mean values for Bielsdown Creek catchment
Figure 6.3: DFFCs based on the adopted different DCS mean value for the Belar Creek catchment
A 50% change in the DCS mean value for the Oxley River shows an under-estimation in the flood quantile estimates to all the ARIs (2 to 100 years) by up to 17%, with 1% under- estimation for 2-year ARI when the DCS is increased by 50% and up to 28% under-estimation University of Western Sydney Page 157
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when the mean of DCS is reduced by 50% (see Table B.6.1 in Appendix B). For the
Bielsdown Creek catchment, the 50% increase in the mean value of the DCS data shows an over-estimation in flood quantile estimates by up to 8% except for Q50, which shows an under-estimation of 2% (see Table B.6.2 in Appendix B); whereas, the decrease by 50% shows an under-estimation by up to 35% in flood quantiles. For the Belar Creek catchment, the 50% increase in the mean value of DCS data shows an overall over-estimation by up to
28% in the flood quantile estimates. In contrast, the decrease in the mean value of DCS data by 50% causes an overall under-estimation in flood quantiles by up to 52% (see Table B.6.3 in Appendix B for details).
Use of the different values of the standard deviation of the DCS data, the obtained DFFCs for the Oxley River, Bielsdown Creek and Belar Creek catchments indicates that the variation in the standard deviation value has a relatively smaller to moderate impact (as compared to the mean of the DCS data) as illustrated in Figures 6.4, 6.5 and 6.6. In the case for the Oxley River, the differences in the flood quantile estimates appear to be around 5% under- estimation to most of the ARIs with the maximum increase and decrease in standard deviation values by up to 20% as shown in Table B.6.4 (see Appendix B). Only few ARIs exhibit up to 7% under-estimation with this change in DCS standard deviation values. For the
Bielsdown Creek, the 5% to 20% increase in the standard deviation values of DCS show over- estimation and under-estimation in the flood quantile estimates by up to 5% and 6%, respectively as can be seen in Table B.6.5 (see Appendix B). Furthermore, the 5% to 20% decrease shows an overall over-estimation by up to 7% in flood quantile estimates. For the Belar Creek, the resulting differences in DFFCs are summarised in Table B.6.6 (see Appendix B); for all the ARIs, an over-estimation and under-estimation by about 10% are noticed with the increase and decrease in the standard deviation of DCS value by up to 20%.
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Figure 6.4: DFFCs based on the adopted different DCS standard deviation values for the Oxley River catchment
Figure 6.5: DFFCs based on the adopted different DCS standard deviation values for Bielsdown Creek catchment
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Figure 6.6: DFFCs based on the adopted different DCS standard deviation values for the Belar Creek catchment
However, with the ± 50% change in the values of DCS standard deviation, the under- estimation in the flood quantile estimates for the Oxley River catchment goes up to about 11% for some of the ARIs as shown in Table B.6.4 (see Appendix B). In addition, the adopted change in the standard deviation of the DCS data shows an over-estimation by up to 3% to some of the ARIs (see Table B.6.4 in Appendix B). For the Bielsdown Creek, a 50% increase in the standard deviation values of the DCS shows an over-estimation and under- estimation by 1% and up to 16% in the flood quantile estimates, respectively as can be seen in Table B.6.5 (see Appendix B). Furthermore, a 50% decrease shows an overall over- estimation in flood quantile estimates by up to 10%. For the Belar Creek, with the changes by up to 50% in the standard deviation values, the over-estimation and under-estimation in the flood quantile estimates are only up to 17% and 18%, respectively; as shown in Table B.6.6 (see Appendix B). In this table, it can be seen that an increase in the standard deviation of
DCS results an under-estimation in the flood quantile estimates; while, the reduction demonstrates an overall over-estimation.
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6.3.4 Summary of the sensitivity analysis for rainfall DCS
In summary, the sensitivity analysis for DCS shows that a smaller variation (up to 20%) to the mean and standard deviation values of the DCS data would not have much significant impacts on the DFFCs. However, a variation by about 50% to the mean value of DCS would have a significant impact of about 30% to 50% on the DFFCs; whereas a change in the standard deviation values by up to about 50% would cause about 10% to 20% variation in the DFFCs.
This shows that the variation in the DCS mean is more sensitive as compared to the variation in the DCS standard deviation in the application of the EMCST.
6.4 Sensitivity analysis for rainfall inter-event duration (IED)
Similar to the DCS, as described above, the distributional parameters of IED data for the three catchments are also subjected to an arbitrary variation to check the effects of sampling variabilities/uncertainties in the rainfall IED on the resulting DFFC. The IED values of each of the three pluviograph stations can be approximated by two-parameter gamma distribution as discussed in Section 5.5. In the sensitivity analysis, an arbitrary degree of variation is applied to the mean and standard deviation values of the IED data to assess how the uncertainties in these distributional parameters would impact the final DFFCs.
6.4.1 Sensitivity analysis: inter-event duration (IED)
An arbitrary increase and decrease of 5%, 10%, 20% and 50% are applied to the mean and standard deviation of the IED values. As an example, the weighted mean IED for the Oxley River is 104.05 days; an increase by 5%, gives an IED value of 109.25 days. Similarly, a decrease by 5% makes the new mean IED value equals to 98.85 days. The adopted values of the IED mean in the sensitivity analysis for the three catchments are shown in Tables 6.5, 6.6 and 6.7. These new values are used in the simulations to obtain DFFCs.
Table 6.5: Adjusted IED mean and standard deviation values for the Oxley River catchment
Base Percentage (%) increase Percentage (%) decrease Input parameter value 5 10 20 50 5 10 20 50 mean IED (day) 104.05 109.25 114.46 124.86 156.08 98.85 93.65 83.24 52.03 stdev IED (day) 126.39 132.71 139.03 151.67 189.59 120.07 113.75 101.11 63.20
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Table 6.6: Adjusted IED mean and standard deviation values for the Bielsdown Creek catchment
Base Percentage (%) increase Percentage (%) decrease Input parameter value 5 10 20 50 5 10 20 50 mean IED (day) 79.13 83.09 87.04 94.96 118.70 75.17 71.22 63.30 39.57 stdev IED (day) 97.44 102.31 107.18 116.93 146.16 92.57 87.70 77.95 48.72
Table 6.7: Adjusted IED mean and standard deviation values for the Belar Creek catchment
Base Percentage (%) increase Percentage (%) decrease Input parameter value 5 10 20 50 5 10 20 50 mean IED (day) 41.96 44.06 46.16 50.36 62.94 39.86 37.77 33.57 20.98 stdev IED (day) 48.77 51.21 53.65 58.53 73.16 46.33 43.90 39.02 24.39
6.4.2 Derived flood frequency curves (DFFC) based on the adjusted IED values
The first set of DFFC is obtained using the base value of IED data, and then new DFFCs are obtained using the adjusted IED data shown in Tables 6.5 to 6.7 while keeping all other variables/distributional parameters fixed. The procedure is applied for each of the three catchments (the Oxley River, Bielsdown Creek and Belar Creek) separately. The results of this sensitivity analyses are presented below.
6.4.3 Results of the sensitivity analysis for rainfall IED
The DFFCs using the different mean values of the IED distribution indicate small differences in flood quantiles for the Oxley River, Bielsdown Creek and Belar Creek catchments as shown in Figures 6.7, 6.8 and 6.9, respectively. For the Oxley River, the variation in the flood quantile estimates demonstrates an under-estimation by up to 14% with the increases by up to 20% in the IED mean value as shown in Table B.6.7 (see Appendix B); whereas, a decrease by up to 20% in the IED mean value exhibits an over-estimation by up to 20% in the DFFCs. For the Bielsdown Creek, an increase by up to 20% in the IED mean value causes under- estimation in the flood quantile estimates by up to 15% and some over-estimation by up to 6%; while a decrease by up to 20% demonstrates an overall over-estimation by up to 21% as illustrated in Table B.6.8 (see Appendix B). For the Belar Creek, a variation by up to 20% in the IED mean value causes both over- and under-estimation in the flood quantile estimates by up to 17% and 13%, respectively as shown in Table B.6.9 (see Appendix B). In addition, a
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Figure 6.7: DFFCs based on the adopted different IED mean values for the Oxley River catchment
Figure 6.8: DFFCs based on the adopted different IED mean values for the Bielsdown Creek catchment
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Figure 6.9: DFFCs based on the adopted different IED mean values for the Belar Creek catchment
However, a 50% increase in the IED mean value for the Oxley River shows under-estimation by up to 29% in the DFFCs. In contrast, a 50% decrease in the IED data causes an over- estimation by up to 62% in the flood quantile estimates (see Table B.6.7 in Appendix B). For the Bielsdown Creek, a 50% increase in the mean value of IED has also shown an under- estimation by up to 29%. However, a 50% decrease presents an overall over-estimation in the flood quantile estimates by up to 66% (see Table B.6.8 in Appendix B). For the Belar Creek, a 50% increase demonstrates an overall under-estimation in the flood quantile estimates by up to 13%. In contrast, the reduction of 50% has shown an overall over-estimation in flood quantiles by up to 51% (see Table B.6.9 in Appendix B).
Use of different standard deviation values of the IED data for the Oxley River, Bielsdown Creek and Belar Creek catchments show a relatively moderate variability with up to 50% variation in the flood quantile estimates as presented in Figures 6.10, 6.11 and 6.12. An increase and decrease by up to 20% in the standard deviation of the IED value for the Oxley River show an over- and under-estimation by up to 8% in flood quantile estimates as indicated in Table B.6.10 (see Appendix B). For the Bielsdown Creek, the 5% to 20% increases in the standard deviation values show an overall over-estimation in the flood quantile estimates by up to 8%; whereas, a 5% to 20% decrease causes an over- and under-
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Figure 6.10: DFFCs based on the adopted different standard deviation values of IED for the Oxley River catchment
Figure 6.11: DFFCs based on the adopted different standard deviation values of IED for the Bielsdown Creek catchment University of Western Sydney Page 165
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Figure 6.12: DFFCs based on the adopted different standard deviation values of IED for the Belar Creek catchment
An increase of 50% in the standard deviation of the IED, results in up to 24% over-estimation in flood quantile estimates for the Oxley River catchment; while a 50% decrease demonstrates under-estimation in the flood quantile estimates by up to 12% as shown in Table B.6.10 (see Appendix B). For the Bielsdown Creek, a 50% increase results in up to 21% over-estimation in the flood quantile estimates; while 50% decrease shows under- estimation by up to 5% as demonstrated in Table B.6.11 (see Appendix B). For the Belar Creek, a change by ± 50% shows mixed results, with over- and under-estimation in the flood quantile estimates by up to 6% and 11%, respectively (as shown in Table B.6.12, Appendix B).
6.4.4 Summary of the sensitivity analysis for rainfall IED
Based on the investigations presented in this section, it is found that a small variation by about 20% to the mean value of the IED data would not have a significant impact on the DFFCs. However, a variation by about 50% to the mean value of the IED would have significant effects by about 29% to 66% on the DFFCs; whereas, a variation by about 50% in standard deviation values of the IED data would not have that much significant effects on the DFFCs. This shows that the IED mean is more sensitive to DFFC as compared to the IED standard deviation. University of Western Sydney Page 166
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6.5 Sensitivity analysis for rainfall intensity-frequency-duration (IFD) data
Similar to the rainfall DCS and IED, the effects of sampling variability/uncertainty in the rainfall IFD data on the resulting flood quantiles are also examined. The IFD data at a site of interest are estimated from the IFD data of the nearby pluviograph stations using Inverse Distance Weighted Averaging method as discussed in Section 5.6. In the adopted sensitivity analysis, the numbers of nearby pluviograph stations are varied using different station combinations for each of the catchment of interests to obtain weighted average IFD data at the location of interest. These analyses are presented below.
6.5.1 Sensitivity analysis: intensity-frequency-duration (IFD)
In this sensitivity analysis, changes to the number of pluviograph stations (from one to nine) are made to achieve a possible variation in the IFD data at a location of interest. For example, the regional IFD data for the Oxley River catchment is first derived from five nearest pluviograph stations (i.e. stations ID 58109, 58129, 58113, 58158 and 58044). This is then recalculated from the two nearest pluviograph stations (i.e. stations ID 58109 and 58129). The number of IFD stations are then varied to three, four and up to nine nearby pluviograph stations. The selected pluviograph stations and their respective distances for each of the three catchments (the Oxley River, Bielsdown Creek and Belar Creek) are shown in Tables 6.8, 6.9 and 6.10.
Table 6.8: Pluviograph station numbers and distances for the Oxley River catchment Using the IFD/TP of station (ID 58109) with distance 2.36 km and the Input Base station ID: parameter station 2nd 3rd 4th 5th 6th 7th 8th 9th Combined All (20) 58129 58113 58158 58044 58026 58072 58131 56022 IFD/TP Distances (km) within 200 14.08 16.51 18.81 26.87 36.52 41.91 60.93 83.03
Table 6.9: Pluviograph station numbers and distances for the Bielsdown Creek catchment Using the IFD/TP of station (ID 59067) with distance 1.74 km and the Input Base station ID: parameter station 2nd 3rd 4th 5th 6th 7th 8th 9th Combined All (20) 59026 59040 59000 57103 59017 57091 56013 58099 IFD/TP Distances (km) within 200 28.26 40.70 54.31 76.46 81.49 90.57 121.38 122.46
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Table 6.10: Pluviograph station numbers and distances for the Belar Creek catchment (ID 420003) Using the IFD/TP of station (ID 64046) with distance 7.24 km and the Input Base station ID: parameter station 2nd 3rd 4th 5th 6th 7th 8th 9th Combined All (12) 62005 55024 65035 51049 61287 55194 55054 54138 IFD/TP Distances (km) within 200 110.45 114.65 131.01 132.55 137.37 164.78 166.66 178.82
6.5.2 Derived flood frequency curves using different IFD data
Based on the procedure in Section 6.5.1, the DFFCs are computed using the weighted IFD data from five pluviograph stations and the base values listed in Table 6.1 for the Oxley River catchment in the first simulation run. The weighted IFD data from five pluviograph stations is then substituted with the new IFD data from two pluviograph stations and up to nine pluviograph stations in the succeeding simulation runs, while the other model inputs are kept fixed. Further, this procedure is applied using the IFD data from the individual pluviograph stations. This procedure is then repeated to the two other test catchments (i.e. the Bielsdown Creek and Belar Creek).
6.5.3 Results of the sensitivity analysis for rainfall IFD data
The DFFCs using the different sets of IFD data (as calculated above) for the Oxley River, Bielsdown Creek and Belar Creek catchments show small to moderate variability in flood quantile estimates (see Figures 6.13, 6.14 and 6.15). The differences in the flood quantile estimates for the Oxley River are found to be fewer than 5% for all the combinations as shown in Table B.6.13 (see Appendix B). Similar results are found for the Bielsdown Creek, the DFFCs using the adopted new IFD data also show a small variability. The differences in DFFCs are up to 12% as listed in Table B.6.14 (see Appendix B) and these are caused by the increase of number of pluviograph stations for this particular catchment. For the Belar Creek catchment, the differences in DFFCs increase as the distances of the pluviograph stations increase. Example of increasing differences is (for ARI 100 years), within -9% using two pluviograph stations to -24%, with nine stations as shown in Table B.6.15 in Appendix B.
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Figure 6.13: DFFCs based on the adopted different IFD data combinations for the Oxley River catchment
Figure 6.14: DFFCs based on the adopted different IFD data combinations for the Bielsdown Creek catchment
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Figure 6.15: DFFCs based on the adopted different IFD data combinations for the Bielsdown Creek catchment
Use of the IFD data from the single nearest pluviograph station, the DFFCs for the Oxley River, Bielsdown Creek and Belar catchments indicates a wider variability (as illustrated in Figures 6.16, 6.17 and 6.18) as compared to the results using the IFD data derived from a set of nearby stations. The differences in the flood quantile estimates for the Oxley River catchment appear to be mixed with over-estimation of up to 26% and under-estimation of up to 48% as listed in Table B.6.16 (see Appendix B). These results show that the combined IFD data for this catchment is preferable to use. For the Bielsdown Creek, the differences in DFFCs using the IFD data from individual pluviograph stations are up to 74% under- estimation with some over-estimation up to 9% as presented in Table B.6.17 (see Appendix B). For the Belar Creek, the differences in the DFFCs are even bigger when the IFD data of the individual pluviograph station is used. The differences in the flood quantile estimates range from -27% to -81% as shown in Table B.6.18 (see Appendix B).
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Figure 6.16: DFFCs based on the adopted IFD data from each set of pluviograph stations for the Oxley River catchment
Figure 6.17: DFFCs based on the adopted IFD data from each set of pluviograph stations for the Bielsdown Creek catchment
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Figure 6.18: DFFCs based on the adopted IFD data from each set of pluviograph stations for the Belar Creek catchment
6.5.4 Summary of the sensitivity analysis for intensity-frequency-duration (IFD) data
In summary, the sensitivity analysis for rainfall IFD data using the different combinations of IFD data (using stations within 30 km) shows that the regional IFD data does not show significant sensitivity to DFFCs as the change in the flood estimates are less than 10% (and up to 24% for Belar Creek only). However, if there are only few (e.g. two) nearby pluviograph stations, the regional IFD data is quite unstable. In addition, the sensitivity of the weighted IFD data are checked against the IFD data of the individual pluviograph station, the results show that the use of weighted IFD data provides better flood quantile estimates as compared to the estimates using IFD data from individual pluviograph station. The differences in the flood estimates range from 9% to 81% for the three test catchments.
6.6 Sensitivity analysis for temporal patterns (TP) data
Similar to the IFD data, the regionalised TP data sets are calculated using different combinations of nearby pluviograph stations and their impacts on DFFCs are examined in
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6.6.1 Sensitivity analysis: temporal patterns (TP)
A variation from two to nine pluviograph stations is applied to derive different sets of dimensionless TP database. For example, the TP data of the two pluviograph stations (e.g. stations ID 58109 and 58129) with distances 2.36 km and 14.08 km, respectively, are used to derive first set of TP data. The succeeding sets of TP database are derived based on three, four and up to nine pluviograph stations. The number of nearest pluviograph stations and their respective distances for the three catchments (the Oxley River, Bielsdown Creek and Belar Creek) are shown in Tables 6.8, 6.9 and 6.10 (see Section 6.5.1).
6.6.2 Derived flood frequency curves using different sets of TP data
The DFFC are computed using pooled TP data of up to 20 (maximum) pluviograph stations and the base values (see Table 6.1) of other parameter inputs for the Oxley River catchment in the first simulation run. The original set of pooled TP database is then substituted with the pooled TP database for the two and up to nine pluviograph stations in the succeeding simulation runs; while the other design inputs are kept fixed. The pooling of the TP data has been described in Section 3.8. This procedure is repeated for the two other test catchments (i.e. the Bielsdown Creek and Belar Creek).
6.6.3 Results of the sensitivity analysis for temporal patterns (TP)
The DFFCs using the different sets of pooled TP data adopted for the Oxley River, Bielsdown Creek and Belar catchments show mixed results as illustrated in Figures 6.19, 6.20 and 6.21. For the Oxley River, the differences in the flood quantile estimates is found to be under 15% as demonstrated in Table B.6.19 (see Appendix B). For the Bielsdown Creek, the differences in the flood quantile estimates are up to 11% as shown in Table B.6.20 (see Appendix B). For the Belar Creek, the differences in flood quantile estimates are up to 9% as listed in Table 6.21 (see Appendix B).
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Figure 6.19: DFFCs based on the adopted different sets of pooled TP data for the Oxley River catchment
Figure 6.20: DFFCs based on the adopted different pooled TP data for the Bielsdown Creek catchment
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Figure 6.21: DFFCs based on the adopted different sets of pooled TP data for the Belar Creek catchment
6.6.4 Summary of the sensitivity analysis for temporal pattern (TP) data
In summary, it is found that the TP data of different sets does not show significant sensitivity to DFFCs. For the three catchments examined here, the differences in floods quantiles range from 9% to 15%, with the Oxley River catchment showing the highest degree of sensitivity.
6.7 Sensitivity analysis for initial loss (IL) data
In order to check the effects of uncertainties in the IL data on the resulting DFFCs, the distributional parameters of IL are varied within a margin of expected variation. The IL data is generated using a gamma distribution (see Section 5.8 for details). Consequently, to check its sensitivity, the values of the mean and standard deviation of the IL data (i.e. the parameters of the gamma distribution) are subject to variation.
6.7.1 Sensitivity analysis: initial loss (IL)
Similar to the sensitivity analyses of the DCS and IED, the values of the mean and standard deviation of the IL data are increased and decreased by 5%, 10%, 20% and 50%. As an example, the value of IL mean for the Oxley River catchment is 7.24 mm (base value); by adding 5%, it becomes 7.60 mm. The decrease of 5% makes it to be 6.88 mm. The adjusted
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IL mean values for the three catchments, as shown in Tables 6.11, 6.12 and 6.13, are then used in the simulations.
Table 6.11: Adjusted IL mean and standard deviation values for the Oxley River catchment
Input Base Percentage (%) increase Percentage (%) decrease Parameter value 5 10 20 50 5 10 20 50 mean IL (mm) 7.24 7.60 7.96 8.69 10.86 6.88 6.51 5.79 3.62 stdev IL (mm) 4.68 4.92 5.15 5.62 7.03 4.45 4.22 3.75 2.34
Table 6.12: Adjusted IL mean and standard deviation values for the Bielsdown Creek catchment
Input Base Percentage (%) increase Percentage (%) decrease parameter value 5 10 20 50 5 10 20 50 mean IL (mm) 13.61 14.29 14.97 16.34 20.42 12.93 12.25 10.89 6.81 stdev IL (mm) 5.92 6.22 6.51 7.11 8.88 5.63 5.33 4.74 2.96
Table 6.13: Adjusted IL mean and standard deviation values for the Belar Creek catchment
Input Base Percentage (%) increase Percentage (%) decrease parameter value 5 10 20 50 5 10 20 50 mean IL (mm) 36.90 38.75 40.59 44.28 55.35 35.06 33.21 29.52 18.45 stdev IL (mm) 19.25 20.21 21.18 23.10 28.88 18.29 17.33 15.40 9.63
6.7.2 Derived flood frequency curves using the adjusted IL values
The procedures used in Sections 6.3.2 and 6.4.2 are also applied to the IL for the three catchments (the Oxley River, Bielsdown Creek and Belar Creek). For example, the mean value of the IL (7.24 mm) is replaced by the adjusted IL mean value (e.g. 7.60 mm) in the succeeding simulation runs while keeping the other design inputs fixed.
6.7.3 Results of the sensitivity analysis for IL
The DFFCs based on the different mean values of the IL data for the Oxley River, Bielsdown Creek and Belar Creek catchments exhibit relatively small differences in DFFCs as shown in Figures 6.22, 6.23 and 6.24. The change by up to ± 20% in the IL mean value for the Oxley River demonstrates an overall under- and over-estimation by up to 8% in the flood quantile estimates as shown in Table B.6.22 (see Appendix B). For the Bielsdown Creek, an increases
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Enhanced Joint Probability Approach Caballero in the IL mean by up to 20% shows a relatively smaller over- and under-estimation by up to 3% and 6%, respectively; while the decrease in IL mean by up to 20% causes over-estimation in flood quantiles by up to 10% as shown in Table B.6.23 (see Appendix B). For the Belar Creek, a variation by up to ± 20% causes under- and over-estimation in flood quantiles by up to 16% and 17% as shown in Table B.6.24 in Appendix B.
Figure 6.22: DFFCs based on the adopted different IL mean values for the Oxley River catchment
Figure 6.23: DFFCs based on the adopted different IL mean values for the Bielsdown Creek catchment University of Western Sydney Page 177
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Figure 6.24: DFFCs based on the adopted different IL mean values for the Belar Creek catchment
A 50% increase in the mean value of IL data for the Oxley River catchment causes under- estimation by up to 22% in the flood quantile estimates. In contrast, a 50% decrease causes an over-estimation in flood quantile estimates by up to 19% as listed in Table B.6.22 (see Appendix B). For the Bielsdown Creek, a ± 50% change shows an under- and over- estimation in the flood quantile estimates by up to 16% and 17%, respectively as shown in Table B.6.23 (see Appendix B). For the Belar Creek catchment, a 50% increase in the mean IL causes an overall under-estimation by up to 41% in the flood quantile estimates. While the reduction of 50% in IL mean causes an over-estimation by up to 40% in flood quantile estimates (see Table B.6.24 in Appendix B).
Using the different arbitrary standard deviation values of the IL data for the Oxley River, Bielsdown Creek and Belar Creek catchments, the differences in the DFFCs are found to be quite small. The differences in the flood quantile estimates with the increase and decrease by up to 50% cause about 5% variation in the resulting flood quantile estimates as illustrated in Table B.6.25 (see Appendix B). For the Bielsdown Creek, a change up to ± 50% in the IL standard deviation value shows an over- and under-estimation of about 6% in the flood quantile estimates as presented in Table B.6.26 in Appendix B. For the Belar Creek catchment, a change of up to ± 50% in the IL standard deviation values causes an over- and
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Enhanced Joint Probability Approach Caballero under-estimation in the flood quantile estimates in the range of 7% (in one case a 13% over- estimation is noticed) as shown in Table B.6.27 (see Appendix B).
Figure 6.25: DFFCs based on the adopted different IL standard deviation values for the Oxley River catchment
Figure 6.26: DFFCs based on the adopted different IL standard deviation values for the Bielsdown Creek catchment
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Figure 6.27: DFFCs based on the adopted different IL standard deviation values for the Belar Creek catchment
6.7.4 Summary of the sensitivity analysis for initial loss (IL) data
In summary, a change by up to 20% in the IL mean can cause an under- and over-estimation of flood quantiles by up to 20%. A change by 50% to the mean of IL data can cause under- and over-estimation in flood quantiles by about 40%. With regard to the change in the standard deviation of IL data, an increase by up to 50% can cause an over- and under- estimation in the flood quantiles by up to 15%. These results show that the IL mean is more sensitive to DFFCs as compared to the IL standard deviation. Overall, IL shows a significant sensitivity to the DFFCs.
6.8 Sensitivity analysis for continuing loss (CL) data
The CL values are generated by an exponential distribution as discussed in Section 5.9. Thus, in order to check the effects of uncertainties in the CL data on the flood quantile estimates, variations are to be made in the mean value of the CL data. These variations are applied to the CL mean values for the three catchments to check their sensitivity.
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6.8.1 Sensitivity analysis: continuing loss (CL)
The base values of the CL mean are changed by increase and decrease of 5%, 10%, 20% and 50%. For example, the base value of the CL mean for the Oxley River catchment is 0.85 mm/h; by adding 5% to this base value, the new CL mean becomes 0.89 mm/h. Similarly, the 5% decrease in the CL mean make the new CL value equals to 0.81 mm/h. Tables 6.14, 6.15 and 6.16 present the adjusted CL mean values for the three catchments. The adjusted CL mean values are then used in the simulation to obtain DFFCs.
Table 6.14: Adjusted values of CL mean for the Oxley River catchment
Base Percentage (%) increase Percentage (%) decrease Input Parameter value 5 10 20 50 5 10 20 50 mean CL (mm/h) 0.85 0.89 0.94 1.02 1.28 0.81 0.77 0.68 0.43
Table 6.15: Adjusted values of CL mean for the Bielsdown Creek catchment
Base Percentage (%) increase Percentage (%) decrease Input parameter value 5 10 20 50 5 10 20 50 mean CL (mm/h) 0.57 0.60 0.63 0.69 0.86 0.54 0.52 0.46 0.29
Table 6.16: Adjusted values of CL mean for the Belar Creek catchment
Base Percentage (%) increase Percentage (%) decrease Input parameter value 5 10 20 50 5 10 20 50 mean CL (mm/h) 5.64 5.92 6.20 6.77 8.46 5.36 5.08 4.51 2.82
6.8.2 Derived flood frequency curves using the adjusted CL values
Using the three catchments, the procedures described in Sections 6.3.2, 6.4.2 and 6.7.2 are also applied to the CL data. In this analysis, the CL mean value of 0.85 mm/h is replaced with the adjusted CL mean values (e.g. 0.89 mm/h) in the simulation runs while keeping the other design inputs fixed. The simulation run results are then compared to the base flood quantile estimates to check the differences in the DFFCs for different mean values of CL.
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6.8.3 Results of the sensitivity analysis for continuing loss
The results of the sensitivity analyses are displayed in Figures 6.28, 6.29 and 6.30. These show relatively smaller variability in DFFCs for the Oxley River, Bielsdown Creek and Belar Creek catchments. The differences in the flood quantile estimates with the change of up to ± 20% in the CL mean value for the Oxley River demonstrate an under- and over-estimation by up to 4% in the flood quantile estimates as shown in Table B.6.28 (see Appendix B). For the Bielsdown Creek, the change in CL mean by up ± 20% causes in an under- and over- estimation by up to 4% in the flood quantile estimates as listed in Table B.6.29 (see Appendix B). For the other two catchments, the change by up to ± 20% in the CL mean values demonstrates an under- and over-estimation up to 5% in the flood quantile estimates as presented in Table B.6.30 (see Appendix B).
Figure 6.28: DFFCs based on the adopted different CL mean values for the Oxley River catchment
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Figure 6.29: DFFCs base on the adopted different CL mean values for the Bielsdown Creek catchment
Figure 6.30: DFFCs base on the adopted different CL mean values for the Belar Creek catchment
A ± 50% change in the mean CL value for the Oxley River and Bielsdown Creek catchments causes an under- and over-estimation by up to 10% in flood quantile estimates. For the Belar Creek, 50% increase causes an overall under-estimation by up to 9%; whereas, the decrease
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6.8.4 Summary of the sensitivity analysis for continuing loss
A variation by up to ± 20% to the CL mean could under- and over-estimate the resulting flood quantiles by up to 5%. Similarly, a variation of ± 50% to the CL mean could cause under- and over-estimation of flood quantiles by up to 14%. These results indicate that the error by up to ± 20% to the CL mean values would not have significant effects on the DFFCs. In contrast, the changes by ± 50% to the CL mean values would have a moderate effect on the DFFCs.
6.9 Sensitivity analysis for storage delay parameter (k)
The k values are generated from a gamma distribution in the simulation to obtain DFFCs. Accordingly; the values of mean and standard deviation of the observed k data are varied for the three catchments in the analysis.
6.9.1 Sensitivity analysis: Storage delay parameter (k)
To vary the k data, the values of the mean and standard deviation of the observed k values are varied by an increase and decrease of 5%, 10%, 20% and 50%. For example, the base value of the mean k for the Oxley River catchment is 11.47 h; this base value is then increased by 5% that gives a k value equals to 12.04 h. Similarly, a 5% decrease to the mean of the observed k value makes a new k value of 10.89 h. These adjusted k mean values for the three catchments are presented in Tables 6.17, 6.8 and 6.19. The adjusted k mean values are then used to obtain the DFFCs.
Table 6.17: Adjusted k mean and standard deviation values for the Oxley River catchment
Input Base Percentage (%) increase Percentage (%) decrease Parameter value 5 10 20 50 5 10 20 50 mean k (h) 11.47 12.04 12.61 13.76 17.20 10.89 10.32 9.17 5.73 stdev k (h) 1.04 1.09 1.15 1.25 1.56 0.99 0.94 0.83 0.52
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Table 6.18: Adjusted k mean and standard deviation values for the Bielsdown Creek catchment
Input Base Percentage (%) increase Percentage (%) decrease parameter value 5 10 20 50 5 10 20 50 mean k (h) 5.83 6.12 6.41 7.00 8.75 5.54 5.25 4.66 2.92 stdev k (h) 2.82 2.96 3.10 3.38 4.23 2.68 2.54 2.26 1.41
Table 6.19: Adjusted k mean and standard deviation values for the Belar Creek catchment
Input Base Percentage (%) increase Percentage (%) decrease parameter value 5 10 20 50 5 10 20 50 mean k (h) 26.99 28.34 29.69 32.39 40.49 25.64 24.29 21.59 13.50 stdev k (h) 6.33 6.65 6.96 7.60 9.50 6.01 5.70 5.06 3.17
6.9.2 Derived flood frequency curves using the adjusted k values
In the simulation runs, the k mean value of 11.47 h is replaced with the adjusted k mean value (e.g. 12.04 h) while keeping the other design inputs fixed. To check the sensitivity in the DFFCs for different mean k values, the resulting DFFCs are compared as discussed below.
6.9.3 Results of the sensitivity analysis for storage delay parameter
The DFFCs using the adopted different mean values of k for the Oxley River, Bielsdown Creek and Belar Creek catchments exhibit a moderate variation for up to 20% change as shown in Figures 6.31, 6.32 and 6.33. The increases in mean k value by up to 20% for the Oxley River demonstrate an overall under-estimation by up to 13% in the flood quantile estimates; whereas, a decrease by up to 20% in the mean k causes an over-estimation by up to 16% in DFFCs as shown in Table B.6.31 (Appendix B). For the Bielsdown Creek, an increase by up to 20% causes under-estimations in the flood quantile estimates by up to 11%; while a decrease by up to 20% demonstrates mainly over-estimations in flood quantiles by up to 22% as presented in Table B.6.32 (Appendix B). For the Belar Creek, the differences in mean k causes an under-estimation by up to 13% in the flood quantile estimates with the increase by up to 20% in the mean value of k as presented in Table B.6.35 (Appendix B). In contrast, a decrease by up to 20% in mean k causes an over-estimation in DFFCs by up to 20%.
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Figure 6.31: DFFCs based on the adopted different k mean values for the Oxley River catchment
Figure 6.32: DFFCs based on the adopted different k mean values for the Bielsdown Creek catchment
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Figure 6.33: DFFCs based on the adopted different k mean values for the Belar Creek catchment
A 50% increase in the value of mean k for the Oxley River causes under-estimations by up to 27% in the flood quantile estimates as shown in Table B.6.31. In contrast, a 50% decrease in the mean k exhibits a significant over-estimation in DFFCs by up to 57%. For the Bielsdown Creek catchment, the 50% increase in the value of mean k causes an under-estimation by up to 24% in the flood quantile estimates; while a 50% decrease causes significant over- estimations (by 61% to 95%) in the DFFCs (see Table B.6.32 in Appendix B). For the Belar Creek catchment, a 50% increase in the mean k value cause an overall under-estimation by up to 28% in the flood quantile estimates; while a decrease of 50% causes a significant over- estimation in DFFCs (by 63% to 71%).
Using the adopted different standard deviation values of k data for the Oxley River, Bielsdown Creek and Belar Creek catchments, the DFFCs are found to show moderate differences with up to 20% variation in DFFCs as shown in Figures 6.34, 6.35 and 6.36. A variation by up to ± 20% in the standard deviation values of k, the variations in the DFFCs for the Oxley River catchment are found to be up to 3% as shown in Table B.6.34 (Appendix B). For the Bielsdown Creek, an increase by up to 20% in the standard deviation of k value causes an over-estimation by up to 10% in the flood quantile estimates; whereas, a decrease by up to 20% in the standard deviation of k value causes an under-estimation in flood
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Enhanced Joint Probability Approach Caballero quantiles by up to 4% as presented in Table B.6.35 (Appendix B). For the Belar Creek, an increase by up to 20% in the standard deviation of k value causes an over-estimation in the flood quantile estimates by up to 4% as can be seen in Table B.6.36 (Appendix B). In contrast, a decrease by up to 20% in the standard deviation of k value causes an under- estimation by up to 9% in the DFFCs.
An increase by 50% in the standard deviation value of k data for the Oxley River causes an over-estimation by up to 10% and an under-estimation by up to 7% with the 50% decrease (see Table B.6.34 in Appendix B). For the Bielsdown Creek, the 50% increase in the standard deviation of k value causes mainly over-estimation by up to 21% in the DFFCs; while the 50% decrease exhibits an under-estimation by up to 9% as shown in Table B.6.35 (Appendix B). For the Belar Creek, a 50% increase in the standard deviation of k value causes an over- estimation by up to 11% and under-estimation by up to 10% (with the 50% decrease) as listed in Table B.6.36 (see Appendix B).
Figure 6.34: DFFCs based on the adopted different k stdev values for the Oxley River catchment
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Figure 6.35: DFFCs based on the adopted different k stdev values for the Bielsdown Creek catchment
Figure 6.36: DFFCs based on the adopted different k stdev values for the Belar Creek catchment
6.9.4 Summary of the sensitivity analysis for storage delay parameter (k) data
The results indicate that an error by up to ± 20% to the mean values in the k data would have moderate effects in the DFFCs (up to about 20% under- and over-estimation). However, a 50% change in the mean k data would have major effects on DFFCs (up to about 30% under- University of Western Sydney Page 189
Enhanced Joint Probability Approach Caballero estimation and 60% to 95% over-estimation). With regard to standard deviation of the k data, the results show that up to ± 20% variation of the standard deviation values would have minor to moderate effects on the DFFCs (up to about 10% under- and over-estimation). Though, the 50% change in the standard deviation of the k data would have a notable effect on DFFCs (up to about 10% to 20% under- and over-estimation). Therefore, it can be argued that the k is more sensitive on DFFCs with the change in its mean value rather than its standard deviation.
6.10 Summary of Chapter 6
This chapter has examined the sensitivity of the regionalised distributions on the DFFCs in the proposed EMCST. Here, the distributional parameters i.e. the mean and standard deviation values of DCS, IED, IL, CL (mean only), and k data are varied within an arbitrary range e.g. 5%, 10%, 20% and 50%. The number of pluviograph stations are varied arbitrarily (from one to nine) to obtain different sets of IFD and pooled TP database. Based on the results of the sensitivity analyses, the input variables and storage delay parameter are arranged as follows (the most sensitive to less sensitive ones): k (-30% to 95%), IED (-29% to 60%), DCS (-30% to 50%), IL (-40% to 40%), IFD (10% to 24%), TP (9% to 15%) and CL (-10% to 14%).
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Enhanced Joint Probability Approach Caballero CHAPTER 7 Validation of the Developed Enhanced Monte Carlo Simulation Technique
7.1 Introduction
Chapter 6 has presented the sensitivity of the regionalised distributions in the application of the Enhanced Monte Carlo Simulation Technique (EMCST). This chapter presents the validation of the developed regionalised EMCST to assess its performance in the estimation of design floods. The validation is conducted by comparing the estimated flood quantiles from the new EMCST with the currently recommended Design Event Approach (DEA) of Australian Rainfall and Runoff (ARR) 1987, the ARR Regional Flood Frequency Estimation 2012 (ARR-RFFE 2012) model (test version), the Probabilistic Rational Method (PRM) of ARR 1987 and the at-site Flood Frequency Analysis (FFA) estimates for a set of test catchments. The chapter begins with the discussion of the selected test catchments used for the validation. This is followed by the derivation of the flood frequency curves using at-site FFA for the selected test catchments. The design flood estimation using the DEA is then presented. It is then followed by the estimation of design flood using the new EMCST. Then, the design flood estimation using the ARR-RFFE 2012 model (test version) is presented. The design flood estimation using the PRM is presented at the end. Finally, the estimated floods obtained from these different methods are compared using model evaluation statistics i.e. the relative error (RE), ratio (R), relative mean bias (BIAS) and relative root mean square error (RMSE).
It should be noted here that the error values, obtained using these statistics are not a measure of true error associated with the EMCST and other methods since at-site FFA estimates are not error free. For example, the true distribution of annual maximum flood data may not be the LP3; however, LP3 has been used in this study to estimate at-site quantiles as recommended in ARR 1987 (I. E. Aust., 1987). The parameter estimation procedure is not
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Enhanced Joint Probability Approach Caballero error free and there are number of methods available to estimate parameters of the LP3 distribution; here product moment Bayesian parameter estimation procedure has been adopted. The annual maximum flood series data are subject to sampling variability (due to limitation in record length). Furthermore, the annual maximum flood data are subject to a high degree of rating curve error (sometimes up to 50% or higher for 50 and 100 years flood events) (Haddad et al., 2010b). These all affect the accuracy of at-site flood quantiles which are deemed as “accurate” values in the validation.
7.2 Selection of test catchments for validation
In order to check the validity of the new EMCST, the catchments listed in Table 4.3 are used to represent two ranges of catchment sizes: (i) small: the Bielsdown Creek (76 km2) and the West Brook River (80 km2); (ii) medium: the Belar Creek (133 km2), the Orara River (135 km2), the Oxley River (213 km2) and the Wilsons River (223 km2) catchments.. The selected catchments capture a good variability in catchment sizes which provide an opportunity to check the validity of the new EMCST for different catchment sizes within small to medium range. These catchments also have a relatively longer streamflow records (at least 30 years of data). In particular, the concurrent rainfall and streamflow record lengths are also relatively longer, minimum of 30 years as shown in Table 4.4. From these rainfall and streamflow records, model inputs and parameters for the selected test catchments are derived for application of the new EMCST as shown in Table 7.1. The following section describes the derivation of the flood frequency curves using the at-site FFA.
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Table 7.1: Model inputs and parameters for the application of the new EMCST for the six test catchments Oxley Wilsons Bielsdown Orara West Brook Belar Parameter inputs River River Creek River River Creek mean IED (day) 104.05 89.60 79.13 77.36 69.60 41.96 stdev IED (day) 126.39 114.85 97.44 94.38 87.79 48.77
mean DCS (hour) 38.27 36.88 40.73 39.09 25.53 22.06
stdev DCS (hour) 33.75 29.89 41.52 32.75 22.42 19.99 mean IL (mm) 7.24 18.92 13.61 44.99 13.20 36.90 stdev IL (mm) 4.68 12.11 5.92 29.87 5.67 19.25 median IL (mm) 8.66 21.25 14.30 22.30 13.39 47.37 mean CL (mm/h) 0.85 0.73 0.57 3.95 0.26 5.64 median CL (mm/h) 0.81 0.74 0.60 1.45 0.29 6.05 mean k(h) 11.47 44.62 5.83 26.56 4.83 26.99 stdev k(h) 1.04 5.01 2.82 8.19 1.81 6.33 median k(h) 10.89 45.14 7.35 17.54 4.71 24.20 median BF (m3/s) 1.64 3.62 1.68 2.80 0.04 0.22
7.3 Derivation of the flood frequency curves using at-site Flood Frequency Analysis (FFA)
For this analysis, the annual maximum flood series are prepared for the six selected test catchments. As an example, the observed annual maximum flood peaks (m3/sec) for the Oxley River catchment are shown in Table 7.2. The observed annual maximum flood peaks for the other five catchments are shown in Tables B.7.1 to B.7.5 (see Appendix B).
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Table 7.2: Annual maximum flow data for the Oxley River catchment
Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) 1958 524.23 1972 1047.76 1986 24.46 2000 63.26 1959 792.58 1973 595.06 1987 1243.58 2001 1129.73 1960 37.23 1974 1288.81 1988 718.07 2002 6.11 1961 428.92 1975 178.70 1989 1590.56 2003 75.25 1962 688.61 1976 714.00 1990 637.09 2004 768.29 1963 193.48 1977 112.44 1991 740.02 2005 263.87 1964 132.51 1978 716.08 1992 97.60 2006 155.44 1965 743.27 1979 278.34 1993 51.38 2007 110.23 1966 96.38 1980 524.00 1994 57.98 2008 1520.68 1967 453.55 1981 203.42 1995 210.66 2009 402.64 1968 510.07 1982 323.95 1996 718.02 2010 544.28 1969 113.81 1983 450.84 1997 94.85 2011 319.11 1970 688.32 1984 495.52 1998 399.74
1971 289.43 1985 202.85 1999 277.30
Using the observed annual maximum flood peaks for each of the selected test catchments, the at-site FFA estimates and the 90% confidence limits are estimated by applying the FLIKE software (Kuczera, 1999). The results for the Oxley River catchment are presented in Table 7.3. For the other five test catchments, the results are provided in Tables B.7.6 to B.7.10 in Appendix B. Plots of these at-site FFA estimates and the associated confidence limits are also shown in Figure 7.1 to visualise how the fitted at-site flood frequency curves match the observed annual maximum flood peaks. In addition, rating ratios (RRs) with higher ARI flood values are included in the plot to show the RR of the higher flood peaks, which reflects the uncertainty associated with these reported flood data. Here, RR is the ratio of reported discharges and the highest measured discharge at a site as explained in Haddad et al. (2010b). The higher the RR, the greater is the uncertainty in the reported peak flood value.
The at-site FFA plots of the other five test catchments are provided in Figures C.7.1 to C.7.5 (see Appendix C).
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Table 7.3: At-site FFA estimates and 90% confidence limits for the Oxley River catchment
ARI (y) LP3 - expected quantiles LP3 - 5% confidence limit LP3 - 95% confidence limit 1.01 14.03 4.66 31.64 1.1 69.83 41.42 105.92 1.25 136.71 95.54 190.11 1.5 225.28 170.19 298.82 1.75 297.74 229.94 389.05 2 359.49 280.52 462.82 3 542.97 434.05 681.79 5 766.38 621.69 955.26 10 1054.6 863.03 1339.81 20 1323.75 1076.9 1774.1 50 1648.38 1312.93 2436.41 100 1870.22 1449.38 2988.97 200 2072.19 1553.93 3620.59 500 2310.29 1655.69 4527.43
Figure 7.1: At-site FFA estimates for the Oxley River catchment
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7.4 Derivation of flood quantiles using Design Event Approach (DEA)
Using the DEA procedure described in Sections 3.13.2 with its predetermined storm duration values, median values of IL, CL, k and BF (listed in Table 7.1), and catchment areas (as listed in Table 4.3), flood quantiles are obtained for the six test catchments. The flood quantiles are summarised in Table 7.4 with their predetermined storm durations and specified ARIs for the Oxley River catchment. From this table, the flood quantiles (bold text) for the 12-hour duration are taken as the DEA estimates for the Oxley River catchment as it represents the highest values corresponding to the critical duration of 12-hour.
Similarly, for the other five test catchments, the DEA-based flood quantiles (bold text) are estimated, which are provided in Tables B.7.11 to B.7.15 (see Appendix B). For the Wilsons River catchment, the majority of the flood quantiles are found to be the highest for 48-hour duration, but with one for 12-hour duration and another for 72-hour duration. For the Bielsdown Creek catchment, the 24-hour duration is found to be the critical duration. For the Orara River catchment, the critical duration is found to be 48-hour. For the West Brook River catchment, the critical duration is found to be 12-hour. For the Belar Creek catchment, the critical duration ranges from 6-hour to 72-hour.
Table 7.4: Flood quantiles (m3/s) summary for the Oxley River catchment using DEA Flood 1-hr 2-hr 3-hr 6-hr 12-hr 24-hr 48-hr 72-hr quantiles
Q2 536.95 706.88 767.52 804.09 859.73 776.36 508.70 498.71
Q5 765.33 1009.94 1080.11 1143.15 1251.43 1144.90 740.25 720.55
Q10 910.21 1189.83 1267.98 1344.37 1492.78 1377.55 887.65 863.61
Q20 1123.14 1424.66 1526.48 1619.64 1811.41 1689.95 1079.90 1049.51
Q50 1389.93 1793.43 1878.33 1933.74 2084.64 1894.51 1244.50 1241.80
Q100 1593.21 2058.11 2151.72 2214.64 2409.34 2201.73 1433.78 1435.71
The time of concentration (tc) for the six test catchments are computed (Table 7.5) using equation 3.28 (the recommended equation for eastern NSW in ARR1987) to compare it with the duration that produces the highest flood peak (I. E. Aust., 1987). The values of the computed tc are too low as compared with the identified time of concentration from the
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application of the DEA. The only value of the computed tc close enough with the identified one is for the 2-year ARI flood quantile of the Belar Creek catchment which is 6-hour. The rest are 12-hour to 72-hour.
Table 7.5: Catchment data and time of concentration (tc) values for the six test catchments
Time of Catchment Elevation Latitude Longitude Catchment name Area (km2) concentration station ID (m) (tc, hours) 201001 -28.3537 153.2931 Oxley River 213 15 5.83 203014 -28.7561 153.3955 Wilsons River 223 5 5.93 204017 -30.3057 152.7146 Bielsdown Creek 76 632 3.94 204025 -30.2528 153.0333 Orara River 135 105 4.90 210080 -32.4716 151.2837 West Brook River 80 0 4.02 420003 -31.3845 149.2023 Belar Creek 133 0 4.87
These results show the difficulty in selecting a critical duration in the application of the DEA and the unusual higher values of critical duration of up to 72 hours for catchments smaller than 250 km2. The new EMCST does not require selection of a critical duration as it treats rainfall duration as a random variable.
Plots of the DEA estimated flood quantiles and observed annual maximum flood peaks for the selected test catchments are presented in Figure 7.2 for visual assessment. The flood quantiles obtained for these catchments using the DEA show mixed results. The two catchments (Oxley River and Bielsdown Creek) show an over-estimation, two catchments (Wilsons River and Belar Creek) show a reasonable fit, and two catchments (Orara River and West Brook River) show over-estimation for 10-year and smaller ARIs and under-estimation for higher ARIs .
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(a) (b)
(c) (d)
(e) (f)
Figure 7.2: Observed flood peaks and flood quantiles (using FLIKE and the DEA) for the six test catchments
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7.5 Derived flood frequency curve (DFFC) using EMCST
Using the stochastic inputs (e.g. Table 7.6), the DFFCs are obtained using the new EMCST. The DFFCs are plotted against the observed annual maximum flood peaks as shown in Figure 7.3. For clearer visualisation of this figure, bigger plots were prepared in Appendix C (see Figures C.7.6 to C.7.11). As shown in Figure 7.3 or Figures C.7.6 to C.7.11, the Oxley River catchment shows under-estimation for ARIs greater than 2-year, while the other four catchments (the Wilsons River, Bielsdown Creek, Orara River and Belar Creek) demonstrate a good agreement between the DFFCs and observed annual maximum flood peaks. For the West Brook River, a reasonable agreement for ARIs up to 3-year is noticed, but with under- estimation after 3-year ARIs.
Both the EMCST and the DEA estimates, show a reasonable agreement with the at-site FFA results for four test catchments (the Wilsons River, Orara River, West Brook River and Belar Creek). For the Oxley River, the results are quite mixed where EMCST shows under- estimation (in particular for higher ARIs) and significant over-estimation for the DEA. For the Bielsdown Creek, DEA shows a better agreement with the at-site FFA results as compared to the EMCST. In most of the cases, EMCST estimates fall within the 90% confidence limits of the at-site FFA results.
It should be noted here that the at-site flood values (for higher ARIs) have notably larger RR values (>> 1) as indicated in Figure 7.3. Hence, there is a high degree of uncertainty associated with these higher values of individual flood discharges. Overall, the new EMCST shows better results than the currently recommended DEA based on visual assessment.
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Table 7.6: Parameter values for the six selected test catchment to apply EMCST Program mcdffc4id3.for Parameter file oxleyu.psh wilsow.psh bielsr.psh oraray.psh westbv.psh belarq.psh Description Parameter Parameter Parameter Parameter Parameter Parameter Catchment name OxleyRiver WilsoRiver BielsCreek OraraRiver WestBRiver BelarCreek Run sequence U W R Y V Q Number of simulations 30000 30000 30000 30000 30000 30000 IED mean (days) 104.05 89.60 79.13 77.36 69.60 41.96 IED stdev (days) 126.39 114.85 97.44 94.38 87.79 48.77
DCS mean (hours) 38.27 36.88 40.73 39.09 25.53 22.06
DCS stdev (hours) 33.75 29.89 41.52 32.75 22.42 19.99 Catchment area (km2) 213 223 76 135 80 133 Weighted IFD table 201001.wad 203014.wad 204017.wad 204025.wad 210080.wad 420003.wad TP parameter file listw.oxl listw.wil listz.bie listw.ora listw.wes listw.bel IL mean (mm) 7.24 18.92 13.61 20.04 13.20 56.34 IL stdev (mm) 4.68 12.11 5.92 10.23 5.67 18.49 TP interval 10 10 10 10 10 10 CL mean (mm/h) 0.85 0.73 0.57 1.34 0.26 5.64 m (assumed) 0.80 0.80 0.80 0.80 0.80 0.80 k mean (hours) 11.47 44.62 5.83 17.31 4.83 26.99 k stdev (hours) 1.04 5.01 2.82 1.89 1.81 6.33 BF (m3/s) 1.64 3.62 1.68 2.80 0.04 0.22
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(a) (b)
(c) (d)
(e) (f)
Figure 7.3: Observed annual flood peaks, flood quantiles (using FLIKE and the DEA) and DFFC (using EMCST) for the selected test catchment
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Using the model evaluation statistics adopted in this thesis (equations 3.33 to 3.36), the performance of the EMCST and DEA are assessed. Results of various error statistics are summarised in Tables 7.7 to 7.10. Over the six test catchments and 6 ARIs, the overall RE is 26% for the EMCST and 34% for DEA. The Orara River and West Brook River catchments have very similar values of RE as can be seen in Table 7.7. For the Bielsdown Creek catchment, the RE of the EMCST is much smaller than that of DEA. For Wilson Creek and Belar Creek, the RE of both the EMCST and DEA are smaller than 20%; however, in these two catchments DEA has much smaller RE than that of EMCST. Overall, EMCST shows a better results than the DEA in terms of RE.
Table 7.7: Summary of relative error (RE) for the selected test catchments using EMCST and DEA Absolute Relative Error (RE) Catchment EMCST DEA Oxley River 27% 44% Wilsons River 17% 5% Bielsdown Creek 11% 71% Orara River 16% 13% West Brook River 68% 65% Belar Creek 15% 9% Average 26% 34%
Table 7.8: Summary of ratio (R) for the selected test catchments using EMCST and DEA Ratio (R) Catchment EMCST DEA Oxley River 0.73 1.44 Wilsons River 0.83 1.02 Bielsdown Creek 0.89 1.71 Orara River 0.84 0.98 West Brook River 0.46 0.83 Belar Creek 0.92 0.92 Average 0.78 1.15
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Table 7.9: Summary of relative mean bias (BIAS) for the selected test catchments using EMCST and DEA Relative Mean Bias (BIAS) Catchment EMCST DEA Oxley River -0.24 0.63 Wilsons River -0.12 0.05 Bielsdown Creek -0.07 0.90 Orara River -0.14 0.03 West Brook River -0.33 0.50 Belar Creek -0.04 -0.16 Average -0.16 0.33
Table 7.10: Summary of relative root mean square error (RMSE) for the selected test catchments using EMCST and DEA Relative Root Mean Square Error (RMSE) Catchment EMCST DEA Oxley River 0.26 0.77 Wilsons River 0.17 0.13 Bielsdown Creek 0.11 1.02 Orara River 0.15 0.20 West Brook River 0.65 1.67 Belar Creek 0.16 0.29 Average 0.25 0.68
In terms of ratio (R) of predicted and observed floods, as shown in Table 7.8, the EMCST shows an overall under-estimation and DEA an overall over-estimation. However, for five out of the six test catchments, the R values associated with the EMCST are close to 0.80 (an average of 0.84); however, for the West Brook River, the R value for EMCST is much smaller (0.46). For DEA, the R values for the Oxley River and Bielsdown Creek are remarkably high (1.44 and 1.71, respectively). For the Belar Creek, the R values are the same for both the EMCST and DEA. For the Wilson River and Orara River, the R values of DEA are very close to 1, representing an excellent agreement. Overall, DEA shows a better ratio value than the EMCST.
For the relative bias (BIAS), EMCST shows a negative value for all the six test catchments, but for four of the six test catchments, the BIAS values for EMCST are within -0.33 to 0. For
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Enhanced Joint Probability Approach Caballero the DEA, the BIAS values for three catchments are notably high (0.50, 0.63 and 0.90). Overall, the BIAS values for the entire six test catchments for EMCST is -0.16 as compared to 0.33 for the DEA; hence, the overall BIAS of EMCST is closer to ideal value of zero than the DEA.
In terms of RMSE, EMCST shows much smaller values than DEA; for five test catchments, the RMSE values for EMCST is much smaller than those of DEA, and for the remaining catchment the RMSE values are very similar for the EMCST (0.17) and DEA (0.13). Overall, the EMCST shows a RMSE value of 0.25, which is much smaller than 0.68 for the DEA. Overall, EMCST performs much better than the DEA with respect to RMSE.
Based on the above results, it may be argued that the EMCST has performed better than the DEA, e.g. in terms of RE, EMCST is better, in terms of R, DEA is better, in terms of BIAS, EMCST is better) and in terms of RMSE, EMCST is much better). Overall, the EMCST shows a better agreement with the at-site FFA results than the DEA.
7.6 Flood quantile estimates using ARR RFFE 2012 Model (test version)
The new regional flood estimation method in the ARR is not yet finalised; however, a test version is released called ARR RFFE 2012 model (test version). This method is applied to the six test catchments. The ARR RFFE 2012 method needs five inputs: latitude and longitude (in degrees) of the catchment outlet location, catchment area (in km2), ARR1987 design rainfall intensity (in mm/hr) of 2-year ARI and 12-hour duration and the region where the catchment falls. For the state of NSW the region code is 1. For the selected test catchments, these inputs are provided in Table 7.11.
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Table 7.11: Inputs for the selected test catchments for using ARR RFFE 2012 model (test version)
Catchment Area Rainfall intensity Zone Latitude Longitude Catchment name 2 station ID (km ) (I2-12, mm/h) (NSW) 201001 -28.3537 153.2931 Oxley River @ Eugella 213 11.40 1 203014 -28.7561 153.3955 Wilsons River @ Eltham 223 9.89 1 Bielsdown Creek @ Dorrigo 204017 -30.3057 152.7146 76 12.30 1 No. 2 and No. 3 204025 -30.2528 153.0333 Orara River @ Karangi 135 11.40 1 West Brook River @ Upper 210080 -32.4716 151.2837 80 5.67 1 Stream Glendon Brook Belar Creek@ Warkton 420003 -31.3845 149.2023 133 5.83 1 (Blackburns)
Using the data listed in Table 7.11, and the ARR RFFE 2012 model, the flood quantile estimates and the 90% confidence limits are obtained for the selected test catchments (shown in Figure 7.4). For clearer visualisation of this figure, bigger plots were prepared in Appendix C (see Figures C.7.12 to C.7.17). The flood quantile estimates for the Oxley River catchment are provided in Table 7.12. The flood quantile estimates for the other five test catchments are given in Table B.7.16 to B.7.20 (see Appendix B). The estimated flood quantiles using ARR RFFE 2012 model show reasonable agreement with the observed annual maximum flood peaks for the four catchments (the Oxley River, Wilsons River, Bielsdown Creek and Belar Creek) as illustrated in Figure 7.4. The flood quantile estimates for the Orara River show under-estimation while the West Brook River an over-estimation.
Table 7.12: Flood quantile estimates using ARR RFFE 2012 model for the Oxley River catchment
ARI Expected 5% Confidence 95% Confidence (years) quantiles (m3/s) limit (m3/s) limit (m3/s) 2 292.9 131.3 672.0 5 768.4 344.9 1739.9 10 1190.1 528.9 2699.2 20 1652.1 725.5 3786.9 50 2311.9 996.0 5423.8 100 2836.7 1200.1 6726.8
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(a) (b)
(c) (d)
(e) (f)
Figure 7.4: Flood quantile estimates using the ARR RFFE 2012 model and observed annual maximum flood series for the six selected test catchments
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7.7 Flood quantile estimates using the Probabilistic Rational Method
The Probabilistic Rational Method (PRM) from ARR1987 is also applied to the six test catchments. Following the procedure of the PRM outlined in Book IV of ARR 1987 (I. E. Australia, 1987), the flood quantile estimates are obtained and summarised in Table 7.13.
Table 7.13: Flood quantile estimates using Probabilistic Rational Method for the selected test catchments
3 Catchment Flood quantiles (m /s) Catchment name station ID Q1 Q2 Q5 Q10 Q20 Q50 Q100 201001 Oxley River 523 827 1252 1570 1970 2377 2811 203014 Wilsons River 264 411 601 737 909 1168 1421 204017 Bielsdown Creek 84 145 245 331 442 612 765 204025 Orara River 236 373 567 712 894 1077 1272 210080 West Brook River 23 36 55 71 93 123 152 420023 Belar Creek 31 58 113 168 252 419 602
The flood quantile estimates obtained from the EMCST, ARR RFFE 2012 model and PRM are plotted against the observed annual maximum flood peaks in Figure 7.5 (for clearer visualisation, bigger plots are prepared and given in Appendix C, see Figures C.7.18 to C.7.23). From these figures, it can be seen that the flood quantile estimates using the PRM show over-estimation for the four test catchments (the Oxley River, Wilsons River, Orara River and Belar Creek) as compared to the observed annual maximum flood peaks. For the Bielsdown Creek catchment, the PRM-based flood quantile estimates demonstrate a reasonable fit to the observed annual maximum flood peaks. The PRM-based flood quantile estimates for the West Brook River catchment shows a reasonable fit for ARIs up to 2-year; while under-estimation for ARIs greater than 5-year.
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(a) (b)
(c) (d)
(e) (f)
Figure 7.5: Observed flood peaks, flood quantiles (using ARR RFFE 2012 model (test version) and the ARR1987 Probabilistic Rational Method) and DFFC (using EMCST) for the selected test catchments
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A comparison between the EMCST, ARR RFFE 2012 model (test version) and PRM is presented in Figure 7.5, which demonstrates that overall EMCST provides better results than the PRM. The DFFCs from the EMCST for the five test catchments (the Wilsons River, Bielsdown Creek, Orara River, West Brook River and Belar Creek) show a better match with the observed annual maximum flood series as compared to the ARR RFFE 2012 model (test version) and PRM. For the Oxley River catchment, the EMCST shows under-estimation for ARIs greater than 2-year; while the ARR RFFE 2012 model shows over-estimation for ARIs greater than 10-year and the PRM shows significant over-estimation. However, given the higher RRs of the observed higher annual flood peaks, a significant uncertainty is associated with the at-site FFA for the higher ARIs.
The performance of the EMCST with the ARR RFFE 2012 model (test version) and the PRM are also assessed using the model evaluation statistics. Tables 7.14 to 7.17 summarises various error statistics. The EMCST shows superiority over the two other methods (ARR RFFE 2012 model and PRM). For EMCST, five catchments show smaller RE values as compared to ARR RFFE 2012 (test version). The EMCST outperforms the PRM for all the six test catchments in terms of RE. For ratio R (Table 7.15), four catchments have R values closer to 1 for the EMCST as compared to the PRM, and for all the six test catchments, the R values for the EMCST are closer to 1 than the ARR-RFFE 2012 model as can be seen in Table 7.15.
Table 7.14: Summary of relative error (RE) for the selected test catchments using EMCST, ARR RFFE 2012 model (test version) and DEA Absolute Relative Error (RE) Catchment EMCST ARR-RFFE 2012 PRM Oxley River 27% 22% 50% Wilsons River 17% 62% 56% Bielsdown Creek 11% 44% 23% Orara River 16% 142% 38% West Brook River 68% 77% 85% Belar Creek 15% 28% 42% Average 26% 63% 49%
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Table 7.15: Summary of ratio (R) for the selected test catchments using EMCST, ARR RFFE 2012 model (test version) and DEA Ratio (R) Catchment EMCST ARR-RFFE 2012 PRM Oxley River 0.73 1.19 1.50 Wilsons River 0.83 1.62 1.56 Bielsdown Creek 0.89 1.44 0.77 Orara River 0.84 2.42 1.38 West Brook River 0.46 0.23 0.15 Belar Creek 0.92 1.28 1.42 Average 0.78 1.36 1.13
Table 7.16: Summary of relative mean bias (BIAS) for the selected test catchments using EMCST, ARR RFFE 2012 model (test version) and DEA Relative Mean Bias (BIAS) Catchment EMCST ARR-RFFE 2012 PRM Oxley River -0.24 0.19 0.64 Wilsons River -0.12 0.64 0.62 Bielsdown Creek -0.07 0.42 -0.20 Orara River -0.14 1.31 0.44 West Brook River -0.33 -0.74 -0.76 Belar Creek -0.04 0.36 0.57 Average -0.16 0.36 0.22
Table 7.17: Summary of relative root mean square error (RMSE) for the selected test catchments using EMCST, ARR RFFE 2012 model (test version) and DEA Relative Root Mean Square Error Catchment EMCST ARR-RFFE 2012 PRM Oxley River 0.26 0.30 0.71 Wilsons River 0.17 0.82 0.64 Bielsdown Creek 0.11 0.52 0.22 Orara River 0.15 1.39 0.49 West Brook River 0.65 0.75 0.79 Belar Creek 0.16 0.41 0.70 Average 0.25 0.70 0.59
For the BIAS, the EMCST have five catchments with BIAS values closer to 0, the ARR- RFFE 2012 model (test version) has one catchment that has BIAS value closer to 0 and none
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Overall, the new EMCST shows better results than the DEA, ARR-RFFE 2012 (test version) and PRM method (see Table 7.18). It should be noted here that the ARR-RFFE 2012 model is not finalised as yet, the final model is due to be released in early 2014.
Table 7.18: Ranking of the four methods based on the model evaluation statistics for the selected test catchments
Model evaluation statistics Rank 1 Rank 2 Rank 3 Rank 4 Absolute relative error (RE) EMCST DEA PRM ARR-RFFE 2012 Ratio (R) PRM DEA EMCST ARR-RFFE 2012 Relative mean bias (BIAS) EMCST PRM DEA ARR-RFFE 2012 Relative root mean square error (RMSE) EMCST PRM DEA ARR-RFFE 2012
7.8 Summary of Chapter 7
This chapter has presented the validation of the new EMCST using six test catchments in NSW. A comparison has been made among the new EMCST, DEA, ARR RFFE 2012 model (test version), PRM and the at-site FFA results. It has been found that in many cases, the estimates from one method show notable differences from the other methods. This highlights the challenges in regional hydrologic modelling in Australia which has a notable variable hydrology than many other countries e.g. the UK. Overall, the new EMCST provides a better result than the DEA, ARR RFFE 2012 model (test version) and the PRM.
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Enhanced Joint Probability Approach Caballero CHAPTER 8 Summary, Conclusions and Recommendations
8.1 General
This thesis has focused on development of a new regionalised Enhanced Monte Carlo Simulation Technique (EMCST). It has used data from the State of New South Wales (NSW) in Australia to derive regional distributions of various stochastic model inputs/parameters (rainfall duration, rainfall inter-event duration, rainfall depth, rainfall temporal pattern, initial loss, continuing loss and runoff routing model’s storage delay parameter). These regionalised stochastic inputs/parameters are then used with the new EMCST to obtain derived flood frequency curve (DFFC) at a number of selected catchments in NSW. A sensitivity analysis has been undertaken to assess the impacts of possible uncertainty in these input/parameter values on the DFFCs. This chapter presents a summary of the research undertaken in this thesis, conclusions drawn from the investigations and recommendations for further study.
8.2 Summary of the research undertaken in this thesis
The research undertaken in this thesis has been presented in eight chapters and four appendices. The research undertaken in this thesis is summarised below.
Literature review: Chapter 2 has presented a literature review relevant to this study. Here, various rainfall-based design flood estimation methods with a particular emphasis on the Design Event Approach (DEA) and Joint Probability Approach (JPA)/ Monte Carlo Simulation Technique (MCST) have been critically reviewed. It has been found that the DEA has serious limitations in selecting the input variables in rainfall runoff modelling as DEA ignores the probabilistic nature of the input variables except for the rainfall depth. To overcome the limitations associated with the DEA, alternative methods have been proposed
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Enhanced Joint Probability Approach Caballero such as continuous simulation, ‘Improved’ DEA, JPA and the runoff files approach. It has been found that only continuous simulation and the JPA have the potential to fully overcome the limitations associated with the DEA. Continuous simulation generates flood runoff sequences from rainfall time series and other climatic characteristics and loss parameters using a continuous simulation type water balance and flood routing models. The continuous simulation needs a large data set, and for larger catchments, data handling may become cumbersome, and moreover, model formulation and calibration could become quite challenging. While the JPA estimates design floods using the same rainfall runoff modelling input variables as the DEA, it treats input variables and the flood output as random variables and accounts for the necessary correlations of the input variables. Thus, the JPA has the potential to offer considerable improvements in rainfall-based design flood estimation with modest efforts as compared to the continuous simulation approach. A number of research studies have demonstrated that the JPA can overcome the major limitations associated with the DEA.
It has also been found that the analytical methods in the JPA are quite complicated due to its mathematical complexity and cannot be applied in most practical situations for flood modelling with real catchments. In contrast, the approximate form of the JPA such as MCST has enough flexibility for practical application as demonstrated by some previous studies. Although the JPA/MCST has shown significant promise to become a practical tool in flood modelling by replacing the currently recommended DEA, no development and testing of the JPA/MCST over a large region has been made to-date. To achieve this objective, it needs regionalisation of the model inputs and parameters considering data from a large number of pluviograph and stream gauging stations within a region. This thesis thus proposes to enhance the MCST called the EMCST by regionalising the inputs/parameters for the State of New South Wales (NSW) in Australia so that the new EMCST can be applied to any arbitrary ungauged or poorly gauged catchment location in eastern NSW. The new EMCST is based on complete storm and incorporates inter-event duration as a random variable in the EMCST in addition to rainfall duration, intensity, temporal pattern, initial loss, continuing loss and storage delay parameter of the runoff routing model. It should be noted here that the use of inter-event duration in this thesis is a novel approach as previous applications of MCST in Australia did not use inter-event duration. It has been found that a spatial proximity method is
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Enhanced Joint Probability Approach Caballero the preferred approach to regionalise the parameters of the input distributions for application with the new EMCST.
Methodology: Chapter 3 has presented various methods adopted with the development and validation of the new EMCST. Here, the rainfall events are selected based on complete storms. A single non-linear storage model is selected for runoff routing purpose. Seven input variables are selected for stochastic representation which are: complete storm duration (DCS), inter-event duration (IED), rainfall depth in terms of intensity-frequency-duration (IFD) data, temporal pattern (TP), initial loss (IL), continuing loss (CL), and runoff routing model’s storage delay parameter (k).
In this research, concurrent rainfall and streamflow events are selected from a set of selected catchments in eastern NSW to estimate the losses and to calibrate the adopted runoff routing model. Marginal probability distribution of an input variable is identified from the observed data of the input variable by fitting two different probability distributions. These are the one- parameter exponential distribution and two-parameter gamma distribution. The suitability of these distributions is assessed using three goodness-of-fit tests (Chi-Squared, Kolmogorov- Smirnov and Anderson-Darling) at 5% level of significance. The development of JPA-based IFD curves considered the strong relationship between rainfall complete storm duration and average rainfall intensity for the observed complete storm events at the specified pluviograph station. The development and application of TP database are based on historic TPs (non- dimensional) which can be drawn randomly from a regional database formed based on an appropriate number of pluviograph stations during the simulation corresponding to the generated DCS value.
The marginal probability distributions of the input variables/parameters are regionalised so that the regional EMCST can be applied to any arbitrary ungauged location in eastern NSW. Since there are not enough pluviograph and streamflow gauging stations in western NSW with data of adequate length and quality, the EMCST has been developed based on the data from eastern NSW only. The DCS, IED and IFD data are regionalised using the spatial proximity method with the aid of Inverse Distance Weighted Averaging (IDWA) method. The EMCST is implemented by simulating the possible combinations of model inputs to generate a rainfall event hyetograph and an inter-event duration and runoff routing model’s University of Western Sydney Page 216
Enhanced Joint Probability Approach Caballero storage delay parameter k value. The annual maximum flood series are formed from the generated partial duration series flood peak data resulted from the simulations using inter- event duration (as discussed in Section 3.11). These annual maximum flood series are then used to construct the DFFC using a non-parametric frequency approach.
In the validation of the EMCST, the DFFCs obtained from this method are compared with: (i) at-site flood frequency analysis (FFA) results obtained from FLIKE software (Kuczera, 1999); (ii) flood quantiles estimated by the currently recommended DEA in Australian Rainfall and Runoff (ARR) 1987; (iii) flood quantile estimates obtained from the ARR Regional Flood Frequency Estimation (RFFE) 2012 model (test version); and (iv) the flood quantile estimates by the Probabilistic Rational Method (PRM) from the ARR 1987.
Selection of study area and data: To develop and test the EMCST, the eastern part of NSW State is selected as it represents good data coverage in terms of quantity and quality of pluviograph and stream gauging stations (Chapter 4). The selection of catchments and pluviograph stations and collation of the pluviograph and streamflow data have been discussed in Chapter 4. The criteria for the selection of pluviograph stations and study catchments have been presented in Chapter 4. These criteria included that the selected pluviograph stations should have at least 30 years of continuous data, and for calibration of runoff routing model and estimation of losses, both the stream gauging and pluviograph stations should have at least 10 years of concurrent data. Based on these criteria, this study has selected 86 pluviograph stations and 12 catchments from eastern NSW. From the selected catchments, six relatively smaller catchments are used in the calibration of the adopted runoff routing model while the other six catchments are used for the validation of the EMCST.
From Australian Bureau of Meteorology (BOM), the basic pluviograph data are obtained and then extracted using the HYDSTRA program while streamflow data are extracted using the HYDSTRA program in-built in PINNEENA CD of NSW Department of Water. These extracted data are then analysed for identifying the stochastic input variables/model parameters and subsequent regionalisation.
Derivation of stochastic variables/model parameters and their regionalisation: The rainfall events data are extracted from the selected 86 pluviograph stations based on the
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Enhanced Joint Probability Approach Caballero adopted storm selection criteria. In addition, the concurrent rainfall and streamflow events data are selected for the analysis of losses and storage delay parameter from the selected catchments. It has been shown that rainfall DCS, IED, IL and k data can be approximated by two-parameter gamma distribution, while the CL data by one-parameter exponential distribution (Chapter 5). These results are summarised in Table 8.1 where the typical values of the parameters of the selected distributions are provided. It has been found that the IFD data can be regionalised by using the IFD data of the nearby pluviograph stations within 30 km radius of the centre of the catchment of interest (that gives typically1 to 5 pluviograph station(s) in the case of eastern NSW). For TP, 15 nearby pluviograph stations’ non- dimensional TP data can be used (to capture the regional variability in TP) to obtain a regional TP database at the location of interest, which can be used for random sampling during the simulation of rainfall events in the new EMCST.
Table 8.1: Stochastic model inputs/parameter values for eastern NSW and typical parameter values of the respective marginal distributions Probability distributions (mean, stdev; regional Model inputs values)
Rainfall complete storm duration (DCS) Gamma (25.89 hrs, 22.09 hrs) Rainfall inter-event duration (IED) Gamma (69.78 days, 83.47 days) Initial loss (IL) Gamma (26.03 mm, 13.90 mm) Continuing loss (CL) Exponential (3.19 mm/hr) Storage delay parameter (k) Gamma (8.12 hrs, 4.09 hrs)
IFD data set at an individual pluviograph station was obtained by fitting an exponential distribution to partial duration series intensity values and D data; in Rainfall depth (intensity-frequency- CS regionalisation, the pluviograph stations located within duration, IFD) 30 km radius (that gives typically 1 to 5 pluviograph station(s)) from the location of the catchment of interest are used to derive IFD data adopting an IDWA method. 15 nearby pluviograph stations’ non-dimensional TP data can be used to form a regional TP database for a Rainfall temporal pattern (TP) catchment of interest. This database can be used for random sampling during the simulation of rainfall events in the EMCST.
Sensitivity of the regionalised stochastic distributions on the DFFC: Chapter 6 has presented sensitivity analyses to assess the sensitivity as to how the variation in a distributional parameter(s) or in the number of stations to be used in obtaining the regional University of Western Sydney Page 218
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IFD and TP database could affect the DFFC. The mean and standard deviation values of DCS, IED, IL, CL (mean only), and k data are varied within an arbitrary range, e.g. ± 5%, ± 10%, ± 20% and ± 50%. The numbers of pluviograph stations were also varied arbitrarily (from one to nine pluviograph stations, or 0 to 30 km distance) for IFD and TP to obtain different sets of IFDs and pooled TP database. Based on the results of the sensitivity analyses, the input variables and storage delay parameter (k) are arranged as follows (the most sensitive to less sensitive ones): k (-30% to 95%), IED (-29% to 60%), DCS (-30% to 50%), IL (-40% to 40%), IFD (10% to 24%), TP (9% to 15%) and CL (-10% to 14%). It has been shown that up to about 10% variations in the stochastic model inputs and parameters do not make any notable differences on the DFFCs.
Validation of the new EMCST: Chapter 7 has presented the validation of the new EMCST to six test catchments in NSW. A comparison has been made among the new EMCST, DEA, ARR RFFE 2012 model (test version), ARR1987 PRM and the at-site flood frequency analysis results. It has been found that in many cases, the estimates from one method show notable differences from the other method highlighting the challenges in regional flood estimation in Australia, which has the most variable hydrology in the world. Based on the model evaluation statistics adopted, the EMCST outperforms the DEA, PRM and ARR-RFFE 2012 model (test version).
8.3 Conclusions
This thesis presents development of a regionalised Enhanced Monte Carlo Simulation Technique (EMCST) using data from eastern New South Wales (NSW), Australia. The following conclusions can be drawn from this thesis:
It has been found that various stochastic model inputs/parameters in the rainfall runoff modelling can be regionalised using readily available observed pluviograph and streamflow data.
It has been found that the distributions of rainfall complete storm event duration
(DCS), inter-event duration (IED), initial loss (IL) and runoff routing model’s storage delay parameter (k) in eastern NSW can be approximated by two-parameter gamma
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distribution and the continuing loss (CL) by one-parameter exponential distribution. The typical distributional parameter value(s) of these input variables/storage delay parameter k for eastern NSW are provided in Table 8.1.
It has been shown that the rainfall intensity-frequency-duration (IFD) data developed from the selected individual pluviograph stations can be used to derive IFD data at any arbitrary ungauged location in eastern NSW. This is obtained using IFD data from pluviograph stations within 30 km radius from the centre of the catchment of interest (giving typically 1 to 5 pluviograph stations) with the aid of an Inverse Distance Weighted Averaging (IDWA) method. This method gives a greater weight to a pluviograph station that is located closer to the catchment of interest than the station which is located at a greater distance. It has been found that IDWA method, adopted here, generates a consistent set of IFD curves at any arbitrary ungauged location in eastern NSW.
It has been found that the dimensionless temporal pattern (TP) data at the individual pluviograph stations can be pooled together (from about 15 nearby pluviograph stations) to obtain a regional TP database at any arbitrary ungauged location in NSW.
In the sensitivity analysis, it has been found that the DFFCs are sensitive to the individual regional stochastic model inputs/parameters in the following order (most
sensitive to the least sensitive ones): k (-30% to 95%), IED (-29% to 60%), DCS (- 30% to 50%), IL (-40% to 40%), IFD (10% to 24%), TP (9% to 15%) and CL (-10% to 14%). It has been shown that up to about 10% variations in the stochastic model inputs/parameters do not make any notable differences in the derived flood frequency curves (DFFC).
The DEA shows a wide range of critical duration values for catchments of similar sizes, which are relatively much longer than the expected values of critical durations highlighting the difficulties in selecting a critical duration for a given application. The new EMCST does not need to select a critical duration value as it considers storm duration as a stochastic/random variable.
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It has been found that in general the new EMCST provides more accurate design flood estimates than the currently recommended Design Event Approach (DEA), Probabilistic Rational Method and the new Australian Rainfall and Runoff (ARR) Regional Flood Frequency Estimation (RFFE) Model 2012 (test version). It should be noted here that EMCST provides the complete streamflow hydrograph at any ungauged catchment location; however, the PRM and ARR-RFFE 2012 model give only the flood peak estimates of given ARIs.
The newly added variables in the EMCST can easily be derived using the existing data (rainfall, streamflow and catchment characteristics) and subsequent data analysis techniques developed in this thesis. In this thesis, it has been shown that a regional MCST (EMCST) can be developed and all the input data for the EMCST can be regionalised and hence user can use these regionalised data with the EMCST.
The regional stochastic input variables/model parameters derived in this thesis are applicable to eastern NSW; however, the developed regionalisation framework can be adapted to other parts of Australia and other countries. The particular advantage of this new EMCST is that it does not need selection of a critical duration like the DEA, and it reduces the subjectivity in selecting the representative value(s) of other model inputs such as TP, IL, CL and k. The regional EMCST will be particularly useful to derive a complete design flood hydrograph at any arbitrary ungauged location in eastern NSW using the regional distributions of the stochastic inputs/model parameters derived in this thesis (given in Table 8.1). This in essence will facilitate the shifting from the old DEA (as per ARR 1987) to the MCST (the recommended method in ARR 2014).
8.4 Recommendations for further study
The EMCST developed in this study is based on the database of pluviograph and stream gauging stations available in eastern NSW. The method should be extended to western NSW when a longer period of pluviograph and streamflow data will be available in the next decade or so.
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This study has tested the developed EMCST using a single-storage runoff routing model for small to medium catchments. In the future study, the EMCST should be integrated with a semi-distributed runoff routing model like RORB so that the method could consider the areal variability of the model parameters and hence could be applied to larger catchments. In this regard, a new runoff routing model based on the concept of ‘distributed joint probabilistic rainfall runoff modelling’ could be developed. Such a model would have a wider applicability in the water industry in Australia and other countries.
Further study should focus on a comprehensive uncertainty analysis of the EMCST using a Bayesian statistical technique that would allow development of 90% confidence limits of the derived flood frequency curves (DFFCs). In this case, each of the distributional parameters of the specified distributions (e.g. exponential/gamma) for an input variable would have a prior distribution i.e. a distributional parameter itself would be regarded as a random variable.
In future research on MCST, baseflow and areal distribution of rainfall depth should be considered as a random variable. For some catchments, baseflow during flood could be highly variable and could be a major proportion of total flood flow, and hence its probabilistic representation would be useful.
In future study, continuing loss can be expressed as function of storm duration so that it reduces with storm duration, this would be in particular useful for larger catchments and longer duration events. Other loss parameters such as ‘initial loss-proportion loss model’ could be used instead of ‘initial loss continuing loss model’. Moreover, antecedent precipitation index (API) could be used along with the loss models to represent catchment wetness in a more comprehensive manner.
The impacts of climate change on various model inputs/parameters, and thereby on DFFCs should also be investigated in future. This would be particularly useful where there is a strong influence of climate change on floods.
The regional EMCST presented in this study should be tested to other Australian states with a greater number of pluviograph and stream gauging stations and with catchments of smaller to larger sizes.
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The EMCST developed in this thesis should be compared with the final ARR-RFFE model when it will be released in 2014.
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A.1 Eagleson’s Joint Probability Approach based on kinematic runoff model Three major steps involved: (i) rainfall model, (ii) runoff model, and (iii) transformation from rainfall to runoff. In this method, the probability density function of point rainstorm duration tr (in hours) is approximated by exponential distribution
tr f (tr ) e tr 0 (A.1.1)
and the probability density function of point rainstorm intensity i0 is approximated by
i0 i 0 f (i0 ) e 0 (A.1.2)
where parameter 30 when i0 is in inches per hour and by definition, the point storm depth d is related to point intensity and duration by:
i0 d tr (A.1.3)
By means of equation (A.1.3) the cumulative distribution of may be expressed by:
i0tr F(i0 ) dtr f (d tr ) f (tr )dd (A.1.4) 0 0
By means of equations (A.1.1) and (A.1.2), equation (A.1.4) becomes:
i0tr i0 tr 1 e e dtr f (d tr )dd (A.1.5) 0 0
Based on the observations of Grayman and Eagleson (1969), it indicates that the function f (d tr ) can be represented well by a gamma function but is quite difficult to manipulate analytically. One function that does satisfy equation (A.1.5) is the exponential function which
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d tr (d tr ) ( tr )e tr 0 d 0 (A.1.6) was compared with the observations and it was pointed out that when equation (A.1.3) is used with (A.1.6) the conditional distribution of i0 as expressed by equation (A.1.7) can be derived.
i0 f (i0 tr ) e f (i0 ) (A.1.7)
Here, equation (A.1.6) implies the independence of the point rainfall variables i0 and tr.
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A.2 Total Probability Theorem
The Total Probability Theorem can be summarised as below. If Bi where i varies from 1 to n, and n is a positive integer, represents a set of events which satisfies the following two conditions: (i) mutually exclusive, i.e. P(B1 B2 ...Bn ) P(B1 ) P(B2 ) ... P(Bn ) and
(ii) collectively exhaustive, i.e. P(B1 B2 ... Bn ) 1, then the probability of another event A can be determined by using the Total Probability Theorem. This is expressed as:
P(A) P(AB1 ) P(AB2 ) P(A B3 ) ... P(ABn ) (A.2.1)
This theorem represents the expansion of the probability of an event in terms of its conditional probabilities, conditioned on a set of mutually exclusive, collectively exhaustive events (Rahman et al., 1998). It is often a useful expansion in problems where it is desired to compute the probability of an event A, since the terms in the sum may be more readily obtainable than the probability of A itself (Benjamin and Cornell, 1970).
The Total Probability Theorem can also be expanded to two or more dimensions. As an example, the theorem can be expressed in the dimensions B, C, D as follows:
n m q P(A) P(A Bi ,C j , Dk )P(Bi C j Dk ) (A.2.2) i1 j1 k1
If B ,C ,D are independent events, equation (2.10) becomes: i j k
n m q P(A) P(A Bi ,C j , Dk )P(Bi )P(C j )P(Dk ) (A.2.3) i1 j1 k1
In the application of the Total Probability Theorem to the calculation of flood probability, the explanations of the terms involved in equation (A.2.3) are as follows:
P(A) is the unconditional probability of a flood (to be exceeded in any given year);
P(A Bi ) is the conditional probability of a flood given an input Bi that occurs at the same time as A, not just in the same year;
P(Bi ) is the probability of obtaining a value of Bi for the input B; and
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B, C, D are random variables to the design, for example temporal pattern, losses, storm duration, etc.
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Pluviograph stations and selected events from NSW
Record Average Station Station Number Station name length of event code ID of event (years) per year 1 48027 COBAR MO 49 315 6.43 2 48031 COLLARENEBRI (ALBERT ST) 36 207 5.75 3 51049 TRANGIE RESEARCH STATION AWS 43 229 5.33 4 53048 MOREE COMPARISON 32 187 5.84 5 54102 BARRABA (ROSEVALE) 41 288 7.02 6 54104 PINDARI DAM 40 273 6.83 7 54105 BUNDARRA (GRANITE HEIGHTS) 37 249 6.73 8 54138 UPPER HORTON (DUNBEACON) 35 183 5.23 9 55024 GUNNEDAH RESOURCE CENTRE 66 456 6.91 10 55054 TAMWORTH AIRPORT 35 257 7.34 11 55136 WOOLBROOK (DANGLEMAH ROAD) 41 296 7.22 12 55194 GOWRIE NORTH 41 286 6.98 13 55302 NUNDLE (CHAFFEY DAM) 34 162 4.76 14 56013 GLEN INNES AG RESEARCH STN 41 331 8.07 15 56018 INVERELL RESEARCH CENTRE 64 500 7.81 16 56022 LEGUME (NEW KOREELAH) 38 191 5.03 17 56140 EMMAVILLE (BEN VALE) 50 155 3.10 18 56202 BLACK SWAMP (MAXWELL) 40 178 4.45 19 57091 URALLA (BLUE NOBBY) 36 159 4.42 20 57095 TABULAM (MUIRNE) 42 280 6.67 21 57103 KOOKABOOKRA 42 302 7.19 22 57104 YARROWITCH (MARETTO) 53 177 3.34 23 58026 GREVILLIA (SUMMERLAND WAY) 38 179 4.71 24 58044 NIMBIN POST OFFICE 48 135 2.81 25 58072 FEDERAL POST OFFICE 33 120 3.64 26 58099 WHIPORIE POST OFFICE 39 165 4.23 27 58109 TYALGUM (KERRS LANE) 32 98 3.06 28 58113 GREEN PIGEON (MORNING VIEW) 34 143 4.21 29 58129 KUNGHUR (THE JUNCTION) 44 123 2.80 30 58131 ALSTONVILLE TROPICAL FRUIT RESEARCH STAT 49 263 5.37 31 58158 MURWILLUMBAH (BRAY PARK) 39 179 4.59 32 59000 BELLBROOK (EAST STREET) 55 208 3.78 33 59017 KEMPSEY (WIDE STREET) 55 153 2.78 34 59026 UPPER ORARA (AURANIA) 41 176 4.29 35 59040 COFFS HARBOUR MO 51 276 5.41 36 59067 DORRIGO (MYRTLE ST) 46 207 4.50 37 60030 TAREE (ROBERTSON ST) 42 197 4.69 38 60080 COMBOYNE SOUTH 45 223 4.96
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Table B.4.1: continued
Record Average Station Station Number Station name length of event code ID of event (years) per year 39 60085 YARRAS (MOUNT SEAVIEW) 43 282 6.56 40 60104 NOWENDOC (GREEN HILLS) 41 208 5.07 41 60106 NUMBER ONE (MURRAYS CREEK) 34 147 4.32 42 61078 WILLIAMTOWN RAAF 59 317 5.37 43 61089 SCONE SCS 60 330 5.50 44 61151 CHICHESTER DAM 52 277 5.33 45 61158 GLENDON BROOK (LILYVALE) 48 232 4.83 46 61211 COLO HEIGHTS (MOUNTAIN PINES) 49 221 4.51 47 61212 LIDDELL (POWER STATION) 31 114 3.68 48 61238 POKOLBIN (SOMERSET) 50 324 6.48 49 61250 PATERSON (TOCAL AWS) 37 200 5.41 50 61287 MERRIWA (ROSCOMMON) 43 143 3.33 51 61288 LOSTOCK DAM 42 150 3.57 52 61309 MILBRODALE (HILLSDALE) 42 269 6.40 53 61311 GRAHAMSTOWN (HUNTER WATER BOARD) 32 109 3.41 54 61334 GLEN ALICE 42 203 4.83 55 61351 PEATS RIDGE (WARATAH ROAD) 30 142 4.73 56 62005 CASSILIS POST OFFICE 37 160 4.32 57 63023 COWRA RESEARCH CENTRE (EVANS ST) 70 420 6.00 58 63039 KATOOMBA (MURRI ST) 46 181 3.93 59 63043 KURRAJONG HEIGHTS (BELLS LINE OF ROAD) 47 190 4.04 60 63108 OBERON DAM 34 243 7.15 61 64046 COONABARABRAN (WESTMOUNT) 41 266 6.49 62 65035 WELLINGTON RESEARCH CENTRE 45 352 7.82 63 66037 SYDNEY AIRPORT AMO 50 202 4.04 64 66062 SYDNEY (OBSERVATORY HILL) 99 483 4.88 65 67033 RICHMOND RAAF 43 203 4.72 66 67035 LIVERPOOL(WHITLAM CENTRE) 38 157 4.13 67 68076 NOWRA RAN AIR STATION 34 76 2.24 68 68117 ROBERTSON (ST.ANTHONYS) 43 112 2.60 69 68131 PORT KEMBLA (BHP CENTRAL LAB) 49 116 2.37 70 69049 NERRIGA COMPOSITE 41 99 2.41 71 69055 GREEN CAPE LIGHTHOUSE 36 82 2.28 72 69127 ARALUEN LOWER (ARALUEN RD) 32 65 2.03 73 70012 BUNGONIA (INVERARY PARK) 46 185 4.02 74 70014 CANBERRA AIRPORT COMPARISON 74 495 6.69 75 70015 CANBERRA FORESTRY 40 232 5.80 76 70073 CHAKOLA (RIVERSDALE) 46 195 4.24 77 70080 TARALGA POST OFFICE 34 109 3.21 78 70199 NUMERALLA (BADJA COMPOSITE) 46 166 3.61 79 71042 INGEBYRA (GROSSES PLAINS) 41 201 4.90 80 72023 HUME RESERVOIR 57 458 8.04 81 72060 KHANCOBAN SMHEA 34 275 8.09 82 72150 WAGGA WAGGA AMO 67 388 5.79
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Table B.4.1: continued
Record Average Station Station Number Station name length of event code ID of event (years) per year 83 73007 BURRINJUCK DAM 101 622 6.16 84 74114 WAGGA WAGGA RESEARCH CENTRE 58 338 5.83 85 75028 GRIFFITH CSIRO 59 272 4.61 86 75050 NARADHAN (URALBA) 42 201 4.79 Minimum 30 65 2.03
Maximum 101 622 8.09
Average 45 229 4.99
Total number of events 19718
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Complete storm duration data statistics
Average of record Number Lower Upper At-site Standard Station start start end end rainfall Station name length of rainfall limit limit mean deviation Skew ID year month year month event per (years) event (hour) (hour) (hour) (hour) year 48027 COBAR MO 1962 6 2010 9 49 315 6.43 1 83 14.187 11.550 1.879 48031 COLLARENEBRI (ALBERT ST) 1976 1 2011 5 36 207 5.75 1 84 15.932 13.667 1.826 51049 TRANGIE RESEARCH STATION AWS 1968 8 2011 4 43 229 5.33 1 68 15.079 12.788 1.441 53048 MOREE COMPARISON 1964 4 1995 6 32 187 5.84 1 80 14.952 13.605 1.946 54102 BARRABA (ROSEVALE) 1971 1 2011 2 41 288 7.02 1 91 18.632 15.914 1.259 54104 PINDARI DAM 1971 8 2011 2 40 273 6.83 1 80 16.722 14.565 1.447 54105 BUNDARRA (GRANITE HEIGHTS) 1975 1 2010 11 37 249 6.73 1 83 18.169 14.803 1.539 54138 UPPER HORTON (DUNBEACON) 1976 11 2011 2 35 183 5.23 1 88 20.661 16.223 1.396 55024 GUNNEDAH RESOURCE CENTRE 1946 4 2011 4 66 456 6.91 1 70 17.044 13.531 1.148 55054 TAMWORTH AIRPORT 1958 8 1992 12 35 257 7.34 2 75 18.195 15.001 1.321 55136 WOOLBROOK (DANGLEMAH ROAD) 1971 1 2011 2 41 296 7.22 1 70 16.584 14.475 1.147 55194 GOWRIE NORTH 1971 1 2011 4 41 286 6.98 1 91 19.290 15.132 1.706 55302 NUNDLE (CHAFFEY DAM) 1977 11 2010 8 34 162 4.76 1 88 18.302 16.075 1.780 56013 GLEN INNES AG RESEARCH STN 1970 6 2011 2 41 331 8.07 1 101 18.073 16.578 1.669 56018 INVERELL RESEARCH CENTRE 1947 8 2010 6 64 500 7.81 1 81 16.326 14.223 1.474 56022 LEGUME (NEW KOREELAH) 1973 4 2010 11 38 191 5.03 1 111 21.440 23.174 1.692 56140 EMMAVILLE (BEN VALE) 1962 1 2011 2 50 155 3.10 1 81 18.458 14.599 1.406 56202 BLACK SWAMP (MAXWELL) 1971 8 2011 2 40 178 4.45 1 134 27.360 27.521 1.549 57091 URALLA (BLUE NOBBY) 1975 1 2010 2 36 159 4.42 1 143 26.692 28.734 1.746 57095 TABULAM (MUIRNE) 1969 12 2011 4 42 280 6.67 1 165 30.286 31.257 1.450 57103 KOOKABOOKRA 1969 12 2011 2 42 302 7.19 1 160 21.109 23.433 2.157 57104 YARROWITCH (MARETTO) 1959 4 2011 6 53 177 3.34 1 153 27.277 29.903 1.561 58026 GREVILLIA (SUMMERLAND WAY) 1963 4 2000 10 38 179 4.71 1 122 24.011 26.452 1.684 58044 NIMBIN POST OFFICE 1963 4 2010 11 48 135 2.81 1 149 38.711 34.909 0.955 58072 FEDERAL POST OFFICE 1965 11 1998 2 33 120 3.64 2 120 37.033 28.177 0.769
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Table B.4.2: continued
Average of record Number Lower Upper At-site Standard Station start start end end rainfall Station name length of rainfall limit limit mean deviation Skew ID year month year month event per (years) event (hour) (hour) (hour) (hour) year 58099 WHIPORIE POST OFFICE 1973 3 2011 5 39 165 4.23 1 124 28.800 27.313 1.189 58109 TYALGUM (KERRS LANE) 1965 10 1996 8 32 98 3.06 2 147 38.163 33.212 1.064 58113 GREEN PIGEON (MORNING VIEW) 1978 1 2010 11 34 143 4.21 1 164 34.916 33.946 1.265 58129 KUNGHUR (THE JUNCTION) 1965 10 2008 11 44 123 2.80 1 164 35.967 33.269 1.169 58131 ALSTONVILLE TROPICAL FRUIT RESEARCH STAT 1963 2 2011 5 49 263 5.37 1 142 35.996 27.440 0.981 58158 MURWILLUMBAH (BRAY PARK) 1972 10 2011 3 39 179 4.59 1 137 36.341 29.521 0.888 59000 BELLBROOK (EAST STREET) 1956 1 2010 8 55 208 3.78 1 152 35.490 32.739 1.020 59017 KEMPSEY (WIDE STREET) 1956 12 2011 2 55 153 2.78 1 99 31.856 25.166 0.677 59026 UPPER ORARA (AURANIA) 1970 4 2010 12 41 176 4.29 1 157 39.773 33.029 1.183 59040 COFFS HARBOUR MO 1960 11 2011 7 51 276 5.41 1 146 35.395 26.785 1.061 59067 DORRIGO (MYRTLE ST) 1954 7 1999 5 46 207 4.50 1 220 40.787 42.042 1.394 60030 TAREE (ROBERTSON ST) 1964 6 2005 5 42 197 4.69 1 143 34.650 25.594 0.895 60080 COMBOYNE SOUTH 1966 11 2011 2 45 223 4.96 1 181 40.578 38.016 1.104 60085 YARRAS (MOUNT SEAVIEW) 1969 1 2011 2 43 282 6.56 1 142 29.415 31.593 1.468 60104 NOWENDOC (GREEN HILLS) 1971 2 2011 5 41 208 5.07 1 139 32.712 31.801 1.246 60106 NUMBER ONE (MURRAYS CREEK) 1977 7 2011 2 34 147 4.32 1 141 25.605 27.094 1.610 61078 WILLIAMTOWN RAAF 1952 12 2011 2 59 317 5.37 1 113 28.445 21.274 0.953 61089 SCONE SCS 1952 7 2011 5 60 330 5.50 1 82 17.400 14.552 1.655 61151 CHICHESTER DAM 1960 6 2011 5 52 277 5.33 1 211 32.462 29.583 1.544 61158 GLENDON BROOK (LILYVALE) 1964 4 2011 5 48 232 4.83 1 91 22.315 21.056 1.234 61211 COLO HEIGHTS (MOUNTAIN PINES) 1962 11 2010 11 49 221 4.51 1 141 29.955 26.651 1.245 61212 LIDDELL (POWER STATION) 1964 8 1995 3 31 114 3.68 1 116 17.965 18.114 2.243 61238 POKOLBIN (SOMERSET) 1962 8 2011 7 50 324 6.48 1 94 21.731 18.755 1.197 61250 PATERSON (TOCAL AWS) 1975 1 2011 7 37 200 5.41 1 86 22.885 20.824 1.016 61287 MERRIWA (ROSCOMMON) 1969 3 2011 5 43 143 3.33 1 63 15.937 13.209 1.235 61288 LOSTOCK DAM 1969 10 2011 5 42 150 3.57 1 112 30.440 24.527 0.711 61309 MILBRODALE (HILLSDALE) 1969 10 2011 2 42 269 6.40 1 81 20.357 17.366 1.173 61311 GRAHAMSTOWN (HUNTER WATER BOARD) 1975 1 2006 9 32 109 3.41 2 97 27.385 20.481 0.871
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Table B.4.2: continued
Average of record Number Lower Upper At-site Standard Station start start end end rainfall Station name length of rainfall limit limit mean deviation Skew ID year month year month event per (years) event (hour) (hour) (hour) (hour) year 61334 GLEN ALICE 1970 7 2011 5 42 203 4.83 1 85 16.887 15.727 1.613 61351 PEATS RIDGE (WARATAH ROAD) 1981 10 2010 12 30 142 4.73 1 143 35.556 27.264 0.921 62005 CASSILIS POST OFFICE 1967 5 2004 1 37 160 4.32 2 91 18.369 16.171 1.619 63023 COWRA RESEARCH CENTRE (EVANS ST) 1941 10 2011 5 70 420 6.00 1 82 16.548 13.330 1.505 63039 KATOOMBA (MURRI ST) 1965 6 2010 5 46 181 3.93 1 175 48.945 38.910 0.843 63043 KURRAJONG HEIGHTS (BELLS LINE OF ROAD) 1965 5 2011 2 47 190 4.04 1 143 38.305 28.745 0.987 63108 OBERON DAM 1955 1 1988 5 34 243 7.15 1 105 18.370 15.717 1.963 64046 COONABARABRAN (WESTMOUNT) 1971 7 2011 5 41 266 6.49 1 152 22.064 19.988 1.983 65035 WELLINGTON RESEARCH CENTRE 1961 1 2005 2 45 352 7.82 1 68 15.276 12.491 1.363 66037 SYDNEY AIRPORT AMO 1962 7 2011 5 50 202 4.04 1 115 30.480 22.307 1.029 66062 SYDNEY (OBSERVATORY HILL) 1913 1 2011 4 99 483 4.88 1 178 36.292 27.398 1.295 67033 RICHMOND RAAF 1953 1 1994 10 43 203 4.72 1 106 25.438 23.866 1.179 67035 LIVERPOOL(WHITLAM CENTRE) 1965 1 2001 12 38 157 4.13 1 105 27.287 22.429 0.851 68076 NOWRA RAN AIR STATION 1964 8 1997 12 34 76 2.24 2 133 34.276 25.422 1.441 68117 ROBERTSON (ST.ANTHONYS) 1962 11 2005 6 43 112 2.60 2 184 55.080 33.696 0.860 68131 PORT KEMBLA (BHP CENTRAL LAB) 1963 5 2011 5 49 116 2.37 1 151 31.552 25.466 1.550 69049 NERRIGA COMPOSITE 1971 2 2011 2 41 99 2.41 1 101 26.828 22.049 1.057 69055 GREEN CAPE LIGHTHOUSE 1967 3 2002 4 36 82 2.28 1 141 24.854 21.116 2.543 69127 ARALUEN LOWER (ARALUEN RD) 1980 6 2011 5 32 65 2.03 1 102 29.677 24.074 1.101 70012 BUNGONIA (INVERARY PARK) 1965 5 2010 5 46 185 4.02 1 92 23.578 18.700 0.994 70014 CANBERRA AIRPORT COMPARISON 1937 12 2010 11 74 495 6.69 1 72 16.897 12.503 1.000 70015 CANBERRA FORESTRY 1932 1 1971 2 40 232 5.80 2 77 16.957 12.716 1.735 70073 CHAKOLA (RIVERSDALE) 1965 12 2011 5 46 195 4.24 1 98 17.918 16.002 1.874 70080 TARALGA POST OFFICE 1977 6 2010 7 34 109 3.21 1 102 24.495 20.336 1.312 70199 NUMERALLA (BADJA COMPOSITE) 1965 12 2011 4 46 166 3.61 2 156 34.777 29.474 1.343 71042 INGEBYRA (GROSSES PLAINS) 1971 2 2011 5 41 201 4.90 1 111 29.920 24.597 1.127 72023 HUME RESERVOIR 1955 3 2011 5 57 458 8.04 2 128 21.253 14.317 1.796 72060 KHANCOBAN SMHEA 1961 1 1994 1 34 275 8.09 1 125 26.800 20.583 1.549
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Table B.4.2: continued
Average of record Number Lower Upper At-site Standard Station start start end end rainfall Station name length of rainfall limit limit mean deviation Skew ID year month year month event per (years) event (hour) (hour) (hour) (hour) year 72150 WAGGA WAGGA AMO 1945 1 2011 3 67 388 5.79 1 74 16.039 11.801 1.326 73007 BURRINJUCK DAM 1911 5 2011 3 101 622 6.16 1 113 24.367 17.435 1.372 74114 WAGGA WAGGA RESEARCH CENTRE 1946 9 2004 1 58 338 5.83 1 61 15.917 10.771 1.136 75028 GRIFFITH CSIRO 1931 6 1989 6 59 272 4.61 2 69 15.901 11.942 1.631 75050 NARADHAN (URALBA) 1970 4 2011 6 42 201 4.79 1 53 15.020 11.006 1.275 Minimum 30 65 2.03 1.00 53.00 14.19 10.77 0.68
Maximum 101 622 8.09 2.00 220.00 55.08 42.04 2.54
Average 45 229 4.99 1.13 115.66 25.89 22.09 1.35
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Table B.5.1: Summary of calibration results for the Byron Creek catchment
Initial loss Alpha Continuing Storage delay Standardised Selected Year (mm) values loss (mm/hr) parameter (k, hr) (k, hr/km2) events 1978 12.18 0.003 3.234 4.65 0.12 Event 1 1979 0.64 0.003 3.832 12.62 0.32 Event 2 1979 42.26 0.002 11.809 10.16 0.26 Event 4 1979 17.68 0.001 1.956 8.90 0.23 Event 5 1983 49.53 0.005 3.510 12.46 0.32 Event 9 1983 24.82 0.010 10.822 6.85 0.18 Event 10 1984 38.27 0.003 3.638 4.70 0.12 Event 11 1984 28.61 0.001 2.723 11.32 0.29 Event 13 1985 11.37 0.010 1.866 8.22 0.21 Event 14 1988 50.67 0.003 3.279 10.85 0.28 Event 17 1988 20.40 0.002 2.030 9.94 0.25 Event 18 1988 30.96 0.003 3.266 11.70 0.30 Event 19 1989 9.32 0.003 8.149 25.20 0.65 Event 20 1989 6.87 0.004 5.326 18.41 0.47 Event 21 1990 10.84 0.009 4.883 7.19 0.18 Event 23 1994 31.68 0.003 2.806 9.94 0.25 Event 24
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Table B.5.2: Summary of calibration results for the Pokolbin Creek catchment
Initial loss Alpha Continuing Storage delay Standardised Selected Year (mm) values loss (mm/hr) parameter (k, hr) (k, hr/km2) events 1967 42.11 0.002 5.206 3.04 0.12 Event 8 1968 24.76 0.005 1.489 10.22 0.41 Event 10 1971 22.21 0.003 2.078 5.21 0.21 Event 17 1971 68.33 0.004 0.910 9.36 0.37 Event 19 1972 20.26 0.001 2.194 8.84 0.35 Event 22 1974 28.87 0.009 1.584 4.98 0.20 Event 34 1976 77.48 0.001 2.390 7.27 0.29 Event 40 1976 38.18 0.004 0.689 14.12 0.56 Event 41 1981 79.98 0.001 3.288 8.14 0.33 Event 60 1982 16.81 0.001 0.374 3.95 0.16 Event 64 1982 35.60 0.003 3.070 8.26 0.33 Event 65 1989 21.07 0.002 1.347 4.25 0.17 Event 84 1990 98.20 0.002 2.014 2.01 0.08 Event 87 1990 14.93 0.003 0.379 9.20 0.37 Event 90 1992 51.01 0.003 3.586 8.85 0.35 Event 94 1992 40.57 0.005 3.668 5.95 0.24 Event 95 1998 38.67 0.004 2.066 13.18 0.53 Event 110 2002 88.60 0.006 0.509 5.69 0.23 Event 120 2004 114.37 0.001 0.090 5.04 0.20 Event 124 2005 66.76 0.004 0.049 7.00 0.28 Event 126 2008 45.22 0.001 0.973 17.04 0.68 Event 136 2009 50.28 0.010 4.224 13.65 0.55 Event 139 2009 23.37 0.006 2.624 7.60 0.30 Event 140
Table B.5.3: Summary of calibration results for the Antiene Creek catchment
Initial loss Alpha Continuing Storage delay Standardised Selected Year (mm) values loss (mm/hr) parameter (k, hr) (k, hr/km2) events 1976 29.41 0.010 0.0001 2.48 0.19 Event 5 1978 26.08 0.007 0.0001 3.03 0.23 Event 11 1981 50.08 0.003 3.0665 2.20 0.17 Event 14 1982 20.86 0.003 7.3604 2.10 0.16 Event 17 1982 19.61 0.006 3.4620 1.59 0.12 Event 19 1984 6.00 0.002 1.9040 3.08 0.24 Event 22 1987 28.63 0.003 4.5377 4.07 0.31 Event 29 1988 38.95 0.006 1.4267 5.25 0.40 Event 30 1988 17.49 0.004 1.8596 3.52 0.27 Event 33 1992 35.26 0.003 1.7238 2.57 0.20 Event 40
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Table B.5.4: Summary of calibration results for Toongabbie Creek catchment
Initial loss Alpha Continuing Storage delay Standardised Selected Year (mm) values loss (mm/hr) parameter (k, hr) (k, hr/km2) events 1982 1.30 0.007 16.994 9.36 0.13 Event 3 1983 8.55 0.001 3.856 13.35 0.19 Event 4 1983 0.37 0.002 3.418 8.12 0.12 Event 5 1984 4.87 0.001 0.895 12.58 0.18 Event 7 1985 9.95 0.003 2.300 8.77 0.13 Event 10 1987 21.69 0.001 1.737 15.59 0.22 Event 12 1989 2.31 0.001 0.735 3.91 0.06 Event 16 1997 0.76 0.004 0.907 5.65 0.08 Event 29 1998 4.59 0.006 1.301 7.06 0.10 Event 33 1999 11.35 0.002 1.447 9.18 0.13 Event 34 2000 4.09 0.001 0.267 9.13 0.13 Event 35 2000 15.57 0.001 0.811 7.20 0.10 Event 36 2001 3.68 0.003 1.787 14.52 0.21 Event 37
Table B.5.5: Summary of calibration results for the Mill Post Creek catchment
Initial loss Alpha Continuing Storage delay Standardised Selected Year (mm) values loss (mm/hr) parameter (k, hr) (k, hr/km2) events 1959 22.21 0.001 0.062 0.62 0.04 Event 2 1959 21.24 0.010 0.0001 4.99 0.31 Event 3 1959 15.98 0.010 0.881 6.28 0.39 Event 4 1961 22.21 0.002 8.111 4.18 0.26 Event 11 1962 31.62 0.004 1.151 6.69 0.42 Event 15 1962 14.30 0.010 2.620 2.82 0.18 Event 16 1962 26.58 0.009 6.998 4.45 0.28 Event 17 1963 30.58 0.004 5.144 5.63 0.35 Event 18 1963 16.47 0.003 0.715 2.57 0.16 Event 19 1968 54.90 0.001 0.685 0.66 0.04 Event 25 1970 12.97 0.004 0.969 2.74 0.17 Event 31 1973 16.94 0.002 4.152 4.49 0.28 Event 38 1974 20.38 0.002 5.880 5.76 0.36 Event 42 1974 15.49 0.002 12.933 8.73 0.55 Event 43 1974 33.20 0.010 6.190 9.96 0.62 Event 44 1974 17.26 0.006 0.548 4.33 0.27 Event 46 1975 43.61 0.010 0.100 6.63 0.41 Event 48 1975 14.15 0.001 1.733 11.63 0.73 Event 49 1976 28.46 0.004 4.780 5.52 0.35 Event 53
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Table B.5.6: Goodness-of-fit test results for DCS data
Station Chi-Squared test Kolmogorov-Smirnov test Anderson-Darling test ID Exponential Gamma Exponential Gamma Exponential Gamma 48027 1 1 1 0 1 0 48031 1 1 0 0 0 0 51049 1 1 0 0 0 0 53048 0 0 0 0 0 0 54102 1 1 0 0 1 0 54104 1 1 1 1 1 0 54105 1 1 1 0 1 0 54138 1 1 1 0 1 0 55024 1 1 1 1 1 0 55054 1 1 1 0 1 0 55136 1 1 1 1 0 1 55194 1 1 1 0 1 0 55302 1 1 0 0 1 0 56013 1 1 0 0 0 0 56018 1 1 1 0 1 0 56022 0 0 1 0 1 0 56104 1 1 1 0 1 0 56202 0 0 0 0 0 0 57091 0 0 1 0 0 0 57095 1 1 1 1 1 1 57103 1 1 1 1 1 1 57104 1 0 1 1 1 0 58026 0 0 1 0 1 0 58044 0 1 0 1 0 1 58072 1 0 0 0 0 0 58099 0 1 0 1 0 0 58109 0 0 0 0 0 0 58113 0 0 0 0 0 1 58129 0 0 0 0 0 0 58131 1 1 1 0 1 0 58158 1 0 0 0 0 0 59000 1 1 0 1 0 1 59017 1 1 0 1 0 1 59026 1 0 0 0 0 0 59040 1 1 1 0 1 0 59067 0 0 1 1 1 1 60030 1 1 1 1 1 1 60080 1 1 1 1 1 1 60085 1 1 1 0 1 1 60104 1 1 0 0 0 0 60106 1 1 1 0 0 0 61078 1 1 1 0 1 1 61089 1 1 1 0 1 0 61151 1 0 0 0 0 0
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Table B.5.6: continued
Station Chi-Squared test Kolmogorov-Smirnov test Anderson-Darling test ID Exponential Gamma Exponential Gamma Exponential Gamma 61158 0 0 0 0 0 0 61211 1 1 0 0 0 0 61212 1 1 0 0 0 0 61238 1 1 0 1 0 0 61250 1 1 0 1 0 1 61287 1 1 0 0 0 0 61288 1 1 0 1 0 1 61309 1 1 0 1 0 0 61311 1 0 0 0 0 0 61334 1 1 0 0 0 0 61351 1 1 0 0 0 1 62005 1 1 0 0 0 0 63023 1 1 1 0 1 0 63039 1 1 1 1 0 1 63043 1 0 1 0 1 0 63108 1 1 1 0 1 0 64046 1 1 0 0 0 0 65035 1 1 1 0 1 0 66037 1 1 1 0 1 0 66062 1 1 1 0 1 0 67033 1 1 0 1 0 1 67035 1 1 0 1 0 0 68076 1 0 0 0 1 0 68117 1 0 1 0 1 0 68131 1 0 0 0 0 0 69049 1 0 0 0 0 0 69055 1 1 0 0 0 0 69127 0 0 0 0 0 0 70012 1 1 0 0 0 0 70014 1 1 1 1 1 1 70015 1 1 1 0 1 0 70073 1 1 1 0 1 0 70080 1 0 0 0 0 0 70199 1 0 0 0 0 0 71042 1 1 0 0 0 0 72023 1 1 1 0 1 0 72060 1 1 1 0 1 0 72150 1 1 1 0 1 0 73007 1 1 1 0 1 0 74114 1 1 1 0 1 0 75028 1 1 1 0 1 0 75050 1 1 1 0 1 0 Count 13 24 43 65 44 68 Percentage 15% 28% 50% 76% 51% 79%
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Table B.5.7: Rainfall Inter-Event Duration (Original Data) Data Statistics
Record Number of Average of Lower Upper At-site Standard Station Start Start End End Station name length inter-events inter-events limit limit mean deviation Skew ID year month year month (years) (days) per year (days) (days) (days) (days) 48027 COBAR MO 1962 6 2010 9 49 314 6.41 0.58 510.33 55.93 71.16 2.77 48031 COLLARENEBRI (ALBERT ST) 1976 1 2011 5 36 206 5.72 0.83 1424.67 62.34 121.04 7.52 51049 TRANGIE RESEARCH STATION AWS 1968 8 2011 4 43 228 5.30 0.33 2858.58 67.81 197.77 12.56 53048 MOREE COMPARISON 1964 4 1995 6 32 186 5.81 0.67 399.83 60.28 69.89 1.88 54102 BARRABA (ROSEVALE) 1971 1 2011 2 41 287 7.00 0.58 474.83 50.65 59.02 2.59 54104 PINDARI DAM 1971 8 2011 2 40 272 6.80 0.50 596.50 52.11 68.54 3.34 54105 BUNDARRA (GRANITE HEIGHTS) 1975 1 2010 11 37 248 6.70 0.58 286.33 52.66 57.94 1.89 54138 UPPER HORTON (DUNBEACON) 1976 11 2011 2 35 182 5.20 0.75 456.75 68.15 76.65 2.08 55024 GUNNEDAH RESOURCE CENTRE 1946 4 2011 4 66 455 6.89 0.50 708.42 51.42 71.61 3.89 55054 TAMWORTH AIRPORT 1958 8 1992 12 35 256 7.31 0.67 299.33 48.95 57.95 1.98 55136 WOOLBROOK (DANGLEMAH ROAD) 1971 1 2011 2 41 295 7.20 0.50 407.42 49.41 64.07 2.22 55194 GOWRIE NORTH 1971 1 2011 4 41 285 6.95 0.83 524.42 51.48 65.43 2.82 55302 NUNDLE (CHAFFEY DAM) 1977 11 2010 8 34 161 4.74 0.75 4444.25 70.74 349.57 12.39 56013 GLEN INNES AG RESEARCH STN 1970 6 2011 2 41 330 8.05 0.42 712.83 44.34 63.92 4.73 56018 INVERELL RESEARCH CENTRE 1947 8 2010 6 64 499 7.80 0.42 469.25 45.52 60.65 2.87 56022 LEGUME (NEW KOREELAH) 1973 4 2010 11 38 190 5.00 0.58 366.25 69.68 82.03 1.62 56140 EMMAVILLE (BEN VALE) 1962 1 2011 2 50 154 3.08 1.33 10845.50 115.32 872.43 12.32 56202 BLACK SWAMP (MAXWELL) 1971 8 2011 2 40 177 4.43 0.75 2492.92 80.91 203.67 9.69 57091 URALLA (BLUE NOBBY) 1975 1 2010 2 36 158 4.39 0.58 4391.83 81.06 352.43 11.81 57095 TABULAM (MUIRNE) 1969 12 2011 4 42 279 6.64 0.75 492.67 53.87 75.64 2.54 57103 KOOKABOOKRA 1969 12 2011 2 42 301 7.17 0.58 284.17 49.78 66.59 1.91 57104 YARROWITCH (MARETTO) 1959 4 2011 6 53 176 3.32 0.75 4460.83 106.60 349.45 11.27 58026 GREVILLIA (SUMMERLAND WAY) 1963 4 2000 10 38 178 4.68 0.50 357.17 74.23 91.26 1.62 58044 NIMBIN POST OFFICE 1963 4 2010 11 48 134 2.79 0.92 778.25 129.27 172.15 2.02 58072 FEDERAL POST OFFICE 1965 11 1998 2 33 119 3.61 1.08 1034.83 97.90 145.36 3.46 58099 WHIPORIE POST OFFICE 1973 3 2011 5 39 164 4.21 0.83 1156.83 84.12 129.49 4.41 58109 TYALGUM (KERRS LANE) 1965 10 1996 8 32 97 3.03 2.00 737.00 109.60 143.51 2.04 58113 GREEN PIGEON (MORNING VIEW) 1978 1 2010 11 34 142 4.18 0.67 1118.17 84.03 122.83 4.74 58129 KUNGHUR (THE JUNCTION) 1965 10 2008 11 44 122 2.77 1.17 595.17 125.40 129.56 1.27
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Table B.5.7: Continued Record Number of Average of Lower Upper At-site Standard Station Start Start End End Station name length inter-events inter-events limit limit mean deviation Skew ID year month year month (years) (days) per year (days) (days) (days) (days) ALSTONVILLE TROPICAL FRUIT RESEARCH 58131 1963 2 2011 5 49 262 5.35 0.92 470.00 67.05 77.14 2.07 STAT 58158 MURWILLUMBAH (BRAY PARK) 1972 10 2011 3 39 178 4.56 0.83 498.08 78.63 96.73 1.77 59000 BELLBROOK (EAST STREET) 1956 1 2010 8 55 207 3.76 0.83 739.83 95.33 118.18 2.12 59017 KEMPSEY (WIDE STREET) 1956 12 2011 2 55 152 2.76 0.42 2565.50 129.04 256.17 6.66 59026 UPPER ORARA (AURANIA) 1970 4 2010 12 41 175 4.27 0.92 612.67 79.83 99.64 2.15 59040 COFFS HARBOUR MO 1960 11 2011 7 51 275 5.39 0.50 343.33 66.64 72.04 1.62 59067 DORRIGO (MYRTLE ST) 1954 7 1999 5 46 206 4.48 0.58 613.08 79.09 97.30 2.11 60030 TAREE (ROBERTSON ST) 1964 6 2005 5 42 196 4.67 0.42 696.50 75.56 95.26 2.87 60080 COMBOYNE SOUTH 1966 11 2011 2 45 222 4.93 0.67 435.00 72.13 81.70 1.71 60085 YARRAS (MOUNT SEAVIEW) 1969 1 2011 2 43 281 6.53 0.50 1429.00 54.44 105.02 8.55 60104 NOWENDOC (GREEN HILLS) 1971 2 2011 5 41 207 5.05 1.08 1481.58 70.58 121.47 7.96 60106 NUMBER ONE (MURRAYS CREEK) 1977 7 2011 2 34 146 4.29 0.67 602.50 82.41 93.57 1.96 61078 WILLIAMTOWN RAAF 1952 12 2011 2 59 316 5.36 0.83 993.67 66.77 88.78 4.78 61089 SCONE SCS 1952 7 2011 5 60 329 5.48 0.50 850.75 65.02 85.85 3.71 61151 CHICHESTER DAM 1960 6 2011 5 52 276 5.31 0.67 1159.58 66.55 100.03 5.46 61158 GLENDON BROOK (LILYVALE) 1964 4 2011 5 48 231 4.81 0.58 541.00 74.24 92.01 1.95 61211 COLO HEIGHTS (MOUNTAIN PINES) 1962 11 2010 11 49 220 4.49 0.58 598.67 79.58 95.40 2.04 61212 LIDDELL (POWER STATION) 1964 8 1995 3 31 113 3.65 0.50 1888.08 97.75 215.37 6.23 61238 POKOLBIN (SOMERSET) 1962 8 2011 7 50 323 6.46 0.50 338.50 54.83 62.18 1.72 61250 PATERSON (TOCAL AWS) 1975 1 2011 7 37 199 5.38 0.67 492.83 66.34 89.19 2.18 61287 MERRIWA (ROSCOMMON) 1969 3 2011 5 43 142 3.30 0.75 2453.92 107.94 319.36 6.38 61288 LOSTOCK DAM 1969 10 2011 5 42 149 3.55 0.92 5953.42 101.52 489.33 11.72 61309 MILBRODALE (HILLSDALE) 1969 10 2011 2 42 268 6.38 0.67 336.17 55.87 71.15 1.93 61311 GRAHAMSTOWN (HUNTER WATER BOARD) 1975 1 2006 9 32 108 3.38 1.00 4398.33 106.16 424.80 9.83 61334 GLEN ALICE 1970 7 2011 5 42 202 4.81 0.50 2403.58 72.56 183.08 10.54 61351 PEATS RIDGE (WARATAH ROAD) 1981 10 2010 12 30 141 4.70 0.83 476.00 75.23 82.96 1.79 62005 CASSILIS POST OFFICE 1967 5 2004 1 37 159 4.30 0.58 1227.25 83.45 154.84 4.72 63023 COWRA RESEARCH CENTRE (EVANS ST) 1941 10 2011 5 70 419 5.99 0.33 1028.17 60.00 86.69 4.76 63039 KATOOMBA (MURRI ST) 1965 6 2010 5 46 180 3.91 0.67 2332.17 90.33 199.96 8.42 63043 KURRAJONG HEIGHTS (BELLS LINE OF ROAD) 1965 5 2011 2 47 189 4.02 0.83 1450.83 87.64 137.05 5.85 63108 OBERON DAM 1955 1 1988 5 34 242 7.12 0.50 883.67 50.18 92.03 4.90
University of Western Sydney Page 260
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Table B.5.7: Continued Record Number of Average of Lower Upper At-site Standard Station Start Start End End Station name length inter-events inter-events limit limit mean deviation Skew ID year month year month (years) (days) per year (days) (days) (days) (days) 64046 COONABARABRAN (WESTMOUNT) 1971 7 2011 5 41 265 6.46 0.75 2046.83 54.55 155.35 10.43 65035 WELLINGTON RESEARCH CENTRE 1961 1 2005 2 45 351 7.80 0.50 284.83 45.52 50.56 1.96 66037 SYDNEY AIRPORT AMO 1962 7 2011 5 50 201 4.02 1.08 706.67 87.61 99.80 2.31 66062 SYDNEY (OBSERVATORY HILL) 1913 1 2011 4 99 482 4.87 0.50 554.42 74.29 81.33 1.92 67033 RICHMOND RAAF 1953 1 1994 10 43 202 4.70 0.50 505.00 72.38 83.66 1.81 67035 LIVERPOOL(WHITLAM CENTRE) 1965 1 2001 12 38 156 4.11 0.92 1226.33 81.86 122.78 5.66 68076 NOWRA RAN AIR STATION 1964 8 1997 12 34 75 2.21 1.00 2594.42 161.18 328.07 6.08 68117 ROBERTSON (ST.ANTHONYS) 1962 11 2005 6 43 111 2.58 2.08 2418.92 137.87 254.09 6.90 68131 PORT KEMBLA (BHP CENTRAL LAB) 1963 5 2011 5 49 115 2.35 0.67 3570.50 151.83 352.56 8.26 69049 NERRIGA COMPOSITE 1971 2 2011 2 41 98 2.39 1.08 4631.00 147.92 470.53 9.10 69055 GREEN CAPE LIGHTHOUSE 1967 3 2002 4 36 81 2.25 1.33 1109.42 149.23 187.71 3.08 69127 ARALUEN LOWER (ARALUEN RD) 1980 6 2011 5 32 64 2.00 2.17 980.00 170.85 189.42 2.11 70012 BUNGONIA (INVERARY PARK) 1965 5 2010 5 46 184 4.00 0.75 3531.50 87.82 265.30 12.10 70014 CANBERRA AIRPORT COMPARISON 1937 12 2010 11 74 494 6.68 0.67 832.50 53.79 74.47 4.34 70015 CANBERRA FORESTRY 1932 1 1971 2 40 231 5.78 0.67 1003.50 61.53 97.77 5.08 70073 CHAKOLA (RIVERSDALE) 1965 12 2011 5 46 194 4.22 0.67 1160.42 84.90 127.61 4.30 70080 TARALGA POST OFFICE 1977 6 2010 7 34 108 3.18 0.83 3509.25 108.40 341.21 9.44 70199 NUMERALLA (BADJA COMPOSITE) 1965 12 2011 4 46 165 3.59 0.50 520.00 98.36 117.88 1.69 71042 INGEBYRA (GROSSES PLAINS) 1971 2 2011 5 41 200 4.88 0.42 473.33 71.46 82.70 1.94 72023 HUME RESERVOIR 1955 3 2011 5 57 457 8.02 0.42 451.33 44.75 60.19 3.05 72060 KHANCOBAN SMHEA 1961 1 1994 1 34 274 8.06 0.92 391.83 43.72 49.12 2.91 72150 WAGGA WAGGA AMO 1945 1 2011 3 67 387 5.78 0.42 3821.83 62.30 204.77 16.37 73007 BURRINJUCK DAM 1911 5 2011 3 101 621 6.15 0.67 1907.42 58.58 148.79 7.75 74114 WAGGA WAGGA RESEARCH CENTRE 1946 9 2004 1 58 337 5.81 0.67 1057.00 61.21 111.63 6.10 75028 GRIFFITH CSIRO 1931 6 1989 6 59 271 4.59 0.58 1761.58 77.13 134.14 8.22 75050 NARADHAN (URALBA) 1970 4 2011 6 42 200 4.76 0.67 2877.42 74.66 230.41 10.11 Minimum 30 64 2.13 0.33 284.17 43.72 49.12 1.27
Maximum 101 621 6.15 2.17 10845.50 170.85 872.43 16.37
Average 45 228 5.04 0.74 1487.28 79.42 153.46 5.00
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Table B.5.8: Goodness-of-fit test results for IED data (1st set)
Station Kolmogorov-Smirnov test Anderson-Darling test ID Exponential Gamma Exponential Gamma 48027 1 0 1 0 48031 1 1 1 1 51049 1 1 1 1 53048 1 0 1 0 54102 0 0 0 0 54104 1 1 1 1 54105 1 0 0 0 54138 0 0 0 0 55024 1 1 1 1 55054 1 0 1 0 55136 1 0 1 1 55194 1 0 1 1 55302 1 1 1 1 56013 1 1 1 1 56018 1 1 1 1 56022 1 0 1 0 56140 1 1 1 1 56202 1 1 1 1 57091 1 1 1 1 57095 1 1 1 1 57103 1 0 1 1 57104 1 1 1 1 58026 1 0 1 0 58044 1 0 1 0 58072 1 1 1 1 58099 1 1 1 1 58109 1 0 1 0 58113 1 1 1 1 58129 0 0 0 0 58131 0 0 0 0 58158 1 0 1 0 59000 1 0 1 0 59017 1 1 1 1 59026 1 0 1 0 59040 0 0 1 0 59067 1 0 1 0 60030 0 0 1 0 60080 1 0 1 0 60085 1 1 1 1
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Table B.5.8: Continued
Station Kolmogorov-Smirnov test Anderson-Darling test ID Exponential Gamma Exponential Gamma 60104 1 1 1 1 60106 1 0 1 0 61078 0 1 1 1 61089 1 0 1 1 61151 1 1 1 1 61158 1 0 1 0 61211 1 0 1 0 61212 1 1 1 1 61238 1 0 1 0 61250 1 0 1 0 61287 1 1 1 1 61288 1 1 1 1 61309 1 0 1 1 61311 1 1 1 1 61334 1 1 1 1 62005 1 1 1 1 63023 1 1 1 1 63039 1 1 1 1 63043 1 1 1 1 63108 1 1 1 1 64046 1 1 1 1 65035 1 0 0 0 66037 0 0 0 0 66062 1 0 1 0 67033 1 0 1 0 67035 1 1 1 1 68076 0 1 0 1 68117 1 1 1 1 68131 1 1 1 1 69049 1 1 1 1 69055 0 0 0 0 69127 0 0 0 0 70012 1 1 1 1 70014 1 1 1 1 70015 1 1 1 1 70073 1 1 1 1 70080 1 1 1 1 70199 1 0 1 0 71042 0 0 0 0 72023 1 1 1 1
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Table B.5.8: Continued Kolmogorov-Smirnov test Anderson-Darling test Station ID Exponential Gamma Exponential Gamma 72060 0 1 0 1 72150 1 1 1 1 73007 1 1 1 1 74114 1 1 1 1 75028 1 1 1 1 75050 1 1 1 1 Count 13 37 12 32 Percentage 15% 43% 14% 37%
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Table B.5.9: Rainfall Inter-Event Duration (Trimmed Data) Data Statistics
Record Number of Average of Lower Upper At-site Standard Station Start Start End End Station name length inter-events inter-events limit limit mean deviation Skew ID year month year month (years) (days) per year (days) (days) (days) (days) 48027 COBAR MO 1962 6 2010 9 49 314 6.41 0.58 510.33 55.93 71.16 2.77 48031 COLLARENEBRI (ALBERT ST) 1976 1 2011 5 36 205 5.69 0.83 411.83 55.70 74.69 2.39 51049 TRANGIE RESEARCH STATION AWS 1968 8 2011 4 43 227 5.28 0.33 356.17 55.52 68.36 2.22 53048 MOREE COMPARISON 1964 4 1995 6 32 186 5.81 0.67 399.83 60.28 69.89 1.88 54102 BARRABA (ROSEVALE) 1971 1 2011 2 41 287 7.00 0.58 474.83 50.65 59.02 2.59 54104 PINDARI DAM 1971 8 2011 2 40 272 6.80 0.50 596.50 52.11 68.54 3.34 54105 BUNDARRA (GRANITE HEIGHTS) 1975 1 2010 11 37 248 6.70 0.58 286.33 52.66 57.94 1.89 54138 UPPER HORTON (DUNBEACON) 1976 11 2011 2 35 182 5.20 0.75 456.75 68.15 76.65 2.08 55024 GUNNEDAH RESOURCE CENTRE 1946 4 2011 4 66 455 6.89 0.50 708.42 51.42 71.61 3.89 55054 TAMWORTH AIRPORT 1958 8 1992 12 35 256 7.31 0.67 299.33 48.95 57.95 1.98 55136 WOOLBROOK (DANGLEMAH ROAD) 1971 1 2011 2 41 295 7.20 0.50 407.42 49.41 64.07 2.22 55194 GOWRIE NORTH 1971 1 2011 4 41 285 6.95 0.83 524.42 51.48 65.43 2.82 55302 NUNDLE (CHAFFEY DAM) 1977 11 2010 8 34 160 4.71 0.75 218.00 43.40 43.78 1.58 56013 GLEN INNES AG RESEARCH STN 1970 6 2011 2 41 330 8.05 0.42 712.83 44.34 63.92 4.73 56018 INVERELL RESEARCH CENTRE 1947 8 2010 6 64 499 7.80 0.42 469.25 45.52 60.65 2.87 56022 LEGUME (NEW KOREELAH) 1973 4 2010 11 38 190 5.00 0.58 366.25 69.68 82.03 1.62 56140 EMMAVILLE (BEN VALE) 1962 1 2011 2 50 153 3.06 1.33 324.33 45.19 60.99 2.46 56202 BLACK SWAMP (MAXWELL) 1971 8 2011 2 40 176 4.40 0.75 480.50 67.20 91.02 2.07 57091 URALLA (BLUE NOBBY) 1975 1 2010 2 36 157 4.36 0.58 350.17 53.61 71.60 1.98 57095 TABULAM (MUIRNE) 1969 12 2011 4 42 279 6.64 0.75 492.67 53.87 75.64 2.54 57103 KOOKABOOKRA 1969 12 2011 2 42 301 7.17 0.58 284.17 49.78 66.59 1.91 57104 YARROWITCH (MARETTO) 1959 4 2011 6 53 173 3.26 0.75 406.50 73.57 86.80 1.71 58026 GREVILLIA (SUMMERLAND WAY) 1963 4 2000 10 38 178 4.68 0.50 357.17 74.23 91.26 1.62 58044 NIMBIN POST OFFICE 1963 4 2010 11 48 132 2.75 0.92 713.67 119.46 153.58 1.92 58072 FEDERAL POST OFFICE 1965 11 1998 2 33 118 3.58 1.08 628.00 89.96 117.24 2.41 58099 WHIPORIE POST OFFICE 1973 3 2011 5 39 163 4.18 0.83 625.58 77.54 98.61 2.19 58109 TYALGUM (KERRS LANE) 1965 10 1996 8 32 96 3.00 2.00 671.00 103.06 128.93 1.76 58113 GREEN PIGEON (MORNING VIEW) 1978 1 2010 11 34 141 4.15 0.67 353.50 76.70 86.61 1.55 58129 KUNGHUR (THE JUNCTION) 1965 10 2008 11 44 122 2.77 1.17 595.17 125.40 129.56 1.27
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Table B.5.9: Continued Record Number of Average of Lower Upper At-site Standard Station Start Start End End Station name length inter-events inter-events limit limit mean deviation Skew ID year month year month (years) (days) per year (days) (days) (days) (days) 58131 ALSTONVILLE TROPICAL FRUIT RESEARCH STAT 1963 2 2011 5 49 262 5.35 0.92 470.00 67.05 77.14 2.07 58158 MURWILLUMBAH (BRAY PARK) 1972 10 2011 3 39 178 4.56 0.83 498.08 78.63 96.73 1.77 59000 BELLBROOK (EAST STREET) 1956 1 2010 8 55 206 3.75 0.83 616.83 92.21 109.54 1.75 59017 KEMPSEY (WIDE STREET) 1956 12 2011 2 55 150 2.73 0.42 729.33 104.90 129.05 2.32 59026 UPPER ORARA (AURANIA) 1970 4 2010 12 41 175 4.27 0.92 612.67 79.83 99.64 2.15 59040 COFFS HARBOUR MO 1960 11 2011 7 51 275 5.39 0.50 343.33 66.64 72.04 1.62 59067 DORRIGO (MYRTLE ST) 1954 7 1999 5 46 206 4.48 0.58 613.08 79.09 97.30 2.11 60030 TAREE (ROBERTSON ST) 1964 6 2005 5 42 196 4.67 0.42 696.50 75.56 95.26 2.87 60080 COMBOYNE SOUTH 1966 11 2011 2 45 222 4.93 0.67 435.00 72.13 81.70 1.71 60085 YARRAS (MOUNT SEAVIEW) 1969 1 2011 2 43 280 6.51 0.50 387.00 49.53 65.36 2.24 60104 NOWENDOC (GREEN HILLS) 1971 2 2011 5 41 206 5.02 1.08 330.08 63.73 71.18 1.68 60106 NUMBER ONE (MURRAYS CREEK) 1977 7 2011 2 34 146 4.29 0.67 602.50 82.41 93.57 1.96 61078 WILLIAMTOWN RAAF 1952 12 2011 2 59 315 5.34 0.83 534.67 63.82 71.85 2.29 61089 SCONE SCS 1952 7 2011 5 60 328 5.47 0.50 515.25 62.63 74.15 2.21 61151 CHICHESTER DAM 1960 6 2011 5 52 275 5.29 0.67 368.50 62.58 75.27 1.77 61158 GLENDON BROOK (LILYVALE) 1964 4 2011 5 48 231 4.81 0.58 541.00 74.24 92.01 1.95 61211 COLO HEIGHTS (MOUNTAIN PINES) 1962 11 2010 11 49 220 4.49 0.58 598.67 79.58 95.40 2.04 61212 LIDDELL (POWER STATION) 1964 8 1995 3 31 111 3.58 0.50 649.17 72.87 94.25 2.92 61238 POKOLBIN (SOMERSET) 1962 8 2011 7 50 323 6.46 0.50 338.50 54.83 62.18 1.72 61250 PATERSON (TOCAL AWS) 1975 1 2011 7 37 199 5.38 0.67 492.83 66.34 89.19 2.18 61287 MERRIWA (ROSCOMMON) 1969 3 2011 5 43 139 3.23 0.75 615.75 62.74 73.04 3.79 61288 LOSTOCK DAM 1969 10 2011 5 42 148 3.52 0.92 432.75 61.98 80.86 2.12 61309 MILBRODALE (HILLSDALE) 1969 10 2011 2 42 268 6.38 0.67 336.17 55.87 71.15 1.93 61311 GRAHAMSTOWN (HUNTER WATER BOARD) 1975 1 2006 9 32 107 3.34 1.00 558.42 66.05 82.06 2.83 61334 GLEN ALICE 1970 7 2011 5 42 201 4.79 0.50 534.67 60.96 79.90 2.49 61351 PEATS RIDGE (WARATAH ROAD) 1981 10 2010 12 30 141 4.70 0.83 476.00 75.23 82.96 1.79 62005 CASSILIS POST OFFICE 1967 5 2004 1 37 157 4.24 0.58 712.17 70.14 99.96 2.98 63023 COWRA RESEARCH CENTRE (EVANS ST) 1941 10 2011 5 70 418 5.97 0.33 498.50 57.68 72.66 2.50 63039 KATOOMBA (MURRI ST) 1965 6 2010 5 46 178 3.87 0.67 539.33 73.46 92.12 2.09 63043 KURRAJONG HEIGHTS (BELLS LINE OF ROAD) 1965 5 2011 2 47 188 4.00 0.83 625.50 80.39 94.30 1.96 63108 OBERON DAM 1955 1 1988 5 34 241 7.09 0.50 523.67 46.72 74.83 3.48
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Table B.5.9: Continued Record Number of Average of Lower Upper At-site Standard Station Start Start End End Station name length inter-events inter-events limit limit mean deviation Skew ID year month year month (years) (days) per year (days) (days) (days) (days) 64046 COONABARABRAN (WESTMOUNT) 1971 7 2011 5 41 263 6.41 0.75 360.83 41.96 48.77 2.36 65035 WELLINGTON RESEARCH CENTRE 1961 1 2005 2 45 351 7.80 0.50 284.83 45.52 50.56 1.96 66037 SYDNEY AIRPORT AMO 1962 7 2011 5 50 201 4.02 1.08 706.67 87.61 99.80 2.31 66062 SYDNEY (OBSERVATORY HILL) 1913 1 2011 4 99 482 4.87 0.50 554.42 74.29 81.33 1.92 67033 RICHMOND RAAF 1953 1 1994 10 43 202 4.70 0.50 505.00 72.38 83.66 1.81 67035 LIVERPOOL(WHITLAM CENTRE) 1965 1 2001 12 38 155 4.08 0.92 375.08 74.48 81.31 1.55 68076 NOWRA RAN AIR STATION 1964 8 1997 12 34 73 2.15 1.00 616.50 114.11 110.38 1.93 68117 ROBERTSON (ST.ANTHONYS) 1962 11 2005 6 43 109 2.53 2.08 496.33 111.31 115.65 1.49 68131 PORT KEMBLA (BHP CENTRAL LAB) 1963 5 2011 5 49 113 2.31 0.67 588.42 114.78 124.57 1.50 69049 NERRIGA COMPOSITE 1971 2 2011 2 41 97 2.37 1.08 523.00 101.70 110.41 1.48 69055 GREEN CAPE LIGHTHOUSE 1967 3 2002 4 36 79 2.19 1.33 569.00 126.30 120.38 1.25 69127 ARALUEN LOWER (ARALUEN RD) 1980 6 2011 5 32 62 1.94 2.17 524.83 147.92 140.15 1.21 70012 BUNGONIA (INVERARY PARK) 1965 5 2010 5 46 183 3.98 0.75 332.83 69.00 72.50 1.50 70014 CANBERRA AIRPORT COMPARISON 1937 12 2010 11 74 493 6.66 0.67 575.17 52.21 65.74 3.01 70015 CANBERRA FORESTRY 1932 1 1971 2 40 230 5.75 0.67 467.33 57.43 75.55 2.67 70073 CHAKOLA (RIVERSDALE) 1965 12 2011 5 46 193 4.20 0.67 729.75 79.32 101.56 2.48 70080 TARALGA POST OFFICE 1977 6 2010 7 34 107 3.15 0.83 417.17 76.62 85.98 1.71 70199 NUMERALLA (BADJA COMPOSITE) 1965 12 2011 4 46 165 3.59 0.50 520.00 98.36 117.88 1.69 71042 INGEBYRA (GROSSES PLAINS) 1971 2 2011 5 41 200 4.88 0.42 473.33 71.46 82.70 1.94 72023 HUME RESERVOIR 1955 3 2011 5 57 457 8.02 0.42 451.33 44.75 60.19 3.05 72060 KHANCOBAN SMHEA 1961 1 1994 1 34 274 8.06 0.92 391.83 43.72 49.12 2.91 72150 WAGGA WAGGA AMO 1945 1 2011 3 67 385 5.75 0.42 406.67 50.20 55.55 2.22 73007 BURRINJUCK DAM 1911 5 2011 3 101 613 6.07 0.67 706.08 43.83 62.17 4.27 74114 WAGGA WAGGA RESEARCH CENTRE 1946 9 2004 1 58 334 5.76 0.67 685.33 52.85 68.19 3.91 75028 GRIFFITH CSIRO 1931 6 1989 6 59 270 4.58 0.58 702.50 70.89 86.45 3.34 75050 NARADHAN (URALBA) 1970 4 2011 6 42 198 4.71 0.67 340.50 53.86 67.19 2.18 Minimum 30 62 2.07 0.33 218.00 41.96 43.78 1.21
Maximum 101 613 6.07 2.17 729.75 147.92 153.58 4.73
Average 45 227 5.03 0.74 500.13 69.78 83.47 2.25
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Table B.5.10: Goodness-of-fit test results for IED data (2nd set)
Station Chi-Squared test Kolmogorov-Smirnov test Anderson-Darling test ID Exponential Gamma Exponential Gamma Exponential Gamma 48027 1 1 1 0 1 0 48031 0 1 1 0 1 0 51049 1 1 1 0 1 0 53048 0 1 1 0 1 0 54102 1 1 0 0 0 0 54104 1 1 1 1 1 1 54105 0 1 1 0 0 0 54138 0 0 0 0 0 0 55024 1 1 1 1 1 1 55054 1 0 1 0 1 0 55136 1 1 1 1 1 1 55194 1 1 1 0 1 0 55302 1 1 0 0 0 0 56013 1 1 1 1 1 1 56018 1 1 1 1 1 1 56022 1 1 1 0 1 0 56104 1 1 1 1 1 1 56202 1 1 1 0 1 1 57091 1 0 1 0 1 0 57095 1 1 1 1 1 1 57103 1 1 1 0 1 1 57104 1 0 1 0 1 0 58026 1 1 1 0 1 0 58044 1 1 1 0 1 0 58072 1 1 1 0 1 0 58099 1 1 1 0 1 0 58109 1 0 1 0 1 0 58113 1 0 1 0 1 0 58129 0 0 0 0 0 0 58131 1 1 0 0 0 0 58158 1 1 1 0 1 0 59000 1 1 1 0 1 0 59017 0 0 0 0 1 0 59026 1 0 1 0 1 0 59040 0 0 0 0 1 0 59067 1 1 1 0 1 0 60030 1 1 0 0 1 0 60080 1 1 1 0 1 0 60085 1 1 1 1 1 1
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Table B.5.10: Continued Station Chi-Squared test Kolmogorov-Smirnov test Anderson-Darling test ID Exponential Gamma Exponential Gamma Exponential Gamma 60104 1 1 0 0 1 0 60106 1 1 1 0 1 0 61078 0 1 0 0 0 0 61089 1 1 1 0 1 0 61151 1 1 1 0 1 0 61158 1 1 1 0 1 0 61211 1 1 1 0 1 0 61212 1 1 0 0 1 0 61238 1 1 1 0 1 0 61250 1 1 1 0 1 0 61287 0 1 0 0 0 0 61288 1 0 1 0 1 0 61309 1 1 1 0 1 0 61311 1 1 0 0 0 0 61334 1 1 1 0 1 0 61351 0 0 0 0 0 0 62005 1 1 1 1 1 1 63023 1 1 1 1 1 1 63039 0 0 1 0 1 0 63043 1 1 1 0 1 0 63108 0 1 1 1 1 1 64046 1 1 0 0 1 0 65035 1 1 1 0 0 0 66037 0 0 0 0 0 0 66062 1 1 1 0 1 0 67033 1 0 1 0 1 0 67035 0 0 0 0 0 0 68076 0 0 0 0 0 0 68117 0 0 0 0 0 0 68131 0 0 0 0 0 0 69049 0 0 0 0 0 0 69055 0 0 0 0 0 0 69127 0 0 0 0 0 0 70012 0 0 0 0 0 0 70014 1 1 1 1 1 1 70015 1 1 1 0 1 0 70073 1 1 1 0 1 0 70080 0 0 0 0 0 0 70199 1 1 1 0 1 0 71042 1 1 0 0 1 0
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Table B.5.10: Continued Station Chi-Squared test Kolmogorov-Smirnov test Anderson-Darling test ID Exponential Gamma Exponential Gamma Exponential Gamma 72023 1 1 1 1 1 1 72060 1 1 0 1 0 1 72150 1 1 0 0 0 0 73007 1 1 1 1 1 1 74114 1 1 0 1 0 1 75028 1 1 0 0 0 0 75050 1 1 1 1 1 1 Count 22 24 30 69 25 67 Percentage 26% 28% 35% 80% 29% 78%
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Table B.6.1: Differences in DFFCs when increasing and decreasing DCS mean values for the Oxley River catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage (%) ARI using (%) increases in weighted DCS mean value as given below: decreases in weighted DCS mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 180 181 0% 182 1% 183 2% 178 -1% 179 -1% 177 -2% 172 -4% 130 -28% 5 367 364 -1% 370 1% 366 0% 344 -6% 365 0% 370 1% 363 -1% 303 -17% 10 522 512 -2% 521 0% 511 -2% 475 -9% 521 0% 525 1% 518 -1% 449 -14% 20 692 667 -4% 688 -1% 658 -5% 618 -11% 668 -4% 697 1% 672 -3% 601 -13% 50 963 921 -4% 928 -4% 911 -5% 842 -13% 906 -6% 931 -3% 882 -8% 856 -11% 100 1172 1128 -4% 1110 -5% 1098 -6% 1016 -13% 1098 -6% 1104 -6% 1077 -8% 1027 -12%
Table B.6.2: Differences in DFFCs when increasing and decreasing DCS mean values for the Bielsdown Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in weighted DCS mean value as given below: (%) decreases in weighted DCS mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 85 87 2% 89 4% 90 5% 92 8% 84 -1% 82 -4% 79 -8% 55 -35% 5 175 182 4% 178 2% 182 4% 182 4% 178 1% 174 0% 168 -4% 132 -25% 10 248 253 2% 254 2% 256 3% 254 2% 249 0% 247 -1% 240 -3% 198 -20% 20 326 331 2% 331 2% 341 5% 330 1% 320 -2% 323 -1% 321 -2% 272 -17% 50 438 449 2% 440 1% 445 2% 430 -2% 423 -3% 425 -3% 431 -2% 373 -15% 100 512 549 7% 531 4% 548 7% 520 2% 518 1% 515 1% 538 5% 447 -13%
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Enhanced Joint Probability Approach Caballero
Table B.6.3: Differences in DFFCs when increasing and decreasing DCS mean values for the Belar Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in weighted DCS mean value as given below: (%) decreases in weighted DCS mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 78 81 4% 83 7% 89 14% 99 28% 77 -1% 73 -6% 67 -14% 37 -52% 5 160 165 3% 165 4% 173 9% 188 18% 157 -2% 153 -4% 143 -10% 101 -36% 10 229 233 2% 225 -2% 239 4% 252 10% 224 -2% 218 -5% 203 -11% 156 -32% 20 299 306 2% 293 -2% 302 1% 324 8% 293 -2% 281 -6% 271 -10% 214 -28% 50 400 394 -2% 381 -5% 408 2% 412 3% 387 -3% 385 -4% 352 -12% 318 -21% 100 496 512 3% 466 -6% 476 -4% 499 1% 465 -6% 467 -6% 417 -16% 393 -21%
Table B.6.4: Differences in DFFCs when increasing and decreasing DCS standard deviation values for the Oxley River catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage (%) Q (m3/s) and relative differences (%) using different percentage (%) ARI using increases in value of weighted DCS standard dev. as given below: decreases in value of weighted DCS standard dev. as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 180 179 0% 177 -1% 174 -3% 160 -11% 181 1% 180 0% 185 3% 185 3% 5 367 364 -1% 364 -1% 366 0% 341 -7% 368 0% 372 1% 371 1% 371 1% 10 522 527 1% 513 -2% 520 0% 486 -7% 519 -1% 514 -2% 521 0% 510 -2% 20 692 688 -1% 675 -2% 677 -2% 648 -6% 691 0% 680 -2% 668 -3% 681 -2% 50 963 929 -4% 925 -4% 909 -6% 879 -9% 918 -5% 894 -7% 922 -4% 910 -5% 100 1172 1119 -5% 1148 -2% 1125 -4% 1059 -10% 1117 -5% 1106 -6% 1119 -5% 1083 -8%
University of Western Sydney Page 272
Enhanced Joint Probability Approach Caballero
Table B.6.5: Differences in DFFCs when increasing and decreasing DCS standard deviation values for the Bielsdown Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage (%) Q (m3/s) and relative differences (%) using different percentage (%) ARI using increases in value of weighted DCS standard dev. as given below: decreases in value of weighted DCS standard dev. as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 85 86 0% 83 -3% 81 -5% 72 -16% 87 2% 89 4% 90 5% 94 10% 5 175 177 1% 178 1% 171 -2% 158 -10% 179 2% 183 5% 183 5% 190 9% 10 248 249 0% 256 3% 247 -1% 226 -9% 250 1% 257 3% 260 5% 262 6% 20 326 331 2% 336 3% 324 0% 309 -5% 326 0% 334 3% 347 7% 337 4% 50 438 444 1% 453 3% 426 -3% 420 -4% 443 1% 438 0% 448 2% 437 0% 100 512 534 4% 543 6% 516 1% 518 1% 534 4% 524 2% 540 6% 534 4%
Table B.6.6: Differences in DFFCs when increasing and decreasing DCS standard deviation values for the Belar Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage (%) Q (m3/s) and relative differences (%) using different percentage (%) ARI using increases in value of weighted DCS standard deviation as given below: decreases in value of weighted DCS standard deviation as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 78 77 -1% 76 -2% 72 -7% 64 -18% 80 3% 81 4% 84 9% 91 17% 5 160 158 -1% 158 -1% 156 -2% 141 -11% 165 4% 166 4% 169 6% 182 14% 10 229 221 -3% 220 -4% 219 -4% 202 -12% 229 0% 228 0% 234 2% 253 11% 20 299 285 -5% 284 -5% 284 -5% 271 -9% 298 0% 300 0% 298 -1% 319 6% 50 400 379 -5% 370 -8% 368 -8% 357 -11% 396 -1% 411 3% 392 -2% 420 5% 100 496 460 -7% 461 -7% 444 -10% 422 -15% 468 -6% 508 2% 472 -5% 505 2%
University of Western Sydney Page 273
Enhanced Joint Probability Approach Caballero
Table B.6.7: Difference in DFFC when increasing and decreasing IED mean values for the Oxley River catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in weighted IED mean value as given below: (%) decreases in weighted IED mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 180 174 -3% 167 -7% 155 -14% 128 -29% 185 3% 192 7% 215 20% 291 62% 5 367 355 -3% 350 -5% 331 -10% 289 -21% 382 4% 386 5% 420 15% 523 43% 10 522 509 -3% 494 -5% 473 -9% 429 -18% 540 4% 538 3% 578 11% 703 35% 20 692 661 -5% 650 -6% 639 -8% 579 -16% 710 3% 713 3% 731 6% 898 30% 50 963 906 -6% 893 -7% 871 -10% 807 -16% 952 -1% 940 -2% 994 3% 1209 25% 100 1172 1101 -6% 1067 -9% 1075 -8% 999 -15% 1139 -3% 1168 0% 1200 2% 1473 26%
Table B.6.8: Differences in DFFCs when increasing and decreasing IED mean values for the Bielsdown Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in weighted IED mean value as given below: (%) decreases in weighted IED mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 85 83 -3% 79 -8% 73 -15% 61 -29% 90 5% 92 8% 103 21% 142 66% 5 175 173 -1% 170 -3% 160 -8% 141 -19% 185 5% 191 9% 204 17% 256 47% 10 248 246 -1% 245 -1% 233 -6% 211 -15% 255 3% 264 6% 279 12% 338 36% 20 326 321 -2% 324 0% 309 -5% 283 -13% 331 2% 348 7% 358 10% 426 31% 50 438 426 -3% 439 0% 425 -3% 388 -11% 449 3% 455 4% 483 10% 556 27% 100 512 517 1% 542 6% 508 -1% 474 -7% 538 5% 577 13% 579 13% 664 30%
University of Western Sydney Page 274
Enhanced Joint Probability Approach Caballero
Table B.6.9: Differences in DFFCs when increasing and decreasing IED mean values for the Belar Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in weighted IED mean value as given below: (%) decreases in weighted IED mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 78 74 -5% 73 -6% 67 -13% 57 -27% 82 5% 85 9% 91 17% 118 51% 5 160 156 -2% 153 -4% 143 -10% 131 -18% 165 3% 172 8% 178 11% 216 35% 10 229 222 -3% 222 -3% 205 -10% 193 -16% 229 0% 236 3% 244 6% 284 24% 20 299 293 -2% 286 -5% 268 -10% 256 -15% 294 -2% 303 1% 316 5% 352 18% 50 400 380 -5% 382 -5% 363 -9% 344 -14% 389 -3% 399 0% 411 3% 459 15% 100 496 468 -6% 460 -7% 457 -8% 421 -15% 474 -5% 501 1% 471 -5% 547 10%
Table B.6.10: Difference in DFFCs when increasing and decreasing IED standard deviation values for the Oxley River catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage (%) Q (m3/s) and relative differences (%) using different percentage (%) ARI using increases in weighted IED standard deviation value as given below: decreases in weighted IED standard deviation value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 180 183 2% 186 3% 194 8% 224 24% 174 -3% 171 -5% 166 -8% 158 -12% 5 367 372 1% 373 2% 394 7% 433 18% 362 -1% 351 -4% 350 -5% 332 -9% 10 522 521 0% 527 1% 545 5% 582 12% 512 -2% 503 -4% 497 -5% 473 -9% 20 692 675 -3% 698 1% 714 3% 776 12% 686 -1% 671 -3% 663 -4% 632 -9% 50 963 915 -5% 926 -4% 961 0% 1034 7% 944 -2% 914 -5% 883 -8% 852 -11% 100 1172 1107 -6% 1117 -5% 1156 -1% 1242 6% 1130 -4% 1110 -5% 1109 -5% 1042 -11%
University of Western Sydney Page 275
Enhanced Joint Probability Approach Caballero
Table B.6.11: Differences in DFFCs when increasing and decreasing IED standard deviation values for the Bielsdown Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage (%) Q (m3/s) and relative differences (%) using different percentage (%) ARI using increases in weighted IED standard deviation value as given below: decreases in weighted IED standard deviation value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 85 87 2% 89 4% 90 6% 103 21% 84 -1% 84 -2% 84 -2% 81 -5% 5 175 180 3% 184 5% 186 6% 205 17% 176 0% 176 1% 175 0% 169 -3% 10 248 257 3% 261 5% 257 3% 284 14% 253 2% 246 -1% 246 -1% 244 -2% 20 326 335 3% 339 4% 334 3% 371 14% 330 1% 327 0% 322 -1% 320 -2% 50 438 445 1% 441 1% 439 0% 487 11% 448 2% 434 -1% 448 2% 427 -3% 100 512 554 8% 520 2% 543 6% 562 10% 550 7% 524 2% 536 5% 529 3%
Table B.6.12: Differences in DFFCs when increasing and decreasing IED standard deviation values for the Belar Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage (%) Q (m3/s) and relative differences (%) using different percentage (%) ARI using increases in weighted IED standard deviation value as given below: decreases in weighted IED standard deviation value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 78 80 2% 79 1% 78 0% 81 4% 79 2% 79 2% 81 4% 82 6% 5 160 161 1% 162 1% 164 3% 168 5% 162 2% 165 3% 162 2% 160 0% 10 229 225 -2% 229 0% 228 0% 232 2% 227 -1% 228 0% 226 -1% 227 -1% 20 299 293 -2% 299 0% 296 -1% 299 0% 293 -2% 296 -1% 296 -1% 288 -4% 50 400 394 -2% 387 -3% 392 -2% 398 -1% 385 -4% 383 -4% 378 -5% 371 -7% 100 496 478 -4% 479 -3% 484 -2% 486 -2% 462 -7% 459 -8% 481 -3% 442 -11%
University of Western Sydney Page 276
Enhanced Joint Probability Approach Caballero
Table B.6.13: Differences in DFFCs when changing station combinations (one to nine stations, except five stations) for the Oxley River catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using IFD data from different station combinations ARI using (increase by one station in each run) as given below: (years) base value one station two stations three stations four stations six stations seven stations eight stations nine stations 2 205 216 5% 210 2% 206 0% 209 2% 201 -2% 202 -2% 203 -1% 201 -2% 5 381 390 2% 383 0% 378 -1% 384 1% 374 -2% 376 -1% 377 -1% 373 -2% 10 509 515 1% 507 0% 501 -1% 510 0% 500 -2% 502 -1% 504 -1% 499 -2% 20 666 669 0% 661 -1% 655 -2% 667 0% 656 -2% 659 -1% 661 -1% 655 -2% 50 890 880 -1% 875 -2% 872 -2% 888 0% 878 -1% 882 -1% 885 -1% 878 -1% 100 1067 1053 -1% 1044 -2% 1038 -3% 1064 0% 1050 -2% 1055 -1% 1058 -1% 1049 -2%
Table B.6.14: Differences in DFFCs when changing station combinations (one station and three to nine stations) for the Bielsdown Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using IFD data from different station combinations ARI using (increase by one station in each run) as given below: (years) base value one station three stations four stations five stations six stations seven stations eight stations nine stations 2 94 93 -1% 94 0% 92 -2% 90 -4% 88 -6% 86 -8% 85 -9% 84 -10% 5 186 187 1% 185 0% 181 -3% 176 -5% 174 -7% 170 -9% 168 -10% 165 -11% 10 261 264 1% 261 0% 255 -2% 249 -5% 246 -6% 241 -8% 239 -9% 235 -10% 20 339 345 2% 336 -1% 329 -3% 320 -5% 315 -7% 309 -9% 305 -10% 301 -11% 50 459 466 2% 454 -1% 444 -3% 435 -5% 428 -7% 420 -8% 416 -9% 410 -11% 100 560 565 1% 557 -1% 546 -2% 533 -5% 527 -6% 515 -8% 510 -9% 504 -10%
University of Western Sydney Page 277
Enhanced Joint Probability Approach Caballero
Table B.6.15: Differences in DFFCs when changing station combinations (two to nine stations) for the Belar Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using IFD data from different station combinations ARI using (increase by one station in each run) as given below: (years) base value two station three stations four stations five stations six stations seven stations eight stations nine stations 2 71 63 -11% 59 -17% 55 -22% 51 -27% 49 -30% 48 -32% 47 -33% 47 -33% 5 144 131 -9% 124 -13% 118 -18% 111 -23% 107 -26% 105 -27% 103 -28% 103 -28% 10 205 188 -9% 179 -13% 170 -17% 161 -22% 156 -24% 153 -25% 151 -26% 151 -27% 20 269 247 -8% 238 -12% 225 -16% 215 -20% 208 -23% 204 -24% 202 -25% 202 -25% 50 354 327 -8% 313 -12% 299 -16% 286 -19% 278 -22% 271 -23% 267 -25% 266 -25% 100 426 386 -9% 372 -13% 361 -15% 344 -19% 336 -21% 331 -22% 326 -24% 325 -24%
Table B.6.16: Differences in DFFCs when using different pluviograph stations (1st to 8th station) for the Oxley River catchment
Q (m3/s) ARI using Q (m3/s) and relative differences (%) using IFD data from different stations (different station in each run) as given below: (years) base value 1st station 2nd station 3rd station 4th station 5th station 6th station 7th station 8th station 2 205 216 5% 174 -15% 177 -14% 237 16% 148 -28% 107 -48% 227 11% 240 17% 5 381 390 2% 338 -11% 341 -11% 457 20% 339 -11% 213 -44% 422 11% 443 16% 10 509 515 1% 460 -9% 465 -9% 622 22% 488 -4% 293 -42% 566 11% 594 17% 20 666 669 0% 612 -8% 614 -8% 813 22% 659 -1% 388 -42% 743 12% 774 16% 50 890 880 -1% 830 -7% 835 -6% 1119 26% 922 4% 529 -41% 999 12% 1036 16% 100 1067 1053 -1% 993 -7% 998 -6% 1327 24% 1129 6% 631 -41% 1191 12% 1247 17%
University of Western Sydney Page 278
Enhanced Joint Probability Approach Caballero
Table B.6.17: Differences in DFFCs when using different pluviograph stations (1st to 8th station) for the Bielsdown Creek catchment
3 Q (m /s) 3 ARI using Q (m /s) and relative differences (%) using IFD data from different stations (different station in each run) as given below: (years) base value 1st station 2nd station 3rd station 4th station 5th station 6th station 7th station 8th station 2 94 93 -1% 98 4% 102 9% 52 -44% 36 -62% 47 -49% 24 -74% 48 -48% 5 186 187 1% 179 -4% 187 0% 108 -42% 74 -60% 98 -47% 52 -72% 95 -49% 10 261 264 1% 245 -6% 253 -3% 153 -42% 105 -60% 142 -46% 74 -72% 135 -49% 20 339 345 2% 310 -9% 328 -3% 205 -40% 140 -59% 187 -45% 98 -71% 177 -48% 50 459 466 2% 415 -10% 432 -6% 279 -39% 189 -59% 255 -44% 134 -71% 237 -48% 100 560 565 1% 505 -10% 528 -6% 340 -39% 225 -60% 315 -44% 161 -71% 288 -49%
Table B.6.18: Differences in DFFCs when using different pluviograph stations (2nd to 9th station) for the Belar Creek catchment
3 Q (m /s) 3 ARI using Q (m /s) and relative differences (%) using IFD data from different stations (different station in each run) as given below: (years) base value 2nd station 3rd station 4th station 5th station 6th station 7th station 8th station 9th station 2 71 22 -69% 31 -56% 21 -70% 13 -81% 24 -66% 32 -55% 35 -50% 43 -39% 5 144 58 -60% 78 -46% 56 -61% 45 -69% 64 -55% 75 -48% 79 -45% 96 -33% 10 205 88 -57% 118 -43% 86 -58% 72 -65% 100 -51% 113 -45% 115 -44% 142 -31% 20 269 123 -54% 161 -40% 119 -56% 103 -62% 137 -49% 152 -43% 153 -43% 190 -29% 50 354 167 -53% 223 -37% 159 -55% 146 -59% 185 -48% 200 -43% 204 -42% 253 -29% 100 426 200 -53% 267 -37% 192 -55% 176 -59% 224 -47% 241 -43% 244 -43% 309 -27%
University of Western Sydney Page 279
Enhanced Joint Probability Approach Caballero
Table B.6.19: Differences in DFFCs when using combinations of pooled TP data from different pluviograph stations (two to nine station combinations) for the Oxley River catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using pooled temporal pattern data ARI using from different pluviograph station combinations as given below: (years) base value two stations three stations four stations five stations six stations seven stations eight stations nine stations 2 180 174 -3% 175 -2% 183 2% 181 1% 181 1% 180 0% 180 0% 203 13% 5 367 353 -4% 355 -3% 381 4% 376 3% 369 1% 366 0% 366 0% 381 4% 10 522 498 -5% 507 -3% 540 3% 529 1% 518 -1% 516 -1% 519 -1% 517 -1% 20 692 657 -5% 678 -2% 723 4% 699 1% 681 -2% 685 -1% 688 -1% 671 -3% 50 963 886 -8% 937 -3% 960 0% 959 0% 952 -1% 937 -3% 937 -3% 868 -10% 100 1172 1102 -6% 1119 -5% 1246 6% 1152 -2% 1166 -1% 1137 -3% 1149 -2% 1021 -13%
Table B.6.20: Differences in DFFCs when using combinations of pooled TP data from different pluviograph stations (two to nine station combinations) for the Bielsdown Creek catchment
Q (m3/s) ARI using Q (m3/s) and relative differences (%) using temporal pattern data from different station combinations as given below: (years) base value two stations three stations four stations five stations six stations seven stations eight stations nine stations 2 85 88 3% 88 3% 89 4% 85 0% 85 -1% 86 1% 85 0% 85 0% 5 175 180 3% 184 5% 184 5% 178 2% 175 0% 178 2% 177 1% 176 0% 10 248 254 2% 257 3% 257 4% 248 0% 247 -1% 254 2% 250 1% 244 -2% 20 325 339 4% 338 4% 342 5% 331 2% 328 1% 334 3% 327 0% 320 -2% 50 438 449 3% 469 7% 465 6% 438 0% 454 4% 459 5% 450 3% 425 -3% 100 512 560 9% 555 8% 559 9% 529 3% 557 9% 567 11% 538 5% 516 1%
University of Western Sydney Page 280
Enhanced Joint Probability Approach Caballero
Table B.6.21: Differences in DFFCs when using combinations of pooled TP data from different pluviograph stations (two to nine station combinations) for the Belar Creek catchment
Q (m3/s) ARI using Q (m3/s) and relative differences (%) using temporal pattern data from different station combinations as given below: (years) base value two stations three stations four stations five stations six stations seven stations eight stations nine stations 2 78 73 -7% 77 -1% 77 -1% 78 0% 75 -4% 74 -5% 76 -2% 76 -2% 5 160 154 -3% 163 2% 158 -1% 155 -3% 156 -2% 156 -2% 157 -1% 156 -2% 10 229 218 -5% 226 -1% 220 -4% 213 -7% 220 -4% 215 -6% 222 -3% 218 -5% 20 299 285 -5% 296 -1% 290 -3% 277 -8% 289 -4% 287 -4% 293 -2% 288 -4% 50 400 388 -3% 390 -3% 405 1% 377 -6% 381 -5% 385 -4% 398 -1% 389 -3% 100 496 461 -7% 476 -4% 494 -1% 464 -7% 451 -9% 468 -6% 485 -2% 473 -5%
Table B.6.22: Differences in DFFCs when changing the values of IL mean for the Oxley River catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in IL mean value as given below: (%) decreases in IL mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 180 173 -4% 173 -4% 165 -8% 141 -22% 182 1% 186 3% 194 8% 214 19% 5 367 359 -2% 361 -1% 348 -5% 315 -14% 371 1% 378 3% 388 6% 412 12% 10 522 510 -2% 515 -1% 498 -5% 464 -11% 516 -1% 530 2% 541 4% 573 10% 20 692 688 -1% 678 -2% 659 -5% 635 -8% 689 -1% 703 1% 714 3% 748 8% 50 963 959 0% 909 -6% 923 -4% 894 -7% 954 -1% 969 1% 993 3% 1041 8% 100 1172 1151 -2% 1122 -4% 1136 -3% 1064 -9% 1159 -1% 1199 2% 1183 1% 1224 4%
University of Western Sydney Page 281
Enhanced Joint Probability Approach Caballero
Table B.6.23: Differences in DFFCs when changing the values of IL mean for the Bielsdown Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in IL mean value as given below: (%) decreases in IL mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 85 84 -2% 82 -3% 80 -6% 72 -16% 88 2% 89 4% 93 9% 100 17% 5 175 174 0% 173 -1% 169 -3% 161 -8% 179 3% 181 4% 184 5% 194 11% 10 248 245 -1% 248 0% 244 -2% 232 -7% 248 0% 253 2% 261 5% 270 9% 20 325 324 0% 328 1% 321 -1% 306 -6% 330 1% 331 2% 340 4% 354 9% 50 438 440 0% 433 -1% 429 -2% 416 -5% 447 2% 447 2% 457 4% 460 5% 100 512 527 3% 508 -1% 519 1% 496 -3% 534 4% 564 10% 551 8% 560 9%
Table B.6.24: Differences in DFFCs when changing the values of IL mean for the Belar Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in IL mean value as given below: (%) decreases in IL mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 78 76 -2% 73 -6% 65 -16% 46 -41% 83 7% 85 9% 91 17% 109 40% 5 160 156 -2% 153 -4% 146 -9% 124 -22% 164 3% 164 3% 176 10% 194 22% 10 229 220 -4% 218 -5% 206 -10% 186 -19% 232 2% 230 1% 241 5% 260 14% 20 299 295 -2% 285 -5% 275 -8% 253 -15% 300 0% 308 3% 316 6% 323 8% 50 400 388 -3% 398 -1% 368 -8% 332 -17% 397 -1% 405 1% 415 4% 445 11% 100 496 470 -5% 478 -4% 452 -9% 394 -21% 488 -2% 514 4% 499 0% 546 10%
University of Western Sydney Page 282
Enhanced Joint Probability Approach Caballero
Table B.6.25: Difference in DFFC when changing the values of IL standard deviation for the Oxley River catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in IL standard deviation value as given below: (%) decreases in IL standard deviation value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 180 180 0% 182 1% 182 1% 187 4% 180 0% 177 -1% 176 -2% 170 -6% 5 367 364 -1% 367 0% 372 2% 379 3% 369 1% 369 1% 363 -1% 353 -4% 10 522 519 -1% 520 0% 525 1% 538 3% 512 -2% 521 0% 508 -3% 512 -2% 20 692 692 0% 687 -1% 696 0% 704 2% 678 -2% 683 -1% 678 -2% 686 -1% 50 963 930 -3% 939 -3% 970 1% 950 -1% 929 -4% 956 -1% 960 0% 954 -1% 100 1172 1164 -1% 1167 0% 1200 2% 1131 -4% 1122 -4% 1173 0% 1150 -2% 1148 -2%
Table B.6.26: Difference in DFFC when changing the values of IL standard deviation for the Bielsdown Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in IL standard deviation value as given below: (%) decreases in IL standard deviation value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 85 86 1% 86 1% 87 1% 87 2% 85 -1% 85 0% 84 -2% 82 -4% 5 175 181 4% 179 3% 178 2% 179 2% 177 1% 177 1% 177 1% 174 -1% 10 248 250 1% 251 1% 250 0% 254 2% 252 1% 248 0% 250 1% 247 -1% 20 325 331 2% 329 1% 325 0% 332 2% 326 0% 323 -1% 330 2% 323 -1% 50 438 443 1% 440 0% 441 1% 441 1% 434 -1% 434 -1% 445 2% 438 0% 100 512 538 5% 520 2% 544 6% 524 2% 531 4% 525 3% 526 3% 529 3%
University of Western Sydney Page 283
Enhanced Joint Probability Approach Caballero
Table B.6.27: Difference in DFFC when changing the values of IL standard deviation for the Belar Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in IL standard deviation value as given below: (%) decreases in IL standard deviation value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 78 81 4% 81 4% 82 5% 88 13% 78 0% 78 0% 77 -1% 74 -5% 5 160 166 4% 163 2% 163 2% 166 4% 158 -1% 157 -2% 161 1% 155 -3% 10 229 230 0% 227 -1% 226 -1% 235 3% 222 -3% 226 -1% 227 -1% 224 -2% 20 299 298 -1% 299 0% 294 -2% 301 1% 290 -3% 295 -2% 295 -1% 288 -4% 50 400 397 -1% 414 3% 391 -2% 398 -1% 387 -3% 397 -1% 404 1% 382 -5% 100 496 472 -5% 493 -1% 484 -3% 494 -1% 471 -5% 479 -3% 472 -5% 459 -7%
Table B.6.28: Differences in DFFCs when changing the values of CL mean for the Oxley River catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in CL mean value as given below: (%) decreases in CL mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 180 178 -1% 176 -2% 174 -3% 166 -8% 181 1% 183 2% 186 4% 198 10% 5 367 364 -1% 362 -1% 358 -2% 351 -4% 368 0% 370 1% 374 2% 385 5% 10 522 520 0% 517 -1% 514 -2% 505 -3% 523 0% 524 0% 529 1% 543 4% 20 692 690 0% 687 -1% 683 -1% 673 -3% 695 0% 697 1% 702 1% 716 3% 50 963 962 0% 960 0% 957 -1% 947 -2% 964 0% 967 0% 971 1% 980 2% 100 1172 1171 0% 1170 0% 1165 -1% 1155 -1% 1173 0% 1176 0% 1180 1% 1197 2%
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Table B.6.29: Differences in DFFCs when changing the values of CL mean for the Bielsdown Creek catchment
Q (m3/s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in CL mean value as given below: (%) decreases in CL mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 85 85 -1% 84 -1% 83 -3% 80 -7% 86 1% 87 2% 89 4% 94 10% 5 175 174 -1% 173 -1% 171 -2% 166 -5% 176 1% 177 1% 179 2% 187 7% 10 248 248 0% 247 -1% 245 -1% 239 -4% 250 1% 251 1% 253 2% 260 5% 20 325 324 0% 323 -1% 322 -1% 314 -3% 326 0% 328 1% 331 2% 340 4% 50 438 437 0% 435 -1% 433 -1% 425 -3% 440 0% 441 1% 443 1% 451 3% 100 512 511 0% 509 -1% 506 -1% 502 -2% 513 0% 515 1% 518 1% 527 3%
Table B.6.30: Differences in DFFCs when changing the values of CL mean for the Belar Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in CL mean value as given below: (%) decreases in CL mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 78 77 -1% 76 -2% 74 -4% 71 -9% 78 1% 79 2% 81 5% 89 14% 5 160 159 -1% 157 -2% 156 -2% 151 -6% 162 1% 163 2% 166 4% 175 10% 10 229 227 -1% 226 -1% 224 -2% 218 -5% 229 0% 231 1% 234 2% 248 8% 20 299 298 -1% 297 -1% 294 -2% 288 -4% 302 1% 302 1% 306 2% 320 7% 50 400 398 -1% 393 -2% 387 -3% 381 -5% 403 1% 405 1% 411 3% 422 6% 100 496 495 0% 494 0% 492 -1% 484 -2% 496 0% 496 0% 496 0% 509 3%
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Table B.6.31: Differences in DFFCs when changing the values of k mean for the Oxley River catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in k mean value as given below: (%) decreases in k mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 180 173 -4% 168 -6% 160 -11% 138 -23% 184 3% 191 6% 203 13% 265 48% 5 367 352 -4% 342 -7% 327 -11% 280 -24% 378 3% 390 6% 418 14% 558 52% 10 522 509 -2% 491 -6% 460 -12% 395 -24% 540 3% 554 6% 600 15% 800 53% 20 692 676 -2% 652 -6% 616 -11% 521 -25% 714 3% 738 7% 805 16% 1078 56% 50 963 906 -6% 879 -9% 836 -13% 710 -26% 1000 4% 1020 6% 1095 14% 1473 53% 100 1172 1134 -3% 1101 -6% 1049 -11% 859 -27% 1205 3% 1216 4% 1320 13% 1836 57%
Table B.6.32: Differences in DFFCs when changing the values of k mean for the Bielsdown Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in k mean value as given below: (%) decreases in k mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 85 83 -3% 82 -4% 76 -11% 65 -24% 89 4% 92 8% 99 16% 138 61% 5 175 172 -2% 165 -6% 156 -11% 135 -23% 185 6% 189 8% 205 17% 297 70% 10 248 242 -3% 234 -6% 222 -11% 189 -24% 259 4% 270 9% 290 17% 425 71% 20 325 322 -1% 311 -5% 290 -11% 251 -23% 340 5% 353 9% 391 20% 573 76% 50 438 422 -4% 405 -8% 393 -10% 338 -23% 464 6% 473 8% 523 19% 786 79% 100 512 508 -1% 493 -4% 466 -9% 401 -22% 556 9% 576 12% 626 22% 998 95%
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Table B.6.33: Differences in DFFCs when changing the values of k mean for the Belar Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in k mean value as given below: (%) decreases in k mean value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 78 75 -3% 72 -8% 68 -13% 56 -28% 81 4% 85 9% 93 19% 128 65% 5 160 155 -3% 151 -5% 139 -13% 116 -27% 168 5% 175 10% 192 20% 265 66% 10 229 223 -2% 214 -6% 200 -13% 165 -28% 236 3% 249 9% 272 19% 373 63% 20 299 292 -2% 284 -5% 262 -13% 219 -27% 309 3% 326 9% 359 20% 505 69% 50 400 377 -6% 375 -6% 354 -12% 289 -28% 412 3% 433 8% 482 20% 684 71% 100 496 470 -5% 452 -9% 436 -12% 360 -28% 495 0% 524 6% 563 13% 813 64%
Table B.6.34: Differences in DFFCs when changing the values of k standard deviation for the Oxley River catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in k standard deviation value as given below: (%) decreases in k standard deviation value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 180 181 1% 179 -1% 181 1% 185 3% 177 -1% 177 -1% 178 -1% 176 -2% 5 367 366 0% 370 1% 372 1% 382 4% 366 0% 364 -1% 359 -2% 355 -3% 10 522 521 0% 526 1% 533 2% 554 6% 517 -1% 513 -2% 508 -3% 503 -4% 20 692 693 0% 709 2% 711 3% 746 8% 678 -2% 682 -1% 670 -3% 665 -4% 50 963 961 0% 975 1% 993 3% 1055 10% 957 -1% 932 -3% 942 -2% 906 -6% 100 1172 1161 -1% 1168 0% 1212 3% 1259 7% 1138 -3% 1168 0% 1159 -1% 1093 -7%
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Table B.6.35: Differences in DFFCs when changing the values of k standard deviation for the Bielsdown Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in k standard deviation value as given below: (%) decreases in k standard deviation value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 85 87 1% 86 1% 89 4% 93 9% 86 0% 84 -1% 84 -2% 82 -4% 5 175 181 3% 179 3% 184 5% 197 12% 174 -1% 174 0% 171 -2% 164 -6% 10 248 251 1% 254 2% 259 4% 283 14% 245 -1% 242 -3% 238 -4% 230 -7% 20 325 331 2% 333 2% 345 6% 367 13% 327 0% 319 -2% 312 -4% 303 -7% 50 438 447 2% 450 3% 458 5% 505 15% 423 -3% 425 -3% 421 -4% 399 -9% 100 512 540 6% 538 5% 560 10% 621 21% 517 1% 516 1% 512 0% 471 -8%
Table B.6.36: Differences in DFFCs when changing the values of k standard deviation for the Belar Creek catchment
3 Q (m /s) Q (m3/s) and relative differences (%) using different percentage Q (m3/s) and relative differences (%) using different percentage ARI using (%) increases in k standard deviation value as given below: (%) decreases in k standard deviation value as given below: (years) base value 5% increase 10% increase 20% increase 50% increase 5% decrease 10% decrease 20% decrease 50% decrease 2 78 78 0% 79 1% 80 3% 83 7% 77 -1% 77 0% 77 0% 75 -3% 5 160 161 1% 160 1% 165 4% 175 9% 160 0% 158 -1% 157 -1% 153 -4% 10 229 230 0% 231 1% 232 1% 248 8% 226 -1% 227 -1% 225 -2% 219 -4% 20 299 303 1% 304 2% 309 3% 325 8% 295 -2% 293 -2% 291 -3% 282 -6% 50 400 405 1% 405 1% 418 4% 444 11% 394 -2% 395 -1% 382 -5% 371 -7% 100 496 496 0% 491 -1% 508 2% 544 10% 481 -3% 482 -3% 451 -9% 447 -10%
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Table B.7.1: Annual maximum flow data for the Wilsons River catchment
Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) 1958 315.12 1972 381.73 1986 433.98 2000 104.20 1959 233.25 1973 112.87 1987 460.85 2001 370.75 1960 9.21 1974 438.13 1988 377.62 2002 32.14 1961 318.23 1975 291.94 1989 302.77 2003 106.25 1962 540.31 1976 741.18 1990 160.77 2004 108.03 1963 378.86 1977 313.75 1991 128.53 2005 431.12 1964 79.62 1978 338.70 1992 48.57 2006 412.50 1965 30.91 1979 111.50 1993 47.92 2007 33.41 1966 268.88 1980 281.77 1994 148.83 2008 274.69 1967 340.30 1981 328.20 1995 348.90 2009 413.82 1968 93.79 1982 569.72 1996 198.79 2010 177.36 1969 46.35 1983 235.15 1997 39.14 2011 569.37 1970 251.89 1984 380.77 1998 20.59
1971 84.73 1985 456.09 1999 139.68
Table B.7.2: Annual maximum flow data for the Bielsdown Creek catchment
Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) 1972 243.67 1982 114.09 1992 84.70 2002 16.11 1973 377.25 1983 31.94 1993 54.97 2003 88.56 1974 391.63 1984 199.11 1994 37.48 2004 259.52 1975 213.79 1985 663.42 1995 356.07 2005 79.71 1976 302.05 1986 156.81 1996 189.31 2006 169.70 1977 391.41 1987 77.72 1997 75.10 2007 137.83 1978 152.50 1988 272.47 1998 19.52 2008 185.96 1979 185.76 1989 423.38 1999 390.60 2009 317.76 1980 57.88 1990 181.83 2000 37.03 2010 50.45 1981 138.04 1991 94.55 2001 749.31 2011 281.36
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Table B.7.3: Annual maximum flow data for the Orara River catchment
Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) 1970 288.31 1981 273.21 1992 190.09 2003 85.49 1971 150.86 1982 243.61 1993 64.53 2004 160.14 1972 410.87 1983 156.71 1994 15.76 2005 86.56 1973 238.36 1984 231.44 1995 285.39 2006 146.56 1974 305.32 1985 367.29 1996 434.20 2007 268.15 1975 190.78 1986 112.86 1997 55.04 2008 138.83 1976 206.86 1987 109.23 1998 19.92 2009 805.22 1977 960.16 1988 308.71 1999 324.08 2010 200.45 1978 143.74 1989 720.01 2000 58.08 2011 235.56 1979 143.78 1990 156.54 2001 368.18
1980 270.10 1991 264.56 2002 63.36
Table B.7.4: Annual maximum flow data for the West Brook River catchment
Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) 1970 13.89 1981 48.95 1992 54.69 2003 22.91 1971 127.99 1982 98.61 1993 49.44 2004 22.76 1972 174.50 1983 10.82 1994 13.45 2005 20.49 1973 7.34 1984 80.60 1995 25.25 2006 2.51 1974 17.00 1985 798.16 1996 12.91 2007 666.13 1975 13.31 1986 5.92 1997 67.07 2008 138.83 1976 128.77 1987 247.47 1998 241.97 2009 243.62 1977 287.21 1988 842.63 1999 62.89 2010 27.70 1978 26.74 1989 69.83 2000 222.36 2011 28.88 1979 72.22 1990 362.34 2001 322.73
1980 1.45 1991 1.57 2002 75.28
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Table B.7.5: Annual maximum flow data for the Belar Creek catchment
Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) Year Q (m3/s) 1973 43.84 1983 78.37 1993 23.54 2003 6.21 1974 72.16 1984 153.67 1994 0.66 2004 5.97 1975 6.47 1985 25.20 1995 67.83 2005 61.80 1976 80.63 1986 13.76 1996 61.87 2006 0.09 1977 45.43 1987 10.01 1997 31.87 2007 61.80 1978 15.81 1988 44.55 1998 98.60 2008 4.10 1979 6.52 1989 63.52 1999 74.38 2009 17.65 1980 7.02 1990 79.27 2000 54.34 2010 365.14 1981 24.66 1991 40.24 2001 0.55 2011 1.63 1982 9.35 1992 19.34 2002 0.15
Table B.7.6: At-site FFA estimates and 90% confidence limits for the Wilsons River catchment
ARI LP3 - Expected fitted line LP3 - 5% Confidence limit LP3 - 95% Confidence limit 1.01 12.05 4.64 23.78 1.1 53.21 32.96 76.90 1.25 97.07 69.59 127.53 1.5 150.06 115.89 188.09 1.75 190.38 152.39 233.45 2 223.04 181.54 271.07 3 312.69 262.94 373.97 5 410.18 349.87 485.15 10 521.30 450.06 615.67 20 612.85 529.94 731.04 50 709.93 615.00 871.34 100 768.73 663.78 973.77 200 817.33 702.99 1069.10 500 868.85 742.45 1192.25
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Table B.7.7: At-site FFA estimates and 90% confidence limits for the Bielsdown Creek catchment
ARI LP3 - Expected fitted line LP3 - 5% Confidence limit LP3 - 95% Confidence limit 1.01 10.14 3.47 21.03 1.1 37.28 21.94 55.40 1.25 66.04 45.92 90.03 1.5 102.54 75.96 135.05 1.75 132.03 99.68 171.81 2 157.17 120.04 203.07 3 232.83 180.88 298.33 5 328.50 256.62 422.66 10 459.90 359.73 622.77 20 592.78 454.84 868.39 50 769.31 564.02 1284.34 100 902.47 633.49 1669.96 200 1034.51 693.51 2131.54 500 1206.34 753.66 2898.50
Table B.7.8: At-site FFA estimates and 90% confidence limits for the Orara River catchment
ARI LP3 - Expected fitted line LP3 - 5% Confidence limit LP3 - 95% Confidence limit 1.01 25.80 12.46 42.38 1.1 65.25 44.74 87.68 1.25 100.31 76.20 127.29 1.5 141.35 111.61 175.21 1.75 173.12 139.12 213.37 2 199.63 161.83 245.55 3 277.88 225.96 342.94 5 375.94 304.28 472.95 10 512.27 407.79 672.76 20 654.30 510.59 912.96 50 851.91 639.11 1304.31 100 1009.04 729.37 1658.65 200 1172.71 811.80 2081.24 500 1398.87 912.71 2766.81
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Table B.7.9: At-site FFA estimates and 90% confidence limits for the West Brook River catchment
ARI LP3 - Expected fitted line LP3 - 5% Confidence limit LP3 - 95% Confidence limit 1.01 1.18 0.48 2.40 1.1 5.85 3.16 9.84 1.25 12.97 7.79 20.17 1.5 25.15 16.14 37.81 1.75 37.69 24.89 56.17 2 50.39 33.65 75.30 3 100.92 66.96 156.62 5 195.79 125.24 326.02 10 398.05 238.86 728.00 20 715.17 401.39 1434.91 50 1382.96 713.16 3098.11 100 2146.57 1046.29 5213.06 200 3209.88 1483.85 8389.97 500 5226.99 2253.30 14923.97
Table B.7.10: At-site FFA estimates and 90% confidence limits for the Belar Creek catchment
ARI LP3 - Expected fitted line LP3 - 5% Confidence limit LP3 - 95% Confidence limit 1.01 0.19 0.03 0.65 1.1 1.99 0.78 4.08 1.25 5.48 2.79 9.54 1.5 11.74 6.83 18.84 1.75 18.05 11.09 28.09 2 24.20 15.38 37.20 3 46.33 30.79 70.49 5 80.58 54.67 123.72 10 136.13 91.78 216.43 20 199.60 133.56 339.95 50 291.70 190.32 562.50 100 365.09 230.04 782.13 200 439.93 266.85 1049.31 500 539.00 312.40 1516.34
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Table B.7.11: Flood quantiles (m3/s) summary for the Wilsons River catchment using DEA Flood 1-h 2-h 3-h 6-h 12-h 24-h 48-h 72-h quantiles
Q2 96.64 154.30 190.37 249.75 287.02 282.97 283.78 276.09
Q5 148.58 230.39 281.86 361.13 406.85 397.73 409.61 405.94
Q10 180.33 276.42 335.28 428.31 485.38 468.65 488.17 487.18
Q20 227.31 343.62 411.35 521.06 586.80 561.32 590.47 593.91
Q50 286.88 426.26 514.86 648.26 722.16 698.44 736.69 719.26
Q100 338.21 499.47 602.64 745.68 828.20 795.35 845.87 831.64
Table B.7.12: Flood quantiles (m3/s) summary for the Bielsdown Creek catchment using DEA Flood 1-h 2-h 3-h 6-h 12-h 24-h 48-h 72-h quantiles
Q2 196.87 276.00 305.52 368.90 426.22 454.43 405.51 280.54
Q5 285.58 402.12 439.77 546.99 624.30 664.52 602.70 415.55
Q10 345.73 480.46 525.18 662.33 752.87 808.22 736.76 506.55
Q20 416.96 591.63 639.56 813.38 921.64 991.27 908.91 623.29
Q50 525.29 723.14 790.17 977.30 1117.33 1176.73 1082.89 748.84
Q100 609.57 831.81 902.91 1141.69 1300.79 1376.03 1277.34 874.62
Table B.7.13: Flood quantiles (m3/s) summary for the Orara River catchment using DEA Flood 1-h 2-h 3-h 6-h 12-h 24-h 48-h 72-h quantiles
Q2 67.68 108.84 133.42 166.52 228.34 229.63 283.32 186.80
Q5 117.34 175.89 210.49 259.86 346.84 350.87 420.45 287.73
Q10 147.45 218.41 259.62 317.86 422.62 428.62 509.37 348.72
Q20 186.67 275.33 326.05 396.18 521.34 529.19 627.05 432.08
Q50 248.37 354.00 419.33 499.99 641.45 641.15 738.46 520.10
Q100 295.38 425.02 495.90 583.52 749.89 753.88 859.37 789.48
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Table B.7.14: Flood quantiles (m3/s) summary for the West Brook River catchment using DEA Flood 1-h 2-h 3-h 6-h 12-h 24-h 48-h 72-h quantiles
Q2 114.09 162.96 177.72 205.87 246.32 241.48 198.78 120.18
Q5 193.17 254.09 261.29 306.56 341.62 330.41 272.85 163.56
Q10 241.63 307.84 315.06 367.33 399.48 385.13 320.37 191.08
Q20 310.14 384.26 388.87 451.37 473.72 457.90 382.14 226.83
Q50 402.69 480.67 477.16 537.37 556.94 521.63 437.02 261.91
Q100 481.73 564.17 559.84 620.10 635.54 595.18 501.86 298.23
Table B.7.15: Flood quantiles (m3/s) summary for the Belar Creek catchment using DEA Flood 1-h 2-h 3-h 6-h 12-h 24-h 48-h 72-h quantiles
Q2 0.22 0.22 0.22 7.93 2.80 0.81 2.77 1.79
Q5 0.22 2.82 11.64 32.04 27.51 39.53 36.07 69.84
Q10 0.22 19.13 31.91 61.50 57.17 68.04 93.35 129.50
Q20 13.01 52.96 73.28 120.26 114.19 136.84 178.13 214.32
Q50 52.89 113.37 144.24 186.81 195.45 219.85 273.24 225.48
Q100 88.74 166.59 207.90 260.14 264.90 307.98 329.59 324.21
Table B.7.16: Flood quantile estimates using RFFE 2012 model for the Wilsons River catchment
ARI Expected 5% Confidence 95% Confidence (years) quantiles (m3/s) limit (m3/s) limit (m3/s) 2 195.8 91.7 429.3 5 505.4 236.7 1095.4 10 778.0 360.3 1694.1 20 1075.6 491.1 2366.9 50 1499.9 668.1 3391.2 100 1837.2 801.6 4223.8
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Table B.7.17: Flood quantile estimates using RFFE 2012 model for the Bielsdown Creek catchment
ARI Expected 5% Confidence 95% Confidence (years) quantiles (m3/s) limit (m3/s) limit (m3/s) 2 144.2 68.9 310.1 5 391.4 187.4 831.3 10 625.6 295.9 1333.8 20 896.9 416.7 1939.6 50 1309.7 590.5 2915.3 100 1658.6 734.7 3761.9
Table B.7.18: Flood quantile estimates using RFFE 2012 model for the Orara River catchment
ARI Expected 5% Confidence 95% Confidence (years) quantiles (m3/s) limit (m3/s) limit (m3/s) 2 205.9 101.1 429.5 5 558.8 274.8 1156.8 10 893.4 432.5 1855.9 20 1281.2 608.7 2711.1 50 1871.4 861.8 4081.2 100 2370.5 1068.5 5271.8
Table B.7.19: Flood quantile estimates using RFFE 2012 model for the West Brook River catchment
ARI Expected 5% Confidence 95% Confidence (years) quantiles (m3/s) limit (m3/s) limit (m3/s) 2 24.8 10.5 60.6 5 65.0 27.7 155.4 10 101.7 43.0 244.0 20 143.1 59.7 344.7 50 204.2 84.2 499.7 100 254.4 103.1 636.3
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Table B.7.20: Flood quantile estimates using RFFE 2012 model for the Belar Creek catchment
ARI Expected 5% Confidence 95% Confidence (years) quantiles (m3/s) limit (m3/s) limit (m3/s) 2 43.0 18.2 104.7 5 113.4 48.4 270.7 10 177.5 75.1 424.4 20 249.6 104.7 599.5 50 355.5 147.7 869.0 100 442.2 179.6 1098.0
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Figure C.3.1: Converted rainfall intensities in tabulated form for the Oxley River catchment
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Figure C.3.2: Temporal pattern hyetographs for Zone 1
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Figure C.3.3: Temporal pattern hyetographs for Zone 2
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Figure C.3.4: Temporal pattern hyetographs for Zone 3
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Figure C.3.5: Temporal pattern percentages per period for Zone 1
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Figure C.3.6: Temporal pattern percentages per period for Zone 2
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Figure C.3.7: Temporal pattern percentages per period for Zone 3
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Figure C.7.1: At-site FFA estimates and 90% confidence limits for the Wilsons River catchment
Figure C.7.2: At-site FFA estimates and 90% confidence limits for the Bielsdown Creek catchment
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Figure C.7.3: At-site FFA estimates and 90% confidence limits for the Orara River catchment
Figure C.7.4: At-site FFA estimates and 90% confidence limits for the West Brook River catchment
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Figure C.7.5: At-site FFA estimates and 90% confidence limits for the Belar Creek catchment
Figure C.7.6: Flood quantile estimates using the DEA and FLIKE, observed annual peaks and DFFC using EMCST for the Oxley River catchment
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Figure C.7.7: Flood quantile estimates using the DEA and FLIKE, observed annual peaks and DFFC using EMCST for the Wilsons River catchment
Figure C.7.8: Flood quantile estimates using the DEA and FLIKE, observed annual peaks and DFFC using EMCST for the Bielsdown Creek catchment
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Figure C.7.9: Flood quantile estimates using the DEA and FLIKE, observed annual peaks and DFFC using EMCST for the Orara River catchment
Figure C.7.10: Flood quantile estimates using the DEA and FLIKE, observed annual peaks and DFFC using EMCST for the West Brook River catchment
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Figure C.7.11: Flood quantile estimates using the DEA and FLIKE, observed annual peaks and DFFC using EMCST for the Belar Creek catchment
Figure C.7.12: Flood quantile estimates using the BGLS-ROI and observed streamflow data for the Oxley River catchment
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Figure C.7.13: Flood quantile estimates using the BGLS-ROI and observed streamflow data for the Wilsons River catchment
Figure C.7.14: Flood quantile estimates using the BGLS-ROI and observed streamflow data for the Bielsdown Creek catchment
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Figure C.7.15: Flood quantile estimates using the BGLS-ROI and observed streamflow data for the Orara River catchment
Figure C.7.16: Flood quantile estimates using the BGLS-ROI and observed streamflow data for the West Brook River catchment
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Figure C.7.17: Flood quantile estimates using the BGLS-ROI and observed streamflow data for the Belar Creek catchment
Figure C.7.18: Flood quantile estimates using the PRM and ARR RFFE 2012, observed annual peaks and DFFC using EMCST for the Oxley River catchment
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Figure C.7.19: Flood quantile estimates using the PRM and ARR RFFE 2012, observed annual peaks and DFFC using EMCST for the Wilsons River catchment
Figure C.7.20: Flood quantile estimates using the PRM and ARR RFFE 2012, observed annual peaks and DFFC using EMCST for the Bielsdown Creek catchment
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Figure C.7.21: Flood quantile estimates using the PRM and ARR RFFE 2012, observed annual peaks and DFFC using EMCST for the Bielsdown Creek catchment
Figure C.7.22: Flood quantile estimates using the PRM and ARR RFFE 2012, observed annual peaks and DFFC using EMCST for the Oxley River catchment
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Figure C.7.23: Flood quantile estimates using the PRM and ARR RFFE 2012, observed annual peaks and DFFC using EMCST for the Oxley River catchment
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Enhanced Joint Probability Approach Caballero APPENDIX D
D.1 FORTRAN program for selecting complete storm events
Program name: mcsa5cs1.for
Length of the program: 2209 lines
Objectives of the program: to identify complete storm events from the pluviograph data
Input to the program: The input to the program is provided in Table D.1.
Output of the program: The output from the program is provided in Table D.2.
Example input parameter file: P58109.psa
Table D.1: Example input files to program mcsa5cs1.for for selecting complete storm events Parameter Description a58109 Pluviograph station ID P58109.dat Hourly pluviograph data file, rainfall in mm 6 Dry period between successive complete storm events, hours 0.4 Reduction factor to identify significant complete storm events 0.5 Reduction factor to identify significant complete storm events 47.30 Log-normal design rainfall intensity, 2 years ARI-1 hour duration, mm 11.00 Log-normal design rainfall intensity, 2 years ARI-12 hour duration, mm 3.66 Log-normal design rainfall intensity, 2 years ARI-72 hour duration, mm 87.30 Log-normal design rainfall intensity, 50 years ARI-1 hour duration, mm 23.40 Log-normal design rainfall intensity, 50 years ARI-12 hour duration, mm 7.91 Log-normal design rainfall intensity, 50 years ARI-72 hour duration, mm 0.09 Skewness 213 Catchment area, km2 201001a.txt Hourly streamflow data file, streamflow in m3/s
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Example of output parameter files:
Table D.2: Example output files from program mcsa5cs1.for for selecting complete storm events Parameter Description a58109.dcs Complete storm durations, hour(s) a58109.dit Total rainfall depth accumulated for a complete storm a58109.ied Inter-event durations, day(s) a58109.ifc Accumulated rainfall depth in 1 hour, mm a58109.tpc Temporal patterns' data
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D.2 MATLAB program for inverse distance weighted averaging method to regionalise intensity-frequency-duration data
Program names: Distance_Computation_1M.m
stadiscomp2012.m
ifd_1h.m, ifd_2h.m, ifd_6h.m, ifd_24h.m, ifd_48h.m, ifd_72h.m and ifd_100h.m
Length of the program: 1076 lines
Objectives of the program: to calculate regional value of rainfall intensity at a given location
Input to the program: The input to the program is the IFD data of the nearby pluviograph stations.
Output of the program: The output from the program is the regional IFD data of the target location.
Codes for Distance_Computation_1M.m clear, clc
% Distance Computation (Using Inverse Distance Weighting) % This program will access files from a specified directory, % do the calculation needed and plot the weighted average IFD curves % for up to ARI 1000000 years.
% open file for reading Complete Storm Analysis Data directory1 = 'E:\Programs in MATLAB\Complete Storm Analysis Data 2012\'; csa_list = dir('E:\Programs in MATLAB\Complete Storm Analysis Data 2012'); for i = 3 : size(csa_list)
filename1 = csa_list(i).name; end
% Enter the number of the ungauge station typing the (xstation) xstation = input('Enter the station number of the ungauge station : ');
[dist] = stadiscomp2012(filename1); % function stadiscomp
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% open file for reading station data sdr = fopen('E:\Programs in MATLAB\My Station Data 2012\NSW_Pluvio_Station_Data_2012.txt', 'r'); if (sdr < 0) error('could not open file "NSW_Pluvio_Station_Data_2012.txt"'); else % read data from station_data.txt file sta_data = fscanf(sdr,'%f',[4,inf]); csta_data = sta_data';
% close the station_data.txt file fclose(sdr);
% sort the distances for station data and rank the data % ssdata = sort station data ssdata = sortrows(csta_data, 4); end distance = input('Enter the distance in kilometers : '); count = 0; k = 1; while (ssdata(k, 4) < distance) k = k + 1; count = count + 1; end if (count < 1) fprintf('The stations are not enough\n') else fprintf('The stations having distances lesser than %i is equal to %i\n', distance, count); % enter the number of stations (nos) needed for weighted average nos = input('Enter the number of stations : '); fprintf('\n'); end
% getting the different distances for the stations selected in ascending order j = 0; vardist = [ ]; while (j < nos) j = j + 1; vardist(j) = ssdata(j,4); fprintf('The Station ID is %i with a distance of %9.5f\n',ssdata(j,1), ssdata(j,4)); end
% getting the product of the distances pvardist = 1; for k1 = 1 : nos pvardist = pvardist*vardist(k1); end
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% getting the terms for weighted average by dividing the product of all the % distances of the selected stations by the corresponding station distances k2 = 1 : nos; term = pvardist./vardist(k2);
% getting the weighted percentage of each term by diviting the each term by % the sum of all the terms tterm = 0; for k3 = 1 : nos tterm = tterm + term(k3); end weight = term/tterm; cweight = weight';
% checking the total weighted percentage if it is equal to 1 tweight = 0; for k4 = 1 : nos tweight = tweight + weight(k4); end
% open file for writing calculated distances for weighted average data cwad = fopen(['E:\Programs in MATLAB\My Calculated Distances 2012\', num2str(xstation),'.mcd'], 'w'); if (cwad < 0) error('could not open file "xstation.mcd"'); else for k = 1: nos; % write data to xstation.mcd file cwad1 = [ssdata(k,1), ssdata(k,4), weight(k)];
fprintf(cwad, '%i %9.5f %9.5f\n', cwad1); end
% close the xstation.mcd file fclose(cwad); end
% open file for reading My IFD Results Data directory4 = 'E:\Programs in MATLAB\My IFD Results 2012\'; ifd_list = dir('E:\Programs in MATLAB\My IFD Results 2012'); twad = [0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0; 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0];
% rainfall intensities from 0.1 to 1000000 years for plotting University of Western Sydney Page 321
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ARI = [ 0.1 1.0 1.11 1.25 2.0 5.0 10.0 20.0 50.0 100.0 500.0 1000.0 1000000.0 ]; ARI_all = [1.0 2.0 6.0 24.0 48.0 72.0 100.0]; staID4 = [ ]; % station for Calculating Weighted Average for m = 3 : size(ifd_list) filename4 = ifd_list(m).name; dataset4 = fopen([directory4 filename4], 'r'); staID4(m-2) = fscanf(dataset4, '%f', [1 1]); data4a = fscanf(dataset4, '%f',[13, 1]); data4b = fscanf(dataset4, '%f',[14, inf]);
cdata4a = data4a'; cdata4b = data4b';
for k5 = 1 : nos staID5(k5) = ssdata(k5, 1); if (staID4(m-2) == staID5(k5)) wadata = cdata4b(:, 2:14).*cweight(k5, 1); twad = twad + wadata;
% open file for writing calculated weighted average data wad = fopen(['E:\Programs in MATLAB\My Weighted Averages 2013\', num2str(xstation),'.wad'], 'w'); if (wad < 0) error('could not open file "xstation.wad"'); else % write data to xstation.wad file wad1 = [staID5(1), ARI]; % closest station to the Calculated Weighted Average wad2 = [ARI_all' twad];
fprintf(wad, '%12.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f\n', wad1); fprintf(wad, '%12.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f\n', wad2');
% close the xstation.wad file fclose(wad); end
figure(xstation); loglog(ARI_all', twad) title(['IFD Curves for Station ',num2str(xstation)]) xlabel('Log10 Dc, hr') ylabel('Log10 Ic, mm/hr') legend('0.1 year(s)','1','1.11','1.25','2','5','10','20','50','100','500','1000','10000 00') grid on
saveas(gcf, ['E:\Programs in MATLAB\My Weighted Average Figures 2013\', num2str(xstation), '.fig'], 'fig');
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end end end fclose('all');
% open file for reading My Weighted Averages Data directory6 = 'E:\Programs in MATLAB\My Weighted Averages 2013\'; wad_list = dir('E:\Programs in MATLAB\My Weighted Averages 2013'); diffdata = [ ]; % data differences from Calculated Weighted Average percent = [ ]; % percentages of the differences from Calculated Weighted Average minval = [ ]; % minimum value of the percentages maxval = [ ]; % maximum value of the percentages for n = 3 : size(wad_list) filename6 = wad_list(n).name; dataset6 = fopen([directory6 filename6], 'r'); staID6(n-2) = fscanf(dataset6, '%f', [1 1]); data6a = fscanf(dataset6, '%f',[13, 1]); data6b = fscanf(dataset6, '%f',[14, inf]);
cdata6a = data6a'; cdata6b = data6b';
% open file for reading My IFD Results Data directory7 = 'E:\Programs in MATLAB\My IFD Results 2012\'; ifd_list = dir('E:\Programs in MATLAB\My IFD Results 2012');
staID7 = [ ]; % station for Calculating Weighted Average for p = 3 : size(ifd_list) filename7 = ifd_list(p).name; dataset7 = fopen([directory7 filename7], 'r'); staID7 = fscanf(dataset7, '%f', [1 1]); data7a = fscanf(dataset7, '%f',[13, 1]); data7b = fscanf(dataset7, '%f',[14, inf]);
cdata7a = data7a'; cdata7b = data7b';
if (staID7 + nos == staID6) diffdata = cdata6b(:, 2:14) - cdata7b(:, 2:14); percent = (diffdata./cdata7b(:, 2:14))*100; absper = abs(percent); minval = min(absper); maxval = max(absper);
bar(ARI(4:8), maxval(4:8),0.8) axis([ARI(4) ARI(8) 0 15]) title(['Maximum Percentage Plot for Station ',num2str(xstation+1),' - ',num2str(nos), ' stations']) xlabel('ARI, years') ylabel('Percentage, %') grid on
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saveas(gcf, ['E:\Programs in MATLAB\My Percentage Figures 2012\', num2str(xstation+1), '.fig'], 'fig');
bar(ARI(9:12), maxval(9:12),0.8) axis([ARI(9) ARI(12) 0 15]) title(['Maximum Percentage Plot for Station ',num2str(xstation+2),' - ',num2str(nos), ' stations']) xlabel('ARI, years') ylabel('Percentage, %') grid on
saveas(gcf, ['E:\Programs in MATLAB\My Percentage Figures 2012\', num2str(xstation+2), '.fig'], 'fig');
% open file for writing differences between weighted average and % closest station data dif = fopen(['E:\Programs in MATLAB\My IFD Results Differences 2012\', num2str(xstation),'.dif'], 'w'); if (dif < 0) error('could not open file "xstation.dif"'); else % write data to xstation.dif file dif1 = [xstation, ARI]; dif2 = [ARI_all' diffdata];
fprintf(dif, '%12.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f\n', dif1); fprintf(dif, '%12.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f\n', dif2');
% close the xstation.dif file fclose(dif); end
% open file for writing percentages of differences between weighted average and % closest station data per = fopen(['E:\Programs in MATLAB\My IFD Results Percentages 2012\', num2str(xstation),'.per'], 'w'); if (per < 0) error('could not open file "xstation.per"'); else % write data to xstation.dif file per1 = [xstation, ARI]; per2 = [ARI_all' percent];
fprintf(per, '%12.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f\n', per1); fprintf(per, '%12.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f %11.3f\n', per2'); fprintf(per, '\n'); fprintf(per, 'The percentage minimum value is %5.2f\n', minval); fprintf(per, '\n'); University of Western Sydney Page 324
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fprintf(per, 'The percentage maximum value is %5.2f\n', maxval);
% close the xstation.dif file fclose(per);
end end end fclose('all'); end return;
Codes for stadiscomp2012.m function [dist] = stadiscomp2012(filename1) % Station Distances Computation % This program will access files, calculate the station distances from % a specified location with longitude and latitude
% Enter the location by typing the latitude (xlat) and longitude (xlon) xlat = input('Enter the latitude of the location : '); xlon = input('Enter the longitude of the location : '); fprintf('\n'); directory = 'E:\Programs in MATLAB\Station Data 2012 PLU\'; station_list = dir('E:\Programs in MATLAB\Station Data 2012 PLU'); for i = 3 : size(station_list) filename = station_list(i).name; dataset1 = fopen([directory filename], 'r'); data = fscanf(dataset1,'%f',[3,inf]); cdata = data';
N = (1000); N(i-2,1) = length(data); % count the stations (by rows) close all
for j = 1 : N(i-2,1) stationID = cdata(:,1); % copy first column of cdata into stationID lat = cdata(:,2); % copy second column of cdata into latitude lon = cdata(:,3); % copy third column of cdata into longitude end end
% FORMULA FOR DISTANCE CALCULATIONS ( in kilometers ) % distance = 6378.7*acos(sin(LAT1/57.2958)*sin(LAT2/57.2958)+cos(LAT1/57.2958)*cos(LAT2/ 57.2958)*cos(LON2/57.2958-LON1/57.2958)) % radius = 6378.7 kilometers ( assumed radius of the earth ) % conversion factor = 57.2958
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% convert latitude and longitude values by 57.29577951 cxlat = xlat/57.29577951; cxlon = xlon/57.29577951; clat = lat/57.29577951; clon = lon/57.29577951; dist = 6378.7*acos(sin(cxlat)*sin(clat)+cos(cxlat)*cos(clat).*cos(clon- cxlon));
% create 1 matrix for all the data sta_data = [stationID lat lon dist];
% Open file for writing station data sd = fopen('E:\Programs in MATLAB\My Station Data 2012\NSW_Pluvio_Station_Data_2012.txt', 'w'); if (sd < 0) error('could not open file "NSW_Pluvio_Station_Data_2012.txt"'); end;
% write data to station_data.txt file % fprintf(sd, 'Station ID Latitude Longitude Distance\n'); fprintf(sd, '%7.0f %12.4f %10.4f %10.4f\n', [stationID'; lat'; lon'; dist']);
% close the station_data.txt file fclose(sd);
Codes for ifd_1h.m function [D1_log10, I1_log10] = ifd_1h(sdata, D, I) % This function calculates the complete storm duration for 1 hour % sort, compute the log10 and plot the data
limit = 30; k1 = 1; while (D(k1) == 1) k1 = k1 + 1; end
d1 = k1 - 1; disp(d1);
% checking if total of 1 hour duration is more than or equal to 30 if (d1 >= limit) D1_log10 = log10(sdata(1:d1,1)); I1_log10 = log10(sdata(1:d1,2)); %plot(D1_log10,I1_log10, 'o'); %title('1 hour Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
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else add = limit - d1; disp(add)
ka = 1; while (D(d1+add) == D(d1+add+ka)) ka = ka + 1; disp(ka) end
D1_log10 = log10(sdata(1:d1+add+ka-1,1)); I1_log10 = log10(sdata(1:d1+add+ka-1,2)); %plot(D1_log10,I1_log10, 'o'); %title('1 hour Representative Point'); %xlabel('Log10(Dc), h'); %ylabel('Log10(Ic), mm/h'); %grid on; end end
Codes for ifd_2h.m function [D2_log10, I2_log10] = ifd_2h(sdata, D, I) % This function calculates the complete storm duration for 2 hours % sort, compute the log10 and plot the data
limit = 30; k1 = 1; while (D(k1) == 1) k1 = k1 + 1; end
d1 = k1 - 1;
k2 = k1; while (D(k2) > 1 && D(k2) <= 3) k2 = k2 + 1; end
d2 = k2 - 1; disp(d2)
% checking if total of 2 hours duration is more than or equal to 30 if (d2 - d1 >= limit) D2_log10 = log10(sdata(1+d1:d2,1)); I2_log10 = log10(sdata(1+d1:d2,2)); %plot(D2_log10,I2_log10, 'o'); %title('2 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
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D2_log10 = log10(sdata(1:d2,1)); I2_log10 = log10(sdata(1:d2,2)); %plot(D2_log10,I2_log10, 'o'); %title('2 hours Representative Point'); %xlabel('Log10(Dc), h'); %ylabel('Log10(Ic), mm/h'); %grid on;
else add = limit - d2; disp(add)
ka = 1; while (D(d2+add) == D(d2+add+ka)) ka = ka + 1; disp(ka) end
D2_log10 = log10(sdata(1:d2+add+ka-1,1)); I2_log10 = log10(sdata(1:d2+add+ka-1,2)); %plot(D2_log10,I2_log10, 'o'); %title('2 hour Representative Point'); %xlabel('Log10(Dc), h'); %ylabel('Log10(Ic), mm/h'); %grid on; end end
Codes for ifd_6h.m function [D6_log10, I6_log10] = ifd_6h(sdata, D, I) % This function calculates the complete storm duration for 6 hours % sort, compute the log10 and plot the data
limit = 30; k1 = 1; while (D(k1) == 1) k1 = k1 + 1; end
d1 = k1 - 1; disp(d1);
k2 = k1; while (D(k2) > 1 && D(k2) <= 3) k2 = k2 + 1; d2 = k2 - 1; end
k6 = k2; while (D(k6) > 3 && D(k6) <= 12) k6 = k6 + 1; end
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d6 = k6 - 1; disp(d6);
% checking if total of 6 hours duration is more than or equal to 30 if (d6 - d2 >= limit) D6_log10 = log10(sdata(1+d2:d6,1)); I6_log10 = log10(sdata(1+d2:d6,2)); %plot(D6_log10,I6_log10, 'o'); %title('6 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
elseif (d6 - d1 >= limit) D6_log10 = log10(sdata(1+d1:d6,1)); I6_log10 = log10(sdata(1+d1:d6,2)); %plot(D6_log10,I6_log10, 'o'); %title('6 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
else add = limit - d6; disp(add)
ka = 1; while (D(d6+add) == D(d6+add+ka)) ka = ka + 1; disp(ka) end
D6_log10 = log10(sdata(1+d1:d6+add+ka-1,1)); I6_log10 = log10(sdata(1+d1:d6+add+ka-1,2)); %plot(D6_log10,I6_log10, 'o'); %title('6 hour Representative Point'); %xlabel('Log10(Dc), h'); %ylabel('Log10(Ic), mm/h'); %grid on; end end
Codes for ifd_24h.m function [D24_log10, I24_log10] = ifd_24h(sdata, D, I) % This function calculates the complete storm duration for 24 hours % sort, compute the log10 and plot the data
limit = 30; k1 = 1; while (D(k1) == 1) k1 = k1 + 1; end
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d1 = k1 - 1; disp(d1);
k2 = k1; while (D(k2) > 1 && D(k2) <= 3) k2 = k2 + 1; end
d2 = k2 - 1; disp(d2);
k6 = k2; while (D(k6) > 3 && D(k6) <= 12) k6 = k6 + 1; end
d6 = k6 - 1; disp(d6);
if (max(D) > 36) k24 = k6; while (D(k24) > 12 && D(k24) <= 36) k24 = k24 + 1; end
d24 = k24 - 1; disp(d24);
% checking if total of 48 hours duration is more than or equal to 30 if (d24 - d6 >= limit) D24_log10 = log10(sdata(1+d6:d24,1)); I24_log10 = log10(sdata(1+d6:d24,2)); %plot(D24_log10,I24_log10, 'o'); %title('24 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
else while (D(k24) < max(D)) k24 = k24 + 1; end
d24 = k24 - 1; disp(d24);
if (d24 - d6 >= limit) D24_log10 = log10(sdata(1+d6:d24+1,1)); I24_log10 = log10(sdata(1+d6:d24+1,2)); %plot(D24_log10,I24_log10, 'o'); %title('24 hours Representative Point'); %xlabel('Log10(Dc), h'); %ylabel('Log10(Ic), mm/h'); %grid on;
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else back = limit - (d24+1 - d6); disp(back);
kb = 1; while(D(d24-back) == D(d24-back-kb)) kb = kb + 1; disp(kb); end
D24_log10 = log10(sdata(d6-back-kb+1:d24+1,1)); I24_log10 = log10(sdata(d6-back-kb+1:d24+1,2)); %plot(D24_log10,I24_log10, 'o'); %title('24 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on; end end else k24 = k6; while (D(k24) < max(D)) k24 = k24 + 1; end
d24 = k24 - 1; disp(d24);
if (d24 - d6 >= limit) D24_log10 = log10(sdata(1+d6:d24+1,1)); I24_log10 = log10(sdata(1+d6:d24+1,2)); %plot(D24_log10,I24_log10, 'o'); %title('24 hours Representative Point'); %xlabel('Log10(Dc), h'); %ylabel('Log10(Ic), mm/h'); %grid on;
else back = limit - (d24+1 - d6); disp(back);
kb = 1; while(D(d24-back) == D(d24-back-kb)) kb = kb + 1; disp(kb); end
D24_log10 = log10(sdata(d6-back-kb+1:d24+1,1)); I24_log10 = log10(sdata(d6-back-kb+1:d24+1,2)); %plot(D24_log10,I24_log10, 'o'); %title('24 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on; end end end
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Codes for ifd_48h.m function [D48_log10, I48_log10] = ifd_48h(sdata, D, I) % This function calculates the complete storm duration for 48 hours % sort, compute the log10 and plot the data
limit = 30; k1 = 1; while (D(k1) == 1) k1 = k1 + 1; end
d1 = k1 - 1; disp(d1);
k2 = k1; while (D(k2) > 1 && D(k2) <= 3) k2 = k2 + 1; end
d2 = k2 - 1; disp(d2);
k6 = k2; while (D(k6) > 3 && D(k6) <= 12) k6 = k6 + 1; end
d6 = k6 - 1; disp(d6);
k24 = k6; while (D(k24) > 12 && D(k24) <= 36) k24 = k24 + 1; end
d24 = k24 - 1; disp(d24)
if (max(D) > 96) k48 = k24; while (D(k48) > 36 && D(k48) <= 96) k48 = k48 + 1; end
d48 = k48 - 1; disp(d48);
% checking if total of 48 hours duration is more than or equal to 30 if (d48 - d24 >= limit) D48_log10 = log10(sdata(d24+1:d48,1)); I48_log10 = log10(sdata(d24+1:d48,2));
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%plot(D48_log10,I48_log10, 'o'); %title('48 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
else while (D(k48) < max(D)) k48 = k48 + 1; end
d48 = k48 - 1; disp(d48)
if (d48 - d24 >= limit) D48_log10 = log10(sdata(d24+1:d48+1,1)); I48_log10 = log10(sdata(d24+1:d48+1,2)); %plot(D48_log10,I48_log10, 'o'); %title('48 hours Representative Point'); %xlabel('Log10(Dc), h'); %ylabel('Log10(Ic), mm/h'); %grid on;
else back = limit - (d48+1 - d24); disp(back)
kb = 1; while(D(d24-back) == D(d24-back-kb)) kb = kb + 1; disp(kb) end
D48_log10 = log10(sdata(d24-back-kb+1:d48+1,1)); I48_log10 = log10(sdata(d24-back-kb+1:d48+1,2)); %plot(D48_log10,I48_log10, 'o'); %title('48 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on; end end else k48 = k24; while (D(k48) < max(D)) k48 = k48 + 1; end
d48 = k48 - 1; disp(d48);
% checking if total of 48 hours duration is more than or equal to 30
if (d48 - d24 >= limit) D48_log10 = log10(sdata(d24+1:d48+1,1)); I48_log10 = log10(sdata(d24+1:d48+1,2));
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%plot(D48_log10,I48_log10, 'o'); %title('48 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
else back = limit - (d48+1 - d24); disp(back)
kb = 1; while(D(d24-back) == D(d24-back-kb)) kb = kb + 1; disp(kb); end
D48_log10 = log10(sdata(d24-back-kb+1:d48+1,1)); I48_log10 = log10(sdata(d24-back-kb+1:d48+1,2)); %plot(D48_log10,I48_log10, 'o'); %title('48 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
end end end
Codes for ifd_72h.m function [D72_log10, I72_log10] = ifd_72h(sdata, D, I) % This function calculates the complete storm duration for 72 hours % sort, compute the log10 and plot the data
limit = 30; k1 = 1; while (D(k1) == 1) k1 = k1 + 1; end
d1 = k1 - 1; disp(d1)
k2 = k1; while (D(k2) > 1 && D(k2) <= 3) k2 = k2 + 1; end
d2 = k2 - 1; disp(d2)
k6 = k2; while (D(k6) > 3 && D(k6) <= 12) k6 = k6 + 1; end
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d6 = k6 - 1; disp(d6)
k24 = k6; while (D(k24) > 12 && D(k24) <= 36) k24 = k24 + 1; end
d24 = k24 - 1; disp(d24)
k48 = k24; while (D(k48) > 36 && D(k48) <= 45) k48 = k48 + 1; end
d48 = k48 - 1; disp(d48)
if(max(D) > 100) k72 = k48; while (D(k72) > 45 && D(k72) <= 100) k72 = k72 + 1; end
d72 = k72 - 1; disp(d72)
% checking if total of 48 hours duration is more than or equal to 30 if (d72 - d48 >= limit) D72_log10 = log10(sdata(d48+1:d72,1)); I72_log10 = log10(sdata(d48+1:d72,2)); %plot(D72_log10,I72_log10, 'o'); %title('72 hours Representative Point'); %xlabel('Log10(Dc), h'); %ylabel('Log10(Ic), mm/h'); %grid on;
else while (D(k72) < max(D)) k72 = k72 + 1; end
d72 = k72 - 1; disp(d72);
if (d72 - d48 >= limit) D72_log10 = log10(sdata(d48+1:d72+1,1)); I72_log10 = log10(sdata(d48+1:d72+1,2)); %plot(D72_log10,I72_log10, 'o'); %title('72 hours Representative Point'); %xlabel('Log10(Dc), h'); %ylabel('Log10(Ic), mm/h');
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%grid on;
else back = limit - (d72+1 - d48); disp(back)
kb = 1; while(D(d48-back) == D(d48-back-kb)) kb = kb + 1; end
disp(kb)
D72_log10 = log10(sdata(d48-back-kb+1:d72+1,1)); I72_log10 = log10(sdata(d48-back-kb+1:d72+1,2)); %plot(D72_log10,I72_log10, 'o'); %title('72 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
end end else k72 = k48; while (D(k72) < max(D)) k72 = k72 + 1; end
d72 = k72 - 1; disp(d72);
% checking if total of 72 hours duration is more than or equal to 30 if (d72 - d48 >= limit) D72_log10 = log10(sdata(d48+1:d72+1,1)); I72_log10 = log10(sdata(d48+1:d72+1,2)); %plot(D72_log10,I72_log10, 'o'); %title('72 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
else back = limit - (d72+1 - d48); disp(back)
kb = 1; while(D(d48-back) == D(d48-back-kb)) kb = kb + 1; end
disp(kb)
D72_log10 = log10(sdata(d48-back-kb+1:d72+1,1)); I72_log10 = log10(sdata(d48-back-kb+1:d72+1,2)); %plot(D72_log10,I72_log10, 'o');
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%title('72 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
end end end
Codes for ifd_100h.m function [D100_log10, I100_log10] = ifd_100h(sdata, D, I) % This function calculates the complete storm duration for 100 hours % sort, compute the log10 and plot the data
limit = 30; k1 = 1; while (D(k1) == 1) k1 = k1 + 1; end
d1 = k1 - 1; disp(d1)
k2 = k1; while (D(k2) > 1 && D(k2) <= 3) k2 = k2 + 1; end
d2 = k2 - 1; disp(d2)
k6 = k2; while (D(k6) > 3 && D(k6) <= 12) k6 = k6 + 1; end
d6 = k6 - 1; disp(d6)
k24 = k6; while (D(k24) > 12 && D(k24) <= 36) k24 = k24 + 1; end
d24 = k24 - 1; disp(d24)
k48 = k24; while (D(k48) > 36 && D(k48) <= 50) k48 = k48 + 1;
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end
d48 = k48 - 1; disp(d48)
if(max(D) > 100) k100 = k48; while (D(k100) > 50 && D(k100) < max(D)) k100 = k100 + 1; end
d100 = k100 - 1; disp(d100);
% checking if total of 100 hours duration is more than or equal to 30
if (d100 - d48 >= 30) D100_log10 = log10(sdata(d48+1:d100+1,1)); I100_log10 = log10(sdata(d48+1:d100+1,2)); %plot(D100_log10,I100_log10, 'o'); %title('100 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
else back = limit - (d100+1 - d48); disp(back)
kb = 1; while(D(d48-back) == D(d48-back-kb)) kb = kb + 1; end
disp(kb)
D100_log10 = log10(sdata(d48-back-kb+1:d100+1,1)); I100_log10 = log10(sdata(d48-back-kb+1:d100+1,2)); %plot(D100_log10,I100_log10, 'o'); %title('48 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
end
else k100 = k48; while (D(k100) < max(D)) k100 = k100 + 1; end
d100 = k100 - 1; disp(d100);
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% checking if total of 100 hours duration is more than or equal to 30
if (d100 - d48 >= limit) D100_log10 = log10(sdata(d48+1:d100+1,1)); I100_log10 = log10(sdata(d48+1:d100+1,2)); %plot(D100_log10,I100_log10, 'o'); %title('100 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
else back = limit - (d100+1 - d48); disp(back)
kb = 1; while(D(d48-back) == D(d48-back-kb)) kb = kb + 1; end
disp(kb)
D100_log10 = log10(sdata(d48-back-kb+1:d100+1,1)); I100_log10 = log10(sdata(d48-back-kb+1:d100+1,2)); %plot(D100_log10,I100_log10, 'o'); %title('100 hours Representative Point'); %xlabel('Log10(Dc), h');ylabel('Log10(Ic), mm/h'); %grid on;
end end end
Example input parameter file:
Table D.3: Example input files to program Distance_Computation_1M.m for inverse distance weighted averaging method Parameter Description a58109.dit Total rainfall depth accumulated for a complete storm a58109.ifc Accumulated rainfall depth in 1 hour, mm 58109.noy Number of years Pluviograph stations' ID, latitude and longitude for NSW_ Pluvio_Station_ Details_ 2012.txt distance computations
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Example of output parameter files:
Table D.4: Example output files from program Distance_Computation_1M.m for inverse distance weighted averaging method Parameter Description 58109.ifd Intensity-frequency-duration (IFD) table 58109.fig Intensity-frequency-duration (IFD) curves 201001.fig Weighted average intensity-frequency-duration (IFD) curves 201001.mcd Computed distances from centre of catchment 201001.wad Weighted average intensity-frequency-duration (IFD) curves
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D.3 FORTRAN programs for initial loss analysis
Program name: mcsa5cs1.for
Length of the program: 2209 lines
Objectives of the program: to identify complete storm events from the pluviograph data
Input to the program: The input to the program is provided in Table D.5.
Output of the program: The output from the program is provided in Table D.6.
The output of this program becomes input to the loss calculation program (losssca.for)
Example input parameter file: L58109.psa
Table D.5: Example input files to program mcsa5cs1.for for loss analysis Parameter Description L58109 Pluviograph station ID C58109.dat Matched hourly pluviograph data file, rainfall in mm 6 Dry period between successive complete storm events, hours 0.6 Reduction factor to identify significant complete storm events 0.7 Reduction factor to identify significant complete storm events 47.30 Log-normal design rainfall intensity, 2 years ARI-1 hour duration, mm 11.00 Log-normal design rainfall intensity, 2 years ARI-12 hour duration, mm 3.66 Log-normal design rainfall intensity, 2 years ARI-72 hour duration, mm 87.30 Log-normal design rainfall intensity, 50 years ARI-1 hour duration, mm 23.40 Log-normal design rainfall intensity, 50 years ARI-12 hour duration, mm 7.91 Log-normal design rainfall intensity, 50 years ARI-72 hour duration, mm 0.09 Skewness 213 Catchment area, km2 C201001.dat Matched hourly streamflow data file, streamflow in m3/s
Example of output parameter file:
Table D.6: Example output files from program mcsa5cs1.for for loss analysis Parameter Description L58109.scs Start of complete storm events
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Program name: losssca.for
Length of the program: 994 lines
Objectives of the program: to identify initial losses of the selected streamflow events
Input to the program: The input to the program is provided in Table D.7.
Output of the program: The output from the program is provided in Table D.8.
Example input parameter file: L201001.lan
Table D.7: Example input files to losssca.for for loss analysis Parameter Description L58109 Pluviograph station ID 213 Catchment area, km2 C58109.dat Matched hourly pluviograph data file, rainfall in mm C201001.dat Matched hourly streamflow data file, streamflow in m3/s
Example of output parameter files:
Table D.8: Example output files from program losssca.for for loss analysis Parameter Description L58109.ics Initial loss values for complete storm events L58109.psc Concurrent rainfall and streamflow events Complete storm initial loss statistics: lower limit, L58109.slp upper limit, mean and standard deviation
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Program name: Cali2.for
Length of the program: 272 lines
Objectives of the program: to calibrate the runoff routing model
Input to the program: The input to the program is provided in Table D.9.
Output of the program: The output from the program is provided in Table D.10.
Example input parameter files:
Table D.9: Example input files to cali2.for for loss analysis Parameter Description Oxley_River_E2Q.txt Streamflow data of the selected complete storm event Oxley_River_E2R.txt Rainfall data of the selected complete storm event
Example of output parameter file:
Table D.10: Example output file from program cali2.for for loss analysis Parameter Description Oxley_River_E2OCQ.out Calibrated streamflow data
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D.4 FORTRAN program for simulation of streamflow hydrograph
Program name: mcdffc4id3.for
Length of the program: 1705 lines
Objectives of the program: to simulate streamflow hydrographs
Input to the program: The input to the program is provided in Table 7.6 (Chapter 7).
Output of the program: The output from the program is provided in Table D.11.
Example input parameter file to simulation of streamflow hydrograph:
oxleyu.psh (see Table 7.6 in Chapter 7)
Example of output parameter files:
Table D.11: Example output files from program mcdffc4id3.for Parameter Description OxleyR.ffn Derived flood frequency curve data OxleyR.g12 Generated temporal patterns data greater than 12 hours duration OxleyR.gcl Generated continuing loss values OxleyR.gdc Generated complete storm durations OxleyR.gid Generated inter-event durations OxleyR.gkv Generated storage delay parameter (k) values OxleyR.glc Generated complete storm initial loss values OxleyR.gsp Generated streamflow hydrograph peaks OxleyR.gtc Generated temporal patterns data OxleyR.l12 Generated temporal patterns data lesser than 12 hours duration
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D.5 FORTRAN program for Design Event Approach
Program name: routss_2013.for
Length of the program: 235 lines
Objectives of the program: to calculate streamflow hydrograph as per Design Event Approach
Input to the program: The input to the program is explained in Section 3.13.2.
Output of the program: The output from the program is provided in Table 7.4 (Chapter 7).
Example input parameter file: (see section 3.13.2)
Example of output files: (see Table 7.4, summary of flood quantiles for Oxley River catchment)
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