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Design Flood Estimation for Ungauged Catchments in Victoria: Ordinary & Generalised Least Squares Methods Compared

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Design Flood Estimation for Ungauged Catchments in Victoria: Ordinary & Generalised Least Squares Methods Compared Khaled Haddad - 98072705 M.Eng(Hons) Thesis Design Flood Estimation for Ungauged Catchments in Victoria: Ordinary & Generalised Least Squares Methods Compared By Khaled Haddad B.Eng (Hons) Civil Student ID: 98072705 Principal Supervisor: Dr Ataur Rahman Associate Supervisors: Associate Professor Surendra Shrestha Associate Professor Chin Leo School of Engineering University of Western Sydney Feb 2008 i Khaled Haddad - 98072705 STATEMENT OF AUTHENTICATION I hereby declare that the work presented in this thesis is solely my own work and that to the best of my knowledge the work is original except where otherwise indicated by references to other authors or works. No part of this thesis has been submitted for any other degree or diploma. Signature…… ………………………….. Date …23…/…06…/2008……… ii Khaled Haddad - 98072705 ACKNOWLEDGEMENTS The author would like to gratefully acknowledge: • His main supervisor Dr Ataur Rahman, for his excellent guidance, inspiration, invaluable suggestions, timely advice and willingness to help at any time throughout the course of this research. • Mr Erwin Weinmann of Monash University for his constructive comments, valuable guidance, advice and encouragement throughout this research. • His associate supervisors Associate Professor Surendra Shrestha and Associate Professor Chin Leo for their encouragement and advice. • Department of Sustainability and Environment and Thiess Services Victoria for providing the streamflow data. • The Bureau of Meteorology for providing climatic data CDs. • Professor George Kuczera, Associate Professor James Ball, Mr Mark Babister, Mr Robert French and Dr William Weeks for their suggestions and input to the project. • Many thanks to Mr Wilfredo Caballero for providing some of the data used in this study which were abstracted as a part of his BEng (Honours) thesis in the University of Western Sydney. • My parents and family for being very encouraging and proud of what I have achieved. iii Khaled Haddad - 98072705 ABSTRACT Design flood estimation in small to medium sized ungauged catchments is frequently required in hydrologic analysis and design and is of notable economic significance. For this task Australian Rainfall and Runoff (ARR) 1987, the National Guideline for Design Flow Estimation, recommends the Probabilistic Rational Method (PRM) for general use in South- East Australia. However, there have been recent developments that indicated significant potential to provide more meaningful and accurate design flood estimation in small to medium sized ungauged catchments. These include the L moments based index flood method and a range of quantile regression techniques. This thesis focuses on the quantile regression techniques and compares two methods: ordinary least squares (OLS) and generalised least squares (GLS) based regression techniques. It also makes comparison with the currently recommended Probabilistic Rational Method. The OLS model is used by hydrologists to estimate the parameters of regional hydrological models. However, more recent studies have indicated that the parameter estimates are usually unstable and that the OLS procedure often violates the assumption of homoskedasticity. The GLS based regression procedure accounts for the varying sampling error, correlation between concurrent flows, correlations between the residuals and the fitted quantiles and model error in the regional model, thus one would expect more accurate flood quantile estimation by this method. This thesis uses data from 133 catchments in the state of Victoria to develop prediction equations involving readily obtainable catchment characteristics data. The GLS regression procedure is explored further by carrying out a 4-stage generalised least squares analysis where the development of the prediction equations is based on relating hydrological statistics such as mean flows, standard deviations, skewness and flow quantiles to catchment characteristics. This study also presents the validation of the two techniques by carrying out a split-sample validation on a set of independent test catchments. The PRM is also tested by deriving an iv Khaled Haddad - 98072705 updated PRM technique with the new data set and carrying out a split sample validation on the test catchments. The results show that GLS based regression provides more accurate design flood estimates than the OLS regression procedure and the PRM. Based on the average variance of prediction, standard error of estimate, traditional statistics and new statistics, rankings and the median relative error values, the GLS method provided more accurate flood frequency estimates especially for the smaller catchments in the range of 1-300 km 2. The predictive ability of the GLS model is also evident in the regression coefficient values when comparing with the OLS method. However, the performance of the PRM method, particularly for the larger catchments appears to be satisfactory as well. v Khaled Haddad - 98072705 TABLE OF CONTENTS Page Front Cover i Statement ii Acknowledgements iii Abstract iv Table of Contents vi List of Figures xiii List of Tables xvii List of Notations xviii List of Abbreviations xx CHAPTER 1: INTRODUCTION 1 1.1 Background to the proposed research 1 1.2 The need for this research 3 1.3 Objectives of this research 5 1.4 Outline of the thesis 5 CHAPTER 2: REVIEW OF REGIONAL FLOOD FREQUENCY ESTIMATION TECHNIQUES 9 2.1 General 9 2.2 Basic Issues 9 2.2.1 Flood Frequency Analysis 9 2.2.2 Regional Flood Frequency Analysis 11 2.2.3 Regional Homogeneity 11 2.2.4 Inter – Site Dependence 12 2.2.5 Distributional Choices 13 2.3 Methods for identification of Homogenous Regions 14 2.4 Regional Flood Frequency Analysis Methods 15 vi Khaled Haddad - 98072705 2.4.1 Index Flood Method 15 2.4.2 Station Year Method 19 2.4.3 Bayesian Method 19 2.4.4 Probabilistic Rational Method 19 2.5 Quantile Regression Technique 21 2.5.1 Introduction 21 2.5.2 Generalised Least Squares and Weighted Least Squares 23 2.5.3 Application of Generalised Least Squares Regression 24 2.5.4 An Operational GLS Model for Hydrological Regression 25 2.5.5 Operational Bayesian GLS Regression for Regional Hydrological Analysis 25 2.5.6 The Use of GLS Regression in Regional Hydrologic Analysis 26 2.5.7 Application of Generalised Least Squares to Low – Flow Frequency Analysis 26 2.6 Quantile Regression Technique In Australia 28 2.7 Summary 30 CHAPTER 3: METHODOLOGY OF STATISTICAL TECHNIQUES USED IN THIS REGIONAL FLOOD FREQUENCY ANALYSIS STUDY 32 3.1 General 32 3.2 Methods for Assessing the Degree of Homogeneity of a Region 34 3.2.1 L-moments 35 3.2.2 Tests Based on L-moments (Goodness of Fit Tests) 35 3.3 Regional Homogeneity Tests 36 3.4 At – Site Flood Frequency Analysis 38 3.4.1 FLIKE 39 3.4.2 Log – Pearson Type 3 Distribution 40 3.5 Multiple Regression Analysis 41 3.5.1 Ordinary Least Squares 42 3.5.2 Dealing with Assumption Violations of Ordinary Least Squares 43 vii Khaled Haddad - 98072705 3.5.3 The Basic Problem – Generalised Least Squares 43 3.5.4 Weighted Least Squares 46 3.5.5 Dealing with Data Problems 48 3.6 Operational Generalised Least Squares – 4 Stage Generalised Least Squares Analysis 49 3.6.1 Regional Skew Analysis 53 3.6.2 Variance of Sample Estimators by Bootstrap Var (gi) 55 3.7 Ordinary Least Squares – Model Development Techniques Used 56 3.8 Generalised Least Squares – Model Development 59 3.8.1 Regression Model for Skewness 59 3.9 Setting up of the Residual Error Covariance Matrices 60 3.9.1 Regression Model for Standard Deviation 60 3.9.2 Regression Model for Mean 60 3.9.3 GLS Regression Model for the Quantiles 61 3.10 Measures of Model and Prediction Error 61 3.11 Development of the Probabilistic Rational Method 63 3.12 Summary 66 CHAPTER 4: STUDY AREA AND PREPARATION OF STREAMFLOW DATA 68 4.1 General 68 4.2 Study Area 68 4.3 Selection of Initial Catchment Candidate Catchments 69 4.4 Filling Missing Records in Annual Maximum Flood Series 71 4.5 Trend Analysis – Mann Kendall Test for Trend and Distribution Free CUSUM Test 74 4.6 Rating Curve Extrapolation Error 78 4.7 Impact of Rating Curve Error on Flood Frequency Analysis 80 4.8 Impacts of Rating Ratio on Flood Frequency Analysis – Sensitivity analysis 81 4.9 Selected Catchments 82 4.10 Checking for Outliers in the Annual Maximum Series 84 viii Khaled Haddad - 98072705 4.11 Selection of Test Catchments 87 4.12 Summary 87 CHAPTER 5: SELECTION AND ESTIMATION OF CLIMATIC AND CATCHMENT CHARACTERISTICS 88 5.1 General 88 5.2 Categories of Catchment Characteristics Considered 89 5.2.1 Climatic Characteristics 89 5.2.2 Morphometric Characteristics 89 5.2.3 Catchment Cover and Land Use Characteristics 89 5.2.4 Geology 90 5.3 Selection Criteria 90 5.4 Catchment Characteristics Considered for the Proposed Research 91 5.4.1 Rainfall Intensity 91 5.4.2 Mean Annual Rainfall 92 5.4.3 Mean Annual Evapotranspiration 93 5.4.4 Catchment Area 93 5.4.5 Slope S1085 93 5.4.6 Stream Density 94 5.4.7 Fraction Forest Area 94 5.4.8 Quaternary Sediment Area 94 5.5 Exploratory Data Analysis – Transformations 100 5.6 Exploratory Data Analysis – Correlation Matrix 111 5.7 Summary 112 CHAPTER 6: SEARCHING FOR HOMOGENEOUS REGIONS 113 6.1 Selection Criteria 113 6.2 Formation of Homogeneous Groups 113 6.3 Measuring the Degree of Heterogeneity in a Group 114 ix Khaled Haddad - 98072705 6.4 Forming One Homogenous Group 115 6.5 Forming Two Homogenous Groups 115 6.5.1 Homogenous Regions Based on the North of the Great Dividing Range 116 6.5.2 Homogenous Regions Based on the South of the Great Dividing Range 116 6.6 Forming Three Homogenous
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