Modeling Hydrologic Chanae Statistical Methods Richard H. McCuen Department of Civil and Environmental Engineering University of Maryland m LEWIS PUBLISHERS A CRC Press Company Boca Raton London New York Washington, D.C.
Contents Chapter 1 Data, Statistics, and Modeling 1 1.1 Introduction 1 1.2 Watershed Changes 2 1.3 Effect on Flood Record 3 1.4 Watershed Change and Frequency Analysis 4 1.5 Detection of Nonhomogeneity 5 1.6 Modeling of Nonhomogeneity 6 1.7 Problems 7 Chapter 2 Introduction to Time Series Modeling 9 2.1 Introduction 9 2.2 Components of a Time Series 10 2.2.1 Secular Trends 11 2.2.2 Periodic and Cyclical Variations 11 2.2.3 Episodic Variation 14 2.2.4 Random Variation 15 2.3 Moving-Average Filtering 16 2.4 Autocorrelation Analysis 26 2.5 Cross-Correlation Analysis 30 2.6 Identification of Random Components 34 2.7 Autoregression and Cross-Regression Models 34 2.7.1 Deterministic Component 35 2.7.2 Stochastic Element 35 2.7.3 Cross-Regression Models 36 2.8 Problems 36 Chapter 3 Statistical Hypothesis Testing 39 3.1 Introduction 39 3.2 Procedure for Testing Hypotheses 42 3.2.1 Step 1: Formulation of Hypotheses 44 3.2.2 Step 2: Test Statistic and Its Sampling Distribution 45 3.2.3 Step 3: Level of Significance 45 3.2.4 Step 4: Data Analysis 47 3.2.5 Step 5: Region of Rejection 47 3.2.6 Step 6: Select Appropriate Hypothesis 48 3.3 Relationships among Hypothesis Test Parameters 50
3.4 Parametric and Nonparametric Tests 53 3.4.1 Disadvantages of Nonparametric Tests 54 3.4.2 Advantages of Nonparametric Tests 55 3.5 Problems 55 Chapter 4 Outlier Detection 57 4.1 Introduction 57 4.2 Chauvenet's Method 58 4.3 Dixon-Thompson Test 61 4.4 Rosner's Outlier Test 63 4.5 Log-Pearson Type III Outlier Detection: Bulletin 17b 68 4.6 Pearson Type III Outlier Detection 70 4.7 Problems 73 Chapter 5 Statistical Frequency Analysis 77 5.1 Introduction 77 5.2 Frequency Analysis and Synthesis 77 5.2.1 Population versus Sample 78 5.2.2 Analysis versus Synthesis 78 5.2.3 Probability Paper 79 5.2.4 Mathematical Model 80 5.2.5 Procedure 81 5.2.6 Sample Moments 81 5.2.7 Plotting Position Formulas 82 5.2.8 Return Period 83 5.3 Population Models 83 5.3.1 Normal Distribution 84 5.3.2 Lognormal Distribution 88 5.3.3 Log-Pearson Type III Distribution 91 5.4 Adjusting Flood Record for Urbanization 95 5.4.1 Effects of Urbanization 95 5.4.2 Method for Adjusting Flood Record 99 5.4.3 Testing Significance of Urbanization 107 5.5 Problems 108 Chapter 6 Graphical Detection of Nonhomogeneity 113 6.1 Introduction 113 6.2 Graphical Analyses 113 6.2.1 Univariate Histograms 114 6.2.2 Bivariate Graphical Analysis 116 6.3 Compilation of Causal Information 125 6.4 Supporting Computational Analyses 128 6.5 Problems 131
Chapter 7 Statistical Detection of Nonhomogeneity '. 135 7.1 Introduction 135 7.2 Runs Test 136 7.2.1 Rational Analysis of Runs Test 139 7.3 Kendall Test for Trend : 141 7.3.1 Rationale of Kendall Statistic 145 7.4 Pearson Test for Serial Independence 146 7.5 Spearman Test for Trend 149 7.5.1 Rationale for Spearman Test 151 7.6 Spearman-Conley Test 152 7.7 Cox-Stuart Test for Trend 153 7.8 Noether's Binomial Test for Cyclical Trend 156 7.8.1 Background 158 7.8.2 Test Procedure 158 7.8.3 Normal Approximation 159 7.9 Durbin-Watson Test for Autocorrelation 161 7.9.1 Test for Positive Autocorrelation 162 7.9.2 Test for Negative Autocorrelation 163 7.9.3 Two-Sided Test for Autocorrelation 163 7.10 Equality of Two Correlation Coefficients 165 7.11 Problems 167 Chapter 8 Detection of Change in Moments 173 8.1 Introduction 173 8.2 Graphical Analysis 173 8.3 The Sign Test 174 8.4 Two-Sample f-test 178 8.5 Mann-Whitney Test 181 8.5.1 Rational Analysis of the Mann-Whitney Test 183 8.6 The f-test for Two Related Samples 184 8.7 The Walsh Test 188 8.8 Wilcoxon Matched-Pairs, Signed-Ranks Test 191 8.8.1 Ties 194 8.9 One-Sample Chi-Square Test 196 8.10 Two-Sample F-Test 199 8.11 Siegel-Tukey Test for Scale 200 8.12 Problems 204 Chapter 9 Detection of Change in Distribution 209 9.1 Introduction 209 9.2 Chi-Square Goodness-of-Fit Test 209 9.2.1 Procedure 210 9.2.2 Chi-Square Test for a Normal Distribution 214 9.2.3 Chi-Square Test for an Exponential Distribution 219
9.2.4 Chi-Square Test for Log-Pearson III Distribution 221 9.3 Kolmogorov-Smirnov One-Sample Test 223 9.3.1 Procedure 223 9.4 The Wald-Wolfowitz Runs Test 230 9.4.1 Large Sample Testing 232 9.4.2 Ties 233 9.5 Kolmogorov-Smirnov Two-Sample Test 238 9.5.1 Procedure: Case A 239 9.5.2 Procedure: Case B 241 9.6 Problems 243 Chapter 10 Modeling Change 247 10.1 Introduction 247 10.2 Conceptualization 247 10.3 Model Formulation 250 10.3.1 Types of Parameters 250 10.3.2 Alternative Model Forms 252 10.3.3 Composite Models 255 10.4 Model Calibration 257 10.4.1 Least-Squares Analysis of a Linear Model 257 10.4.2 Standardized Model 259 10.4.3 Matrix Solution of the Standardized Model 259 10.4.4 Intercorrelation 260 10.4.5 Stepwise Regression Analysis 261 10.4.6 Numerical Optimization 267 10.4.7 Subjective Optimization 276 10.5 Model Verification 278 10.5.1 Split-Sample Testing 278 10.5.2 Jackknife Testing 279 10.6 Assessing Model Reliability 282 10.6.1 Model Rationality 284 10.6.2 Bias in Estimation 285 10.6.3 Standard Error of Estimate 286 10.6.4 Correlation Coefficient 287 10.7 Problems 288 Chapter 11 Hydrologic Simulation 293 11.1 Introduction 293 11.1.1 Definitions 293 11.1.2 Benefits of Simulation 294 11.1.3 Monte Carlo Simulation 295 11.1.4 Illustration of Simulation 297 11.1.5 Random Numbers 298 11.2 Computer Generation of Random Numbers... 298 11.2.1 Midsquare Method 299
11.2.2 Arithmetic Generators 300 11.2.3 Testing of Generators 300 11.2.4 Distribution Transformation 300 11.3 Simulation of Discrete Random Variables 304 11.3.1 Types of Experiments 304 11.3.2 Binomial Distribution 304 11.3.3 Multinomial Experimentation 306 11.3.4 Generation of Multinomial Variates 308 11.3.5 Poisson Distribution 309 11.3.6 Markov Process Simulation 310 11.4 Generation of Continuously Distributed Random Variates 314 11.4.1 Uniform Distribution, U(a, j8) 314 11.4.2 Triangular Distribution 315 11.4.3 Normal Distribution 316 11.4.4 Lognormal Distribution 317 11.4.5 Log-Pearson Type III Distribution 320 11.4.6 Chi-Square Distribution 320 11.4.7 Exponential Distribution 321 11.4.8 Extreme Value Distribution 322 11.5 Applications of Simulation 323 11.6 Problems... 328 Chapter 12 Sensitivity Analysis 333 12.1 Introduction '. 333 12.2 Mathematical Foundations of Sensitivity Analysis 334 12.2.1 Definition 334 12.2.2 The Sensitivity Equation 334 12.2.3 Computational Methods 335 12.2.4 Parametric and Component Sensitivity 336 12.2.5 Forms of Sensitivity 338 12.2.6 A Correspondence between Sensitivity and Correlation 342 12.3 Time Variation of Sensitivity 346 12.4 Sensitivity in Model Formulation 348 12.5 Sensitivity and Data Error Analysis 350 12.6 Sensitivity of Model Coefficients 356 12.7 Watershed Change 361 12.7.1 Sensitivity in Modeling Change 361 12.7.2 Qualitative Sensitivity Analysis 362 12.7.3 Sensitivity Analysis in Design 362 12.8 Problems 363 Chapter 13 Frequency Analysis under Nonstationary Land Use Conditions 367 13.1 Introduction 367
13.1.1 Overview of Method 367 13.1.2 Illustrative Case Study: Watts Branch 368 13.2 Data Requirements 369 13.2.1 Rainfall Data Records 369 13.2.2 Streamflow Records 369 13.2.3 GISData 369 13.3 Developing a Land-Use Time Series 370 13.4 Modeling Issues 372 13.4.1 Selecting a Model 372 13.4.2 Calibration Strategies.375 13.4.3 Simulating a Stationary Annual Maximum-Discharge Series 376 13.5 Comparison of Flood-Frequency Analyses 381 13.5.1 Implications for Hydrologic Design 381 13.5.2 Assumptions and Limitations 383 13.6 Summary 383 13.7 Problems 384 Appendix A Statistical Tables 387 Appendix B Data Matrices 419 References 425 Index 429