Modeling Hydrologic Chanae

Transcription

1 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.

2 Contents Chapter 1 Data, Statistics, and Modeling Introduction Watershed Changes Effect on Flood Record Watershed Change and Frequency Analysis Detection of Nonhomogeneity Modeling of Nonhomogeneity Problems 7 Chapter 2 Introduction to Time Series Modeling Introduction Components of a Time Series Secular Trends Periodic and Cyclical Variations Episodic Variation Random Variation Moving-Average Filtering Autocorrelation Analysis Cross-Correlation Analysis Identification of Random Components Autoregression and Cross-Regression Models Deterministic Component Stochastic Element Cross-Regression Models Problems 36 Chapter 3 Statistical Hypothesis Testing Introduction Procedure for Testing Hypotheses Step 1: Formulation of Hypotheses Step 2: Test Statistic and Its Sampling Distribution Step 3: Level of Significance Step 4: Data Analysis Step 5: Region of Rejection Step 6: Select Appropriate Hypothesis Relationships among Hypothesis Test Parameters 50

3 3.4 Parametric and Nonparametric Tests Disadvantages of Nonparametric Tests Advantages of Nonparametric Tests Problems 55 Chapter 4 Outlier Detection Introduction Chauvenet's Method Dixon-Thompson Test Rosner's Outlier Test Log-Pearson Type III Outlier Detection: Bulletin 17b Pearson Type III Outlier Detection Problems 73 Chapter 5 Statistical Frequency Analysis Introduction Frequency Analysis and Synthesis Population versus Sample Analysis versus Synthesis Probability Paper Mathematical Model Procedure Sample Moments Plotting Position Formulas Return Period Population Models Normal Distribution Lognormal Distribution Log-Pearson Type III Distribution Adjusting Flood Record for Urbanization Effects of Urbanization Method for Adjusting Flood Record Testing Significance of Urbanization Problems 108 Chapter 6 Graphical Detection of Nonhomogeneity Introduction Graphical Analyses Univariate Histograms Bivariate Graphical Analysis Compilation of Causal Information Supporting Computational Analyses Problems 131

4 Chapter 7 Statistical Detection of Nonhomogeneity ' Introduction Runs Test Rational Analysis of Runs Test Kendall Test for Trend : Rationale of Kendall Statistic Pearson Test for Serial Independence Spearman Test for Trend Rationale for Spearman Test Spearman-Conley Test Cox-Stuart Test for Trend Noether's Binomial Test for Cyclical Trend Background Test Procedure Normal Approximation Durbin-Watson Test for Autocorrelation Test for Positive Autocorrelation Test for Negative Autocorrelation Two-Sided Test for Autocorrelation Equality of Two Correlation Coefficients Problems 167 Chapter 8 Detection of Change in Moments Introduction Graphical Analysis The Sign Test Two-Sample f-test Mann-Whitney Test Rational Analysis of the Mann-Whitney Test The f-test for Two Related Samples The Walsh Test Wilcoxon Matched-Pairs, Signed-Ranks Test Ties One-Sample Chi-Square Test Two-Sample F-Test Siegel-Tukey Test for Scale Problems 204 Chapter 9 Detection of Change in Distribution Introduction Chi-Square Goodness-of-Fit Test Procedure Chi-Square Test for a Normal Distribution Chi-Square Test for an Exponential Distribution 219

5 9.2.4 Chi-Square Test for Log-Pearson III Distribution Kolmogorov-Smirnov One-Sample Test Procedure The Wald-Wolfowitz Runs Test Large Sample Testing Ties Kolmogorov-Smirnov Two-Sample Test Procedure: Case A Procedure: Case B Problems 243 Chapter 10 Modeling Change Introduction Conceptualization Model Formulation Types of Parameters Alternative Model Forms Composite Models Model Calibration Least-Squares Analysis of a Linear Model Standardized Model Matrix Solution of the Standardized Model Intercorrelation Stepwise Regression Analysis Numerical Optimization Subjective Optimization Model Verification Split-Sample Testing Jackknife Testing Assessing Model Reliability Model Rationality Bias in Estimation Standard Error of Estimate Correlation Coefficient Problems 288 Chapter 11 Hydrologic Simulation Introduction Definitions Benefits of Simulation Monte Carlo Simulation Illustration of Simulation Random Numbers Computer Generation of Random Numbers Midsquare Method 299

6 Arithmetic Generators Testing of Generators Distribution Transformation Simulation of Discrete Random Variables Types of Experiments Binomial Distribution Multinomial Experimentation Generation of Multinomial Variates Poisson Distribution Markov Process Simulation Generation of Continuously Distributed Random Variates Uniform Distribution, U(a, j8) Triangular Distribution Normal Distribution Lognormal Distribution Log-Pearson Type III Distribution Chi-Square Distribution Exponential Distribution Extreme Value Distribution Applications of Simulation Problems Chapter 12 Sensitivity Analysis Introduction ' Mathematical Foundations of Sensitivity Analysis Definition The Sensitivity Equation Computational Methods Parametric and Component Sensitivity Forms of Sensitivity A Correspondence between Sensitivity and Correlation Time Variation of Sensitivity Sensitivity in Model Formulation Sensitivity and Data Error Analysis Sensitivity of Model Coefficients Watershed Change Sensitivity in Modeling Change Qualitative Sensitivity Analysis Sensitivity Analysis in Design Problems 363 Chapter 13 Frequency Analysis under Nonstationary Land Use Conditions Introduction 367

7 Overview of Method Illustrative Case Study: Watts Branch Data Requirements Rainfall Data Records Streamflow Records GISData Developing a Land-Use Time Series Modeling Issues Selecting a Model Calibration Strategies Simulating a Stationary Annual Maximum-Discharge Series Comparison of Flood-Frequency Analyses Implications for Hydrologic Design Assumptions and Limitations Summary Problems 384 Appendix A Statistical Tables 387 Appendix B Data Matrices 419 References 425 Index 429