Modeling Hydrologic Change: Statistical Methods

by McCuen; Richard H.

• ISBN13: 9781566706001
• ISBN10: 1566706009
• Edition: 1st
• Format: Hardcover
• Copyright: 2002-10-29
• Publisher: CRC Press

Summary

Modeling hydrologic changes and predicting their impact on watersheds is a dominant concern for hydrologists and other water resource professionals, civil and environmental engineers, and urban and regional planners. As such changes continue, it becomes more essential to have the most up-to-date tools with which to perform the proper analyses and modeling of the complex ecology, morphology, and physical processes that occur within watersheds. An application-oriented text, Modeling Hydrologic Change: Statistical Methods provides a step-by-step presentation of modeling procedures to help you properly analyze and model real-world data.The text addresses modeling systems where change has affected data that will be used to calibrate and test models of the system. The use of actual hydrologic data will help you learn how to handle the vagaries of real-world hydrologic-change data. All four elements of the modeling process are discussed: conceptualization, formulation, calibration, and verification. Although the book is oriented towards the statistical aspects of modeling, a strong background in statistics is not required. The statistical and modeling methods discussed here will be of value to all disciplines involved in modeling change. With approximately 100 illustrations, Modeling Hydrologic Change will equip you with an understanding with which to perform the proper analyses and modeling of the complex processes that occur across various disciplines.

Author Biography

Richard H. McCuen, professor of civil engineering at the University of Maryland at College Park

Table of Contents

Data, Statistics, and Modeling	1	(9)
Introduction	1	(1)
Watershed Changes	2	(1)
Effect on Flood Record	3	(1)
Watershed Change and Frequency Analysis	4	(1)
Detection of Nonhomogeneity	5	(1)
Modeling of Nonhomogeneity	6	(1)
Problems	7	(2)
Introduction to Time Series Modeling	9	(30)
Introduction	9	(1)
Components of a Time Series	10	(6)
Secular Trends	11	(1)
Periodic and Cyclical Variations	11	(3)
Episodic Variation	14	(1)
Random Variation	15	(1)
Moving-Average Filtering	16	(10)
Autocorrelation Analysis	26	(4)
Cross-Correlation Analysis	30	(4)
Identification of Random Components	34	(1)
Autoregression and Cross-Regression Models	34	(2)
Deterministic Component	35	(1)
Stochastic Element	35	(1)
Cross-Regression Models	36	(1)
Problems	36	(3)
Statistical Hypothesis Testing	39	(18)
Introduction	39	(3)
Procedure for Testing Hypotheses	42	(8)
Step 1: Formulation of Hypotheses	44	(1)
Step 2: Test Statistic and Its Sampling Distribution	45	(1)
Step 3: Level of Significance	45	(2)
Step 4: Data Analysis	47	(1)
Step 5: Region of Rejection	47	(1)
Step 6: Select Appropriate Hypothesis	48	(2)
Relationships among Hypothesis Test Parameters	50	(3)
Parametric and Nonparametric Tests	53	(2)
Disadvantages of Nonparametric Tests	54	(1)
Advantages of Nonparametric Tests	55	(1)
Problems	55	(2)
Outlier Detection	57	(20)
Introduction	57	(1)
Chauvenet's Method	58	(3)
Dixon--Thompson Test	61	(2)
Rosner's Outlier Test	63	(5)
Log-Pearson Type III Outlier Detection: Bulletin 17b	68	(2)
Pearson Type III Outlier Detection	70	(3)
Problems	73	(4)
Statistical Frequency Analysis	77	(36)
Introduction	77	(1)
Frequency Analysis and Synthesis	77	(6)
Population versus Sample	78	(1)
Analysis versus Synthesis	78	(1)
Probability Paper	79	(1)
Mathematical Model	80	(1)
Procedure	81	(1)
Sample Moments	81	(1)
Plotting Position Formulas	82	(1)
Return Period	83	(1)
Population Models	83	(12)
Normal Distribution	84	(4)
Lognormal Distribution	88	(3)
Log-Pearson Type III Distribution	91	(4)
Adjusting Flood Record for Urbanization	95	(13)
Effects of Urbanization	95	(4)
Method for Adjusting Flood Record	99	(8)
Testing Significance of Urbanization	107	(1)
Problems	108	(5)
Graphical Detection of Nonhomogeneity	113	(22)
Introduction	113	(1)
Graphical Analyses	113	(12)
Univariate Histograms	114	(2)
Bivariate Graphical Analysis	116	(9)
Compilation of Causal Information	125	(3)
Supporting Computational Analyses	128	(3)
Problems	131	(4)
Statistical Detection of Nonhomogeneity	135	(38)
Introduction	135	(1)
Runs Test	136	(5)
Rational Analysis of Runs Test	139	(2)
Kendall Test for Trend	141	(5)
Rationale of Kendall Statistic	145	(1)
Pearson Test for Serial Independence	146	(3)
Spearman Test for Trend	149	(3)
Rationale for Spearman Test	151	(1)
Spearman--Conley Test	152	(1)
Cox--Stuart Test for Trend	153	(3)
Noether's Binomial Test for Cyclical Trend	156	(5)
Background	158	(1)
Test Procedure	158	(1)
Normal Approximation	159	(2)
Durbin--Watson Test for Autocorrelation	161	(4)
Test for Positive Autocorrelation	162	(1)
Test for Negative Autocorrelation	163	(1)
Two-Sided Test for Autocorrelation	163	(2)
Equality of Two Correlation Coefficients	165	(2)
Problems	167	(6)
Detection of Change in Moments	173	(36)
Introduction	173	(1)
Graphical Analysis	173	(1)
The Sign Test	174	(4)
Two-Sample t-Test	178	(3)
Mann--Whitney Test	181	(3)
Rational Analysis of the Mann--Whitney Test	183	(1)
The t-Test for Two Related Samples	184	(4)
The Walsh Test	188	(3)
Wilcoxon Matched-Pairs, Signed-Ranks Test	191	(5)
Ties	194	(2)
One-Sample Chi-Square Test	196	(3)
Two-Sample F-Test	199	(1)
Siegel--Tukey Test for Scale	200	(4)
Problems	204	(5)
Detection of Change in Distribution	209	(38)
Introduction	209	(1)
Chi-Square Goodness-of-Fit Test	209	(14)
Procedure	210	(4)
Chi-Square Test for a Normal Distribution	214	(5)
Chi-Square Test for an Exponential Distribution	219	(2)
Chi-Square Test for Log-Pearson III Distribution	221	(2)
Kolmogorov--Smirnov One-Sample Test	223	(7)
Procedure	223	(7)
The Wald--Wolfowitz Runs Test	230	(8)
Large Sample Testing	232	(1)
Ties	233	(5)
Kolmogorov--Smirnov Two-Sample Test	238	(5)
Procedure: Case A	239	(2)
Procedure: Case B	241	(2)
Problems	243	(4)
Modeling Change	247	(46)
Introduction	247	(1)
Conceptualization	247	(3)
Model Formulation	250	(7)
Types of Parameters	250	(2)
Alternative Model Forms	252	(3)
Composite Models	255	(2)
Model Calibration	257	(21)
Least-Squares Analysis of a Linear Model	257	(2)
Standardized Model	259	(1)
Matrix Solution of the Standardized Model	259	(1)
Intercorrelation	260	(1)
Stepwise Regression Analysis	261	(6)
Numerical Optimization	267	(9)
Subjective Optimization	276	(2)
Model Verification	278	(4)
Split-Sample Testing	278	(1)
Jackknife Testing	279	(3)
Assessing Model Reliability	282	(6)
Model Rationality	284	(1)
Bias in Estimation	285	(1)
Standard Error of Estimate	286	(1)
Correlation Coefficient	287	(1)
Problems	288	(5)
Hydrologic Simulation	293	(40)
Introduction	293	(5)
Definitions	293	(1)
Benefits of Simulation	294	(1)
Monte Carlo Simulation	295	(2)
Illustration of Simulation	297	(1)
Random Numbers	298	(1)
Computer Generation of Random Numbers	298	(6)
Midsquare Method	299	(1)
Arithmetic Generators	300	(1)
Testing of Generators	300	(1)
Distribution Transformation	300	(4)
Simulation of Discrete Random Variables	304	(10)
Types of Experiments	304	(1)
Binomial Distribution	304	(2)
Multinomial Experimentation	306	(2)
Generation of Multinomial Variates	308	(1)
Poisson Distribution	309	(1)
Markov Process Simulation	310	(4)
Generation of Continuously Distributed Random Variates	314	(9)
Uniform Distribution, U(α, β)	314	(1)
Triangular Distribution	315	(1)
Normal Distribution	316	(1)
Lognormal Distribution	317	(3)
Log-Pearson Type III Distribution	320	(1)
Chi-Square Distribution	320	(1)
Exponential Distribution	321	(1)
Extreme Value Distribution	322	(1)
Applications of Simulation	323	(5)
Problems	328	(5)
Sensitivity Analysis	333	(34)
Introduction	333	(1)
Mathematical Foundations of Sensitivity Analysis	334	(12)
Definition	334	(1)
The Sensitivity Equation	334	(1)
Computational Methods	335	(1)
Parametric and Component Sensitivity	336	(2)
Forms of Sensitivity	338	(4)
A Correspondence between Sensitivity and Correlation	342	(4)
Time Variation of Sensitivity	346	(2)
Sensitivity in Model Formulation	348	(2)
Sensitivity and Data Error Analysis	350	(6)
Sensitivity of Model Coefficients	356	(5)
Watershed Change	361	(2)
Sensitivity in Modeling Change	361	(1)
Qualitative Sensitivity Analysis	362	(1)
Sensitivity Analysis in Design	362	(1)
Problems	363	(4)
Frequency Analysis under Nonstationary Land Use Conditions	367	(20)
Introduction	367	(2)
Overview of Method	367	(1)
Illustrative Case Study: Watts Branch	368	(1)
Data Requirements	369	(1)
Rainfall Data Records	369	(1)
Streamflow Records	369	(1)
GIS Data	369	(1)
Developing a Land-Use Time Series	370	(2)
Modeling Issues	372	(9)
Selecting a Model	372	(3)
Calibration Strategies	375	(1)
Simulating a Stationary Annual Maximum-Discharge Series	376	(5)
Comparison of Flood-Frequency Analyses	381	(2)
Implications for Hydrologic Design	381	(2)
Assumptions and Limitations	383	(1)
Summary	383	(1)
Problems	384	(3)
Appendix A Statistical Tables	387	(32)
Appendix B Data Matrices	419	(6)
References	425	(4)
Index	429