Modeling Hydrologic Change: Statistical Methods is about modeling systems where change has affected data that will be used to calibrate and test models of the systems and where models w
Trang 1LEWIS PUBLISHERS
A CRC Press Company Boca Raton London New York Washington, D.C
Statistical Methods
Richard H McCuen
Department of Civil and Environmental Engineering University of Maryland
Modeling
Hydrologic Change
Modeling
Hydrologic Change
© 2003 by CRC Press LLC
Trang 2This book contains information obtained from authentic and highly regarded sources Reprinted material
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Library of Congress Cataloging-in-Publication Data
McCuen, Richard H., 1941
Modeling hydrologic change: statistical methods / Richard H McCuen.
p cm.
Includes bibliographical references and index.
ISBN 1-56670-600-9
1 Hydrologic models 2 Hydrologic—Statistical methods I Title.
GB656.2.H9 M33 2002
551.48 ′01′1—dc21 2002073063
CIP Catalog record is available from the Library of Congress
Trang 3Modeling Hydrologic Change: Statistical Methods is about modeling systems where
change has affected data that will be used to calibrate and test models of the systems and where models will be used to forecast system responses after change occurs The focus is not on the hydrology Instead, hydrology serves as the discipline from which the applications are drawn to illustrate the principles of modeling and the detection of change All four elements of the modeling process are discussed: conceptualization, formulation, calibration, and verification Analysis and synthesis are discussed in order to enable both model builders and users to appreciate the importance of both aspects of modeling The book also focuses on the art and science
of modeling
While modeling techniques may be of great interest to hydrology-oriented pro-fessionals, they have value to all disciplines involved in modeling changes While the book is oriented toward the statistical aspects of modeling, a strong background
in statistics is not required Although the emphasis is on the analysis of temporal and spatial sequences of data, the fundamentals that comprise most of the book are far more applicable Statistical and modeling methods can be applied to a broad array of problems This book is not appropriate as a general text for an undergraduate introductory course in probability and statistics It is intended for advanced under-graduates, graduate students, and practicing professionals
It includes topics that serve as background material for its central focus and topics related to the graphical and statistical detection of change and the fundamen-tals of modeling While Chapters 2, 3, and 5 can be considered foundational, other chapters also introduce basic concepts Chapters 4 and 6 through 9 are devoted to important graphical and statistical procedures used in modeling Chapters 10 through
13 provide modeling tools useful in dealing with nonstationary systems
In Chapter 2, some fundamental time-series concepts are introduced, with a special emphasis on concepts relevant to changing systems Changes to real systems affect data observations The different forms that these changes introduce into data are defined and illustrated
In Chapter 3, basic concepts related to the fundamentals of hypothesis testing are introduced While most of this material will serve as a review for readers with background in statistical analysis, the chapter includes the basic concepts important
to understanding the statistical tests introduced in the middle chapters
Extreme events contained in measured data are the topics of Chapter 4 They can distort calibrated model parameters and predictions based on models Thus, their proper assessment and handling are essential in the early stages of modeling Frequency analysis is a rank-order statistical method widely used to connect the magnitudes and probabilities of occurrence of a random variable The basic elements
of frequency analysis as applied in hydrology are introduced in Chapter 5
Trang 4While statistical methods are important tools for the detection of nonstationarity, they are less effective when not accompanied by graphical analyses In Chapter 6, the uses of graphical methods in the modeling process are introduced While graph-ical analysis alone is inadequate for characterizing hydrologic change, it is a nec-essary component of the modeling process
In Chapter 7, the fundamentals of detecting nonhomogeneity in time series are introduced Special emphasis is placed on selecting the statistical method most sensitive to the types of changes to be evaluated
Hydrologic change may be evident in the moments of the measured data or more generally in the distribution of the data The statistical detection of change to moments is discussed in Chapter 8, while the detection of changes in probability distribution is the topic of Chapter 9 Statistical methods sensitive to different types
of change are introduced in these chapters
Chapter 10 covers many fundamentals of model calibration Basic regression techniques along with advanced topics such as composite modeling and jackknifing are included
Computer simulation is a valuable tool for modeling expected watershed changes The manipulation of a model to simulate alternative scenarios of change can be valuable to decision makers The fundamentals of simulation are presented
in Chapter 11
Sensitivity analysis is an important tool in modeling It is useful for making error analyses and for assessing the relative importance of causative factors The mathematical basis of sensitivity analysis and its uses are discussed in Chapter 12 Chapter 13 presents the role that geographic information systems (GIS) can play
in the assessment of hydrologic change The inclusion of large databases in modeling
is discussed The effects of urbanization on flood frequency analysis are shown
Trang 5The Author
Richard H McCuen, professor of civil engineering at the University of Maryland
at College Park, received degrees from Carnegie Mellon University and the Georgia Institute of Technology He received the Icko Iben Award from the American Water Resource Association and was co-recipient of the 1988 Outstanding Research Award from the American Society of Civil Engineers Water Resources Planning and Man-agement Division Topics in statistical hydrology and stormwater manMan-agement are his primary research interest
He is the author of 17 books and more than 200 professional papers, including
Modeling Hydrologic Change (CRC Press, 2002); Hydrologic Analysis and Design, Second Edition (Prentice-Hall, 1998); The Elements of Academic Research (ASCE
Press, 1996); Estimating Debris Volumes for Flood Control (Lighthouse Publica-tions, 1996; with T.V Hromadka); and Dynamic Communication for Engineers
(ASCE Press, 1993; with P Johnson and C Davis)
Trang 6Three people contributed greatly to this book I very much appreciate Glenn Moglen’s willingness to contribute the chapter on GIS and its role in modeling change This book initially was developed as a joint effort with Wilbert O Thomas, Jr., Baker Engineering, Alexandria, Virginia, but his workload did not permit par-ticipation beyond planning and review of earlier material His insights are appreci-ated Finally, the assistance of Dominic Yeh, University of Maryland, for typing the many, many drafts was essential to the completion of the manuscript His efforts are also very much appreciated
Richard H McCuen
College Park, Maryland
Trang 7Chapter 1 Data, Statistics, and Modeling
1.1 Introduction
1.2 Watershed Changes
1.3 Effect on Flood Record
1.4 Watershed Change
and Frequency Analysis
1.5 Detection of Nonhomogeneity
1.6 Modeling of Nonhomogeneity
1.7 Problems
Chapter 2 Introduction to Time Series Modeling
2.1 Introduction
2.2 Components of a Time Series
2.2.1 Secular Trends
2.2.2 Periodic and Cyclical Variations
2.2.3 Episodic Variation
2.2.4 Random Variation
2.3 Moving-Average Filtering
2.4 Autocorrelation Analysis
2.5 Cross-Correlation Analysis
2.6 Identification of Random Components
2.7 Autoregression and Cross-Regression Models
2.7.1 Deterministic Component
2.7.2 Stochastic Element
2.7.3 Cross-Regression Models
2.8 Problems
Chapter 3 Statistical Hypothesis Testing
3.1 Introduction
3.2 Procedure for Testing Hypotheses
3.2.1 Step 1: Formulation of Hypotheses
3.2.2 Step 2: Test Statistic and Its Sampling Distribution 3.2.3 Step 3: Level of Significance
3.2.4 Step 4: Data Analysis
3.2.5 Step 5: Region of Rejection
3.2.6 Step 6: Select Appropriate Hypothesis
3.3 Relationships among Hypothesis
Test Parameters
Trang 83.4 Parametric and Nonparametric Tests
3.4.1 Disadvantages of Nonparametric Tests 3.4.2 Advantages of Nonparametric Tests 3.5 Problems
Chapter 4 Outlier Detection
4.1 Introduction
4.2 Chauvenet’s Method
4.3 Dixon–Thompson Test
4.4 Rosner’s Outlier Test
4.5 Log-Pearson Type III Outlier
Detection: Bulletin 17b
4.6 Pearson Type III Outlier Detection
4.7 Problems
Chapter 5 Statistical Frequency Analysis
5.1 Introduction
5.2 Frequency Analysis and Synthesis
5.2.1 Population versus Sample
5.2.2 Analysis versus Synthesis
5.2.3 Probability Paper
5.2.4 Mathematical Model
5.2.5 Procedure
5.2.6 Sample Moments
5.2.7 Plotting Position Formulas
5.2.8 Return Period
5.3 Population Models
5.3.1 Normal Distribution
5.3.2 Lognormal Distribution
5.3.3 Log-Pearson Type III Distribution 5.4 Adjusting Flood Record for Urbanization 5.4.1 Effects of Urbanization
5.4.2 Method for Adjusting Flood Record 5.4.3 Testing Significance of Urbanization 5.5 Problems
Chapter 6 Graphical Detection of Nonhomogeneity 6.1 Introduction
6.2 Graphical Analyses
6.2.1 Univariate Histograms
6.2.2 Bivariate Graphical Analysis
6.3 Compilation of Causal Information
6.4 Supporting Computational Analyses
6.5 Problems
Trang 9Chapter 7 Statistical Detection of Nonhomogeneity 7.1 Introduction
7.2 Runs Test
7.2.1 Rational Analysis of Runs Test
7.3 Kendall Test for Trend
7.3.1 Rationale of Kendall Statistic
7.4 Pearson Test for Serial Independence
7.5 Spearman Test for Trend
7.5.1 Rationale for Spearman Test
7.6 Spearman–Conley Test
7.7 Cox–Stuart Test for Trend
7.8 Noether’s Binomial Test for Cyclical Trend
7.8.1 Background
7.8.2 Test Procedure
7.8.3 Normal Approximation
7.9 Durbin–Watson Test for Autocorrelation
7.9.1 Test for Positive Autocorrelation
7.9.2 Test for Negative Autocorrelation
7.9.3 Two-Sided Test for Autocorrelation
7.10 Equality of Two Correlation Coefficients
7.11 Problems
Chapter 8 Detection of Change in Moments
8.1 Introduction
8.2 Graphical Analysis
8.3 The Sign Test
8.4 Two-Sample t-Test
8.5 Mann–Whitney Test
8.5.1 Rational Analysis of the Mann–Whitney Test 8.6 The t-Test for Two Related Samples
8.7 The Walsh Test
8.8 Wilcoxon Matched-Pairs, Signed-Ranks Test
8.8.1 Ties
8.9 One-Sample Chi-Square Test
8.10 Two-Sample F-Test
8.11 Siegel–Tukey Test for Scale
8.12 Problems
Chapter 9 Detection of Change in Distribution
9.1 Introduction
9.2 Chi-Square Goodness-of-Fit Test
9.2.1 Procedure
9.2.2 Chi-Square Test for a Normal Distribution 9.2.3 Chi-Square Test for an Exponential Distribution
Trang 109.2.4 Chi-Square Test for Log-Pearson III Distribution 9.3 Kolmogorov–Smirnov One-Sample Test
9.3.1 Procedure
9.4 The Wald–Wolfowitz Runs Test
9.4.1 Large Sample Testing
9.4.2 Ties
9.5 Kolmogorov–Smirnov Two-Sample Test
9.5.1 Procedure: Case A
9.5.2 Procedure: Case B
9.6 Problems
Chapter 10 Modeling Change
10.1 Introduction
10.2 Conceptualization
10.3 Model Formulation
10.3.1 Types of Parameters
10.3.2 Alternative Model Forms
10.3.3 Composite Models
10.4 Model Calibration
10.4.1 Least-Squares Analysis of a Linear Model 10.4.2 Standardized Model
10.4.3 Matrix Solution of the Standardized Model 10.4.4 Intercorrelation
10.4.5 Stepwise Regression Analysis
10.4.6 Numerical Optimization
10.4.7 Subjective Optimization
10.5 Model Verification
10.5.1 Split-Sample Testing
10.5.2 Jackknife Testing
10.6 Assessing Model Reliability
10.6.1 Model Rationality
10.6.2 Bias in Estimation
10.6.3 Standard Error of Estimate
10.6.4 Correlation Coefficient
10.7 Problems
Chapter 11 Hydrologic Simulation
11.1 Introduction
11.1.1 Definitions
11.1.2 Benefits of Simulation
11.1.3 Monte Carlo Simulation
11.1.4 Illustration of Simulation
11.1.5 Random Numbers
11.2 Computer Generation of Random Numbers
11.2.1 Midsquare Method
Trang 1111.2.2 Arithmetic Generators
11.2.3 Testing of Generators
11.2.4 Distribution Transformation
11.3 Simulation of Discrete Random Variables
11.3.1 Types of Experiments
11.3.2 Binomial Distribution
11.3.3 Multinomial Experimentation
11.3.4 Generation of Multinomial Variates
11.3.5 Poisson Distribution
11.3.6 Markov Process Simulation
11.4 Generation of Continuously Distributed Random Variates
11.4.1 Uniform Distribution, U(α , β )
11.4.2 Triangular Distribution
11.4.3 Normal Distribution
11.4.4 Lognormal Distribution
11.4.5 Log-Pearson Type III Distribution
11.4.6 Chi-Square Distribution
11.4.7 Exponential Distribution
11.4.8 Extreme Value Distribution
11.5 Applications of Simulation
11.6 Problems
Chapter 12 Sensitivity Analysis
12.1 Introduction
12.2 Mathematical Foundations
of Sensitivity Analysis
12.2.1 Definition
12.2.2 The Sensitivity Equation
12.2.3 Computational Methods
12.2.4 Parametric and Component Sensitivity
12.2.5 Forms of Sensitivity
12.2.6 A Correspondence between Sensitivity and Correlation 12.3 Time Variation of Sensitivity
12.4 Sensitivity in Model Formulation
12.5 Sensitivity and Data Error Analysis
12.6 Sensitivity of Model Coefficients
12.7 Watershed Change
12.7.1 Sensitivity in Modeling Change
12.7.2 Qualitative Sensitivity Analysis
12.7.3 Sensitivity Analysis in Design
12.8 Problems
Chapter 13 Frequency Analysis under Nonstationary
Land Use Conditions
13.1 Introduction