This textbook covers the main applications of statistical methods in hydrology. It is written for upper undergraduate and graduate students but can be used as a helpful guide for hydrologists, geographers, meteorologists and engineers. The book is very useful for teaching, as it covers the main topics of the subject and contains many worked out examples and proposed exercises. Starting from simple notions of the essential graphical examination of hydrological data, the book gives a complete account of the role that probability considerations must play during modelling, diagnosis of model fit,…mehr
This textbook covers the main applications of statistical methods in hydrology. It is written for upper undergraduate and graduate students but can be used as a helpful guide for hydrologists, geographers, meteorologists and engineers. The book is very useful for teaching, as it covers the main topics of the subject and contains many worked out examples and proposed exercises. Starting from simple notions of the essential graphical examination of hydrological data, the book gives a complete account of the role that probability considerations must play during modelling, diagnosis of model fit, prediction and evaluating the uncertainty in model predictions, including the essence of Bayesian application in hydrology and statistical methods under nonstationarity.
The book also offers a comprehensive and useful discussion on subjective topics, such as the selection of probability distributions suitable for hydrological variables. On a practical level, it explains MS Excel charting and computing capabilities, demonstrates the use of Winbugs free software to solve Monte Carlo Markov Chain (MCMC) simulations, and gives examples of free R code to solve nonstationary models with nonlinear link functions with climate covariates.
Prof. Dr. Mauro da Cunha Naghettini: Civil Engineer, Federal University of Minas Gerais, Belo Horizonte, Brazil, 1977. MSc in Applied Hydrology, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, 1979. PhD in Civil and Environmental Engineering, University of Colorado at Boulder, Boulder, USA, 1994. From 1979 to 1989: Engineering Hydrologist at CEMIG, the Minas Gerais State power company. From 1989 to 2014: Professor of Civil and Environmental Engineering at the Brazilian Federal University of Minas Gerais with teaching, research and management responsibilities. Retired in 2014.
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Chapter 1: Introduction to Statistical Hydrology
1.1 Hydrologic Processes and Phenomena
1.2 Hydrological Variables
1.3 Hydrological Series
1.4 Population and Samples
1.5 Hydrological Data
Chapter 2: Preliminary Analysis of Hydrological Data
2.1 Graphical Depiction of Hydrological Data
2.2 Numeric Summaries and Descriptive Statistics
2.3 Exploratory Methods
2.4 Associations between Variables
Chapter 3: Elementary Theory of Probability
3.1 Random Events
3.2 Notion and Measure of Probability
3.3 Conditional Probability and Statistical Independence
3.4 Total Probability and Bayes Theorems
3.5 Random Variables
3.6 Population Measures of Random Variables
3.7 Joint Probability Distribution Functions
3.7 Probability Distributions of Functions of Random Variables
Chapter 4: Discrete Random Variables: Distributions and Applications
4.1 The Bernoulli Processes and Related Probability Distributions
4.2 The Poisson Process and Related Probability Distributions
4.3 The Hypergeometric and Multinomial Probability Distributions
4.4 Summary of Main Characteristics of Discrete Probability Distributions
Chapter 5: Continuous Random Variables: Distributions and Applications
5.1 Uniform Distribution
5.2 Normal Distribution
5.3 Log-Normal Distribution
5.4 Exponential Distribution
5.5 Gamma Distribution
5.6 Beta Distribution
5.7 Extremal Distributions
5.8 Pearson Distributions
5.9 Distributions of Sample Statistics
5.10 The Bivariate Normal Distribution
5.11 Summary of Main Characteristics of Continuous Probability Distributions
Chapter 6: Parameter Estimation
6.1 Overview of Parameter Point Estimation
6.2 Method of Moments
6.3 Method of Maximum Likelihood
6.4 L-Moment Method
6.5 Confidence Interval for Quantiles
6.6 Summary of Point Estimation for Common Probability Distributions
Chapter 7: Hypothesis Testing
7.1 Elements of Hypothesis Testing
7.2 Some Parametric Tests for Normal Populations
7.3 Some Non-Parametric Tests for Hydrological Random Variables
7.4 Some Goodness of Fit of Distributions (Models)
7.5 Detection and Identification of Outliers in Hydrological Samples
Chapter 8: At-Site Frequency Analysis of Hydrological Variables
8.1 At-Site Frequency Analysis with Probability Charts
8.2 Analytic At-Site Frequency Analysis
8.3 At-Site Frequency Analysis with Frequency Factors
8.4 Calculation of Confidence Intervals for Quantiles
8.5 At-Site Frequency Analysis of Partial Duration Series
Chapter 9: Correlation and Regression
9.1 Pearson Correlation Coefficient
9.2 Simple Linear Regression
9.3 Coefficient of Determination
9.4 Base Hypotheses for Analysing Simple Linear Regression
9.5 Testing Hypotheses on Coefficients of Simple Linear Regression
9.6 Simple Linear Regression Evaluation
9.7 Non-Linear Regression
9.8 Multiple Linear Regression
Chapter 10: Regional Frequency Analysis of Hydrological Variables
10.1 The Rationale of Regional Frequency Analysis
10.2 Identifying Homogeneous Regions
10.2.1 Geographical Convenience
10.2.2 Subjective Grouping
10.2.3 Objective Grouping
10.2.4 Cluster Analysis
10.2.5 Other Methods
10.3 Methods for Regional Analysis
10.3.1 Method for Regionalizing Quantiles Associated with a Specified Risk
10.3.2 Method of Regionalizing the Parameters of Probability Distributions
10.3.3 Index-Flood Method
10.4 The Index-Flood Method with L-Moments
10.4.1 Screening the Data with the Discordancy Measure
10.4.2 Identifying Homogeneous Regions with the Heterogeneity Measure
10.4.3 Choosing the Regional Distribution with the Goodness-of-Fit Measure
10.4.4 Estimating the Regional Frequency Distribution Model
10.4.5 Discussion on Regional Frequency Analysis
Chapter 11: Introduction of Bayesian Analysis and Its Applications in Hydrology
11. 1 Basic Concepts
11.2 Prior Distributions
11.3 Bayesian Estimation and Credibility Intervals
11.4 Calculation Methods for Bayesian Estimation
11.5 Example Applications
Chapter 12: Introduction to the Analysis and Modelling of Nonstationary Hydrological Series
12.1 Methods for Detecting Nonstationarities
12.2 Hypotheses Testing for Monotonic Trends and Change Points
12.3 Kernel Estimation of Poisson Point Process Rates
12.4 Introduction to Generalized Linear Models
12.5 Nonstationary Models Based on Extremal Distributions
12.6 Return Period and Hydrological Risk under Nonstationary Conditions
