Chapter 1: Introduction to Statistical Hydrology -- Chapter 2: Preliminary Analysis of Hydrological Data -- Chapter 3: Elementary Theory of Probability -- Chapter 4: Discrete Random Variables: Distributions and Applications -- Chapter 5: Continuous Random Variables: Distributions and Applications -- Chapter 6: Parameter Estimation -- Chapter 7: Hypothesis Testing -- Chapter 8: At-Site Frequency Analysis of Hydrological Variables -- Chapter 9: Correlation and Regression -- Chapter 10: Regional Frequency Analysis of Hydrological Variables -- Chapter 11: Introduction of Bayesian Analysis and Its Applications in Hydrology -- Chapter 12: Introduction to the Analysis and Modelling of Nonstationary Hydrological Series.
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..