Fundamentals of Statistical Hydrology
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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. Front Matter....Pages i-xi Introduction to Statistical Hydrology....Pages 1-20 Preliminary Analysis of Hydrologic Data....Pages 21-56 Elementary Probability Theory....Pages 57-97 Discrete Random Variables: Probability Distributions and Their Applications in Hydrology....Pages 99-122 Continuous Random Variables: Probability Distributions and Their Applications in Hydrology....Pages 123-201 Parameter and Quantile Estimation....Pages 203-250 Statistical Hypothesis Testing....Pages 251-309 At-Site Frequency Analysis of Hydrologic Variables....Pages 311-389 Correlation and Regression....Pages 391-440 Regional Frequency Analysis of Hydrologic Variables....Pages 441-495 Introduction to Bayesian Analysis of Hydrologic Variables....Pages 497-536 Introduction to Nonstationary Analysis and Modeling of Hydrologic Variables....Pages 537-577 Back Matter....Pages 579-660
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