Statistical Methods in Hydrology and Hydroclimatology

This book is divided into four major parts, each containing several chapters. In the context of climate change and its impacts on water resources, hydrology and hydroclimatology are increasingly being studied hand in hand. The random variability of hydrologic variables is a long-recognized fact, and several statistical techniques are currently in use. The correspondence between climatic and hydrologic variability has resulted in a relatively new interdisciplinary field known as hydroclimatology. This book focuses on the statistical methods that have proven effective for both hydrology and hydroclimatology. Several new statistical methodologies are being developed and introduced in this subject area to tackle emerging challenges. The first part deals with the basics of probability and statistical theory, discussing the concept of random variables and the probability distributions most commonly used in hydrology and hydroclimatology. The second part focuses on linear and multiple regression models, hypothesis testing, analysis of variance (ANOVA), frequency analysis, and measures of dependence among various hydrologic and atmospheric variables. The third part explores time series analysis and forecasting. Deterministic and stochastic models, probabilistic prediction, uncertainty quantification, prediction using exogenous inputs, and measures of model performance are the main components of this section. The fourth and final part introduces the theory of copulas, its applications in hydrology and hydroclimatology, demonstrating the frequency analysis of hydrologic extreme events, time series analysis, and probabilistic prediction using copulas. This part also introduces a relatively newer domain, known as Bayesian hydrology, the philosophy behind which differs from traditional statistical methods that uses “frequentists” approach. This book contains numerous worked-out examples that help students prepare for their coursework. The use of MATLAB in solving many of these problems is highly beneficial, and short code snippets are provided wherever necessary.