Copulas And Their Applications In Water Resources Engineering

Complex environmental and hydrological processes are characterized by more than one correlated random variable. These events are multivariate and their treatment requires multivariate frequency analysis. Traditional analysis methods are, however, too restrictive and do not apply in many cases. Recent years have therefore witnessed numerous applications of copulas to multivariate hydrologic frequency analyses. This book describes the basic concepts of copulas, and outlines current trends and developments in copula methodology and applications. It includes an accessible discussion of the methods alongside simple step-by-step sample calculations. Detailed case studies with real-world data are included, and are organized based on applications, such as flood frequency analysis and water quality analysis. Illustrating how to apply the copula method to multivariate frequency analysis, engineering design, and risk and uncertainty analysis, this book is ideal for researchers, professionals and graduate students in hydrology and water resources engineering.

This book presents an overview of copula theory and its application in hydrology, and provides valuable insights, useful methods and practical applications for multivariate hydrological analysis using copulas. In addition, it extends the traditional bivariate model to trivariate or multivariate models. The specific applications covered include the study of flood frequency analysis, drought frequency analysis, dependence analysis, flood coincidence risk analysis and statistical simulation using copulas. The book offers a valuable guide for researchers, scientists and engineers working in hydrology and water resources, and will also benefit graduate or doctoral students with a basic grasp of copula functions who want to learn about the latest research developments in the field.

This book provides a compilation of statistical analysis methods used to analyze and assess critical variables in the hydrological cycle.

This book is about the theoretical and practical aspects of the statistics of Extreme Events in Nature. Most importantly, this is the first text in which Copulas are introduced and used in Geophysics. Several topics are fully original, and show how standard models and calculations can be improved by exploiting the opportunities offered by Copulas. In addition, new quantities useful for design and risk assessment are introduced.

1. Introduction : Dependence modeling / D. Kurowicka -- 2. Multivariate copulae / M. Fischer -- 3. Vines arise / R.M. Cooke, H. Joe and K. Aas -- 4. Sampling count variables with specified Pearson correlation : A comparison between a naive and a C-vine sampling approach / V. Erhardt and C. Czado -- 5. Micro correlations and tail dependence / R.M. Cooke, C. Kousky and H. Joe -- 6. The Copula information criterion and Its implications for the maximum pseudo-likelihood estimator / S. Gronneberg -- 7. Dependence comparisons of vine copulae with four or more variables / H. Joe -- 8. Tail dependence in vine copulae / H. Joe -- 9. Counting vines / O. Morales-Napoles -- 10. Regular vines : Generation algorithm and number of equivalence classes / H. Joe, R.M. Cooke and D. Kurowicka -- 11. Optimal truncation of vines / D. Kurowicka -- 12. Bayesian inference for D-vines : Estimation and model selection / C. Czado and A. Min -- 13. Analysis of Australian electricity loads using joint Bayesian inference of D-vines with autoregressive margins / C. Czado, F. Gartner and A. Min -- 14. Non-parametric Bayesian belief nets versus vines / A. Hanea -- 15. Modeling dependence between financial returns using pair-copula constructions / K. Aas and D. Berg -- 16. Dynamic D-vine model / A. Heinen and A. Valdesogo -- 17. Summary and future directions / D. Kurowicka

This second edition focuses on the application of statistical methods in the field of hydrology and hydroclimatology. Among the latest theories being used in these fields, the book introduces the theory of copulas and its applications in this context. The purpose is to develop an understanding and illustrate the usefulness of the statistical techniques with detailed theory and numerous worked out examples. Apart from this, sample scripts based on MATLAB, Python and R for some examples are also provided to assist the readers to handle real life data. Besides serving as a textbook for graduate courses on stochastic modeling in hydrology and related disciplines, the book offers a valuable resource for researchers and professionals involved in the field of hydrology and climatology.

Water quality and management are of great significance globally, as the demand for clean, potable water far exceeds the availability. Water science research brings together the natural and applied sciences, engineering, chemistry, law and policy, and economics, and the Treatise on Water Science seeks to unite these areas through contributions from a global team of author-experts. The 4-volume set examines topics in depth, with an emphasis on innovative research and technologies for those working in applied areas. Published in partnership with and endorsed by the International Water Association (IWA), demonstrating the authority of the content Editor-in-Chief Peter Wilderer, a Stockholm Water Prize recipient, has assembled a world-class team of volume editors and contributing authors Topics related to water resource management, water quality and supply, and handling of wastewater are treated in depth

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.

Modern assessment of the state of the world's water resources for researchers and policy-makers.

Handbook of Probabilistic Models carefully examines the application of advanced probabilistic models in conventional engineering fields. In this comprehensive handbook, practitioners, researchers and scientists will find detailed explanations of technical concepts, applications of the proposed methods, and the respective scientific approaches needed to solve the problem. This book provides an interdisciplinary approach that creates advanced probabilistic models for engineering fields, ranging from conventional fields of mechanical engineering and civil engineering, to electronics, electrical, earth sciences, climate, agriculture, water resource, mathematical sciences and computer sciences. Specific topics covered include minimax probability machine regression, stochastic finite element method, relevance vector machine, logistic regression, Monte Carlo simulations, random matrix, Gaussian process regression, Kalman filter, stochastic optimization, maximum likelihood, Bayesian inference, Bayesian update, kriging, copula-statistical models, and more. Explains the application of advanced probabilistic models encompassing multidisciplinary research Applies probabilistic modeling to emerging areas in engineering Provides an interdisciplinary approach to probabilistic models and their applications, thus solving a wide range of practical problems