# Theory of Copula in Hydrology and Hydroclimatology

## Abstract

This chapter starts with an introduction to copulas. The copula theory is relatively new to hydrology and hydroclimatology but has already established itself to be highly potential in frequency analysis, multivariate modeling, simulation and prediction. Development of joint distribution between multiple variables is the key to analyze utilizing the potential of copulas. The chapter starts with the mathematical theory of copulas and gradually move on to the application. If the readers are already aware of the background theory and look for application of copula theory, they can directly proceed to Sect. 10.8. Basic mathematical formulations for most commonly used copulas are discussed, and illustrative examples are provided. It will enable the readers to carry out applications to other problems. All the illustrative examples are designed with very few data points. This helps to show the calculation steps explicitly. Please note that any statistical analysis should be done with sufficiently long data. Once the readers understand the steps, computer codes can be written easily for large data sets. Example of MATLAB codes is also provided at the end.

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