Multivariate non-normally distributed random variables in climate research – introduction to the copula approach

TLDR

Probability distributions of multivariate random variables are more complex due to nonlinear dependence, and copulas—popular in econometrics, finance, risk management, and insurance—offer a promising approach, yet the field’s controversy and breadth make a comprehensive overview difficult. The aim of this paper is to provide a brief overview of copulas for application in meteorology and climate research. We examine the advantages and disadvantages of copulas relative to alternative approaches such as mixture models, summarize the current challenges of goodness‑of‑fit tests, discuss their connection with multivariate extremes, and illustrate the method with an application to station data that highlights its simplicity, capabilities, and limitations. Observations of daily precipitation and temperature fitted to a bivariate copula model demonstrate that copulas are a valuable complement to commonly used methods. Abstract.

Abstract

Abstract. Probability distributions of multivariate random variables are generally more complex compared to their univariate counterparts which is due to a possible nonlinear dependence between the random variables. One approach to this problem is the use of copulas, which have become popular over recent years, especially in fields like econometrics, finance, risk management, or insurance. Since this newly emerging field includes various practices, a controversial discussion, and vast field of literature, it is difficult to get an overview. The aim of this paper is therefore to provide an brief overview of copulas for application in meteorology and climate research. We examine the advantages and disadvantages compared to alternative approaches like e.g. mixture models, summarize the current problem of goodness-of-fit (GOF) tests for copulas, and discuss the connection with multivariate extremes. An application to station data shows the simplicity and the capabilities as well as the limitations of this approach. Observations of daily precipitation and temperature are fitted to a bivariate model and demonstrate, that copulas are valuable complement to the commonly used methods.