Ensemble Copula Coupling as a Multivariate Discrete Copula Approach

TL;DR

This paper introduces multivariate discrete copulas and their theoretical foundations, enabling the ensemble copula coupling method for multivariate weather forecast postprocessing, bridging theory and practical application.

Contribution

It develops the concept of multivariate discrete copulas, proves their equivalence to stochastic arrays, and formulates a multivariate version of Sklar's theorem, providing a theoretical basis for ensemble copula coupling.

Findings

Establishes the theoretical framework for multivariate discrete copulas.

Proves the equivalence between multivariate discrete copulas and stochastic arrays.

Provides a multivariate version of Sklar's theorem.

Abstract

In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. In this paper, we introduce the concept of multivariate discrete copulas, discuss their equivalence to stochastic arrays, and provide a multivariate discrete version of Sklar's theorem. These results provide the theoretical frame for the ensemble copula coupling approach proposed by Schefzik et al. (2013) for the multivariate statistical postprocessing of weather forecasts made by ensemble systems.