Ensemble Postprocessing Methods Incorporating Dependence Structures

Abstract Focusing on the key example of weather prediction, ensemble postprocessing methods that account for intervariable, spatial, and/or temporal dependence structures are reviewed. One strategy is to design postprocessing methods that yield truly multivariate predictive distributions. For many such multivariate approaches, copulas and Sklar's theorem provide the mathematical background. Essentially, two classes of multivariate ensemble postprocessing methods can be distinguished. Parametric approaches, such as Gaussian copula-based techniques, are typically tailored to specific intervariable, spatial, or temporal settings and work well in low-dimensional scenarios. In contrast, nonparametric, empirical copula-based approaches, including ensemble copula coupling and Schaake shuffle-based methods, are more general and can handle nearly any dimensionality. In such techniques, univariate postprocessed ensemble forecasts are arranged according to the rank order structure of a specifically chosen template. Alternatively, there are postprocessing methods yielding univariate predictive distributions, but accounting for dependencies by means of the design of the estimation procedure for the model parameters.