Using ensemble copula coupling for multivariate post-processing of ensemble prediction

In many cases, ensemble weather forecasts produced by numerical weather prediction (NWP) models exhibit systematic bias and under-dispersion. Over the past two decades, various ensemble post-processing approaches have been developed to address this issue. These approaches include classical methods such as ensemble model output statistics (EMOS), Bayesian model averaging (BMA), and advanced machine learning-based approaches.In most ensemble post-processing approaches, it is implicitly assumed that there is statistical independence between different forecast margins, such as lead time, location, and meteorological variables. However, this assumption is not valid for realistic forecast application scenarios. End users may be interested in scenarios such as total hydrological basin precipitation, temporal evolution of precipitation, or the interaction of precipitation and temperature, especially when temperatures are close to zero degrees Celsius. Important examples include hydrological applications, air traffic management, and energy forecasting. Such dependencies exist in raw ensemble forecasts, but these dependencies are ignored if standard univariate post-processing methods are applied separately to each margin.In recent years, various multivariate post-processing methods have been proposed. These methods can be categorized into two approaches. The goal of the first approach is to directly model the joint distribution by fitting a specific multivariate probability distribution. This approach is mainly used in low-dimensional problems or when a specific structure is chosen for the application at hand. For example, multivariate models for temperature across space, for wind vectors, and joint models for temperature and wind speed.The second approach is a two-step approach. In the first step, univariate post-processing methods are applied independently to all dimensions, and samples are generated from the resulting probability distributions. In the second step, the multivariate dependencies are recovered by reordering the univariate sample values according to the ranking order structure of a specific multivariate dependence pattern. Mathematically, this is equivalent to using a copula (parametric or nonparametric). Examples include ensemble copula coupling (ECC), Schaake Shuffle, and the Gaussian copula approach.This paper presents multivariate ensemble post-processing of temperature, two meter above ground using the ECC approach. The EMOS method is used for univariate post-processing. The performance of the raw ensemble, EMOS post-processed ensemble, and ECC systems is evaluated using energy score (ES) and variogram score (VS). The ECMWF 51-member ensemble system is used as raw data for the period from January 1, 2018 to December 31, 2023.The results showed that in addition to eliminating the bias of the raw ensemble forecast, the ECC method also preserved the dependence structure between the ensemble members. In contrast, the EMOS method only eliminated the biases without considering the dependence between the ensemble members. Because of its ability to preserve the dependence structure, the ECC method was able to achieve significantly better results than the EMOS method on a variety of metrics, including energy scores and variogram score. This suggests that the ECC method is a valuable tool for ensemble post-processing, and that it should be considered for a wide range of applications.