Abstract
Abstract. Many practical applications of statistical post-processing methods for ensemble weather forecasts require accurate modeling of spatial, temporal, and inter-variable dependencies. Over the past years, a variety of approaches has been proposed to address this need. We provide a comprehensive review and comparison of state-of-the-art methods for multivariate ensemble post-processing. We focus on generally applicable two-step approaches where ensemble predictions are first post-processed separately in each margin and multivariate dependencies are restored via copula functions in a second step. The comparisons are based on simulation studies tailored to mimic challenges occurring in practical applications and allow ready interpretation of the effects of different types of misspecifications in the mean, variance, and covariance structure of the ensemble forecasts on the performance of the post-processing methods. Overall, we find that the Schaake shuffle provides a compelling benchmark that is difficult to outperform, whereas the forecast quality of parametric copula approaches and variants of ensemble copula coupling strongly depend on the misspecifications at hand.
Highlights
Despite continued improvements, ensemble weather forecasts often exhibit systematic errors that require correction via statistical post-processing methods
We focus on comparisons of the relative predictive performance of the different multivariate postprocessing methods and apply proper scoring rules for forecast evaluation
The differences between Gaussian copula approach (GCA) and Schaake shuffle (SSh) appear to generally be negligible, and GCA does not perform worse than ECCQ for any of the simulation parameter combinations. These differences between the results for GCA in terms of energy score (ES) and VS may be explained by the greater sensitivity of the VS to misspecifications in the correlation structure, whereas the ES shows a stronger dependence on the mean vector
Summary
Ensemble weather forecasts often exhibit systematic errors that require correction via statistical post-processing methods. Such calibration approaches have been developed for a wealth of weather variables and specific applications. Important examples include hydrological applications (Scheuerer et al, 2017), air traffic management (Chaloulos and Lygeros, 2007), and energy forecasting (Pinson and Messner, 2018). Such dependencies are present in the raw ensemble predictions but are lost if standard univariate post-processing methods are applied separately in each margin
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