Comparison of multivariate post‐processing methods using global ECMWF ensemble forecasts

Abstract

An influential step in weather forecasting was the introduction of ensemble forecasts in operational use owing to their capability to account for the uncertainties in the future state of the atmosphere. However, ensemble weather forecasts are often underdispersive and might also contain bias, which calls for some form of post‐processing. A popular approach to calibration is the ensemble model output statistics approach resulting in a full predictive distribution for a given weather variable. However, this form of univariate post‐processing may ignore the prevailing spatial and/or temporal correlation structures among different dimensions. Since many applications call for spatially and/or temporally coherent forecasts, multivariate post‐processing aims to capture these possibly lost dependencies. We compare the forecast skill of different non‐parametric multivariate approaches to modeling temporal dependence of ensemble weather forecasts with different forecast horizons. The focus is on two‐step methods, where, after univariate post‐processing, the ensemble model output statistics predictive distributions corresponding to different forecast horizons are combined to a multivariate calibrated prediction using an empirical copula. Based on global ensemble predictions of temperature, wind speed, and precipitation accumulation of the European Centre for Medium‐Range Weather Forecasts from January 2002 to March 2014, we investigate the forecast skill of different versions of ensemble copula coupling (ECC) and Schaake shuffle. In general, compared with the raw and independently calibrated forecasts, multivariate post‐processing substantially improves the forecast skill. Although even the simplest ECC approach with low computational cost provides a powerful benchmark method, recently proposed advanced extensions of the ECC and the Schaake shuffle are found to not provide any significant improvements over their basic counterparts.

Statistical post‐processing of visibility ensemble forecasts

“…Finally, so far, we have focused on univariate forecasts for a single location and forecast horizon. However, in the last decade, a wide range of multivariate post‐processing techniques have been developed, which are able to restore dependence structures lost during the univariate calibration, for an overview see, for example, Lerch et al (2020) or Lakatos et al (2023). The investigation of spatially and/or temporally consistent calibrated visibility forecasts might be another interesting direction of our future work.…”

A two‐step machine‐learning approach to statistical post‐processing of weather forecasts for power generation

“…In this context, the MLPex and MLP‐S forecasts can serve as initial independent predictions for two‐step approaches, where, after univariate calibration, the temporal dependence is restored with the help of an empirical copula calculated using, for example, the actual ensemble forecasts (ensemble copula coupling; Schefzik et al, 2013) or historical observations (Schaake shuffle; Clark et al, 2004). For a detailed comparison of the state‐of‐the‐art multivariate methods with the help of simulated and real ensemble data, we refer the reader to Lerch et al (2020) and Lakatos et al (2023) respectively.…”

Assessing the calibration of multivariate probabilistic forecasts

“…Although the Schaake shuffle can leverage an arbitrary number of previous observations in this dependence template, only 11 observations are used here, so that the resulting ensemble forecasts have the same number of members as those generated using ECC. Further details regarding these two approaches can be found in Lakatos et al (2023) and references therein. Several variants of both ECC and the Schaake shuffle have also recently been proposed, but we restrict attention here to the two most widely used implementations; Lakatos et al (2023) find that these extensions do not provide significant benefits.…”

“…Further details regarding these two approaches can be found in Lakatos et al (2023) and references therein. Several variants of both ECC and the Schaake shuffle have also recently been proposed, but we restrict attention here to the two most widely used implementations; Lakatos et al (2023) find that these extensions do not provide significant benefits.…”