Weather forecasting is challenging due to the exceptional complexity of the atmospheric phenomena involved. Modern weather forecasts are typically in the form of an ensemble of forecasts obtained from multiple runs of numerical weather prediction models. Ensemble forecasts are often biased and affected by dispersion errors, and they should be statistically corrected to gain accuracy. The standard correction methods, such as Ensemble Model Output Statistics (EMOS), only apply to a single variable of the forecasting problem at a time. This results in a loss of the dependence structure of the multivariate forecasts, which is problematic in several applications. Recent work shows that the lost dependence structure can be efficiently reconstructed via non-parametric multivariate post-processing approaches based on empirical copulas. Popular methods of this type are Schaake Shuffle, Ensemble Copula Coupling (ECC), and SimSchaake. In this work, we inquire into the limitations of the empirical copula methods for the statistical correction of temperature forecasts of the Austrian ensemble system ALADIN-LAEF. Our setting is challenging: ALADIN-LAEF has been running operationally for six years only, and, in general, it might not be considered fully exchangeable. Given these issues which affect ECC and SimSchaake in different ways, a natural question arises whether or not these multivariate modeling approaches are still effective. In this paper, we present a case study aiming at answering this question. We consider three groups of stations with different characteristics: three close stations in a valley, three stations on top of mountains, and three randomly chosen stations within a distance of several hundreds of kilometers. For each group of stations, we compare the performance of SimSchaake, ECC, and individual EMOS to correct the multivariate temperature forecasts. Our analysis suggests that the non-exchangeability of the ALADIN-LAEF system is not a limitation to applying ECC to this ensemble system. Though, our results show that SimSchaake outperforms individual EMOS and ECC in all cases, supporting the claim that even in such an unfavorable scenario we can benefit from the use of empirical copula methods.

中文翻译：

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以经验copula方法对ALADIN-LAEF系统的预测进行统计校正的案例研究

由于所涉及的大气现象异常复杂，天气预报具有挑战性。现代天气预报通常采用从多次数值天气预报模型运行中获得的一组预报的形式。集合预测通常会受到分散误差的影响，因此应对其进行统计校正以提高准确性。标准校正方法（例如集成模型输出统计信息（EMOS））一次仅适用于预测问题的单个变量。这导致多元预测的依赖结构的损失，这在一些应用中是有问题的。最近的工作表明，可以通过基于经验copulas的非参数多元后处理方法来有效地重建丢失的依赖结构。这种类型的流行方法是Schaake Shuffle，Ensemble Copula Coupling（ECC）和SimSchaake。在这项工作中，我们探究了经验copula方法在奥地利集合系统ALADIN-LAEF的温度预报的统计校正中的局限性。我们的设置具有挑战性：ALADIN-LAEF在运行中仅运行了6年，总的来说，它可能无法完全互换。考虑到这些以不同方式影响ECC和SimSchaake的问题，自然会出现一个问题，即这些多元建模方法是否仍然有效。在本文中，我们提出了一个旨在回答这个问题的案例研究。我们考虑了三组具有不同特征的站点：山谷中的三个封闭站点，山顶的三个站点，以及数百公里外的三个随机选择的站点。对于每组站，我们将SimSchaake，ECC和单个EMOS的性能进行比较，以校正多元温度预测。我们的分析表明，ALADIN-LAEF系统的不可交换性并不限制将ECC应用于该集成系统。但是，我们的结果表明，SimSchaake在所有情况下均优于单独的EMOS和ECC，从而支持了这样的主张：即使在这种不利的情况下，我们也可以受益于使用经验copula方法。我们的分析表明，ALADIN-LAEF系统的不可交换性并不限制将ECC应用于该集成系统。但是，我们的结果表明，SimSchaake在所有情况下均优于单独的EMOS和ECC，从而支持了这样的主张：即使在这种不利的情况下，我们也可以受益于使用经验copula方法。我们的分析表明，ALADIN-LAEF系统的不可交换性并不限制将ECC应用于该集成系统。但是，我们的结果表明，SimSchaake在所有情况下均优于单独的EMOS和ECC，从而支持了这样的主张：即使在这种不利的情况下，我们也可以受益于使用经验copula方法。