Statistical postprocessing is used to translate ensembles of raw numerical weather forecasts into reliable probabilistic forecast distributions. In this study, we examine the use of permutation-invariant neural networks for this task. In contrast to previous approaches, which often operate on ensemble summary statistics and dismiss details of the ensemble distribution, we propose networks that treat forecast ensembles as a set of unordered member forecasts and learn link functions that are by design invariant to permutations of the member ordering. We evaluate the quality of the obtained forecast distributions in terms of calibration and sharpness and compare the models against classical and neural network-based benchmark methods. In case studies addressing the postprocessing of surface temperature and wind gust forecasts, we demonstrate state-of-the-art prediction quality. To deepen the understanding of the learned inference process, we further propose a permutation-based importance analysis for ensemble-valued predictors, which highlights specific aspects of the ensemble forecast that are considered important by the trained postprocessing models. Our results suggest that most of the relevant information is contained in a few ensemble-internal degrees of freedom, which may impact the design of future ensemble forecasting and postprocessing systems.

翻译：统计后处理用于将原始数值天气预报集合转换为可靠的概率预报分布。本研究探讨了针对该任务使用排列不变神经网络的方法。与以往常基于集合统计特征、忽略集合分布细节的方法不同，我们提出的网络将预报集合视为无序成员预报的集合，并学习在成员排列下具有不变性的链接函数。我们从校准性和锐度角度评估了所得预报分布的质量，并将模型与基于经典方法和神经网络方法的基准进行了比较。在针对地表温度和阵风预报后处理的案例研究中，我们展示了最先进的预测质量。为了加深对所学推理过程的理解，进一步提出了基于排列的集合型预测变量重要性分析方法，该方法揭示了训练后的后处理模型认为重要的集合预报特定特征。研究结果表明，大多数相关信息集中在集合内部的少数自由度上，这对未来集合预报及后处理系统的设计可能具有重要影响。