Postprocessing of Ensemble Weather Forecasts Using Permutation-invariant Neural Networks

TL;DR

This paper introduces permutation-invariant neural networks for ensemble weather forecast postprocessing, improving probabilistic forecast calibration and sharpness by treating ensemble members as unordered sets, and analyzing the importance of ensemble features.

Contribution

It proposes a novel neural network approach that respects the permutation invariance of ensemble members, outperforming classical methods in forecast quality.

Findings

State-of-the-art forecast calibration and sharpness achieved.

Most relevant information is contained in a few ensemble-internal features.

Permutation-based importance analysis reveals key ensemble aspects.

Abstract

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.