Graph Neural Networks and Spatial Information Learning for Post-Processing Ensemble Weather Forecasts

TL;DR

This work addresses biases in ensemble numerical weather predictions by developing a graph neural network (GNN) post-processing method that treats weather stations as graph nodes and uses attention to share information across locations. The approach extends distributional post-processing by jointly learning per-station Gaussian parameters $(\mu,\sigma)$ using a graph architecture with station embeddings, residual GNN blocks, and Deep Set aggregation across ensemble members. On the EUPPBench European dataset for 2-meter temperature at lead times 24, 72, and 120 hours, the Graph Attention Network (GAT) outperforms a strong distributional baseline (DRN) and other ablations, with significant CRPS gains at many stations and improved calibration. The results demonstrate the value of incorporating spatial dependencies in post-processing, with practical implications for operational ensemble forecasting and potential extensions to spatio-temporal GNNs and alternative graph constructions.

Abstract

Ensemble forecasts from numerical weather prediction models show systematic errors that require correction via post-processing. While there has been substantial progress in flexible neural network-based post-processing methods over the past years, most station-based approaches still treat every input data point separately which limits the capabilities for leveraging spatial structures in the forecast errors. In order to improve information sharing across locations, we propose a graph neural network architecture for ensemble post-processing, which represents the station locations as nodes on a graph and utilizes an attention mechanism to identify relevant predictive information from neighboring locations. In a case study on 2-m temperature forecasts over Europe, the graph neural network model shows substantial improvements over a highly competitive neural network-based post-processing method.

Figures (5)

• Figure 1: Schematic illustration of the GNN model for ensemble post-processing. The input graph $\mathcal{G}$ is created from the $N$-member ensemble forecasts at $S$ stations. Next, the embedded station IDs are concatenated and passed to the GNN. The GNN block is repeated $K$ times with residual connections, followed by the node aggregation. Finally, a softplus function is applied to $\sigma$ to ensure positivity.
• Figure 2: Station-specific improvement in terms of the CRPS of the GAT model over DRN, computed in terms of the CRPSS; where higher values indicate larger improvements by the GAT model.
• Figure A.1: Weather stations in the EUPPBench dataset with their corresponding altitude.
• Figure A.2: PIT histograms of the post-processed forecasts of the DRN and GAT model for 24;72;120 lead times based on the R2R and R2F tasks.
• Figure A.3: Relative feature importance of the GAT model for the R2F (top) and the R2R task (bottom). Error bars show the standard deviation, which is calculated based on 10 training runs of the individual GNNs.