Distributional Regression U-Nets for the Postprocessing of Precipitation Ensemble Forecasts

TL;DR

This paper tackles the challenge of postprocessing gridded precipitation ensemble forecasts by introducing Distributional Regression U-Nets (DRU), a global, grid-aware model that outputs parametric distribution parameters at each grid point through a U-Net architecture. DRU extends distributional regression networks to gridded data by leveraging spatial structure and input from ensemble summary statistics and constant fields, enabling extrapolation via tail distributions (GTCND or CSGD) and CRPS-based training. Empirical results show DRU yields CRPS performance comparable to quantile regression forests, with notable strengths in predicting heavy precipitation events, though calibration in high-precipitation regions and border effects remain challenges. The work demonstrates a scalable, grid-based approach to probabilistic precipitation postprocessing with potential for extensions to temporal or graph-structured architectures and alternative scoring rules.

Abstract

Accurate precipitation forecasts have a high socio-economic value due to their role in decision-making in various fields such as transport networks and farming. We propose a global statistical postprocessing method for grid-based precipitation ensemble forecasts. This U-Net-based distributional regression method predicts marginal distributions in the form of parametric distributions inferred by scoring rule minimization. Distributional regression U-Nets are compared to state-of-the-art postprocessing methods for daily 21-h forecasts of 3-h accumulated precipitation over the South of France. Training data comes from the Météo-France weather model AROME-EPS and spans 3 years. A practical challenge appears when consistent data or reforecasts are not available. Distributional regression U-Nets compete favorably with the raw ensemble. In terms of continuous ranked probability score, they reach a performance comparable to quantile regression forests (QRF). However, they are unable to provide calibrated forecasts in areas associated with high climatological precipitation. In terms of predictive power for heavy precipitation events, they outperform both QRF and semi-parametric QRF with tail extensions.

Figures (10)

• Figure 1: Domains covered by AROME-EPS (blue), ANTILOPE (green) and the region of interest (red).
• Figure 2: Constants fields used as predictors in distributional regression U-Nets: altitude, land-sea mask, four first components of AURHELY procedure, and distance to the sea.
• Figure 3: Architecture of distributional regression U-Nets. Conv stands for convolution, BN stands for batch normalization, ReLU stands for rectified linear unit and Bilin. Upsampling stands for bilinear upsampling. $p$ is the number of distribution parameters: for GTCND and CSGD, $p=3$.
• Figure 4: Predictive performance of the benchmark methods in terms of CRPS. (a) Expected CRPS of the raw ensemble, (b) CRPSS of QRF w.r.t. the raw ensemble and CRPSS w.r.t. QRF of (c) QRF+GTCND and (d) QRF+CSGD.
• Figure 5: Predictive performance of the distributional regression U-Nets in terms of CRPS. CRPSS w.r.t. the raw ensemble of (a) U-Net+GTCND and (b) U-Net+CSGD and CRPSS w.r.t. QRF of (c) U-Net+GTCND and (d) U-Net+CSGD.