Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias

2026-06-29

AI Summary

In practical probabilistic downscaling, the mean–residual framework often suffers from systematic biases and underdispersion in generated ensembles due to mismatched residual distributions between training and testing phases. This work proposes ReMatch, which identifies for the first time that the root cause lies in the mis-specification of the residual target distribution. To address this, ReMatch explicitly aligns the training and testing residual distributions by introducing optimal transport within a PCA-based low-dimensional subspace. Integrating principal component analysis, optimal transport, and probabilistic generative modeling, the method substantially mitigates underdispersion and achieves superior calibration performance—measured by SSR and CRPS—compared to strong existing baselines, as demonstrated on both synthetic data and real-world HRRR–ERA5 wind field downscaling tasks.

Abstract

Probabilistic downscaling is the task of modeling the conditional distribution of high-resolution fields given coarse inputs, and is a central challenge to atmospheric science, climate modeling, and other multiscale physical systems. A widely used paradigm decomposes the problem into a deterministic mean predictor followed by a stochastic residual generator. While effective in idealized settings, this mean--residual approach frequently produces biased and under-dispersive ensembles in real-world applications. Is this merely generic predictive uncertainty miscalibration? We show that the root cause is more fundamental: residual target misspecification, the residual distribution induced during training differs systematically from the one required at test time due to downscaling bias. To close this gap, we introduce ReMatch (Residual Distribution Matching). ReMatch aligns the training residual distribution toward the test-time regime via optimal transport in a low-dimensional PCA space. This preserves the statistical benefits of the mean--residual framework while reducing the train--test mismatch in the residual targets seen by the stochastic generator. On a controlled synthetic benchmark with varying bias levels and a real-world HRRR--ERA5 wind field downscaling task, ReMatch substantially reduces under-dispersion, improves calibration (SSR and CRPS), and outperforms strong baselines, including the standard mean--residual model and its variants, as well as state-of-the-art super-resolution models. Our code is available at https://github.com/sdean-group/ReMatch.git.

Problem

• probabilistic downscaling
• residual gap
• distribution mismatch
• under-dispersion
• bias

Innovation

• probabilistic downscaling
• residual distribution matching
• optimal transport
• train-test mismatch
• ensemble calibration