Downscaling Extreme Precipitation with Wasserstein Regularized Diffusion

TL;DR

WassDiff introduces a Wasserstein Regularized Diffusion framework to downscale long-duration, low-resolution precipitation records (55 km CPC and 31 km ERA5) to high-resolution $1\text{km}$ fields by conditioning a diffusion model on multivariate inputs. The key innovation is a sliced Wasserstein distance regularizer applied during denoising, which mitigates intensity biases and improves calibration in the distribution tails, particularly for extreme rainfall events. Empirical results show WassDiff outperforms state-of-the-art baselines in recovering extreme phenomena (tropical storms, fronts, hail) and provides well-calibrated ensembles, enabling century-scale, kilometer-scale precipitation reconstructions via tiled diffusion for continental-scale applications. The approach supports open-source generation of high-resolution, long-duration rainfall archives, with practical implications for flood risk assessment, climate adaptation planning, and hydrologic modeling, while acknowledging runtime and distributional limits in regions outside the training domain.

Abstract

Understanding the risks posed by extreme rainfall events requires analysis of precipitation fields with high resolution (to assess localized hazards) and extensive historical coverage (to capture sufficient examples of rare occurrences). Radar and mesonet networks provide precipitation fields at 1 km resolution but with limited historical and geographical coverage, while gauge-based records and reanalysis products cover decades of time on a global scale, but only at 30-50 km resolution. To help provide high-resolution precipitation estimates over long time scales, this study presents Wasserstein Regularized Diffusion (WassDiff), a diffusion framework to downscale (super-resolve) precipitation fields from low-resolution gauge and reanalysis products. Crucially, unlike related deep generative models, WassDiff integrates a Wasserstein distribution-matching regularizer to the denoising process to reduce empirical biases at extreme intensities. Comprehensive evaluations demonstrate that WassDiff quantitatively outperforms existing state-of-the-art generative downscaling methods at recovering extreme weather phenomena such as tropical storms and cold fronts. Case studies further qualitatively demonstrate WassDiff's ability to reproduce realistic fine-scale weather structures and accurate peak intensities. By unlocking decades of high-resolution rainfall information from globally available coarse records, WassDiff offers a practical pathway toward more accurate flood-risk assessments and climate-adaptation planning.

Figures (11)

• Figure 1: Overview of precipitation signals used for downscaling in this study.(a) Weather events recorded using sparse gauge instruments (CPC at 55km resolution) lack local precipitation dynamics, unlike modern radar that provides high resolution measurements (MRMS at 1km resolution). (b) Predating modern radar observations, there are decades of historical weather events documented only through coarse CPC gauge instruments and ERA5 reanalysis. In this study, we aim to downscale low-resolution historical weather events (1979 -- 2015) by leveraging high-resolution target training data (2015 -- present). (c) We propose a novel diffusion model named WassDiff to achieve this. WassDiff can downscale 55km inputs to 1km precipitation fields, recovering local and extreme precipitation dynamics.
• Figure 2: Overview of the proposed downscaling model WassDiff. (a) WassDiff generates 1km precipitation data conditioned on coarse-scale inputs. (b) Coarse-scale inputs are acquired from CPC gauge records (at 55km) and ERA5 reanalysis (at 31km). These ERA5 reanalysis variables provide essential atmospheric and environmental context linked to precipitation dynamics.
• Figure 3: Wasserstein Distance Regularization (WDR) mitigates biases during denoising. With WDR, sample average intensity ($\mu_\mathbf{x}$) is well controlled in the denoising process (dashed blue lines), resulting in a sample intensity distribution (blue curve) that closely matches the target distribution (black curve). Conventional score-matching objective does not explicitly control biases during denoising (dashed purple lines), and the resulting intensity distribution (purple curve) deviates from the target distribution.
• Figure 4: Demonstration of precipitation downscaling of extreme weather events. Conditioned on ERA5 inputs (31km) and CPC precipitation (55km), WassDiff produces 1km precipitation estimates, shown next to 1km MRMS targets. Downscaling is demonstrated on these weather events: (a) Tropical Storm Bill, 2015-06-18 UTC. (b) A cold front, 2015-12-02 UTC. (c) A hailstorm, 2015-06-11 UTC. WassDiff produces structured patterns---such as spiral bands in (a) and a sharp rain boundary in the lower right corner of (b)---consistent with the MRMS targets while accurately capturing extreme rainfall.
• Figure 5: Visual comparison of outputs from different downscaling methods. Six representative examples from the test dataset are shown for each downscaling method in Table \ref{['tab:model_comparison']}. The samples are arranged in the order of increasing max rainfall intensity ($R_\text{max}$) to highlight performance differences. Deterministic methods (CPC-Int and CNN) yield blurry predictions that fail to capture extreme precipitation dynamics. Among generative models, diffusion-based approaches (last three) demonstrate noticeably higher perceptual quality than CorrectorGAN. Our model (WassDiff) recovers extreme precipitation signals more reliably than the other two diffusion-based models (CorrDiff and SBDM).