Residual Diffusion Modeling for Km-scale Atmospheric Downscaling

Predictions of weather hazard require expensive km-scale simulations driven by coarser global inputs. Here, a cost-effective stochastic downscaling model is trained from a high-resolution 2-km weather model over Taiwan conditioned on 25-km ERA5 reanalysis. To address the multi-scale machine learning challenges of weather data, we employ a two-step approach Corrector Diffusion (\textit{CorrDiff}), where a UNet prediction of the mean is corrected by a diffusion step. Akin to Reynolds decomposition in fluid dynamics, this isolates generative learning to the stochastic scales. \textit{CorrDiff} exhibits skillful RMSE and CRPS and faithfully recovers spectra and distributions even for extremes. Case studies of coherent weather phenomena reveal appropriate multivariate relationships reminiscent of learnt physics: the collocation of intense rainfall and sharp gradients in fronts and extreme winds and rainfall bands near the eyewall of typhoons. Downscaling global forecasts successfully retains many of these benefits, foreshadowing the potential of end-to-end, global-to-km-scales machine learning weather predictions.