Residual Corrective Diffusion Modeling for Km-scale Atmospheric Downscaling

TL;DR

This work introduces CorrDiff, a two-step generative downscaling framework that first predicts the conditional mean using a UNet and then generates the residual with a diffusion model to produce high-resolution km-scale weather fields from coarse global inputs. By decomposing x into μ + r, CorrDiff handles multi-variable, channel-synthesis tasks (e.g., radar reflectivity) more robustly than single-step conditional diffusion, achieving improved CRPS scores and more realistic spectra and distributions over Taiwan when downscaling from 25-km ERA5 to 2-km WRF-like targets. Case studies on frontal systems and tropical cyclones demonstrate that CorrDiff sharpens gradients, co-locates fine-scale features with high-impact events, and extends wind and radar reflectivity realism beyond the input data, albeit with calibration and temporal-coherence challenges remaining. The approach promises substantial gains in speed and energy efficiency over dynamical downscaling, enabling scalable global-to-regional multi-scale simulations and potential integration with data assimilation for operational forecasting.

Abstract

The state of the art for physical hazard prediction from weather and climate requires expensive km-scale numerical simulations driven by coarser resolution global inputs. Here, a generative diffusion architecture is explored for downscaling such global inputs to km-scale, as a cost-effective machine learning alternative. The model is trained to predict 2km data from a regional weather model over Taiwan, conditioned on a 25km global reanalysis. To address the large resolution ratio, different physics involved at different scales and prediction of channels beyond those in the input data, we employ a two-step approach where a UNet predicts the mean and a corrector diffusion (CorrDiff) model predicts the residual. CorrDiff exhibits encouraging skill in bulk MAE and CRPS scores. The predicted spectra and distributions from CorrDiff faithfully recover important power law relationships in the target data. Case studies of coherent weather phenomena show that CorrDiff can help sharpen wind and temperature gradients that co-locate with intense rainfall in cold front, and can help intensify typhoons and synthesize rain band structures. Calibration of model uncertainty remains challenging. The prospect of unifying methods like CorrDiff with coarser resolution global weather models implies a potential for global-to-regional multi-scale machine learning simulation.

Figures (16)

• Figure 1: The workflow for training and sampling CorrDiff for generative downscaling. Top: Coarse-resolution global weather data at 25 km scale is used to first predict the mean $\boldsymbol{\mu}$ using a regression model, which is then stochastically corrected using an Elucidated Diffusion Model (EDM) ${\bf r}$, together producing the probabilistic high-resolution 2 km-scale regional forecast. Bottom right: diffusion model is conditioned with the coarse-resolution input to generate the residual ${\bf r}$ after a few denoising steps. Bottom left: the score function for diffusion is learned based on the UNet architecture.
• Figure 2: Power spectra and distributions for the interpolated ERA5 input, CorrDiff, RF, UNet, and WRF. These results reflect reductions over space, time and for CorrDiff across 32 different samples per each time. Left: Power spectra for kinetic energy (top), 2-meter temperature (middle) and radar reflectivity (bottom). Right: distributions of windspeed, (top), 2-meter temperature (middle) and radar reflectivity (bottom). Radar reflectivity is not included in the ERA5 dataset. We show the log-PDF to highlight the differences at the tails of the distributions. Here wavenumber is the inverse of a wavelength.
• Figure 3: Evaluation of model calibration base do the same validation set used in figure \ref{['fig:spectra_distributions']} and \ref{['tab:big-score']}. Left column - the ensemble standard deviation as a function of the RSME of mean prediction for the 4 channels. The standard deviation is adjusted with a factor $\sqrt(1+1/n)$ so that a ratio of one represents a perfectly tuned model. Right column shows the corresponding rank histograms.
• Figure 4: Demonstration of the stochastic prediction of radar reflectivity (in dBZ). Top to bottom: 2023-09-03 00:00:00 , 2021-02-17 21:00:00, 2021-03-04 01:00:00 and 2022-02-13 20:00:00 UTC. Left to right: sample mean, sample standard deviation, sample number 32 and the target forecast.
• Figure 5: Examining the downscaling of a cold front on 2022-02-13 20:00:00 UTC. Left to right: prediction of ERA5, CorrDiff and Target for different fields, followed by their averaged cross section from 21 lines parallel to the thin dashed line in the contour figures. Top to bottom: 2-meter temperature (arrows are wind vectors), along front wind (arrows are along-front component of the wind vector) and across front wind (arrows are across-front component of the wind vector). At the right column the cross sections of the WRF (black line) and ERA5 (red line) are compared with the mean of a 32 member ensemble prediction from CorrDiff (orange line) where the shading shows $\pm$ one standard deviation.