Domain-Adaptive Climate Downscaling Under Temporal Distribution Shift

High-resolution regional climate simulations provide critical information for climate impacts assessments but remain computationally expensive, motivating the development of machine-learning downscalers and emulators. A key challenge is determining how limited high-resolution simulations should be distributed across a changing climate trajectory to capture both forced climate response and internal variability. Using the CESM2 Large Ensemble over the western United States, we compare three training-year selection strategies under fixed data budgets: a contiguous block of historical years, years drawn from both the beginning and end of the simulation period, and years distributed throughout the full climate trajectory. Including both historical and future years consistently outperforms training on historical years alone, demonstrating the importance of exposing downscaling models to climate states outside the historical record and highlighting limitations of stationarity assumptions common in statistical downscaling. Training on years distributed throughout the full climate trajectory performs best overall, indicating that broad sampling of internal variability provides additional information beyond exposure to the forced climate response alone. Models trained on temporally distributed subsets more successfully reproduce variability in unseen ensemble members while retaining strong performance across a wide range of climate diagnostics. Even when trained on only one-tenth of the available high-resolution years, temporally distributed models remain highly competitive with full-data training. These results suggest that, under fixed computational budgets, broad sampling of climate states is more valuable than temporal continuity when allocating scarce high-resolution simulations. The findings provide practical guidance for regional climate downscaling and large-ensemble projection workflows.

The proliferation of data-driven models in weather and climate sciences has marked a significant paradigm shift, with advanced models demonstrating exceptional skill in medium-range forecasting. However, these models are often limited by long-term instabilities, climatological drift, and substantial computational costs during training and inference, restricting their broader application for climate studies. Addressing these limitations, Guan et al. (2024) introduced LUCIE, a lightweight, physically consistent climate emulator utilizing a Spherical Fourier Neural Operator (SFNO) architecture. This model is able to reproduce accurate long-term statistics including climatological mean and seasonal variability. However, LUCIE's native resolution (~300 km) is inadequate for detailed regional impact assessments. To overcome this limitation, we introduce a deep learning-based downscaling framework, leveraging probabilistic diffusion-based generative models with conditional and posterior sampling frameworks. These models downscale coarse LUCIE outputs to 25 km resolution. They are trained on approximately 14,000 ERA5 timesteps spanning 2000-2009 and evaluated on LUCIE predictions from 2010 to 2020. Model performance is assessed through diverse metrics, including latitude-averaged RMSE, power spectrum, probability density functions and First Empirical Orthogonal Function of the zonal wind. We observe that the proposed approach is able to preserve the coarse-grained dynamics from LUCIE while generating fine-scaled climatological statistics at ~28km resolution.

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.