EnScale: Temporally-consistent multivariate generative downscaling via proper scoring rules

TL;DR

EnScale tackles the challenge of generating high-resolution, temporally coherent, multivariate climate fields conditioned on coarse GCM outputs. It introduces a two-step downscaling framework with coarse correction (p_{Z|X}) followed by a progressive multistage super-resolution (p_{Y|Z}), trained with the energy score, a proper multivariate scoring rule. The temporal extension EnScale-t adds autoregressive time-consistency, and a sparse local stochastic architecture enables scalable, location-specific variability modeling. Across multiple GCM–RCM pairs and four climate variables, EnScale achieves strong calibration, realistic spatial structure, reliable extremes, and favorable multivariate dependencies, while reducing computational cost by about an order of magnitude relative to diffusion-baseline methods. The work provides a comprehensive evaluation framework and demonstrates that stochastic, temporally-consistent emulation of RCMs is feasible and practically impactful for regional climate impact assessments.

Abstract

The practical use of future climate projections from global circulation models (GCMs) is often limited by their coarse spatial resolution, requiring downscaling to generate high-resolution data. Regional climate models (RCMs) provide this refinement, but are computationally expensive. To address this issue, machine learning models can learn the downscaling function, mapping coarse GCM outputs to high-resolution fields. Among these, generative approaches aim to capture the full conditional distribution of RCM data given coarse-scale GCM data, which is characterized by large variability and thus challenging to model accurately. We introduce EnScale, a generative machine learning framework that emulates the full GCM-to-RCM map by training on multiple pairs of GCM and corresponding RCM data. It first adjusts large-scale mismatches between GCM and coarsened RCM data, followed by a super-resolution step to generate high-resolution fields. Both steps employ generative models optimized with the energy score, a proper scoring rule. Compared to state-of-the-art ML downscaling approaches, our setup reduces computational cost by about one order of magnitude. EnScale jointly emulates multiple variables -- temperature, precipitation, solar radiation, and wind -- spatially consistent over an area in Central Europe. In addition, we propose a variant EnScale-t that enables temporally consistent downscaling. We establish a comprehensive evaluation framework across various categories including calibration, spatial structure, extremes, and multivariate dependencies. Comparison with diverse benchmarks demonstrates EnScale's strong performance and computational efficiency. EnScale offers a promising approach for accurate and temporally consistent RCM emulation.

Figures (25)

• Figure 1: Illustration of the dataset. The first row shows the GCM data from CNRM-CM5 on two example days with similar precipitation fields, displayed on the full spatial extent that is used as the model input. The second row presents the same GCM data cropped to approximately match the target area used in this study. The fourth row shows the corresponding target RCM data (ALADIN63 and RegCM4-6) that downscaled this GCM. The third row presents these RCM fields manually coarsened to a resolution comparable to the GCM data. Small differences between shape and domain of cropped GCM (row two) and coarsened RCM (row three) are due to small resolution differences and misaligned grids.
• Figure 2: Downscaling via coarse correction for EnScale. We approximate the conditional distribution of RCM data $Y$ given GCM data $X$ with a two-step approach. In the second row, $Z$ represents RCM data manually coarsened through average pooling. The map learning the conditional $p_{Z|X}$ is called the coarse model, and the map for the conditional $p_{Y|Z}$ the super-resolution model. All $X, Z, Y$ include multiple climate variables and grid points, and represent daily data.
• Figure 3: Time series generation with temporal consistency in EnScale-t using an autoregressive roll-out. At each time step $t$, the model predicts coarsened RCM data $\hat{Z}_t$ using the sample from the previous day, $\hat{Z}_{t-1}$, and the GCM data from the same day, $X_t$. The super-resolution model is applied to independently to each $\hat{Z}_t$ to generate the final high-resolution time series. For simplicity, this figure presents only one variable (precipitation), but the approach uses all variables jointly.
• Figure 4: Sparse local stochastic layers from EnScale's super-resolution model. As an example, we demonstrate modeling the distribution in an example pixel of interest (top left corner, orange); the same procedure is applied to all pixels. For each intermediate map (small arrows), light blue shaded pixels serve as inputs and orange pixels as the targets. First, a deterministic upsampling step processes each target variable (tas, pr, sfcWind, rsds) separately, linearly interpolating nearest pixels in the low-resolution input with learnable weights. Second, the intermediate upsampled variables are stacked and concatenated with noise channels. Next, each pixel again interpolates linearly from its nearest neighbors with learnable location-specific weights (this time using all variables and the noise as inputs). Finally, an MLP is applied to each pixel independently, using the same weights at each location.
• Figure 5: Summary of performance of EnScale compared to the benchmarks in several selected categories, shown for the interpolation test period (2030-39). Energy score (see Sec. \ref{['sec:results:overall_performance']}), Calibration (see Sec. \ref{['sec:results:calibration']}), Spatial structure (see Sec. \ref{['sec:results:spatial_structure']}), Temporal structure (see Sec. \ref{['sec:results:temporal']}), Extremes (see Sec. \ref{['sec:results:extremes']}), Multivariate dependencies (Sec. \ref{['sec:results:dependencies']}). The chosen metrics for the categories are outlined in more detail in the main text. All metrics are normalized such that EnScale attains a score of 1 in the respective category and all other scores are expressed relative to EnScale. In all categories, lower values indicate better performance. As calibration for deterministic models is not meaningful, we do not show it for NN-det.