Investigating the Robustness of Extreme Precipitation Super-Resolution Across Climates

Abstract

The coarse spatial resolution of gridded climate models, such as general circulation models, limits their direct use in projecting socially relevant variables like extreme precipitation. Most downscaling methods estimate the conditional distributions of extremes by generating large ensembles, complicating the assessment of robustness under distributional transformations, such as those induced by climate change. To better understand and potentially improve robustness, we propose super-resolving the parameters of the target variable's probability distribution directly using analytically tractable mappings. Within a perfect-model framework over Switzerland, we demonstrate that vector generalized linear and additive models can super-resolve the generalized extreme value distribution of summer hourly precipitation extremes from coarse precipitation fields and topography. We introduce the notion of a "robustness gap", defined as the difference in predictive error between present-trained and future-trained models, and use it to diagnose how model structure affects the generalization of each quantile to a pseudo-global warming scenario. By evaluating multiple model configurations, we also identify an upper limit on the super-resolution factor based on the spatial auto- and cross-correlation of precipitation and elevation, beyond which coarse precipitation loses predictive value. Our framework is broadly applicable to variables governed by parametric distributions and offers a model-agnostic diagnostic for understanding when and why empirical downscaling generalizes to climate change and extremes.

Figures (10)

• Figure 1: Contraction of empirical distributions of precipitation extremes in Switzerland with decreasing resolution. Histograms (bars), kernel density estimates (curves), and mean values (dashed vertical lines) for present (blue) and +4K (green) climates at horizontal resolutions of 2.2 km, 13.2 km, 26.4 km, and 52.8 km.
• Figure 2: Spatial partitioning of the domain into training (white), validation (dark gray), and test (light gray) regions. The spatial blocks used to define the coarse-resolution data—13.2 km (yellow), 26.4 km (green), and 52.8 km (blue)—follow the rotated grid of the COSMO climate model.
• Figure 3: Drop in Akaike Information Criterion (AIC) values, showing each feature’s explanatory power for the target GEV's location ($\mu$), scale ($\sigma$), and shape ($\xi$) parameters when super-resolving from 13.2 km (a) and 52.8 km (b). Coarse-resolution features (gray) become less informative than elevation statistics (blue) as the super-resolution factor increases from 6 (left) to 24 (right).
• Figure 4: Maps of GEV location parameters and errors using reference climate data. (Left) Location parameter values from the fine-resolution reference, VGAM prediction, and 13.2 km-resolution baseline. (Right) Corresponding Cramér–von Mises errors for the model and the baseline. The VGAM improves spatial detail, particularly over complex terrain.
• Figure 5: Spline functions for the GEV parameters in \ref{['equa_VGAMmodel']}. The first five panels describe the additive components for the location parameter $\mu$, and the last three for $\log \sigma$. Each line shows the functions learned by models trained on present (brown) and future (blue) climate data, with 95% confidence intervals overlaid and sample distributions shown on the x-axis.