Trade-offs between predictive accuracy and distributional fidelity in surrogate modeling of extreme precipitation

Abstract. Extreme precipitation remains a major challenge for regional climate modeling due to strong nonlinearities, spatial heterogeneity, and sensitivity to poorly constrained parameterizations. In this study, we assess the ability of surrogate models to represent extreme precipitation under parametric uncertainty in a regional climate model. An ensemble of simulations is generated using Latin Hypercube sampling of key parameters in the SUBEX large-scale cloud and precipitation scheme, and several surrogate approaches are evaluated, including polynomial chaos expansions (PCE), Gaussian process regression (Kriging), hybrid Polynomial Chaos-Kriging (PCK), and stochastic spectral embedding (SSE).
Model performance is assessed using both predictive metrics (RMSE, R²) and distribution-based metrics (Kolmogorov--Smirnov distance, Wasserstein distance, Kullback--Leibler divergence, and Energy distance), with validation performed on an independent dataset. Results reveal a clear trade-off: PCK provides the most accurate pointwise predictions, whereas SSE more faithfully reproduces the statistical distribution of extreme precipitation, particularly in the upper tail. Notably, the observed event occupies a low-probability region of the modeled distribution, although its position varies spatially. This suggests that standard model configurations may struggle to reproduce the intensity of individual extreme events, as they are typically calibrated to capture mean climatological variability rather than rare extremes. Sensitivity analysis indicates that extreme precipitation variability is primarily controlled by parameters governing precipitation efficiency over land and ocean, while spatial analysis shows that uncertainty is concentrated in coastal and mountainous regions where nonlinear interactions are strongest.
These findings demonstrate that no single surrogate model is optimal for all objectives and emphasize the need to distinguish between predictive accuracy and distributional fidelity when modeling extremes. They provide new insight into how model calibration, parameter uncertainty, and surrogate structure jointly influence the representation of extreme precipitation in climate simulations.