HEWITT, HOETING, DONE, AND TOWLER Figure 4: Comparison of Ranked probability scores (RPS) for probabilistic categorical pre- dictions on the leave-one-out test datasets for the RESP and comparison models. RPS scores are reported relative to the median RPS for the CLIM reference model’s unconditional pre- dictions. The RESP model generally has better (i.e., lower) and slightly less variable skill than the “Sub” and “Common” comparison models. 18.1). Formulas and details for RPS and Heidke skill scores can be found in Supplement A ?? . The RESP model (3) expands geostatistical frameworks that incorporate the effect of both local and remote covariates on spatially correlated responses, like precipitation, but can be extended to address additional spatio-temporal modeling needs. For example, while we use the RESP model to draw inference on entire response fields, the model’s process-formulation also allows it to be applied to more standard spatial interpolation problems as well. Since there is great uncertainty in global climate model (GCM) predictions of future precipitation, statistical downscaling methods have been widely used in regional climate change studies. Validating the RESP model on historical data marks an improvement on existing approaches 24 4 Discussion