Multiple Testing for Spatial Extremes with Application to Reanalysis Data Evaluation

Climate data products, such as reanalysis datasets, require careful evaluation to determine their reliability. While most climate data evaluations focus on the mean and dependency of climate processes, we focus on marginal extreme behavior, including return levels that often have devastating impacts on our ecosystems and societies. In particular, we aim to identify where the two climate extreme fields exhibit different marginal behavior, by simultaneously evaluating the differences over all spatial locations through multiple testing techniques. The large variation inherited in extreme model fitting makes this evaluation more challenging than that for the mean and dependency structure. We propose a new multiple testing procedure, bivariate conditional local FDR (BiCLfdr), to efficiently detect signals from highly variable but spatially correlated hypotheses. Our method takes advantage of both the smoothness of large scale spatial variability and the local spatial correlation to enhance the power of comparing the marginal extreme distribution of two spatial extremes. We apply BiCLfdr to evaluate ERA5 reanalysis in its representation of winter precipitation extremes across the United States, using CPC-CONUS observations as reference. Our analysis identifies locations along the West Coast, the western Great Plains, and the Southeast where ERA5 appears to inadequately represent observed winter precipitation extremes.