Scale‐separation diagnostics and the Symmetric Bounded Efficiency for the inter‐comparison of precipitation reanalyses

The ERA5 global reanalysis has been compared against a high-resolution regional reanalysis (COSMO-REA6) by means of scale-separation diagnostics based on 2d Haar discrete wavelet transforms. The presented method builds upon existing methods and enables the assessment of bias, error and skill for individual spatial scales, separately. A new skill score (evaluated against random chance) and the Symmetric Bounded Efficiency are introduced. These are compared to the Nash-Sutcliffe and the Kling-Gupta Efficiencies, evaluated on different scales, and the benefits of symmetric statistics are illustrated. As expected, the wavelet statistics show that the coarser resolution ERA5 products underestimate small-to-medium scale precipitation compared to COSMO-REA6. The newly introduced skill score shows that the ERA5 control member (EA-HRES), despite its higher variability, exhibits better skill in representing small-to-medium scales with respect to the smoother ensemble members. The Symmetric Bounded Efficiency is suitable for the inter-comparison of reanalyses, since it is invariant with respect to the order of comparison.