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

Global reanalyses are routinely used to assess the state of the climate and to evaluate the ongoing climate change. 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. Validation and inter-comparison of reanalysis products lead to a better understanding of their strengths and weaknesses, for a more robust interpretation of climate studies.

The presented method builds upon existing methods and enables the assessment of bias, error and skill for individual spatial scales, separately.  The energy scale-separation verification diagnostics (square-root energy, energy percentages, and their normalized bias) enable to assess the bias across the scales and differences in the scale structure of the reanalysis products.

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. We illustrate the enhanced diagnostic capabilities of the introduced scale-separation diagnostics while comparing ERA5 control and ensemble members to COSMO-REA6 precipitation reanalyses. Furthermore, the Symmetric Bounded Efficiency enables the comparison of gridded datasets with different resolutions, without penalizing the -more noisy- finer resolution products.

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, 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.