Hydrological objective functions and ensemble averaging with the Wasserstein distance

Abstract. When working with hydrological data, the ability to quantify similarity of different datasets is useful. The choice how make this quantification has a direct influence on results, measures emphasising particular sources error (for example, errors in amplitude as opposed displacements time and/or space). Wasserstein distance considers mass distributions through transport lens. In context, it “effort” required rearrange one distribution water into other. While being more broadly applicable, interest paid hydrographs work. adapted for two ways and tested calibration “averaging” hydrograph context. This alternative definition fit shown be successful accounting timing due imprecise rainfall measurements. averaging an ensemble suitable when differences among members are peak shape but not total volume, where traditional mean works well.