Graphical Abstract

Duc, L., Y. Sawada, 2024: Geometry of rainfall ensemble means: from arithmetic averages to Gaussian-Hellinger barycenters in unbalanced optimal transport. J. Meteor. Soc. Japan, 102.
Early Online ReleaseGraphical Abstract New GA


Plain Language Summary: It is well-known in rainfall ensemble forecasts that ensemble means suffer substantially from the diffusion effect resulting from the averaging operator. Therefore, ensemble means are rarely used in practice. This study has used the limitation of ensemble means as evidence to support the viewpoint that the geometry of rainfall distributions is not the familiar Euclidean space but a different space. The rigorously mathematical theory underlying this space has already developed in the theory of unbalanced optimal transport. This geometry is associated with the Gaussian-Hellinger distance. This distance is the optimal cost to push a source distribution to a destination distribution with penalties on the mass discrepancy between mass transportation and original mass distributions. In the new geometry, ensemble means are identified with Gaussian-Hellinger barycenters, and the diffusion effect, as in the case of arithmetic means, is avoided. The new ensemble means being placed side-by-side with deterministic forecasts provide useful information for forecasters in decision-making.