We propose a methodology for evaluating the performance of climate
models based on the use of the Wasserstein distance. This distance
provides a rigorous way to measure quantitatively the difference between
two probability distributions. The proposed approach is flexible and can
be applied in any number of dimensions; it allows one to rank climate
models taking into account all the moments of the distributions.
Furthermore, by selecting the combination of climatic variables and the
regions of interest, it is possible to highlight the deficiencies of
each of the models under study. The Wasserstein distance thus enables a
comprehensive evaluation of climate model skill. We apply this approach
to a selected number of physical fields, ranking the models in terms of
their performance in simulating them, as well as pinpointing their
weaknesses in the simulation of some of the selected physical fields in
specific areas of the Earth.