  We propose a methodology for intercomparing climate models and evaluating
their performance against benchmarks based on the use of the Wasserstein
distance (WD). 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. By
selecting the combination of climatic variables and the regions of interest, it
is possible to highlight specific model deficiencies. The WD 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, and pinpointing their weaknesses in the
simulation of some of the selected physical fields in specific areas of the
Earth.

Atmospheric and Oceanic Physics;Statistical Mechanics;Chaotic Dynamics