  It has been argued persuasively that, in order to evaluate climate models,
the probability distributions of model output need to be compared to the
corresponding empirical distributions of observed data. Distance measures
between probability distributions, also called divergence functions, can be
used for this purpose. We contend that divergence functions ought to be proper,
in the sense that acting on modelers' true beliefs is an optimal strategy.
Score divergences that derive from proper scoring rules are proper, with the
integrated quadratic distance and the Kullback-Leibler divergence being
particularly attractive choices. Other commonly used divergences fail to be
proper. In an illustration, we evaluate and rank simulations from fifteen
climate models for temperature extremes in a comparison to re-analysis data.
