Abstract
A diagram has been devised that can provide a concise statistical
summary of how well patterns match each other in terms of their correlation,
their root-mean-square difference and the ratio of their variances.
Although the form of this diagram is general, it is especially useful
in evaluating complex models, such as those used to study geophysical
phenomena. Examples are given showing that the diagram can be used
to summarize the relative merits of a collection of different models
or to track changes in performance of a model as it is modified.
Methods are suggested for indicating on these diagrams the statistical
significance of apparent differences, and the degree to which observational
uncertainty and unforced internal variability limit the expected
agreement between model-simulated and observed behaviors. The geometric
relationship between the statistics plotted on the diagram also provides
some guidance for devising skill scores that appropriately weight
among the various measures of pattern correspondence.
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