Taylor diagram

Description (see Taylor Diagram Primer for further details)

To quantify how well models simulate an observed climate field, it is useful to rely on three non-dimensional statistics:

• the ratio of the variances of the two fields: ² = ²_mod/ ²_obs
• the correlation between the two fields (R, which is computed after removing the overall means),
• and the r.m.s difference between the two fields (E, which is normalised by the standard deviation of the observed field).

The ratio of variance indicates the relative amplitude of the simulated and observed variations, whereas the correlation indicates whether the fields have similar patterns of variation, regardless of amplitude. The normalised r.m.s error can be resolved into a part due to differences in the overall means (E₀), and a part due to errors in the pattern of variations (E').

These statistics provide complementary, but not completely independent, information. Often the overall differences in means (E₀) is reported separately from the three pattern statistics (E', , and R), but they are in fact related by the following equation:

E'² = E² - E₀² = 1 + ²-2 R

This relationship makes it possible to display the three pattern statistics on a two-dimensional plot. The plot is constructed based on the Law of Cosines. The observed field is represented by a point at unit distance from the origin along the abscissa. All other points, which represent simulated fields, are positioned such that is the radial distance from the origin, R is the cosine of the azimuthal angle, and E' is the distance to the observed point. When the distance to the point representing the observed field is relatively short, good agreement is found between the simulated and observed fields. In the limit of perfect agreement (which is, however, generally not achievable because there are fundamental limits to the predictability of climate), E' would approach zero, and and R would approach unity.