Taylor diagram

This diagram, invented by Karl E. Taylor in 1994 (published in 2001[1]) facilitates the comparative assessment of different models.

Although Taylor diagrams have primarily been used to evaluate models designed to study climate and other aspects of Earth's environment,[2] they can be used for purposes unrelated to environmental science (e.g., to quantify and visually display how well fusion energy models represent reality[3]).

Taylor diagrams can be constructed with a number of different open source and commercial software packages, including: GrADS,[4][5] IDL,[6] MATLAB,[7][8][9] NCL,[10] Python,[11][12][13] R,[14] and CDAT.

[15] The sample Taylor diagram shown in Figure 1[16] provides a summary of the relative skill with which several global climate models simulate the spatial pattern of annual mean precipitation.

Models lying on the dashed arc have the correct standard deviation (which indicates that the pattern variations are of the right amplitude).

Mathematically, the three statistics displayed on a Taylor diagram are related by the error propagation formula (which can be derived directly from the definition of the statistics appearing in it): where ρ is the correlation coefficient between the test and reference fields, E′ is the centered RMS difference between the fields (with any difference in the means first removed), and

is the angle between sides a and b) provides the key to forming the geometrical relationship between the four quantities that underlie the Taylor diagram (shown in Figure 2).

One approach suggested by Taylor (2001) was to add lines, whose length is equal to the bias to each data point.

The bias, like the standard deviation, should also be normalized in order to plot multiple parameters on a single diagram.

Furthermore, the mean square difference between a model and the data can be calculated by adding in quadrature the bias and the standard deviation of the errors.