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standard deviation (which indicates that the pattern variations are of the right amplitude). In Figure 1 it can be seen that models A and C generally agree best with observations, each with about the same RMS error. Model A, however, has a slightly higher correlation with observations and has the same standard deviation as the observed, whereas model C has too little spatial variability (with a standard deviation of 2.3 mm/day compared to the observed value of 2.9 mm/day). Of the poorer performing models, model E has a low pattern correlation, while model D has variations that are much larger than observed, in both cases resulting in a relatively large (~3 mm/day) centered RMS error in the precipitation fields. Although models D and B have about the same correlation with observations, model B simulates the amplitude of the variations (i.e., the standard deviation) much better than model D, resulting in a smaller RMS error.
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reproduces observations. For each model, three statistics are plotted: the
Pearson correlation coefficient (gauging similarity in pattern between the simulated and observed fields) is related to the azimuthal angle (blue contours); the centered RMS error in the simulated field is proportional to the distance from the point on the x-axis identified as “observed” (green contours); and the standard deviation of the simulated pattern is proportional to the radial distance from the origin (black contours). It is evident from this diagram, for example, that for Model F the correlation coefficient is about 0.65, the RMS error is about 2.6 mm/day and the standard deviation is about 3.3 mm/day. Model F's standard deviation is clearly greater than the standard deviation of the observed field (indicated by the dashed contour at radial distance 2.9 mm/day).
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normalization of dimensional quantities (dividing both the RMS difference and the standard deviation of the "test" field by the standard deviation of the observations) so that the "observed" point is plotted at unit distance from the origin along the x-axis, and statistics for different fields (with
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designed to graphically indicate which of several approximate representations (or models) of a system, process, or phenomenon is most realistic. This diagram, invented by Karl E. Taylor in 1994 (published in 2001) facilitates the comparative assessment of different models. It is used to quantify
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with which several global climate models simulate the spatial pattern of annual mean precipitation. Eight models, each represented by a different letter on the diagram, are compared, and the distance between each model and the point labeled “observed” is a measure of how realistically each model
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Taylor diagrams display statistics useful for assessing the similarity of a variable simulated by a model (more generally, the “test” field) to its observed counterpart (more generally, the “reference” field). Mathematically, the three statistics displayed on a Taylor diagram are related by the
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The relative merits of various models can be inferred from Figure 1. Simulated patterns that agree well with observations will lie nearest the point marked "observed" on the x-axis. These models have relatively high correlation and low RMS errors. Models lying on the dashed arc have the correct
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Lemon, Jim; Bolker, Ben; Oom, Sander; Klein, Eduardo; Rowlingson, Barry; Wickham, Hadley; Tyagi, Anupam; Eterradossi, Olivier; Grothendieck, Gabor; Toews, Michael; Kane, John; Turner, Rolf; Witthoft, Carl; Stander, Julian; Petzoldt, Thomas; Duursma, Remko; Biancotto, Elisa; Levy, Ofir; Dutang,
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Although Taylor diagrams have primarily been used to evaluate models designed to study climate and other aspects of Earth's environment, they can be used for purposes unrelated to environmental science (e.g., to quantify and visually display how well fusion energy models represent reality).
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use of an arrow to connect two related points on the diagram. For example, an arrow can be drawn from the point representing an older version of a model to a newer version, which makes it easier to indicate more clearly whether or not the model is moving toward "truth," as defined by
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One of the main limitation of the Taylor diagram is the absence of explicit information about the prediction bias. A variant of the Taylor diagram that accounts for the prediction bias is provided by the solar diagram (see, Wadoux et al., 2022).
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Taylor diagrams can be constructed with a number of different open source and commercial software packages, including: GrADS, IDL, MATLAB, NCL, Python, R, and CDAT.
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Fig. 1: Sample Taylor diagram displaying a statistical comparison with observations of eight model estimates of the global pattern of annual mean precipitation.
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Christophe; Solymos, Peter; Engelmann, Robby; Hecker, Michael; Steinbeck, Felix; Borchers, Hans; Singmann, Henrik; Toal, Ted; Ogle, Derek; Baral, Darshan;
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Wadoux, AMJ-C; Walvoort, DJJ; Brus, DJ (2022). "An integrated approach for the evaluation of quantitative soil maps through Taylor and solar diagrams".
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The means of the fields are subtracted out before computing their second-order statistics, so the diagram does not provide information about overall
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extension to a second "quadrant" (to the left of the quadrant shown in Figure 1) to accommodate negative correlations;
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Fig. 2: Geometrical relationship between statistics plotted on Taylor diagrams according to the law of cosines.
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the degree of correspondence between the modeled and observed behavior in terms of three statistics: the
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Terry, P.W.; et al. (2008). "Validation in fusion research: Towards guidelines and best practices".
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Among the several minor variations on the diagram that have been suggested are (see, Taylor, 2001):
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formula (which can be derived directly from the definition of the statistics appearing in it):
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Taylor, K.E. (2001). "Summarizing multiple aspects of model performance in a single diagram".
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The sample Taylor diagram shown in Figure 1 provides a summary of the relative
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