*2.1. Weather Data Comparison Methodology*

Once the weather data from the *on-site* weather station and the *third-party* are gathered, the first analysis is the comparison using a Taylor Diagram [45,46]. This provides a simple way of visually showing how closely a pattern matches an observation, and it is a useful tool to easily compare different parameters at a glance using the same plot. This type of comparison is widely used when weather parameters are analyzed [28,47–51]. Developed by Taylor in 2001, this diagram shows the correspondence between two patterns (in this case, *third-party* weather data as the test field (*f*) and *on-site* weather data as the reference field (*r*)) using three statistical metrics: the correlation *R*, the centered root-mean-squared difference *RMSdi f f* , and the standard deviation *σ* of the test and reference field.

The correlation *R* (3) is used to show how strongly the two fields are related, and it ranges from −1 to 1. The centered root-mean-squared difference *RMSdi f f* (4) measures the degree of adjustment in amplitude. The closer to 0, the more similar the patterns are. Both indexes provide complementary information quantifying the correspondence between the two fields, but to have a more complete characterization, their variances are also necessary, which are represented by their standard deviations *σ<sup>f</sup>* (1) and *σ<sup>r</sup>* (2) [46]. To allow the comparison between different weather parameters and to show them in the same plot, *RMSdi f f* and *σ<sup>f</sup>* are normalized by dividing both by the standard deviation of the

observations (*σr*). Thus, the normalized reference data have the following values: *σ<sup>r</sup>* = 1, *RMSdi f f* = 0, and *R* = 1.

Figure 2 shows the Taylor diagram baseline plot and how it is constructed. The reference point appears in the x-axis as a grey point. The azimuthal positions show the correlation coefficient *R* between the two fields. The standard deviation for the test field *σ<sup>f</sup>* is proportional to the radial distance from the origin, with the solid dashed arc as the reference standard deviation *σr*. Finally, the centered root-mean-squared difference *RMSdi f f* between the test and reference patterns is proportional to the distance to the reference point, and the arcs indicate its value. The diagram allows us to determine the ranking of the *test* fields by comparing the distance to the reference point.

In Figure 2, two test fields are represented as an example: Example 2 has a correlation ±0.99, a *RMSdi f f* ±0.24, and a *σ<sup>f</sup>* ±1.15. Example 1 has a correlation ±0.48, a *RMSdi f f* ±1.40, and a *σ<sup>f</sup>* ±1.55. Example 2 performs better than Example 1 since all the metrics are better. The diagram shows this in a visual way as Example 2 is closer to the reference point.

$$
\sigma\_f^2 = \frac{1}{N} \sum\_{n=1}^N (f\_n - \bar{f})^2 \tag{1}
$$

$$
\sigma\_r^2 = \frac{1}{N} \sum\_{n=1}^{N} (r\_n - \overline{r})^2 \tag{2}
$$

$$R = \frac{\frac{1}{N} \sum\_{n=1}^{N} (f\_n - \bar{f})(r\_n - \bar{r})}{\sigma\_f \sigma\_r} \tag{3}$$

$$RMS\_{diff} = \left[\frac{1}{N} \sum\_{n=1}^{N} [(f\_n - \bar{f}) - (r\_n - \bar{r})]^2\right]^{1/2} \tag{4}$$

**Figure 2.** A Taylor diagram example.
