*4.1. Data Validation*

Regression analysis during wave storm conditions reveals that values of the regression coefficient, *r*2, for *Hm*<sup>0</sup> are quite good, both in the north and south points, although with slightly higher values in the north (0.66 for BGN) than in the south (0.62 for BTS). Figure 4 shows three examples of the significant height evolution, both measured and modeled, during storm conditions. It can be observed that, even with significantly high values of *r*2, models may overestimate (panel a, *r*<sup>2</sup> = 0.82) or underestimate (panel c,

*r*<sup>2</sup> = 0.87) the experimental measures, although, often, the degree of correspondence is quite good or very good in some cases (panel b, *r*<sup>2</sup> = 0.92). In this sense, it is interesting to underline that although the general trend of the models is to underestimate experimental observations during extreme events (e.g., [16,17]), the results in this study include cases in which storms are underestimated, overestimated, as well as events considerably well reproduced, especially on the northern side of the islands. These results should not be surprising taking into account factors such as the altitude and complexity of the archipelago's topography, the irregularity of the coastline, and the islands' self and mutual shading effects, among others, which limit the ability of models to correctly reproduce wind and wave conditions in these areas.

**Figure 4.** Examples of simulated and measured *Hm*<sup>0</sup> sequences during wave storm episodes measured and simulated at BTS (**a**,**c**) and BGN (**b**), with corresponding regression coefficients *r*<sup>2</sup> = 0.82 (**a**), *r*<sup>2</sup> = 0.92 (**b**), and *r*<sup>2</sup> = 0.87 (**c**).

Regarding the simultaneous evolution of wind and wave directions, the analysis of both parameters as obtained from the buoy and by the model, during storms shown in Figure 4a,b, reveals that there is a fairly good correlation between the experimental measurements and the simulations. A quantitative measure of the correlation between two circular variables can be obtained by means of the circular correlation coefficient, *ρ<sup>c</sup>* [29]. The value of this coefficient for wind measured and simulated directions observed at BTS during the storm of Figure 4a is 0.29, while for the storm detected at BGN during the storm depicted in Figure 4b is 0.78. On the other side, the circular correlation coefficients for wave measured and simulated directions in these two cases are 0.59 and 0.88. In other words, there is a better degree of correlation between wave direction measurements and simulations than between wind direction measurements and simulations. Moreover, the correlation coefficient between both circular variables is higher in the north than in the south. These results can be explained by the lower directional variability of waves than that of wind, as well as the superior ability of the models to simulate wind and wave conditions to the north than to the south of the islands, due to the complexity of their orography. Unfortunately, there is no directional information for the latter case (Figure 4c) since it occurred prior to 2003, the date on which the directional sensors were incorporated into the buoys.

An overview of wind and wave directional variability, as well as their respective combined variability with wind speed, significant wave height, and peak period, can be qualitatively explored by means of wind and wave roses, as shown in Figure 5, for both measured and simulated data at point IP3, south of Tenerife. Panels on the left and in the middle show overall good agreement between average measured and simulated wave direction, although the models slightly overestimate directional dispersion around the mean. Regarding wave height (panels a and d) and period (panels b and e), it can be

observed that, in general, the wave model tends to slightly overestimate the significant wave height while weakly underestimating the peak period.

**Figure 5.** Directional distributions of *Hm*<sup>0</sup> (**a**,**d**), *Tp* (**b**,**e**) and wind speed (**c**,**f**) during wave storm periods for simulated (IP3, upper plots: (**a**–**c**)) and measured (BTS, lower plots (**d**–**f**) data.

The aforementioned increment in directional dispersion is more noticeable in the case of wind (panels c and f), revealing some weaknesses of the atmospheric model for reproducing wind conditions south of the archipelago during stormy conditions. However, despite the above differences, mostly due to large orographic complexity, the average wind direction and wind intensity are reasonably well reproduced. It is important to note that these effects are much less important in the north of the islands, and are substantially attenuated, both north and south, when all data, not only those of stormy scenarios, are considered. In conclusion, even though the models exhibit some weaknesses, there is overall fairly good agreement between wave measurements and simulations, so that the model results may be used to explore the spatiotemporal variability of wave storms in the study area, although not without some caution.
