# A New Index Assessing the Viability of PAR Application Projects Used to Validate PAR Models
## 4 Discussion  
The clustering led to a division into two regions, one of them located in the north and northwest of mainland Spain and the other one located in the central, southern, and eastern areas of the territory. The division obtained in the clustering coincides with the two main climatological regions in mainland Spain [67; 68]: Oceanic and Mediterranean. The northern cluster fits reasonably well with areas of Spain that have an oceanic climate, while the southern cluster coincides with the areas that have a Mediterranean climate. The presence of mountain ranges can explain the inclusions of the oceanic cluster in the Mediterranean one [58]. According to the results, it is not easy to infer what the best model is. It is necessary to assess all the statistics together to choose the best option. However, all the statistics used except the EPI are based on the comparison between the observed value and the corresponding modeled value. For its part, EPI is not based on a point-to-point comparison from which a compound index is obtained. Instead, the index is calculated comparing exceedance probabilities, which are the result of an entire set of points. Therefore, EPI is the best index to assess the goodness of a model that is going to be used to estimate the viability of a project. The rest of the statistics are used to assess the extent to which the model adequately reproduces the observed data. In that sense, for the evaluation of the models, we should use the EPI separately from the rest of the statistics, and propose two rankings of models: one focused on the degree of goodness when reproducing the observed data, and another focused on the goodness when assessing the viability of possible projects. First, the models were ranked according to the first five statistics (the slope, the intercept, the R\({}^{2}\), the RMSE, and the MBE). Analyzing the performance of both MR and ANN models from the slope, R\({}^{2}\), and RMSE, the worst combination of variables is that of Models 6 and 8, that is, the models that did not include _GHI_ as an input. As Figures 2 and 3 illustrate, the slopes obtained with Models 6 and 8 either with MR or ANN for all the stations were the farthest from one. The same happened with the R\({}^{2}\); the lower values were found in Models 6 and 8. Regarding RMSE, the highest values were obtained with Models 6 and 8. Indeed, the RMSEs of Models 6 and 8 were more than twice the RMSEs of the other models in the case of MR. The slope was close to one in the rest of the models. All the models obtained R\({}^{2}\) higher than 0.99, except Models 6 and 8. In the case of the RMSE, lower results were obtained with Models 1 and 7. According to the intercept, the worst models are 4 and 6 for both MR and ANN, and Model 9 in the case of MR whose intercepts were in all cases above 16 \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\). On the other hand, the three best models are 1, 2, and 3, because their intercepts in all cases were below 25 \(\upmu\)mol m\({}^{-2}\) s\({}^{-1}\). Regarding the MBE, the closest to zero per cent results were obtained with Model 8 when using MR, and Model 7 in the case of ANN; for these models, the MBE statistics were in all cases within the range (\(-\)2%-2%). However, the worst models according to their MBE are 4 and 9, since their numbers were the farthest to zero per cent in all cases. Thus, according to these five statistics (the slope, the R\({}^{2}\), the RMSE, the intercept, and the MBE), the best performance was obtained with Model 1, for both MR and ANN models. Figure 5: Comparison between the statistical results obtained by MR Model 8 and its site-adaptation correction. Regarding the differences between ANN and MR models, in the case of the slope, they were not significant in Models 1, 2, 6, and 7. Model 3 was the only one in which the MR slopes were higher than ANN, and the difference between them was in the order of one hundredth in all stations.