# A New Index Assessing the Viability of PAR Application Projects Used to Validate PAR Models
## 4 Discussion
For instance, in Cordoba--IFAPA, the MBE improved, but the slope got worse, the same as in Vitoria--NEIKER, or in Villaviciosa--SERIDA and Zaragoza--AULA DEI where the slope improved but MBE worsened, whereas in Lugo--USC, the MBE improved, but the slope remained almost the same, and in Salamanca--CIALE, the MBE improved, but the slope got worse. In all cases, the intercept improved significantly using the site adaptation, whereas there were no significant differences in RMSE and R\({}^{2}\). According to the EPI, the site adaptation improved the results in Albacete--ITAP, Lugo--USC, Salamanca--CIALE, and Zaragoza--AULA DEI, while in the remaining three stations, EPI got worse. Bearing this in mind, it can be concluded that there was no clear improvement either by using the site-adaptation correction to Model 1--assessing the slope, the intercept, the R\({}^{2}\), the RMSE, and the MBE--or using the site-adaptation correction to Model 8--assessing the EPI. Models 1 and 8 were compared to four hourly _PAR_ models of the bibliography [32; 34; 41; 59]. The following equations describe the models of the bibliography chosen for the comparison, where the coefficients were transformed to the units used in this work when needed:  
In [41], the model in Equation (15) is proposed using the product of the clearness index (\(k_{t}\)) and the cosine of the solar zenith angle (cos \(\theta\)). \[PAR=2681.00\cdot k_{t}\cdot\cos\theta \tag{15}\]  
The model described in Equation (16) was introduced in [59]. \[PAR=1.80\cdot GHI \tag{16}\]  
Equation (17) shows the model suggested in [34]. \[PAR=2.24\cdot GHI \tag{17}\]  
The last model was introduced in [32] and is expressed in Equation (18). \[PAR=(1.83-0.19\cdot k_{t}+0.10\cdot\cos\theta)\cdot GHI \tag{18}\]  
According to the results shown in Figure 6, the best performance of models found in the literature was reached with the model described in Equation (15). Comparing the slopes, in all the seven locations, the models closer to one were those obtained by the model proposed in [41]. No clear tendency on the intercepts was observed. Comparing the R\({}^{2}\), the models [32; 34; 59] were close to one in all the stations. However, the model proposed in [41] was further from one. Regarding the MBE statistics, the lowest values were also obtained using the model proposed in [41]. However, the lowest RMSE was obtained with the model proposed in [34] by a scarce difference. As far as EPI is concerned, the lowest results were those of the model proposed in [41]. The differences between the EPI of model [41] and the remaining models of the bibliography, which reached one magnitude order, are remarkable. Comparing to the performance of Models 1 and 8, the slopes found with Model 1 were closer to one than those of the model proposed in [41], whereas the slopes obtained using Model 8 and the model proposed in [41] were quite similar. The intercepts of the model proposed in [41] were clearly closer to zero than those of Models 1 and 8, except in Cordoba--IFAPA and Salamanca--CIALE. Regarding R\({}^{2}\), the results of Model 1 were the closest to one, while those of Model 8 and the model proposed in [41] were similar. The MBE obtained with the model proposed in [41] was further from zero than in the case of Models 1 and 8. The same happened with RMSE, but in this case, the difference between the numbers of Model 1 and the model proposed in [41] was higher than the difference between Model 8 and the model proposed in [41]. Regarding EPI, the values of the model proposed in [41] were higher than those obtained in Models 1 and 8.