# A New Index Assessing the Viability of PAR Application Projects Used to Validate PAR Models
## 4 Discussion
Inversely, the ANN slopes were higher than the MR slopes in Models 4, 5, 8, and 9; additionally, in these models, the largest differences reached three hundredths. Likewise, the differences between the intercepts of MR and ANN were not significant in Models 1, 2, 6, and 7. Only in Model 3 the ANN intercepts were above the MR intercepts (except in the case of Cordoba--IFAPA station); in the remaining models, MR intercepts were higher than ANN, and these differences reached the maximum in Model 9 where they were above 10 \(\mu\)mol m\({}^{-2}\) s\({}^{-1}\) for all stations and up to 30 \(\mu\)mol m\({}^{-2}\) s\({}^{-1}\) in Cordoba--IFAPA station. The differences between the R\({}^{2}\) obtained with MR and ANN were negligible, except in the case of Model 3 whose differences found on Cordoba--IFAPA and Salamanca--CIALE stations reached the order of one hundredth. Regarding the MBE, the differences were negligible in Models 1, 2, and 6. The largest differences in MBE were found in Model 9 (up to 1.71%), and the MBEs of ANN were closer to zero than the MBE of MR. In the case of RMSE, the differences were not significant in Models 1, 2, 6, and 8. In Models 4, 5, and 9, there were only significant differences in Villaviciosa--SERIDA and Zaragoza--AULA DEI stations. In Model 7, the RMSE of ANN was higher than the RMSE of MR. The largest differences (higher than 3.50%) were found in Model 3 in Cordoba--IFAPA and Salamanca--CIALE stations. As the difference between Model 1 using ANN and MR was very small, Model 1 was chosen with MR as the best model because of its time of computation, which was more than two times lower compared to ANN. The second ranking compared the EPI results. This index seemed to have similar behavior regarding the MBE and intercept, since EPI was determined from exceedance probabilities, that is, the complementary percentiles. If a model overestimates (or underestimates), its percentiles should be higher (or lower) than the observed data percentiles. Hence, EPI moved away from zero, the same as the MBE and intercept. Indeed, as happened with the intercept and MBE, in the case of EPI, the worst models were 4 and 9, whose average EPIs on all stations were, respectively, 0.043 and 0.039 for MR and 0.032 and 0.025 for ANN. The rest of the models were quite similar--except 5--obtaining EPI in the order of 0.01. However, Model 8 appeared as the best one of the MR models (its average EPI on all stations was 0.009), whereas for ANN models, Model 3 had the best EPI results by a narrow margin (its average EPI on all stations was 0.010). Thus, Model 8 with MR was chosen as the best model for the second ranking due again to its lower time of computation. It is a remarkable fact that Model 8 is among the worst models according to the rest of the indices and that _GHI_ is not an input variable for this model. As previously mentioned, the slope, the intercept, the R\({}^{2}\), the RMSE, and the MBE estimate the closeness of the model to the observed data point by point, so _GHI_ is a necessary variable to adequately reproduce the _PAR_, as this variable is intrinsically associated with _GHI_ (some _PAR_ models are limited to expressing a ratio of _GHI_). In this work, the best combination of variables to achieve this purpose without _GHI_ was the one proposed in Model 8 (\(k_{t}\), cos \(\theta\), \(T\), and _RH_). Nevertheless, though _GHI_ is not used explicitly, in fact, it is utilized implicitly since \(k_{t}\) is defined as the ratio between the variables _GHI_ and \(G_{0}\). Thus, the information carried in _GHI_ is one way or another needed to obtain good _PAR_ estimates. According to Figure 4, the results utilizing the site-adaptation technique improved slightly in Albacete--ITAPA station. However, in the remaining stations, some statistics improved but others got worse.