# Combination of Models to Generate the First PAR Maps for Spain
## 4 Discussion  
The PAR model introduced in this work has been validated in seven stations located throughout mainland Spain with different types of climate (see Table 1), according to the Koppen-Geiger classification. This model was elaborated as a linear combination of the two models developed in [17]. These two previous models exhibited different performances depending on the climate of the location. Thus, while the model developed from CM-SAF demonstrated good results in places with Mediterranean or dry climates, the model developed from MODIS obtained its better results in locations with oceanic or humid climates. The new proposed PAR model has been also compared with three models proposed by other authors [20; 49]. The model proposed in [20] is described in the following equation:  
\[\text{PAR}=2.242\cdot\text{GHI} \tag{8}\]  
Different PAR models were proposed by [49] depending of the land use of the site. One of them was developed for pasture lands and is shown in Equation (9), while the expression for forest lands is shown in Equation (10). \[\text{PAR}=2.023\cdot\text{GHI}+28.557 \tag{9}\]  
\[\text{PAR}=1.922\cdot\text{GHI}+3.630 \tag{10}\]  
Table 5 illustrates the comparison between the results of the previous models and the new model, carried out with the validation data set of each station. Comparing the slopes, the closest value to the unit was obtained with the new model at every station except at Alava-NEIKER where the closest value was obtained with [PERSON] et al. 's pasture model. Likewise, the intercepts closest to zero belonged to the new model. By contrast, the results of R\({}^{2}\) were similar to those of any of the six models. With regard to the MBE, the closest values to zero were obtained with the new model except at Albacet-ITAP and Salamanca-CIALE, where the MODIS model and the CM-SAF model obtained the closest values to zero, respectively. However, the new model obtained the lowest RMSE results at all stations. Figure 7: Daily PAR estimates for a year in mainland Spain. Furthermore, the results of the new model were similar at all stations: all the slopes were close to the unit; all the intercepts were close to zero, with 3.70 umol m\({}^{-2}\) s\({}^{-1}\) being the highest value (at Salamanca-CIALE); similarly, all the MBEs were close to zero, with \(-0.39\%\) being the highest value (at Albacete-ITAP); and the highest RMSE was 6.21% (at Lugo-USC). According to these results, the new model showed no clear tendency as evaluated with these datasets and its performance was similar on every station, regardless of the climate. This result is a consequence of the combination of two previous models. One of them performed well in Mediterranean climates, while the second model obtained good results for oceanic climates. With regard to the PAR maps, they were developed using the new PAR model introduced in this study. As expected, PAR irradiance levels increase during the summer months and decrease during the winter months. However, some trends and features remain the same every month. For example, PAR maximums are always reached in the southeast and central areas of the Iberian Peninsula along with the Guadalquivir and Ebro valleys. However, minimums of PAR irradiance were reached in northern areas of the Iberian Peninsula and mountain ranges, such as the Pyrenees, the Central Range, the Iberian Range, and the Betic Range. Furthermore, the same features are noted on the annual PAR map, where the minimums and maximums of PAR irradiance are reached in the same areas. Surprisingly, there are locations on mountain ranges, particularly in the Pyrenees in winter months, that the model significantly underestimates, producing a result near zero.