# Combination of Models to Generate the First PAR Maps for Spain
## 2 Materials and Methods  
The two models elaborated in [17] used estimates from two satellite datasets--CM-SAF and MODIS--that cover the location of the Iberian Peninsula, where mainland Spain is located. The grid of both data sets ranges from 35.3\({}^{\circ}\)N to 44.0\({}^{\circ}\)N in latitude and from 9.5\({}^{\circ}\)W to 3.5\({}^{\circ}\)E in longitude. The CM-SAF grid had a resolution of 0.1\({}^{\circ}\)\(\times\) 0.1\({}^{\circ}\), while the MODIS grid had a resolution of 5 km. In particular, the CM-SAF data set corresponded to the years 1999 to 2011 of the Spectral Resolved Irradiance (SRI) product, which belongs to the EUMETSAT Satellite Application Facility network [42; 43]. On the other hand, the MODIS data set corresponded to the dates from 1 January 2018, to 31 May 2019 of the MCD18A1-MODIS/Terra+Aqua Surface Radiation Daily/3 Hour L3 Global 5 km SIN Grid [44] and MCD18A2-MODIS/Terra+Aqua Photosynthetically Active Radiation Daily/3-Hour L3 Global 5 km SIN Grid [45; 46] products. Both models developed in [17] have the following mathematical structure:  
\[\text{PAR}=\alpha\text{-GHI}+\beta \tag{1}\]  
where \(\alpha\) and \(\beta\) are specific coefficients for each point of the grid corresponding to mainland Spain. Thus, both models are valid for the whole study territory, giving specific estimates for each point. For the present work, data from seven radiometric stations belonging to the GEOPAR Project (Project CGL2016-79284-P AEI/FEDER/UE) were used. Figure 1 shows the loca tions of the stations that provided data on GHI, PAR, air temperature, and relative humidity. Further details of each station can be found in Table 1.  
Depending on their climate, the stations can be classified into two groups: those that feature a humid climate (oceanic varieties) and those with a dry climate (Mediterranean varieties). In the first group are Alava-NEIKER, Asturias-SERIDA, and Lugo-USC. Albacete-ITAP, Cordoba-IFAPA, Salamanca-CIALE, and Zaragoza-Aula Dei belong to the second group. As none of the GEOPAR project stations were located in the Spanish archipelagos, the study field was set to mainland Spain because the climate on the islands is quite particular and there was no way to validate the estimates of the PAR model in those places. Daily averages of PAR and GHI data from radiometric stations were collected over a period of more than two years, specifically from 7 May 2019 to 30 June 2021. This data \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Station**} & **Altitude** & **Latitude** & **Longitude** & \multirow{2}{*}{**Climate**} \\  & **(m)** & (\({}^{\circ}\), +N) & (\({}^{\circ}\), +E) & \\ \hline Alava-NEIKER & 520 & 42.85 & \(-\)2.62 & oceanic \\ Albacete-ITAP & 698 & 39.04 & \(-\)2.08 & Mediterranean \\ Asturias-SERIDA & 6 & 43.48 & \(-\)5.44 & oceanic \\ Cordoba-IFAPA & 91 & 37.86 & \(-\)4.80 & Mediterranean \\ Lugo-USC & 447 & 43.00 & \(-\)7.54 & oceanic \\ Salamanca-CIALE & 777 & 40.98 & \(-\)5.72 & Mediterranean \\ Zaragoza-Aula Dei & 226 & 41.73 & \(-\)0.81 & Mediterranean \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of the location of the seven stations belonging to the GEOPAR project. Note that the altitude is given in meters above sea level, whereas the latitude and longitude are given in degrees (\({}^{\circ}\)), where positive values indicate north and east, respectively. Figure 1: Location of the stations belonging to the GEOPAR project that provided the data. set was randomly divided into two subsets with the same number of recordings. The first subset was used to train the PAR model, whereas the second subset was used to validate the model. To develop the PAR model, an analogous technique to that described in [47; 48] was applied. This methodology consisted of a linear fit between the estimates of the models developed in [17] from MODIS and CM-SAF and the measurements at the radiometric stations, as Equation (2) indicates.