# A New Index Assessing the Viability of PAR Application Projects Used to Validate PAR Models
## 2 Materials and Methods  
Two datasets were used; the first one was utilized for the development and the second one for the training of the models. _GHI_ and _PAR_ training data were downloaded from MODIS Land Products (MCD18) [44], particularly, the products handled were MCD18A1 [45] and MCD18A2 [46], respectively. This dataset covers a grid 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. It has a resolution of 5 km (0.045 \(\times\) 0.045\({}^{\circ}\)) and covers the period from 1 January 2018 to 31 December. Hourly \(T\) and dew point (\(T_{d}\)) data were provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) [47]. These data cover a grid 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. In this case, the resolution was 11 km (0.1 \(\times\) 0.1\({}^{\circ}\)) from 1 January 2018 to 31 December 2018. These grids correspond to the location of the Iberian Peninsula where mainland Spain is located. Data from seven _PAR_ measurement stations belonging to the GEOPAR project (Project CGL2016-79284-P AEI/FEDER/UE) were used to validate the models. These stations provide _PAR_, _GHI_, _RH_, and \(T\) minute data. Each of these stations includes Apogee SP-110 and Apogee SQ-110 pyranometers for _GHI_ and _PAR_ measuring, respectively, and a HOBO S-THB Temperature/Humidity M002 psychrometer for _RH_ and \(T\) measuring. Figure 1 illustrates the locations of these stations, and Table 1 summarizes these data. Figure 1: Result of \(k_{\mathrm{PAR}}\) clustering over the territory of study. The oceanic cluster is represented in green, while the Mediterranean one is in yellow. The locations of the seven stations used for validating the models are also represented. For obtaining \(RH\) data to develop the models, \(T\) and \(T_{d}\) data provided by ECMWF were used according to Equation (1), derived from the Magnus formula and the Arden Buck Equation [48]. \[RH=100\cdot e^{\frac{bT_{d}}{c^{*}T_{d}}-(b-\frac{T}{d})\cdot(\frac{T}{c^{*}T})} \tag{1}\]  
where \(RH\) is the relative humidity, \(T\) the air temperature, \(T_{d}\) is the dew point, \(b\) = 18.678, \(c\) = 257.14 \({}^{\circ}\)C, and \(d\) = 234.5 \({}^{\circ}\)C.  
The clearness index (\(k_{t}\)) and solar zenith angle cosine (cos \(\theta\)) were also employed for developing and validating the models. These variables were calculated following Equations (2) and (4). \[k_{t}=\frac{GHI}{G_{0}} \tag{2}\]  
where \(G_{0}\) is the hourly global extraterrestrial irradiance, calculated as Equation (3) indicates:  
\[G_{0}=I_{SC}\cdot\epsilon\cdot\frac{24}{2\pi}\Big{(}\sin\phi\cdot\sin\delta \cdot\Big{(}\omega_{f}-\omega_{i}\Big{)}+\cos\phi\cdot\cos\delta\cdot\Big{(} \sin\omega_{f}-\sin\omega_{i}\Big{)}\Big{)} \tag{3}\]  
where \(I_{SC}\) is the solar constant and equal to 1367 Wm\({}^{-2}\), \(\phi\) the latitude, \(\omega_{i}\) the hour angle at the beginning of the measurement period, \(\omega_{f}\) the hour angle at the end of the measurement period, \(\delta\) the declination angle, and \(\epsilon\) the eccentricity of the terrestrial orbit [49; 50]. \[\cos\theta=\sin\phi\cdot\sin\delta+\cos\phi\cdot\cos\delta\cdot\cos\omega \tag{4}\]  
where \(\omega\) refers to the hour angle. To obtain the models, multilinear regressions and ANNs were used. ANNs are a machine learning technique proposed by [51], inspired by the connections of biological neurons. Briefly, this technique consists of an iterative process in which the network assigns different weights to the input signals until it reaches the nearest output to a target dataset [52; 53; 54]. This process is the so-called network training, once the ANN is trained can be fed with inputs to produce an estimated value. The raw data from MCD18A1 [45] and MCD18A2 [46] provided by MODIS are 3 h averages covering mainland Spain with a resolution of 5 km.