# A New Index Assessing the Viability of PAR Application Projects Used to Validate PAR Models
## 3 Results
### Regional PAR Models
#### 3.1.1 \(k_{\text{PAR}}\) Clustering  
Figure 1 shows the division of the territory into two regions obtained after clustering \(k_{PAR}\) following the k-means method. The number of optimal clusters employed was two. Details of the method can be found in [58].  
Compared to the climatological regions present in Spain [67; 68], the two regions obtained throughout the clustering analysis fit with the Oceanic and the Mediterranean areas, respectively. Indeed, Oceanic climate is present in northern and northwest regions of Spain and fit reasonably with the green cluster, whereas eastern, southern, and central areas of Spain have a Mediterranean climate and fit well with the yellow cluster, though there are two different climatic varieties. In the eastern and coastal zones, the Mediterranean subtype is standard, and in the inner zones, the Mediterranean subtype is continental. In mainland Spain, there is another climate called the mountain climate. As its name indicates, this climate is typical of mountain ranges and high locations. This climate appears in mainland Spain in the main mountain ranges, such as the Pyrenees, Central Range, Iberian Range, and the Sierra Nevada. The cluster division did not account for this mountain climate, but the inclusions of the green cluster into the yellow cluster are located in the main mountain ranges in mainland Spain. This indicates that the mountain climate locations have been included in the green cluster [58; 69].  
According to this division, three stations are placed in the oceanic cluster: Lugo--USC; Villaviciosa--SERIDA; and Vitoria--NEIKER. However, the remaining four stations belong to the Mediterranean cluster (Albacete--ITAP; Cordoba--IFAPA; Salamanca--CIALE; and Zaragoza--AULA DEI). Therefore, the validation of the oceanic models employed only data from the three oceanic stations, and the validation of the Mediterranean models employed data from the other four stations.  
Since the field of study was divided into two regions, there were only two sets of nine models generated, one set for the oceanic region and another set for the Mediterranean region. Thus, the same set of equations was used for validating the three oceanic stations, and another set of equations was utilized for validating the Mediterranean stations, as Table 3 illustrates.  
ANN setup had one input layer and one output layer, and the number of hidden layers was chosen according to the best performance reached. All ANNs were feedforward type and were fed with the set of inputs corresponding to each model. In total, 70 % of training data served to train the ANN, while the remaining 30 % of data validated the performance of the ANN to find the optimal number of hidden layers. In this case, the ANN training for each region utilized data from the corresponding region.  
Validating with data from surface stations obtained the results illustrated in Figures 2 and 3. The statistics utilized to evaluate the performance of the different models were the slope and intercept in a scatterplot, the mean bias error (MBE), the root mean square error (RMSE), and the EPI.