# Extension of PAR Models under Local All-Sky Conditions to Different Climatic Zones
## 4 Extension of the Models to Other Locations
If the results are analysed by climatic zones, it can be seen that there were hardly any differences in the fit (\(R^{2}\)); all values were higher than 0.98 regardless of the sky type analysed. Figures 4 and 5 show the _nRMSE_ values for the four sky categories (all-sky type, clear, partial, and overcast) at all stations, for the MLR and the ANN models. When analysing the results for all sky types, the highest error occurred in the cold semi-arid zone (Bsk) (far from the climatic zone for which the regression and ANN models were obtained) and the lowest RMSE in continental zones with greater similarity to the climatic zone in which the models were obtained in Burgos. For clear skies in both the MLR and ANN models, the errors were slightly lower at all stations; the lowest RMSE was also obtained in continental climate zones (Dfb and Dfa) and the highest error in desert zones (Bwh). The errors at all stations were somewhat higher for overcast skies ranging from 4.6 to 11.07, although the ANN model still yielded the highest RMSE for the hot desert zone (Bwh). The overcast skies can present very different conditions depending on parameters, such as the degree of cloud cover, its thickness, and the presence of aerosols, which have a great influence on the phenomena of absorption and dispersion of solar radiation. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**MLR**} & \multicolumn{3}{c}{**ANN**} \\ \hline
**USA Stations** & \(R^{2}\) & _nRMSE (\%)_ & _nMBE (\%)_ & \(R^{2}\) & _nRMSE (\%)_ & _nMBE (\%)_ \\ \hline Bondville, & & & & & \\ Illinois & 0.984 & 6.29 & \(-\)0.23 & 0.984 & 7.13 & 3.32 \\ \hline Table Mountain, Boulder, & & & & & \\ Colorado & 0.992 & 4.60 & 0.70 & 0.992 & 6.23 & 4.18 \\ \hline Desert Rock, & & & & & \\ Nevada & 0.993 & 7.91 & 5.81 & 0.993 & 11.07 & 9.40 \\ \hline Fort Peck, & & & & & \\ Montana & 0.989 & 6.11 & 2.61 & 0.988 & 8.48 & 6.37 \\ \hline Goodwin Creek, & & & & & \\ Mississippi & 0.987 & 5.75 & 0.19 & 0.986 & 6.82 & 3.48 \\ \hline Penn State, & & & & & \\ Univ. Pennsylvania & 0.987 & 6.11 & \(-\)1.67 & 0.987 & 6.15 & 1.91 \\ \hline Sioux Falls, & & & & & \\ South Dakota & 0.989 & 6.07 & 1.88 & 0.988 & 8.14 & 5.54 \\ \hline \end{tabular}
\end{table} 
Table 10: Model fit values for MLR (left) and ANN (right) under overcast sky conditions. \begin{table}
\begin{tabular}{c c c c|c c c} \hline  & \multicolumn{2}{c}{**MLR**} & \multicolumn{3}{c}{**ANN**} \\ \hline
**USA Stations** & \(R^{2}\) & _nRMSE (\%)_ & _nMBE (\%)_ & \(R^{2}\) & _nRMSE (\%)_ & _nMBE (\%)_ \\ \hline Bondville, & & & & & \\ Illinois & 0.990 & 5.66 & 3.15 & 0.990 & 5.67 & 3.19 \\ \hline Table Mountain, Boulder, & & & & & \\ Colorado & 0.994 & 6.21 & 4.67 & 0.994 & 6.24 & 4.72 \\ \hline Desert Rock, & & & & & \\ Nevada & 0.996 & 9.29 & 8.23 & 0.996 & 9.33 & 8.31 \\ \hline Fort Peck, & & & & & \\ Montana & 0.991 & 8.06 & 6.51 & 0.991 & 8.08 & 6.56 \\ \hline Goodwin Creek, & & & & & \\ Mississippi & 0.992 & 5.87 & 4.00 & 0.992 & 5.90 & 4.04 \\ \hline Penn State, & & & & & \\ Univ. Pennsylvania & 0.991 & 5.00 & 2.27 & 0.991 & 5.00 & 2.30 \\ \hline Sioux Falls, & & & & & & \\ South Dakota & 0.992 & 7.62 & 6.22 & 0.992 & 7.64 & 6.26 \\ \hline \end{tabular}
\end{table} 
Table 9: Model fit values for MLR (left) and ANN (right) under partial sky conditions.