## 3 Results
### Annual Sky Status
\begin{table}
\begin{tabular}{l l} \hline
**Sky Conditions Regression Type** & **Regression Equation and Statistics** \\ \hline \multirow{3}{*}{Clear skies Linear fit} & SSD = DCS = \(-93.2462\times\varphi+4957.8727\) \\  & R\({}^{2}\) = 0.6088, SEE = 139.1117 h \\  & \(\rho\) = 0.7802, MBE = 0.0007 h, RMSE = 135.8380 h \\ \hline \multirow{3}{*}{Clear skies Non-linear fit} & SSD = DCS = 0.0314 \(\times\)\(\varphi^{6}-7.7403\times\varphi^{5}+788.9171\times\varphi^{4}-42,568.8275\times\varphi^{3}+\) \\  & 1,283,513.7786 \(\times\)\(\varphi^{2}-20,516,430.9885\times\varphi+135,895,710.1637\) \\ \cline{1-1}  & R\({}^{2}\) = 0.6758, SEE = 135.1449 h \\ \cline{1-1}  & \(\rho\) = -0.8017, MBE = -617.5914 h, RMSE = 734.5978 h \\ \hline \multirow{3}{*}{Intermediate skies Linear fit} & DIS = \(-11.6328\times\varphi+2097.1513\) \\  & R\({}^{2}\) = 0.0242, SEE = 137.3808 h \\  & \(\rho\) = 0.1557, MBE = -0.0006 h, RMSE = 134.1479 h \\ \hline \multirow{3}{*}{Intermediate skies Non-linear fit} & DIS = 0.7466 \(\times\)\(\varphi^{6}-171.7414\times\varphi^{5}+16,447.7466\times\varphi^{4}-839,383.0735 \times\varphi^{3}+\) \\  & 24,074,471.9759 \(\times\)\(\varphi^{2}-367,933,208.7171\times\varphi+2,340,906,375.2554\) \\ \cline{1-1}  & R\({}^{2}\) = 0.1613, SEE = 135.9527 h, MBE = 124.862 h, RMSE = 496.1667 h \\ \hline \multirow{3}{*}{Overcast skies Linear fit} & DOS = \(77.5583\times\varphi-1898.8673\) \\  & R\({}^{2}\) = 0.5840, SEE = 121.8230 h \\  & \(\rho\) = 0.7642, MBE = 0.0000 h, RMSE = 118.9562 h \\ \hline \multirow{3}{*}{Overcast skies Non-linear fit} & DOS = \(0.9297\times\varphi^{6}-212.0317\times\varphi^{5}+20,137.1181\times\varphi^{4}-1,019,440.4094\times\varphi^{3}+\) \\  & 29,014,851.7739 \(\times\)\(\varphi^{2}-440,201,405.0524\times\varphi+2,781,298,726.7945\) \\ \cline{1-1}  & R\({}^{2}\) = 0.6972, SEE = 110.9131 h \\ \cline{1-1}  & \(\rho\) = 0.7905, MBE = 172.4234 h, RMSE = 289.5424 h \\ \hline \end{tabular}
\begin{tabular}{l l} (i) & The accuracy of the estimates in the DIS case is much lower than that for the DCS or DOS ones; this visual observation is confirmed by the R\({}^{2}\) values in Table 1. (ii) \\  & The non-linear regression equations provide better fits to the data points; this result is confirmed by the higher R\({}^{2}\) values of the non-linear expressions in comparison to those for the linear equations. (iii) \\  & For the DCS and DOS cases, the linear fits are close to the non-linear ones (comparable R\({}^{2}\) values). (iv) \\  & The dispersion of the data points around the linear/non-linear regression lines is almost the same in any of the three sky types (consult the SEE values); this outcome shows that the choice of the selected regression equations gives the best possible results. (v) \\  & There is a strong/weaker decreasing trend in the duration of the DCS/DIS sky conditions with increasing \(\varphi\). (vi) \\  & There is a positive trend in the DOS sky conditions with increasing \(\varphi\); this is due to the prevalence of more cloudy weather as one moves from southern to northern Greece. (vii) \\  & There is a good correlation and a good anti-correlation between the observed and estimated values in the DCS case for the linear and non-linear fit, respectively, as shown by the \(\rho\) values in Table 1. Good positive correlation exists in both linear and non-linear models in the DOS case. On the contrary, the correlations in the DIS case are poor. (viii) \\  & The almost zero values of the MBEs in the linear fits to all sunshine duration cases imply an almost perfect match between estimated and observed values. \\ \hline \end{tabular}
\end{table} 
Table 1: Expression of the annual cases (in h) for clear, intermediate, and overcast skies over Greece as function of the geographical latitude (\(\varphi\) in degrees N) of the sites. The fits are linear and non-linear. R\({}^{2}\) = coefficient of determination; SEE = standard error of the estimate; \(\rho\) = Pearson correlation coefficient; MBE = mean bias error; RMSE = root mean square error.