## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **Clearness Level** & **R2** & **RMSE (W/m2)** & **rRMSE (\%)** & **MBE (W/m2)** & **rMBE (\%)** \\ \hline \multirow{4}{*}{Beyer} & \(k_{T}\leq 0.25\) & 0.68 & 90.02 & 79.40 & \(-30.26\) & \(-26.69\) \\  & \(0.25<k_{T}\leq 0.5\) & 0.88 & 145.46 & 41.45 & \(-83.68\) & \(-23.85\) \\  & \(0.5<k_{T}\leq 0.75\) & 0.95 & 133.29 & 20.98 & \(-12.83\) & \(-2.02\) \\  & \(k_{T}>0.75\) & 0.99 & 145.97 & 16.85 & 121.16 & 13.98 \\  & \(k_{T}\) & 0.91 & 137.38 & 35.09 & \(-30.12\) & \(-7.69\) \\ \hline \multirow{4}{*}{Hammer} & \(k_{T}\leq 0.25\) & 0.73 & 84.34 & 78.64 & \(-21.65\) & \(-20.18\) \\  & \(0.25<k_{T}\leq 0.5\) & 0.87 & 105.56 & 40.14 & \(-11.01\) & \(-4.18\) \\  & \(0.5<k_{T}\leq 0.75\) & 0.96 & 106.23 & 19.89 & 0.39 & 0.07 \\  & \(k_{T}>0.75\) & 0.98 & 126.50 & 15.88 & 90.87 & 11.41 \\  & \(\text{All}\,k_{T}\) & 0.94 & 103.92 & 26.54 & 0.09 & 0.02 \\ \hline \multirow{4}{*}{Perez} & \(k_{T}\leq 0.25\) & 0.52 & 84.73 & 89.46 & \(-1.10\) & \(-1.16\) \\  & \(0.25<k_{T}\leq 0.5\) & 0.82 & 122.56 & 40.55 & \(-16.96\) & \(-5.61\) \\ \cline{1-1}  & \(0.5<k_{T}\leq 0.75\) & 0.96 & 111.29 & 20.46 & \(-17.50\) & \(-3.21\) \\ \cline{1-1}  & \(k_{T}>0.75\) & 0.98 & 103.03 & 16.35 & 57.88 & 9.19 \\ \cline{1-1}  & \(\text{All}\,k_{T}\) & 0.93 & 112.57 & 28.64 & 14.53 & 3.70 \\ \hline \multirow{4}{*}{Hybrid} & \(k_{T}\leq 0.25\) & 0.64 & 82.83 & 85.03 & 2.32 & 2.38 \\ \cline{1-1}  & \(0.25<k_{T}\leq 0.5\) & 0.85 & 113.39 & 40.90 & \(-7.36\) & \(-2.65\) \\ \cline{1-1}  & \(0.5<k_{T}\leq 0.75\) & 0.97 & 89.60 & 15.67 & \(-19.17\) & \(-3.35\) \\ \cline{1-1}  & \(\text{All}\,k_{T}\) & 0.95 & 48.24 & 5.47 & 10.06 & 1.14 \\ \cline{1-1}  & \(\text{All}\,k_{T}\) & 0.95 & 97.08 & 24.12 & \(-7.24\) & \(-1.80\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Accuracy of the GHI models by level of clearness index. than the Rigollier model. The hybrid model also took advantage of a simple clear-sky irradiance formula and improved accuracy. As a result, a simple model can be better than a complicated one if the clear-sky model is not sufficiently accurate. Figure 7 shows variations of solar irradiance under clear-sky and overcast conditions on exemplary days. In general, all the semi-empirical models were capable of estimating hourly variations. However, all the models consistently overestimated or underestimated, for instance, for the morning on 9 April, afternoon on 9 April, morning on 2 December, and so on. Such consistent estimations, regardless of model, demonstrate that either the atmospheric data to produce clear-sky irradiance are inaccurate or the assumption that only the cloud amount contributes to reducing solar irradiance is incorrect. Pollen and yellow sand dust often occur during the spring season in Korea, but clear-sky irradiance models in Table 3 may not suitably account for such regional features. More importantly, rain and snow are likely to affect solar irradiance. As evidenced by large RMSE values when \(k_{T}\) is low from Table 6, the consideration of the effects of rain and snow can improve model accuracy. In order to investigate seasonal variations of model performance, monthly rRMSE and rMBE were plotted in Figures 8 and 9. Even though seasonal variations of rRMSE are not so noticeable in Figure 8, prediction accuracy was slightly better in the spring and fall seasons. Probably, the reason was that sky in both of the seasons tends to be  
Figure 7: Daily variations of solar irradiance: (**a**) clear sky conditions and (**b**) overcast conditions. clear in Korea. Unlike rRMSE in Figure 8, rMBE in Figure 9 reveals remarkable seasonal variations independent of the model. Except for the Beyer model, overestimation only occurs during the summer season. The closer to the winter season the time gets, the larger the underestimation becomes. This seasonal change of accuracy is caused by ground albedo change [2; 47].