## 4 Results and Discussion
Note that \(k_{T}\leq\) 0.25, 0.25 \(<k_{T}\leq\) 0.5, 0.5 \(<k_{T}\leq\) 0.75, and \(k_{T}>\) 0.75 were described as cloudy, partially cloudy, clear, and clearest sky conditions, respectively. The scatterplots in Figure 6 indicate that all the semi-empirical models worked well within a \(k_{T}\) range from 0.25 to 0.75. The [PERSON] model, the simplest model, was unable to estimate the GHI when \(k_{T}>0.75\). It is obvious that the Rigollier model underestimates when \(k_{T}\) is small, and the opposite when \(k_{T}\) is large. Error metrics for the comparisons in Figure 6 are summarized in Table 6. As indicated in Figure 6b, MBE values confirmed the biased estimation by the [PERSON] model for  
Figure 6: Comparison of modeling results with measurement data by the level of the clearness index; (**a**) [PERSON], (**b**) [PERSON], (**c**) [PERSON], (**d**) [PERSON], and (**e**) hybrid models. The clearness index, \(k_{T}\), was divided into four classes with the interval of 0.25.  
different \(k_{T}\) levels. The [PERSON] model also exhibited a similar trend to the [PERSON] model, even though MBE values were reduced. Probably, the change from underestimation to overestimation as \(k_{T}\) increases is a common feature of Helisat-2 models. On the other hand, RMSE generally decreases with \(k_{T}\), which implies difficulties in generating accurate CI or limitations of CI-based modeling. The accuracy for all sky conditions means the annual performance throughout 2018. All the models yielded promising results, in which they did not exceed 35.09% of rRMSE and \(-9.45\%\) of rMBE. It was found that the [PERSON] model outperformed the other three semi-empirical models, with the best agreement of RMSE and MBE, as 103.92 W/m\({}^{2}\) and 0.09 W/m\({}^{2}\), respectively. Despite the fact that the [PERSON] model performed the best, the differences in accuracy among the [PERSON], [PERSON], and [PERSON] models were small. The deviation in the rRMSE between the [PERSON] and [PERSON] models was only 2.1%, whereas that between the [PERSON] and [PERSON] models was only 2.64%. In contrast, the [PERSON] model exhibited the largest MBE, with the value reaching \(-36.84\) W/m\({}^{2}\). The hybrid model had slightly improved RMSE and rRMSE compared to the [PERSON] model, with the differences of 6.84 W/m\({}^{2}\) and 2.42%, respectively. Meanwhile, the MBE and rMBE of the hybrid model were slightly larger than those of the [PERSON] model, with the absolute differences 7.15 W/m\({}^{2}\) and 1.82%, respectively. However, the rMBE of the [PERSON] model significantly varies with \(k_{T}\), such that rMBE exceeds \(-20\%\) when \(k_{T}\leq 0.25\). The rMBE of the hybrid model is fairly constant regardless of \(k_{T}\) under the maximum absolute value of 3.35%. The separation of \(\text{GHI}_{c}\) into \(\text{DNI}_{c}\) and \(\text{DHI}_{c}\), such as in [PERSON] and Hammer models (refer to Table 3) does not guarantee better accuracy. As shown in Table 6, the [PERSON] and Rigollier models demonstrated contrasting accuracies, either very good or very poor, in this study. Although the Beyer model adopted a very simple formula that does not address atmospheric conditions via \(T_{L}\), it produced better accuracy