## 5 Conclusions  
Four semi-empirical models that use pixel values from a COMS geostationary satellite in order to extract GHI were evaluated. The models were compared using the same data time-resolution and location. The investigation was also deepened by separating the GHI based on daily, monthly, and annual evaluations, as well as on a clearness index. This study demonstrated that the Hammer model was selected as the most appropriate model for deriving the GHI over Korea, according to the RMSE and MBE. The hybrid model, which was developed from the combination of correlation formulas, was found to exhibit moderately improved accuracy and successfully simplified a lengthy procedure in the Hammer and Rigollier models. The hybrid model was also able to slightly decrease the RMSE and rRMSE of the Hammer model from 103.92 W/m\({}^{2}\) and 26.54%, to 97.08 W/m\({}^{2}\) and 24.12%, respectively. In order to replace the trial-and-error combination of the hybrid model, a machine learning model of LSTM was also presented. The LSTM model was able to predict GHI more accurately than the hybrid model, with an enhancement in rRMSE of 2%, although its rMBE was still comparable to that of the hybrid model. Semi-empirical models can accurately determine the GHI with a small number of inputs, such as \(\theta_{\text{z}}\), \(\varphi\), \(T_{L}\), \(\psi\), and z. In the context of Korea, this study provided a comparison of well-known semi-empirical models and suggested improved methods using hybrid formulas and the LSTM method. Hopefully, this study will be helpful for utilizing a semi-empirical approach to estimating solar irradiance in regions with a hot summer continental climate. P.M.P.G.--conceptualization, methodology, software, validation, formal analysis, data curation, writing--original draft preparation; R.A.A.R.--software, validation, data curation, writing--original draft preparation; H.-J.L.-- conceptualization, methodology, formal analysis, writing--review and editing, funding acquisition. All authors have read and agreed to the published version of the manuscript. Please add: This study is financially supported by grants from the National Research Foundation of Korea (NRF), Ministry of Science and ICT (2018M1A3A3A02065823, 2019R1A2C1009501) and the Korea Evaluation Institute of Industrial Technology (KEIT) (20011377) funded by the Ministry of Trade, Industry & Energy. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **RMSE (W/m\({}^{2}\))** & **rRMSE (\%)** & **MBE (W/m\({}^{2}\))** & **rMBE (\%)** \\ \hline \hline \multirow{2}{*}{Beyer} & 118.95 & 28.10 & \(-\)88.05 & \(-\)20.80 \\  & 143.45 & 41.09 & \(-\)107.27 & \(-\)30.72 \\  & 88.36 & 25.31 & \(-\)35.44 & \(-\)10.15 \\  & 89.67 & 25.75 & \(-\)28.71 & \(-\)8.24 \\  & 86.14 & 23.92 & \(-\)19.70 & \(-\)5.47 \\  & 76.45 & 21.92 & \(-\)24.28 & \(-\)6.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Accuracy of the semi-empirical models and LSTM model from October to December 2018. Data Availability Statement: Data are contained within this study. Conflicts of Interest: The authors declare no conflict of interest.