## 3 Global Horizontal Irradiance Models
### GHI Conversion Formula  
After CI and \(\mathrm{GHI}_{c}\) are given, the \(\mathrm{GHI}\) can be calculated from \(\mathrm{GHI}_{c}\) by appropriately reducing it according to CI. The reduction factor is called the clear-sky index (\(k_{c}\)) and is expressed as a correlation function. Finally, the conversion equations are presented in Table 4.  
\[\mathrm{GHI}=k_{c}\mathrm{GHI}_{c} \tag{32}\]  
Table 5 presents the input variables of all the semi-empirical models utilized in this study. Compared to the other three models, the Beyer model is the simplest and does not require \(T_{L}\) to account for the atmospheric conditions. On the other hand, the [PERSON] and [PERSON] models are the best options in terms of versatility and comprehensiveness. These \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Equation** & \\ \hline \multirow{2}{*}{Beyer} & \(\mathrm{GHI}_{B}=k_{cB}\mathrm{GHI}_{CB}\) & (33) \\  & \(k_{cB}=1-\mathrm{CI}_{B}\) & (34) \\ \hline \multirow{6}{*}{Rigollier} & \(\mathrm{GHI}_{B}=k_{cB}\mathrm{GHI}_{CR}\) & (35) \\  & \(\mathrm{CI}_{B}\leq-0.2;k_{cR}=1.2\) & (36) \\ \cline{1-1}  & \(-0.2<\mathrm{CI}_{B}\leq 0.8;k_{cR}=1-\mathrm{CI}_{R}\) & \\ \cline{1-1}  & \(0.8<\mathrm{CI}_{R}\leq 1.1;k_{cR}=2.0667-3.6667\mathrm{CI}_{R}+1.6667\mathrm{CI}_{R} {}^{2}\) & \\ \cline{1-1} \cline{2-3}  & \(k_{cP}=2.36\mathrm{CI}_{P}{}^{5}-6.2\mathrm{CI}_{P}{}^{4}+6.22\mathrm{CI}_{P}{} ^{3}-2.63\mathrm{CI}_{P}{}^{2}-0.58\mathrm{CI}_{P}{}^{2}-0.58\mathrm{CI}_{P}{} ^{2}-0.58\mathrm{CI}_{P}{}^{2}+1\) & (40) \\ \hline \multirow{2}{*}{Hybrid} & \(\mathrm{GHI}_{M}=(0.02+0.98987k_{cM})\mathrm{GHI}_{CM}\) & (41) \\  & \(k_{cM}=1-\mathrm{CI}_{M}\) & (42) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Global horizontal irradiance (GHI) conversion used for each semi-empirical model. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Equation** & \\ \hline \multirow{6}{*}{Rigollier} & \(\mathrm{GHI}_{cB}=0.7\mathrm{I}_{0}\varepsilon\cos^{1.15}\theta_{x}\) & (14) \\ \cline{2-3}  & \(\mathrm{GHI}_{cR}=\mathrm{DNI}_{CR}\cos\theta_{x}+\mathrm{DHI}_{cR}\) & (15) \\  & \(\mathrm{DNI}_{CR}=\mathrm{I}_{0}\varepsilon\cos\theta_{x}\exp(-0.8662T_{L} \delta_{R}AM)\) & (16) \\  & \(\mathrm{DHI}_{cR}=\mathrm{I}_{0}\varepsilon T_{H}\varepsilon R_{R}\) & (17) \\  & \(T_{rd}=-0.015843+0.03543T_{L}+0.0003797T_{L}{}^{2}\) & (18) \\  & \(F_{R}=A_{0}+A_{1}\cos\theta_{x}+A_{2}\cos^{2}\theta_{x}\) & (19) \\  & \(A_{0}=0.26463-0.061581T_{L}+0.0031408T_{L}{}^{2}\) & (20) \\  & \(A_{1}=2.0402-0.018945T_{L}+0.01161T_{L}{}^{2}\) & (21) \\  & \(A_{2}=-1.3025-0.039231T_{L}+0.0085079T_{L}{}^{2}\) & (22) \\ \hline \multirow{6}{*}{Hammer} & \(\mathrm{GHI}_{M}=\mathrm{DNI}_{CR}\cos\theta_{x}+\mathrm{DHI}_{cH}\) & (23) \\  & \(\mathrm{DNI}_{CH}=\mathrm{I}_{0}\varepsilon\cos\theta_{x}\exp(-0.8662T_{L} \delta_{R}AM)\) & (24) \\  & \(\mathrm{DHI}_{cH}=\mathrm{G}_{ext}\epsilon\left[\begin{array}{c}0.0065+(-0.045+0. 0646T_{L})\cos\theta_{x}+\\ (0.014-0.0326T_{L})\cos^{2}\theta_{x}\end{array}\right]\) & (25) \\ \hline \multirow{6}{*}{[PERSON]} & \(\mathrm{GHI}_{cP}=cg1I_{0}\cos\theta_{x}\exp[-cg2 AM(fh1+fh2(T_{L}-1))]\exp(0.01 AM ^{1.8})\) & (26) \\  & \(fh1=\exp\left(\frac{-2}{800}\right)\) & (27) \\  & \(fh2=\exp\left(\frac{-2}{1250}\right)\) & (28) \\  & \(cg1=0.0000509x+0.868\) & (29) \\  & \(cg2=0.0000392x+0.0387\) & (30) \\ \hline Hybrid & \(\mathrm{GHI}_{CM}=0.84I_{0}\cos\theta_{x}\exp[-0.027 AM(fh1+(T_{L}-1)fh2)]\) & (31) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Clear-sky irradiance formulas used for each semi-empirical model. models allow generating three components at once, i.e., GHI, DNI, and DHI, under clear skies. They were also demonstrated to be accurate in major areas of Europe and Africa, which include regions with a similar climate to Korea [6; 12]. The Perez model could also be a prudent candidate for application in Korea, based on the number of input variables. Note that one variable is implicit in the Perez model; [PERSON] et al.