# Geographical Distribution of Global Radiation and Sunshine Duration over the Island of Cyprus
## 3 Results and Discussion
### Hourly Values  
#### 3.2.1 Hourly Global Irradiances as a Function of Solar Zenith Angle and Clearness Index  
The variation of the hourly measured global radiation with the solar zenith angle and the associated clearness index is illustrated in Figure 15 for the station of Pentakomo. Similar graphs were obtained from the other stations. High global irradiances are associated with high clearness index. Global irradiance decreased almost exponentially with increasing the SZA for a given \(k_{t}\) interval. The top three layers of \(k_{t}\) show the clear-sky conditions. This relationship can be expressed as:  
\[G=G_{max}*\left(\cos\theta_{2}\right)^{b} \tag{16}\]  
where \(G_{max}\) is the maximum global irradiance for each \(k_{t}\) interval and \(b\) describes how \(G\) changes with the cosine of the SZA. The dependence of \(G_{max}\) on \(k_{t}\) can be described by the cubic equation as:  
\[G_{max}=a+c*k_{t}+d*k_{t}^{2}+e*k_{t}^{3} \tag{17}\] \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Station** & **Elevation (m)** & **Period** & **Linear Equation (\(K_{T}\) vs. \(\sigma\))** & **R\({}^{2}\)** & **Quadratic Equation (\(G_{d}\) vs. \(S_{d}\))** & **R\({}^{2}\)** \\ \hline Larnaka AP & 2 & 2013–2015 & \(K_{T}=0.261+0.528^{\circ}\sigma\) & 0.91 & & \\ Larnaka AP & 2 & 2020–2021 & \(K_{T}=0.323+0.527^{\circ}\sigma\) & 0.70 & \(G_{d}=0.781+3.160^{\circ}S_{d}-0.066^{\circ}S_{d}{}^{2}\) & 0.72 \\ Pafos AP & 8 & 2020–2021 & \(K_{T}=0.231+0.561^{\circ}\sigma\) & 0.89 & \(G_{d}=5.539+0.421^{\circ}S_{d}+0.123^{\circ}S_{d}{}^{2}\) & 0.88 \\ Polis & 22 & 2019–2021 & \(K_{T}=0.239+0.519^{\circ}\sigma\) & 0.85 & \(G_{d}=6.193-0.054^{\circ}S_{d}+0.136^{\circ}S_{d}{}^{2}\) & 0.91 \\ Pentakomo & 23 & 2019–2021 & \(K_{T}=0.210+0.507^{\circ}\sigma\) & 0.87 & \(G_{d}=7.230-0.773^{\circ}S_{d}+0.185^{\circ}S_{d}{}^{2}\) & 0.89 \\ Avdimou & 51 & 2019–2021 & \(K_{T}=0.180+0.615^{\circ}\sigma\) & 0.89 & \(G_{d}=6.621-0.847^{\circ}S_{d}+0.237^{\circ}S_{d}{}^{2}\) & 0.87 \\ Menoyia & 140 & 2013–2017 & \(K_{T}=0.242+0.505^{\circ}\sigma\) & 0.91 & \(G_{d}=6.073+0.277^{\circ}S_{d}+0.116^{\circ}S_{d}{}^{2}\) & 0.85 \\ Athalassa & 158 & 2020–2021 & \(K_{T}=0.281+0.455^{\circ}\sigma\) & 0.90 & \(G_{d}=6.656-0.109^{\circ}S_{d}+0.138^{\circ}S_{d}{}^{2}\) & 0.89 \\ Athalassa & 158 & 2013–2015 & \(K_{T}=0.260+0.498^{\circ}\sigma\) & 0.91 & & \\ Choulou & 316 & 2011–2013 & \(K_{T}=0.219+0.559^{\circ}\sigma\) & 0.93 & \(G_{d}=5.453+0.481^{\circ}S_{d}+0.107^{\circ}S_{d}{}^{2}\) & 0.90 \\ Mathiatis & 395 & 2019–2021 & \(K_{T}=0.166+0.574^{\circ}\sigma\) & 0.92 & \(G_{d}=4.912+0.190^{\circ}S_{d}+0.123^{\circ}S_{d}{}^{2}\) & 0.93 \\ Kalopanayiotis & 587 & 2019–2021 & \(K_{T}=0.176+0.685^{\circ}\sigma\) & 0.95 & \(G_{d}=4.180+0.777^{\circ}S_{d}+0.135^{\circ}S_{d}{}^{2}\) & 0.94 \\ Mallia & 633 & 2019–2021 & \(K_{T}=0.174+0.610^{\circ}\sigma\) & 0.93 & \(G_{d}=6.497-0.140^{\circ}S_{d}+0.163^{\circ}S_{d}{}^{2}\) & 0.88 \\ Kambos & 634 & 2019–2021 & \(K_{T}=0.181+0.617^{\circ}\sigma\) & 0.90 & \(G_{d}=5.440+0.257^{\circ}S_{d}+0.132^{\circ}S_{d}{}^{2}\) & 0.92 \\ Farmakas & 833 & 2019–2021 & \(K_{T}=0.168+0.701^{\circ}\sigma\) & 0.95 & \(G_{d}=3.940+0.961^{\circ}S_{d}-0.117^{\circ}S_{d}{}^{2}\) & 0.93 \\ Agros & 998 & 2019–2021 & \(K_{T}=0.099+0.693^{\circ}\sigma\) & 0.88 & \(G_{d}=3.936+0.265^{\circ}S_{d}+0.146^{\circ}S_{d}{}^{2}\) & 0.92 \\ Amiantos & 1355 & 2019–2021 & \(K_{T}=0.170+0.686^{\circ}\sigma\) & 0.93 & \(G_{d}=3.988+1.092^{\circ}S_{d}+0.095^{\circ}S_{d}{}^{2}\) & 0.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: (a) Linear (\(K_{T}\) vs. \(\sigma\)) and quadratic equations (\(G_{d}\) vs. \(S_{d}\)) for the estimation of daily global irradiation (MJ/m\({}^{2}\)). (b) Linear equations between \(K_{T}\) vs. \(\sigma\) and \(G_{d}\) vs. \(S_{d}\) for the estimation of mean monthly daily global irradiation (MJ/m\({}^{2}\)). In the second step, \(b\) was obtained from analyzing the relationship between hourly \(G\) and the cosine of the zenith angle using a non-linear statistical method.