# Geographical Distribution of Global Radiation and Sunshine Duration over the Island of Cyprus
## 2 Materials and Methods
### Estimation of Global Solar and Extraterrestrial Irradiances on a Horizontal Surface  
The irradiance falling on a plain at normal incidence at the top of the atmosphere (\(G_{0n}\)) can be estimated from the following equation [16]:  
\[G_{0n}=G_{sc}*[1+0.033*\cos(360*d_{n}/365)]\quad\left(\mathrm{W}/\mathrm{m}^{2}\right) \tag{1}\]  
where \(d_{n}\) is the day of the year (1.365) and \(G_{sc}\) is the solar constant (1367 \(\mathrm{W}/\mathrm{m}^{2}\)). Then, the irradiance on a horizontal plain at the top of the atmosphere can be estimated by the following equation:  
\[G_{0}=G_{0n}*\cos\theta_{z}=G_{0n}*(\cos\phi*\cos\delta*\cos\omega+\sin\phi* \sin\delta)\quad\left(\mathrm{W}/\mathrm{m}^{2}\right) \tag{2}\]  
where \(\theta_{z}\) is the solar zenith angle (SZA), which is given by:  
\[\cos\theta_{z}=\cos\phi*\cos\delta*\cos\omega+\sin\phi*\sin\delta \tag{3}\]  
\(\phi\) is the latitude of the location, \(\delta\) is the solar declination angle (deg), and \(\omega\) is the hour angle (deg). The solar declination and hour angles are estimated by the following equations:  
\[\delta=23.45*\sin[360*(284+d_{n})/365] \tag{4}\]  
\[\omega=180*(t-12)/12 \tag{5}\]  
where \(t\) is the hour of the day. The daily total global irradiation, which is obtained by a horizontal plain at the top of the atmosphere (\(G_{0d}\)), is given by the following equation:  
\[G_{0d}=(24*3.6/\pi)*G_{0n}*[(\cos\phi*\cos\delta*\sin\omega_{s}+(\pi*\omega_{s }/180)*\sin\phi*\sin\delta)]\,\left(\mathrm{kJ}/\mathrm{m}^{2}\right) \tag{6}\]  
where \(\omega_{s}\) is the sunset hour angle and is given by:  
\[\omega_{s}=\cos^{-1}(-\tan\phi*\tan\delta) \tag{7}\]  
The daily values of the radiation components are obtained from the sums of the hourly values. Furthermore, the astronomical day length (\(S_{0d}\)), which is the computed time during which the center of the solar disk is above an altitude of zero degrees (without allowance for atmospheric refraction), is given by:  
\[S_{0d}=(1/7.5)*\cos^{-1}(-\tan\phi*\tan\delta)\quad(\mathrm{h}) \tag{8}\]  
The clear-sky irradiance was estimated using the [PERSON] [39] model, which is a function of the zenith angle. This model was tested by [PERSON] [40] in Israel showing high performance. The equation involved in the said model is shown below:  
\[G_{c}=1098*\cos\theta_{z}*\exp(-0.057/\cos\theta_{z}) \tag{9}\]  
Almost a similar equation was obtained using the maximum values of global irradiances of the actinometric station of Farmakas:  
\[G_{c}=2170.5*(\cos\theta_{z})^{-0.175}*\exp(-0.578/\cos\theta_{z}) \tag{10}\]The horizontal beam irradiance (\(B\)) can be calculated from the normal beam irradiance (\(B_{n}\)) from the following equation [16]:  
\[G_{0}=G_{0n}*\cos\theta_{z}=G_{0n}*(\cos\phi*\cos\delta*\cos\omega+\sin\phi* \sin\delta)\quad\left(\mathrm{W}/\mathrm{m}^{2}\right) \tag{2}\]0  
Then, the hourly diffuse irradiance (\(D\)) is the difference of global (\(G\)) and direct horizontal irradiance (\(B\)):  
\[G_{0}=G_{0n}*\cos\theta_{z}=G_{0n}*(\cos\phi*\cos\delta*\cos\omega+\sin\phi* \sin\delta)\quad\left(\mathrm{W}/\mathrm{m}^{2}\right) \tag{2}\]1  
Estimation of Radiation Indices and Classification of the Sky Conditions  
For the classification of the sky conditions, we use the clearness index (\(k_{t}\)), which is defined as the ratio of global irradiance (\(G\)) to the extraterrestrial irradiance (\(G_{0}\)) both measured on horizontal surfaces:  
\[G_{0}=G_{0n}*\cos\theta_{z}=G_{0n}*(\cos\phi*\cos\delta*\cos\omega+\sin\phi* \sin\delta)\quad\left(\mathrm{W}/\mathrm{m}^{2}\right) \tag{2}\]2  
The upper bound of the \(k_{t}\) ratio is 1, although it can be slightly higher than 1 during partially cloudy conditions, when total irradiance may be enhanced due to the reflection of solar irradiance from the base of the clouds and from the scattering of direct irradiance due to cloud particles. Such periods of enhanced solar irradiance may last from several seconds to some minutes depending on the cloud motion [41]. Four sky categories have been proposed by [PERSON] et al.