# Geographical Distribution of Global Radiation and Sunshine Duration over the Island of Cyprus
## 2 Materials and Methods
### Quality Control Process  
#### 2.2.1 Quality Control of Hourly Values  
Fingerprint plots demonstrating the variation of each radiation component are used to check for any major problems with the data before testing every single variable. In these plots, the x-axis represents a day in the year and the y-axis represents an hour of the day, with a color scale from blue to red showing the various levels of the presented variables. The graphs of all the stations do not show any major problem with the measurements. The quality control procedures for the solar irradiances are based on checking whether the measurements are within certain limits, such as physically possible limits (PPL) and extremely rare limits (ERL) as proposed by BSRN network [42]. The PPL process checks extremely large errors in radiation data, while the ERL process identifies cases that exceed the rare limits over very short time periods. The lower bound of the limits is naturally zero, although BSRN suggests \(-4\) W/m\({}^{2}\) for PPL and \(-2\) W/m\({}^{2}\) for ERL lower limits of the radiation components. The upper bound of these limits is shown in Table 2.  
The following plot illustrates the various tests outlined in the preceding paragraphs based on the hourly measurements. Figure 2 shows the highest limits of global irradiances as a function of solar zenith angle, at Pentakomo (coastal location). Similar graphs were obtained from the other locations. The analysis shows that all the data are within the proposed limits. Lefkara Dam and Zygi were excluded from the analysis because they did not pass these quality control limits. The comparison tests were concentrated on the ratios of \(k_{b}\), \(k_{d}\), and \(k_{t}\). The ratio \(k_{b}\) is always lower than 1. The upper bound of the \(k_{d}\) ratio is 1, although it can be slightly higher than 1 (i.e., 1.15). This usually occurs in the morning after sunrise or in the afternoon before sunset when the solar elevation angle is low, and the diffuse irradiance is slightly higher than that of global irradiance due to the cosine effect of the lower sun angles. Therefore, to avoid this problem, cases of diffuse irradiances below 5\({}^{\circ}\) of sun elevation angle were excluded from the dataset [43]. Only few observations were considered invalid when low \(k_{d}\) values are associated with low \(k_{t}\) values. This occurs when the sensor was covered with environmental debris. The step test was based on time consistency, which compares the difference between successive measurements. If the difference exceeds an allowed value, then both observations are flagged as suspects. [PERSON] et al. [44] proposed the following values for different \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & \multicolumn{2}{c}{**Upper Bound (W/m\({}^{2}\))**} \\ \hline  & **PPL** & **ERL** \\ \hline Global Irradiance (\(G\)) & \(1.5*G_{\text{On}}*(\cos\theta_{z})^{1.2}+100\) & \(1.2*G_{\text{On}}*(\cos\theta_{z})^{1.2}+50\) \\ \hline Direct Normal Irradiance (\(B_{n}\)) & \(G_{0n}\) & \(0.95*G_{\text{On}}*(\cos\theta_{z})^{0.2}+10\) \\ \hline Direct Horizontal. Irr (\(B\)) & \(G_{0n}*\cos\theta_{z}\) & \(0.95*G_{\text{On}}*(\cos\theta_{z})^{1.2}+10\) \\ \hline Diffuse Irradiance (\(D\)) & \(0.95*G_{\text{On}}*(\cos\theta_{z})^{1.2}+50\) & \(0.75*G_{\text{On}}*(\cos\theta_{z})^{1.2}+30\) \\ \hline \end{tabular}
\end{table} 
Table 2: The upper bounds for the “physically possible” (PPL) and “extremely rare” (ERL) limits as proposed by BSRN group, which are used for checking the radiation parameters. Figure 2: Hourly global irradiances (W/m\({}^{2}\)) as a function of solar zenith angle (SZA) with their PPL and ERL limits at Pentakomo (coastal location). variables: for hourly global irradiance, the limit was 555 W/m\({}^{2}\), and for hourly temperature, it was set to 7 \({}^{\circ}\)C, while for relative humidity he suggested the value was 45%. The dataset confirmed the limits of the above variables. Finally, the persistency test was applied to check the variability of the measurements.