## 3 Results
### Validation of Diurnal Radiation
#### 3.2.2 Validation under Daily Cloudy-Sky Conditions  
In overcast conditions, the median values of R\({}^{2}\) across all the locations remained at less than 0.85. The ASO location in India shows the lowest median R\({}^{2}\) value, of approximately 0.23 (followed by 0.43 for CAB in the EU region), while it was highest for VUW. Under cloudy conditions, among the Japanese sites, R\({}^{2}\) values drop to approximately 0.61 for TAT and 0.71 for ABS, as illustrated in Figure 5D. In contrast, the African region shows a less pronounced reduction under similar conditions, with median R\({}^{2}\) values falling to about 0.72 for GOB and 0.88 for VUW, from a baseline of near-perfect correlation (R\({}^{2}\) = 0.98) on clear days. Similarly, in the KSA location, the decrease in R\({}^{2}\) value seen on cloudy days is to approximately 0.88, underscoring a universal trend of diminished solar radiation, which is predictable during overcast weather.  
Furthermore, the MB in solar radiation estimates under cloudy skies also varies significantly between these regions. In Japan, the MB indicates an average overestimation of +22.7 W\(\cdot\)m\({}^{-2}\), with a wide range spanning from \(-\)80.9 to +125.2 W\(\cdot\)m\({}^{-2}\). Conversely, the African sites display a diverse pattern of estimation errors; GOB records a median MB of \(-\)77.3 W\(\cdot\)m\({}^{-2}\), suggesting a predominant underestimation, whereas VUW shows an overestimation, with a median MB of +20.6 W\(\cdot\)m\({}^{-2}\). The KSA location experiences a minimal underestimation with a median MB of \(-\)15.6 W\(\cdot\)m\({}^{-2}\), ranging narrowly from \(-\)30.9 to \(-\)2.2 W\(\cdot\)m\({}^{-2}\), as depicted in Figure 5E. The satellite estimates particularly performed well in KSA and HON locations, as indicated by the lower IQRs and ranges of MB in these locations (Figure 5E).  
Figure 5: Comparison of ground and Heliosat-2 GHI estimates in terms of R\({}^{2}\), MB (in W\(\cdot\)m\({}^{-2}\)), and RMSE (in W\(\cdot\)m\({}^{-2}\)) values for the diurnal radiation, considering both clear (left column) and cloudy (right column) sky conditions. Clear-sky conditions (**A–C**) are characterized by high agreement indices (R\({}^{2}\)) and low error indices (MB and RMSE), as compared to cloudy-sky conditions (**D–F**) for all the sites.  
Additionally, the RMSE increases across all locations during cloudy conditions, indicating greater variability in solar radiation estimates. Japan experiences a substantial spread in RMSE values, from 23.7 to 185.9 W\(\cdot\)m\({}^{-2}\), with a median of approximately 95.8 W\(\cdot\)m\({}^{-2}\). As for the African sites, GOB in particular shows higher RMSE values, of 151.3 compared to VUW's 84.9 W\(\cdot\)m\({}^{-2}\), suggesting a higher error magnitude under cloudy skies at the GOB site (Figure 5F). The KSA location also sees an elevation in RMSE, with values ranging from 62.3 to 148.2 W\(\cdot\)m\({}^{-2}\) and a median of about 91.8 W\(\cdot\)m\({}^{-2}\), reinforcing the global trend of increased uncertainty in solar radiation measurements during cloudier weather. The locations of EU, GOB, and ASO show higher RMSE values, consistently reaching up to 150.0 W\(\cdot\)m\({}^{-2}\), under cloudy days (Figure 5F).