## 4 Discussion
### Regional and Seasonal Variability in Solar Irradiance  
The analyses of high RMSE and MB, as well as low R\({}^{2}\) values, in certain months across different locations reveals significant insights into the regional and temporal variability of solar irradiance estimation using Heliosat-2. In Europe, locations like CAB and CNR experience high RMSE values, particularly during winter months (e.g., January, February, and November), which coincides with low R\({}^{2}\) values, which drop below 0.3. The substantial seasonal variability, including cloudy weather and low solar angles, contributes to these discrepancies. The persistently positive MB values in CAB and CNR indicate a tendency to overestimate solar irradiance due to frequent cloud cover and varying atmospheric conditions such as aerosols and humidity levels [56].  
Japanese sites, such as ABS and TAT, demonstrate consistently high R\({}^{2}\) values, often exceeding 0.85 in March, May, and June, and robust values throughout the year. Thisstability is due to relatively predictable weather patterns and moderate latitudes [57; 58]. However, the MB values fluctuate, with significant overestimation during March-April and August-September, reflecting seasonal changes and specific events like the cherry blossom season. The RMSE values are notably lower, usually falling below 65.0 W\(\cdot\)m\({}^{-2}\) between January and March and October-December.  
In African regions, such as GOB and VUW, the R\({}^{2}\) values remain exceptionally high throughout the year, particularly from July to November, frequently surpassing 0.92. The RMSE values, however, are higher during warmer months (January, February, March, and December) and lower during cooler months (July, August, and September). GOB consistently shows a trend of underestimation, which is attributed to reflective desert surfaces. VUW exhibits a general overestimation, one influenced by seasonal vegetative changes affecting ground albedo [59; 60].  
In Saudi Arabia, the R\({}^{2}\) values are consistently high, generally exceeding 0.93, with peaks often rising above 0.97 during January, August, and September. The MB values indicate that the GHI estimates of the model are generally underestimated during January, September, and November. The RMSE values are exceptionally low, mostly below 50.2 W\(\cdot\)m\({}^{-2}\), with January and September showing values consistently below 30.0 W\(\cdot\)m\({}^{-2}\), due to the clear desert skies and minimal atmospheric disturbances [61].  
In India, sites like ASO and HON show a distinct seasonal pattern, with lower R\({}^{2}\) values during monsoon months (June-September) due to heavy cloud cover and unpredictable weather. The monsoon season significantly impacts solar irradiance estimation by introducing dense cloud formations, high humidity, and frequent rainfall, all of which reduce the accuracy of the model [62]. The MB values for ASO and HON indicate both overestimation and underestimation, influenced by seasonal variability. The RMSE values are relatively lower, reflecting the impacts of monsoon and non-monsoon periods.  
The deviations in R\({}^{2}\), MB, and RMSE values across different locations and months are driven by climatic and geographical factors such as weather variability, solar angles, atmospheric conditions, and surface reflectivity. In particular, the monsoon season in India, with its heavy cloud cover and frequent rain, greatly affects the accuracy of solar irradiance estimates, highlighting the influences of local weather processes on solar energy modeling. These factors collectively influence the accuracy of solar irradiance estimates, leading to significant monthly and regional deviations.