## 1 Introduction
Various methods are utilized to extract solar irradiance from satellite data, including empirical models that rely on historical data, physical models based on principles of physics, statistical methods used for analyzing data patterns, machine learning approaches trained on satellite-ground measurements, and radiative transfer (RT) models simulating the solar radiation's interaction with the atmosphere [13]. Each method offers unique advantages and limitations, catering to differences in data availability, computational resources, and accuracy requirements. Among the methods employed for extracting solar irradiance from satellite data, the Heliosat method [14; 15] stands out for its unique approach to approximating cloud transmission, one based on satellite-observed digital counts or calibrated radiance values. This method is particularly useful in converting satellite cloud index data to solar irradiance values, which is essential for solar radiation forecasting and energy applications. Case studies in which the Heliosat method has been used include short-term forecasting of solar radiation [11; 16; 17], solar energy assessment using remote sensing technologies [18; 19], and the deriving of shortwave solar radiation from satellite images [11; 20]. The advantages of the Heliosat method include its ability to derive cloud transmission values from satellite data, its adaptability to different satellite sensors, and its capability to provide estimates of solar irradiance based on cloud cover information, contributing to improved solar energy forecasting and resource assessment. The accuracy of solar irradiance data derived from the Meteosat Second Generation Spinning Enhanced Visible and Infrared Imager (SEVIRI) satellite operating over countries in the European Union (EU), particularly southern Spain and Switzerland, was assessed for the year 2015 using a Heliosat-based method called HelioMont, with reference to in situ measurements [21]. The results indicate that under all-sky conditions, the mean biases (MB) varied from approximately \(-5.0\) W\(\cdot\)m\({}^{-2}\) to \(55.0\) W\(\cdot\)m\({}^{-2}\). The root mean square error (RMSE) ranged approximately between \(175.0\) W\(\cdot\)m\({}^{-2}\) and \(195.0\) W\(\cdot\)m\({}^{-2}\). The validation approach employed revealed correlation coefficients (specifically Pearson's correlation coefficient, r) for HelioMont and the in situ data within a range of 0.79 to 0.92. This indicates a robust correlation between the satellite-derived solar irradiance data and the ground-based measurements. For parts of the Indian subcontinent in the South Asian region, the utilization of the Heliosat method indicates a generally positive bias in the estimated daily Global Horizontal Irradiance (GHI), as compared to ground measurements, from 2000 to 2007, typically within a range of 5%, with an RMSE averaging around 12.0% [22]. Conversely, another study [23] conducted in the Indian subcontinent employed a remote sensing-based method known as the Indian Solar Irradiance Operational System (INSIOS) to assess ground GHI measurements for the year 2018. The GHI output determined through this method during clear-sky conditions predominantly resulted in underestimations when compared to ground measurements. The MB (and RMSE) ranged from \(-\)12.5 (and \(-\)19.7) to \(-\)143.3 (206.5) W\(\cdot\)m\({}^{-2}\) across different seasons. Similarly, during cloudy conditions, the model tended to overestimate ground observations. The MB (and RMSE) varied from \(-\)35.7 (47.4) to 389.6 (427.3) W\(\cdot\)m\({}^{-2}\). Meanwhile, for parts of the Middle East region, the Heliosat method, when used for the time range of 2011-2014, yielded predominantly negative biases for the hourly data, with results ranging from \(-\)7.0% to 4.0% for all-sky conditions, and from \(-\)8.0% to 3.0% for clear-sky conditions. Under cloudy-sky conditions, biases vary significantly between stations, ranging from 16.0% to 85.0%.