## 3 Global Horizontal Irradiance Models
### Cloud Index Formula  
The schematic diagram in Figure 2 illustrates the flow to derive the GHI using the semi-empirical models. The two important procedures are the CI estimation, which represents the cloudiness over the earth's surface based on a satellite image, and the calculation of the clear-sky irradiance using atmospheric data. Thus, the GHI can be determined as the decrease in the clear-sky irradiance due to the CI. Normalization of satellite image data is mandatory to obtain a CI that is independent from optical and geometric effects [1]. The air mass and backscatter effects mainly cause optical distortion in image data. The air mass effect occurs because sunlight is scattered and absorbed by particles when it passes through the atmosphere. As a result, the closer the sun is to the horizon, the stronger the air mass effect is. The backscatter effect, which is also known as the hot-spot effect, implies that sunlight more significantly goes back in the sun's direction after scattering by atmospheric particles. Thus, the sensor system overestimates the ground albedo when the satellite is close to the sun. Each semi-empirical model has its own correction formula, which was originally developed using its satellite systems and local stations. The conversion formulas from raw satellite pixel data (\(C_{sat}\)) to normalized data (\(CC\)) are presented in Table 2. The Beyer and Hammer models include a correction factor (\(C_{0}\)) for the air mass and backscattering effects, where \(C_{0}\) is determined through \(\theta_{x}\), backscattering angle (\(\psi\)), and satellite zenith angle (\(\varphi\)). Figure 2: Procedure to derive solar irradiance from satellite images. The production of the solar constant (\(I_{0}\)) and the eccentricity correction of the sun-to-earth distance (\(\varepsilon\)) represent the extraterrestrial irradiance. The Rigollier model extracted its correction factor (\(C_{0R}\)) using some equations from the European Solar Radiation Atlas (ESRA) model. To obtain \(C_{R}\), clear-sky diffuse irradiance (DHI\({}_{CR}\)), transmittance from the sun to the earth (\(T\)), and transmittance from the earth to the satellite system (\(T_{sat}\)) were computed. The parameters \(\theta_{z}\), \(\varphi\), and \(T_{L}\) were the key input variables for determining the energy that is scattered in the atmosphere and evaluated via the ESRA model. The maximum total irradiance of the visible sensor (\(I_{0 met}\)) was obtained from the convolution of the spectral distribution of \(I_{0}\) by the spectral sensitivity curve of the radiometer [3]. To obtain further details on the normalization process, the reader is encouraged to refer to [PERSON] et al. [3] and the ESRA [32]. Contrary to the other three models, the [PERSON] model introduced dependence on the sun elevation (\(\gamma\)) and air mass (\(AM\)) to normalize pixels from air mass effect. [PERSON] et al. [2] evaluated the backscatter correction by deriving different lower boundaries of the dynamic range from several years of recorded satellite data. However, the present study only used the data of a single year, and the backscatter effect was not considered. In addition to the models chosen in this study, more models are available throughout the literature. The combination of formulas used by various models was attempted to investigate the possibility of increasing prediction accuracy. As a result, the normalization equations provided by [PERSON] et al. [5], the clear-sky irradiance equation given by [PERSON] [33], and the GHI conversion equation proposed by [PERSON] et al. [2] were combined to create a single model. In this study, this model will be referred to as the hybrid model. Originally, [PERSON] et al. [5] used \(\theta_{z}\) and \(\psi\) as the correction factor (\(C_{0M}\)) to normalize ground albedo (\(C_{\min}\)). Clouds are the main factor attenuating solar irradiance when sunlight penetrates the atmospheric layer.