Calculation and downscaling of solar irradiance

①Calculation of total irradiance
Per Schmetz pointed out that Cl should be proportional to the total clear sky index kt=GHI/GHIclear. A linear relationship is used in several semi-empirical model applications, such as the Heliosat model. The relationship in the SUNY model has some non-linear characteristics, as shown in equation (1) and equation (2). The following is mainly based on experience and inferred this relationship through the analysis of 8 locations in the United States and Europe.

GHI=ktGHJIclear(0.001ktGHIclear ＋0.9)——(1)

GHI=KItm GHJIclear(0.001km GHIclear +0.9)——(2)

Kt=2.36CI5﹣6.3CI4＋6.22CI3﹣2.63CI2﹣0.58CI＋1——(3)

Some steps introduced by the SolarGIS model improve the calculation result of the clear sky index.
·The global clear sky index kt* calibration is applicable to each group of satellites (MSG, MFG, GOES and MTSAT) to explain the reasons for the differences in the spectral response functions of the visible channels of different types of satellites.
·In the original SUNY model, a fixed (decayed) upper limit (UB) is used to represent cloudy days. In the SolarGIS model, the dynamic changes of UB can account for spatial differences and seasonal changes. This importance is especially reflected in high altitude areas.
·The configuration of specific solar-terrestrial satellites can be empirically corrected. In this process, spectral effects and hot spot effects reduce the accuracy of Cl and kt. The relationship between Cl and kt in the SolarGIS model is shown in equation (4).
Kt*=CI(CI(CI(CI((0.100303 CI)-0.189451)+0.596357)-0.714985)-0.63526)+1.0 ——(4)

②Calculation of direct solar irradiance
In a rigorous physical model, the direct solar irradiance can be calculated through the radiative transmission modeling process and the total irradiance and scattered irradiance.
The main input value in the semi-empirical model, that is, the visible light radiation measured by the satellite is essentially the measured value of GHI. Therefore, in the absence of external input values ​​necessary for the transmission model to describe the structure of the atmosphere and cloud field, the most effective way to estimate DNI is to estimate DNI and scattering from GHI using a so-called decomposition model. Both SUNY model and SolarGIS adopt DIRINDEX model. The total irradiance-direct irradiance conversion model is based on the relationship between GHI and DNI (or scattering) clear sky index. These relationships can come from formal radiation transmission, or from empirical observations. The DIRINDEX model is derived from a simplified radiation transmission model, evolved from the DIRINT model, which was jointly established by Perez and his colleagues at ASHRAE. DIRINT itself is based on NREL’s pseudo-physical DISC model, which can dynamically Adjust the DISC forecast value up or down as a function of the GHI time series. DIRINDEX has further calibrated DIRINT, so its clear sky conditions are consistent with the GHI of the satellite inversion model. In essence, the DIRINT model runs twice, once using the satellite GHI is used as the input value, and the other time GHI is used as the input value. The ratio between the two is multiplied by DNIclear. The satellite DNIclear is obtained.
An example of DNI drawing is shown in Figure 1.

③Using high-resolution topographic information to downscale solar irradiance
SolarGIS post-processing GHI adopts the terrain decomposition algorithm of Ruiz-Arias et al. Since SolarGIS represents the most effective local effect of the terrain, its application is limited to the shadow effect of the terrain (excluding direct elements and scattering elements around the sun). The spatial resolution of the terrain information used by the terrain decomposition algorithm is up to 90m. This method shows that the complex terrain conditions themselves have a great impact on the irradiance (see Figure 2 for details) and reduce the average deviation, especially in the sun. Under clear sky conditions with a low altitude angle.