# Method for converting satellite measurements into downward solar irradiance

A variety of methods developed on the basis of the combination of radiation transmission theory and observations can convert satellite measurements into downward solar irradiance.

We divide these methods into one-step and two-step methods (Figure 1). According to the different information used, the one-step method can be further subdivided into two categories.

Take the two-step method of retrieving solar radiation on the surface as an example. First, use satellite retrieval of cloud attributes. The next step is to use cloud properties and auxiliary information (for example, surface reflectance, including understanding of snow cover, atmospheric humidity, and aerosol concentration.) in the radiation transfer model to retrieve the surface solar radiation.

The two-step method is especially suitable for short-term solar forecasting. When using the two-step method, users can determine cloud properties in the first step, including cloud height, type, and optical thickness. As shown in Figure 1, NWP models such as the Global Prediction System (GFS) can be used to understand the wind at the height of the cloud, thereby understanding the advection movement of the cloud. In the prediction stage, by determining the position of advection clouds, the radiation transmission model can predict the surface solar radiation. With the increase in the number of satellite channels available, it is expected that the inversion of cloud properties will also improve. In addition, radiation transmission models of different complexity can be selected according to the required accuracy.

1. One step method
The one-step method has both physical and semi-empirical characteristics.

① Empirical model
The empirical model uses the relationship between satellite and ground measurements to invert surface radiation (Figure 1), as Tarpley and Cano et al. have proposed such methods. Most empirical methods assume a quasi-linear relationship between transmittance and satellite measurements based on the energy balance relationship. The formula used here to retrieve the total horizontal radiation (GHI) is as follows:
GHI=GHI(max)x(1-N)+GHI(min)

Among them, GHI (max) is the value of clear sky; GHI (min) is the smaller value under dense cloud conditions; N is the cloud index, defined by Cano et al.:
N=(C-C(min))/(C(max)-C(min))

Among them, C, C (min) and C (max) are the current value, minimum value (usually under clear sky conditions) and maximum value of satellite observations, respectively. There is a linear correlation between these values ​​and satellite radiation, but the calculation process is independent of corrective measures. The standardized value can avoid changes caused by the geometric structure of the sun and the distance between the sun and the earth. In addition, the longer atmospheric path and backscatter “hot spot” angles have been corrected.

②Physical method
Another one-step method directly inverts the surface radiation observed by satellites based on the radiation transmission theory, which we call the physical method (Figure 1). Regardless of whether the calculation of radiation transmission involves a single broadband calculation or multiple calculations in different bands, this type of model can be divided into two types: broadband method and spectroscopy. Gautier et al.’s broadband method used several days of satellite pixels to determine thresholds under clear sky and cloudy conditions, and then used separate clear sky and cloudy models to calculate direct surface radiation (DNI) and GHI. The clear sky model initially included only water vapor and Rayleigh scattering, and then gradually included ozone and aerosols. On the assumption that the atmosphere has no significant attenuation under clear sky and cloudy conditions, Dedieu et al. established a method that combines the influence of clouds with the atmosphere. This method also uses the time sequence of the images to determine the clear sky instance used to calculate the surface reflectance. Darnell et al. established a parametric model that can calculate the surface radiation using the product of the top of the atmosphere (TOA) radiation, the atmospheric transmittance and the cloud transmittance. The model was established using polar orbiting satellite data and using surface and satellite measurements to establish the relationship between cloud transmittance and planetary reflectivity.

Moser and Raschke established a model based on the premise that GHI is related to partial cloud cover. The model retrieved solar radiation in Europe by using Eurometeor Satellite data. In the visible range, part of the cloud cover is a function of satellite measurements. This method uses a radiative transfer model to determine the boundary between clear sky and cloudy sky. Stuhlmann et al. improved the model by adding altitude dependence, additional components, and multiple reflections in the full sky mode. Pinker and Ewing established an important spectral model, dividing the solar spectrum into 12 sections, and applying Delta-Eddington radiation transmission to a three-layer atmosphere. The main input value of the model is the optical thickness of the cloud that can be obtained from a variety of sources. The model was improved by Pinker and Laszlo and used in conjunction with the cloud information of the International Satellite Cloud and Climate Project (ISSCP).

2 two-step method
Once the cloud and aerosol properties are obtained by the inversion method, a separate radiation transfer model can be used to calculate the surface radiation. The input value and computing power determine the type of radiation transfer model used. When auxiliary data such as aerosol optical thickness and water vapor profile are available, complex high-precision radiation transmission models can be used to perform the above calculations.

In recent years, a variety of two-step models have been continuously developed and improved, ranging from simple empirical broadband fitting to complex multi-stream version models, and the latter can independently retrieve solar radiation in a variety of wavelength ranges. For example, the simple ASHRAE model, Heliosat-1, Heliosat-2, SOLIS model and its simplified version, Bird model, REST2, Iqbal model and simple model of solar atmospheric radiation transmission (SMARTS). For the application of renewable energy, it is very important to have the ability to accurately predict DNI and GHI under clear sky conditions. Gueymard compared 18 comprehensive clear sky models and ranked them according to accuracy. Generally speaking, models with fewer input values ​​have the advantages of simplicity and complexity, but at the same time they have lower accuracy. On the other hand, the optical properties of clouds in the two-step method make it possible to calculate the surface solar radiation more accurately under cloudy conditions.

Chandrasekhar theoretically developed the discrete ordinate radiation transfer method for solving the radiation transfer equation. Similar methods have also been used to formulate some stable computer solutions, such as the discrete ordinate radiative transmission (DISORT) developed by Stamnes et al. and used to build some multi-stream accurate radiative transmission models, such as the Santa Barbara DISORT atmospheric radiation transmission model (SBDART), Streamer model, AER rapid radiant transfer model (RRTM) and MODTRAN model.