# Cloud extinction: cloud index

Cloud extinction can be calculated directly using satellite information. The calculation process includes determining the cloud index (CI) according to the satellite imager and its application in adjusting the clear sky irradiance inversion.

The basic principle of calculation is actually to use the quasi-linear relationship between the satellite remote sensing results and the ground GHI, but the operation needs to be handled carefully and requires a considerable number of characteristic site remote sensing observations.

Before cloud index processing, satellite data needs to be quality control and position correction. Sometimes it is necessary to perform geometric correction on the satellite data to eliminate the small position error (that is, the error in the range of 1 to 2 pixels). Especially the older satellite sensors will have position errors. Sometimes it is necessary to use special post-processing to deal with larger position errors.

To infer the cloud index from the satellite sensor visible light remote sensing data, the first step is to multiply the visible light remote sensing data by the reciprocal of the zenith angle cosine, so all image pixels have the same sun-earth geometry. Per Schmetz (1989) pointed out that the cosine correction value must be approximately proportional to the global clear sky index t’, that is, the second step of GHL/GHIlcaro is to define the dynamic range of each image pixel. For a specified location, its dynamic range is between the smallest possible value and the largest possible value, that is, the domain of cosine-corrected remote sensing data from clear sky to dense cloud cover. Figure 1 shows the dynamic range of the sample position over the Atlantic Ocean from the perspective of the GOES-East satellite. It is worth noting that over time, the dynamic range evolves into a function of ground albedo (generally with seasonal periodicity), satellite calibration attenuation, and satellite variation.

Within a specified time and a specified location, the cloud index CI is determined by the cosine-corrected remote sensing value CCC, taking into account the local dynamic range of each equation.
CI=(UB﹣CCC)/(UB﹣LB)

In the formula, UB and LB respectively represent the upper and lower limits of the dynamic range at a specific time point and space.
Using dynamic range in semi-empirical models such as the SUNY model has operational advantages: the model can be automatically calibrated, so the user does not need to accurately understand the calibration of the satellite. They can determine the upper and lower limits of the dynamic range based on their specific location data history.

The upper limit of the dynamic range indicates dense cloud cover, that is, deep convective cloud cover with high cloud tops. In the SUNY model, it is assumed that these conditions are common to all positions and solar geometries①. Therefore, over time, the variability of the upper limit of the dynamic range is only caused by satellite calibration attenuation or satellite changes (see Figure 1 for details). For a specific satellite, the upper limit of the dynamic range is determined based on the data history of a few sample positions by matching a simple exponential decay model with the data.

During the implementation of SolarGIS, before calculating the CI, the satellite count is converted to the on-board radiance using the calibration parameters distributed with the satellite data, and the upper limit of the dynamic range is achieved under the condition of no sensor degradation or signal changes between different satellites. The stability.

The lower limit of the dynamic range is a function of ground reflectivity (albedo), which is variable over time.

At the same time, it is also a function of the sun-terrestrial geometry and the sun-satellite geometry. Due to differences in vegetation and soil moisture, the ground albedo may change over time. However, this kind of change changes gradually with the seasons, and the 60-day (SUNY model) and 30-day (SolarGISt model) drag windows can be used to keep track of the data history to capture them.

The SolarGIS model has other algorithms to handle non-standard data behaviors in more complex geographic environments (such as deserts and equatorial tropical regions with thicker clouds and rare clear skies), and it is also used to process close to satellite images (with extreme satellite views) Geometry) data that appears on the edge.

The effect of solar geometry that affects the lower limit of the dynamic range includes the following aspects:
Specular ground reflectivity: The ground albedo varies according to the angle of the solar satellite. The ground albedo in the arid zone is the strongest, especially the salt bed in the desert of the southwestern United States, almost like a mirror. Ground albedo, also known as directional reflectivity, can be observed on ocean surfaces and snow-covered surfaces. Ground albedo will also appear on other types of ground, but it has a small impact on the results of satellite remote sensing.

Hot spots appear when the sun-satellite relative azimuth is zero degrees: According to several authors, when the sun-satellite relative azimuth is close to zero degrees, the reflectivity will increase. The reasons include the following two aspects: ①Rayleigh backscatter-forward Ray Rayleigh scattering and reverse Rayleigh reflection are the strongest, so when the sun is behind the satellite, the clear sky may appear brighter. ②Shadow suppression effect-when the shadow is cast on the ground object, if the sun is behind the satellite, the ground elements or trees cannot be observed from the satellite’s dominant position, and the ground appears brighter.

Upper atmosphere quality effect: When the sun’s zenith angle is large, the total horizontal irradiance received by the ground under clear sky conditions is approximately proportional to the reciprocal of air quality. But the atmospheric column above the ground will still receive more radiation from the side. Since the bright side atmosphere above the observation point reflects radiation to the satellite, the cosine calibration pixels will be brighter than expected. Early versions of the SUNY model and other models have established empirical formulas to try to explain different sun-geometric structure effects. However, the effective method adopted by most current models is to consider the history of several dynamic ranges, that is, one dynamic range per time interval (according to the satellite every hour, every half hour, or even every quarter hour). In just a few days, each dynamic range maintains roughly the same sun-satellite geometric structure, while the dynamic range at different times exhibits different geometric structures. Figure 2 shows the difference between the lower limit of the dynamic range in the morning and afternoon in the arid southwestern United States with strong specular reflectivity.

In the SolarGIS method, the albedo of each time interval is calculated according to all the classified clear sky values ​​in the sliding 30-d window. Therefore, the lower limit is represented by a smooth two-dimensional surface (day dimension and time gap dimension) instead of determining a value every day. The lower limit reflects the daily and seasonal changes in surface albedo (see Figure 3 for details). When it snows, the length of the sliding time window is shortened.