Cloud attenuation calculations make direct use of satellite information. The process involves the determination of a cloud index (CI) from satellite images and its application so as to modulate clear-sky irradiance.
As mentioned previously, the basic principle is very simple: applying the quasi-linear relationship between satellite count and surface GHI. However, its operational implementation is delicate and requires a fair amount of site – specific accounting.
Prior to CI processing, satellite data are subject to quality control and positional correction. Geometric corrections to satellite data are sometimes needed to eliminate small positional errors (in the range of 1 to 2 pixels), which occur especially with older satellite sensors. Occasionally, larger positional misplacements have to be managed by special postprocessing.
FIGURE 2.7 Comparison of AOD data: measured AERONET(Aerosol Robotic Network) daily average, MACC-modeled daily averages, and MACC-modeled monthly averages (January 2003 to January 2004); Ouagadougou, BurkinaFaso. This figure is reproduced in color in the color section.
The first step in extracting CI from a satellite sensor’s visible count is to multiply the latter by the inverse of the zenith angle’s cosine so that all image pixels have the same Sun-Earth geometry. Per Schmetz (1989), this cosine – corrected count should be approximately proportional to the global clear-sky index kt*defined as GHI/GHIclear.
The second step is to define an operational dynamic range for each image pixel. For a given location, the dynamic range represents the domain of the cosine- corrected count from its lowest possible value to its highest value—that is, from clear-sky conditions to thick overcast conditions. Figure 2.8 shows the dynamic range for a sample location over the Atlantic Ocean in the field of view of GOES-East. Note that the dynamic range evolves over time as a function of ground albedo (typically a seasonal cycle), satellite calibration decay, and satellite change.
FIGURE 2.8 Sample of dynamic range for a site over the Atlantic Ocean from the visible channel of the GOES-East satellite. GOES-13 replaced GOES-12 in May 2010, resulting in a change in the dynamic range. This figure is reproduced in color in the color section.
For a given time and location, CI is determined by the value of the cosine- corrected count, CCC, with respect to the local dynamic range per equation (equation 2.8).
UB – CCC UB-LB
where UB and LB represent, respectively, the upper and lower bound of the dynamic range at a given point in time and space.
Use of a dynamic range in semi-empirical models such as the SUNY model has the operational advantage that the satellite calibration need not be known precisely because the models are self-calibrating, as they determine the top and bottom of the dynamic range from their location-specific data history.
The top of the dynamic range represents heavily overcast conditions—deep convective cloudiness with high cloud tops. In the SUNY model, it is assumed that these conditions are common to all locations and solar geometries. Therefore, variability in the dynamic range’s upper bound over time is caused only by satellite calibration decay and/or satellite change (refer to Figure 2.8). For a given satellite, the range’s upper bound is established from data history at a few sample locations by fitting a simple exponential decay model to the data.
In the SolarGIS implementation, the satellite count is converted to on – satellite radiances prior to the CI calculation. The transformation uses calibration parameters distributed along with the satellite data and allows achieving a stable top of the dynamic range without sensor-degradation effects or signal changes between different satellites.
The lower bound of the dynamic range is a function of ground reflectivity (albedo) and its variability over time, as well as a function of both Sun-Earth and Sun-satellite geometry. Ground albedo may change over time because of vegetation – and soil-moisture content. Such seasonal changes are gradual and can be captured by keeping track of the data history using a trailing window of 60 (SUNY) and 30 (SolarGIS) days. The SolarGIS model has additional algorithms to deal with “nonstandard” data behavior in more complex geographies, such as deserts and equatorial tropical regions with thick clouds and rare occurrences of clear-sky situations, and to deal with data occurring closer to the rim of the satellite disk (with extreme satellite-view geometry).
The solar-geometry effects influencing the lower bound of the dynamic range include the following.
Specular ground reflectivity. The albedo of the ground changes as a function of the Sun-satellite angle. This phenomenon is most intense over arid areas, particularly high-reflectivity salt beds found in southwestern U. S. deserts, which act almost as mirrors. This phenomenon is also known as directional reflectance
and is observable over oceans and snow-covered surfaces. For other types of surface, these effects are also present but have a lower impact on satellite counts. Hot spot at zero Sun-satellite angle. Several authors have reported an intensification of reflectivity when the Sun-satellite angle approaches zero. The reasons advanced for this include (1) Raleigh backscattering—Rayleigh scattering is most intense in both forward and backward directions, so the clear atmosphere may appear brighter when the Sun is behind the satellite; and (2) a shadow suppression effect whereby any shadows cast on the ground by objects, ground features, or trees disappear from the satellite vantage point when the Sun is behind it and the ground appears brighter. High air-mass effect. At large solar-zenith angles, global irradiance received at the ground during clear conditions is approximately proportional to the inverse of the air mass. However, the atmosphere column above still receives considerably more solar radiation from the side. Thus, a cosine-corrected pixel will be brighter than expected because of the side-lit bright atmosphere above the considered point, scattering radiation back to the satellite.
Empirical formulations were developed in earlier versions of the SUNY model as well as in other models to attempt to individually account for these solar – geometry effects (Perez et al. 2002, 2004). However, an effective approach now used by most models is to consider several dynamic range histories: one for each time slot (hourly, half-hourly, or even quarter-hourly depending on the satellite). Over a short span of days, each dynamic range conserves roughly the same Sun-satellite geometry conditions, while dynamic ranges from different time slots represent different geometry conditions. Figure 2.9 illustrates the difference between morning and afternoon dynamic ranges’ lower bounds in an arid southwestern U. S. location with strong specular reflectivity.
In the SolarGIS approach, albedo is calculated individually for each time slot based on all classified cloudless values in a moving 30-d window. Thus, instead of identifying one value per day, the lower bound is represented by a smooth two-dimensional surface (in day and time-slot dimensions) that reflects diurnal and seasonal changes in surface albedo (Figure 2.10). The length of the moving time window is reduced in case of snow.