Earth Space Research Group Earth Space Research Group
The method used to compute the surface solar radiation flux, originally developed by Gautier et al. (1980), is based on simple, physical modeling of the most important radiative processes occurring within the atmosphere, namely scattering and absorption by molecules, clouds, and aerosols. Since variability of surface solar flux results primarily from changes in solar zenith angle and cloudiness, the method focuses on determining the effect of clouds on surface solar flux since solar zenith angle can be computed accurately from simple formulas. The method accomplishes this by computing cloud albedo, the governing cloud parameter, from GMS VISSR measurements in the visible. The repeat coverage of the GMS VISSR data (one observation every 30 minutes) allows an adequate sampling of the diurnal cloud variability.
Images composed of 888x 444 pixels centered on equator and 155E and covering a region of 400,000 km2 are acquired every30 minutes form GMS-6 over the TOGA-COARE area from the University of Hawaii (Courtesy of P.Flament). These data have been averaged over 5x5 km2. The first step of the computational procedure is to calibrate the radiances measured by the VISSR sensor. The next step is to estimate the surface albedo. For this, we first determine from a time series of satellite images (typically 15 days), the minimum brightness value for each pixel at each observation time during the day. This minimum value defines a threshold (taken a few counts higher) that is used to classify each GOES VISSR pixel as clear or cloudy. This procedure does not allow us to determine whether the pixel is partially contaminated by clouds or not. But since we utilize full resolution data, the error introduced by not modeling the resulting effect on surface solar flux is minimized. Once the pixel's nature ( clear or cloudy) has been determined, we apply clear and cloudy sky radiative transfer models accordingly.
In clear sky conditions, surface solar flux is expressed as: Io = So (rro)2 cos q exp ( - C1/cos q)/(1- C2As)X exp [ - ao(uo×cos×q)bo] exp[ - aw(uwcos×q)bw] (1)
where So is the solar constant, r/ro is the ratio of actual to mean earth-sun distance, q is solar zenith angle, uo and uw are ozone and water vapor amounts, respectively, As is surface albedo, and ao, bo, aw, bw, C1, and C2 are coefficients (C1 and C2 depend on the type and concentration of aerosols). The term 1-C2As accounts for photons that have sustained multiple surface reflections. Equation (1), proposed by Frouin et al., (1989), differs from that of the original model, but not in essence. Ozone and water vapor amounts are specified from climatology and As is obtained by solving the following equation:
Asat (Bmin) = a + (1 - a)(1 - a1)(1 - a'o )As (2)
where Asat is the albedo measured at the satellite (the surface is assumed to reflect solar radiation isotropically), Bmin is the minimum brightness, a and a1 are direct and diffuse reflection coefficients, respectively, and a'o characterizes ozone absorption. Eq. (2) simply states that Asat is the sum of an atmospheric component (photons reflected back to space without surface reflection), and the signal reflected by the surface and diffusely transmitted to space.In cloudy sky conditions, the clear sky formulation is modified to account for reflection and absorption by clouds which are assumed to occur in one layer. Cloudy sky surface solar flux is therefore given by:
Ic = Io(1 - Ac - ac)/(1 -Ac As) (3)
where Ac is cloud albedo and ac is cloud absorption. The denominator represents the effect of multiple reflections between the cloud and the surface. This effect is generally small, except over snow/ice, condition which was encountered in the present study. Cloud albedo is obtained by solving the following quadratic equation:
Asat = a + (1 - a)(1 - a1)(1 - a'o )Ac + (1 - Ac - ac) 2 (1 - a1)(1 - ao )As (4)
where Asat is the top-of-atmosphere albedo, assuming that clouds reflect solar radiation isotropically. This equation, in fact, gives Ac in the GMS VISSR solar channel (mostly wavelengths in the visible). We assume that Ac takes the same value in the spectral interval of total surface solar flux. Depending on liquid water path, the ratio or narrowband to broadband albedo increases or decreases with sun zenith angle but the difference is small, in general.
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