where pas(!) is reflectance due to single scattering by aerosol. Since the contribution to scattering by air molecules is essentially constant, the radiance at the sensor's viewing angle due to Rayleigh scattering is a known function of solar elevation, wavelength and surface atmospheric pressure483 and so pr(!) can be calculated and is the same for all pixels.
To estimate the aerosol contribution, advantage is taken of the fact that water absorbs light strongly in the red/near-infrared region, and so essentially all the radiance measured at this end of the spectrum can be attributed to scattering within the atmosphere. SeaWiFS bands 7 (765 nm) and 8 (865 nm) are suitable for the purpose. At these wavelengths pw(4) in eqn 7.6 can be assumed to be zero, Rayleigh scattering can be calculated as we have indicated, the reflectance attributable to aerosol accordingly is
and so we obtain the ratio of aerosol reflectance for the two wavebands e(l7, l8)=pas||y (7.8)
The aerosol reflectance ratio, as in eqn 7.8, is a smoothly varying function of wavelength, which usually conforms approximately to e(4;, 40=0^" (7.9)
where n is known as the Angstr0m exponent. In the simple situation, envisaged above, in which multiple scattering is small enough to be disregarded, e(47, 48) could be determined from experimental data in accordance with eqn 7.8, and then used to determine the n exponent in eqn 7.9. With this value of n, e(4i, 48) could be calculated for the other wavebands of interest, and then in turn the corresponding values of pas(4).
When, as is more often than not the case, multiple scattering is too significant to be ignored, it is [pa(4) + par(4)], rather than pas(4), which must be calculated. In the approach used by Gordon and Wang (1994) it is assumed, once again, that pw(4) is zero at 765 and 865 nm, so for these wavebands we can write
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