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A remote sensing reflectance model, which describes the transfer of irradiant light within a homogeneous water column has previously been used to simulate the nadir viewing reflectance just above or below the water surface by Bostater, et al. Wavelength dependent features in the water surface reflectance depend upon the nature of the down welling irradiance, bottom reflectance and the water absorption and backscatter coefficients. The latter are very important coefficients, and depend upon the constituents in water and both vary as a function of the water depth and wavelength in actual water bodies. This paper describes a preliminary approach for the analytical solution of the radiative transfer equations in a two-stream representation of the irradiance field with variable coefficients due to the depth dependent water concentrations of substances such as chlorophyl pigments, dissolved organic matter and suspended particulate matter. The analytical model formulation makes use of analytically based solutions to the 2-flow equations. However, in this paper we describe the use of the unique Cauchy boundary conditions previously used, along with a matrix solution to allow for the prediction of the synthetic water surface reflectance signatures within a nonhomogeneous medium. Observed reflectance signatures as well as model derived 'synthetic signatures' are processed using efficient algorithms which demonstrate the error induced using the layered matrix approach is much less than 1 percent when compared to the analytical homogeneous water column solution. The influence of vertical gradients of water constituents may be extremely important in remote sensing of coastal water constituents as well as in remote sensing of submerged targets and different bottom types such as corals, sea grasses and sand.
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