Effects of optically shallow bottoms on upwelling radiances: Inhomogeneous and sloping bottoms

If the benthic boundary in optically shallow waters is spatially inhomogeneous or sloping, the underwater light field is inherently three-dimensional (3D). Numerical simulations of 3D underwater radiances were made for environmental conditions observed in shallow Bahamian waters. The simulations show that if the pattern of bottom reflectance for an inhomogeneous but level bottom has a spatial scale much smaller than the bottom area seen by a radiometer, the inhomogeneous bottom can be replaced by a homogeneous bottom whose reflectance is the areaweighted average of the actual bottom reflectances. For large-scale patterns of bottom reflectance, the 3D light fields near the edges of bottom patches of different reflectances can be predicted from analytical models incorporating the sensor geometry and one-dimensional (1D) light fields computed for homogeneous bottoms, with errors of order 10% when compared to the exact 3D solutions. The same holds true for uniformly sloping bottoms, whose 3D light fields can be modeled in terms of the 1D light fields computed for level bottoms, with errors of less than 10% for bottom slopes of 208 or less. Optically shallow bottoms affect the reflected, upwelling radiance in various ways. Mobley et al. (2003) investigated how the bidirectional reflectance distribution function (BDRF) of a level homogeneous bottom determines the magnitude and angular distribution of the bottom-reflected radiance. If the bottom is inhomogeneous, or patchy, the upwelling radiance is a spatial function of horizontal location as well as depth; the same is true if the bottom is not level. This paper considers the effects of patchy and sloping bottoms on the upwelling radiances. One-dimensional (1D) radiative transfer models like Hydrolight (Mobley et al. 1993; Mobley 1994) are computationally extremely fast. However, to achieve their mathematical efficiency, such models require that the water inherent optical properties (IOPs, namely the absorption coefficient and the volume scattering function) and the boundary conditions (the sea surface wave statistics and the bottom BRDF) be horizontally homogeneous. Thus, the computed in-water light field can vary spatially with depth, but not with horizontal location. If the bottom BRDF varies with position, or if the bottom is not level, then the assumption of a horizontally homogeneous bottom boundary condition is violated and 1D models cannot be used. In these cases, the inherently three-dimensional (3D) light field generated by horizontal variations in the bottom boundary condition can be computed by Monte Carlo techniques. Consider, for example, a level bottom with a large seagrass patch next to a large sand patch. In principle, the entire light field is then 3D. However, near the center of the sea1 Corresponding author ([email protected]).