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

Abstract

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 20Њ or less.

A semianalytical ocean color inversion algorithm with explicit water column depth and substrate reflectance parameterization

“…However, within a 1 km 3 1 km pixel, a degree of depth variability and seafloor slope is almost certain. Mobley and Sundman [2003] showed that a sloping seafloor can have an effect on water-leaving radiances and it may be possible to correct for a sloping seafloor to a certain extent by adjusting the solar incidence geometry. Investigating both the effect of a sloping seafloor on SWIM-derived products and a subsequent correction scheme is an interesting avenue of future work.…”

Environmental and Sensor Limitations in Optical Remote Sensing of Coral Reefs: Implications for Monitoring and Sensor Design

“…Linear spectral mixing at the bottom of the water column was therefore assumed [24]. The figure of 200 spectra per class was determined experimentally to ensure the variation in the in situ libraries was fully exploited while, for computational efficiency, excessive numbers of spectra were not propagated through the model (see Results and Discussion.…”

“…The benthic classes were each initially represented by a set of in situ recorded spectral reflectances linearly mixed according to the benthic composition (Table 3, Figure 4, collection methods given in [24]). In the analysis these basic reflectance spectra were translated by modelling to give total spectral reflectance above the water surface, R t , based on the parameters defined by a given set of the other system component classes and incorporating sensor noise.…”

Effects of channel morphology and sensor spatial resolution on image-derived depth estimates

“…2a). Mobley and Sundman (2003) reasoned 334 that the primary effect of a sloping bottom was to change the 335 solar incidence angle and that the slope could be accounted 336 for by using Lambert's cosine law to correct the radiance 337 computed for a level bottom (i.e., with Hydrolight). We used 338 Eqs.…”

“…We used 338 Eqs. (9) and (10) of Mobley and Sundman (2003) to 339 compute the radiance from a sloping streambed as…”