The remote-sensing reflectance R(rs) is not directly measurable, and various methodologies have been employed in its estimation. I review the radiative transfer foundations of several commonly used methods for estimating R(rs), and errors associated with estimating R(rs) by removal of surface-reflected sky radiance are evaluated using the Hydrolight radiative transfer numerical model. The dependence of the sea surface reflectance factor rho, which is not an inherent optical property of the surface, on sky conditions, wind speed, solar zenith angle, and viewing geometry is examined. If rho is not estimated accurately, significant errors can occur in the estimated R(rs) for near-zenith Sun positions and for high wind speeds, both of which can give considerable Sun glitter effects. The numerical simulations suggest that a viewing direction of 40 deg from the nadir and 135 deg from the Sun is a reasonable compromise among conflicting requirements. For this viewing direction, a value of rho approximately 0.028 is acceptable only for wind speeds less than 5 m s(-1). For higher wind speeds, curves are presented for the determination of rho as a function of solar zenith angle and wind speed. If the sky is overcast, a value of rho approximately 0.028 is used at all wind speeds.

In earlier studies of passive remote sensing of shallow-water bathymetry, bottom depths were usually derived by empirical regression. This approach provides rapid data processing, but it requires knowledge of a few true depths for the regression parameters to be determined, and it cannot reveal in-water constituents. In this study a newly developed hyperspectral, remote-sensing reflectance model for shallow water is applied to data from computer simulations and field measurements. In the process, a remote-sensing reflectance spectrum is modeled by a set of values of absorption, backscattering, bottom albedo, and bottom depth; then it is compared with the spectrum from measurements. The difference between the two spectral curves is minimized by adjusting the model values in a predictor-corrector scheme. No information in addition to the measured reflectance is required. When the difference reaches a minimum, or the set of variables is optimized, absorption coefficients and bottom depths along with other properties are derived simultaneously. For computer-simulated data at a wind speed of 5 m/s the retrieval error was 5.3% for depths ranging from 2.0 to 20.0 m and 7.0% for total absorption coefficients at 440 nm ranging from 0.04 to 0.24 m(-1). At a wind speed of 10 m/s the errors were 5.1% for depth and 6.3% for total absorption at 440 nm. For field data with depths ranging from 0.8 to 25.0 m the difference was 10.9% (R2 = 0.96, N = 37) between inversion-derived and field-measured depth values and just 8.1% (N = 33) for depths greater than 2.0 m. These results suggest that the model and the method used in this study, which do not require in situ calibration measurements, perform very well in retrieving in-water optical properties and bottom depths from above-surface hyperspectral measurements.

For analytical or semianalytical retrieval of shallow-water bathymetry and/or optical properties of the water column from remote sensing, the contribution to the remotely sensed signal from the water column has to be separated from that of the bottom. The mathematical separation involves three diffuse attenuation coefficients: one for the downwelling irradiance (K(d)), one for the upwelling radiance of the water column (K(u)(C)), and one for the upwelling radiance from bottom reflection (K(u)(B)). Because of the differences in photon origination and path lengths, these three coefficients in general are not equal, although their equality has been assumed in many previous studies. By use of the Hydrolight radiative-transfer numerical model with a particle phase function typical of coastal waters, the remote-sensing reflectance above (R(rs)) and below (r(rs)) the surface is calculated for various combinations of optical properties, bottom albedos, bottom depths, and solar zenith angles. A semianalytical (SA) model for r(rs) of shallow waters is then developed, in which the diffuse attenuation coefficients are explicitly expressed as functions of in-water absorption (a) and backscattering (b(b)). For remote-sensing inversion, parameters connecting R(rs) and r(rs) are also derived. It is found that r(rs) values determined by the SA model agree well with the exact values computed by Hydrolight (~3% error), even for Hydrolight r(rs) values calculated with different particle phase functions. The Hydrolight calculations included b(b)/a values as high as 1.5 to simulate high-turbidity situations that are occasionally found in coastal regions.

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