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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Numerical simulations show that underwater radiances, irradiances, and reflectances are sensitive to the shape of the scattering phase function at intermediate and large scattering angles, although the exact shape of the phase function in the backscatter directions (for a given backscatter fraction) is not critical if errors of the order of 10% are acceptable. We present an algorithm for generating depth- and wavelength-dependent Fournier-Forand phase functions having any desired backscatter fraction. Modeling of a comprehensive data set of measured inherent optical properties and radiometric variables shows that use of phase functions with the correct backscatter fraction and overall shape is crucial to achieve model-data closure.

Science, resource management, and defense need algorithms capable of using airborne or satellite imagery to accurately map bathymetry, water quality, and substrate composition in optically shallow waters. Although a variety of inversion algorithms are available, there has been limited assessment of performance and no work has been published comparing their accuracy and efficiency. This paper compares the absolute and relative accuracies and computational efficiencies of one empirical and five radiative-transfer-based published approaches applied to coastal sites at Lee Stocking Island in the Bahamas and Moreton Bay in eastern Australia. These sites have published airborne hyperspectral data and field data. The assessment showed that (1) radiative-transfer-based methods were more accurate than the empirical approach for bathymetric retrieval, and the accuracies and processing times were inversely related to the complexity of the models used; (2) all inversion methods provided moderately accurate retrievals of bathymetry, water column inherent optical properties, and benthic reflectance in waters less than 13 m deep with homogeneous to heterogeneous benthic/substrate covers; (3) slightly higher accuracy retrievals were obtained from locally parameterized methods; and (4) no method compared here can be considered optimal for all situations. The results provide a guide to the conditions where each approach may be used (available image and field data and processing capability). A re-analysis of these same or additional sites with satellite hyperspectral data with lower spatial and radiometric resolution, but higher temporal resolution would be instructive to establish guidelines for repeatable regional to global scale shallow water mapping approaches.Optically shallow waters, those where the bottom is visible from the water surface and measurably influences the waterleaving radiance, include inland waters through to estuarine and tropical coral reef and temperate coastal ecosystems. Over

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A spectrum-matching and look-up-table (LUT) methodology has been developed and evaluated to extract environmental information from remotely sensed hyperspectral imagery. The LUT methodology works as follows. First, a database of remote-sensing reflectance ͑R rs ͒ spectra corresponding to various water depths, bottom reflectance spectra, and water-column inherent optical properties (IOPs) is constructed using a special version of the HydroLight radiative transfer numerical model. Second, the measured R rs spectrum for a particular image pixel is compared with each spectrum in the database, and the closest match to the image spectrum is found using a least-squares minimization. The environmental conditions in nature are then assumed to be the same as the input conditions that generated the closest matching HydroLight-generated database spectrum. The LUT methodology has been evaluated by application to an Ocean Portable Hyperspectral Imaging Low-Light Spectrometer image acquired near Lee Stocking Island, Bahamas, on 17 May 2000. The LUT-retrieved bottom depths were on average within 5% and 0.5 m of independently obtained acoustic depths. The LUT-retrieved bottom classification was in qualitative agreement with diver and video spot classification of bottom types, and the LUT-retrieved IOPs were consistent with IOPs measured at nearby times and locations.