Hyperspectral remote sensing for shallow waters I A semianalytical model

TLDR

Shallow‑water remote‑sensing retrieval requires separating the water‑column signal from bottom contributions, which involves three distinct diffuse attenuation coefficients that are generally unequal, contrary to assumptions in earlier studies. The study develops a semianalytical model expressing the bottom‑reflected reflectance r(rs) in terms of in‑water absorption and backscattering to enable remote‑sensing inversion. Using the Hydrolight radiative‑transfer model with coastal‑water phase functions, the authors compute R(rs) and r(rs) across varying optical properties, bottom albedos, depths, and solar zenith angles, then derive the SA model coefficients and the parameters linking R(rs) and r(rs). The SA model reproduces Hydrolight r(rs) values within approximately 3 % error, even under high‑turbidity conditions and across different particle phase functions.

Abstract

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.