An analytical model for subsurface irradiance and remote sensing reflectance in deep and shallow case-2 waters

Abstract

Subsurface remote sensing signals, represented by the irradiance reflectance and the remote sensing reflectance, were investigated. The present study is based on simulations with the radiative transfer program Hydrolight using optical properties of Lake Constance (German: Bodensee) based on in-situ measurements of the water constituents and the bottom characteristics. Analytical equations are derived for the irradiance reflectance and remote sensing reflectance for deep and shallow water applications. The input of the parameterization are the inherent optical properties of the water-absorption a(λ) and backscattering b_b(λ). Additionally, the solar zenith angle θ_s, the viewing angle θ_v, and the surface wind speed u are considered. For shallow water applications the bottom albedo R_B and the bottom depth z_B are included into the parameterizations. The result is a complete set of analytical equations for the remote sensing signals R and R_rs in deep and shallow waters with an accuracy better than 4%. In addition, parameterizations of apparent optical properties were derived for the upward and downward diffuse attenuation coefficients K_u and K_d.