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

Subsurface remote sensing signals, represented by the irradiance re fl ectance and the remote sensing re fl ectance, 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 re fl ectance and remote sensing re fl ectance for deep and shallow water applications. The input of the parameterization are the inherent optical properties of the water - absorption a(lambda) and backscattering bb(lambda). Additionally, the solar zenith angle thetas, the viewing angle thetav , and the surface wind speed u are considered. For shallow water applications the bottom albedo RB and the bottom depth zB are included into the parameterizations. The result is a complete set of analytical equations for the remote sensing signals R and Rrs 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 Ku and Kd.