Comparative analysis of radiative transfer approaches for calculation of plane transmittance and diffuse attenuation coefficient of plane-parallel light scattering layers.

We present an analysis of a number of different approximations for the plane transmittance Tp and diffuse attenuation coefficient Kd of a semi-infinite, unbounded, plane-parallel, and optically homogeneous layer. The maximally wide optical conditions (from the full absorption to the full scattering and from the fully forward to the fully backward scattering) were considered. The approximations were analyzed from the point of view of their physical limitations and closeness to the numerical solution of the radiative transfer equation for the plane transmittance. The main criterion for inclusion of the models for analysis was the possibility of practical use, i.e., approximations were well parameterized and included only easily measured or estimated parameters. A detailed analysis of errors for different Tp and Kd models showed that the two-stream radiative transfer Ben-David model yields the best results over all optical conditions and depths. However, the quasi-single-scattering and polynomial Gordon's approximations proved to be the best for the depths close to zero.

Comparative analysis of radiative transfer approaches for calculation of diffuse reflectance of plane-parallel light-scattering layers.

We present an analysis of a number of different approximations for the diffuse reflectance (spherical and plane albedo) of a semi-infinite, unbounded, plane-parallel, and optically homogeneous layer. The maximally wide optical conditions (from full absorption to full scattering and from fully forward to fully backward scattering) at collimated, diffuse, and combined illumination conditions were considered. The approximations were analyzed from the point of view of their physical limitations and compared to the numerical radiative transfer solutions, whenever it was possible. The main factors impacting the spherical and plane albedo were revealed for the known and unknown scattering phase functions. The main criterion for inclusion of the models in analysis was the possibility of practical use, i.e., approximations were well parameterized and only included easily measured or estimated parameters. We give a detailed analysis of errors for different models. An algorithm for recalculation of results under combined (direct and diffuse) illumination also has been developed.

Comparison of chlorophyll a concentration detected by remote sensors and other chlorophyll indices in inhomogeneous turbid waters.

A new analytical approach for retrieval of the vertically weighted chlorophyll a concentration (Chl(rs)) detected by remote sensors is presented. Model calculations were carried out for the turbid waters of Lake Kinneret, Israel, and showed that Chl(rs) may be replaced by the average chlorophyll a concentration (Chl(p)) within the upper "penetration layer" 0-Z(p). The study also showed a high correlation between Chl(rs) and Chl concentration averaged in the other depth layers, namely, the 0-1 m layer, the euphotic layer (0-Z(e)), and the production layer (0-Z(pr)). Our findings are closely related to models developed for the world ocean, with the exception of periods when the dinoflagellate Peridinium gatunense blooms in the lake. We showed the effect of the pattern of vertical Chl distributions within the penetration layer on the difference between Chl(rs) and other Chl indices was conspicuous when the Chl maximum was in the uppermost 0- m layer of the water column. We assume that the presented approaches are instrumental for further development of optimal, locally adapted algorithms for remote sensing of Chl in any type of natural waters.