Remotely sensed reflectance and its dependence on vertical structure: a theoretical derivation

An exact expression for the remotely sensed reflectance (RSR, upwelling radiance divided by downwelling scalar irradiance) just beneath the surface of the ocean is derived from the equation of radiative transfer. It is shown that the RSR at a given depth in the ocean depends only on the inherent optical properties, the attenuation coefficient for upwelling radiance, and two shape factors that depend on the radiance distribution and volume scattering function. The shape factors are shown to be close to unity. An exact expression for the RSR just beneath the surface as a function of the vertical structure of inherent and apparent optical properties is derived. This expression is solved for an N-layered system, which presents the possibility of inverting remotely sensed reflectance data to obtain the vertical structure of chlorophyll in the ocean.