Properties of reflected sunlight derived from a Green's function method

The inference of optical depth and particle size of clouds and aerosols using remotely sensed reflected radiance at solar wavelengths has received much attention recently. The information these measurements provide is path integrated. However, very little is known about the vertical distribution of this weighting. To characterize it, we first solve the radiative transfer equation (RTE) by a Green's function approach, and then investigate the sensitivity of the weighting to vertical inhomogeneities in the extinction by introducing a function that is closely related to the Green's function, herein called the contribution function. This function calculates the contributions to the radiance at the upper boundary of the medium by underlying layers. Three hypothetical clouds of identical optical depth but exhibiting different extinction profiles were used in this study. The contribution function was found very sensitive to the extinction profile. The global reflection and transmission matrices used to construct the Green's function, derived using an eigenmatrix method, resulted in an efficient, stable, and accurate method for calculating the emerging radiances that can be extended to multi-layered media.