An array of models and techniques exist for the calculation of the atmospheric backscattered radiance and ground reflected radiance received at satellite altitudes. In remote sensing applications, where one deals in mega-byte units of data, it is essential that these models be computationally fast while retaining a reasonable degree of accuracy. We have evaluated a number of such models (Lowtran 6, Turner, Discrete ordinates method, 5S) relative to an accurate multiple scattering, multi-layer (Dave) model in order to assess the performance of these models in an inversion scheme for aerosol optical depth. The Turner and single scatter Lowtran 6 models generally produced large errors in apparent reflectance. Overall, the Turner model was not significantly better than the Lowtran 6 model except at near nadir geometries and non zero albedos. The 5S model which is orders of magnitude more rapid than the DOM model was significantly more accurate than the L6 and Turner models. The accuracy of the inversion procedures for the extraction of aerosol optical depth from satellite apparent reflectance was then analyzed for the two most precise models (DOM and 5S). For typical measurement conditions, the 5S inversion errors were found to be of the order of .1 in a turbid atmosphere case (aerosol optical depth approximately .5). The DOM produced the most impressive results in terms of comparisons with the Dave computations. It's time of execution, however, is a serious constraint with respect to satellite remote sensing applications.