Global climate models will require maps of land surface albedo as one of their inputs, and this calls for satellite based estimates of land surface hemispherical reflectances to be made. Land surfaces reflect light in a complicated way, the intensity of reflected light is a function of two directions, one incoming and one outgoing. Consequently, estimates of hemispherical reflectance made from a single look contain a systematic error. The new generation of multi-look satellite instruments should improve the estimates of hemispherical reflectance from space, but appropriate atmospheric corrections will be required. These corrections must not be computationally expensive because of the large quantities of data that must be handled in a short space of time. Nevertheless, it is important to test the corrections with more detailed calculations in order to find the uncertainties introduced by various simplifying assumptions. It cannot be assumed that the reflectance is a function of the angle between the two directions, or even that it has mirror symmetry about the plane of incidence. This asymmetry can occur when there is a preferred direction on the ground such as occurs in row plantations.We present a method for incorporating such general reflectances into stratified atmospheric radiative transfer models. We also present some preliminary results that show that a preferred direction on the ground can have an influence on the exiting radiation at the top of the atmosphere even when the optical depth is as thick as one half, and can influence the downwelling radiation at the ground under very clear sky conditions.