Effect of limb darkening functions variations on deconvolution of wide-field-of-view measurements of earth emitted radiation

A solution is presented to the problem of deconvolving wide field of view measurements of earth-emitted radiation for the case of limb-darkening functions which are geographically dependent. The method of linear perturbations is used and the effects of limb-darkening function variations at various scales are evaluated. A simple model for the geographical variation of the limb-darkening function based on the radiant exitance is introduced. It is shown that the effect of these variations on the global average radiant exitance vanishes identically, and is insignificant for large spatial scales. For wave numbers six through twelve, the limb-darkening effects are small but possibly significant. At wave numbers greater than twelve, the noise due to meteorological variability dominates for an orbit altitude of 1100 km. The smallness of these effects is due to the smoothness of the monthly averaged radiant exitance field.