Deconvolution of Wide Field-of-View Radiometer Measurements of Earth-Emitted Radiation. Part I: Theory

Abstract

The problem of relating satellite measurements from wide field-of-view (WFOV) radiometers to the radiant exitance emitted from the top of the atmosphere is treated. The problem is formulated as an integral equation to be solved for the radiant exitance distribution in terms of the measurements. An analytical solution to this integral equation in terms of spherical harmonies is presented for the case in which the directional dependence of the outgoing radiation is a function of zenith angle only. It is shown that the resolution which can be obtained under real conditions is limited. The sensitivity of the derived radiant exitance distribution to the directional dependence of the out-going radiation is studied, and results are presented for WFOV flat-plate and spherical radiometers and for restricted field-of-view flat-plate radiometers. It is demonstrated that this sensitivity is a function of the scale of spatial resolution; thus higher resolutions in the radiant exitance distribution are more sensitive to variations in the directional dependence. The technique is applied to measurements of earth-emitted radiation from the Nimbus 6 ERB (Earth Radiation Budget) experiment WFOV radiometer to produce a resolution enhanced map of emitted radiation for the month of August 1975. For this case, the limit of resolution appeared to be spherical harmonies of degree 15. Comparison with results from the ERB scanning radiometer shows very good agreement.