Deconvolution of Wide-Field-of-View Measurements of Reflected Solar Radiation

Abstract

Wide-field-of-view (WFOV) radiometers have been flown as part of the Earth Radiation Budget instrument on the Nimbus 6 and 7 spacecraft and as part of the Earth Radiation Budget Experiment (ERBE) instruments aboard the ERBE spacecraft and also the NOAA 9 and 10 operational spacecraft. The measurement is the integral of the reflected solar flux distribution at the top of the earth-atmosphere system over the field-of-view of the radiometer. This paper develops the solution to this two-dimensional integral equation for the albedo distribution in terms of the measurements. The assumption is made that the bidirectional function is known and is invariant with longitude. The resulting axial symmetry of the integral operator permits the separation of the two-dimensional integral equation into a set of uncoupled one-dimensional integral equations for the latitudinal functions. This permits a better understanding of the problem while also considerably reducing the computer resources required for the solution. The one-dimensional integral equations are each approximated by a matrix equation. The matrices are each ill-conditioned, due to the resolution of WFOV data. The solution is expressed in terms of observable and unobservable components. In order to produce acceptable albedo fields from WFOV measurements, it is necessary to use ancillary data for these unobservable components. The limits of resolution are also indicated.