Confirmation of Helmholtz Reciprocity Using ScaRaB Satellite Data

The Helmholtz reciprocity principle is often invoked to derive the bidirectional reflectance distribution functions, then the anisotropic function, used for converting satellite radiance measurements into fluxes in Earth radiation budget studies. However, it has seldom been checked by satellite observation. This is only possible using satellites in low but non-Sun-synchronous Earth orbit, and even in this case situations allowing reciprocity verification are rare. The ScaRaB (Scanner for Radiation Budget) radiometer on board Meteor-3-07 provided non-Sun-synchronous observations of the Earth from March 1994 to February 1995. Considering only clear-sky desert scenes which may be presumed to be unchanging, enough viewing/illumination geometry pairs to check the reciprocity principle, using reflectances averaged over a small (1.25°×1.25°) study areas can be obtained. We define a normalized reciprocity departure, which is zero when reciprocity is perfectly respected. The distribution of this parameter shows that the reciprocity principle is verified to better than 5% in 75% of the cases (and 1% in a third of the cases). We also define a parameter analogous to the normalized reciprocity departure, measuring anisotrophy of reflectance for arbitrary viewing/illumination geometry pairs, which would be zero for Lambertian reflection. Comparing the distributions of these parameters with the normalized reciprocity departure, we show that the reciprocal viewing/illumination geometry pairs are very distinct from the arbitrary pairs. This confirmation of the Helmholtz reciprocity principle reinforces our confidence in using it to construct anisotropic reflectance function from measurements for which not all viewing or illumination geometries are sampled.