Radiative transfer in spherical shell atmospheres: I. Rayleigh scattering

A comparison is made between the plane-parallel approximation and the more realistic spherical shell approximation for the radiance reflected from a planetary atmosphere. In this paper we have considered a planet of radius 6371 km (the Earth) with a homogeneous, conservative, Rayleigh scattering atmosphere extending to a height of 100 km. We have found significant departures from the plane-parallel approximation. Radiance versus height distributions for both single and multiple scattering are presented. Results are presented for the fractional radiance from altitudes in the atmosphere which contribute to the total unidirectional reflected radiance at the top of the atmosphere. We have referred to this as the radiance versus height distribution in the sequel. These data will be very useful for both remote sensing applications and planetary spectroscopy. We have also found that gross violations of the principle of reciprocity do occur in the spherical shell approximation.