Evaluation of the pseudo-spherical approximation for backscattered ultraviolet radiances and ozone retrieval

The pseudo-spherical approximation for solving the radiative transfer equation has been used for many years in an attempt to account for the sphericity of the atmosphere. However, even with this ''correction'' there has been some uncertainty about the accuracy of the radiances calculated by using this method at large solar zenith angles. With a new model for numerically solving the radiative transfer equation in a spherical atmosphere the accuracy of the pseudo-spherical approximation can now be evaluated. The comparisons between the pseudospherical and spherical models presented in this paper for backscattered ultraviolet (BUV) radiances show virtually no difference for the nadir direction. The off-nadir radiances, however, show large differences (+/-8%) for a solar zenith angle of 85 degrees and depend on the solar zenith angle and azimuth angle as well as the view angle. These differences increase rapidly at larger solar zenith angles to nearly 20% at 88 degrees. This disagreement is primarily caused by the incorrect attenuation of the solar radiation along the observers' line of sight in the pseudo-spherical method. Differences are also exhibited in the multiple-scatter component but are generally much smaller than the solar attenuation term. In general, the resultant error in total ozone estimation can be as large as 6% but is less than 1% for the Nimbus 7 total ozone mapping spectrometer.