Fast and accurate 4 and 6 stream linearized discrete ordinate radiative transfer models for ozone profile retrieval

The global and long-term measurement of ozone vertical and horizontal distributions is one of the most important tasks in the monitoring of the earth's atmosphere. A number of satellite instruments are capable of delivering ozone profile distributions from UV nadir backscatter measurements. Retrieval algorithms should be efficient enough to deliver profiles in real-time without compromising accuracy. Such algorithms require a radiative transfer model that can generate quickly and accurately both simulated radiances and Jacobian matrices of weighting functions. We develop fast and analytic 4 stream and 6 stream linearized discrete ordinate models designed to satisfy performance and accuracy requirements for such an algorithm. The models have the pseudo-spherical treatment of the direct beam attenuation. For anisotropic scattering we use the delta-M scaling method to deal with strong forward scattering peaks. We demonstrate that the accuracy of the models is improved greatly upon application of a single scatter correction based on an exact specification of the phase function. For wide-angle off-nadir viewing, a sphericity correction is developed to deal more precisely with attenuation in a curved atmosphere. Radiances and weighting functions for the 4 and 6 stream models are compared with 20 stream output from the LIDORT model. We show that for the UV range pertinent to ozone profile retrieval from space, the 4 stream model generates backscatter radiances to an accuracy > 1.25% for all viewing situations in a clear sky Rayleigh and background aerosol reference atmosphere, and up to 1.75% for a number of special scenarios with optically thick particulate layers. Six stream radiances are accurate to the 0.25% level for clear sky situations, and 0.65% for the special cases; weighting functions for the 6 stream output are accurate to 2% in all cases. We discuss the implications of these comparisons regarding the performance and accuracy of the radiative transfer forward model in the ozone profile retrieval context. (C) 2002 Elsevier Science Ltd. All rights reserved.