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

Abstract 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.