An Improved Two-Stream Radiative Transfer Scheme Using Small-Angle Approximation for Multiple Scattering Computation in a Cloudy Atmosphere

Abstract:

We develop a two-stream radiative transfer scheme by combining the two-stream approximation (TSA) and the small-angle approximation (SAA) (TSA+SAA) to solve multiple scattering of incident solar radiation in a cloudy atmosphere. The TSA has been efficiently incorporated into many radiative transfer solvers for climate modeling applications. In a cloudy layer, if forward scattering is too strong, TSA may introduce nonnegligible errors. Although some scaling techniques are used to truncate the forward scattering peak and improve accuracy, significant errors are still unavoidable, especially when the cloud or aerosol layer is optically thin. The SAA has been successfully implemented in radiative transfer computations for remote sensing applications. Forward scattering can be analytically solved by SAA, which is fast and accurate in particular for an optically thin layer. In the combined TSA+SAA model, the radiative transfer equation is separated into a diffuse and a forward component. The TSA solves the diffuse component and the SAA solves the forward component. We evaluate the TSA+SAA model by comparing with other TSA schemes and the 128-stream discrete ordinate method in terms of computational accuracy and speed for flux and heating rate computations.