Application and Evaluation of the Small-Angle Approximation in the Forward Radiative Transfer Program

Cloud has a significant impact on radiative forcing. It has a heating effect by absorbing the thermal radiation from surface and a cooling effect by reflecting the solar radiation back to space. Cooling effect is actually a multiple scattering process of the solar radiation. When the ensemble particle size is much larger than the solar wavelength, the single scattering of the ensemble particles has a strong forward peak. The direct computation of the multiple scattering process is time-consuming. However, the multiple scattering effect associated with the forward peak is only restricted in small angles. Consequently, the single scattering is decomposed into the forward component and the regular component. The regular component can be solved using the successive order of scattering method while the forward component can be quickly solved using the small-angle approximation. The computational time is significantly reduced and the accuracy is verified with the benchmark results.

In this presentation, the small-angle approximation is applied and evaluated in the forward radiative transfer program. The reflected and transmitted radiations in clear sky and cloudy condition are shown by given an atmospheric profile and a predefined cloud layer. Moreover, the comparisons are given in cloudy condition between applications of the small-angle approximation and other truncation method.