A 1D radiative transfer benchmark with polarization via doubling and adding

Abstract

Highly precise numerical solutions to the radiative transfer equation with polarization present a special challenge. Here, we establish a precise numerical solution to the radiative transfer equation with combined Rayleigh and isotropic scattering in a 1D-slab medium with simple polarization. The 2-Stokes vector solution for the fully discretized radiative transfer equation in space and direction derives from the method of doubling and adding enhanced through convergence acceleration. Updates to benchmark solutions found in the literature to 7 places for reflectance and transmittance as well as for angular flux follow. Finally, we conclude with the numerical solution in a partially randomly absorbing heterogeneous medium.

Sonlu Bir Düzlem Paralel Ortamda Vektör Transfer Denkleminin Çözümü

“…These values are agreement with Refs. [3,4]. In Figure 1, the behavior of albedo and transmission factors are given according to optical variable for general Rayleigh scattering case and 0 = 0.…”

“…This equation is important to define the polarization of light in the studies including molecular atmosphere, aerosols and clouds. There are many studies on the calculations of albedo, transmission factor and two-Stokes parameters in finite plane-parallel atmosphere with different methods [1][2][3][4][5].…”

A benchmark for testing the accuracy and computational cost of shortwave top-of-atmosphere reflectance calculations in clear-sky aerosol-laden atmospheres

“…Wind speed is set to 10 m s −1 , but the Mishchenko and Travis (1997) code assumes an isotropic Gaussian distribution of (oceanic) surface slopes, so the wind orientation is not taken into account. The salinity is set to 34.3 ‰ and water refractive indices are interpolated, for each wavelength, from the data provided in Hale and Querry (1973) as inputs to the Mishchenko and Travis (1997) routine (available at https://www.giss.nasa.gov/staff/mmishchenko/ brf/, last access: 19 February 2019). The effect of shadowing is also taken into account.…”