A new numerical model to compute photolysis rates and solar heating with anisotropic scattering in spherical geometry

For calculating photolysis rates and solar heating in the atmosphere, the radiation field has to be calculated very accurately. Previous investigations have shown that for large solar zenith angles a solution of the radiation equation which accounts for the Earth's curvature is needed. A new simplified version of the 3D radiation equation in spherical geometry allowing for anisotropic scattering is presented. The horizontal variation of physical quantities, the variation of the solar zenith angle with different longitude and latitude for the scattering calculation for one vertical column of air and any effects of refraction are neglected. A numerical model is introduced which efficiently solves this new 3D radiation equation accurately. The effects of anisotropic scattering are shown to be very important for the directional dependence of the scattered intensity. Anisotropic scattering by aerosols and air molecules can change the intensity in certain directions by up to 180% and 25%, respectively. However, most of these changes cancel each other out when averaged over all angles, so that the effect of anisotropic scattering for large solar zenith angles on the mean intensity (actinic flux) is much smaller, i.e. less than 10%. For the heating rates, the effect of anisotropic scattering for large solar zenith angles is even smaller, being less than a few percent. Generally, the effects of anisotropic scattering and the effects of including aerosols are the larger on higher altitudes the larger the solar zenith angle is. Results of the model are shown to compare well with results of previous investigations, including the independent work of Dahlback and Stamnes. The agreement is especially good in the case of isotropic scattering by air molecules and neglecting the effects of aerosols.