A rapid and accurate method for calculation of stratospheric photolysis rates with molecular scattering

Abstract

A method is presented for rapid and accurate calculations of photodissociation rates needed for photochemical modeling of the stratosphere, which include the effects of molecular scattering. Under the assumption of isotropic scattering and diffuse surface reflection, the linearity of the radiative transfer equation is used to decompose the total diffuse radiance field into two subfields that are referred to as the atmospheric and surface components. The atmospheric component accounts for the portion of the diffuse field that arises from scattering of the direct solar beam, while the surface component accounts for the portion of the diffuse field associated with radiation (direct plus diffuse) reflected by the surface that is subsequently scattered. Furthermore, the surface component has been normalized with respect to the total reflected radiation, so that it represents a relative field that is independent of solar angle and surface radiation properties that are contained in a surface scaling parameter. This independence can be effectively utilized when calculating photolysis rates for a series of sun angles, since the surface field need only be computed once. When the atmospheric and surface components are appropriately normalized, the wavelength variation of the resultant fields is sufficiently smooth that by using nine nodal points between 300 and 730 nm and cubic spline interpolation, accurate values of these fields at intermediate wavelengths are rapidly obtained. Further reductions in computational time are achieved by applying Sokolov's iterative procedure of averaging functional corrections to calculate approximate solutions for the atmospheric and surface fields at the nodal points. For wavelengths greater than 340 nm, a single iteration is sufficient to give results that agree with the exact values to better than 10% at altitudes above 15 km. Three iterations are used at shorter wavelengths due to increases in optical depth. The accuracy of the method for calculating photodissociation rates of 27 photolysis processes at 40 altitude levels between 0 and 53 km is typically better than 5% for altitudes above 10 km and all zenith angles.