A NEW SPHERICAL MODEL FOR COMPUTING THE RADIATION-FIELD AVAILABLE FOR PHOTOLYSIS AND HEATING AT TWILIGHT

Accurate computation of atmospheric photodissociation and heating rates is needed in photochemical models. These quantities are proportional to the mean intensity of the solar radiation penetrating to various levels in the atmosphere. For large solar zenith angles a solution of the radiative transfer equation valid for a spherical atmosphere is required in order to obtain accurate values of the mean intensity. Such a solution based on a perturbation technique combined with the discrete ordinate method is presented. Mean intensity calculations are carried out for various solar zenith angles. We compare these results with calculations from a plane parallel radiative transfer model in order to assess the importance of using correct geometry around sunrise and sunset. This comparison shows, in agreement with previous investigations, that for solar zenith angles less than 90-degrees adequate solutions are obtained for plane parallel geometry as long as spherical geometry is used to compute the direct beam attenuation; but for solar zenith angles greater than 90-degrees this "pseudo-spherical" plane parallel approximation overestimates the mean intensity. At 400 nm this overestimation is as much as 30% between 10 and 30 km for a solar zenith angle of 98-degrees, while at 300 nm it is about 20% between 40 and 60 km for a solar zenith angle of 96-degrees. The assumption of isotropic rather than Rayleigh (molecular) scattering may lead to an incorrect assessment of the radiation field available for photolysis and heating. Thus, at 450 nm isotropic scattering leads to an underestimation of the mean intensity of a few percent when the Sun is above the horizon increasing to as much as 15% when the Sun is below the horizon. Model computations of zenith sky intensities agree well with twilight observations of Umkehr curves including the location of the minimum point (second Umkehr).