A note on the use of the two‐stream delta‐scaling approximation for calculating atmospheric photolysis rate coefficients

Abstract

The delta‐scaling approximation is widely used in radiative transfer models to improve the accuracy of calculated irradiances under strongly forward scattering conditions. At completion of the scaled radiative transfer calculations, the inverse transformation (or descaling) is applied to partition the total downward irradiance, which is assumed invariant with respect to the scaling/descaling transformation, into its diffuse and direct components. However, this invariance does not apply to the total downward actinic flux, and ambiguities arise when the actinic flux components are calculated from either scaled or descaled components of the irradiance. The problem is particularly severe in two‐stream models because of the lack of angular resolution. We use a realistic example (the calculation of the photodissociation rate coefficient, or J value, for the photolysis reaction NO2 → NO + O(3P)) to show in particular that, for high Sun and low surface albedo, the use of descaled J values leads to large overestimation of rather constant or modest increases of J values below a thin cloud or aerosol layer. Even larger overestimations of J values are found near the top of a thick cloud layer at high Sun when descaling is used. Use of scaled values appears preferable under most practical conditions, although they, too, suffer from inaccuracies generally associated with two‐stream methods.