Diffusivity-Factor Approximation for Spectral Outgoing Longwave Radiation

Accurate integration of directional radiance shows that the conventional diffusivity-factor approximation with a constant diffusivity angle results in an overestimation of the outgoing longwave radiation (OLR) in the window band and an underestimation in the absorption band. We propose an analytical estimation of a spectrally dependent diffusivity angle for clear-sky spectral OLR, considering actual atmospheric conditions and realistic optical path geometry. Beginning with the plane-parallel geometry, we present a new, physical explanation of the conventional diffusivity angle that applies to the gas absorption bands and derives an alternative solution for the window bands. Then a correction scheme is developed to account for the impact of the spherical Earth geometry on the diffusivity angle. The proposed method achieves higher accuracy, reducing biases to generally less than 2% in all spectral regions.