Perturbation Solution for 3D Radiative Transfer in a Horizontally Periodic Inhomogeneous Cloud Field

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  • 1 Atmospheric Science Program, Department of Physics, Dalhousie University, Halifax, Nova Scotia, Canada
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Abstract

For a vertical homogeneous plane-parallel layer with horizontal cosinusoidal periodic variations of the extinction coefficient, k = k0{1 + ε[cos(ax) + cos(by)]}, the first-order perturbation solution of the three-dimensional radiative transfer equation has been obtained. The first-order perturbation correction in cloud albedo cancels when a horizontal domain averaging is done. A correspondence exists between the distribution of the extinction coefficient and the distribution of the upwelling intensity. However, under certain conditions, the distribution of the upwelling intensity is opposite to the distribution of the extinction coefficient. If the solar zenith angle is large, shifts in the configurations of the distribution of the upwelling intensity may appear. The single scattering parameters can influence the distribution of the diffuse radiative intensity. The distribution of the heating rate inside the cloud and the distribution of the extinction coefficient are nearly coincident with each other.

Abstract

For a vertical homogeneous plane-parallel layer with horizontal cosinusoidal periodic variations of the extinction coefficient, k = k0{1 + ε[cos(ax) + cos(by)]}, the first-order perturbation solution of the three-dimensional radiative transfer equation has been obtained. The first-order perturbation correction in cloud albedo cancels when a horizontal domain averaging is done. A correspondence exists between the distribution of the extinction coefficient and the distribution of the upwelling intensity. However, under certain conditions, the distribution of the upwelling intensity is opposite to the distribution of the extinction coefficient. If the solar zenith angle is large, shifts in the configurations of the distribution of the upwelling intensity may appear. The single scattering parameters can influence the distribution of the diffuse radiative intensity. The distribution of the heating rate inside the cloud and the distribution of the extinction coefficient are nearly coincident with each other.

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