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Four-Stream Isosector Approximation for Solar Radiative Transfer

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  • 1 Canadian Centre for Climate, Atmospheric Environment Service, University of Victoria, Victoria, British Columbia, Canada
  • | 2 Atmospheric Science Program, Dalhousie University, Halifax, Nova Scotia, Canada
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Abstract

For radiative transfer in a thin atmosphere, an analytical four-stream isosector approximation for solar radiative transfer is presented. This approximation method is based on the assumption of four spherical sectors of isotropic intensities. Calculations show that the four-stream isosector approximation model substantially improves the accuracy in reflection, transmission, and absorption with respect to the Coakley–Chýlek model. For an optical thickness less than unity, the four-stream isosector approximation has errors mostly under 5%, in contrast to errors up to 20% or higher for the Coakley–Chýlek model. This four-stream isosector approximation can be applied to atmospheric aerosol layers or thin cirrus clouds.

Corresponding author address: Dr. Jiangnan Li, Canadian Centre for Climate, Atmospheric Environment Service, P.O. Box 1700, University of Victoria, Victoria, BC V8P 2Y2 Canada.

Email: acrnrjl@ec.gc.ca

Abstract

For radiative transfer in a thin atmosphere, an analytical four-stream isosector approximation for solar radiative transfer is presented. This approximation method is based on the assumption of four spherical sectors of isotropic intensities. Calculations show that the four-stream isosector approximation model substantially improves the accuracy in reflection, transmission, and absorption with respect to the Coakley–Chýlek model. For an optical thickness less than unity, the four-stream isosector approximation has errors mostly under 5%, in contrast to errors up to 20% or higher for the Coakley–Chýlek model. This four-stream isosector approximation can be applied to atmospheric aerosol layers or thin cirrus clouds.

Corresponding author address: Dr. Jiangnan Li, Canadian Centre for Climate, Atmospheric Environment Service, P.O. Box 1700, University of Victoria, Victoria, BC V8P 2Y2 Canada.

Email: acrnrjl@ec.gc.ca

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