Radiative Transfer through Arbitrarily Shaped Optical Media. Part II. Group Theory and Simple Closures

Graeme L. Stephens Colorado State University, Department of Atmospheric Science, Ft. Collins, Colorado

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Abstract

This paper presents a formulation of the radiative transfer equation which allows for the distinction between various groups of spatial scales of variation that comprise the radiance field. Such a formulation provides a convenient means for studying the effects of spatial inhomogeneity and scale interaction on the radiative transfer. Notions of scale hierarchy and closure are introduced into the radiative transfer equation, and it is demonstrated how the customary treatment of partial cloudiness based on cloud amount as a weighting parameter is a special form of closure. Discussion of this particular closure and other assumptions relevant to this partial cloud treatment are presented. Another simple example of closure is described which allows for the treatment of spatial inhomogeneities as a new form of optical property. This concept is introduced into a two-stream model to demonstrate, in a gross way, the effects of inhomogeneities on radiative transfer. Comparisons with the more formal calculations of Part I are presented.

Abstract

This paper presents a formulation of the radiative transfer equation which allows for the distinction between various groups of spatial scales of variation that comprise the radiance field. Such a formulation provides a convenient means for studying the effects of spatial inhomogeneity and scale interaction on the radiative transfer. Notions of scale hierarchy and closure are introduced into the radiative transfer equation, and it is demonstrated how the customary treatment of partial cloudiness based on cloud amount as a weighting parameter is a special form of closure. Discussion of this particular closure and other assumptions relevant to this partial cloud treatment are presented. Another simple example of closure is described which allows for the treatment of spatial inhomogeneities as a new form of optical property. This concept is introduced into a two-stream model to demonstrate, in a gross way, the effects of inhomogeneities on radiative transfer. Comparisons with the more formal calculations of Part I are presented.

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