Discrete angle radiative transfer. 1. Scaling and similarity, universality and diffusion

Details Discrete angle radiative transfer. 1. Scaling and similarity, universality and diffusion Discrete angle radiative transfer. 1. Scaling and similarity, universality and diffusion

Jul 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990jgr....9511699l&link_type=abstract

Journal of Geophysical Research, Volume 95, Issue D8, p. 11699-11715

Physics

16

Atmospheric Composition And Structure: Cloud Physics And Chemistry

Scientific paper

In order to facilitate study of very inhomogeneous optical media such as clouds, the difficult angular part of radiative transfer calculations is simplified by considering systems in which scattering occurs only in certain directions. These directions are selected in such a way that the intensity field decouples into an infinite number of independent (e.g., orthogonal) families in direction space, each coupled only within its family. Further discretization, this time in space, lends itself readily to both analytical renormalization approaches (part 2) and to numerical calculations (part 2). We are particularly interested in scaling systems in which the optical density field has no characteristic size over a wide range of scales; these include internally homogeneous media of any shape but are more generally internally inhomogeneous and better described as fractals or multifractals. In this case, the albedo and transmission obey power laws in the thick cloud limit if scattering is conservative. By deriving powerful discrete angle (DA) similarity relations, we show that the scaling exponents that characterize these laws are ``universal'' in the sense that they are independent of the DA phase functions. We argue that these universality classes may be generally expected to extend beyond DA to include standard (continuous angle) phase functions and transfer equations. By comparing the DA equations with the diffusion equation, we show that in general the thick cloud limits of the two will be different: the thick cloud regime will only be ``diffusive'' in very homogeneous clouds, hence the term ``universality class'' is more appropriate. The DA similarity relations indicate that in scaling systems spatial variability is of primary importance, this suggests that far more research should be made to realistically model the spatial variability and to investigate its effect on radiative response, even if the angular aspect of the transfer process is made much less sophisticated than is possible in the classical plane-parallel type medium.

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