The Scaling Group of the Radiative Transfer Equation

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  • 1 Theoretical Physics Group, School of Physics, University of Melbourne, Parkville Victoria 3052, Australia
  • | 2 Institute of Atmospheric Physics, The University of Arizona, Tuscon, AZ 85721
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Abstract

We show that the equation of radiative transfer is invariant under a group of simultaneous transformations of the scale (i.e., the optical thickness) and the phase function. In this way, we provide a unified explanation of various empirical scaling laws, similarity relations and other approximations (especially delta-function approximations) which have been proposed in the literature. Connections with critical-point behavior in statistical mechanics are also indicated.

Abstract

We show that the equation of radiative transfer is invariant under a group of simultaneous transformations of the scale (i.e., the optical thickness) and the phase function. In this way, we provide a unified explanation of various empirical scaling laws, similarity relations and other approximations (especially delta-function approximations) which have been proposed in the literature. Connections with critical-point behavior in statistical mechanics are also indicated.

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