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PHYSICA, A, in press, 2009.
Scattering in thick multifractal clouds, Part II: Multiple scattering.
S. Lovejoy, B. P. Watson, Y. Grosdidier, D. Schertzer
Abstract
In Part I of this paper, we developed asymptotic approximations for single photon scattering in
thick, highly heterogeneous, "Log-Lévy" multifractal clouds. In Part II, theoretical multiple scattering
predictions are numerically tested using Monte Carlo techniques, which show that, due to long
range correlations, the photon paths are "subdiffusive" with the corresponding fractal dimensions
tending to increase slowly with mean optical thickness. We develop reasonably accurate statistical
relations between N scatter statistics in thick clouds and single scatter statistics in thin clouds. This
is explored further using discrete angle radiative transfer (DART) approach in which the radiances
decouple into non-interacting families with only four (for 2-D clouds) radiance directions each.
Sparse matrix techniques allow for rapid and extremely accurate solutions for the transfer; the
accuracy is only limited by the spatial discretization.
By "renormalizing" the cloud density, we relate the mean transmission statistics to those of an
equivalent homogeneous cloud. This simple idea is remarkably effective because two complicating
effects act in contrary directions: the "holes" which lead to increased single scatter transmission
and the tendency for multiply scattered photons to become "trapped" in optically dense regions,
thus decreasing the overall transmission.
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