Numerical Tests of Asymptotic Single Scattering Statistics in Universal Multifractal Clouds
Abstract
In previous contributions we have presented asymptotic forms for single scattering statistics in thick universal multifractal clouds with parameters 1 < α < 2 and H=0. An essential feature was that short- and long-photon paths exhibit qualitatively different scaling behaviors. In the near regime the direct transmission is approximately exponential with a renormalized extinction coefficient κ eff< κ , where the transmission behaves as if all scattering were from the most probable singularity in the cloud density field. In the far regime, the transmission falls off much more slowly (on account of "Levy holes"). A study of the moments of the photon pathlengths also supports this idea. The negative moments obey a scaling law algebraic in κ , while the positive moments follow logarithmic scaling according to (log κ )-α . We present now the results of numerical simulations (Monte Carlo and discrete angle radiative transfer equations) that address the degree to which the above are relevant to light scattering in real clouds. Three issues are addressed. First, the asymptotic formulas rely on the underlying assumption that the actual multifractal water density field over all but the largest length scales may be replaced by the bare field developed to the same scale. A second issue is that real cloud density fields are not conserved but have H≈ 1/3. Finally, we have argued that if density correlations are ignored the multiple scattering should be well-described by an even softer effective extinction coefficient κ eff≈ (log κ ){α /2}. We examine the validity of this conjecture and the degree to which correlations require modification.
- Publication:
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AGU Spring Meeting Abstracts
- Pub Date:
- May 2004
- Bibcode:
- 2004AGUSMNG22A..06W
- Keywords:
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- 0360 Transmission and scattering of radiation;
- 3210 Modeling;
- 3250 Fractals and multifractals