The study of radiative transfer in multifractal clouds is of great interest, an important application being to Global Climate Models. In this work we develop a formalism analogous to the multifractal singularity formalism for understanding photon scattering statistics in radiative transfer in multifractals, and test the results numerically on lognormal multifractals. Although the results are only exactly valid in the thick cloud limit, the approximation is found to be quite accurate down to optical thickness of $ tau approx1$-10, so the results may be widely applicable. Furthermore we show the possibility of "renormalizing" the multifractal by replacing it with a near equivalent homogeneous medium but with a "renormalized" optical thickness $ tau sp{1/(1+C sb1)}$ where C$ sb1$ is the codimension of the mean singularity of the cloud. We argue that this approximation is likely to continue to be valid for multiple scattering, and is also compatible with recent results for diffusion on multifractals. Finally we analyze cloud liquid water content data and estimate the universal multifractal indices. We find that the scaling is respected over the whole range 5m-330km and that the cloud can in fact be reasonably described by a lognormal multifractal.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.68158 |
| Date | January 1994 |
| Creators | Brösamlen, Gerd |
| Contributors | Lovejoy, Shaun (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001401134, proquestno: AAIMM94415, Theses scanned by UMI/ProQuest. |
Page generated in 0.0358 seconds