Early scaling stochastic models of cloud and rain fields were designed to obey the simple scale invariance symmetry. The linear nature of these additive processes is intrinsically related to their single fractal dimension which is in sharp contrast with the non-linear nature of the dynamical processes within the atmosphere and with the observed multiple scaling of rain and cloud fields. We consider stochastic models corresponding to coupled cascade processes, non linearly conserving the fluxes of energy and concentration variance. Multiplicative processes, previously based on discrete cascade procedures, are generalized to their continuous limit using a dynamical generator of the cascade characterized by only two parameters which determine the full multifractal spectrum of dimensions. We show how to numerically simulate such multifractal processes with both gaussian and Levy generators, and how to perform a scale invariant "zooming" procedure in the case of clouds passively advected by a turbulent velocity field.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.60551 |
| Date | January 1991 |
| Creators | Wilson, Jean |
| 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 Meteorology.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001259815, proquestno: AAIMM72137, Theses scanned by UMI/ProQuest. |
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