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Proceedings Paper

Universal multifractal theory and observations of land and ocean surfaces, and of clouds
Author(s): Daniel Lavallee; Shaun Lovejoy; Daniel Schertzer
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Paper Abstract

The extreme variability of geophysical fields can be characterized by scale invariant (sensor resolution independent) 'codimension' functions, which are exponents characterizing the probability distribution. These codimension functions form a three parameter universality class. The parameter H measures the degree of nonstationarity of the process, C1 characterizes the sparseness/inhomogeneity of the mean of the process, (alpha) characterizes the degree of multifractality; (alpha) equals 0 is monofractal, (alpha) equals 2 is the maximum. We review the properties of these multifractal processes and describe the 'double trace moment' technique that is the first data analysis technique specifically designed to estimate these parameters. The technique is then applied to digital elevation maps of Deadman's Butte, to the topography of France, to a pair of aircraft photos of the ocean surface, and to a visible satellite image of a cloud field.

Paper Details

Date Published: 11 November 1991
PDF: 16 pages
Proc. SPIE 1558, Wave Propagation and Scattering in Varied Media II, (11 November 1991); doi: 10.1117/12.49613
Show Author Affiliations
Daniel Lavallee, Univ. of California/Santa Barbara (United States)
Shaun Lovejoy, McGill Univ. (Canada)
Daniel Schertzer, Meteorologie Nationale (France)


Published in SPIE Proceedings Vol. 1558:
Wave Propagation and Scattering in Varied Media II
Vijay K. Varadan, Editor(s)

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