Multifractal versus monofractal analysis of wetland topography |
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| Authors: | I Tchiguirinskaia S Lu F J Molz T M Williams D Lavallée |
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| Institution: | (1) Department of Environmental Engineering and Science, Clemson University, Clemson Research Park, 342 Computer Court, Anderson, South Carolina 29625, USA, US;(2) Baruch Forest Science Institute, Clemson University, P.O. Box 596, Georgetown, South Carolina 29442, USA, US;(3) Institute for Crustal Studies, University of California, Santa Barbara, California 93106, USA, US |
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| Abstract: | The land surface elevation distribution will serve as fundamental input data to any wetland flow model. As an alternative
to the traditional smooth function approach to represent or interpolate elevation data, we explore the use of Levy monofractals
and universal multifractals as a means for defining a statistically equivalent topography. The motivation behind this effort
is that fractals, like natural topography, are irregular, they offer a way to relate elevation variations measured at different
scales, and the relationships are of a statistical nature. The study site was a riparian wetland near Savannah, GA, that contained
beavers, and a total of four elevation transects were examined. The elevation increments showed definite non-Gaussian behavior,
with parameter values, such as the Hurst coefficient and Lévy index (α), depending on the question of presence of beaver activity.
It was obvious that the data were highly irregular, especially the transects influenced by beavers. Significantly different
α values were obtained depending on whether the entire data set or just the tails were examined, which demonstrated inability
of the monofractal model to reflect fully the irregularity of wetland data. Further analysis confirmed definite multifractal
scaling, and it is concluded that the multifractal model is superior for this data set. Universal multifractal parameters
are calculated and compared to those obtained previously for more typical terrain. Although it is difficult to consider a
unique universal multifractal parameter α for the entire wetland, multifractal-like scaling was evident in each transect as
reflected by the nonlinear behaviors of the scaling functions. We demonstrate a good agreement between theory and measurements
up to a critical order of statistical moments, q
D
, close to 3.5 and obtain realistic unconditioned simulations of multifractal wetland topography based on our parameter estimates.
Future work should be devoted to conditioning multifractal realizations to data and to obtaining larger data sets so that
the question of anisotropy may be studied. |
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| Keywords: | : wetland elevation scaling stochastic multifractal intermittency |
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