Multifractal versus monofractal analysis of wetland topography

The land surface elevation distribution will serve as fundamental input dat a to any wetland flow model. As an alternative to the traditional smooth fu nction approach to represent or interpolate elevation data, we explore the use of Levy monofractals and universal multifractals as a means for definin g 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 relati onships are of a statistical nature. The study site was a riparian wetland near Savannah, GA, that contained beavers, and a total of four elevation tr ansects were examined. The elevation increments showed definite nonGaussian behavior, with parameter values, such as the Hurst coefficient and Levy in dex (alpha), depending on the question of presence of beaver activity. It w as obvious that the data were highly irregular, especially the transects in fluenced by beavers. Significantly different alpha values were obtained dep ending on whether the entire data set or just the tails were examined, whic h demonstrated inability of the monofractal model to reflect fully the irre gularity of wetland data. Further analysis confirmed definite multifractal scaling, and it is concluded that the multifractal model is superior for th is data set. Universal multifractal parameters are calculated and compared to those obtained previously for more typical terrain. Although it is diffi cult to consider a unique universal multifractal parameter alpha for the en tire wetland, multifractal-like scaling was evident in each transect as ref lected 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 estim ates. Future work should be devoted to conditioning multifractal realizatio ns to data and to obtaining larger data sets so that the question of anisot ropy may be studied.