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GEOPHYSICAL RESEARCH LETTERS, VOL. 31, L06501, doi:10.1029/2003GL019093, 2004

Allometric power-law relationships in a Hortonian fractal digital elevation model

B. S. Daya Sagar

Faculty of Engineering and Technology, Melaka Campus, Multimedia University, Melaka, Malaysia


Tay Lea Tien

Faculty of Engineering, Multimedia University, Jalan Multimedia, Selangor, Malaysia


Abstract

We provide a topologically viable model that is geomorphologically realistic from the point of its Hortonity and general allometric scaling laws. To illustrate this, we consider a fractal binary basin, generated in such a way that it follows certain postulates, and decompose it into various coded topologically prominent regions the union of which is defined as geomorphologically realistic Fractal-DEM. We derive two unique topological networks from this Hortonian fractal DEM based on which we derive allometric power-law relationships among the basic measures of decomposed sub-basins of all orders ranging from ω = 1 to ω = Ω. Our results are in good accord with optimal channel networks and natural river basins.

Received 18 November 2003; accepted 5 February 2004; published 17 March 2004.

Index Terms: 1848 Hydrology: Networks; 3250 Mathematical Geophysics: Fractals and multifractals; 3210 Mathematical Geophysics: Modeling; 1824 Hydrology: Geomorphology (1625).

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Citation: Sagar, B. S. D., and T. L. Tien (2004), Allometric power-law relationships in a Hortonian fractal digital elevation model, Geophys. Res. Lett., 31, L06501, doi:10.1029/2003GL019093.