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

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.