Role of coupled flow dynamics and real network structures on Hortonian scaling of peak flows

Abstract

We investigate how channel flow dynamics on real river networks produces scaling in peak flows. Scaling relations have been defined by log–log linearity between peak flow statistics and drainage areas for idealized mean self-similar networks like Peano and Mandelbrot Viscek. Unlike idealized basins, drainage areas and link lengths in real basins vary statistically. We use Horton–Strahler order as scale parameter instead of drainage area, and use the Hortonian framework to analyze these network structures. A river-network oriented GIS is used to extract the drainage network for the Walnut Gulch basin, Arizona in the United States. It provides the link connectivity structure and the geometric variables for numerically solving coupled link-based mass and momentum conservation equations. The equations are solved for spatially uniform and instantaneous injection of runoff under three different scenarios of flow in the channels: (1) Constant Velocity, (2) Constant Friction, and (3) Spatially Variable Friction. We find that Hortonian scaling in peak flows does not hold for the constant friction scenario. The scaling exponents of peak flows for the other two cases are larger than the scaling exponent of the peaks of the width functions. This property of scaling exponents for a real network is opposite to previous findings for idealized mean self-similar networks. An empirical scaling analysis of peak flows on the Walnut Gulch basin is briefly explained to provide preliminary empirical support to our theoretical findings.