Generalized hydraulic geometry: Insights based on fluvial instability analysis and a physical model

The power law dependencies between channel morphology and river flows, known as at-station hydraulic geometry (HG), have been recently shown to have exponents that systematically vary with scale (contributing area). To explain these empirical trends, a generalized HG model whose parameters are explicit functions of scale was derived by Dodov and Foufoula-Georgiou [2004], based on a statistical multiscaling formalism. In this paper we attempt to provide a physical explanation for this scale dependence. The hypothesis we pose is that it arises from the scale dependence of fluvial instability, which induces systematic variation in river planform geometry (e.g., sinuosity, meander wavelength, and radius of curvature) and consequent variations in channel cross-sectional shape with scale. In other words, we postulate that the scale-dependent HG is a direct consequence of the systematic increase of channel cross-sectional asymmetry over reaches of increasing scale. To test this hypothesis, we employ both a direct analysis of observations and also a physical model of meandering rivers, which is based on linearization of the fully coupled equations of mass and momentum balance for water and sediment. We show that the HG emerging from this physical model is scale-dependent and agrees with the empirical observations and the statistical multiscaling model.