Hydraulic geometry hypothesis allows reverse engineering of 3D quasi-equilibrium landscapes from 2D channel networks

A fluvial catchment consists of unchannelized hillslopes drained by a channel network. Catchments can be fully characterized by their three-dimensional (3D) topography and the bankfull characteristics of their channels. Here we use a probabilistic algorithm to generate a set of scale-free, two-dimensional (2D) pixelized river networks of increasing complexity. We then integrate reach-scale hydraulic geometry equations, originally developed for single-channel gravel-bedded river reaches, to reverse engineer the corresponding 3D landscape topography of these 2D synthetic networks (Reverse Engineered Fluvial Landscape, REFL). To do so requires specification of outlet flood discharge and a characteristic bed grain size. By incorporating hillslope-channel coupling, represented by a characteristic hillslope length and slope, we can fully specify the 3D topography of the entire watershed. Our results suggest that under appropriate constraints, the equilibrium hydraulic geometry hypothesis can be extended beyond isolated river reaches to encompass entire fluvial landscapes. The class of landscapes we consider are relatively low-slope montane catchments with subdued tectonics. The streams that drain the catchment are assumed to be alluvial or quasi-alluvial well upstream of the outlet. A simplified model analogous to the subgrid model of the Large Eddy Simulation model of turbulent flow is used to describe processes upstream of the limit of alluviated channels.