Hydraulic geometry hypothesis allows reverse engineering of 3D quasi-equilibrium landscapes from 2D channel networks: Earth, Mars, Titan.

The 2D dendritic structure of stream networks within fluvial catchments has not previously been linked to reach-scale channel processes. Existing extensions of 2D network models to 3D landscapes yield only pixelized landscapes, without resolving channels or their properties. At-a-point relations for hydraulic geometry alone provide no insight into how fluvial processes sculpt 3D landscapes in which channels are embedded. We provide this insight by reverse-engineering generic fluvial landscapes with scalable dimensions for all attributes. We do this by coupling a) a 2D network generator, b) dimensionless, physically grounded relations for gravel-bed river hydraulic geometry, and c) a simplified hillslope model. Catchment hypsometric curve and relief, as well as relations between local channel properties and basin structure, cannot be predicted with just one of these components. Our model predicts in specific, dimensioned terms not only how attributes such as hypsometric curve change with changing bed grain size, precipitation and catchment area, but also why, because each model element can be interrogated individually or jointly. Our method offers a tool for studying the effect of varied mean annual precipitation and intensity on catchment structure. Our central application is to tectonically inactive, quasi-equilibrium, low-relief montane landscapes on Earth. We underline the insight provided by our formulation through application to analogous planetary fluvial landscapes. We implement this for Mars and Titan using appropriate values for gravitational acceleration and sediment submerged specific gravity, both freely variable in our model. Our reverse-engineering methodology indicates why and how an analogous class of landscapes should differ in different planetary settings.