Efficient Hydrodynamic Modeling at the Landscape Scale: Quantifying River Width and Shear Stress Variability to Decode Tectonic Signals

Basal shear stresses exerted by river flow control the capacity of river to erode and transport sediment. Material properties (e.g. lithology, grain size) modulate how basal shear stress translates into morphological change. Quantifying the spatial variability of basal shear stress is therefore essential to assess fluvial erosion processes and to infer the tectonic and climatic forcings recorded in landscape morphology. 

Direct and systematic measurement of the basal shear stress in rivers is not feasible at large scales, making numerical hydrodynamic modelling the primary tool for its estimation. However, applications beyond the reach scale remain computationally prohibitive due to (i) the need for high-resolution topography to resolve channels, banks, and bars, and (ii) the numerical cost of solving the Shallow Water Equations (SWEs), which require small time steps to propagate changes induced and complex solvers. 

Here, we present a novel numerical framework that substantially reduces the computational cost of hydrodynamic modelling for morphometric analysis, enabling simulations over large, high-resolution DEMs and ranges of hydrological conditions. The approach reformulates the SWEs into a simplified stationary scheme, linearizing algorithmic complexity, and allowing scalable computations. In addition, we employ GPU-accelerated, graph-based flow accumulation algorithms to compute discharge efficiently. Together, these developments reduce computation time by up to three orders of magnitude compared to conventional hydraulic modelling approaches. 

The method is implemented in the pyfastflow package within the TopoToolbox ecosystem. We apply it to more than 100 watersheds in the Mendocino Triple Junction (California, USA), a region characterized by strong spatial gradients in tectonic uplift. Hydrodynamics are computed for five hydrological states constrained by precipitation data, spanning low flow to flood conditions. We quantify spatial variations in river width and shear stress and show that these metrics capture complementary temporal signatures of uplift timing and magnitude. Basin-wide shear stress responds quickly to uplift onset but exhibits a significantly delayed response during relaxation, whereas channel width displays a more variable and spatially contrasted transient signal upstream of the onset.