Reconstructing landscapes: An adjoint model of the stream power and diffusion erosion equation

Abstract

We simulate landscape evolution using a diffusion-advection equation with a source term, where the advection velocity is derived from the classical parametrization of the Stream Power Law. This formulation allows for forward modeling of uplift, hillslope and fluvial erosion within a finite-element framework, and enables the use of adjoint methods for sensitivity analysis and parameter inversion. When considered individually, model parameters such as the diffusion coefficient, fluvial erodibility, initial topography, and time-dependent uplift can be inverted using constraints from final topography, sediment flux, or cumulative denudation at specific locations. Sensitivity analysis on a real landscape reveals that sensitivity to erosion parameters is higher in steep, high-relief areas and that hillslope diffusion and fluvial incision affect the model differently. After a series of tests on synthetic topographies, we apply the adjoint model to two natural cases: (1) reconstructing the pre-incision topography of the southeastern French Massif Central, which appears as a smooth, flat footwall bounded by a linear escarpment along a major lithological boundary; and (2) estimating the Quaternary uplift rate along the Wasatch Range, USA, where our model suggests a significant increase in uplift from 0.2 to 1 mm yr-1 over the last ∼2 million years.