Reconstructing landscapes: an adjoint model of the Stream Power and diffusion erosion equation

Abstract. We simulate landscape evolution using a diffusion–advection equation, where the advection velocity is derived from the erodibility parameters of the Stream Power Law. This formulation allows for forward modeling within a finite-element framework, and enables the use of adjoint methods for sensitivity analysis and parameter inversion – specifically for spatially variable erodibility and diffusion coefficients. When considered individually, model parameters such as the diffusion coefficient, 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. 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, consistent with recent geological estimates.