Inferring uplift histories from landscapes using hypsometric curves

One of the main ways in which deep seated tectonic or geodynamic processes influence the Earth's surface is by driving rock uplift. Variations in rock uplift through space and time combine with surface processes, such as erosion in rivers and on hillslopes, to shape the surface landscape. These relationships imply that, if we can adequately parameterise surface processes, we may be able to infer rock uplift histories from observations of present day topography. Efforts to do so formally using inverse modelling have mostly focused on the shapes of river profiles. Such approaches can reproduce well observed profiles, and yield uplift histories broadly consistent with independent constraints. However, they generally assume a fixed drainage planform, and neglect any information stored in the rest of landscape (i.e., in hillslope topography). Landscape evolution models, which include descriptions of hillslope processes and allow drainage planforms to evolve, may address these issues, but come with their own challenges. In particular, a strong dependence of modelled drainage planforms on the initial condition, which is generally poorly constrained, complicates direct comparison of observed and modelled topography.

Here, we explore the utility of hypsometric curves – cumulative distribution functions of elevation within a domain – in inverse landscape evolution modelling (we also include equivalent functions for slope and curvature). These curves' integrative nature should make them relatively insensitive to the precise positions of individual valleys and ridgelines. By comparing hypsometric curves from many simulations, with and without added noise, we assess their sensitivity to initial conditions, erosional parameters and uplift histories. We confirm that hypsometric curves are insensitive to initial conditions, particularly when normalised by the mean – rather than, as is traditional, the maximum – value in the domain. For landscapes in a dynamic equilibrium with the imposed uplift rate, the main control on the normalised hypsometric curve is the relative importance of fluvial and hillslope processes. Multiple erosional parameters influence this balance, introducing trade-offs to the misfit space. Nevertheless, individual parameters do have subtle secondary effects that allow them to be determined independently, at least for relatively low noise levels. In transient landscapes, features of simple uplift histories – such as timings and amplitudes of step changes in uplift rate – also appear to be recoverable. We conclude that hypsometric curves can form useful bases for inverse landscape evolution modelling, which could in turn provide novel insights into the tectonic and geodynamic processes that drive rock uplift.