Estimating the disequilibrium in denudation rates due to divide migration at the scale of river basins

Abstract

Basin-averaged denudation rates may locally exhibit a wide dispersion, even in areas where the topographic steady state is supposedly achieved regionally. This dispersion is often attributed to the accuracy of the data or to some degree of natural variability of local erosion rates which can be related to stochastic processes such as landsliding. Another physical explanation of this dispersion is local and transient disequilibrium between tectonic forcing and erosion at the scale of catchments. Recent studies have shown that basin divide migration can potentially induce such perturbations, and they propose metrics to assess divide mobility based on cross-divide contrasts in headwater topographic features. Here, we use a set of landscape evolution models assuming spatially uniform uplift, rock strength and rainfall to assess the effect of divide mobility on basin-wide denudation rates. We propose using basin-averaged aggressivity metrics based on cross-divide contrasts (1) in channel χ, an integral function of position in the channel network; (2) in channel local gradient; and (3) in channel height, measured at a reference drainage area. From our simulations, we show that the metric based on differences in χ is the most reliable to diagnose local disequilibrium. The other metrics are more suitable for relatively active tectonic regions such as mountain belts, where contrasts in local gradient and elevation are more important. We find that the ratio of basin denudation associated with drainage migration to uplift can reach a factor of 2, regardless of the imposed uplift rate, erodibility, diffusivity coefficient or critical hillslope gradient. A comparison with field observations in the Great Smoky Mountains (southern Appalachians, USA) underlines the difficulty of using the metric based on χ, which depends on the – poorly constrained – elevation of the outlet of the investigated catchment. Regardless of the considered metrics, we show that observed dispersion is controlled by catchment size: a smaller basin may be more sensitive to divide migration and hence to disequilibrium. Our results thus highlight the relevance of divide stability analysis from digital elevation models as a fundamental preliminary step for basin-wide denudation rate studies based on cosmogenic radionuclide concentrations.