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

Abstract

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.

Drainage divide networks – Part 2: Response to perturbations

“…In the Rotating and Spheres models, we also observed that maximum divide orders occasionally extend to higher values, but these changes are rather small. We note that the above observations also prevail when considering divide distance instead of divide order because the two are linearly related (Scherler and Schwanghart, 2020a), with divide distance ∼ 430 m × divide order. The 430 m corresponds to the mean length of the divide segments.…”

“…For each modeled topography and at each time step (dt = 40 000 years), we first computed flow directions and flow accumulation, and we subsequently identified the stream network using a drainage area threshold of 0.2 km 2 . We next derived the drainage divide network on the basis of the stream network and using the algorithm proposed in Scherler and Schwanghart (2020a). We calculated divide distances and divide orders based on the Topo ordering scheme (Scherler and Schwanghart, 2020a).…”

“…We next derived the drainage divide network on the basis of the stream network and using the algorithm proposed in Scherler and Schwanghart (2020a). We calculated divide distances and divide orders based on the Topo ordering scheme (Scherler and Schwanghart, 2020a). As topographic metrics, we included elevation (z), hillslope relief (HR), and horizontal flow distance to the stream network (FD).…”

“…Motivated by the observation of constant values in hillslope relief and flow distance in the Reference model, as well as in actual landscapes (Scherler and Schwanghart, 2020a), and by our expectation that small values in either one would be found where one catchment loses area to another (Fig. 1), we next compared how minimum hillslope relief (HR min ), minimum flow distance (FD min ), and the divide asymmetry index (DAI) vary with divide distance in the Reference model and the three models with landscape perturbances (Fig.…”

“…In their analysis, however, they focused on divide motion that is perpendicular to the regional drainage direction and averaged divide migration rates as well as topographic metrics across the entire width of the model domain so that each time step is associated with single values for divide migration rate, erosion rate difference, and the tested topographic metrics. In part 1 of this study (Scherler and Schwanghart, 2020a), we presented a new approach for the automatic identification and ordering of drainage divide networks in a digital elevation model (DEM), which removes the necessity of manually selecting drainage divides for comparison. Here, we present experiments with a numerical landscape evolution model that we conducted to investigate how drainage divide networks respond to different perturbations, including fault activity and differences in erodibility.…”