INTERPLAY OF LANDSCAPE RESPONSE TO TECTONIC OR CLIMATIC PERTURBATIONS AND COSMOGENIC-NUCLIDE CONCENTRATIONS: IMPLICATIONS FOR CALCULATING BASIN-SCALE EROSION RATES

The assumption of steady-state nuclide concentrations is implicit in cosmogenic-nuclide-based calculations of basin-scale erosion rates. This assumption, which provides a simple inverse relationship between nuclide concentration and local erosion rate, is justified in basins where the erosion rate varies slowly relative to the time scale for equilibration of the nuclide concentration, which itself is a function of the erosion rate. However, in some drainage basins, the time scale for landscape response to changes in tectonic or climatic forcing is comparable to or less than the time scale for nuclide equilibration, thereby calling into question the steady-state assumption.

We present results of a theoretical analysis of cosmogenic nuclide accumulation in a drainage basin responding to a step-function change in spatially uniform uplift rate or precipitation rate. Our approach combines a standard model of depth-dependent nuclide production with established theory of bedrock-channel evolution. We assume the bedrock-channel erosion rate obeys a power-law relationship involving local stream gradient and upstream contributing area, which Hack's Law relates to distance downstream from the basin divide. The drainage basin lithology is homogeneous, and hillslope processes keep pace with erosion in the bedrock channel. The elevation of the drainage-basin outlet is steady. Under these assumptions, the elevation of the bedrock channel obeys a kinematic-wave equation with downstream-increasing celerity.

We use this model to analyze landscape response and the associated evolution of the cosmogenic-nuclide concentration throughout the transient drainage basin. A single dimensionless number, the ratio of response times for nuclides and the bedrock channel, controls evolution of the nuclide concentration. Assuming no fluvial storage, we calculate the average erosion rate in the transient drainage basin as a function of time and compare it to the average erosion rate calculated under the assumption of steady-state nuclide concentration. Our analysis suggests that this assumption can lead to systematic errors of a factor of two in calculated rates of erosion, demonstrating the need to consider non-steady-state perturbations when using cosmogenic nuclides to evaluate basin-scale erosion.