Resistant rock layers amplify cosmogenically-determined erosion rates

Prior numerical modeling work has suggested that incision into sub-horizontal layered stratigraphy with variable erodibility induces non-uniform erosion rates even if base-level fall is steady and sustained. Erosion rates of cliff bands formed in the stronger rocks in a stratigraphic sequence can greatly exceed the rate of base-level fall. Where quartz in downstream sediment is sourced primarily from the stronger, cliff-forming units, erosion rates estimated from concentrations of cosmogenic beryllium-10 (¹⁰Be) in detrital sediment will reflect the locally high erosion rates in retreating cliff bands. We derive theoretical relationships for threshold hillslopes and channels described by the stream-power incision model as a quantitative guide to the potential magnitude of this amplification of ¹⁰Be-derived erosion rates above the rate of base-level fall. Our analyses predict that the degree of erosion rate amplification is a function of bedding dip and either the ratio of rock erodibility in alternating strong and weak layers in the channel network, or the ratio of cliff to intervening-slope gradient on threshold hillslopes. We test our predictions in the cliff-and-bench landscape of the Grand Staircase in southern Utah, USA. We show that detrital cosmogenic erosion rates in this landscape are significantly higher (median 300 m/Ma) than the base-level fall rate (~75 m/Ma) determined from the incision rate of a trunk stream into a ~0.6 Ma basalt flow emplaced along a 16 km reach of the channel. We infer a 3–6-fold range in rock strength from near-surface P-wave velocity measurements. The approximately four-fold difference between the median ¹⁰Be-derived erosion rate and the long-term rate of base-level fall is consistent with our model and the observation that the stronger, cliff-forming lithologies in this landscape are the primary source of quartz in detrital sediments.