We used measurements of cosmogenic 10Be in alluvium to estimate erosion rates on a 103–104 yr time scale for small (0.01–47 km2), unglaciated basins in northern Colorado, southern Wyoming, and adjacent western Nebraska (western United States). Basins formed in Proterozoic cores of Laramide ranges are eroding more slowly (23 ± 7 mm k.y.–1, n = 19) than adjacent basins draining weakly lithified Cenozoic sedimentary rocks (75 ± 36 mm k.y. –1, n = 20). Erosion rates show a relationship to rock resistance and, for granitic rocks, to basin slope, but not to mean annual precipitation. We estimated longer-term (>105 yr time scale) erosion rates for the granitic core of the Front Range by measuring the concentration of 10Be and 26Al produced mainly by muon interactions at depths 1.7–10 m below the surface. Concentrations imply erosion rates of 9–31 mm k.y. –1, similar to shorter-term erosion rates inferred from alluvial sediment. The spatial distribution of erosion rates and stratigraphic evidence imply that relief in the southern Rocky Mountains increased in the late Cenozoic; modern relief probably dates from post-middle Miocene time.

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