Spatial variability of erosion rates inferred from the frequency distribution of cosmogenic 3He in olivines from Hawaiian river sediments

To constrain the spatial distribution of erosion rates in the Waimea river watershed, on the western side of the island of Kauai, Hawaii, we calculate the frequency distribution of cosmogenic 3He concentrations ([3He]c) from helium isotopic measurements in olivine grains from a single sample of river sediment. Helium measurements were made in 26 aliquots of ∼ 30 olivine grains each. The average [3He]c from the 26 aliquots was used to estimate a basin-wide average erosion rate of 0.056 mm/yr, a value that is similar to erosion rates obtained from geochemical analyses of river sediments from tectonically stable landforms. However, forward models of cosmogenic nuclide production and sediment generation rates are inconsistent with the hypothesis that the observed [3He]c frequency distribution is the result of a homogeneous, basin wide, erosion rate. Instead, a distribution of erosion rates, from ∼ 0 to 4 mm/yr, may account for the observed frequency distribution. The distribution of erosion rates can be modeled by both non-linear slope- and curvature-dependent erosion rates with power law exponents ranging from 2.0 to 2.5. However, the spatial distribution of cosmogenic nuclides for slope- and curvature-dependent erosion rates are distinct, and we propose strategies to test further the extent to which erosion rates are controlled by the macroscale topographic features. These results demonstrate that the observed frequency distribution of cosmogenic nuclide concentrations in river sediments, combined with numerical modeling of erosion rates, can provide constraints on both the spatial variability of erosion rates in a drainage basin and the form of parameterized erosion laws.