Time-integrating cosmogenic nuclide inventories under the influence of variable erosion, exposure, and sediment mixing

Cosmogenic nuclide concentrations in rocks and sediments are widely used to study the evolution of landscapes that have experienced complex exposure/burial and erosion histories. Measured nuclide concentrations are typically compared with those obtained by time-integrating hypothetical histories of erosion and exposure. The presence of erosion, in particular, complicates the time-integration of nuclide concentrations, because erosion removes nuclides while at the same time increasing their production in new material advected towards the surface. This relative movement between sample and surface calls for a choice between a Eulerian reference frame, in which the integration point is fixed relative to the surface, or a Lagrangian reference frame, in which the integration point rides the sample on its way to the surface. The equations developed in the early 1990s to compute changes in cosmogenic nuclide inventories for geological settings undergoing steady erosion are now used routinely, but they are not directly applicable for time-integrating nuclide concentrations related to variable exposure and erosional transience. In this study, we lay out the fundamental equations associated with the Eulerian and Lagrangian approaches to compute cosmogenic nuclide concentrations under the influence of variable exposure and erosion, and discuss the pros and cons of the two approaches for different scenarios. We then extend our analysis to unconsolidated sediment/soil profiles by outlining a new and flexible approach to modelling cosmogenic-nuclide depth profiles that include depth-dependent mixing processes, combined with variable erosion rates and complex exposure/burial histories. We conclude with a few guidelines for reporting the steps involved with computing cosmogenic nuclide concentrations in geological settings influenced by variable exposure and erosional transience.