General models for episodic surface denudation and its measurement by cosmogenic nuclides

In order to use cosmogenic nuclides to infer erosion rates and exposure ages, it is necessary to apply a quantitative model for the accumulation of these nuclides in an eroding surface. The most straightforward model assumes that the surface continuously erodes at a constant rate. In many cases, however, the erosion is episodic: denudation is the result of the spalling off of slabs of rock in a series of discrete events. In a previous paper, we discussed two models for such episodic erosion; in one model slabs of rock spalled off periodically, while in the other slabs spalled off at stochastic time intervals. In both models we took the slabs to have a given, fixed width. In this paper we expand the previously treated models to allow for a statistical distribution of widths; this makes the models more realistic, and broadens our discussion of the fluctuations in the nuclide concentration that may be observed. We present general results for both models, results which allow for any distribution of widths. We then explore the stochastic model in more detail, applying a particular choice of width distribution. This allows us to address an interesting limiting case: when the widths are very small, the average nuclide concentration is accurately given by the standard continuous erosion model; yet, perhaps surprisingly, the fluctuations about this average can be quite significant.