Inferring exposure ages and erosion rates from cosmogenic nuclides: A probabilistic formulation

Cosmogenic nuclides have become an important tool in geomorphology; the concentration of such nuclides in minerals in an eroding surface is directly related to the exposure time and the erosion rate. In principle, measurement of the two nuclides ¹⁰Be and ²⁶Al allows for the determination of both the erosion rate and the exposure age. In practice, due to a variety of factors such as the similar lifetimes of the two nuclides and the limits on measurement precision, this determination is often not possible. We propose a new approach to this problem, showing how to construct a joint probability distribution for the age and erosion rate by using the concentration of one (or two) nuclides measured at the surface. We explain the Bayesian approach to this problem; the construction of the prior is a crucial element of this Bayesian method, and we devote particular attention to this issue. By analyzing previously published data, we show how this method improves on the standard approach of computing a “model age” and “model erosion rate.”