Combined linear regression and Monte Carlo approach to modelling exposure age depth profiles

Abstract. We introduce a set of methods for analyzing cosmogenic-nuclide depth profiles that formally integrates surface erosion and muogenic production, while retaining the advantages of the linear inversion. For surfaces with erosion, we present solutions for both erosion rate and total eroded thickness, each with their own advantages. For practical applications, erosion must be constrained from external information, such as soil-profile analysis. By combining linear inversion with Monte Carlo simulation of error propagation, our method jointly assesses uncertainty arising from measurement error and erosion constraints. Using example depth profile data sets from the Beida River, northwest China and Lees Ferry, Arizona, we show that our methods robustly produce comparable ages for surfaces with different erosion rates and inheritance. Through hypothetical examples, we further show that both the erosion rate and eroded-thickness approaches produce reasonable age estimates so long as the total erosion less than twice the nucleon attenuation length. Overall, lack of precise constraints for erosion rate tends to be the largest contributor of age uncertainty, compared to the error from omitting muogenic production or radioactive decay.