Doing more with less: Bayesian estimation of erosion models with detrital thermochronometric data

Detrital low temperature thermochronometric data provides spatial and temporal information on catchment erosion, which is relevant to problems in climate, tectonics and geomorphology. However, direct inference of erosion rates from such data is not trivial and only the simplest inverse problems have been addressed previously. In this paper, we present a new approach that relies on the Bayesian interpretation of probability and uses a Markov chain Monte Carlo algorithm for inversion, which affords flexibility in the choice of specific model parametrization and transparent assessment of model uncertainty. We demonstrate how a single detrital sample sourced from a high relief catchment can constrain long-term (> 106 years) changes in erosion rate that are in good agreement with published bedrock age–elevation profiles. Furthermore, we use detrital data to jointly invert for long-term exhumation history and spatial variability in short-term (< 103 years) sediment supply, information relevant to many geomorphic studies. Where cooling histories are simple, we show that even small sample sizes (< 20 grains) reliably estimate long-term rates of exhumation. We suggest that the presented approach to modeling detrital low-temperature thermochronometric data is both a powerful and efficient tool for solving tectonic and geomorphic problems.