Bias and error in modelling thermochronometric data: resolving a potential increase in Plio-Pleistocene erosion rate

Abstract. Thermochronometry provides one of few methods to quantify rock exhumation rate and history, including potential changes in exhumation rate. Thermochronometric ages can resolve rates, accelerations, and complex histories by exploiting different closure temperatures and path lengths using data distributed in elevation. We investigate how the resolution of an exhumation history is determined by the distribution of ages and their closure temperatures through an error analysis of the exhumation history problem. We define the sources of error, defined in terms of resolution, model error and methodological bias in the inverse method used by Herman et al. (2013) which combines data with different closure temperatures and elevations. The error analysis provides a series of tests addressing the various types of bias, including addressing criticism that there is a tendency of thermochronometric data to produce a false inference of faster erosion rates towards the present day because of a spatial correlation bias (Schildgen et al., 2018). Tests based on synthetic data demonstrate that the inverse method used by Herman et al. (2013) has no methodological or model bias towards increasing erosion rates. We do find significant resolution errors with sparse data, but these errors are not systematic, tending rather to leave inferred erosion rates at or near a Bayesian prior. To explain the difference in conclusions between our analysis and that of Schildgen et al. (2018), we examine their paper and find that their model tests used an incorrect geotherm calculation, invalidating their models. We also found that Schildgen et al. (2018) applied a biased operator to the results of Herman et al. (2013) thereby distorting the original results producing a bias that was falsely attributed to the original inverse model. Our reanalysis and interpretation show that the original results of Herman et al. (2013) are correct and there is no evidence for a systematic bias.