How many grains are needed for quantifying catchment erosion from tracer thermochronology?

Abstract

Detrital tracer thermochronology utilizes the relationship between bedrock thermochronometric age–elevation profiles and a distribution of detrital grain ages collected from riverine, glacial, or other sediment to study spatial variations in the distribution of catchment erosion. If bedrock ages increase linearly with elevation, spatially uniform erosion is expected to yield a detrital age distribution that mimics the shape of a catchment's hypsometric curve. Alternatively, a mismatch between detrital and hypsometric distributions may indicate spatial variability of sediment production within the source area. For studies seeking to identify the pattern of sediment production, detrital samples rarely exceed 100 grains due to the time and costs related to individual measurements. With sample sizes of this order, detecting the dissimilarity between two detrital age distributions produced by different catchment erosion scenarios can be difficult at a high statistical confidence level. However, there are no established software tools to quantify the uncertainty inherent to detrital tracer thermochronology as a function of sample size and spatial pattern of sediment production. As a result, practitioners are often left wondering “how many grains is enough to detect a certain signal?”. Here, we investigate how sample size affects the uncertainty of detrital age distributions and how such uncertainty affects the ability to infer a pattern of sediment production of the upstream area. We do this using the Kolmogorov–Smirnov statistic as a metric of dissimilarity among distributions. From this, we perform statistical hypothesis testing by means of Monte Carlo sampling. These techniques are implemented in a new tool (ESD_thermotrace) to (i) consistently report the confidence level allowed by the sample size as a function of application-specific variables and given a set of user-defined hypothetical erosion scenarios, (ii) analyze the statistical power to discern each scenario from the uniform erosion hypothesis, and (iii) identify the erosion scenario that is least dissimilar to the observed detrital sample (if available). ESD_thermotrace is made available as a new open-source Python-based script alongside the test data. Testing between different hypothesized erosion scenarios with this tool provides thermochronologists with the minimum sample size (i.e., number of bedrock and detrital grain ages) required to answer their specific scientific question at their desired level of statistical confidence.