02 Mar 2021

02 Mar 2021

Review status: a revised version of this preprint is currently under review for the journal GChron.

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

Andrea Madella, Christoph Glotzbach, and Todd A. Ehlers Andrea Madella et al.
  • Department of Geosciences, University of Tuebingen, Schnarrenbergstr. 94-96, 72076 Tuebingen, Germany

Abstract. Detrital tracer thermochronology exploits the relationship between bedrock thermochronometric age-elevation profiles and a distribution of detrital grain-ages collected from river, glacial, or other sediment to study spatial changes in the distribution of catchment erosion. If ages increase linearly with elevation, spatially uniform erosion is expected to yield a detrital age distribution that mirrors the catchment's hypsometric curve. Alternatively, a mismatch between detrital and hypsometric distributions may indicate non-uniform erosion within a catchment. For studies seeking to identify the pattern of erosion, measured grain-age populations rarely exceed 100 grains due largely to the time and costs related to individual measurements. With sample sizes of this order, discerning between two detrital age distributions produced by different catchment erosion scenarios can be difficult at a high statistical confidence level. However, there is no established method to quantify the sample-size-dependent uncertainty inherent to detrital tracer thermochronology, and practitioners are often left wondering how many grains is enough?. Here, we investigate how sample size affects the uncertainty of detrital age distributions and how such uncertainty affects the ability to uniquely infer the erosional pattern of the upstream area. We do this using the Kolmogorov-Smirnov statistic as metric of dissimilarity among distributions, based on which the statistical confidence of detecting an erosional pattern is determined through Monte Carlo sampling. The techniques are implemented in a new tool (ESD_thermotrace) to consistently report confidence levels as a function of sample size and application-specific variables. The proposed tool is made available as a new open-source Python-based script along with 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. Furthermore, in cases of unavoidably small sample size (e.g., due to poor grain quality or low sample volume), we provide a means to calculate the confidence level of interpretations made from the data.

Andrea Madella et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gchron-2021-6', Anonymous Referee #1, 06 Apr 2021
    • AC1: 'Reply on RC1', Andrea Madella, 09 Apr 2021
  • RC2: 'Comment on gchron-2021-6', Claire E Lukens, 01 May 2021
    • AC2: 'Reply on RC2', Andrea Madella, 27 May 2021

Andrea Madella et al.

Model code and software

ESD_thermotrace, A new software to interpret tracer thermochronometry datasets and quantify related confidence levels Andrea Madella, Christoph Glotzbach, and Todd A. Ehlers

Andrea Madella et al.


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Short summary
Cooling ages date the time at which minerals cross a certain isotherm on the way up to Earth's surface. Such ages can be measured from bedrock material as well as from river sand. If spatial variations of bedrock ages are known in a river catchment, the spatial distribution of erosion can be inferred from the distribution of the ages measured from the river sand grains. Here we develop a new tool to help such analyses, with particular emphasis on quantifying uncertainties due to sample size.