12 May 2022
12 May 2022

Calculation of Uncertainty in the (U-Th)/He System

Peter E. Martin, James R. Metcalf, and Rebecca M. Flowers Peter E. Martin et al.
  • Department of Geological Sciences, University of Colorado Boulder, CO 80309

Abstract. Currently there is no standardized approach for reporting date uncertainty in the (U-Th)/He system, partly due to the fact that the methods and formulae for calculating single-grain uncertainty have never been published. This creates challenges for interpreting the expected distribution of dates within individual samples and of dates generated by differing labs. Here we publish two procedures to derive (U-Th)/He single-grain date uncertainty (linear and Monte Carlo uncertainty propagation), based on input 4He, radionuclide, and isotope-specific FT values and uncertainties. We also describe a newly released software package, HeCalc, that performs date calculation and uncertainty propagation for (U-Th)/He data. Using this software, we find that date uncertainty decreases with increasing age for constant relative input uncertainties. Skew in date probability distributions (i.e., asymmetrical uncertainty) yielded by the Monte Carlo method varies with age and increases with increasing relative input uncertainty. Propagating uncertainties in 4He and radionuclides using a compilation of real (U-Th)/He data (N = 1978 apatites, and 1753 zircons) reveals that the uncertainty budget in this dataset is dominated by uncertainty stemming from the radionuclides, yielding median relative uncertainty values of 2.9 % for apatites and 1.7 % for zircons. When uncertainties in FT of 2 % or 5 % are assumed and additionally propagated, these values increase to 3.3 % and 5.0 % for apatite, and 2.4 % and 4.7 % for zircon. The potentially strong influence of FT on the uncertainty budget indicates the need to better quantify and routinely propagate FT uncertainty into (U-Th)/He dates. Skew is generally positive and can be significant, with ~14 % of apatite dates and ~5 % of zircon dates characterized by skew of 10 % or greater. This outcome indicates the value of applying Monte Carlo uncertainty propagation to identify samples with substantially skewed uncertainties that should be considered during data interpretation. The formulae published here and the associated HeCalc software can aid in more consistent (U-Th)/He uncertainty reporting and enable a more rigorous understanding of when and why multiple aliquots from a sample differ beyond what is expected from analytical and FT uncertainties.

Peter E. Martin 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 egusphere-2022-299', Pieter Vermeesch, 16 May 2022
    • AC1: 'Reply on RC1', Peter Martin, 27 May 2022
  • RC2: 'Comment on egusphere-2022-299', Ryan Ickert, 11 Aug 2022
    • AC2: 'Reply on RC2', Peter Martin, 29 Aug 2022

Peter E. Martin et al.

Model code and software

HeCalc P. E. Martin

Peter E. Martin et al.


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Short summary
There is currently no standardized method of performing uncertainty propagation in the (U-Th)/He system, causing difficulties in data interpretation. We present two methods of uncertainty propagation and describe a free, open-source software (HeCalc) to apply these methods. A compilation of real data using only analytical uncertainty, and 2 % and 5 % uncertainties in FT yields respective median relative date uncertainties of 2.9 %, 3.3 % and 5.0 % for apatites and 1.7 %, 3.3 % and 5.0 % for zircons.