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

. Currently there is no standardized approach for reporting date uncertainty in the (U-Th)/He system, partly due to 5 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 4 He, radionuclide, and isotope-specific F T 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 10 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 4 He 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 15 uncertainties in F T 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 F T on the uncertainty budget indicates the need to better quantify and routinely propagate F T 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 20 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 F T uncertainties. 4 He, 238 U, 232 Th, and (for apatite) 147 Sm. To best represent these distributions, we take the median value and 68% confidence interval calculated using the percentile approach described in Sect. 3.3, which are shown in Table 3. These results indicate that the uncertainty for each measured value is lower in a typical zircon analysis than in a typical apatite analysis, likely due to the higher concentration of radionuclides in a typical zircon grain and the greater retentivity of 4 He, resulting in analytical measurements that have greater count rates and are less impacted by the uncertainty associated with blank and background levels.