Full Propagation of Analytical Uncertainties in Δ47 Measurements

Abstract

Clumped-isotope measurements in CO2 and carbonates (Δ47) present a number of technical challenges and require correcting for various sources of analytical nonlinearity. For now, we lack a formal description of the analytical errors associated with these correction steps, which are not accounted for in most data processing methods currently in use. Here we formulate a quantitative description of Δ47 error propagation, fully taking into account standardization errors and their properties. We find that standardization errors are highly sensitive to the isotopic compositions (δ47, Δ47) of unknown samples relative to the standards used for analytical corrections, and in many cases constitute a non-negligible source of uncertainty, causing true measurements errors to exceed traditionally reported error estimates by a factor of 1.5 (typically) to 3.5 (in extreme cases). Using Monte Carlo simulations based on the full InterCarb data set, we find that this model yields accurate error estimates in spite of small non-Gaussian effects which remain entirely negligible in practice. We also describe various standardization strategies, along with the assumptions they rely on, in the context of this model, and propose a new, “pooled” standardization approach designed to yield more robust/accurate corrections. Among other uses, the mathematical framework described here may be helpful to improve standardization protocols (e.g., anchor/unknown ratios) and inform future efforts to define community reference materials. What is more, these models imply that the inter-laboratory scatter (N = 5,329) observed in the InterCarb exercise (Bernasconi, Daëron, et al., 2021) can be entirely explained as the effects of current standardization procedures. Based on these findings, we recommend that future studies systematically report full analytical uncertainties taking standardization errors into account. In line with this recommendation, we provide user-friendly online resources and an open-source Python library designed to facilitate the use of these error models.