Full Propagation of Analytical Uncertainties in Δ₄₇ Measurements

Abstract

Clumped-isotope measurements in CO 2 and carbonates (Δ 47 ) present a number of technical challenges and require correcting for various sources of analytical non-linearity. 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 Δ 47 error propagation, fully taking into account standardization errors and their properties. We 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.User-friendly online resources and an open-source Python library are also provided to facilitate the use of these error models. 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.

InterCarb: A Community Effort to Improve Interlaboratory Standardization of the Carbonate Clumped Isotope Thermometer Using Carbonate Standards

“…In addition, the error increases for unknown samples whose compositions lie outside the "anchor triangle" defined by ETH-1/2/3. This is illustrated by the increased scatter and errors associated with MERCK, the carbonate farthest from the "anchor triangle," consistent with the models of Daëron (2021) (see also Kocken et al, 2019).…”

“…To avoid artifacts arising from different calculation/standardization procedures, rounding errors, and 17 O correction parameters, raw data from all laboratories were processed by a single Python script (http://doi. org/10.5281/zenodo.4314448) based on data reduction, standardization and error propagation methods described in detail in the companion paper (Daëron, 2021). Here we briefly summarize these calculations.…”

“…In the figures and tables, final measurement uncertainties are reported as standard errors and/or 95% confidence limits, considering fully propagated errors taking into account reference frame corrections. In Figures 2 and 4, different types of error bars are used to represent analytical errors only considering uncertainties in the analyses of a given sample or the full uncertainty considering standardization uncertainties (the "autogenic" errors of Daëron, 2021). In both cases, the analytical error assigned to each individual raw Δ 47 analysis is equal to the pooled "external" repeatability of raw Δ 47 measurements for all samples (anchors and unknowns) within each session.…”

“…The smaller range in Δ 47 compared to HG's and EG's requires higher precision and also a larger number of replicates of both standards and samples. Daëron (2021) and Kocken et al (2019) suggest ∼50:50 ratio of standard to sample replicates to keep standardization errors small.…”

“…In addition, the laboratories with BERNASCONI ET AL. (Daëron, 2021). (Petersen et al, 2019) the smallest number of replicate measurements have uncertainties that are systematically larger (Table 1).…”