Making the Case for Reconciled Δ47 Calibrations Using Omnivariant Generalized Least-Squares Regression

For fundamental thermodynamic reasons, ¹³C-¹⁸O bonds in carbonate minerals formed under isotopic equilibrium conditions are more abundant than predicted for a random distribution of isotopes, yielding positive Δ₄₇ clumped-isotope signatures which decrease as a function of formation temperature [1]. Although most Earth-surface carbonates are unlikely to achieve complete isotopic equilibrium, Δ₄₇ values of many biogenic and abiotic calcites formed under very different crystallization conditions (and with irreconcilable water-calcite oxygen-18 fractionation laws) appear to follow indistinguishable temperature calibrations, as independently documented by various groups over the years [e.g., 2-4]. That is not to say that all groups agree on a single calibration linking Δ₄₇ and temperature, and a recent comparison of 14 reprocessed calibration studies still found evidence for statistically significant inter-laboratory discrepancies [3]. Rigorous statistical tests aiming to prove or disprove consistency between Δ₄₇ calibrations are particularly challenging because of potentially large and non-independent analytical errors associated with standardization procedures [5], and even in some cases by large correlations in the uncertainties of estimated formation temperatures, making classical least-squares regression approaches ill suited to model these calibration data sets.

Here I propose a new formulation for least-squares regression of data with an arbitrarily complex covariance structure linking all predictor and response observations, generally applicable to all sorts of geochemical data. I use this “Omnivariant Generalized Least-Squares” (OGLS) approach to compare 7 published Δ₄₇ calibration data sets which have been (re)processed according to the newly established InterCarb Carbon Dioxide Equilibrium Scale (I-CDES), supposedly allowing robust comparisons between Δ₄₇ measurements across laboratories [6]. None of these reprocessed calibration data sets are found to deviate significantly from a single, unified regression line, with an overall reduced chi-squared statistic (adjusted for data covariance according to OGLS) of 0.8 consistent with slightly overestimated uncertainties on temperature constraints. This finding marks another milestone in the 17-year-long progress of Δ₄₇ thermometry, which has now solved most of the methodological challenges standing in the way of its widespread application to many scientific issues. In short: carbonate clumped-isotope thermometry is all grown up now.

[1] Schauble et al. (2006) 10.1016/j.gca.2006.02.011
[2] Kele et al. (2015) 10.1016/j.gca.2015.06.032
[3] Petersen et al. (2019) 10.1029/2018GC008127
[4] Anderson et al. (2021) 10.1029/2020GL092069
[5] Daëron (2021) 10.1029/2020GC009592
[6] Bernasconi et al. (2021) 10.1029/2020GC009588