4.3 Non-linear temperature dependence of clumped isotopes in aragonites
Current clumped isotope calibrations (Meinicke et al., 2020; 2021; Anderson et al., 2021) show subtle differences in the low-temperature end of the calibration (<30°C) that would result in ~1.5°C colder temperatures when applying Anderson et al. (2021) compared to Meinicke et al. (2020). This has led some authors to suggest that forcing of the linear ∆47-\(\frac{1}{T^{2}}\) regression through warm (>30°C) datapoints in the Anderson et al. (2021) calibration creates a “cold bias” in this calibration on the cold end of the calibration domain (e.g. Meckler et al., 2022). In addition, the cold-water (<30°C) carbonate based Meinicke et al. (2020) calibration more closely resembles the modelled temperature relationship for calcites in Guo et al. (2009). The difference between ∆47-\(\frac{1}{T^{2}}\) regressions through the low-temperature (<30°C) and the full dataset (seesection 3.2 ; Fig 2 ) likely highlights non-linear behavior of the ∆47-\(\frac{1}{T^{2}}\) relationship in aragonites. In fact, previous studies based on both clumped isotope analyses and ab initio modelling have suggested a non-linear ∆47-\(\frac{1}{T^{2}}\) relationship to be a better fit for both calcites (Guo et al., 2009; Jautzy et al., 2020) and dolomites (Guo et al., 2009; Müller et al., 2019) precipitated on a large range of known temperatures. Non-linear behavior is also observed in the Anderson et al. (2021) dataset, where Δ47 values of calcites precipitated between 100°C and 1000°C are underestimated by the linear relationship, while the hottest datapoints (calcites heated to 1100°C) fall on the linear regression, mimicking the reduced ∆47-\(\frac{1}{T^{2}}\) slope at the high temperature end of the polynomial regressions through calcite and dolomite data (Guo et al., 2009; Jautzy et al., 2020; Müller et al., 2019). A linear ∆47-\(\frac{1}{T^{2}}\) relationship through a calibration dataset with a large temperature range will thus overestimate temperatures for samples with ∆47 values between 0.2‰ and 0.4‰ (temperatures of 100°C‒1000°C; see residuals in Anderson et al., 2021) and underestimate temperatures of cold (<30°C) samples, as confirmed by regressions through our low-temperature datapoints (see Fig. 2-3 and section 4.4 ). Therefore, more high-temperature aragonite datapoints are needed to constrain the clumped isotope-temperature relationship for temperatures >100°C.