Temperature Dependence of Clumped Isotopes (∆₄₇) in Aragonite

Abstract

Clumped isotope thermometry can independently constrain the formation temperatures of carbonates, but a lack of precisely temperature‐controlled calibration samples limits its application on aragonites. To address this issue, we present clumped isotope compositions of aragonitic bivalve shells grown under highly controlled temperatures (1–18°C), which we combine with clumped isotope data from natural and synthetic aragonites from a wide range of temperatures (1–850°C). We observe no discernible offset in clumped isotope values between aragonitic foraminifera, mollusks, and abiogenic aragonites or between aragonites and calcites, eliminating the need for a mineral‐specific calibration or acid fractionation factor. However, due to non‐linear behavior of the clumped isotope thermometer, including high‐temperature (>100°C) datapoints in linear clumped isotope calibrations causes them to underestimate temperatures of cold (1–18°C) carbonates by 2.7 ± 2.0°C (95% confidence level). Therefore, clumped isotope‐based paleoclimate reconstructions should be calibrated using samples with well constrained formation temperatures close to those of the samples.

Key Points

• Precise control on carbonate formation temperatures enables more accurate clumped isotope‐temperature calibrations

• Isotopic ordering and acid fractionation in aragonite have a similar temperature dependence as in calcite, enabling combined calibrations

• The Δ₄₇ $-\frac{1}{T^2}$ relation in carbonate is non‐linear, therefore adding hot calibration data offsets calibrations in the cold temperature range

1. Introduction

Since its first applications (e.g., Ghosh et al., ²⁰⁰⁶; Schauble et al., ²⁰⁰³; Wang et al., ²⁰⁰⁴), carbonate clumped isotope analysis has developed into a valuable tool for paleothermometry in the geosciences. Clumped isotope analysis is based on the thermodynamic principle that molecules with multiple heavy isotopes (so‐called “multiply‐substituted isotopologues”) have lower vibrational energies than molecules containing lighter isotopes (Urey, 1947). Consequently, the increase in system entropy at higher temperatures causes a decrease in the occurrence of multiply‐substituted isotopologues, and “clumping” of heavy isotopes within the same molecule is favored in low‐energy systems (Eiler, 2007). In carbonates, this principle causes heavy carbonate ions (e.g., ¹³C¹⁸O¹⁶O₂; mass 63 or ¹²C¹⁸O₂ ¹⁶O; mass 64) to become more abundant with decreasing calcification temperatures (Ghosh et al., 2006). The distribution of these isotopologues is proportional in the CO₂ gas after reaction of carbonates with acid (e.g., ¹³C¹⁸O¹⁶O; mass 47 and ¹²C¹⁸O₂, mass 48 respectively) and is measured with reference to the distribution of isotopologues in a fully scrambled heated CO₂ gas with the same isotopic composition:

$${\Delta }_{47}[‰]=\left(\frac{R^{47}}{R^{47}\ast }-1\right)$$ (1)

In which R ⁴⁷ is the ratio of CO₂ molecules with mass 47 (predominantly ¹³C¹⁸O¹⁶O) relative to CO₂ with the most common mass 44 (¹²C¹⁶O₂) in the sample, and R ⁴⁷* is the same ratio in stochastic equilibrium (Daëron et al., 2016). This ∆₄₇ value is a measure for the degree of “clumping” in the sample which depends on its calcification temperature.

The main advantage of carbonate clumped isotope analysis over previous paleothermometers is its basis on thermodynamic principles and its independence from the chemistry of the precipitation fluid (Eiler, 2007). The latter represents an improvement over the often‐used oxygen isotope paleothermometer (δ¹⁸O), which requires knowledge of the oxygen isotope composition of the precipitation fluid (δ¹⁸O_w; e.g., Epstein et al., ¹⁹⁵³; Kim & O’Neil, ¹⁹⁹⁷). The clumped isotope method has many applications, notably to reconstruct absolute temperature variability throughout Earth's history (e.g., Agterhuis et al., ²⁰²²; de Winter, Müller et al., ²⁰²¹; Meckler et al., ²⁰²²; Henkes et al., ²⁰¹⁸; Rodríguez‐Sanz et al., ²⁰¹⁷; Vickers, Lengger, et al., ²⁰²⁰).

Inter‐lab standardization of carbonate ∆₄₇ measurements has reconciled former offsets between laboratories using different CO₂ preparation methods and reconciled the clumped isotope temperature calibration of calcites with the results of thermodynamic ab initio models (Bernasconi et al., 2018, ²⁰²¹; Jautzy et al., ²⁰²⁰; Petersen et al., ²⁰¹⁹). A unified linear Δ₄₇ $-\frac{1}{T^2}$ calibration was established through re‐standardized ∆₄₇ values of carbonates precipitated at a wide range of known temperatures (0.5–1,100°C; Anderson et al., ²⁰²¹). This eliminates concerns over the confounding effects of differences in the origin of carbonates (e.g., biogenic vs. inorganic; Henkes et al., ²⁰¹³), varying mineralization rates (Daëron et al., 2019), different acid digestion temperatures and different carbonate mineralogies (e.g., dolomite vs. calcite; Müller et al., ²⁰¹⁹) on the clumped isotope thermometer. However, it remains unclear whether biological process (i.e., “vital effects”) influence isotopic ordering in some biogenic carbonates.

The unified calibration data set includes only one aragonitic carbonate, insufficient to test for different clumped isotope temperature dependencies between aragonites and calcites (Anderson et al., 2021). Results of ab initio models suggest that such a difference between the two polymorphs may exist (Guo et al., 2009; Schauble et al., ²⁰⁰⁶) and experimental studies disagree on a difference in acid fractionation factor (AFF) between calcite and aragonite (Guo et al., 2009; Müller et al., ²⁰¹⁹; Petersen et al., ²⁰¹⁹). These uncertainties are confounded by the fact that most carbonates used in current calibrations are precipitated under natural circumstances with indirectly estimated or else poorly controlled temperature regimes (e.g., Kele et al., ²⁰¹⁵; Peral et al., ²⁰¹⁸). The potential ∆₄₇ offset between aragonite and calcite might introduce an unknown bias when using the unified temperature calibration on aragonite data (e.g., Caldarescu et al., ²⁰²¹); a severe limitation given the common occurrence of aragonite in biogenic calcifiers (e.g., bivalves; Kennedy et al., ¹⁹⁶⁹, gastropods; Taylor & Reid, ¹⁹⁹⁰, and foraminifera; Hansen, ¹⁹⁷⁹) as well as inorganic natural carbonates (e.g., speleothems; Frisia et al., ²⁰⁰⁰, and travertines; Kele et al., ²⁰¹⁵).

This study presents new clumped isotope results from precisely temperature controlled, lab‐grown aragonitic Arctica islandica bivalve shells. The bivalve Arctica islandica is a highly utilized climate archive, and a promising substrate for clumped isotope‐based paleothermometry (e.g., Buchardt & Símonarson, ²⁰⁰³; Butler et al., ²⁰¹³; Schöne & Fiebig, ²⁰⁰⁹; Schöne et al., ²⁰⁰⁵; Witbaard et al., ¹⁹⁹⁷). Combined with preexisting aragonite clumped isotope data (Bernasconi et al., 2018; Breitenbach et al., ²⁰¹⁸; Caldarescu et al., ²⁰²¹; Kele et al., ²⁰¹⁵; Kluge et al., ²⁰¹⁵; Müller et al., ²⁰¹⁷; Piasecki et al., ²⁰¹⁹) standardized to the new Intercarb‐Carbon Dioxide Equilibrium Scale (I‐CDES) reference frame (Bernasconi et al., 2021), our data set resolves potential vital effects on clumped isotopes in aragonitic mollusks by comparing species as well as specimens grown under the same controlled conditions. This study aims to offer a detailed investigation of the clumped isotope temperature dependence in aragonites.

2. Materials and Methods

2.1. Lab Grown Arctica Islandica

Arctica islandica bivalves were cultured inside the lab of the Royal Netherlands Institute for Sea Research (NIOZ, Texel, the Netherlands). Specimens used for this study were grown under four different, constant, and monitored temperature regimes: 1.1 ± 0.2°C, 3.2 ± 0.3°C, 15 ± 0.4°C, and 18 ± 0.3°C (see Table 1; Supporting Information S9, https://doi.org/10.5281/zenodo.6524705). Details on the culturing setup are provided in Supporting Information S1 and Witbaard et al. (1998). Aragonite from cleaned and dried Arctica islandica shells was sampled using a hand‐held Dremel 3,000 rotary drill at low speed equipped with a tungsten‐carbide drill bit (see Supporting Information S1). Gathering enough aragonite for reliable ∆₄₇ analyses for each temperature treatment (>2 mg; Müller et al., ²⁰¹⁷; Fernandez et al., ²⁰¹⁷) typically required combining material from multiple (3–5) specimens grown under the same temperature conditions. To test potential inter‐specimen differences, results were tracked per individual specimen for the 1.1 ± 0.2°C and 18 ± 0.3°C treatments (see Table 1).

Table 1.

Arctica Islandica Clumped Isotope Results Compared to Previous Calibrations “Mixed” = Combined Samples From Multiple Specimens, Number Codes (e.g., “29” or “6A”) = Material From One Individual

Sample	Culturing temperature	∆47 (I‐CDES; ± 95%CL)		N	Offset from Anderson	Offset from Meinicke	Offset from Guo (cc)	Offset from Guo (ar)
Ais1	1.1 ± 0.2°C	Mixed	0.695 ± 0.019‰	34	–	–	–	–
		3	0.661 ± 0.023‰	13	–	–	–	–
		29	0.688 ± 0.025‰	15	–	–	–	–
		6A	0.684 ± 0.028‰	11	–	–	–	–
		6B	0.649 ± 0.026‰	9	–	–	–	–
		TOTAL	0.682 ± 0.010‰	82	+0.008‰	+0.002‰	+0.003‰	−0.016‰
					−2.12°C	−0.61°C	−0.75°C	+4.48°C
Ais3	3.2 ± 0.3°C	Mixed	0.667 ± 0.010‰	72	+0.001‰	−0.005‰+1.24°C	−0.006‰+1.57°C	−0.023‰ +6.80°C
					−0.27°C
Ais15	15 ± 0.4°C	Mixed	0.637 ± 0.009‰	57	+0.013‰	+0.008‰	+0.004‰	−0.013‰
					−3.63°C	−2.10°C	−0.99°C	+4.25°C
Ais18	18 ± 0.3°C	Mixed	0.635 ± 0.010‰	39	–	–	–	–
		67	0.647 ± 0.024‰	9	–	–	–	–
		89	0.640 ± 0.028‰	8	–	–	–	–
		111	0.630 ± 0.022‰	11	–	–	–	–
		TOTAL	0.637 ± 0.005‰	67	+0.021‰	+0.016‰	+0.012‰	−0.004‰
					−6.63°C	−5.10°C	−3.99°C	+1.25°C

Note. “Ais” = Arctica islandica. Significant ∆47 and temperature offsets are labeled in bold. cc = calcite, ar = aragonite.

2.2. Clumped Isotope Analysis

The clumped isotope composition of 278 aliquots of shell aragonite were analyzed over two 6‐month periods (March–August 2020; May–November 2021) on two Thermo isotope ratio mass spectrometers (one MAT253 and one MAT253 plus) coupled to Kiel IV carbonate preparation devices (see Supporting Information S1). After correcting for variability in the pressure baseline (He et al., 2012), clumped isotope results were processed relative to the I‐CDES through an empirical transfer function (ETF) based on measurements of ETH standards (ETH‐1, −2 and −3) and their accepted I‐CDES values (Bernasconi et al., 2021). Isotopic values were calculated using the latest International Union of Pure and Applied Chemistry values (Brand et al., 2010; Daëron et al., ²⁰¹⁶). No AFF was applied after I‐CDES standardization because the carbonate standards used for the ETF undergo the same acid reaction as the samples (Bernasconi et al., 2021). Long‐term accuracy and reproducibility of ∆₄₇ results were assessed based on repeated measurements of the IAEA‐C2 monitoring standard (∆_{47_IAEA} on MAT253 plus: 0.6382 ± 0.026‰; ∆_{47_IAEA} on MAT253: 0.6445 ± 0.046‰; 1σ). Results were indistinguishable from the accepted value for IAEA‐C2 (0.6409 ± 0.003‰; 95% CL; Bernasconi et al., ²⁰²¹). Full results of all sample aliquots and standards used to standardize the results are provided in Supporting Information S2, https://doi.org/10.5281/zenodo.6524705.

2.3. Data Compilation

The Arctica islandica data set was augmented with literature ∆₄₇ values of aragonites with known calcification temperatures (see Supporting Information S3, https://doi.org/10.5281/zenodo.6524705). The data set includes samples from mollusks (Bernasconi et al., 2018; aragonitic Megapitaria aurantiaca samples in Caldarescu et al., ²⁰²¹; this study), foraminifera (Piasecki et al., 2019), travertines (Bernasconi et al., 2018; Kele et al., ²⁰¹⁵), cave deposits (Breitenbach et al., 2018), lab‐grown aragonites (Kluge et al., 2015), and heated aragonites (Müller et al., 2017). Data from several older studies (e.g., Dong et al., ²⁰²¹; Ghosh et al., ²⁰⁰⁶, ²⁰⁰⁷; Tripati et al., ²⁰¹⁰; Wacker et al., ²⁰¹³, ²⁰¹⁴; Zhai et al., ²⁰¹⁹; Zhang et al., ²⁰¹⁸) were not included because they were not corrected for the pressure baseline (Bernasconi et al., 2013; He et al., ²⁰¹²), could not be transferred into the standard reference frame (Dennis et al., 2011), lacked the standardization required to bring ∆₄₇ values into the I‐CDES scale (Bernasconi et al., 2021) or because the aragonite was precipitated out of equilibrium (e.g., Kimball et al., ²⁰¹⁶; Chen et al., ²⁰¹⁹; Supporting Information S1 and Supporting Information S3, https://doi.org/10.5281/zenodo.6524705). Clumped isotope data from the literature was brought to the I‐CDES reference frame using the multi‐linear correction proposed in Appendix A of Bernasconi et al. (2021) using values of carbonate standards reported in the studies (see Supporting Information S1). Uncertainties on the formation temperatures of the non‐temperature controlled datapoints from previous studies were generally in the order of 1°C (1σ; see Supporting Information S1). The full data set including ∆₄₇ values and temperatures with their uncertainties used in this study is provided in Supporting Information S4, https://doi.org/10.5281/zenodo.6524705. Unless stated otherwise, uncertainties are cited at the 95% confidence level.

All data processing for this study was done in R (R Core Team, ²⁰²²) and scripts are provided in Supporting Information S5, https://doi.org/10.5281/zenodo.6524705 and published on Github (https://github.com/nielsjdewinter/Aragonite_clumped). Details on data processing are provided in Supporting Information S1. We compare our data with calibrations by Anderson et al. (2021) and a compilation of foraminifera calibration data from Peral et al. (2018) and Meinicke et al. (2020) as well as with temperature dependencies of aragonite and calcite clumped isotope compositions from ab initio modeling in Guo et al. (2009) brought into the I‐CDES reference frame (see Supporting Information S1).

3. Results

3.1. Clumped Isotope Values in Arctica Islandica

Clumped isotope results from A. islandica are summarized in Table 1 and Figure 1. There is no significant clumped isotope difference between specimens in the same temperature treatment (F(4,77) = 1.937, p = 0.11 for the 1°C specimens and F(3,63) = 0.377, p = 0.77 for the 18°C specimens; see Supporting Information S6, https://doi.org/10.5281/zenodo.6524705). The number of measurements per specimen was large enough to exclude per‐specimen ∆₄₇ differences outside the reproducibility standard deviation of the clumped isotope analyses (0.046‰; see Table 1 and Supporting Information S6, https://doi.org/10.5281/zenodo.6524705). Differences between all temperature treatments are statistically significant (P(3,274) = 15.68, p < 0.01), except for differences between the 15°C and 18°C temperature bin and the difference between 1°C and 3°C (95%CL; Supporting Information S6, https://doi.org/10.5281/zenodo.6524705).

Figure 1.

Arctica islandica ∆₄₇ results. Clumped isotope results are aggregated by specimen or multi‐specimen sample (round symbols; see Table 1). Vertical lines represent 95% CL and number indicate sample size. Data is color‐coded per temperature treatment (1°C, 3°C, 15°C and 18°C), with bold error bars indicating 95% CL, pairs of letter labels (a and b) indicate statistically indistinguishable Δ₄₇ values (p < 0.05). The gray error bar at 6°C highlights (a) islandica data from Bernasconi et al. (2018; recalculated to Intercarb‐Carbon Dioxide Equilibrium Scale (I‐CDES)). Solid and dashed black lines show calibrations by Anderson et al. (2021) and Meinicke et al. (2020; projected on I‐CDES scale; Meinicke et al., ²⁰²¹), respectively. Gray solid and dashed lines represent, respectively, the theoretical calcite (“cc”) and aragonite (“ar”) temperature dependencies from Guo et al. (2009; projected on the I‐CDES scale, see Supporting Information S1). The horizontal axis is scaled to $\frac{{10}^6}{T^2}$, with T in K, to show the assumed linear relationship with the clumped isotope value.

We investigated the ∆₄₇ $-\frac{1}{T^2}$ relationship and how it varies along the temperature domain by performing linear regressions on increasingly large parts of our compilation. Note that the uncertainty on clumped isotope data compared with the small range of temperatures of the lab‐grown A. islandica leaves relatively high uncertainty on a clumped isotope‐temperature regression through these results alone compared with calibrations covering a larger temperature range such as the unified clumped isotope calibration (Anderson et al., 2021). We therefore do not advice using this and other regression equations in Section 3 for calibrating clumped isotope results (see Discussion).

Firstly, a statistically significant temperature relationship (∆₄₇ $-\frac{1}{T^2}$ slope >0; 95% CL) is found for ∆₄₇ exclusively from Arctica islandica samples:

$${\mathrm{\Delta }}_{47}\left(I-\mathrm{C}\mathrm{D}\mathrm{E}\mathrm{S}\right)=0.0280\pm 0.0042\ast \frac{{10}^6}{T^2}+0.304\pm 0.0524\left(\mathrm{T}\mathrm{i}\mathrm{n}\mathrm{K},\pm 1\sigma ;{\sigma }_{\mathrm{r}\mathrm{e}\mathrm{s}}=0.047‰\right)$$ (2)

Secondly, including other aragonitic mollusk data (Caldarescu et al., 2021) yields a regression indistinguishable from the Anderson et al. (2021) unified clumped isotope calibration:

$${\mathrm{\Delta }}_{47}\left(I-\mathrm{C}\mathrm{D}\mathrm{E}\mathrm{S}\right)=0.0443\pm 0.0024\ast \frac{{10}^6}{T^2}+0.097\pm 0.0291\left(\mathrm{T}\mathrm{i}\mathrm{n}\mathrm{K},\pm 1\sigma ;{\sigma }_{\mathrm{r}\mathrm{e}\mathrm{s}}=0.043‰\right)$$ (3)

3.2. Aragonite Clumped Isotope Temperature Dependence

When including clumped isotope values of other low‐temperature (<30°C) aragonites in the compilation, the regression remains indistinguishable from the calibration of Anderson et al. (2021) and similar to the foraminifera‐based calibration by Peral et al. (2018) and Meinicke et al. (2020) combined with reference to I‐CDES in Meinicke et al. (2021) and the Guo et al. (2009) theoretical temperature relationships (Figure 2b):

$${\mathrm{\Delta }}_{47}\left(I-\mathrm{C}\mathrm{D}\mathrm{E}\mathrm{S}\right)=0.0451\pm 0.0024\ast \frac{{10}^6}{T^2}+0.0871\pm 0.0287\left(\mathrm{T}\mathrm{i}\mathrm{n}\mathrm{K},\pm 1\sigma ;{\sigma }_{\mathrm{r}\mathrm{e}\mathrm{s}}=0.042‰\right)$$ (4)

Figure 2.

Aragonite ∆₄₇ temperature dependence. Clumped isotope data of aragonite samples plotted against formation temperature. (a) All data plotted over the full temperature range (1°C–850°C). Individual datapoints, averages and uncertainty on temperature and Δ₄₇ values (95% CL) are color‐coded by study. Symbols highlight different types of aragonite. The solid and dashed black lines show calibrations by Anderson et al. (2021) and Meinicke et al. (2020; ²⁰²¹; plotted for temperatures <30°C). Gray solid and dashed lines represent, respectively, the theoretical calcite (“cc”) and aragonite (“ar”) temperature dependencies from Guo et al. (2009; projected on the Intercarb‐Carbon Dioxide Equilibrium Scale (I‐CDES) scale, see Section 2.5). Colored dashed lines and shaded envelopes show York regressions through aragonite data and their 95% confidence envelopes, respectively. (b) Shows a zoom‐in of the plot in (a) for the low‐temperature domain (1–30°C). Note that the horizontal axis is scaled to $\frac{{10}^6}{T^2}$, with T in K, to show the assumed linear relationship with the clumped isotope value.

Finally, we included higher temperature (>30°C) datapoints, such as the cave deposits of Breitenbach et al. (2018), travertine samples from Kele et al. (2015), precipitated aragonites from Kluge et al. (2015) and heated aragonites from Müller et al. (2017) in the linear regression. This decreases the slope and increases the intercept (see Figure 2):

$${\mathrm{\Delta }}_{47}\left(I-\mathrm{C}\mathrm{D}\mathrm{E}\mathrm{S}\right)=0.0403\pm 0.0005\ast \frac{{10}^6}{T^2}+0.1435\pm 0.0485\left(\mathrm{T}\mathrm{i}\mathrm{n}\mathrm{K},\pm 1\sigma ;{\sigma }_{\mathrm{r}\mathrm{e}\mathrm{s}}=0.040‰\right)$$ (5)

The formation temperatures of our A. islandica data on the very cold end of the calibration domain are significantly underestimated by Anderson et al. (2021; ΔΔ₄₇ = +0.009 ± 0.007‰; −2.71 ± 2.03°C; Figure 3; ΔΔ₄₇ = offset between data and calibration). The theoretical aragonite clumped isotope‐temperature relationship (Guo et al., 2009) severely overestimates our A. islandica temperatures (−0.016 ± 0.007‰; +4.35 ± 1.88°C; Figure 3). Contrarily, the Meinicke et al. (2020, ²⁰²¹) calibration (ΔΔ₄₇ = +0.004 ± 0.007‰; −1.17 ± 2.00°C; Figure 3) and the theoretical calcite temperature relationship (Guo et al., 2009; ΔΔ₄₇ = +0.002 ± 0.007‰; −0.47 ± 1.98°C; Figure 3) do not significantly over‐ or underestimate the formation temperature of our A. islandica shells.

Figure 3.

Offset of A. islandica data from temperature regressions. Shaded gray points show residual ∆₄₇ values relative to four clumped isotope temperature relationships (see horizontal axis). Black symbols with error bars (95% CL) show mean offsets of all A. islandica datapoints (grown at 1°C, 3°C, 6°C, 15°C and 18°C) from the calibrations. The vertical axis on the right shows the temperature offset relative to the weighted mean calcification temperature of the full A. islandica data set (8.6°C; see Supporting Information S4, https://doi.org/10.5281/zenodo.6524705) based on Anderson et al. (2021).

4. Discussion

4.1. Isotope Ordering in Aragonitic Mollusks

Clumped isotope values of our temperature‐controlled A. islandica samples consistently plot on a ∆₄₇ $-\frac{1}{T^2}$ linear relationship with other low‐temperature aragonite datapoints (Figures 1 and 2; see Section 4.2). The absence of a consistent offset between A. islandica datapoints and other aragonites (mean Δ₄₇ difference of +0.003 ± 0.004‰, see Figure 2 and Supporting Information S8, https://doi.org/10.5281/zenodo.6524705) and agreement between the linear ∆₄₇ $-\frac{1}{T^2}$ dependence of the aragonitic mollusk data in this study and the regression through the complete low‐temperature aragonite data set (Figure 1 and Section 3.1) strongly supports a common temperature dependence for all aragonites in this study, biogenic or inorganic, and argues against disequilibrium fractionation in aragonite precipitated inorganically or vital effect in bivalves or foraminifera (see Section 3.1; Figures 1 and 2). Our highly temperature‐controlled growth experiments uniquely allow us to exclude variability in the growth environment between specimens from the same growth treatment as a driver of shell composition. Strong similarity of Δ₄₇ values between individual A. islandica specimens grown at the same temperature thus rules out specimen‐specific vital effects on the clumped isotope composition aragonitic bivalve shells outside the uncertainty of our measurements (see Section 3.1; Figure 1, Table 1 and Supporting Information S6, https://doi.org/10.5281/zenodo.6524705). These findings corroborate measurements in calcitic mollusks showing that clumped isotope values in mollusk carbonates adhere to the same temperature relationship as other carbonates precipitated in equilibrium (except for juvenile oyster shells; Huyghe et al., ²⁰²²). Clumped isotope analyses in (fossil) mollusk shells thus provide an independent temperature proxy, allowing paleoclimatologists to disentangle the effects of variability in temperature and the hydrological cycle (as measured in δ¹⁸O_w) throughout geological history down to the seasonal timescale (e.g., Caldarescu et al., ²⁰²¹; de Winter et al., ²⁰²¹; Letulle et al., ²⁰²²).

4.2. Mineral‐Specific Acid Fractionation Factor

Residuals of aragonite clumped isotope data around the low‐temperature (<30°C) York regression (0.042‰; 1σ; see Section 3.2, Equation 4 and Figure 2) are predominantly explained by analytical uncertainty on Δ₄₇ measurements (external precision of 0.026 and 0.046‰ on the 253Plus and the MAT253 mass spectrometers; 1σ; see Section 2.2). Uncertainty on formation temperatures in the low‐temperature data set (±0.8°C; 1σ; see Supporting Information S4, https://doi.org/10.5281/zenodo.6524705) would add an additional uncertainty of 0.0024‰ (1σ) if applied to the weighted average formation temperature of all low‐temperature (<30°C) data points (22.0°C; see Supporting Information S4, https://doi.org/10.5281/zenodo.6524705). Outside these uncertainties in the compilation data, there is little uncertainty on the temperature relationship in the low‐temperature domain (<30°C; see Section 3.2; Figure 2). If clumped isotope fractionation during acid digestion was indeed different between aragonite and calcite (as suggested in Müller et al., ²⁰¹⁷; Petersen et al., ²⁰¹⁹) this would result in an offset between our aragonite data set and the previous calcite‐based calibrations (e.g., Meinicke et al., ²⁰²⁰, ²⁰²¹). The close similarity between our A. islandica data and the calcite calibration (ΔΔ₄₇ = 0.004 ± 0.007‰; Figure 3; Supporting Information S7, https://doi.org/10.5281/zenodo.6524705) leaves little room for the 0.007 and 0.025‰ difference in AFF reported in Petersen et al. (2019) and Müller et al. (2017), respectively. We therefore conclude that the calcite AFF in Petersen et al. (2019), which are included in the I‐CDES reference scale (Bernasconi et al., 2021) can be used for aragonite samples.

4.3. Non‐Linear Temperature Dependence of Clumped Isotopes in Aragonites

Current clumped isotope calibrations (Anderson et al., 2021; Meinicke et al., ²⁰²⁰, 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). In addition, the cold‐water (<30°C) carbonate based Meinicke et al. (2020) calibration more closely resembles the modeled temperature relationship for calcites in Guo et al. (2009). Including high‐temperature (>30°C) data in our linear regression leads to overestimation of the temperature of warmer (>18°C) datapoints (ΔΔ₄₇ of −0.005 ± 0.006‰, or +${1.8}_{-2.0}^{+2.1}$ °C for samples precipitated at 30°C), while underestimating colder datapoints (ΔΔ₄₇ of +0.009 ± 0.008‰, or −${2.0}_{-2.0}^{+2.0}$ °C for samples precipitated at 0°C; Figure 2; Supporting Information S7, https://doi.org/10.5281/zenodo.6524705). Point‐by‐point offsets of all data from the calibration lines are provided in Supporting Information S8, https://doi.org/10.5281/zenodo.6524705.

This difference between ∆₄₇ $-\frac{1}{T^2}$ regressions through the low‐temperature (<30°C) and the full data set (see Section 3.2; Figure 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 modeling 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) data set, where Δ₄₇ values of calcites precipitated between 100°C and 1,000°C are underestimated by the linear relationship, while the hottest datapoints (calcites heated to 1,100°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 data set 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 Figures 2 and 3 and Section 4.4). Therefore, more high‐temperature aragonite datapoints are needed to constrain the clumped isotope‐temperature relationship for temperatures >100°C.

4.4. Calibrating the Clumped Isotope‐Temperature Relationship in Cold (<30°C) Carbonates

Our lab‐grown A. islandica shells offer more control on formation temperature than naturally grown carbonates precipitated under variable temperatures. Ideally, the temperature of these natural samples is monitored so an average temperature can be calculated for the targeted growth period (e.g., de Winter et al., ²⁰²⁰, de Winter, Dämmer et al., ²⁰²¹; Huyghe et al., ²⁰²²; Kele et al., ²⁰¹⁵). However, formation temperatures are often indirectly estimated through other proxies (e.g., δ¹⁸O_c) and/or estimates of the living environment (e.g., water depth) of the carbonate producer, accumulating uncertainty (e.g., Meinicke et al., ²⁰²⁰; Peral et al., ²⁰¹⁸; Piasecki et al., ²⁰¹⁹). These caveats obscure the full uncertainty of the formation temperatures of natural carbonates as well as the effect of this unknown uncertainty on the calibrations. Considering the methods by which the “known” temperatures of natural carbonates are estimated in previous studies, part of the ∼1.5°C temperature offset between Anderson et al. (2021) and Meinicke et al. (2020; ²⁰²¹; see Figure 3) and the 2.7 ± 2.0°C offset between Anderson et al. (2021) and our A. islandica data might be caused by uncertainty on the formation temperatures of the calibration data set. However, our highly temperature‐controlled A. islandica datapoints reveal that, despite uncertainty on formation temperature, the Meinicke et al. (2021) calibration locally approximates the non‐linear ∆₄₇ $-\frac{1}{T^2}$ relationship in the cold temperature domain with higher accuracy than the Anderson et al. (2021) calibration (Figures 1 and 3; Supporting Information S8, https://doi.org/10.5281/zenodo.6524705). The non‐linear theoretical calcite temperature dependence by Guo et al. (2009) also fits well with the data. Precisely temperature‐controlled carbonates thus better constrain the slope of the ∆₄₇ $-\frac{1}{T^2}$ relationship for cold carbonates (improving calibration accuracy) while reducing the uncertainty on the calibration (improving calibration precision).

The ∼1.5°C difference in reconstructed temperature between the calibrations in the low temperature range (<30°C) may seem trivial and requires the complete A. islandica data set (N = 278; see Figure 3) to resolve. However, in paleoclimate reconstructions (e.g., Agterhuis et al., ²⁰²²; de Winter, Müller et al., ²⁰²¹; de Winter et al., ²⁰¹⁷; Meckler et al., ²⁰²²; Petersen et al., ²⁰¹⁶; Vickers, Fernandez, et al., ²⁰²⁰), this temperature offset may have significant consequences. A ∼1.5°C cold bias in temperature reconstructions may lead to a significant underestimation of climate sensitivity to CO₂ forcing, biasing the physical science basis for informing policymakers about future climate change (e.g., Dennis et al., ²⁰¹³; IPCC, ²⁰²¹; Modestou et al., ²⁰²⁰; Tierney et al., ²⁰²⁰; Westerhold et al., ²⁰²⁰). Accurate clumped isotope‐based temperature reconstructions therefore require calibration data sets with precisely constrained formation temperatures tailored to the temperature range of the samples.

Supporting information

Supporting Information S1

de Winter, N. J. , Witbaard, R. , Kocken, I. J. , Müller, I. A. , Guo, J. , Goudsmit, B. , & Ziegler, M. (2022). Temperature dependence of clumped isotopes (∆₄₇) in aragonite. Geophysical Research Letters, 49, e2022GL099479. 10.1029/2022GL099479

Data Availability Statement

Supplementary materials are deposited on the open‐source repository Zenodo and can be accessed through the following link: https://doi.org/10.5281/zenodo.6524705. R scripts are uploaded on GitHub (https://github.com/nielsjdewinter/Aragonite_clumped) and archived in Zenodo (https://doi.org/10.5281/zenodo.6560188). In addition, all clumped isotope data produced for this study were deposited in the EarthChem Library and are freely accessible through the following DOI: https://doi.org/10.26022/IEDA/112316.