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Introduction

Classic oxygen isotope thermometry typically assumes that respective carbonates form in thermodynamic equilibrium with the ambient seawater, and thus, the carbonates’ isotope composition only depends on temperature (T) and the composition of the ambient water. In biogenic carbonates, however, vital effects exert additional control on the magnitude of the total fractionation. Vital effects are a combination of kinetic and metabolic effects that influence the isotope composition of many biogenic minerals, including coral carbonate. While coral carbonate serves as a valuable high resolution climate archive, interpreting their isotopic code remains challenging due to the complexity of their biomineralisation mechanism.

It has long been noticed that most modern coral carbonate comprises much lower δ¹⁸O and δ¹³C than expected from equilibrium (Weber and Woodhead, 1972

Weber, J.N., Woodhead, P.M.J. (1972) Temperature dependence of oxygen-18 concentration in reef coral carbonates. Journal of Geophysical Research 77, 463–473. https://doi.org/10.1029/JC077i003p00463

; McConnaughey, 1989a

McConnaughey, T. (1989a) ¹³C and ¹⁸O isotopic disequilibrium in biological carbonates: I. Patterns. Geochimica et Cosmochimica Acta 53, 151–162. https://doi.org/10.1016/0016-7037(89)90282-2

; Smith et al., 2000

Smith, J.E., Schwarcz, H.P., Risk, M.J., McConnaughey, T.A., Keller, N. (2000) Paleotemperatures from deep-sea corals: Overcoming “vital effects.” Palaios 15, 25–32. https://doi.org/10.1669/0883-1351(2000)015<0025:pfdsco>2.0.co;2

; Adkins et al., 2003

Adkins, J.F., Boyle, E.A., Curry, W.B., Lutringer, A. (2003) Stable isotopes in deep-sea corals and a new mechanism for “vital effects.” Geochimica et Cosmochimica Acta 67, 1129–1143. https://doi.org/10.1016/s0016-7037(02)01203-6

). Temperature estimates from equilibrium δ¹⁸O–T calibration curves indicate higher T (by >10 °C) compared to actual growth T. Although species-specific δ¹⁸O–T calibrations can partly account for vital effects (Weber and Woodhead, 1972

Weber, J.N., Woodhead, P.M.J. (1972) Temperature dependence of oxygen-18 concentration in reef coral carbonates. Journal of Geophysical Research 77, 463–473. https://doi.org/10.1029/JC077i003p00463

; Smith et al., 2000

Smith, J.E., Schwarcz, H.P., Risk, M.J., McConnaughey, T.A., Keller, N. (2000) Paleotemperatures from deep-sea corals: Overcoming “vital effects.” Palaios 15, 25–32. https://doi.org/10.1669/0883-1351(2000)015<0025:pfdsco>2.0.co;2

), the reconstructed temperatures can remain inaccurate (Marali et al., 2013

Marali, S., Wisshak, M., López Correa, M., Freiwald, A. (2013) Skeletal microstructure and stable isotope signature of three bathyal solitary cold-water corals from the Azores. Palaeogeography, Palaeoclimatology, Palaeoecology 373, 25–38. https://doi.org/10.1016/j.palaeo.2012.06.017

). Likewise, coral growth T determined using clumped isotope thermometry (Δ₄₇) is also biased by >10 °C, but towards lower T (Thiagarajan et al., 2011

Thiagarajan, N., Adkins, J., Eiler, J. (2011) Carbonate clumped isotope thermometry of deep-sea corals and implications for vital effects. Geochimica et Cosmochimica Acta 75, 4416–4425. https://doi.org/10.1016/j.gca.2011.05.004

; Saenger et al., 2012

Saenger, C., Affek, H.P., Felis, T., Thiagarajan, N., Lough, J.M., Holcomb, M. (2012) Carbonate clumped isotope variability in shallow water corals: Temperature dependence and growth-related vital effects. Geochimica et Cosmochimica Acta 99, 224–242. https://doi.org/10.1016/j.gca.2012.09.035

). Accurate coral thermometry will only become feasible if the isotopic bias is accounted for (e.g., Davies et al., 2022

Davies, A.J., Guo, W., Bernecker, M., Tagliavento, M., Raddatz, J., Gischler, E., Flögel, S., Fiebig, J. (2022) Dual clumped isotope thermometry of coral carbonate. Geochimica et Cosmochimica Acta 338, 66–78. https://doi.org/10.1016/j.gca.2022.10.015

).

Dual clumped isotope thermometry (Δ₄₇ and Δ₄₈) is a new approach currently explored to extract quantitative temperature information from carbonate samples affected by kinetic effects (Bajnai et al., 2020

Bajnai, D., Guo, W., Spötl, C., Coplen, T.B., Methner, K., Löffler, N., Krsnik, E., Gischler, E., Hansen, M., Henkel, D., Price, G.D., Raddatz, J., Scholz, D., Fiebig, J. (2020) Dual clumped isotope thermometry resolves kinetic biases in carbonate formation temperatures. Nature Communications 11, 4005. https://doi.org/10.1038/s41467-020-17501-0

). For coral carbonates, Davies et al. (2022)

Davies, A.J., Guo, W., Bernecker, M., Tagliavento, M., Raddatz, J., Gischler, E., Flögel, S., Fiebig, J. (2022) Dual clumped isotope thermometry of coral carbonate. Geochimica et Cosmochimica Acta 338, 66–78. https://doi.org/10.1016/j.gca.2022.10.015

show systematic deviations from clumped isotope equilibrium along slopes characteristic of the underlying kinetic mechanisms. Apparent temperatures are corrected by back-extrapolating to the equilibrium line, providing accurate growth temperature reconstructions with a precision better than ±3 °C (1 s.e.). Here, we propose a similar concept for attaining accurate carbonate growth temperatures but using triple oxygen isotopes.

Triple oxygen isotope analyses involve the simultaneous analysis of δ¹⁷O and δ¹⁸O. Most Earth surface processes result in mass-dependent fractionation, which leads to a nearly perfect correlation between δ¹⁷O and δ¹⁸O values with a slope of approximately 0.5. The mass-dependent fractionation between two phases is described by Equation 1, where θ represents the triple oxygen isotope exponent characteristic of the process and temperature, and α is the equilibrium isotope fractionation factor:

Because the θ values of mass-dependent processes vary within a small range, the Δ’¹⁷O notation (in ppm) is used to visualise differences between them:

Here, we chose 0.528 for λ_RL (Luz and Barkan, 2010

Luz, B., Barkan, E. (2010) Variations of ¹⁷O/¹⁶O and ¹⁸O/¹⁶O in meteoric waters. Geochimica et Cosmochimica Acta 74, 6276–6286. https://doi.org/10.1016/j.gca.2010.08.016

). The logarithmic transformation of the δ-values in Equation 2 is commonly abbreviated as δ’. All oxygen isotope values in this study are reported on the VSMOW (Vienna Standard Mean Ocean Water) scale.

Carbonates forming in thermodynamic equilibrium must fall on the equilibrium curve in Δ’¹⁷O vs. δ’¹⁸O space. Kinetic processes simultaneously drive δ¹⁸O and Δ’¹⁷O away from this curve. The slope (or θ) of any given kinetic process is a physical constant. Yet, apparent slopes may result from a combination of processes (Guo and Zhou, 2019

Guo, W., Zhou, C. (2019) Triple oxygen isotope fractionation in the DIC-H₂O-CO₂ system: A numerical framework and its implications. Geochimica et Cosmochimica Acta 246, 541–564. https://doi.org/10.1016/j.gca.2018.11.018

; Wostbrock et al., 2020a

Wostbrock, J.A.G., Brand, U., Coplen, T.B., Swart, P.K., Carlson, S.J., Brearley, A.J., Sharp, Z.D. (2020a) Calibration of carbonate-water triple oxygen isotope fractionation: Seeing through diagenesis in ancient carbonates. Geochimica et Cosmochimica Acta 288, 369–388. https://doi.org/10.1016/j.gca.2020.07.045

; Herwartz, 2021

Herwartz, D. (2021) Triple oxygen isotope variations in Earth’s crust. Reviews in Mineralogy and Geochemistry 86, 291–322. https://doi.org/10.2138/rmg.2021.86.09

; Bajnai et al., 2024

Bajnai, D., Cao, X., Klipsch, S., Pack, A., Herwartz, D. (2024) Triple oxygen isotope systematics of CO₂ hydroxylation. Chemical Geology 654, 122059. https://doi.org/10.1016/j.chemgeo.2024.122059

). Constraining an empirical slope for the vital effects in corals and using it for back-extrapolation to the equilibrium curve makes accurate paleotemperature reconstructions feasible. In addition, the kinetic slope in triple oxygen isotope space can help in the mechanistic understanding of the underlying vital effects.

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Coral Triple Oxygen Isotope Analyses

We analysed the triple oxygen isotope composition of 17 modern scleractinian (aragonitic) corals, representing four cold-water and five warm-water species. We retrieved seawater temperature and δ¹⁸O_sw for each sample from a global gridded database (Breitkreuz et al., 2018

Breitkreuz, C., Paul, A., Kurahashi‐Nakamura, T., Losch, M., Schulz, M. (2018) A dynamical reconstruction of the global monthly mean oxygen isotopic composition of seawater. Journal of Geophysical Research: Oceans 123, 7206–7219. https://doi.org/10.1029/2018JC014300

), using the interpolation method outlined in Daëron and Gray (2023)

Daëron, M., Gray, W.R. (2023) Revisiting oxygen‐18 and clumped isotopes in planktic and benthic foraminifera. Paleoceanography and Paleoclimatology 38, e2023PA004660. https://doi.org/10.1029/2023PA004660

. For some samples, in situ measured T and δ¹⁸O_sw values were also available, which we used to assess the accuracy of the database estimates. The database and in situ measured values showed close agreement, typically within ±1 °C and ±0.2 ‰ (Fig. S–1). We regarded these average differences as indicative of the precision of the database and additionally factored in the interpolation error (on average ±1 °C and ±0.2 ‰) to obtain the final uncertainty of the database’s seawater T and δ¹⁸O estimates. We used the database values and their uncertainties to calculate the expected equilibrium δ¹⁸O and Δ’¹⁷O values. Seawater Δ’¹⁷O values were not directly measured but universally assumed to be Δ’¹⁷O_sw = −11 ± 6 ppm, which covers most modern seawater data (Luz and Barkan, 2010

Luz, B., Barkan, E. (2010) Variations of ¹⁷O/¹⁶O and ¹⁸O/¹⁶O in meteoric waters. Geochimica et Cosmochimica Acta 74, 6276–6286. https://doi.org/10.1016/j.gca.2010.08.016

; Lin et al., 2021

Lin, Y., Wu, N., Ta, K., Landais, A., Peng, X. (2021) Triple oxygen isotopic compositions of ocean water from the Mariana Trench. ACS Earth and Space Chemistry 5, 3087–3096. https://doi.org/10.1021/acsearthspacechem.1c00187

). Information on the samples is summarised in Tables S-1 and S-3.

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The triple oxygen isotope analyses were conducted at the University of Göttingen using a tuneable infrared laser direct absorption spectrometer (TILDAS), detailed in Bajnai et al. (2023)

Bajnai, D., Pack, A., Arduin Rode, F., Seefeld, M., Surma, J., Di Rocco, T. (2023) A dual inlet system for laser spectroscopy of triple oxygen isotopes in carbonate-derived and air CO₂. Geochemistry, Geophysics, Geosystems 24, e2023GC010976. https://doi.org/10.1029/2023GC010976

. The CO₂ analyte gas was derived from acid digestion at 25 °C. Carbonate-derived CO₂ data were normalised relative to two in-house standards: heavy CO₂ and light CO₂ measured alongside the samples, as detailed in Bajnai et al. (2024)

Bajnai, D., Cao, X., Klipsch, S., Pack, A., Herwartz, D. (2024) Triple oxygen isotope systematics of CO₂ hydroxylation. Chemical Geology 654, 122059. https://doi.org/10.1016/j.chemgeo.2024.122059

(Figs. S–2, S–3). Briefly, the triple oxygen isotope composition of these two reference gases was determined relative to NBS-18 and IAEA-603 measurements and the values reported by Wostbrock et al. (2020b)

Wostbrock, J.A.G., Cano, E.J., Sharp, Z.D. (2020b) An internally consistent triple oxygen isotope calibration of standards for silicates, carbonates and air relative to VSMOW2 and SLAP2. Chemical Geology 533, 119432. https://doi.org/10.1016/j.chemgeo.2019.119432

. A 25 °C acid fractionation factor was applied to the CO₂ data to calculate the isotope composition of the coral aragonite (i.e. ¹⁸α_{25°C-acid-CO2/aragonite} = 1.01063 (Kim et al., 2007

Kim, S.-T., Mucci, A., Taylor, B.E. (2007) Phosphoric acid fractionation factors for calcite and aragonite between 25 and 75 °C: Revisited. Chemical Geology 246, 135–146. https://doi.org/10.1016/j.chemgeo.2007.08.005

) and θ_{25°C-acid-CO2/carbonate} = 0.523 (Wostbrock et al., 2020b

Wostbrock, J.A.G., Cano, E.J., Sharp, Z.D. (2020b) An internally consistent triple oxygen isotope calibration of standards for silicates, carbonates and air relative to VSMOW2 and SLAP2. Chemical Geology 533, 119432. https://doi.org/10.1016/j.chemgeo.2019.119432

)).

In our final dataset, we included the warm-water coral data point reported by Passey et al. (2014)

Passey, B.H., Hu, H., Ji, H., Montanari, S., Li, S., Henkes, G.A., Levin, N.E. (2014) Triple oxygen isotopes in biogenic and sedimentary carbonates. Geochimica et Cosmochimica Acta 141, 1–25. https://doi.org/10.1016/j.gca.2014.06.006

(sample JBC03, Porites porites). To normalise this data point to our carbonate reference frame, we followed the steps outlined in Huth et al. (2022)

Huth, T.E., Passey, B.H., Cole, J.E., Lachniet, M.S., McGee, D., Denniston, R.F., Truebe, S., Levin, N.E. (2022) A framework for triple oxygen isotopes in speleothem paleoclimatology. Geochimica et Cosmochimica Acta 319, 191–219. https://doi.org/10.1016/j.gca.2021.11.002

. Specifically, we applied empirical fractionation factors to the reported O₂/CaCO₃ values to account for fractionations induced by acid digestion and fluorination (¹⁸α_empirical = 1.00812 and θ_empirical = 0.5234). Additionally, to account for the difference in the acid fractionation factors between aragonite and calcite, we shifted the corrected δ¹⁸O value by 0.41 ‰ (Kim et al., 2007

Kim, S.-T., Mucci, A., Taylor, B.E. (2007) Phosphoric acid fractionation factors for calcite and aragonite between 25 and 75 °C: Revisited. Chemical Geology 246, 135–146. https://doi.org/10.1016/j.chemgeo.2007.08.005

). The respective seawater temperature and δ¹⁸O_sw values were determined in the same manner as for our samples.

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Results

The results of the triple oxygen isotope analyses are presented in Tables S-2 and S-3 and shown in Figure 1a. The long-term repeatability of the Δ’¹⁷O measurements of the heavy CO₂ and light CO₂ reference gases was 8–12 ppm. For the coral samples, the standard deviation of 2 to 7 replicate analyses was generally ±5 ppm for Δ’¹⁷O, while for δ¹⁸O it was ±0.1 ‰.

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Discussion

Seeing through vital effects. We chose the theoretical aragonite calibration of Guo and Zhou (2019)

Guo, W., Zhou, C. (2019) Triple oxygen isotope fractionation in the DIC-H₂O-CO₂ system: A numerical framework and its implications. Geochimica et Cosmochimica Acta 246, 541–564. https://doi.org/10.1016/j.gca.2018.11.018

as representative of thermodynamic equilibrium. In triple oxygen isotope space, all cold- and warm-water corals fall below their respective equilibrium lines (Figs. 1, 2). These offsets indicate that these corals did not form carbonate in equilibrium with seawater. Thus, respective δ¹⁸O-temperature estimates are inaccurate (Fig. 3a) and attaining true T requires a correction for vital effects.

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For each coral, we calculated the effective vital effect slope (θ_coral) in triple oxygen isotope space, by connecting the measured and the expected equilibrium values (Fig. 1). The θ_coral values ranged between 0.527 and 0.531, with a mean of 0.529 and a standard deviation of ±0.001 ppm. To evaluate the accuracy of each θ_coral estimate, we used Monte Carlo error propagation, considering measurement errors and growth parameter uncertainties. The error of the individual θ_coral values was approximately ±0.002.

There was no resolvable difference in the vital effect slopes between species or among cold- and warm-water corals (Fig. S-5). In contrast, in dual clumped isotope space, cold- and warm-water corals exhibit distinct kinetic trajectories, explained by differences in the calcification parameters, such as the carbonic anhydrase activity, growth temperature, and the pH of the calcifying fluid (Davies et al., 2022

Davies, A.J., Guo, W., Bernecker, M., Tagliavento, M., Raddatz, J., Gischler, E., Flögel, S., Fiebig, J. (2022) Dual clumped isotope thermometry of coral carbonate. Geochimica et Cosmochimica Acta 338, 66–78. https://doi.org/10.1016/j.gca.2022.10.015

). Variations in these calcification parameters have a smaller impact on the kinetic slope in triple oxygen isotope space because the offset in δ¹⁸O is an order of magnitude larger than in Δ’¹⁷O (Figs. 1b, S-4). The vital effect slopes are, thus, primarily driven by the kinetic fractionation exerting the largest effect while species-specific variations in calcification parameters appear to be less important.

To calculate growth temperatures corrected for vital effects, we back-extrapolated individual data points to their respective equilibrium line using unique vital effect slopes (T_Δ’17O; Figs. 2, 3b, S-6). Rather than employing the previously established mean θ_coral, we calculated a distinct slope for each coral, derived from the data of all other corals except the one under analysis, thereby avoiding circularity in our calculations (Table S-3). The unique slopes were indistinguishable from the mean θ_coral of 0.529 within ±0.001. The reconstructed T_Δ’17O match the respective database T generally within ±3 °C (Fig. 3b). Considering the uncertainty of the isotope analyses and the seawater parameters, the accuracy of T_Δ’17O is much larger, ca. ±10 °C. Sensitivity analyses show that every 1 ppm decrease in Δ’¹⁷O errors corresponds to an approximately 1 °C reduction in the T_Δ’17O errors. Therefore, the ±6 ppm uncertainty in the seawater Δ’¹⁷O alone already accounts for an uncertainty over ±5 °C. Currently, only limited data exist for the triple oxygen isotope composition of seawater (Luz and Barkan, 2010

Luz, B., Barkan, E. (2010) Variations of ¹⁷O/¹⁶O and ¹⁸O/¹⁶O in meteoric waters. Geochimica et Cosmochimica Acta 74, 6276–6286. https://doi.org/10.1016/j.gca.2010.08.016

; Lin et al., 2021

Lin, Y., Wu, N., Ta, K., Landais, A., Peng, X. (2021) Triple oxygen isotopic compositions of ocean water from the Mariana Trench. ACS Earth and Space Chemistry 5, 3087–3096. https://doi.org/10.1021/acsearthspacechem.1c00187

). The inherent uncertainty of global variations in seawater Δ’¹⁷O is reduced when focusing on individual locations and effectively cancels out when reconstructing relative temperature shifts. Disregarding the uncertainty in seawater Δ’¹⁷O improves the accuracy of T_Δ’17O to ±5 °C.

Similar to Wostbrock et al. (2020a)

Wostbrock, J.A.G., Brand, U., Coplen, T.B., Swart, P.K., Carlson, S.J., Brearley, A.J., Sharp, Z.D. (2020a) Calibration of carbonate-water triple oxygen isotope fractionation: Seeing through diagenesis in ancient carbonates. Geochimica et Cosmochimica Acta 288, 369–388. https://doi.org/10.1016/j.gca.2020.07.045

, who explain how to ‘see through’ diagenesis using triple oxygen isotopes, the correction scheme outlined above allows us to see through vital effects. Importantly, a consistent but not necessarily “correct” reference frame is required for reconstructing growth temperatures. That is, the choice of equilibrium calibration does not significantly affect the T_Δ’17O estimates because the empirical slope obtained for a particular equilibrium curve is later used to back-extrapolate to the same curve, resulting in identical T_Δ’17O estimates. The lack of variability in the θ_coral between species means that triple oxygen isotopes can be well suited for correcting vital effects in extinct organisms. This is not limited by the uncertainties in past seawater Δ’¹⁷O values because it was modelled to change only within ±10 ppm during the Phanerozoic (Guo et al., 2022

Guo, M., Wostbrock, J.A.G., Planavsky, N.J., Korenaga, J. (2022) Reconstructing seawater δ¹⁸O and Δ′¹⁷O values with solid Earth system evolution. Earth and Planetary Science Letters 592, 117637. https://doi.org/10.1016/j.epsl.2022.117637

).

Looking at vital effects. Coral calcification models aim to reproduce observed δ¹⁸O–δ¹³C covariations in carbonates and mainly consider: 1) CO₂ absorption leading to disequilibrium between H₂O and DIC in the calcifying fluid; 2) isotope effects at the mineral water interface; and 3) CO_{2 (aq)} diffusion across the cell membranes. Besides the diffusive flux of CO_{2 (aq)} through the lipid membrane, carbon is also sourced directly from seawater. The calcifying fluid is not perfectly isolated from seawater but isolated enough to significantly up-regulate pH via the enzyme Ca-ATPase that pumps Ca²⁺ into and H⁺ out of the calcifying fluid (Rollion-Bard et al., 2003

Rollion-Bard, C., Chaussidon, M., France-Lanord, C. (2003) pH control on oxygen isotopic composition of symbiotic corals. Earth and Planetary Science Letters 215, 275–288. https://doi.org/10.1016/S0012-821X(03)00391-1

). Another prominent enzyme, carbonic anhydrase, accelerates CO_{2 (aq)}–HCO₃⁻ interconversion. Respective enzyme activities moderate both the carbonate precipitation rates and the isotope exchange rates. Biomineralisation models focusing on isotope effects reproduce the observed δ¹⁸O–δ¹³C covariations (McConnaughey, 1989b

McConnaughey, T. (1989b) ¹³C and ¹⁸O isotopic disequilibrium in biological carbonates: II. In vitro simulation of kinetic isotope effects. Geochimica et Cosmochimica Acta 53, 163–171. https://doi.org/10.1016/0016-7037(89)90283-4

; Adkins et al., 2003

Adkins, J.F., Boyle, E.A., Curry, W.B., Lutringer, A. (2003) Stable isotopes in deep-sea corals and a new mechanism for “vital effects.” Geochimica et Cosmochimica Acta 67, 1129–1143. https://doi.org/10.1016/s0016-7037(02)01203-6

; Chen et al., 2018

Chen, S., Gagnon, A.C., Adkins, J.F. (2018) Carbonic anhydrase, coral calcification and a new model of stable isotope vital effects. Geochimica et Cosmochimica Acta 236, 179–197. https://doi.org/10.1016/j.gca.2018.02.032

). Davies et al. (2022)

Davies, A.J., Guo, W., Bernecker, M., Tagliavento, M., Raddatz, J., Gischler, E., Flögel, S., Fiebig, J. (2022) Dual clumped isotope thermometry of coral carbonate. Geochimica et Cosmochimica Acta 338, 66–78. https://doi.org/10.1016/j.gca.2022.10.015

compare dual clumped isotope data of corals with a respective theoretical CO₂ absorption model and show that certain mechanisms (e.g., DIC speciation effects — the classic pH effect) are inconsistent with observed dual clumped isotope fractionation trends. Although contributions from kinetic isotope fractionation at the carbonate–water interface cannot be excluded (Watson, 2004

Watson, E.B. (2004) A conceptual model for near-surface kinetic controls on the trace-element and stable isotope composition of abiogenic calcite crystals. Geochimica et Cosmochimica Acta 68, 1473–1488. https://doi.org/10.1016/j.gca.2003.10.003

; Watkins et al., 2014

Watkins, J.M., Hunt, J.D., Ryerson, F.J., DePaolo, D.J. (2014) The influence of temperature, pH, and growth rate on the δ¹⁸O composition of inorganically precipitated calcite. Earth and Planetary Science Letters 404, 332–343. https://doi.org/10.1016/j.epsl.2014.07.036

), the almost perfect fit of the theoretical model with analytical results led these authors to suggest that CO₂ absorption is the main mechanism inducing kinetic effects. Guo and Zhou (2019)

Guo, W., Zhou, C. (2019) Triple oxygen isotope fractionation in the DIC-H₂O-CO₂ system: A numerical framework and its implications. Geochimica et Cosmochimica Acta 246, 541–564. https://doi.org/10.1016/j.gca.2018.11.018

also attribute the offset from the expected equilibrium in the warm water coral data of Passey et al. (2014)

Passey, B.H., Hu, H., Ji, H., Montanari, S., Li, S., Henkes, G.A., Levin, N.E. (2014) Triple oxygen isotopes in biogenic and sedimentary carbonates. Geochimica et Cosmochimica Acta 141, 1–25. https://doi.org/10.1016/j.gca.2014.06.006

to CO₂ absorption kinetics. The CO₂ absorption mechanism is a classic candidate for vital effects in biogenic carbonates (McConnaughey, 1989a

McConnaughey, T. (1989a) ¹³C and ¹⁸O isotopic disequilibrium in biological carbonates: I. Patterns. Geochimica et Cosmochimica Acta 53, 151–162. https://doi.org/10.1016/0016-7037(89)90282-2

, 1989b

McConnaughey, T. (1989b) ¹³C and ¹⁸O isotopic disequilibrium in biological carbonates: II. In vitro simulation of kinetic isotope effects. Geochimica et Cosmochimica Acta 53, 163–171. https://doi.org/10.1016/0016-7037(89)90283-4

; Adkins et al., 2003

Adkins, J.F., Boyle, E.A., Curry, W.B., Lutringer, A. (2003) Stable isotopes in deep-sea corals and a new mechanism for “vital effects.” Geochimica et Cosmochimica Acta 67, 1129–1143. https://doi.org/10.1016/s0016-7037(02)01203-6

; Thiagarajan et al., 2011

Thiagarajan, N., Adkins, J., Eiler, J. (2011) Carbonate clumped isotope thermometry of deep-sea corals and implications for vital effects. Geochimica et Cosmochimica Acta 75, 4416–4425. https://doi.org/10.1016/j.gca.2011.05.004

; Saenger et al., 2012

Saenger, C., Affek, H.P., Felis, T., Thiagarajan, N., Lough, J.M., Holcomb, M. (2012) Carbonate clumped isotope variability in shallow water corals: Temperature dependence and growth-related vital effects. Geochimica et Cosmochimica Acta 99, 224–242. https://doi.org/10.1016/j.gca.2012.09.035

; Chen et al., 2018

Chen, S., Gagnon, A.C., Adkins, J.F. (2018) Carbonic anhydrase, coral calcification and a new model of stable isotope vital effects. Geochimica et Cosmochimica Acta 236, 179–197. https://doi.org/10.1016/j.gca.2018.02.032

; Guo and Zhou, 2019

Guo, W., Zhou, C. (2019) Triple oxygen isotope fractionation in the DIC-H₂O-CO₂ system: A numerical framework and its implications. Geochimica et Cosmochimica Acta 246, 541–564. https://doi.org/10.1016/j.gca.2018.11.018

; Davies et al., 2023

Davies, A.J., Brand, U., Tagliavento, M., Bitner, M.A., Bajnai, D., Staudigel, P., Bernecker, M., Fiebig, J. (2023) Isotopic disequilibrium in brachiopods disentangled with dual clumped isotope thermometry. Geochimica et Cosmochimica Acta 359, 135–147. https://doi.org/10.1016/j.gca.2023.08.005

), providing a starting point for comparing theoretical and empirical triple oxygen isotope slope values.

The choice of equilibrium calibration affects the θ_coral values and, consequently, how these slopes are interpreted with respect to vital effects. The mean θ_coral value obtained using the Guo and Zhou (2019)

Guo, W., Zhou, C. (2019) Triple oxygen isotope fractionation in the DIC-H₂O-CO₂ system: A numerical framework and its implications. Geochimica et Cosmochimica Acta 246, 541–564. https://doi.org/10.1016/j.gca.2018.11.018

aragonite equilibrium calibration is 0.529 ± 0.001 (within a range of 0.527 to 0.531), reflecting the net effect of several superimposed processes. Using other calibrations affects the mean θ_coral estimates but does not affect the main conclusions drawn here (see Supplementary Information). Although a consistently used reference frame has no impact on the reconstructed T_Δ’17O, only the correct reference frame will provide accurate empirical triple oxygen isotope slope values required to interpret the biomineralisation mechanisms correctly.

Guo and Zhou (2019)

Guo, W., Zhou, C. (2019) Triple oxygen isotope fractionation in the DIC-H₂O-CO₂ system: A numerical framework and its implications. Geochimica et Cosmochimica Acta 246, 541–564. https://doi.org/10.1016/j.gca.2018.11.018

presented theoretical slopes for CO₂ absorption (θ_absorption = 0.538 to 0.541 at pH between 8.4 and 9, respectively), which differ significantly from our observed θ_coral = 0.529 ± 0.001. Assuming that normalisation issues are insignificant, this discrepancy implies that vital effects in corals are not dominated by CO₂ absorption. Shallower slopes hint towards considerable proportions of CO_{2 (aq)} diffusion, which follows much shallower slopes (i.e. θ_diffusion = 0.506; Herwartz, 2021

Herwartz, D. (2021) Triple oxygen isotope variations in Earth’s crust. Reviews in Mineralogy and Geochemistry 86, 291–322. https://doi.org/10.2138/rmg.2021.86.09

). Diffusion has been suggested to be an important contributor to the vital effects in brachiopods (Davies et al., 2023

Davies, A.J., Brand, U., Tagliavento, M., Bitner, M.A., Bajnai, D., Staudigel, P., Bernecker, M., Fiebig, J. (2023) Isotopic disequilibrium in brachiopods disentangled with dual clumped isotope thermometry. Geochimica et Cosmochimica Acta 359, 135–147. https://doi.org/10.1016/j.gca.2023.08.005

). The theoretical θ_absorption range of 0.538 to 0.541 could imply that 34–39 % of the total vital effect is induced by diffusion. An alternative explanation for the observed discrepancy between the observed vital effect slopes and CO₂ absorption in triple oxygen isotope space is that the theoretical CO₂ absorption slopes are inaccurate.

The slope for the hydroxylation reaction (CO₂ + OH⁻ −> HCO₃⁻) hinges on the triple oxygen isotope compositions of the reacting OH⁻ and CO_{2 (aq)}. The model of Guo and Zhou (2019)

Guo, W., Zhou, C. (2019) Triple oxygen isotope fractionation in the DIC-H₂O-CO₂ system: A numerical framework and its implications. Geochimica et Cosmochimica Acta 246, 541–564. https://doi.org/10.1016/j.gca.2018.11.018

considers parameters derived from experimental fractionation factors, which are inconsistent with the most recent theoretical models. Experimental work by Bajnai et al. (2024

Bajnai, D., Cao, X., Klipsch, S., Pack, A., Herwartz, D. (2024) Triple oxygen isotope systematics of CO₂ hydroxylation. Chemical Geology 654, 122059. https://doi.org/10.1016/j.chemgeo.2024.122059

) recently constrained the Δ’¹⁷O values of the two reacting species in CO₂ absorption and yielded consistent results with theory. Accordingly, these authors’ revised estimates for hydroxylation and hydration in seawater are θ_{hydroxylation} ≈ 0.532 and θ_hydration ≈ 0.531 (Fig. S-7). The corrected estimate for the CO₂ absorption slope at pH 8 is 0.532, which is more consistent with the observed empirical slopes but still allows for some superimposed diffusion of up to 19 % of the total vital effect.

From a triple oxygen isotope perspective, it is not possible to distinguish between the diffusion of CO_{2 (aq)} through the membrane and diffusion happening at the mineral–water interface. It is worth pointing out that surface effects are not necessarily related to diffusion (Watson, 2004

Watson, E.B. (2004) A conceptual model for near-surface kinetic controls on the trace-element and stable isotope composition of abiogenic calcite crystals. Geochimica et Cosmochimica Acta 68, 1473–1488. https://doi.org/10.1016/j.gca.2003.10.003

; Watkins et al., 2014

Watkins, J.M., Hunt, J.D., Ryerson, F.J., DePaolo, D.J. (2014) The influence of temperature, pH, and growth rate on the δ¹⁸O composition of inorganically precipitated calcite. Earth and Planetary Science Letters 404, 332–343. https://doi.org/10.1016/j.epsl.2014.07.036

). The θ values for other processes, such as entrapment or the inheritance of isotope signals from amorphous calcium carbonate precursors, are presently unknown and may significantly contribute to coral vital effects without necessarily affecting the observed slope.

Outlook. Robust estimates for the slopes in triple oxygen isotope space for all potentially relevant kinetic processes will allow the evaluation of coral calcification models and corroborate the theoretical triple oxygen isotope framework. Theoretical approaches can calculate full thermodynamic equilibrium (e.g., Guo and Zhou, 2019

Guo, W., Zhou, C. (2019) Triple oxygen isotope fractionation in the DIC-H₂O-CO₂ system: A numerical framework and its implications. Geochimica et Cosmochimica Acta 246, 541–564. https://doi.org/10.1016/j.gca.2018.11.018

), but their confirmation using natural samples remains challenging. This is at least partly related to the diverse suite of methods applied for carbonate Δ’¹⁷O analyses (Passey et al., 2014

Passey, B.H., Hu, H., Ji, H., Montanari, S., Li, S., Henkes, G.A., Levin, N.E. (2014) Triple oxygen isotopes in biogenic and sedimentary carbonates. Geochimica et Cosmochimica Acta 141, 1–25. https://doi.org/10.1016/j.gca.2014.06.006

; Bergel et al., 2020

Bergel, S.J., Barkan, E., Stein, M., Affek, H.P. (2020) Carbonate ¹⁷Oexcess as a paleo-hydrology proxy: Triple oxygen isotope fractionation between H₂O and biogenic aragonite, derived from freshwater mollusks. Geochimica et Cosmochimica Acta 275, 36–47. https://doi.org/10.1016/j.gca.2020.02.005

; Wostbrock et al., 2020a

Wostbrock, J.A.G., Brand, U., Coplen, T.B., Swart, P.K., Carlson, S.J., Brearley, A.J., Sharp, Z.D. (2020a) Calibration of carbonate-water triple oxygen isotope fractionation: Seeing through diagenesis in ancient carbonates. Geochimica et Cosmochimica Acta 288, 369–388. https://doi.org/10.1016/j.gca.2020.07.045

, 2020b

Wostbrock, J.A.G., Cano, E.J., Sharp, Z.D. (2020b) An internally consistent triple oxygen isotope calibration of standards for silicates, carbonates and air relative to VSMOW2 and SLAP2. Chemical Geology 533, 119432. https://doi.org/10.1016/j.chemgeo.2019.119432

; Huth et al., 2022

Huth, T.E., Passey, B.H., Cole, J.E., Lachniet, M.S., McGee, D., Denniston, R.F., Truebe, S., Levin, N.E. (2022) A framework for triple oxygen isotopes in speleothem paleoclimatology. Geochimica et Cosmochimica Acta 319, 191–219. https://doi.org/10.1016/j.gca.2021.11.002

). One way to test equilibrium calibrations is to check if experimental data referenced to them reproduce theoretical θ_KIE calculations. Also, compared to equilibrium models, kinetic isotope models work with far more parameters. In turn, kinetic models provide information on parameters such as precipitation rates and pH, while equilibrium models “only” provide temperature information. The concept of seeing through vital effects aims to reconstruct equilibrium conditions and, consequently, palaeotemperatures. However, triple oxygen isotopes also allow us to look at vital effects and help constrain calcification parameters beyond temperature. By combining triple oxygen isotopes with other isotope systems, such as carbon isotopes and dual clumped isotopes, along with elemental concentrations, it becomes possible to constrain the numerous variables in kinetic models.

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Acknowledgements

The authors are grateful to A. Freiwald, D. Tracey, S. Mills, and G. Bernasconi-Green for providing cold-water coral samples to this study, and J. Fiebig for comments on an earlier version of this manuscript. The S. variabilis sample was collected by NIWA (New Zealand) as part of the ‘Impact of resource use on vulnerable deep-sea communities’ project, funded by the MBIA with support from the Ministry for Primary Industries and NIWA’s ‘Enabling the Management of Marine Mining’ project. S. Klipsch and D. Bajnai contributed equally to this manuscript. This research was funded by the DFG via grants HE 6357/2-2 and HE 6357/4-1.

Editor: Gavin Foster

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References

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Supplementary Information

The Supplementary Information includes:

• Supplementary discussion on systematic errors
• Tables S-1 to S-3
• Figures S-1 to S-7
• Supplementary Information References

Download the Supplementary Information (PDF)

Download Tables S-2 and S-3 (.xlsx)