Samples
Devils Hole vein calcite: A Holocene vein calcite (DHC2-8) that precipitated 4.5–16.9 ka before present, was collected from the Devils Hole cave #2 in Nevada, USA (36.427138 N, 116.291172 W). It is postulated that DHC2-8 precipitated at extremely slow rates, i.e., 0.1–0.8 μm year−1, at a constant temperature of 33.7(±0.8) °C30. For this study, we prepared a ca 0.5 × 0.5 × 1.5 cm slab of calcite. First, we abraded the surface ca 0.5 mm of the slab with a slow-speed hand-held drill to remove impurities. Then, the slab was cleaned in de-ionised water in an ultrasonic bath for 5 min and dried in a vacuum oven at 30 °C before it was crushed and homogenised using an agate mortar and pestle. Material from the same vein was analysed for clumped isotopes in other studies5,32.
Cryogenic cave carbonate: A coarsely crystalline cryogenic cave calcite (MSK 2b) was obtained from Mitterschneidkar Eishöhle in the Austrian Alps (47.1165 N, 11.7407 E). The cave opens at 2258 m above sea level and contained perennial ice in the near-entrance part until 2007. Today the cave is ice-free, and the mean annual air temperature in the interior of the cave is 0.23 °C33. Coarsely crystalline cryogenic cave carbonates generally precipitate slowly and very close to 0 °C, otherwise powder-like fine-crystalline cryogenic cave carbonates form50. Cryogenic cave carbonates occur in several places in the inner part of the cave, and U–Th dating of these carbonates suggests the presence of perennial ice up to about 2600 years before present33. The sample crystals were crushed and homogenised using an agate mortar and pestle and were subsequently dried in a vacuum oven at 30 °C before isotope analysis. Additional information on the potential equilibrium nature of this sample is found in Supplementary Fig. 1.
Cave pool carbonate: A 3.5-cm thick subaqueous calcite sample (Obi 87-i) was collected in 2008 from a perennial pool (Silbersee) in Rasslsystem cave, which is part of the Obir Caves (46.5102 N, 14.5480 E), a series of karst caves in the Southern Alps of Austria, located at approximately 1100 m above sea level. The Obir Caves are hypogene in origin51, i.e., they were not connected to the surface and hence had a very stable microclimate until discovered during mining activities in the 1870s. The Silbersee pool, located in the inner part of Rasslsystem cave, has a surface area of 7 × 4 m and is on average ca 1 m deep. The pool water temperature between 1998 and 2002 was 5.4(±0.1) °C, closely corresponding to the long-term mean annual air temperature outside the cave at this elevation52. The sample analysed in this study is a 4 mm wide subsample retrieved from 2.7 cm above the base of Obi 87, and is estimated to have formed at about 1500 years before present, based on the U–Th dating of a lower layer in Obi 87 (a layer estimated to have formed about 3800 years before present at 1.5 cm above the base of Obi 87) and assuming a constant calcite growth rate of 5.3 μm year−1 (unpublished data, C Spötl). Although the water temperature about 1500 years before present is not precisely known, it likely corresponded to the mean annual air temperature outside the cave at that time in a similar way as the modern pool temperature does. Various temperature proxy data for the Alps suggest that the mean annual air temperature fluctuated by up to ±1.5 °C in the last two millennia before the industrial revolution53. Considering the ca 1.5 °C warming in the Alps during the past century, we estimate the water temperature of Silbersee pool from which Obi 87-i precipitated ca 1500 years ago to be 4.0(±1.5) °C. Experiments demonstrated that subaqueous pool carbonates can precipitate in oxygen isotope equilibrium with water54. Prior to isotope analyses, Obi 87-i was cleaned in de-ionised water in an ultrasonic bath, crushed and homogenised using an agate mortar and pestle, and dried in a vacuum oven at 30 °C.
Synthetic speleothem carbonate: A calcite sample (MHD1) was precipitated in a laboratory, under cave-like conditions55. Solutions super-saturated relative to calcite were pumped to flow down an inclined, sandblasted glass plate in a thin solution film (0.1 mm in thickness), precipitating CaCO3 along the flow path. The experiments were performed in an enclosed space, which allowed control of all surrounding conditions, such as pCO2, temperature, and relative humidity. Specifically, sample MHD1 was precipitated at 30.7(±0.3) °C, with an atmospheric pCO2 of 1007(±47) ppm and a relative humidity of 97.5(±1.2)%. The average δ13C and δ18O values of the atmospheric CO2 were −44.7(±0.8)‰ and −10.6(±0.6)‰ VPDB, respectively. The experimental solution was prepared by dissolving 5 mmol CaCO3 powder in high-purity water while bubbling tank CO2 through the water column. After the complete dissolution of CaCO3 powder, i.e., when there were no visible particles in the solution, the solution was stored for five days at the experimental temperature to obtain isotopic equilibrium among all dissolved inorganic carbon species. This resulted in an initial solution composition of pH = 6.34, [DIC] = 18.19 mM, δ13CHCO3− ≈ −31.9(±1.3)‰, and δ18OHCO3− ≈ −8.69(±0.11)‰ VPDB. After being exposed to lower pCO2 in the climate box, it took ca 18 s for the solution to reach chemical equilibrium with the atmospheric CO2, which increased the solution pH and led to super-saturation with respect to calcite. The calcite sample was scratched off the glass plate after the experiment was completed and corresponded to the first 5 cm of flow, i.e., the first 24 s of CaCO3 precipitation.
Stalagmite: A calcite sample (SPA121-02) was retrieved from a stalagmite in Spannagel Cave in the Austrian Alps (47.0803 N, 11.6717 E), an extensive cave system with the main entrance at 2523 m above sea level. SPA121-02 is a 4-mm-thin layer within SPA121, a stalagmite that records a long growth history from about 240 to 76 ka. SPA121-02 was formed at about 225 ka during Marine Isotope Stage (MIS) 7.4 when this high-alpine cave was buried beneath a warm-based glacier preventing the cave from freezing56. The growth of this stalagmite during MIS 7 likely occurred at constant temperatures around freezing point, i.e., 0(±2) °C. The relatively high δ13C values of SPA121-02 (about 7‰ VPDB, Supplementary Table 1) was attributed to the disequilibrium isotope effects during peak cold times56. A 3 × 6 × 4 mm large piece was cut out from the axial part of the stalagmite SPA121 using a diamond-coated band saw. The piece was then cleaned in an ultrasonic bath in de-ionised water, dried, and crushed and homogenised with an agate mortar and pestle before isotope analysis.
Cold-water coral: A scleractinian, azooxanthellate coral Desmophyllum pertusum (formerly known as Lophelia pertusa) (JR) was collected alive at Traenadjupet, Norwegian Sea (66.973333 N, 11.108833 E) at a water depth of 300 m during cruise POS325-356/1. The annual mean seawater temperature at the collection location is 7.2(±1.0) °C57. With a hand-held drill, a corallite was cut from the axis of the colony, and the septa were removed, i.e., only the theca walls were sampled. The sample was cleaned in an ultrasonic bath using de-ionised water and dried in a vacuum oven at 30 °C before being crushed and homogenised using an agate mortar and pestle.
Warm-water coral: A scleractinian, zooxanthellate coral Porites lutea (PC1_2005) was collected at the Rashdoo Atoll, Maldives (4.293776 N, 72.977115 E) at a water depth of ca 1 m. For isotope analysis, a ca 0.5 cm thick section was cut from the coral core. Based on sclerochronological analysis, this section corresponded to the growth in the year 2005 when the annual mean temperature at this location was 29.3(±1.0) °C58. The mean annual extension rate of the coral is ca 10 mm year−1. To remove material that may have been thermally altered when the section was initially cut from the colony, the surface 0.5 mm was scraped away. Then, the section was cleaned in an ultrasonic bath using de-ionised water and dried in a vacuum oven at 30 °C before being crushed and homogenised using an agate mortar and pestle.
Modern brachiopod shell: A terebratulid brachiopod Magellania venosa (Mv143-b) was collected from Punta Gruesa, Chile (42.409833 S, 72.424333 W) from 20 m below sea level. The annual mean temperature at the collection location is 11.4(±1.7) °C12. Magellania venosa is one of the fastest-growing modern brachiopods, with growth rates ranging from 3.8 mm year−1 (adult) to 17.3 mm year−1 (juvenile)59. For this study, we sampled a ca 2 × 3 cm area in the middle part of the ventral valve. First, we abraded the primary layer of the shell using a slow-speed hand-held drill and a diamond drill bit, cleaned the shell in an ultrasonic bath with de-ionised water, dried it in a vacuum oven at 30 °C, and finally homogenised the material using an agate mortar and pestle. The anterior part of the same specimen showed the largest offset from equilibrium in ∆47 values in a previous study12.
Cretaceous belemnite: A belemnite Belemnopsis sp. (66-4.65) was retrieved from DSDP Site 511 at the Falkland Plateau (51.004667 S, 46.971667 W). The investigated rostrum solidum shows excellent preservation based on cathodoluminescence, and trace element analyses44,60. Burial temperatures remained below 100 °C for this core, which makes the solid-state alteration of the clumped isotope composition of this sample unlikely61,62. The same sample in this study was analysed for its ∆47 values, together with other belemnites, to reconstruct Early Cretaceous southern high latitude palaeotemperatures44.
Mass spectrometry
We performed the CO2 clumped isotope analyses of sample carbonates on a Thermo Scientific 253 Plus gas source isotope ratio mass spectrometer during April 2019–March 2020, in three measurement sessions (April–August 2019, September–December 2019, and January–March 2020), following the method of Fiebig et al.25. Samples were measured in 5–10 replicates. Each replicate analysis consists of 13 acquisitions (10 cycles of reference and samples comparisons in each acquisition and 20 s integration time during each cycle). The raw clumped isotope values (indicated by subscript “raw” on the ∆ symbol) were calculated using the [Brand]/IUPAC isotopic parameters29,63.
Data correction for the reference carbonates
In order to assign the long-term ∆47 (CDES90) and ∆48 (CDES90) values of the ETH 1, ETH 2, and ETH 3 carbonate reference materials finally used for sample correction (Table 1, see the next section), we followed the correction approach outlined by Fiebig et al.25. using equilibrated gases only (subscript “CDES90” on the ∆ symbol indicates that the ∆47 and ∆48 values of these carbonate reference materials are reported on the Carbon Dioxide Equilibrium Scale at a reaction temperature of 90 °C). A total of 36 aliquots of CO2 gases equilibrated at 25 °C and 54 aliquots equilibrated at 1000 °C were considered for the April–August 2019 period (Supplementary Data 1). Data correction for the reference carbonates consisted of two steps: correction for non-linearity followed by correction for scale compression25,64,65. These two steps are detailed below.
Correction for non-linearity: Within errors, the two sets of equilibrium gases, equilibrated either at 1000 °C or 25 °C, had identical slopes in ∆47 (raw) vs δ47 (Supplementary Fig. 3a) and ∆48 (raw) vs δ48 (Supplementary Fig. 3b) spaces, respectively, when the negative m/z 47.5 intensity is directly subtracted from measured m/z 47–49 intensities (scaling factor of −1, see below and in Fiebig et al.25). We, therefore, considered the slopes displayed by the merged data sets for the correction of non-linearity. In ∆47 (raw) vs δ47 space, the equilibrium gases showed a flat line such that non-linearity correction needs not be applied. In ∆48 (raw) vs δ48 space, the slope displayed by the merged data set was −0.0040(±0.0002).
Correction for scale compression: The intercepts for the 1000 °C and the 25 °C gases displayed in ∆47 (raw) vs δ47 and ∆48 (raw) vs δ48 spaces were compared to the corresponding theoretical values66 to constrain empirical transfer functions (Supplementary Data 1).
Finally, we combined the ∆47 (CDES90) and ∆48 (CDES90) values of ETH 1, ETH 2, and ETH 3 determined during the April–August 2019 period (Supplementary Data 1) with those reported in Fiebig et al.25 to calculate the long-term values listed in Table 1 (Supplementary Fig. 4). Shapiro-Wilks tests show that the combined ∆47 (CDES90) and ∆48 (CDES90) data set of the carbonate reference materials have a normal distribution with W-values > 0.95 and p-values >> 0.05.
Data correction for the carbonate samples
Unlike the method described in Fiebig et al.25, we did not make use of equilibrated gases to correct the samples but used our long-term ∆47 (CDES90) and ∆48 (CDES90) values obtained for ETH 1, ETH 2, and ETH 3 instead (Supplementary Data 2–4). This purely carbonate-based correction approach follows the principle of identical treatment of sample and reference materials and allows identification of subtle temporal drifts in the acid reaction environment and correction for them67,68,69. Correction of the sample data consisted of three steps: correction for non-linearity followed by correction for scale compression, and finally correction for variations in the reaction environment. These three steps are detailed below.
Correction for non-linearity: The negative background causing the non-linearities in ∆47 (raw) vs δ47, ∆48 (raw) vs δ48, and ∆49 (raw) vs δ49 spaces was corrected using Easotope70 by subtracting the intensities measured on the m/z 47.5 cup from the intensities measured on the m/z 47–49 cups, after multiplying the former by respective scaling factors. These scaling factors were determined empirically and enable one to calculate accurate negative backgrounds below m/z 47, m/z 48, and m/z 49 from the measured m/z 47.5 intensity. For the three periods of sample analyses, i.e., April–August 2019, September–December 2019, and January–March 2020, we determined the scaling factors in a way that no residual slopes remained between the respective measured values of the frequently analysed ETH 1 and ETH 2 standards in the corresponding ∆ vs δ spaces (Supplementary Figs. 5–7). The uniformity of the measured long-term ∆47 (CDES90) and ∆48 (CDES90) values of ETH 1 and ETH 2, also supported by experimental data71, allowed us to assume that they have identical ∆47 and ∆48 values (Table 1). Consequently, for the April–August 2019 period of sample analyses, scaling factors of −0.988, −0.906, and −0.648, respectively, were applied to correct m/z 47, m/z 48, and m/z 49 intensities based on the monitored m/z 47.5 intensity. For the September–December 2019 period, the corresponding scaling factors were −1.003, −0.938, and −0.581, respectively. For the January–March 2020 period, factors of −1.010, −0.92326, and −0.555, respectively, were applied.
Correction for scale compression: According to the principles outlined above, we used our long-term ∆47 (CDES90) and ∆48 (CDES90) values of ETH 1, ETH 2, and ETH 3 (Table 1) to project the non-linearity corrected, raw clumped isotope values of the carbonate samples to the CDES. We determined empirical transfer functions based on a comparison of our long-term mean ∆47 (CDES90) and ∆48 (CDES90) values of ETH 1, ETH 2, and ETH 3 (Table 1) with their corresponding, non-linearity corrected ∆47 (raw) and ∆48 (raw) averages over the three periods of sample analysis (Supplementary Figs. 5a–b, 6a–b, 7a–b). The application of these transfer functions to non-linearity corrected sample ∆47 (raw) and ∆48 (raw) values yields the ∆47 (CDES90,uc) and ∆48 (CDES90,uc) values of the samples (Supplementary Data 2–4).
Correction for subtle long-term variations in the acid reaction environment: When residuals between the accepted long-term and the measured ∆ (CDES90,uc) for all ETH 1, ETH 2, and ETH 3 replicate analyses are plotted against time, small but systematic temporal variations become detectable. For ∆47 (CDES90,uc), these residuals are on the order of ≤0.010‰ (Supplementary Figs. 8a, 9a, 10a), and for ∆48 (CDES90,uc) they are on the order of ≤0.030‰ (Supplementary Figs. 8b, 9b, 10b). We determined a residual vs measurement time function (Supplementary Data 2–4) and used it to further correct the ∆47 (CDES90,uc) and ∆48 (CDES90,uc) values in order to obtain the final clumped isotope compositions of the investigated carbonate samples (Table 2).
We used the non-linearity corrected ∆49 (raw) values of the carbonate-derived CO2 and the presumably uncontaminated equilibrated CO2 gases to check for potential contamination in the analyte. All ∆49 (raw) values of the carbonates fall within the range of the ∆49 (raw) values of the equilibrated gases, indicating no contamination of the investigated solids (Supplementary Figs. 11a–b, 12a–b, 13a–b). In addition, the lack of correlation between ∆48 (raw) and ∆49 (raw) of the measured analytes further argues that there is no contamination on ∆49 that would influence ∆48 (Supplementary Figs. 11c, 12c, 13c). All measured values can be found in Supplementary Data 1–4.
Acid fractionation factors
To be able to compare the experimentally measured clumped isotope compositions of a carbonate, i.e., the ∆47 (CDES90) and ∆48 (CDES90) values of the CO2 gas derived from the phosphoric acid digestion of that carbonate, with its theoretically predicted composition, i.e., the ∆63 and ∆64 values of the carbonate, we determined25 the clumped isotope fractionation factors associated with the 90 °C acid fractionation during our analysis. These are based on the long-term ∆47 (CDES90) and ∆48 (CDES90) values of ETH 1 and ETH 2 standards which were both potentially equilibrated at 600 °C68. The theoretically predicted calcite ∆63 and ∆64 values at 600 °C are 0.018‰ and 0.002‰28, respectively. These, combined with our experimentally measured ∆47 (CDES90) values of 0.212(±0.002)‰ and ∆48 (CDES90) of 0.140(±0.005)‰, yield acid fractionation factors of 0.194(±0.002)‰ for ∆63–∆47 and 0.138(±0.005)‰ for ∆64–∆48.
Numerical modelling
We used numerical models to simulate the evolution of the isotopic composition of the DIC during (1) CO2 absorption, i.e., the key process involved in coral calcification26, and (2) the laboratory carbonate precipitation of the synthetic speleothem27 (Supplementary Data 5).
(1) CO2 absorption simulations were constructed using the IsoDIC model to mimic the internal calcification environment of scleractinian corals26. Specifically, the modelled calcification environment consisted of an aqueous solution ([DIC] = 2 mM, δ13CDIC = 0, and pH = 8.8 for cold-water corals and pH = 8.5 for warm-water corals), which was exposed to a CO2-containing atmosphere (pCO2 = 1100 ppm72 and δ13CCO2 = −15‰73). The temperature of the modelled calcification environment corresponded to the mean growth temperatures of the cold- and warm-water corals, i.e., 7.2 °C and 28.9 °C, respectively. The catalytic enhancement of the inter-conversion between CO2 (aq) and HCO3− by carbonic anhydrase during coral calcification is simulated by increasing the rate constants of CO2 (aq) (de)hydration reactions26. The initial oxygen and clumped isotope compositions of both the DIC and air CO2 were assumed to be in isotopic equilibrium with the water (δ18OH2O = 0 VSMOW) at the above described temperatures.
(2) To model the isotopic composition of the synthetic speleothem, simulations were constructed using the IsoCave model27, based on the conditions of the laboratory experiment55 (T = 30.7 °C, pCO2 = 1007 ppm, water film thickness of 100 μm, δ13CCO2 = −44.7‰, δ18OCO2 = −10.6‰ VPDB, δ13CCaCO3 = −6‰, δ18OH2O = −9‰ VSMOW, see above as well) and yielded an initial solution composition of pH = 6.3, [DIC] = 18.1 mM, [Ca2+] = 4.9 mM, δ13CHCO3− = −31.2‰, and δ18OHCO3− = −9.0‰ VPDB, which are close to the experimentally determined values (pH = 6.34, [DIC] = 18.2 mM, [Ca2+] = 5 mM, δ13CHCO3− ≈ −31.9(±1.3)‰, and δ18OHCO3− ≈ −8.69(±0.11)‰ VPDB, see above).
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