Oxygen isotope composition of waters recorded in carbonates in strong clumped and oxygen isotopic disequilibrium

Paleoenvironmental reconstructions, which are mainly retrieved from oxygen isotope (δ18O) and clumped isotope (147) compositions of carbonate minerals, are compromised when carbonate precipitation occurs in isotopic disequilibrium. To date, knowledge of these common isotopic disequilibria, known as vital effects in biogenic carbonates, remains limited, and the potential information recorded by δ18O and 147 offsets from isotopic equilibrium values is largely overlooked. Additionally, in carbonates formed in isotopic equilibrium, the use of the carbonate δ18O signature as a paleothermometer relies on our knowledge of the paleowaters’ δ18O value, which is often assumed. Here, we report the largest 147 offsets observed to date (as much as −0.270 ‰), measured on microbial carbonates that are strongly linked to carbonate δ18O offsets (−25 ‰) from equilibrium. These offsets are likely both related to the microorganism metabolic activity and yield identical erroneous temperature reconstructions. Unexpectedly, we show that the δ18O value of the water in which carbonates precipitated, as well as the water–carbonate δ18O fractionation dependence on temperature at equilibrium, can be retrieved from these paired δ18O and 147 disequilibrium values measured in carbonates. The possibility to retrieve the δ18O value of paleowaters, sediments’ interstitial waters or organisms’ body water at the carbonate precipitation loci, even from carbonates formed in isotopic disequilibrium, opens long-awaited research avenues for both paleoenvironmental reconstructions and biomineralization studies.


Introduction
Oxygen isotope composition (δ 18 O) paired with clumped isotope composition ( 47 ) of carbonate minerals is increasingly used for reconstructing paleoenvironmental or diagenetic conditions (Ghosh et al., 2006;Henkes et al., 2018;Mangenot et al., 2018a, b). The δ 18 O of carbonates depends on both the δ 18 O value of the water in which the carbonate precipitated and the precipitation temperature (Urey et al., 1951). Its use to reconstruct paleoenvironments can be combined with the new carbonate C-O "clumped isotope" abundance ( 47 ) thermometer which depends only on the carbonate precipitation temperature (Ghosh et al., 2006). By combining the 47 -derived temperatures and the carbonate δ 18 O value (δ 18 O carbonate ), the δ 18 O value of the water (δ 18 O water ) in which the carbonate precipitated can be retrieved. However, this requires that solid carbonate and water reached isotopic equilibrium, which is often hard to prove. Conversely, carbonate precipitation in isotopic disequilibrium is commonly encountered Loyd et al., 2016). Out of equilibrium, δ 18 O and 47 values are particularly known to occur in biogenic carbonates (Thiagarajan et al., 2011;Bajnai et al., 2018) -the most abundant carbonates in the sedimentary record. To date, the reasons for these isotopic disequilibria in carbonates remain largely under-constrained. While 47 compositions of carbonates seemed at first free of any biologically driven or mineral-specific fractionation known to affect δ 18 O carbonate compositions (Eiler, 2011), recently identified disequilibrium 47 values (Saenger et al., 2012;Affek, 2013;Tang et al., 2014;Burgener et al., 2018) shed new light on and help to unravel the mechanisms responsible for oxygen isotopic disequilibrium in carbonate minerals. Even though the identification of these vital effects does not prevent δ 18 O and 47 tools from being pow-erful paleothermometers as empirical calibrations taking vital effects into account allow temperature reconstructions, it has become crucial to determine if the δ 18 O and 47 disequilibria observed in carbonates as diverse as those found in coral reefs (Saenger et al., 2012), brachiopods (Bajnai et al., 2018), microbialites and methane seep carbonates (Loyd et al., 2016) along with speleothems  could be explained by oxygen isotope disequilibria occurring in dissolved inorganic carbon (DIC) involved in carbonate precipitation. In this case, δ 18 O and 47 disequilibria in biogenic carbonates would record information, however unavailable yet, on the physiological characteristics of carbonate-forming organisms.
In previous experiments we produced microbial calcium carbonates (Millo et al., 2012;Thaler et al., 2017) that recorded the strongest oxygen isotope disequilibrium ever identified between DIC and precipitation water (i.e., −25 ‰ offset from δ 18 O carbonate equilibrium values). We used carbonic anhydrase (CA), an enzyme able to accelerate oxygen isotope equilibration between DIC and water via fast CO 2 hydration and HCO − 3 dehydration. When CA was added to the precipitation water, the carbonate oxygen isotope compositions reached equilibrium with the precipitation water (Thaler et al., 2017). Here, we build on these experiments as they offer a unique opportunity to assess experimentally whether carbonates precipitated from DIC in disequilibrium with water also record 47 disequilibrium values and the type of information that is actually carried by these paired disequilibria. We later show how and to what extent this can be applied to previously published cases of oxygen isotopic offsets from equilibrium values in both biogenic and abiotic carbonates.
In experiments with CA whose δ 18 O results (but not the 47 ones) were recently published in Thaler et al. (2017), the precipitation solution was supplemented with CA at a concentration of 2 mg L −1 . The precipitation solution (with or without CA) was then mixed at a volumetric ratio of 1 : 1 with the ureolytic soil bacteria Sporosarcina pasteurii ( Fig. 1) suspended in Milli-Q ® water, at a final optical density at 600 nm of 0.100 ± 0.010. For this study, 16 gastight Exetainer ® vials were filled with the precipitation solution without CA in or-der to sacrifice them at regular time intervals (i.e., 30, 60, 120, 180 and 360 min and 24 h) and thus obtain information on the kinetics of the reaction, while reproducing the procedure followed for the experiment with CA (Thaler et al., 2017) consisting of 27 vials sacrificed every 10 to 30 min and after 24 h. The vials capped with rubber septa were filled up to the brim, i.e., without headspace, hence preventing any gaseous exchange with the atmosphere or headspace gases. Ureolysis corresponds to two types of hydrolysis: (i) the hydrolysis of urea into ammonia (NH 3 ) and carbamate (H 2 N-COOH) (H 2 N-CO-NH 2 + H 2 O → NH 3 + H 2 N-COOH), which is catalyzed by urease and is the rate-limiting step, and (ii) the rapid and spontaneous hydrolysis of carbamate into ammonia and CO 2(aq) (H 2 N-COOH + H 2 O → NH 3 + CO 2(aq) + H 2 O) (Krebs and Roughton, 1948;Matsuzaki et al., 2013) or H 2 CO 3 (H 2 N-COOH + H 2 O → NH 3 + H 2 CO 3 ) (Mobley and Hausinger, 1989;Krajewska, 2009).
Ureolysis completion was followed by evaluating the production of dissolved inorganic nitrogen (DIN = NH 3 + NH + 4 ). Determination of pH, DIN concentration and amount of precipitated carbonates (Fig. 2), as well as isotopic measurements, was performed for each vial to monitor their evolution as the ureolysis reaction progresses. The pH initially increased from 6.0 to 9.0 due to NH 3 production by ureolysis and consecutive alkalinization of the precipitation solution (Fig. 2a). The subsequent carbonate precipitation (Fig. 2b) lowered pH to 8.6 (without CA) and 8.4 (with CA) and was followed by a second pH increase to 8.8 (without CA) and 8.7 (with CA) when carbonate precipitation stopped while ureolysis continued. At ureolysis completion, all the calcium initially present in solution (i.e., the limiting reagent) had precipitated whereas 35 % to 45 % of the DIC produced by ureolysis remained in solution. Carbonate precipitates, formed at the bottom and on the wall of the vials, were immediately rinsed with a few drops of pure ethanol in order to dehydrate bacteria and prevent further ureolysis, carbonate formation and/or dissolution-reprecipitation processes. Ethanol was then removed, and, prior to their collection, carbonates were dried overnight at 40 • C in the vials placed in a ventilated oven equipped with desiccating beads. The majority of the carbonates precipitated in this study were composed of calcite with minor amounts of aragonite (1 % to 4 %), vaterite (2 % to 4 %) and magnesian calcite with low Mg content (Mg 0.064 , Ca 0.936 )CO 3 (up to 8 %) (Thaler et al., 2017).
All of the measured chemical parameters (pH, DIC, amount of solid carbonates, Ca 2+ concentration, DIN) along with DIC and solid carbonate δ 13 C behave similarly with or without active CA (Thaler et al., 2017). It was not possible to measure 47 for all the precipitated carbonates due to their low amount, particularly for the tubes sacrificed at the beginning of the experiments (Table S1 in the Supplement).  Evolution of pH (a) and amount of precipitated calcium carbonate C CaCO 3 (b) as a function of the production of dissolved inorganic nitrogen DIN (DIN = NH 3 +NH + 4 ) by bacteria during ureolysis, without carbonic anhydrase (CA) (this study) and with CA (data from Thaler et al., 2017). Error bars account for 2 SD and are always smaller than symbols for pH values. The mineralogy of the carbonates precipitated with or without CA was determined by X-ray diffraction, indicating that solid carbonates are mostly composed of calcite (including up to 8 % of low-Mg calcite, (Mg 0.064 , Ca 0.936 )CO 3 ), vaterite (2 %-4 %) and aragonite (1 %-4 %) (Thaler et al., 2017). The influence of mineralogy on isotopic measurements and temperature estimates is discussed in the Supplement, Sect. S1.

δ 18 O and 47 measurements and associated uncertainties
All the isotopic analyses were made at Institut de physique du globe de Paris (IPGP, France). δ 18 O analyses were performed on carbonate powders of ca. 2 mg with a continuoushelium-flow isotope ratio mass spectrometer AP 2003 (Analytical Precision 2003, GV Instruments) coupled to a gas chromatograph column (GC-IRMS, Chrompac Column Type 99960), as described in Millo et al. (2012) and Thaler et al. (2017). External reproducibility on carbonate standards is ±0.1 ‰ (1 SD) and represents the uncertainty assigned to δ 18 O carbonate data.
The analytical procedure used for clumped isotope 47 measurements is only briefly presented here and detailed in . About 5 mg of carbonates was digested at 90 • C for 20 min with 104 % phosphoric acid H 3 PO 4 in a common acid bath. The produced gaseous CO 2 was purified with a manual vacuum line before introduction into a Thermo Scientific MAT 253 dual-inlet mass spectrometer. Each purified CO 2 gas was analyzed for its abundance in isotopologues with m/z from 44 to 49 versus a working gas provided by Oztech Trading Corporation with δ 13 C = −3.71 ‰ Vienna Pee Dee Belemnite (VPDB) and δ 18 O = +24.67 ‰ Vienna Standard Mean Ocean Water (VS-MOW), as determined with the international reference ma-terial NBS19. One single 47 measurement corresponds to 70 cycles of 26 s integration time each (total integration time = 1820 s). Conventional δ 18 O and δ 13 C data were also acquired simultaneously with 47 measurements with this instrument (Tables S1 and S2). They are in excellent consistency with data obtained with the continuous-flow method on smaller samples (Table S1).
The 47 is calculated as a function of the stochastic distribution of the CO 2 isotopologues, as follows:  . For the correction from 17 O interferences, we used the 17 O correction parameters from Brand et al. (2010), as recently recommended (Daëron et al., 2016;Schauer et al., 2016). In order to transfer the obtained raw 47 data into the absolute carbon dioxide equilibrium scale "CDES" ( 47 CDES90 being the 47 values of carbonates reacted within acid at 90 • C), standards of CO 2 gases equilibrated at 25 and 1000 • C and with bulk isotopic compositions covering the range of measured carbonate samples (δ 47 values between −50 ‰ and +24 ‰) were analyzed interspaced with unknown samples (typically 15 equilibrated CO 2 gas analyses by discrete session of analysis, four analytical sessions in total; Table S5). For each analytical session, as recommended in Dennis et al. (2011), the 47 data were finally corrected with a fixed equilibrated gas line slope (only slightly varying from 0.0048 to 0.0062 over our analytical sessions) and an empirical transfer function (slopes varying from 1.0859 to 1.1344) based on the equilibrated CO 2 standards. Finally, the accuracy of our whole dataset and processing procedure was validated on carbonate reference material (i.e., IPGP-Carrara and 102-GC-AZ01), typically analyzed every two unknown samples (Table S5). The 47 values obtained at IPGP over the course of this study are 47 CDES90 = 0.316 ± 0.020 ‰ (1 SD, n = 16) for IPGP-Carrara and 47 CDES90 = 0.620 ± 0.010 ‰ (1 SD, n = 18) for 102-GC-AZ01. Those values are indistinguishable from the values obtained at IPGP over 4 years of analyses on the same instrument (n > 300) or previously reported by other laboratories (Daëron et al., 2016).

Temperature estimates and associated uncertainties
Apparent temperatures obtained from oxygen isotope compositions were calculated based on the measured δ 18 O carbonate values of both the precipitated carbonate and the precipitation water in each experimental vial (Table S1) and using the equation of oxygen isotopes' fractionation between calcite and water from Kim and O'Neil (1997). Apparent temperatures issued from clumped isotope compositions were calculated from 47 CDES90 data using the composite universal 47 -T calibration (Eq. 3 from , with T , the temperature). It is noteworthy that our main observations and conclusions do not change if other calibrations to temperature are used for δ 18 O and/or 47 (e.g., Coplen, 2007;Kelson et al., 2017) (see also Table S3). For both proxies, the uncertainties on temperature estimates reported here correspond to the standard deviation of the mean of replicated isotopic measurements of the same powder propagated in the calibration equation (but the actual errors on the calibration themselves are not considered). Note that the long-term external reproducibility on homogeneous calcite reference materials found in this study (i.e., ±0.020 ‰, 1 SD) is used for samples with only one measurement or with 1 SD lower than 0.020 ‰ (Tables S1 and S5, Sect. S1 in the Supplement).
For the temperature (T ) derived from the 47 data, we chose the calibration determined by  as it integrates a consequent number of data (n > 300), whose statistical weight has been properly considered and covers a wide temperature range (from 1 to 350 • C), three characteristics that were recently shown by several teams as governing the precision on 47 -T calibration equations Kelson et al., 2017;Fernandez et al., 2017). Importantly, this calibration covers the high apparent temperature ranges reported here (i.e., low 47 values) allowing us to avoid loss of precision and accuracy when extrapolating to temperature ranges that have not been experimentally investigated. Finally the  calibration has been checked independently with other methods (Mangenot et al., 2017;Dassié et al., 2018) on the range of temperatures (∼ 30 to 96 • C) where most available calibrations diverge and/or are not well constrained. Indeed, these studies report excellent consistencies: (i) between T 47 and homogenization temperatures from fluid inclusion microthermometry (Mangenot et al., 2017) and (ii) between the δ 18 O water values directly measured in fluid inclusions by cavity ring-down spectroscopy and those calculated from combined T 47 and δ 18 O carbonate of the host mineral (Dassié et al., 2018). Though we recognize that the normalization to carbonate standards presented in Bernasconi et al. (2018) might become commonly used by the community in the future (i.e., with the ongoing intercomparison InterCarb project), we preferred not to use this correction frame here because not enough of the four carbonate standards proposed by Bernasconi et al. (2018) were run together with our samples (n = 14 runs in total of ETH1, ETH2, ETH3 and ETH4 standards; Table S5), and such a normalization method will then introduce larger uncertainty than the normalization we performed with the large number of equilibrated gases ran daily together with our unknowns (n = 104 equilibrated gas; Table S5 -note also 33 secondary carbonate standards 102-GC-AZ01 and IPGP-Cararra, also run in other IPGP studies and some other laboratories). Also remarkably, 47 values obtained here on the four ETH carbonate standards are all systematically higher than values reported in Bernasconi et al. (2018) (Table S4). Though the reason for this positive offset is still unclear, it is noteworthy that positive offsets are also observed when compiling other recent published values (Table S4; Daëron et al., 2016;Schauer et al., 2016;Fiebig et al., 2019).

47 and δ 18 O compositions of microbial carbonates can present strongly correlated vital effects
We performed 47 measurements on (i) microbial carbonates precipitated without CA by faithfully replicating the experiment detailed in Thaler et al. (2017) and (ii) microbial carbonates precipitated in the presence of CA remaining from these experiments. These calcium carbonates were precipitated as the result of microbially driven hydrolysis of urea into DIC and ammonia (Millo et al., 2012). They constitute a reliable model for carbonate precipitation triggered by enzymatic production or transport of DIC, as is the case for microand macro-skeletal carbonates common in the Phanerozoic and for microbially mediated carbonates since the Precambrian.
Without CA, the isotopic values of the very first carbonate precipitates present strong isotopic offsets from equilibrium values. The 47 offset to equilibrium starts from −0.270 ‰ (the largest 47 offset ever measured in solid carbonates), and the offset to equilibrium reaches −24.7 ‰ for δ 18 O carbonate ( Fig. 3  Here, we discuss the potential processes known to generate δ 18 O and 47 isotope fractionations during carbonate precipitation and we identify the main mechanism explaining our paired 47 and δ 18 O carbonate disequilibria. The relatively high precipitation rate (R) in our experiments (log R = −3.95 mol m −2 s −1 ; Thaler et al., 2017) can only account for an oxygen kinetic isotope fractionation (KIF) of about 1 ‰ to 2 ‰ for δ 18 O values (Watkins et al., 2013), while the oxygen isotope disequilibrium recorded in our carbonates reaches −24.7 ‰. Degassing of CO 2 , known to fractionate DIC oxygen isotopes , can be ruled out as there is no gas phase in our experiments (see Sect. 2.1). Any potential kinetic fractionation due to DIC diffusion (Thiagarajan et al., 2011) is also unlikely as precipitation occurred on the bacterial DIC-producing cells, as highlighted by scanning electron microscopy showing bacterial cells trapped within and at the surface of carbonate crystals (Fig. 1). Accordingly, the large offsets from equilibrium values observed for both 47 and δ 18 O in our microbial carbonates can only result from (i) a KIF induced by CO 2 hydration or hydroxylation into HCO − 3 (but only if ureolysis produces CO 2 rather than H 2 CO 3 , which has not been established yet; Matsuzaki et al., 2013) or (ii) a metabolic isotopic signature of the DIC produced by the bacteria, inherited from the initial isotopic composition of urea and/or due to a KIF introduced by the urease enzyme. CO 2 hydration and hydroxylation lead to the formation of HCO − 3 , with two oxygen atoms coming from CO 2 and the third one from H 2 O (hydration) or OH − (hydroxylation). The δ 18 O HCO − 3 value can then be estimated using a simple mass balance calculation (Létolle et al., 1990;Usdowski et al., 1991). The newly formed HCO − 3 is depleted in 18 O compared to the reacting CO 2 because of the incorporation of oxygen coming from H 2 O or OH − , both depleted in 18 O relative to 16 O in contrast to CO 2 (Green and Taube, 1963;Beck et al., 2005). Such a low δ 18 O HCO − 3 value, several per mill lower than the equilibrium one, can then be preserved in the calcium carbonate if precipitation occurs shortly after CO 2 hydration and hydroxylation and before the full equilibration with water (Rollion- Bard et al., 2003). Regarding clumped isotopes, ab initio calculations predict that the fractionation associated with CO 2 hydration and hydroxylation increases the relative abundance of 13 C-18 O bonds and thus the 47 value (Guo, 2009). Even though this predicted fractionation trend has previously been used to explain several datasets for which CO 2 hydroxylation was assumed to occur prior to carbonate precipitation (Tripati et al., 2015;Spooner et al., 2016), such a tendency can only be validated using data acquired on carbonates for which CO 2 hydration and hydroxylation are demonstrated. This is the case of (i) hyperalkaline travertines (Falk et al., 2016) even though part of the reported kinetic isotope fractionation  2017) and Kim and O'Neil (1997) calibrations, respectively. Uncertainties (1 standard deviation, 1 SD) are smaller than the symbol for δ 18 O and C CaCO 3 values (Table S1). Reported 47 uncertainties are detailed in Sect. 2 and Sect. S1 in the Supplement.
can be interpreted as resulting from the CO 2 dissolution process (Clark et al., 1992) and (ii) two experimental samples (Tang et al., 2014) precipitated at high pH where CO 2 hydroxylation dominates. Both studies show, in agreement with the ab initio calculations (Guo, 2009), higher 47 and lower δ 18 O carbonate values compared to equilibrium. Thus, in a case where ureolysis would produce CO 2 in isotopic equilibrium with water, the 47 values affected by CO 2 hydration and hydroxylation recorded in calcium carbonates should be higher than the equilibrium value, while our microbial carbonates show 47 values lower than equilibrium. Thus, we conclude that our low 47 values measured in carbonates can only be explained by a metabolic source effect. In our case it corresponds to the ureolytic production of DIC, either directly as H 2 CO 3 or as CO 2 , with a 47 value low enough to compensate for any potentially succeeding increase due to the KIF associated with CO 2 hydration and hydroxylation. Nonetheless, the slow but continuous increase observed in our experiment without CA for both 47  and water once δ 13 C is equilibrated (Affek, 2013;Clog et al., 2015). This principle has been used to correct for the disequilibrium fractionation factor in speleothems (Affek et al., 2008).

Erroneous yet comparable temperatures reconstructed from disequilibrium 47 and δ 18 O values in carbonates
Apparent temperatures were calculated from disequilibrium 47 values obtained in the experiment without CA using the calibration of . Ranging from 198±21 to 115±8 • C (Fig. 4), they are at odds with the actual precipitation temperature of 30 ± 1 • C (see Sect. 2.1). This shows that when carbonates precipitate from DIC in oxygen isotope disequilibrium with water, the abundance of 13 C-18 O bonds in carbonates does not correlate with precipitation water temperature. Conversely, the temperatures reconstructed from the 47 values of carbonates precipitated in the presence of CA, ranging from 47 ± 6 to 39 ± 2 • C, are much closer to the actual precipitation temperature. Interestingly, the apparent temperatures reconstructed using Kim and O'Neil (1997) calibration from the δ 18 O carbonate and δ 18 O water values of the same samples show comparable offsets from the actual temperature in both experiments without CA (from 218 ± 2 to 139 ± 1 • C) and with CA (from 39 ± 1 to 37 ± 1 • C) (Fig. 4). Practically, this implies that similar temperatures calculated from both carbonate 47 and δ 18 O carbonate values (in a case where the precipitation water δ 18 O can be determined) can neither constitute evidence against O isotope disequilibrium nor confirm that this is the true precipitation temperature.  Kim and O'Neil (1997) and . Reported uncertainties were calculated as the propagation of the 1 standard deviation (1 SD) error of the isotopic data in the calibration equations (Sect. 2 and Sect. S1 in the Supplement).

47 and δ 18 O carbonate paired disequilibria record the δ 18 O of the water in which the carbonates precipitated
The fact that both 47 and δ 18 O carbonate values permit us to calculate similarly evolving apparent temperatures along the (dis)equilibration profile recorded in carbonates as the experiment proceeds indicates that the δ 18 O carbonate , δ 18 O water , 47 and apparent temperature values are all together linked. In a diagram of 47 versus δ 18 O carbonate , all of our data align, irrespectively of the fact that they are in strong isotopic disequilibrium or close to equilibrium (Fig. 5) Kim and O'Neil (1997) was preferred over more recent calibration equations (e.g., Watkins et al., 2013) because it provides the best consistency for temperatures reconstructed from both the carbonate δ 18 O and 47 values at temperatures above 100 • C. Note that Kim and O'Neil (1997) and  calibrations were developed independently, which prevents circular reasoning. Finally, as the calibration of Kim and O'Neil (1997) is the most used calcite calibration to date, it also allows for a broader comparison with previously published results. Despite the fact that the data present a large range of offsets from equilibrium (Fig. 5), the mean δ 18 O water value calculated using Eq. (2) for each combination of 47 and δ 18 O carbonate values measured for our carbonates is −8.0 ± 2.8 ‰ (1 SD), indistinguishable (i.e., within errors) from the δ 18 O water values measured in our experiments (−6.4±0.2 ‰ with CA and −6.8 ± 0.2 ‰ without CA; Fig. 5). Note that such precision in δ 18 O water values found in disequilibrium carbonates is remarkable considering that even for equilibrium carbonates at isotopic equilibrium for both δ 13 C and δ 18 O, δ 18 O water can only be retrieved from paired 47 and δ 18 O carbonate values with a precision of ±1 ‰ at best (see Fig. S1 in the Supplement). This creates the promising opportunity to retrieve the δ 18 O value of the water in which car-bonates precipitated out of equilibrium for both δ 18 O carbonate and 47 .
In order to evaluate the applicability of such an approach to other types of carbonates, Fig. 6 compiles disequilibrium paired δ 18 O carbonate and 47 data from two previously published experimental studies (Tang et al., 2014;Staudigel and Swart, 2018). These studies were chosen to further evaluate the relevancy of our δ 18 O carbonate -47 correlation because they are the only published dataset reporting full sets of measured (rather than calculated) δ 18 O water , δ 18 O carbonate and 47 values, with one or both proxies showing disequilibrium, together with precipitation temperatures. A perfect knowledge (i.e., measurements and not estimates) of these four parameters is mandatory here to adequately test whether the use of our new δ 18 O water proxy could be generalized to a large diversity of carbonates. This thus precludes plotting most published 47 studies on both natural and experimental samples, in which δ 18 O water and/or temperature were not directly measured, in Fig. 6. These two datasets are also recent enough to allow the conversion of their 47 values to the currently used normalization method (i.e., the CDES absolute reference frame). It will then allow comparison with future studies, if measuring and reporting all these four parameters together becomes the rule rather than the exception in 47 studies. Figure 6a shows paired δ 18 O carbonate and 47 values of abiotic carbonates produced at 5, 25 and 40 • C that are known to be affected by KIF due to fast precipitation and for at least two of them by KIF due to CO 2 hydration and hydroxylation prior to precipitation (Tang et al., 2014). Except for these two carbonate samples, the data align on a covariation curve of 47 versus δ 18 O carbonate that cannot be explained solely by temperature variation. As for our microbial carbonates obtained with or without CA, the average calculated δ 18 O water (Eq. 2; −11.2 ± 1.5 ‰) matches within error with the measured δ 18 O water (−9.6 ± 0.2 ‰) (Dietzel et al., 2009). Figure 6b shows paired δ 18 O carbonate and 47 values of abiotic carbonates that were precipitated during an initial CO 2 degassing + DIC equilibration phase followed by solely equilibration with water at 5, 15 and 25 • C (Staudigel and Swart, 2018). During the latter equilibration phase, even though the carbonates precipitated out of isotopic equilibrium, the paired δ 18 O carbonate and 47 values align on a covariation curve of the average calculated δ 18 O water value (Eq. 2; −3.0 ± 1.1 ‰) close to the measured δ 18 O water (−0.65 ‰). As a major outcome of this study, we thus anticipate that reliable δ 18 O water values of precipitation water can be retrieved from carbonates presenting 47 and δ 18 O carbonate values in strong disequilibrium.
Some data presented in Fig. 6 also permit us to evaluate the conditions of applicability of our approach. In Fig. 6a, the two data points deviating from the covariation curve of 47 versus δ 18 O carbonate correspond to carbonates precipitated at pH ∼ 10 and 5 • C (while the others formed at pH and Figure 6. 47 and δ 18 O carbonate relationship to precipitation water δ 18 O water for other solid carbonates presenting oxygen isotope disequilibria. In (a) to (c) the black data series (this study, performed at 30 • C) shows how kinetic oxygen isotope fractionation in the DIC prior to carbonate precipitation can be mistaken for high-temperature isotopic equilibrium. Similarly to Fig. 5, the solid curves were obtained using the δ 18 O water calculated with Eq. (2). (a) Abiotic carbonates from Tang et al. (2014) illustrating the effect of CO 2 hydroxylation on 47 and δ 18 O carbonate values (various pH values plotted with different colors, various temperatures plotted with different symbols). (b) Abiotic carbonates from Staudigel and Swart (2018) illustrating the effect of CO 2 degassing and DIC oxygen isotope equilibration with water on 47 and δ 18 O carbonate values. δ 13 C carbonate stands for the difference between the δ 13 C value measured in carbonates and the final δ 13 C of the data series at the end of equilibration (various δ 13 C ranges plotted with different colors, various temperatures plotted with different symbols). (c) Coccolithophorid E. huxleyi grown at 7, 10, 15, 20 and 25 • C from Katz et al. (2017) showing how coccoliths with equilibrium temperatures ranging from 8.3 to 9 and 5 to 40 • C, respectively) that have recorded a KIF due to CO 2 hydration and hydroxylation prior to precipitation (Tang et al., 2014). At pH = 10, CO 2 reacts at 95 % with OH − , and at 5 • C DIC isotopic equilibration with water takes days. To a lesser extent, the KIF induced by CO 2 hydroxylation also seems visible at pH = 9 (and 40 • C), where CO 2 reacts at 82 % with OH − , but DIC isotopic equilibration with water at 40 • C only takes about 15 h. As previously detailed, the direction of these isotopic offsets from equilibrium is compatible with ab initio calculations (Guo, 2009) and can be intuitively understood as follows: in carbonates derived from CO 2 hydroxylation, the R X stochastic term used for the 47 calculation (Eq. 1) should be strongly modified as the 18 O concentration in OH − and H 2 O is lower than in CO 2 , and the reaction does not add more 13 C than what is present in CO 2 . This might explain why in the case of disequilibria acquired through CO 2 hydroxylation, the correlation between paired δ 18 O and 47 disequilibria and the precipitation water δ 18 O is not preserved, and δ 18 O water cannot be reconstructed by the approach proposed here. The negative slope associated with this KIF on the 47 and δ 18 O carbonate diagram (Fig. 6a) is nevertheless a good tool to identify CO 2 hydroxylation reactions.
In Fig. 6b, during the CO 2 degassing phase of the precipitation experiment (Staudigel and Swart, 2018), the data also deviate from the covariation curve of δ 18 O versus 47 . This behavior was interpreted by the authors as a decoupling between 47 and δ 18 O carbonate values due to variable kinetics of 12 C-O and 13 C-O bonding. A known difference in equilibration kinetics takes place between C and O isotopes in the carbonate system as carbon isotopes equilibrate in seconds, while oxygen isotopes necessitate minutes to hours to equilibrate among the different oxygen-bearing species (i.e., CO 2 , HCO − 3 , CO 2− 3 , H 2 O, OH − ), depending on the pH, temperature and salinity of the solution (Zeebe and Wolf-Gladrow, 2001). However, note that in that experiment, the carbon isotope compositions evolved for several hours as a result of CO 2 degassing (Staudigel and Swart, 2018). We propose here that CO 2 degassing, because it affects both C and O isotopes, modifies the R X stochastic term (in Eq. 1), thus preventing 47 and δ 18 O from varying with the proportionality that allows us to retrieve the δ 18 O water value on a covariation plot of 47 versus δ 18 O. Hence, as for CO 2 hydroxylation, in the case of a KIF induced by CO 2 degassing, δ 18 O water cannot be reconstructed exclusively from disequilibrium δ 18 O carbonate and 47 values.
In summary, we conclude that mechanisms that can drastically change the R X stochastic term in 47 calculation (such as CO 2 hydroxylation and degassing) prevent δ 18 O water reconstructions from paired disequilibrium 47 and δ 18 O carbonate values. Nevertheless, these mechanisms lead to peculiar types of carbonates (e.g., speleothems that form in caves from CO 2 degassing, and travertine that forms on lands where fluids and gas escape from subsurface reservoirs, for CO 2 hydroxylation) that represent only a small fraction of all the carbonates existing on Earth. We hypothesize that ureolysis, which consists in two successive steps of urea hydrolysis, an exchange reaction with the H 2 O molecule from the aqueous medium, might give a DIC whose R X stochastic term in the 47 calculation is already close to that of DIC under equilibration with the δ 18 O water . This would explain why even our most extreme out-of-equilibrium carbonates still fall close to the covariation line of 47 versus δ 18 O carbonate corresponding to the real δ 18 O water value.

Toward a better understanding of body water δ 18 O in biomineralizing organisms
The ability to reconstruct precipitation water δ 18 O water from disequilibrium 47 and δ 18 O carbonate values further allows us to examine the origin of the vital effect observed in organisms for which (i) CO 2 degassing and hydration and hydroxylation KIF can be ruled out, and (ii) only small δ 13 C variations are observed, thus preserving the R X stochastic term in 47 calculation. We hypothesize that such an approach could help to understand how 47 and δ 18 O signals are affected by kinetic effects in most of the biogenic carbonates, provided that CO 2 hydroxylation or degassing does not occur prior to carbonate precipitation. This approach could thus be applied to the vast majority of sedimentary carbonates (Milliman, 1993) (i.e., microbialites, brachiopods, bryozoans, bivalves, foraminifera, coccoliths) and since deep time, even when δ 18 O carbonate variations occur in the shell of the organism. Additionally, the data presented here stand as an experimental demonstration that the mechanisms controlling carbonate δ 18 O equilibration with water (i.e., DIC equilibration with water) also control solid carbonate 47 equilibrium (Watkins and Hunt, 2015). This result can be used to recover information on biomineralization mechanisms. For example, in recent coccolithophorid Emiliania huxleyi culture experiments, the calcitic shell produced by the organism systematically yields a 2 ‰ positive δ 18 O offset from equilibrium values while its 47 values seem to faithfully record precipitation temperature (Katz et al., 2017). These coccolithophorids were grown in waters with different δ 18 O water compositions (i.e., measured at −6.14 ‰, −5.82 ‰ and 0.65 ‰ VSMOW that are respectively seawater A, B and C in Fig. 6c). Based on our results, which demonstrate that no δ 18 O disequilibrium should be recorded in solid carbonates if the associated 47 is at equilibrium, we can assume that the coccoliths precipitated at oxygen isotope equilibrium. We also calculate the actual δ 18 O value of the water in which precipitation took place from Eq. (2) (respectively shifted by 1.0 ± 0.2 ‰, 2.1 ± 0.4 ‰ and 1.1 ± 0.7 ‰ towards more positive values compared to the δ 18 O water value measured for the culture medium water; Fig. 6c). This could reflect a biologically driven difference between the δ 18 O of body water at the precipitation site inside E. huxleyi and the δ 18 O of ambient water (i.e., the culture medium water). This hypothesis is supported by what is known about intracellular precipitation of coccoliths performed by coccolithophorids: each coccolith forms from the accumulation of coccolithosomes, which are vesicles containing up to approximately twelve 7 nm spherical calcium-rich granular units (Outka and Williams, 1971). Water in these ∼ 100 nm vesicles can be considered a finite reservoir whose isotopic composition could be modified through isotopic exchange with DIC affected by metabolic isotope fractionation. Another mechanism that could increase the δ 18 O value of a finite water reservoir by equilibrating it with a comparable reservoir of DIC would be the introduction of DIC systematically as CO 2 . As HCO − 3 and CO 2− 3 are enriched in 16 O in comparison to CO 2 , the CO 2 conversion to HCO − 3 and CO 2− 3 at equilibrium before precipitation would pump 16 O from water.
In both case scenarios, a local change in water isotopic composition requires that the water molecules' turnover (i.e., external inputs) in these cellular organites is slow enough. Coccolithosomes are subunits of the Golgi complex, which is a system of flat stacked vesicles concentrating a lot of membranes in a small location (Outka and Williams, 1971). It is thus plausible that in a single-celled organism, living in seawater and performing intracellular biomineralization, specific osmolarity and water circulation regulation mechanisms are occurring. It is particularly plausible in the Golgi complex, whose water content is isolated from seawater by several membranes. We thus suggest that inside coccolithosomes, coccolith precursors precipitate in equilibrium with the body water for oxygen isotopes but that the body water has a different δ 18 O value than the seawater, which explains the observed δ 18 O apparent fractionation while the 47 composition reflects culture temperature (Katz et al., 2017). It has already been highlighted through geochemical analysis of coccoliths that coccolithosome water has altered pH (Liu et al., 2018) and ion concentrations  in comparison to seawater. We hypothesize that the internal δ 18 O water would thus be another parameter controlled by the coccolithophore algae.
3.6 Ubiquity of the observed δ 18 O carbonate -δ 18 O water -47 -temperature covariations in both equilibrium and disequilibrium carbonates As shown above (Fig. 5), in a diagram of 47 versus δ 18 O carbonate , disequilibrium carbonates precipitated at fixed temperature plot on the theoretical line of equilibrium carbonates precipitated with a similar δ 18 O water but at a different temperature. This is illustrated in Fig. 7 where the three disequilibrium data series studied in this paper (Fig. 5 for this study and Fig. 6a and b for datasets from Tang et al., 2014, andStaudigel andSwart, 2018) align with equilibrium data series. In other words, the values of the disequilibrium 1000 ln α carbonate−water for oxygen isotopes (with α = δ 18 O carbonate +1000 δ 18 O water +1000 ) are similar to the equilibrium 1000 ln α carbonate-water for any given, and independently de-termined, apparent 47 temperature (Fig. 7). In detail, our closest-to-equilibrium data recording low apparent temperatures match better with the predicted equations from Coplen (2007) and Watkins et al. (2013), recently updated (Daëron et al., 2019). This last calibration is based on carbonates from two caves where calcite precipitates extremely slowly and is thus assumed to have precipitated at equilibrium. Note that the use of these two cave samples for determining the dependence on temperature of the equilibrium 1000 ln α carbonate-water relies on the assumption that constant environmental conditions, including temperature in the two caves (7.9 and 33.7 • C) and the δ 18 O water value of the precipitation water, prevailed over the whole period of carbonate precipitation (Coplen, 2007;Kluge et al., 2014). In Fig. 7, the disequilibrium data recording high apparent temperatures (above 100 • C) match better with the predicted equation of Kim and O'Neil (1997). This 1000 ln α carbonate-water dependence on temperature was established on carbonates precipitated in the laboratory at well-known δ 18 O water and temperatures (from 10 to 40 • C) but was suspected to present a small KIF due to a high precipitation rate that lowers the value of the 1000 ln α carbonate-water (Watkins et al., 2013). Despite this, we used this equation to retrieve the δ 18 O water from our experimental carbonates, because most of them are associated with high apparent 47 temperatures. Coplen (2007) or Watkins et al. (2013) equations would have 2 ‰ lower values (ca. −10 ± 2 ‰ compared to −8 ± 3 ‰ calculated with the equation of Kim and O'Neil, 1997). From our results, due to our experimental conditions and the associated error in our dataset, it is not possible and not our intention to argue in favor of one of these calibrations. This however shows how crucial it is to improve knowledge on the equilibrium 1000 ln α carbonate-water at both high and low temperatures in order to improve the accuracy and precision of our new proxy for reconstructing the δ 18 O water from which carbonates, even disequilibrium ones, precipitated. Importantly, we here establish a new method to determine the equilibrium 1000 ln α carbonate-water , which consists in using the kinetics of 47 and δ 18 O covariations during (dis)equilibration. Notably, because of the very large range of apparent temperatures recorded by disequilibrium carbonates (between ∼ 40 and 200 • C; Fig. 7), this method could be particularly adapted to calibrate 1000 ln α carbonate-water at high temperatures for which the differences between the two most popular equations for 1000 ln α carbonate-water dependence on temperature (Kim and O'Neil, 1997;Coplen, 2007) appear larger (Fig. 7). Unfortunately, none of the three experimental setups having produced these disequilibrium carbonates (this study, as well as Tang et al., 2014, andStaudigel andSwart, 2018) were designed for the purpose of calibrating the equilibrium 1000 ln α carbonate-water . It is thus not possible, using these datasets, to propose a meaningful calibration. At least in our experiment, too many phenomena including the relatively high precipitation rate, variations in δ 13 C values (∼ 3 ‰) (Thaler et al., 2017) and presence of traces of arag- Figure 7. The relation to temperature of the equilibrium oxygen isotope fractionation factor between calcium carbonate and water (1000 ln α calcite−water ) appears to be retrievable from solid carbonates (mainly calcites) in strong clumped and oxygen isotope disequilibrium such as our microbial carbonates (black dots, precipitated at 30 • C) and two additional data series of laboratory-grown carbonates showing disequilibrium fractionation (Tang et al., 2014;Staudigel and Swart, 2018) (green and yellow dots, respectively). The data points affected by CO 2 hydroxylation (Tang et al., 2014) or CO 2 degassing (Staudigel and Swart, 2018) (see Fig. 6) are not included. Grey symbols correspond to cave carbonates precipitated at or near equilibrium (Coplen, 2007;Daëron et al., 2019) or laboratory experiments (Kim and O'Neil, 1997;Watkins et al., 2013). Those grey data series are usually considered representative of the equilibrium fractionation factor between calcium carbonate and water whose relations to temperature, extrapolated at high temperature, are illustrated by the different dashed curves. Plotted temperatures correspond to precipitation temperatures except for disequilibrium carbonates for which apparent temperatures have been calculated based on 47 values. The x-axis errors for this study are included in the symbol size. The y-axis error for all the reconstructed temperatures is given on the figure. onite and vaterite in our carbonates (Sect. 2.1 and Sect. S1 in the Supplement) lower the accuracy of the reconstructed equilibrium 1000 ln α carbonate-water values.
From a broader perspective, we anticipate that such an approach will help in determining critical equilibrium fractionation factors for other gaseous isotopic systems (such as isotopologues of molecules containing S-O bonds) or minerals of prime interest in biology and geology if clumped isotope measurements expand further beyond gaseous mass spectrometry (e.g., bonding between Fe-O, Fe-S, Ca-C).

Conclusions
Our experimental results show that the information held in disequilibrium (and apparent disequilibrium) carbonates is diverse and promising. First, a paired 47 and δ 18 O carbonate disequilibrium indicates that carbonates have precipitated in a dynamic environment where DIC and water did not reach isotopic equilibrium. In our microbial carbonate experiments, all the DIC is produced in isotopic disequilibrium with water and precipitates rapidly. Accordingly, the disequilibrium O isotope compositions recorded in those carbonates are maximized compared to what can be expected in nature where newly produced DIC is expected to be mixed with at least partly equilibrated ambient DIC before carbonates precipitate. Second, the combined use of clumped and traditional oxygen isotopic compositions allows the retrieval of the δ 18 O of the precipitation water, i.e., organism body water or environmental water, even for carbonates presenting δ 18 O and/or 47 disequilibria or apparent disequilibria. Hence, except in the case of processes such as CO 2 degassing and CO 2 hydration and hydroxylation, which likely modify the R X stochastic term in 47 calculation, paired 47 and δ 18 O carbonates disequilibria in carbonates can be used to reconstruct the oxygen isotope composition of both DIC and water at the precipitation loci even when precipitation occurred under disequilibrium conditions. Third, the (dis)equilibration trend in a covariation diagram of 47 versus δ 18 O carbonates can be used as a new method to determine the equilibrium fractionation factor between carbonate and water for a wide range of temperatures. Altogether, this opens up new avenues to better constrain not only past climate changes through improved paleoenvironmental reconstructions but also the physiology and habitat of sea life sensitive to ocean acidification. Data availability. All the data generated and analyzed in this study are available within the paper and in its Supplement.
Author contributions. CT and AK conceived the research. CT performed the microbial precipitation experiment and the δ 13 C and δ 18 O analyses during her PhD thesis under the supervision of MA and BM. AK performed the 47 analyses during her PhD thesis under MB's supervision. CT took the lead in the interpretation of the results and the writing of the original draft. All authors provided critical feedback and helped shape the research, analyses and manuscript.
Competing interests. The authors declare that they have no conflict of interest.