Simulating speleothem growth in the laboratory: Determination of the stable isotope fractionation (δ13C and δ18O) between H2O, DIC and CaCO3

Accepted Manuscript Simulating speleothem growth in the laboratory: Determination of the stable isotope fractionation (δ13C and δ18O) between H2O, DIC and CaCO3

Maximilian Hansen, Denis Scholz, Bernd R. Schöne, Christoph Spötl PII: DOI: Reference:

S0009-2541(18)30597-7 https://doi.org/10.1016/j.chemgeo.2018.12.012 CHEMGE 18999

To appear in:

Chemical Geology

Received date: Revised date: Accepted date:

31 October 2017 13 December 2018 17 December 2018

Please cite this article as: Maximilian Hansen, Denis Scholz, Bernd R. Schöne, Christoph Spötl , Simulating speleothem growth in the laboratory: Determination of the stable isotope fractionation (δ13C and δ18O) between H2O, DIC and CaCO3. Chemge (2018), https://doi.org/10.1016/j.chemgeo.2018.12.012

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ACCEPTED MANUSCRIPT

Simulating speleothem growth in the laboratory: Determination of the stable isotope fractionation

(13C and 18O) between H2O, DIC and CaCO3

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Maximilian Hansen1*, Denis Scholz1, Bernd R. Schöne1, Christoph Spötl2

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*corresponding author: [email protected] 1Institute

for Geosciences, University of Mainz, Germany

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2Institute

1

of Geology, University of Innsbruck, Austria

ACCEPTED MANUSCRIPT Abstract Here we present novel cave-analogue experiments directly investigating stable carbon and oxygen isotope fractionation between the major involved species of the carbonate system (HCO3-, CO2, CaCO3 and H2O). In these experiments, which were performed under controlled conditions inside a climate box, a thin film of solution flew down an inclined marble or glass plate. After different distances of flow and, thus, residence times on the plate, pH, electrical conductivity, supersaturation with respect to calcite, precipitation rate as well as the 18O and 13C values of the dissolved inorganic carbon (DIC)

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and the precipitated CaCO3 were obtained. Progressive precipitation of CaCO3 along the plate is accompanied by degassing of CO2 and

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stable isotope fractionation, and the system is driven out of isotope equilibrium. We observe a strong enrichment of the 13C values with increasing residence time and a smaller enrichment in 18O. The

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temporal evolution of the 18O and 13C values of both the DIC and the precipitated CaCO3 can be explained by a Rayleigh fractionation model, but the observed enrichment in 13C values is much larger

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than expected based on isotope equilibrium fractionation factors.

Our setup enables to determine the fractionation between CaCO3 and HCO3-, i.e., CaCO3/HCO3-. 13CaCO3/HCO3-,

is strongly negative for all experiments and much lower

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Carbon isotope fractionation,

than equilibrium isotope fractionation (0-1 ‰). In addition,

13CaCO3/HCO3-

decreases with increasing

residence time on the plate, and thus decreasing supersaturation with respect to calcite. Thus, isotope

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fractionation depends on precipitation rate and is, thus, kinetics. This is in contrast to previous studies, which found no rate-dependence and no or even a positive carbon isotope fractionation between

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CaCO3 and HCO3-. Oxygen isotope fractionation,

18CaCO3/HCO3-,

is also negative and dependent on

precipitation rate. Since no literature values for 18CaCO3/HCO3- are available, we calculated 18CaCO3/HCO3using equilibrium oxygen isotope fractionation factors between water and calcite and water and HCO3-

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, respectively. At the beginning of the plate, the fractionation is in agreement with the fractionation calculated using fractionation factors determined in cave systems.

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The observed fractionation between CaCO3 and water, 1000ln18, is also in good agreement with the values determined in cave systems and shows a very similar temperature dependence (1000𝑙𝑛 18𝛼 = 16.516(±1.267) ∗

103 𝑇

− 26.141(±4.356)). However, with progressive precipitation of

CaCO3 along the plate, the system is forced out of isotope equilibrium with the water, and 1000ln18 increases. The large, negative, rate-dependent isotope fractionations observed in this study suggest that precipitation of speleothem calcite is strongly kinetically controlled and may, thus, have a large effect on speleothem 18O and 13C values. Since these values may erroneously be interpreted as reflecting changes in past temperature, precipitation and/or vegetation density, these results have important implications for paleoclimate reconstructions from speleothems. 2

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Keywords: speleothems, stable carbon isotopes, stable oxygen isotopes, stable isotope fractionation,

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laboratory experiments.

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ACCEPTED MANUSCRIPT 1. Introduction Speleothems are unique paleoclimate archives providing important information on past climate variability in a wide range of climatic zones (Fairchild and Baker, 2012). They can be dated very precisely using U-series disequilibrium methods (Richards and Dorale, 2003; Scholz and Hoffmann, 2008). In combination with the most widely used paleoclimate proxies for speleothems, the stable isotopes of carbon and oxygen (13C and 18O), they provide continuous long-term paleoclimate records (e.g., Asmerom et al., 2010; Bar-Matthews et al., 2003; Boch et al., 2011; Cheng et al., 2016;

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Cruz et al., 2005; Fleitmann et al., 2004). However, the stable isotope signals in a speleothem depend on various processes occurring in the atmosphere, the soil and karst as well as inside the cave

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(Lachniet, 2009; McDermott, 2004). Thus, the interpretation of 13C and 18O records in terms of past climate variability is challenging.

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The majority of speleothem paleoclimate studies are based on the 18O signals of speleothem calcite (e.g., Cheng et al., 2016; Fleitmann et al., 2004; Spötl et al., 2008), which have been shown to

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provide important information about changes in past precipitation patterns in the catchment of the cave (e.g., Bar-Matthews et al., 2003; Cheng et al., 2016), the source of the water vapor and atmospheric circulation (e.g., Cruz et al., 2005; Wassenburg et al., 2016), as well as air temperature (e.g., Mangini et

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al., 2005). In an ideal setting, the 18O signal of meteoric precipitation is directly incorporated into speleothem calcite. In reality, however, the incorporation of the 18O signal into speleothem calcite depends on various parameters, such as the saturation state of the solution entering the cave (i.e.,

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degree of supersaturation with respect to calcite), evaporation (controlled by the relative humidity in

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the soil zone and inside the cave), air temperature and whether chemical equilibrium during precipitation of (speleothem) CaCO3 is established. In addition, prior calcite precipitation (e.g., Treble et al., 2015), mixing of different water sources, varying residence times of the water in the aquifer as

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well as evapotranspiration may obscure the 18O signal recorded in a speleothem (e.g., Mischel et al., 2016; Wackerbarth et al., 2010). Even though mass spectrometric analyses of carbonate samples typically yield both 13C and

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18O values, 13C data of speleothem have been utilized to a lesser extent than 18O data. The major reason for this is that 13C values are influenced by complex processes in the soil, the epikarst, and inside the cave (Dreybrodt and Scholz, 2011; McDermott, 2004). However, various studies have documented the large potential of paleoclimate information preserved in speleothem 13C records. For example, Genty et al. (2003) interpreted rapid changes in the 13C values of a stalagmite from southwest France as reflecting dramatic changes in vegetation above the cave related to DansgaardOeschger events. Similarly, Mischel et al. (2016) and Hellstrom and McCulloch (2000) interpreted speleothem 13C records in terms of changes in vegetation and recharge and supported their interpretation by trace elements. Scholz et al. (2012) showed a relationship between thicker annual laminae and lower 13C values in a speleothem from north-eastern Italy reflecting warmer winter temperatures on annual timescales. On the millennial timescale, they interpreted changes in 13C 4

ACCEPTED MANUSCRIPT values as reflecting the progressive evolution of the soil profile above the cave. Ridley et al. (2015) generated monthly resolved 13C data from a speleothem from Belize providing information on past changes in rainfall, which in turn are related to changes in the Intertropical Convergence Zone. Additionally, Breecker (2017) showed that globally averaged speleothem 13C records potentially traces changes in atmospheric pCO2 for the Pleistocene. All these examples emphasize the large potential of speleothem 13C records for a number of paleoclimate and environmental applications. Since the early studies trying to exploit speleothem stable isotope records as paleoclimate

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proxies (e.g., Fornaca-Rinaldi et al., 1968; Hendy and Wilson, 1968), stable isotope fractionation in speleothems has been discussed controversially. In particular, the question whether “kinetic” or

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equilibrium fractionation processes are more suitable to describe stable isotope fractionation in speleothems is still a matter of debate (e.g., Kluge et al., 2013; Mickler et al., 2006; Riechelmann et al.,

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2013; Watkins et al., 2013). A pioneering theoretical work about stable isotope fractionation in speleothems was presented by Hendy (1971). He suggested that a progressive increase of 13C and

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18O values as well as a positive correlation between 13C and 18O values along individual growth layers is an indication for disequilibrium isotope fractionation. This was subsequently established as the “Hendy test” and has been widely applied to test the suitability of speleothems for paleoclimate

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reconstruction (e.g., Dorale and Liu, 2009). In the last decade, a number of theoretical studies have been published aiming to quantitatively describe the isotope fractionation processes during precipitation of speleothem calcite. In particular, two models have been proposed: a so-called ‘kinetic’

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fractionation model (Dreybrodt, 2008; Dreybrodt and Scholz, 2011) and a Rayleigh distillation model

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(Scholz et al., 2009). The model of Scholz et al. (2009) provides the basis for a more sophisticated model also accounting for changes in cave temperature, cave and soil pCO2, drip rate and splashing effects (Mühlinghaus et al., 2007, 2009). In addition, models describing the effects of evaporation (Deininger et al., 2012; Dreybrodt and Deininger, 2014) as well as isotope exchange between gaseous

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cave CO2 and the dissolved inorganic carbon (DIC) in the thin film of solution on the surface of a speleothem (Dreybrodt et al., 2016; Dreybrodt and Romanov, 2016; Hansen et al., 2017) have been

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developed. So far, all models rely on equilibrium isotope fractionation factors, simply due to the lack of suitable kinetic or disequilibrium isotope fractionation factors, which have not yet been determined for speleothems.

Isotope fractionation processes during precipitation of speleothem calcite have also been investigated in several laboratory experiments using synthetic carbonates. Early experiments were conducted by Emrich et al. (1970), who performed bulk experiments investigating carbon isotope fractionation during precipitation of CaCO3 at different temperatures. Subsequently, Fantidis and Ehhalt (1970) observed increasing stable isotope values along an individual growth layer of a stalagmite and conducted calcite precipitation experiments under laboratory atmosphere in glass tubes, which confirmed the isotopic enrichment observed in the stalagmite. In recent years, several studies aiming to simulate isotope fractionation during precipitation of speleothem calcite were 5

ACCEPTED MANUSCRIPT performed under better controlled conditions. Wiedner et al. (2008) and Polag et al. (2010) carried out experiments in a refrigerator and precipitated calcite in a pure N2 atmosphere by mixing a NaHCO3 and a CaCl2 solution in a glass tube and using a glass fiber stripe as a crystallization substrate. Both studies observed increasing 13C and 18O values with increasing distance of flow of the solution and thus confirmed the theoretical predictions of Hendy (1971). Using a different setup, Day and Henderson (2011) observed a similar result for 18O values using a CaCO3-CO2-H2O solution dripping onto seeded glass plates under an atmosphere containing CO2. All these setups have specific

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advantages and disadvantages. However, they all have in common that they only investigated the spatial and temporal evolution of the isotope composition of the precipitated calcite. None of them investigated the temporal evolution of the 13C and 18O values of the DIC, pH and the Ca2+

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concentration of the solution during the course of the experiments. Thus, determination of the

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fractionation factors between DIC and CaCO3 as a function of the experimental conditions, as would be required for the models described above, has not been achieved so far. Here we present results of novel laboratory experiments simulating all potential processes

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affecting the 13C and 18O values during precipitation of CaCO3 from a flowing thin layer of solution as on the surface of a speleothem. We quantify the temporal evolution of the 13C values of both the

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DIC and the precipitated CaCO3 as well as pH and the precipitation rate of calcite. This enables us for the first time to study isotope fractionation between different species in the carbonate system (i.e.,

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2. Theoretical background

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HCO3-, CO2, CaCO3) and to investigate their dependence on precipitation rate.

2.1 Chemical evolution of a calcite precipitating solution Meteoric precipitation seeps through the soil, where pCO2 may reach values of up to a few volume

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percent (ca. 10 %, Fairchild and Baker, 2012). This leads to formation of carbonic acid, resulting in

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relatively low pH values of the solution (1): 𝐶𝑂2 (𝑔) + 𝐻2 𝑂 ⇔ 𝐻2 𝑂 + 𝐶𝑂2 (𝑎𝑞) ⇔ 𝐻2 𝐶𝑂3.

(1)

Note that the total DIC at low pH values is mainly represented by CO 2(aq), whereas the proportion of carbonic acid is about 600 times smaller (e.g., Appelo and Postma, 2004). When the solution comes into contact with the carbonate host rock, CaCO 3 is dissolved. The overall reaction is: CO2 + H2O + CaCO3  Ca2+ + 2 HCO3-.

(2)

Thus, dissolution of each molecule of CaCO3 consumes one molecule of CO2. This reaction is reversible, depending on the availability of CO2 and, thus, on the pH of the solution. The distribution of the different species of DIC is also controlled by the pCO2 and thus the pH of the solution. In detail, these reactions are considerably more complex, because they involve a series of slow and fast 6

ACCEPTED MANUSCRIPT reactions, controlled by diffusion and/or different reaction constants (Dreybrodt, 1988; Dreybrodt et al., 1997; Zeebe, 2001). Subsequently, the solution enters the cave system, where the pCO2 is generally several orders of magnitude lower than in the soil and epikarst zone. The water dripping onto the top of a stalagmite forms a thin layer of solution, usually about 0.1 mm in thickness, from which the dissolved CO2 degasses in the range of a few seconds (Hansen et al., 2013; Hansen et al., 2017). This is followed by an increase in pH from ca. 6.5 to ca. 8. As a consequence, the portion of CO32- increases (although HCO3-

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is still the dominant species of DIC, about 95 %), the solution reaches supersaturation with respect to calcite, and eventually calcite is precipitated (e.g., Dreybrodt et al., 1997). When the solution flows

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down the stalagmite, CaCO3 progressively precipitates resulting in incremental growth of the stalagmite (e.g., Mühlinghaus et al., 2007; Romanov et al., 2008a). The precipitation rate, F

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[mmol/(cm2 s)], of calcite has, for instance, been determined by Plummer et al. (1978): F = k1 * [H+]s + k2 *[H2CO3]s + k3 – k4 * [Ca2+]s * [HCO3-],

(3)

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where the brackets denote the concentration of the individual aqueous components at the calcite surface, k1, k2, k3 are temperature-dependent rate constants for dissolution, and k4 is the rate constant for precipitation of CaCO3, which also depends on the pCO2 of the solution. If the system is

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supersaturated with respect to calcite, the precipitation term is dominant. If F = 0 (mmol/(cm2 s), the system is in chemical equilibrium. The CO2 molecules produced according to Eq. (2) are almost instantaneously released to the atmosphere by molecular diffusion. However, this step also involves

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the relatively slow conversion of H2CO3 into H2O and CO2(aq), and the precipitation rate is, thus, also

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limited by the rate of conversion of HCO3- into CO2. By combining all three processes, Buhmann and Dreybrodt (1985) and Dreybrodt et al. (Dreybrodt et al., 1997) derived the precipitation rate of CaCO3 from a thin film as on the surface of a speleothem: (4)

 = (0.52 + 0.04*T + 0.004*T2) * 10-5 [cm/s],

(5)

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F =  * ([Ca2+] - [Ca2+]eq) [mol/cm2 s]

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where  is a rate constant, T the temperature in °C, [Ca2+] is the Ca2+ concentration at time t, and [Ca2+]eq is the equilibrium concentration, which depends on cave pCO2. For the typical film thicknesses observed on stalagmites,  only depends on temperature (Baker et al., 1998; Romanov et al., 2008a). Consequently, supersaturation with respect to calcite decreases exponentially during precipitation of calcite with a characteristic decay time, pr (Dreybrodt, 1988), and the temporal evolution of the concentration of [Ca2+] is given by (Buhmann and Dreybrodt, 1985): [𝐶𝑎2+ ](𝑡) = ([𝐶𝑎2+ ]0 − [𝐶𝑎2+ ]𝑒𝑞 ) (exp (−𝑡⁄𝜏𝑝𝑟 ) ) + [𝐶𝑎2+ ]𝑒𝑞 𝜏𝑝𝑟 = 𝑑⁄𝜅 , where [Ca2+]0 is the initial concentration, and d is the thickness of the film. 7

(6) (7)

ACCEPTED MANUSCRIPT 2.2 Basic stable isotope geochemistry for understanding speleothemstable isotope values Isotope effects are commonly expressed by the isotope fractionation factor, . Since isotope effects are small, the fractionation, (usually denoted in the ‰-notation), is defined as the deviation of  from 1: 𝜀𝐵/𝐴 = (𝛼𝐵/𝐴 − 1) ∗ 1000 =

𝑅𝐵 𝑅𝐴

−1,

(8),

where RA and RB are the isotope ratios of two compounds (e.g., H2O and CaCO3), and  denotes the enrichment (or depletion) of the rare isotope during the corresponding process or reaction (for

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details, see e.g., Mook and De Vries, 2000). Three basic types of isotope fractionation are distinguished: equilibrium, non-equilibrium and kinetic isotope fractionation. A non-equilibrium process can be

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described by a “flux” of isotopes from reservoir A to reservoir B, whereas the forward flux has a different value than the backward flux. The term kinetic isotope fractionation has often been used in

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the speleothem literature for isotope values, which cannot be explained by equilibrium fractionation factors. In a natural environment, however, most processes can neither be described by a complete

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equilibrium nor by a strictly one-directional kinetic fractionation process, but rather are nonequilibrium fractionation processes (Mook and De Vries, 2000). Here we use the term kinetic fractionation according to its original definition (Mook and De Vries, 2000, S. 36) and refer to

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disequilibrium isotope fractionation to describe a deviation from the values expected under conditions of equilibrium.

The most commonly used values for

13CaCO3/HCO3-

and

13CO2(aq)/HCO3-

were determined in

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laboratory experiments by precipitating synthetic CaCO3, BaCO3 or SrCO3 from a bulk solution and

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measuring all species in the system (DIC, CaCO3 and CO2(g)) as a function of temperature and/or precipitation rate (e.g., Emrich et al., 1970; McCrea, 1950; Mook et al., 1974; Romanek et al., 1992; Vogel et al., 1970). In addition, several oxygen isotope fractionation factors for

18calcite-water

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available, which were mostly determined in laboratory experiments by precipitating calcite from a

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bulk solution under controlled conditions and simultaneously measuring the 18O values of the precipitated calcite and the water. Performing these kinds of experiments for a range of temperatures

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allowed to estimate the temperature dependence of the equilibrium fractionation (e.g., Friedman and O'Neil, 1977; Kim and O'Neil, 1997; McCrea, 1950; O'Neil et al., 1969). The most widely applied fractionation factor for calcite, also in the speleothem community, is the one determined by Kim and O’Neil (1997). However, other studies recently showed that these fractionation factors might not be valid for all natural settings and may depend on additional parameters, such as precipitation rate (Dietzel et al., 2009; Gabitov et al., 2012; Watkins et al., 2014), reaction kinetics (Watkins et al., 2013) and pH (Watkins et al., 2014; Zeebe et al., 1999). Tremaine et al. (2011) compared calcite farmed in situ in caves with drip water 18O values and found a higher calcite-water than the equilibrium value of Kim and O’Neil (1997). Even larger values for calcite-water were reported by Coplen (2007) based on measurements of very slowly precipitating subaqueous calcite from Devils Hole, Nevada. Fractionation factors between dissolved HCO3- and water, 18HCO3-H2O, as well as dissolved CO2 and water, 18CO2-H2O, 8

ACCEPTED MANUSCRIPT were provided by Beck et al. (2005). However, for the interpretation of speleothem stable isotope data, all these fractionation factors may not be suitable, because the physical and chemical processes in the thin solution film are considerably different than in a large bulk solution. For larger volumes of solution, diffusion is the rate-limiting step of the chemical reactions. In contrast, in thin films diffusion is very fast (e.g., Hansen et al., 2013) and thus not rate-limiting.

2.3 Modeling stable isotope fractionation in speleothems

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The 18O and 13C values of speleothem calcite primarily depend on isotope fractionation during precipitation of CaCO3. Additionally, isotope exchange between the water of the solution, the DIC and

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the CO2 of the cave atmosphere may have an impact on the isotope signature of a speleothem. In past

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decades, several modelling studies were published aiming to quantitatively describe isotope fractionation during precipitation of speleothem calcite. On the one hand, a Rayleigh model, which has often been used to describe precipitation of CaCO3 from aqueous solution and the corresponding

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temporal evolution of the stable isotopes model (e.g., Bar-Matthews et al., 1996; Mickler et al., 2004; Mook and De Vries, 2000; Romanov et al., 2008b; Salomons and Mook, 1986; Scholz et al., 2009), was

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proposed. On the other hand, Dreybrodt (2008) proposed a ‘kinetic’ model. The two models are similar for high supersaturation, but predict a different evolution close to chemical equilibrium. For further details on these models, the reader is referred to Dreybrodt (2008), Scholz et al. (2009) and Dreybrodt and Scholz (2011). In this study, we apply the Rayleigh approach of Scholz et al. (2009) to describe our

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experimental results.

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During precipitation of speleothem calcite, carbon and oxygen isotopes are incorporated into the CaCO3 on the speleothem surface as well as released to the atmosphere via conversion to CO 2 (Eq. (2)). Thus, the DIC reservoir progressively loses C and O atoms. This process is accompanied by

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isotope fractionation, which is the classical case of a Rayleigh fractionation process (progressive removal of a substance from a reservoir accompanied by isotope fraction), which is widely applied in isotope geochemistry (e.g., Mook and De Vries, 2000). Thus, when calcite precipitates with a

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characteristic time constant, pr, from a DIC reservoir (Eq. (6)), this results in a progressive change in the -value of the DIC. Note that isotope fractionation may be different for the different sinks, which is described by the corresponding fractionation factors, . For precipitation of CaCO3, the total carbon isotope fractionation,

13tot,

is a combination of ½ 13CaCO3/HCO3- + ½ 13CO2(g)/HCO3- (e.g., Mickler et al.,

2004; Scholz et al., 2009). In the case of oxygen isotope fractionation, mass balance requires that 1/6 of the oxygen atoms of the DIC are incorporated into H2O, 2/6 into CO2 and 3/6 into CaCO3. The total fractionation,

18tot,

is thus given by the weighted mean of the individual fractionations:

1/6 18H2O/HCO3- + 2/6 18CO2/HCO3- + 3/6 18CaCO3/HCO3- (e.g., Mickler et al., 2006; Scholz et al., 2009). Scholz et al. (2009) derived the temporal evolution of the -value of the DIC in the thin film on the surface of a speleothem using a Rayleigh distillation approach: 9

ACCEPTED MANUSCRIPT 𝛿(𝑡)+1000 𝛿0 +1000

[𝐶𝑎2+ ](𝑡) 𝜀𝑡𝑜𝑡

= ( [𝐶𝑎2+ ] ) 0

−𝑡

= (𝑒𝑥𝑝 𝜏

𝑝𝑟

[𝐶𝑎2+ ]𝑒𝑞

−𝑡

+ ( [𝐶𝑎2+ ] ) ∗ (1 − exp 𝜏 0

𝑝𝑟

𝜀𝑡𝑜𝑡

))

,

(9)

where (t) and 0 denote the corresponding -values at time t and the initial -value, and [Ca2+](t) and [Ca2+]0 are the concentration of Ca2+ in solution at time t and the initial [Ca2+] concentration. For a more detailed deviation, we refer the reader to the original publication (Scholz et al., 2009).

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3. Experimental methods 3.1 Basic concept of the experiments

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Here we present experiments performed under fully controlled, cave-analogue conditions aiming to improve the understanding of the basic processes affecting the fractionation of stable isotopes during

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precipitation of speleothem calcite. The basic idea of our experiments is to simulate all natural processes, which potentially influence the stable isotope values of speleothems in the laboratory as

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close to a natural cave system as possible. For this purpose, we developed a “climate box”, in which our experiments are conducted and which allows to control all experimental parameters, such as relative humidity, temperature, pCO2 and the 13C and 18O values of gaseous CO2. Rubber gloves allow to

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perform the experiments without opening the box and contaminating the atmosphere (Dreybrodt et al., 2016). This setup enables us, for the first time, to determine the fractionation factors between all

DIC species in the system.

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Prior to each experiment, the box was equipped with the experimental material and then

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sealed for at least three days to establish the experimental temperature and a high relative humidity by bubbling the box atmosphere through two water columns. Note that we used the same water for preparation of all solutions and for establishment of the humidity in the system. To control the pCO 2

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inside the box, the air of the box was flushed with nitrogen for about 15 h using a gas washer. After a minimum pCO2 value of ca. 40 ppmV had been reached, a defined amount of CO2, previously

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isotopically equilibrated with the water used for the experiments, was injected into the system. During the experiments, CaCO3-CO2-H2O solutions of different initial concentrations flew down an inclined marble or borosilicate glass plate. We used solution films of about 0.1 mm in thickness (using the method described in detail byHansen et al., 2013). The Ca2+ concentrations of the solutions were 2, 3 and 5 mmol/L. 5 L of solution were prepared for each experiment. The experiments were conducted at three temperatures (10, 20 and 30 °C) and two different pCO2 values (1000 and 3000 ppmV). During the experiments, we measured the temporal evolution of the 13C and 18O values of DIC, the precipitated CaCO3 and the CO2 of the atmosphere. In addition, the temporal evolution of the pH and the electrical conductivity of the solution were measured. This enables the determination of isotope fractionation between the precipitated calcite and the DIC as well as of the precipitation rate at any time during the experiment.

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ACCEPTED MANUSCRIPT The ambient conditions inside the box were continuously logged during the experiments. Five Hobo® and Tinytag® temperature probes were used to measure the temperature on the surface of the plates and of the atmosphere in the box. The average precision was ± 0.15 °C. Relative humidity was measured using a Tinytag® humidity probe. Another important experimental parameter is the stability of the pCO2 of the box atmosphere during, which was logged using a Vaisala® MI70 instrument with a GMP 222 probe (average precision ± 27 ppmV). During the experiments, gaseous CO2 was released into the box due to degassing of dissolved CO2 during chemical equilibration and precipitation of

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CaCO3. In a cave, this effect is negligible, because the pCO2 of the cave atmosphere can be regarded as constant between two subsequent drops. Since the volume of the climate box is finite, we continuously monitored the pCO2. When the pCO2 value increased significantly (up to +100 ppmV), the system was

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shortly flushed with N2 to stabilise the pCO2. In addition, the box atmosphere was sampled at regular

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intervals in order to monitor the stability of the 13C value of the atmosphere. This was done by opening, slewing and closing glass vials, which were pre-flushed with Ar. The experiments are divided into two parts, one to study the dissolved inorganic carbon (DIC)

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and another one for the CaCO3.

3.2 Preparation of solutions

For each experiment, we prepared a CaCO3-CO2-H2O solution by dissolving Merck® high-grade CaCO3

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powder (13C ≈ -6 ‰, 18O ≈ -18 ‰) in 5 L of pure MQ water by bubbling CO2 (13C ≈ -45 ‰, 18O ≈ -

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27 ‰) through the water column. When the solution was clear without any visible particles of CaCO3, the pH was ca. 5. This solution is undersaturated with respect to calcite, and about 80 % of the DIC are represented by dissolved CO2. For a typical cave drip water, which remained sufficiently long in the aquifer above the cave to establish chemical equilibrium with the carbonate host rock, the saturation

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index (SI) is expected to be close to 0 (e.g., Dreybrodt and Scholz, 2011). Here and throughout the text, we use the definition for SI implemented in PHREEQC (Parkhurst and Apello, 1999), which is

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SI = log (IAP/K), where IAP is the ion activity product and K is the solubility product (here of calcite) at the experimental temperature. Hence, we subsequently adjusted the solution to a saturation index of ca. 0 by sparging the solution off CO2 with Ar and measuring pH and electrical conductivity. The corresponding pH value and the mass balance were calculated for each experiment using PHREEQC. For example, for a 5 mmol/L CaCO3 solution at 20 °C, SI ≈ 0 is reached at a pH value of ca. 6.5, with 40 % of the DIC constituted by dissolved CO2. After the saturation index for the corresponding experimental temperature had been adjusted, the solutions were stored inside the box at the experimental temperature for 4 days in order to establish carbon and oxygen isotope equilibrium between all dissolved carbon species. For the precipitation of the DIC, 1.5 mol/L SrCl2 and 1 mol/L NaOH solutions were freshly prepared on the same day for every experiment. 0.4 g of NaOH pallets were added to 10 ml of MQ11

ACCEPTED MANUSCRIPT water, and 8 g of SrCl2 were dissolved in 20 ml MQ-water. Note that we used the same water for all solutions within one experimental run. Prior to the preparation of all solutions, the MQ-water was sparged off dissolved (laboratory) CO2 using Ar for several minutes in order to avoid any (isotopic) contamination. Subsequent to preparation the solutions were stored in Parafilm® sealed beakers and only opened for the precipitation step (see also section 3.3).

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3.3 Experimental setup for the DIC experiments In the first part of the experiments, the temporal evolution of the DIC was investigated. The previously equilibrated CaCO3-CO2-H2O solution was pumped via a peristaltic pump from the reservoir onto a

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small upper marble plate (the “equilibration plate”, Fig. 1), where the solution then flew down as a thin (ca. 0.1 mm) film. On this plate, the dissolved CO2 degasses in the range of a few seconds, the pH rises

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to values of about 8, and the solution reaches supersaturation with respect to calcite (Hansen et al., 2013). The distance of flow required for chemical equilibration of the solution with the pCO 2 of the box

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atmosphere was individually evaluated for each experimental run by measuring the pH and electrical conductivity at the end of the plate. The corresponding “equilibration distance” was then determined by comparing the values with those expected for chemical equilibrium with the box atmosphere as

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calculated using PHREEQC. The drip interval (ca. 4.6 s, corresponding to a drip rate of 13 drips per

min) and drip volume (0.05 ml) were identical for all experiments. Note, that a low drip height of

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ca. 1 cm was used in order to avoid splashing (Hansen et al., 2017).

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The solution then dripped onto a lower, larger marble plate, where a thin, laminar solution film was established and calcite progressively precipitated onto the plate (Fig. 1). In order to mimic the carbonate surface of a stalagmite, a Carrara marble plate was used. Prior to all experiments, the film thickness and flow velocity were determined by measuring the maximum flow speed and the supply

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rate at the end of the plate as described by Hansen et al. (2013). This allows to calculate the residence time of the film on the plate. A sketch of the experimental setup inside the climate box is shown in

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Fig. 1.

During the experiments, the distance of flow on the lower plate was adjusted by shifting the equilibration plate relative to the lower plate (Fig. 1). At the end of the lower plate, the solution dripped into an airlock, where it was collected in a test tube (ca. 5 ml). This allowed to study the solution after different distances of flow and, thus, residence times on the plate. The collection of the sample took about 8 minutes. Note that this is substantially faster than the timescales of carbon and oxygen isotope exchange between the DIC, atmospheric CO2 (the time constants for thin films at our experimental conditions range from 2,000 to 13,000 s , Dreybrodt et al., 2016; Hansen et al., 2017) and water (ca. 1000 min, Beck et al., 2005). For every distance of flow, two samples were taken. The first sample was used to determine pH and electrical conductivity, which enabled us to monitor the temporal evolution of carbonate chemistry of the film and to determine the time constants and precipitation rate of CaCO3. The second sample was taken out of the air lock after collection and then 12

ACCEPTED MANUSCRIPT immediately precipitated as SrCO3 for stable isotope analyses by adding 0.5 ml of SrCl2 and 0.6 ml of NaOH in a 50 ml Luer-Lock® syringe. The syringe was flushed with Ar prior to sampling and then filled with SrCl2 and NaOH in order to minimize any contamination by the laboratory atmosphere. Thereby, the pH of the sample was instantaneously (i.e., in the range of a few seconds) shifted to high values (pH ≈ 12), and as a consequence, the DIC was completely precipitated as SrCO3. This solution was then filtered (Merck Millipore polycarbonate filter, pore size 0.2 m). Subsequently, the sample was rinsed with methanol by connecting a methanol-filled syringe in order to neutralize the pH of the precipitate.

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Note that the syringe contained no laboratory air in order to avoid any contamination of the sample. Subsequent to neutralization, the filter was transferred from the filter holder into a desiccator, which was subsequently evacuated to avoid contamination by the laboratory atmosphere (for details and the

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precision on the DIC precipitation method, see Beck et al., 2005; Dreybrodt et al., 2016). This method

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allows to “freeze” the -value of the DIC for the corresponding distance of flow and to determine its

3.4 Experimental setup for the CaCO3 experiments

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stable isotope values.

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In the second part of the experiments, the temporal evolution of the 13C and 18O values of the precipitated CaCO3 was investigated. The previously described setup was slightly modified by replacing the two marble plates by a single sand-blasted borosilicate glass plate (Fig. 2). Afterwards, the box was sealed again, and the system was flushed with N2 with subsequent adjustment of the pCO2

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as described above. Then the remaining solution (≈ 4 L) was pumped onto the glass plate. The same

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film thickness as in the DIC experiments (≈ 0.1 mm) was established. The distance of flow was increased by the equilibration distance, as previously determined on the equilibration plate for the corresponding DIC experiment to allow degassing of excess CO2 and adjustment of the pH to the pCO2

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of the box atmosphere. During the experiments, CaCO3 was progressively precipitated onto the glass plate along the flow path. The duration of such an experiment was about four days. Subsequent to the CaCO3 experiment, the distance of flow on the glass plate was adjusted according to the DIC

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experiments, and, as in the latter, samples of solution were collected and electrical conductivity measured. This allowed to test whether the precipitation rates of the DIC and the CaCO3 experiment were similar. Finally, the experiment was stopped, and the plate was allowed to dry inside the box. Subsequently, the plate was removed from the system, and CaCO3 samples were scratched off using a spatula at the same distances of flow as for the DIC experiments for stable isotope analysis.

3.4 Stable isotope analysis Stable isotope analyses of the sampled CO2 of the box atmosphere and the water samples were conducted at the University of Innsbruck. 12 ml Labco Exetainer glass vials containing CO2 from the experiments were sent to the laboratory immediately after completion of an experiment to ensure no 13

ACCEPTED MANUSCRIPT leakage of the septa (see Spötl, 2004). 13CCO2 and 18OCO2 values were measured using a DeltaplusXL mass spectrometer and calibrated against calcite standards. Long-term precision was ±0.15 ‰.

Oxygen isotope values of water samples were partly measured on a Picarro L2140-i and partly on a Los Gatos LWIA-24d device. Calibration of both devices was accomplished using standard reference water samples (analytical precision 0.10 ‰), and the results are reported versus the VSMOW scale. Stable isotope analysis of the SrCO3 and CaCO3 samples was performed at the Institute of Geosciences, University of Mainz, using a Thermo Finnigan MAT 253 continuous flow-isotope ratio

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mass spectrometer coupled to a GasBench II. Carbonate powders were reacted for 120 minutes in water-free phosphoric acid in helium-flushed borosilicate exetainers at 72 °C. Isotope data were

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calibrated against an NBS-19 calibrated Carrara marble standard distributed by IVA Analysentechnik e.K. (Düsseldorf, Germany) (13C = +2.01 ‰; 18O = −1.91 ‰). The long-term accuracy (1σ), based

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on 421 blind measurements of NBS-19, was ±0.04 ‰ and ±0.03 ‰ for 18O and 13C values, respectively. The isotope values are reported relative to the Vienna Pee Dee Belemnite scale

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(McKinney et al., 1950).

In the present study, we decided to rely on a single-point calibration, because calibration

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against two reference materials would not have significantly improved the data quality. Previous blind measurements of NBS-18 (n = 171) using the same 1-point calibration as reported above, resulted in 18O and 13C values of −23.14 ±0.09 ‰ and −4.98 ±0.05 ‰, respectively. These data are very close to the published values of NBS-18 (18O = −23.20 ±0.10 ‰; 13C = −5.014 ±0.035 ‰). Using these

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data to interpolate the 1 σ error for the lowest isotope values of carbonates determined in the present

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study (18O = −12.61 ‰; 13C = −36.48 ‰) gives ±0.04 ‰ for 18O and ±0.17 ‰ for 18O, which are both smaller than the 1 σ errors of the measured isotope values of SrCO3 (18O = ±0.12 ‰, 13C = ±0.22 ‰) given by Dreybrodt et al. (2016). Furthermore, as discussed in section 5.2.1, measured

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4. Results

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isotope values of the present study were in good agreement with predicted values.

4.1 DIC experiments

4.1.1 Degassing of CO2, chemical equilibration and establishment of supersaturation The chemical processes occurring during degassing of CO2 from a thin film of water – comparable to those occurring in cave environments – were experimentally studied and discussed by Hansen et al. (2013). In addition to measurements of pH and electrical conductivity, we sampled the reservoir as well as the solution film at the start and the end of the equilibration plate (Fig. 1) and precipitated the DIC as SrCO3 for stable isotope analysis. The equilibration distance for an experiment with a 5 mmol/L CaCO3 solution at 20 °C and 1000 ppmV CO2 was 8 cm, which corresponds to a residence time of 34 s. The pH was 6.6 for the reservoir and 6.7 at the start of the equilibration plate. During the 34 s on the 14

ACCEPTED MANUSCRIPT equilibration plate, the pH increased to 8.0, and the conductivity decreased from 883 to 790 µS/cm (Fig. 3) documenting the loss of CO2 from the solution (Hansen et al., 2013). Degassing of CO2 and chemical equilibration is also apparent from the 13C and 18O values of the DIC. The DIC of the reservoir had a 13C value of 37.6 ‰, and the 13C value at the beginning of the equilibration plate was -37.1 ‰. At the end of the equilibration plate, the 13C value of the DIC was 33.7 ‰ (Fig. 3a). This clearly demonstrates (fast) degassing of CO2. At pH 6.6, about 40 % of the DIC is provided by dissolved CO2, resulting in more negative 13C values of the DIC. After degassing, at a pH of 8.0, about > 98 % of

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the DIC are provided by HCO3-, and the 13C value increased by about 3.4 ‰. The corresponding

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increase of the 18O values on the equilibration plate was +4.8 ‰ (Fig. 3b).

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4.1.2 Temporal evolution of Ca2+ concentration and precipitation rate

The electrical conductivity of the solution is proportional to the Ca2+ concentration, and the corresponding Ca2+ concentration can be calculated using PHREEQC (for details, see Hansen et al.,

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2013). Thus, the temporal evolution of electrical conductivity reflects the evolution of the Ca 2+ concentration in solution. Fig. 4 shows the temporal evolution of electrical conductivity against

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residence time on the lower marble plate for three experiments conducted with a 5 mmol/L CaCO3 solution at 10, 20 and 30°C and a pCO2 of 1000 (Fig. 4 a) and 3000 ppmV (Fig. 4 b), respectively. All experiments show decreasing conductivity with increasing residence time on the plates, documenting

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progressive precipitation of CaCO3. As expected from theoretical predictions (Baker et al., 1998), the

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highest precipitation rate was observed at the highest temperature. Since electrical conductivity is representative of the concentration of Ca2+, the time constant for precipitation of calcite, pr, can be obtained by fitting the conductivity data according to Eq. (6). The time constants for all experiments are compiled in Table 1. Due to the lower precipitation rates at low

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temperatures, chemical equilibrium was not established for the 10 °C experiments. Thus, the data only show the linear part of the exponential function, which results in larger errors of the fit (Fig. 4). For

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the experiments conducted using a 2 mmol/L CaCO3 solution at 10 and 20 °C, the amount of calcite precipitated on the plates was not large enough to determine the 13C and 18O values.

Electrical conductivity was converted into [Ca2+] concentrations using PHREEQC (Parkhurst and Apello, 1999). The change in [Ca2+] concentration can be calculated by differentiating Eq. (6): 𝑑[𝐶𝑎2+ ](𝑡) 𝑑𝑡

1

−𝑡

= − 𝜏 ∗ ([𝐶𝑎2+ ]0 − [𝐶𝑎2+ ]𝑒𝑞 ) ∗ 𝑒𝑥𝑝 𝜏 𝑝𝑟

𝑝𝑟

,

(10)

where t is the residence time on the plate, [Ca2+]0 and [Ca2+]eq are the initial and equilibrium concentrations of [Ca2+] in solution, and pr is the time constant for precipitation. By multiplying with the corresponding film thickness, d, the flux of Ca2+ into the solid, F [mol/(cm2*s)] (Eq. (4)), can be determined. All experimentally observed values (see supplemental Table S 1) are in good agreement 15

ACCEPTED MANUSCRIPT with the theoretically expected values calculated using the approach of Buhmann et al. (1985) and Dreybrodt et al. (1997). 4.1.3 Temporal evolution of 13CDIC The 13C values of the DIC show a progressive increase with increasing residence time along the marble plate. As an example, Fig. 5 shows the evolution of the 13C values for the experiments conducted using a 5 mmol/L CaCO3 solution at 1000 (Fig. 5a) and 3000 ppmV CO2 (Fig. 5b). The enrichment of the experiments conducted at a pCO2 of 1000 ppmV ranges from + 3.6 at 10 °C to + 8.7 ‰ at 30 °C

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(Fig. 5a). Experiments conducted at a higher pCO2 of 3000 ppmV show a lower enrichment ranging from + 2.4 at 10 °C to + 5.9 ‰ at 20 °C. In general, the enrichment increases with increasing

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temperature. The 13C values of the experiment conducted at 30 °C and a pCO2 of 3000 ppmV (blue symbols in Fig. 5b) show a progressive increase until a residence time of approximately 400 s.

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Subsequently, the 13C values reach a plateau and then decrease again.

The results of the experiments conducted using solutions of 2 and 3 mmol/L CaCO3 show a

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similar evolution. From the experiments conducted using a 2 mmol/L CaCO3 solution, only the 30 °C experiment yielded enough CaCO3 to determine the 13C values. The corresponding enrichment is

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+ 2.1 ‰. The experiment conducted using a 3 mmol/L CaCO3-solution at 20 °C shows an enrichment of + 5.4 ‰. The 13CDIC values of all experiments are compiled in supplemental Table S1.

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4.1.4 Temporal evolution of the 18O values of the DIC

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Fig. 6 shows the temporal evolution of 18O values of DIC for the experiments conducted with a 5 mmol/L CaCO3 solution at 10, 20 and 30 °C in a 1000 (Fig. 6a) and a 3000 ppmV CO2 (Fig. 6b) atmosphere. The observed enrichment in the experiments conducted at a pCO 2 of 1000 ppmV ranges

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from +0.4 ‰ at 10 °C to +2 ‰ at 20 °C (Fig. 6a). For the experiments conducted at a higher pCO2 of 3000 ppmV, the total enrichment is lower (ca. 1 ‰, Fig 6b). The enrichment in the 18O values is much

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lower than observed for the 13C values (Fig. 5). For both 1000 and 3000 ppmV, the experiments conducted at 30 °C (blue symbols in Fig. 6) show a progressive increase in 18ODIC values until a maximum is reached. Subsequently, the values decrease again. This phenomenon is more pronounced for higher pCO2 (Fig. 6). The initial 18ODIC values (i.e., at the beginning of the lower plate, Fig. 1) show a clear difference with experimental temperature, with lower 18ODIC values at higher temperature. The results of the experiments conducted with 2 and 3 mmol/L CaCO3 show a similar evolution. However, for the experiments conducted with 2 mmol/L CaCO3, only the experiment conducted at 30 °C provided enough CaCO3 along the flow path to determine electrical conductivity and stable isotope values. For the experiment conducted with 3 mmol/L CaCO3 at 20 °C and 1000 ppmV CO2, the observed enrichment is +0.9 ‰. All 18ODIC values and the corresponding residence times are provided in supplementary Table S1. 16

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4.1.4 Temporal evolution of 18Owater during the DIC experiments The 18O values of the water in the reservoir, at the entry and exit of the equilibration plate as well as after different residence times on the lower marble plate, were measured regularly during the experiments. The observed enrichment of the 18Owater values is generally low (+0.7 ‰) with a maximum value of +0.9 ‰. Thus, evaporation should have a negligible effect, even if it cannot be completely excluded. All 18O values of the water for the DIC experiments are compiled in

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supplementary Table S1.

4.2 CaCO3 experiments

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4.2.1 Mineralogy of the precipitated CaCO3

We studied the CaCO3 from all experiments using micro-Raman spectroscopy. The samples were taken

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at the same distances as the samples for stable isotope analysis. Almost all precipitates consist of calcite. Only for the experiments conducted at high precipitation rates (5 mmol/L CaCO3 at 30°C), a

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few aragonite crystals surrounded by calcite crystals were observed. The corresponding sections were avoided for stable isotope analysis. Thus, we consider our results as representative of speleothem calcite.

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Fig. 7 shows optical microscopy images of four different experiments. The precipitates from all

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experiments show the typical rhombohedral habitus of calcite crystals, which confirms that the main fraction of the precipitated CaCO3 consists of calcite. The size of the crystals is inversely related to precipitation rate. The smallest crystals are observed for the experiment with the highest precipitation concentrations.

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rate (30 °C, 5 mmol/L, Fig. 7a), and the crystal size increases at lower temperatures and lower

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4.2.2 Temporal evolution of the 13C values of the CaCO3 The 13C values of the CaCO3 precipitated on the glass plates show a similar trend as the 13C values of DIC. All experiments show a progressive increase in 13C values with increasing residence time due to progressive precipitation of CaCO3, conversion of HCO3- into CO2 and subsequent degassing. As an example, Fig. 8 shows the corresponding data for the experiments conducted using a 5 mmol/L CaCO3 solution at 10, 20 and 30 °C with a pCO2 of 1000 and 3000 ppmV, respectively. The enrichment for the 1000 ppmV experiments ranges from +5.8 ‰ at 10 °C to +9.7 ‰ at 30 °C (Fig. 8 a). As observed in the DIC experiments, the enrichment is lower for the higher pCO 2 of 3000 ppmV. The corresponding values range from +4.0 ‰ at 10 °C to +7.1 ‰ at 20 °C (Fig. 8 b). As for the DIC experiments, the overall enrichment increases with increasing temperature (Fig. 8). In general, the enrichment observed in the CaCO3 experiments is up to +2 ‰ larger than in the DIC experiments. The experiments 17

ACCEPTED MANUSCRIPT performed at a pCO2 of 3000 ppmV and 30 °C show a progressive increase in the 13C values until a residence time of ca. 300 s. Subsequently, the 13C values reach a plateau followed by a decreasing trend (Fig. 8b). A similar evolution was observed for the corresponding DIC experiment (Fig. 5b). The initial 13C values (i.e., the 13C values at the beginning of the glass plate) are larger for higher temperature (Fig. 8). This is particularly pronounced for the initial 13C values of the experiment conducted at 10 °C and a pCO2 of 3000 ppmV, which are substantially lower than those of the 20 and 30°C experiments (Fig. 8 b).

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The experiments performed with a concentration of 2 and 3 mmol/L CaCO3 show a similar evolution, and the enrichment ranges from +3.9 to +8 ‰. As stated above, the amount of CaCO3

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precipitated during the experiments conducted using a 2 mmol/L CaCO3 solution at 10 and 20 °C was too low to determine the stable isotope values. The enrichment in the 13C values of the CaCO3

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experiments is again slightly larger than for the corresponding DIC experiments. All 13CCaCO3 values

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are compiled in supplemental Table S1.

4.2.3 Temporal evolution of the 18O values of the CaCO3

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The temporal evolution of 18O values of the CaCO3 precipitated on the glass plates shows a similar trend as the 18O values of the DIC. 18O values increase towards more positive values with increasing residence time on the plates. Fig. 9 shows the results for experiments conducted with 5 mmol/L CaCO3

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solutions at 10, 20 and 30 °C and an ambient pCO2 of 1000 (Fig. 9a) and 3000 ppmV (Fig. 9b). For

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1000 ppmV, the total enrichment ranges from +1.4 ‰ at 10 °C to +2.8 ‰ at 30 °C (Fig. 9a). Similarly to the observations for the DIC experiments, the overall enrichment at a pCO 2 of 3000 ppmV is lower and ranges from +0.6 ‰ at 10 °C to +2.1 ‰ at 30 °C (Fig. 9 b). For both pCO2 values, the largest

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enrichment was observed for the highest temperature. In general, the observed enrichment is larger than for the DIC experiments, as observed for the corresponding 13C values (Fig 8). The experiments conducted at 30 °C, and especially the experiment conducted at 30 °C and 3000 ppmV CO2, show an

Fig. 9b).

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initial increase in 18O values and a subsequent decrease towards more negative values (blue symbols,

As observed in the DIC experiments, the initial 18O values (i.e., at the start of the plate, Fig. 2) show a clear dependence on temperature, with lower 18O values at higher temperature (Fig. 9). An exception are the experiments conducted at 1000 ppmV and 20 and 30 °C, which have similar initial values (red and blue symbols, Fig. 9a). The temporal evolution of the 18Ovalues of the experiments conducted with 2 and 3 mmol/L CaCO3 concentrations show a similar evolution, analogously to the results of the DIC experiments. The enrichment observed in these experiments is +2.6 ‰ (2 mmol/L and 30 °C) and +1.5 ‰ (3 mmol/L and 20 °C), respectively. This is again slightly larger than for the corresponding DIC experiments. As 18

ACCEPTED MANUSCRIPT mentioned above, the amount of CaCO3 precipitated within the experiments performed with a 2 mmol/L CaCO3 solution at 10 and 20 °C was too low determine the 18O values. All 18OCaCO3 values and the corresponding residence times on the glass plates are provided in supplementary Table S1.

4.2.2 Temporal evolution of the 18O values of the water during the CaCO3 experiments As for the DIC experiments, the water in the reservoir as well as at the start and end of the glass plate

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was sampled regularly during the experiments. The difference in 18OH2O values between the start and the end of the glass plate (i.e., after 100 cm distance of flow, Fig. 2) is generally low (+0.4 ‰). At the beginning of the experiments, within the first ~24 h, the enrichment in 18OH2O values ranges from

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+0.4 to +1 ‰. With increasing duration of the experiment, however with increasing duration of the

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experiments this effect decreases substantially to values ranging from +0.01 to +0.4 ‰. Thus, minor effects of evaporation on the 18O values of the water cannot be excluded. However, oxygen isotope exchange between water and the carbonate species occurs on much longer time scales (between 6000

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and 60,000 s, Beck et al., 2005) than the maximum duration of our experiments (ca. 600 s). Thus, evaporation should not have an influence on the 18O values of the DIC and the CaCO3. The 18O values

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of the water measured during the experiments are compiled in supplementary Table S1.

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5 Discussion

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5.1 Stability and physical and chemical consistency of the experiments There are two major differences between the DIC and the CaCO 3 experiments: (i) the material of the plate (marble vs. glass) and (ii) the absence of the equilibration plate in the CaCO3 experiments. The second point was accounted for by increasing the distance of flow of the CaCO3 experiments by the

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equilibration distance (time) of the corresponding DIC experiment. Concerning the first point, the comparability of the DIC and CaCO3 experiments was verified by measuring electrical conductivity at

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the end of the glass plate. During the first hours of the CaCO 3 experiment (24 h at maximum), the conductivity values at the end of the glass plate continuously decreased indicating increasing precipitation rates. This probably documents the progressive seeding of the glass plate. Subsequently, the electrical conductivity at the end of the glass plates reached the same value as at the end of the marble plates. This is in agreement with the observations of Stockmann et al. (2014), who performed CaCO3 precipitation experiments using different substrates and found that precipitation rates are independent from the substrate once nucleation has occurred. The conductivity values still slightly decreased after 24 h, but this effect was very small. In addition, the flow velocity on the glass plates was slightly faster than on the marble plates. Flow velocity is related to film thickness, which, in turn, affects the time constant for precipitation of CaCO3 (Eq. (6)). At the end of the CaCO3 experiment (i.e., after about 100 h), the precipitation times for the CaCO3 experiment were determined by adjusting the distances of flow according to the distances of the corresponding DIC experiment and measuring 19

ACCEPTED MANUSCRIPT electrical conductivity. The time constants are in good agreement within the corresponding uncertainty. For instance, for the experiment performed using a 3 mmol/L CaCO3 solution, at 20 °C and 1000 ppmV CO2, the time constants for the DIC and the CaCO3 experiment are 436 ±51 and 539 ±45 s, respectively. The slightly longer time constant for the CaCO3 experiment may still be related to the different substrates and that the glass plate is seeded during the experiment. However, we consider this effect as relatively small since the time constants are generally in good agreement within uncertainty.

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In order to keep the pCO2 stable during the experiments it was continuously monitored. During the experiments, gaseous CO2 was progressively released into the box atmosphere due to degassing

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while the solution equilibrates with the pCO2 of the box and as a consequence of precipitation of CaCO3 (Eq. 2). In a natural setting, the volume of the cave atmosphere is large, and the pCO2 can be regarded

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as stable for the time interval between two drips. In our laboratory setup, however, the box volume is finite. Thus, we shortly flushed the system with N2 when the pCO2 value significantly increased (up to +100 ppmV). The average (1) SD of pCO2 for all experiments was ±30 ppmV, which is in the range

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of the precision of the CO2 probe. In addition, the stability of the 13C and 18O values of the box atmosphere was regularly monitored during the experiments. The average (1) SD of the 18OCO2

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values was ±2.2 ‰, but in general was much lower (Table 1). During all experiments, a slight tendency towards more positive values with increasing duration was observed (Table 1). This might be due to the continuous flushing of the box atmosphere with N2 during the experiments and the corresponding

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isotope fractionation due to convectional flow of CO2 out of the box. Alternatively, the effect may be explained by continuous degassing of isotopically slightly different CO2 from the solution film.

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However, in general, this effect is small and should have no or only a very limited effect on the 18O and 13C values, in particular since the time constants for isotope exchange between gaseous CO2 and the DIC of thin solution films are orders of magnitude larger than the maximum residence time of the

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solution in our experiments (Dreybrodt et al., 2016; Hansen et al., 2017). We emphasize that oxygen isotope exchange between the gaseous CO2 of the box atmosphere and the DIC of solution film cannot

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be distinguished from oxygen isotope exchange with the water, because the CO2 used in our experiments was previously isotopically equilibrated with the water. All pCO2 and 18O and 13C values of the gaseous CO2 are compiled in Table 1. The initial 18O values for both the DIC and the CaCO3 experiment show a clear dependence on the experimental temperature with lower initial 18O values corresponding to higher temperatures (Figs. 6 and 9). This reflects the temperature dependence of oxygen isotope fractionation between water and CaCO3. For lower temperatures, oxygen isotope fractionation between calcite and water is larger than for higher temperatures. An exception are the experiments conducted at 1000 ppmV CO2 and 20 and 30 °C, which have similar initial values (Fig. 6a, red and blue symbols). This results from differences in the 18O values of the water. For the experiment conducted at 20 °C, the 18O values were

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ACCEPTED MANUSCRIPT more negative than for 10 and 30 °C (- 10 ‰ compared to – 9.3 and – 9.6 ‰ VSMOW), which compensates for the temperature effect.

5.2 Modeling the 13C and 18O values of the DIC experiments using a Rayleigh approach In the following, we fit the Rayleigh distillation model described by Scholz et al. (2009) to our experimental data. According to section 2.3.1, a calcite-precipitating solution fractionates carbon and

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oxygen isotopes into two and three different sinks, respectively (Eq. (2)): CaCO3, CO2 and H2O, according to their corresponding fractionation factors. The combination of all three factors then provides the total fractionation for the complete reaction. In the Rayleigh model, the (total)

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enrichment of the 13C and 18O values depends on the [Ca2+] fraction remaining in the solution, and

𝜎(𝑡) 𝜀𝑡𝑜𝑡

𝛿(𝑡) = (

𝜎0

)

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the temporal evolution of the -values can be written as:

∗ (𝛿0 + 1000) − 1000

(11)

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In Fig. 10, the 13C and 18O values of DIC are plotted against the remaining fraction of [Ca2+] in the solution, which is given by (t/0) since conductivity is proportional to [Ca2+]. As an example,

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we show the experiments performed with 5 mmol/L CaCO3 at 10, 20 and 30 °C and a pCO2 of 1000 (Figs. 10a and c) and 3000 ppmV (Figs. 10b and d). From a fit of the experimental data according to Eq. 11, the total fractionation, tot, can be determined. For the examples shown in Fig. 10, 18tot ranges 13tot

ranges from –7.4 ± 0.8 to 13.7 ± 0.7 ‰. The determined

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from -1.8 ± 0.3 to -3.3 ± 0.2 ‰ and

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values for 18tot and 13tot are summarized for all experiments in Table 1. By inserting Eq. (6) into Eq. (11), the temporal evolution along the plate can be derived (Eq. (9)). This equation combines the total isotope fractionation in the Rayleigh model with the precipitation rate of calcite and is identical with Eq. (7) from Scholz et al. (2009) in the delta notation.

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Note that all parameters (pr, 0, eq, 0, tot) can be obtained from our experimental data. Inserting the previously determined parameters into Eq. (9) enables to test whether the model adequately

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describes the temporal evolution of the values. Fig. 11 shows a comparison between model and data for a 5 mmol/L CaCO3 solution at 1000 (Figs. 11 a and c) and 3000 ppmV pCO2 (Figs. 11 b and d). The experimental data are in good agreement with the model clearly demonstrating the general applicability of the Rayleigh distillation model to our data. However, we emphasize that this agreement does neither validate the Rayleigh model (Scholz et al., 2009) nor reject other models (Dreybrodt, 2008) since the evolution of the -values predicted by the different models is almost identical for the time-scales of our experiments (Scholz et al., 2009). In the following, we use the Rayleigh model to compare the DIC and the CaCO3 experiments (see below), which were performed on different substrates and, thus, had slightly different flow velocities. For the interpretation of the experiments conducted at 30 °C and 3000 ppmV CO2, the last two data points were excluded from the fit, because the 18O and 13C values decrease at the end of the 21

ACCEPTED MANUSCRIPT plate (Figs. 10 b and d as well as 11 b and d). This cannot be explained by the Rayleigh approach, which predicts an increase towards an equilibrium isotope value when approaching chemical equilibrium. Including these data points into the fit would lead to a lower slope and thus biased values for tot. The trend towards more negative values for longer residence times can be caused by different processes. Firstly, it could be related to fractionation processes at the calcite surface as proposed by Dreybrodt (2008) and Dreybrodt and Romanov (2016). The return to more negative 18O and 13C values would then be related to their kinetic constant, , which has not been validated experimentally yet.

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Unfortunately, we observed this phenomenon only in two experiments (5 mmol/L, 30 °C, 3000 ppmV CO2), and the residence times in our experiments were not long enough to confirm or reject this hypothesis. Secondly, the decreasing isotope values could be related to isotope exchange between the

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DIC and the gaseous CO2 of the box atmosphere or the water reservoir. The latter has also often

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referred to as “buffering” (Mickler et al., 2006; Mühlinghaus et al., 2009; Scholz et al., 2009; Wiedner et al., 2008). Since both the DIC and the CO2 used in the experiments were previously equilibrated with the water used for the experiments, isotope exchange with the water as well as the CO2 would pull back

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the 18O values of DIC towards oxygen isotope equilibrium with the water. Due to progressive precipitation of CaCO3, the concentration of HCO3- decreases with increasing residence time on the

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plate, and isotope exchange between H2O, HCO3- and CO2 might become significant and eventually be imprinted into the isotope signature of DIC and CaCO3 (Dreybrodt et al., 2016; Dreybrodt and Romanov, 2016). Since the effect of isotope exchange is more pronounced for lower concentrations of DIC and higher pCO2, the effect should be most evident for higher temperatures and pCO2 values. Since

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the decrease in -values at the end of the plate is only visible for the experiments (both DIC and CaCO3)

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conducted at 30 °C and 3000 ppmV, we consider isotope exchange with the CO2 of the box atmosphere as the most reasonable explanation for the observed return to lower 18O and 13C values at the end of the plate (Dreybrodt et al., 2016; Hansen et al., 2017).

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To further evaluate this assumption, we calculated the time constants for carbon isotope exchange for the corresponding experiment using a diffusion-reaction model (Hansen et al., 2017).

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This model calculates the temporal evolution of pH, the concentration of all DIC species and the corresponding 13C values for a thin film of solution exposed to gaseous CO2. For the initial conditions of the experiment (5 mmol/L [Ca2+], corresponding to 10 mmol/L of [HCO3-]), the carbon isotope exchange time, ex, is 1800 s. Compared to the corresponding time constants for the precipitation of CaCO3 for this experiment (pr = 270 s) the exchange times are about 6 times larger and isotope exchange should be negligible. However, at the end of the plate (after a residence time of about 600 s), 61 % of the initial [HCO3⁻] have been lost to the carbonate surface due to precipitation of calcite, which corresponds to a [HCO3⁻] of 3.9 mmol/L. As a consequence the corresponding carbon isotope exchange time also decreases during the experiment. For the final experimental concentration, ex is 800 s. This is close to the maximum residence time on the plate (600 s). Thus, carbon isotope exchange is very

22

ACCEPTED MANUSCRIPT likely to have an influence on the 13C values of this experiment, at least for longer residence times. The effect is also visible in the data of the corresponding CaCO3 experiment (Figs. 8 and 9).

5.3 Determination of fractionation factors 5.3.1 Fractionation between DIC and H2O – determination of 18HCO3-/H2O In the next step, we calculate the isotope fractionation between DIC (which consists to ca. 98 % of

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HCO3- at the pH values of the experiments) and water based on our experiments. The fractionation is simply given by the difference of 18O values of the DIC and the water.

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Prior to the experiments, the bulk solution was stored for several days inside the climate box at the experimental temperature. Thus, it is reasonable to assume isotope equilibrium between all

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involved species. Since water is by far the largest oxygen reservoir, it is expected that all species establish isotope equilibrium with the 18O value of the water. Accounting for the fractions of the

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individual DIC species and the corresponding isotope fractionation, the 18O value of the DIC can be calculated by a mass balance, which reads (Dreybrodt et al., 2016): 2

1

𝛿18 𝑂𝐷𝐼𝐶,𝑒𝑞 = 𝑥 ∗ ( (𝛿 18 𝑂𝐻2𝑂 + 18𝜀𝐶𝑂2 /𝐻2 𝑂 ) + (𝛿 18 𝑂𝐻2 𝑂 + 18𝜀𝑂𝐻 − /𝐻2𝑂 )) + (1 − 𝑥) ∗ 3

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3

(𝛿 18 𝑂𝐻2 𝑂 + 18𝜀𝐻𝐶𝑂3− /𝐻2𝑂 ),

(12)

where x denotes the fraction of dissolved CO2, the 18i are the individual fractionation factors,

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and 18OH2O is the corresponding 18O value of the water. The distribution of the DIC species was

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determined by PHREEQC (Parkhurst and Apello, 1999). Note that if dissolved CO2 is precipitated – in our case as SrCO3 by adding NaOH and SrCl2 (see section 3) – mass balance requires an additional oxygen atom, which is then provided by one OH- molecule. Thus, 2/3 of the oxygen isotopes are

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provided by CO2 and 1/3 are provided by OH- (see e.g., Beck et al., 2005). We illustrate this for the example from section 4.1.1 (Fig. 3, 5 mmol/L CaCO3 solution, 20 °C,

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1000 ppmV CO2). The water used for the experiment had a 18OH2O of -10.2 ‰ (calibrated vs. VSMOW). On the VPDB scale, this corresponds to a 18O value of -39.5 ‰. The pH value was 6.7, corresponding to a species distribution of ca. 34 % CO2 and ca. 66 % HCO3-. Using the isotope fractionations between water and CO2, OH- and HCO3- reported by Beck et al. (2005) and Eq. (12), one obtains a 18O value of about -12.3 ‰. The experimentally measured 18ODIC value (using the SrCO3 precipitation method) is –12.6 ‰, in good agreement with the predicted value. After the equilibration plate (Fig. 1), the pH value of the solution was 8 and about 98 % of the DIC were provided by HCO3-. Using the converted 18OH2O value measured at the end of the equilibration plate of –39.4 ‰, the expected 18ODIC value is –7.2 ‰. The corresponding experimentally observed value was –7.6 ‰, which is in good agreement within the experimental uncertainties of the precipitation method (ca. ±0.5 ‰, Dreybrodt et al.,

23

ACCEPTED MANUSCRIPT 2016). This suggests that the 18O values of DIC are still almost in isotope equilibrium with the water after chemical equilibration documenting that no CaCO3 was precipitated on the equilibration plate. An exception are experiments #9 and #10 conducted with 2 mmol/L CaCO3 at 30°and 3 mmol/L CaCO3 at 20°and 1000 ppmV CO2. For these two experiments, the 18ODIC values calculated using Eq. (12) and the measured 18Owater values are significantly more positive than the measured 18ODIC values (-8.8 vs. -10.3 ‰ for experiment #9 and -8.2 vs. -9.5 ‰ for experiment #10). Due to analytical problems, the water samples (1.5 ml, no headspace) of these two experiments were stored

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for more than 1.5 years in a refrigerator at 4 °C prior to analysis. Thus, and since the other six experiments show isotope equilibrium between all species, we consider it as likely that the 18O values

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of the corresponding samples were enriched during storage due to evaporation. We estimated the amount of water required to evaporate to result in the corresponding enrichment using a Rayleigh is not unrealistic considering the long storage time.

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approach (Eq. 9). This suggests that 0.21 and 0.15 ml of water evaporated from the 1.5 ml vials, which

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Along the plate, the 18O values of the DIC increase (Fig. 6). Thus, the experimentally observed 18O values at the end of the lower marble plate (after 100 cm distance of flow) are substantially more

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positive than the 18O values expected under conditions of equilibrium. This clearly documents that oxygen isotope exchange between water and HCO3- is not fast enough to balance the enrichment in the 18O values of the HCO3- resulting from precipitation of CaCO3. This is reasonable because the residence time on the plate (about 600 s) is substantially shorter (about 98 times) than the time needed for

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establishing isotope equilibrium between DIC and H2O (Beck et al., 2005).

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In summary, the 18O value of the DIC of the bulk solution as well as at the end of the equilibration plate is in equilibrium with the 18O value of the water for the majority of our experiments. This shows that the time for establishing isotope equilibrium between all species in the

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bulk solutions was sufficiently long. In addition, degassing of CO2 and establishment of supersaturation with respect to calcite on the upper plate does not affect the 18O value of the HCO3-. However,

water.

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precipitation of CaCO3 drives the 18O value of the HCO3- out of equilibrium with the 18O value of the

5.3.2 Fractionation between CaCO3 and H2O – determination of 18CaCO3/H2O The oxygen isotope fractionation between the precipitated calcite and water can be determined in an analogue way from our experimental data. The fractionation between CaCO 3 and water is expressed by the fractionation factor, , which is given by: 18

𝛼𝐶𝑎𝐶𝑂3/𝐻2 𝑂 =

24

𝛿 18 𝑂𝐶𝑎𝐶𝑂3 +1000 𝛿 18 𝑂𝐻2 𝑂 +1000

(13)

ACCEPTED MANUSCRIPT  is often also expressed as 1000ln18(≈18). As an example, we apply this to the experiment conducted with a 5 mmol/L CaCO3 solution, at 20 °C and 1000 ppmV CO2. Fig. 12 shows the 18O values of the CaCO3 compared to those of the water. The 18OH2O values of the water only differ by about 0.2 ‰ between the impinging drip point and the end of the glass plate. The initial water values after establishment of the solution film (entry vs. exit of the glass plate) differed by + 0.4 ‰. After 8 h, this difference decreased to +0.2 ‰ and stayed constant for the rest of the experiment. Thus, evaporation only played a minor role, and the 18OCaCO3 value can be compared to the average 18OH2O value. With

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increasing distance of flow, the 18O values of the CaCO3 increased by +1.9 ‰ (Fig. 12a), whereas those of the water remained constant.

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The difference between the 18O values of CaCO3 and water ranged from +29.9 to +31.7 ‰. The increase in fractionation along the plate is also obvious from Fig. 12b, where the observed

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1000ln18 values are plotted against residence time. Also shown are different 1000ln18 values from the literature, which were determined in the laboratory by precipitating CaCO 3 from a bulk solution

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under controlled conditions as well as in natural (cave) systems.

The 1000ln18 values based on the initial values on the plate (i.e., 0 – 80 s residence time) plot

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slightly below the 1000ln18 values given by Johnston et al. (2013) (up to 0.2 ‰) and Tremaine et al. (2011) (up to -0.4 ‰, Fig. 12b), but are significantly larger than the values predicted by Kim and O’Neil (1997) (+0.8 ‰, Fig. 12b). With increasing residence time and, thus, progressive precipitation of CaCO3, the 1000ln18 values increase and eventually exceed the values of Johnston et al. (2013),

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Tremaine et al. (2011) and even Coplen (2007). As discussed above, the solution is progressively

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forced out of oxygen isotope equilibrium with the water due to progressive precipitation of calcite. Thus, only the 1000ln18 values at the beginning of the plate can be expected to reflect equilibrium. The initial values, which should be comparable to the apex of a stalagmite (which has not been subject

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to any PCP), agree best with those of Johnston et al. (2013) and Tremaine et al. (2011), which were determined in cave experiments. Fig. 12 also demonstrate the effect commonly referred to prior calcite precipitation (PCP). If for example on a stalactite already some CaCO3 precipitates from the solution

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the “initial” isotope value at the apex of a stalagmite below would already be enriched and not in equilibrium with the water of the solution from which the CaCO 3 is precipitated from. Fig. 12a shows the gradual isotopic enrichment of CaCO3 during PCP, while the isotope value of the water remains almost constant. As a consequence, calculating the fractionation factor – or vice versa a reconstruction of the temperature during precipitation of speleothem CaCO3 or the initial water isotope value – is only possible if the drip site has not been affected by PCP. PCP is a common process in caves and all fractionation factors determined by cave experiments might be affected by PCP. Similar observations are made for all our experiments. Thus, we interpret the initial values for 1000ln18 of all experiments to reflect oxygen isotope fractionation between drip water and speleothem calcite. Fig. 13 shows the corresponding values of 1000ln18 against the experimental temperature. All our experimentally determined values for 1000ln18 are compiled in Table 1. 25

ACCEPTED MANUSCRIPT As observed for the fractionation between DIC and water (section 5.3.1), experiments #9 and #10 deviate from the other experiments and show lower values for 1000ln18 (Fig. 13; Table 1) in the range of the fractionation factors of Kim and O’Neil (1997). As discussed in section 5.3.1, the measured 18OH2O values are substantially larger than the values expected from the measured 18ODIC values and oxygen isotope equilibrium, probably due to evaporation during storage. Using the measured 18ODIC values and assuming oxygen isotope equilibrium enables to estimate the 18O values of the water prior to evaporation, which are substantially more negative than the measured 18O values

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of the corresponding samples (-10.9 vs. -9.2 ‰ for the 2 mmol/L experiment and –10.4 vs. –9.2 ‰ for the 3 mmol/L experiment). If these corrected 18Owater values (Table 1) are used to calculate the

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fractionation between CaCO3 and H2O, the resulting 1000ln values are in very good agreement with the other experiments and the fractionation factors observed in natural cave systems (ruby and purple

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squares, Fig. 13).

In general, our experimentally determined values agree best with the values reported by

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Tremaine et al. (2011) and Johnston et al. (2013) even though the Ca2+ concentrations and thus, the precipitation rates are substantially lower in the natural cave settings. The values reported by Day and Henderson (2011) are in the same range, but show a higher degree of scatter. The different symbols

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for the Day and Henderson (2011) study represent different drip intervals, where the medium drip intervals represent the highest 1000ln values (circles, Fig. 13). The scatter in their data is probably related to dripping and splashing effects, which were avoided in our study. In addition, their low

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temperature values agree best with the “equilibrium” fractionation factors of Kim and O’Neil (1997),

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whereas our 10 °C data are substantially higher. Fig. 14 shows the experimentally observed 1000ln18 values against 103/T, where T is the temperature in Kelvin. The values for the experiments #9 and #10 were not included due to the

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previously described experimental uncertainties. A linear fit of these data allows to determine the temperature-dependent fractionation between CaCO3 and water based on our experimental data:

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1000𝑙𝑛 18𝛼 = 16.516(±1.267) ∗

103 𝑇

− 26.141(±4.356).

(14)

Fig. 13 shows the relatively wide range of stable oxygen isotope fractionation factors between water and calcite in the literature (ca. 1-2 ‰ in total). These differences were attributed to ‘kinetic’ and ‘disequilibrium’ effects, and it is still an open question and an ongoing discussion in the speleothem community which fractionation factor is best suited for speleothems. The fractionation values observed in our study using synthetic carbonates, which utilized thin films as they occur on the surface of natural speleothems, agree best with the values reported by Tremaine et al. (2011) and Johnston et al. (2013). This suggests that these fractionation factors are indeed better suited for speleothems than other ‘equilibrium’ fractionation factors determined in laboratory experiments (e.g., Kim and O'Neil, 1997).

26

ACCEPTED MANUSCRIPT 5.3.3 Fractionation between DIC and CaCO3 – determination of CaCO3/DIC Comparison of the 18O and 13C values of DIC and CaCO3 enables to directly determine the oxygen isotope fractionation between the individual carbonate species and CaCO3. The fractionation is then simply given by the difference between the corresponding 13C and 18O values. As described in section 5.2, the flow velocity and the precipitation rates on the marble and glass plates are very similar, but not identical (compare Figs. 8 and 9). As a consequence, even though the DIC and CaCO3 samples were taken at the same distances of flow, the residence times are not identical, and it was necessary to

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synchronize the residence times of both experiments. The temporal evolution of the 18ODIC values is described by Eqn. (10). This allows to calculate the -values of the DIC samples for the residence times

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of the corresponding CaCO3 experiment. The corresponding isotope fractionation between CaCO3 and the DIC, which at pH ≈ 8 is represented by HCO3-, CaCO3/DIC, can then be calculated by subtracting the

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value of the DIC from the corresponding -value of CaCO3:

(15)

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𝜀𝐶𝑎𝐶𝑂3⁄𝐷𝐼𝐶 (𝑡) = 𝛿𝐶𝑎𝐶𝑂3 (𝑡) − 𝛿𝐷𝐼𝐶 (t).

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5.3.3.1 Determination of 13CaCO3/HCO3-

Fig. 15 shows the 13C values of the DIC and the corresponding CaCO3 for selected experiments. In addition, the 13C values expected for the CaCO3 in case of equilibrium carbon isotope fractionation

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between HCO3- and CaCO3 are shown. These were calculated using the fractionation factor of Emrich et al. (1970). All experiments show a large negative carbon isotope fractionation between CaCO 3 and

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DIC (i.e., the 13C values of the CaCO3 are more negative than those of the DIC, Fig. 15). However, with increasing residence time on the plate, the difference becomes smaller. The fractionation expected under conditions of carbon isotope equilibrium, in contrast, is small and positive. The decreasing

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isotope fractionation between CaCO3 and DIC with increasing residence time is most obvious for the experiment using a 2 mmol/L CaCO3 solution at 30 °C and 1000 ppmV (Fig. 15d). After about 540 s,

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the fractionation even becomes positive, but is still 1 ‰ more negative than expected under conditions of isotope equilibrium. For some experiments, the error bars are relatively large (e.g., Fig 15a. However, even considering these large errors, the absolute value of the fractionation decreases with decreasing precipitation rate (i.e., increasing residence time on the plate) for all experiments. Strongly negative and rate-dependent isotope fractionation effects are usually associated with kinetic isotope fractionation processes (Mook and De Vries, 2000; Sharp, 2007). Thus, our data suggest that isotope fractionation during precipitation of speleothem calcite is kinetic, in particular for high precipitation rates. We emphasize that our approach avoids the effect of isotope fractionation between DIC and CO2, because we directly compare the 13C values of the DIC and the precipitated calcite. The effect of rapid degassing of CO2, which has often been used to explain speleothem calcite 13C values not in equilibrium with the DIC (e.g., Hendy, 1971; Mickler et al., 2006), can thus be neglected.

27

ACCEPTED MANUSCRIPT Fig. 16 shows the relationship between carbon isotope fractionation between CaCO 3 and DIC, 13

CaCO3/HCO3,

and precipitation rate. The precipitation flux was calculated by Eq, (10) and

multiplication with the film thickness. The uncertainty of the 13C values of the DIC (Fig. 15) was propagated to the calculated fractionation factors. For some experiments, the uncertainties are relatively large (e.g., Fig. 16a). All experiments clearly show decreasing isotope fractionation with decreasing precipitation rate demonstrating a strong influence of precipitation rate on (kinetic) isotope fractionation. Thus, carbon isotope fractionation seems to directly depend on the reaction 13

CaCO3/HCO3-

of the individual

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kinetics during CaCO3 precipitation. However, the absolute values of

experiments show a strong variability ranging from -6.5 to +0.3 ‰. This variability does not show a clear relationship with temperature, pCO2 or concentration of [Ca2+]. For example, for the experiment

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conducted at 10 °C, 5 mmol/L and 1000 ppmV CO2 (Fig. 17a), 13CaCO3/HCO3- ranges from 1.9 to -4.4 ‰.

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The experiment conducted at 10 °C, 5 mmol/L and 3000 ppmV CO2 (Fig 11b), shows much lower values, ranging from -5.1 to -6.4 ‰. Thus, the rate dependence of isotope fractionation is clearly visible in our data set, but determination of absolute values depending on temperature and precipitation rate

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is currently not possible.

This suggests that the different experiments are not directly comparable. Therefore, it is not

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possible to estimate, for instance, the dependence of 13CaCO3/HCO3- on temperature. The relatively large degree of scatter is caused by several minor uncertainties associated with the different experimental setups: (i) the DIC and CaCO3 experiments were conducted using slightly different setups (one glass

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plate vs. two marble plates); (ii) the flow velocities and the corresponding film thicknesses were

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slightly different for the DIC and the CaCO3 experiments; (iii) the distances required for chemical equilibration were different for different experiments. In addition, for the DIC experiments, coprecipitation of small amounts of dissolved CO2 during precipitation as SrCO3 and, thus, slightly biased 13C values for small distances of flow cannot be completely excluded. Most importantly, the large

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degree of scatter between the different experiments is related to varying initial (isotopic) conditions. As described in the methods section, the SI of the solution was adjusted to values of about 0 by sparging

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the excess CO2 with Ar and measuring pH. This is, however, difficult and small deviations from SI = 0 cannot be excluded. This is, for example, visible in the initial 13C values, which show an increasing trend with temperature (Fig. 7). This is particularly prominent for the experiment conducted at 10 °C and a pCO2 of 3000 ppmV, which shows substantially lower initial 13C values than those of the 20 and 30°C experiments (Fig. 7 b). This may be related to the chemical equilibration of the reservoir. At lower temperatures, the solubility of CO2 in water increases (e.g. Murray and Riley, 1971). Thus, at lower temperatures, the fraction of dissolved CO2 (with a more negative 13C value) of the total DIC is higher than at higher temperatures. However, for the 10 °C experiment, we cannot exclude that the saturation index of the solution was still slightly lower than 0 prior to equilibration of the reservoir. Thus, for this experiment, the fraction of dissolved CO2 may have been larger than for the other experiments leading

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ACCEPTED MANUSCRIPT to more negative initial 13C values of the CaCO3. This effect is also visible in the DIC experiments (compare Fig. 5 b), but more obvious in the CaCO3 experiments. The experimentally observed values for 13CaCO3-DIC can also be compared to values observed in cave environments and other experimental studies. Fig. 17 shows a comparison of the rate-dependent fractionation observed in our experiments using a 5 mmol/L CaCO3 solution at 10 °C and 1000 ppmV CO2 with the values of Riechelmann et al. (2013), who used recent CaCO3 precipitated on watch glasses in a cave in western Germany. Linear extrapolation of our experimental data to lower precipitation

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rates shows a good agreement with the fast drip site of Riechelmann et al. (2013). The slower drip site, TS 8, shows a considerably higher value. This is probably related to the slower drip interval, which

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results in a longer residence time of the solution on top of the watch glass, and thus provides more time for precipitation of CaCO3 (Riechelmann et al., 2013). Even if the Ca2+ concentration of the cave

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drip water is substantially lower (ca. 2.3 mmol/L for TS 1 and ca. 1.9mmol/L for TS 8, Riechelmann et al., 2011), this shows the general comparability of our experimentally observed data to a cave

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environment.

Also shown are the values observed in the laboratory by Romanek et al. (1992), who had comparable surrounding conditions within their experiments. In contrast to our experiments,

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Romanek et al. (1992) did not observe a negative, rate-dependent isotope fractionation, even though they had comparable experimental conditions, but higher initial Ca2+ concentrations and thus higher precipitation rates (Fig. 17, purple symbols, note the break in the x-axis). This may be related to

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significant differences in their experimental setup compared to our study. They precipitated CaCO3 in

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a beaker, which was continuously stirred, and used a constant supply of CO2, with a potentially very different 13C value than the CO2 evolving from the precipitation of CaCO3. Thus, carbon isotope exchange between the HCO3- of the solution and the gaseous CO2 bubbled through the solution may have affected the 13C value of the DIC, possibly obscuring the rate effect (Dreybrodt et al., 2016;

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Dreybrodt and Romanov, 2016; Hansen et al., 2017). In contrast, in our experimental setup, the CO2 produced by the precipitation of CaCO3 is almost instantaneously removed from the thin solution film,

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which also behaves completely different than a large solution body, where diffusive processes are considerably different. Kinetic isotope fractionation has also been reported from natural environments, such as calcite precipitating springs (e.g.,Dandurand et al., 1982; Michaelis et al., 1985; Usdowski et al., 1979). Within these studies, the temporal evolution of the solution chemistry and the stable isotope signals of both DIC and CaCO3 was investigated. Different calcite precipitating streams were monitored from the spring downstream and sampled after different distances of flow. In principle, their experiments in the natural environment are, thus, comparable to our laboratory setup. They report continuous precipitation of CaCO3 alongside with a progressive enrichment in the stable isotope signals with increasing distance of flow of the corresponding stream. They observed a carbon isotope fractionation between CaCO3 and HCO3- of about 0, which was interpreted as disequilibrium isotope fractionation due to high precipitation rates (Dandurand et al., 1982; Michaelis et al., 1985; 29

ACCEPTED MANUSCRIPT Usdowski et al., 1979). Thus, they also observed more negative 13C values than expected under conditions of equilibrium, which is in agreement with our study even if the effect is less pronounced. The more negative fractionation observed in our experiments suggests an even stronger kinetic fractionation. However, a detailed comparison is not possible, because the precipitation rates in the natural environment and in particular their temporal evolution along the stream are not well constrained. Thus, the variability in precipitation rate in our experiments may be much larger and better resolved than in their study, which encompassed a distance of several hundreds of meters

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downstream of the spring. In addition, as already stated for the Romanek et al. (1992) experiments, the conditions of a flowing stream were considerably different from our experiments. In particular, the stream is associated with high turbulence and has a solution volume several orders of magnitude

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larger than our thin films.

5.3.3.2 Determination of 18CaCO3/HCO3-

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Fig. 18 shows the 18O values of DIC and CaCO3 for selected experiments. The uncertainty of the 18O values of the DIC (Fig. 18) was calculated by error propagation. To our knowledge, literature 18CaCO3/HCO3-,

are not available. Thus, we

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values for the fractionation between HCO3- and CaCO3,

combine the available fractionation factors for CaCO3/H20 and HCO3-/H2O 18

𝜀𝐶𝑎𝐶𝑂3⁄𝐻𝐶𝑂3− =

18

𝜀𝐶𝑎𝐶𝑂3⁄𝐻2𝑂 − 18𝜀𝐻𝐶𝑂3− ⁄𝐻2 𝑂 ,

(16)

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Both the 18OHCO3- and the 18OCaCO3 values increase along the plate due to progressive

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precipitation of CaCO3. The difference between the 18O values of CaCO3 and HCO3- (i.e., 18CaCO3/HCO3-), however, decreases with increasing residence time in most of our experiments (Figs. 18a, c, e, f, g, h). Since supersaturation with respect to calcite also decreases with increasing residence time, this

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indicates, as observed for carbon isotopes, a relationship between isotope fractionation and precipitation rate. This is also visible in Fig. 19, where oxygen isotope fractionation,

18CaCO3/HCO3-,

is

plotted against precipitation rate. We also show four different values for CaCO3/HCO3- based on the

factors for

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combination of the fractionation for 18

18

𝜀𝐻𝐶𝑂3−⁄𝐻2 𝑂 (Beck et al., 2005) and four different fractionation

𝜀𝐶𝑎𝐶𝑂3⁄𝐻2 𝑂 . The fractionation,

18CaCO3/HCO3-,

observed in our experiments ranges from -

0.34 to 2.55 ‰ (Fig. 19). In most cases, the initial 18OCaCO3 values (i.e., at the start of the plate) are in good agreement with the values expected using the fractionation factors of Tremaine et al. (2011) and Johnston et al. (2013), although the precipitation rates in the natural settings were substantially lower. With increasing residence time on the plates, the 18OCaCO3 values increase and even exceed the value expected using the fractionation factor of Coplen (2007) (green lines, Fig. 19). In case of equilibrium isotope fractionation, a constant fractionation between HCO3- and CaCO3 would be expected, which is only visible in two experiments (Fig. 18b; 5 mmol/L CaCO3-solution, 20°C, 1000 ppmV CO2; Fig. 19d; 5 mmol/L CaCO3 solution, 10 °C, 3000 ppmV CO2). This strongly suggests 30

ACCEPTED MANUSCRIPT disequilibrium or kinetic fractionation. The largest change in fractionation and, thus, the strongest dependence on precipitation rate is observed for the highest temperatures (30 °C, Figs. 19 c and f). A similar observation has been reported by Watkins et al. (2014; 2013) and Dietzel et al. (2009), who investigated the fractionation between water and calcite in dependence of the reaction kinetics, such as temperature, precipitation rate and pH. Their findings suggest that almost all fractionation factors determined in laboratory experiments are influenced by kinetic effects during precipitation and thus do not reflect isotope equilibrium. They concluded that the most likely case of equilibrium

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fractionation, if ever achieved, is in a natural system where calcite precipitates slowly under constant conditions as for example in Devils Hole (Coplen, 2007). Their results are in good agreement with our experimental data, where isotope fractionation depends on precipitation rates for both CaCO3/DIC and

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whereas our initial values range from -6.98 to -7.53 (Fig. 19).

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CaCO3/H2O. The precipitation rates of Watkins et al. (2013) show log10F values between -5.73 and -6.65,

Our results clearly show that oxygen isotope fractionation between CaCO 3 and HCO3- during

values observed for

18CaCO3/HCO3-

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precipitation of (speleothem) calcite does not occur under conditions of equilibrium. However, the in different experiments vary, even for the same temperature

(Fig. 19). Thus, providing values for the fractionation,

18CaCO3/HCO3-,

as a function of experimental

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temperature and precipitation rate is difficult. This is consistent with the results of the 13C values (see section 5.3.3.1) and probably related to the same uncertainties during the experiments: (i) slightly different flow velocities in the DIC and CaCO3 experiments (Hansen et al., 2013), (ii) slightly different

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setups (one glass plate vs. two marble plates), and (iii) slightly different initial chemical and isotopic

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conditions of the solution for the individual experiments.

5.3.3.3 Fractionation between HCO3- and CO2 – determination of 13CO2/HCO3-

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Based on the total isotope fractionation, tot, calculated in section 5.1 and the isotope fractionation between CaCO3 and HCO3, the isotope fractionation- between HCO3- and CO2 can be calculated (see

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sections 2.3 and 5.2):

13

𝜀𝐶𝑂

2

⁄𝐻𝐶𝑂3−

= ( 13𝜀𝑡𝑜𝑡 − 0.5 ∗ 13𝜀𝐶𝑎𝐶𝑂3⁄𝐻𝐶𝑂3− ) ∗ 2.

At isotopic equilibrium, values between -7.29 and -9.47 ‰ are expected for

(17) 13CO2/HCO3-

at the

temperatures of our experiments (Emrich et al., 1970). The average values in our experiments range from -11.3 to -24 ‰ and are, thus, much more negative than expected under conditions of isotope equilibrium. This indicates kinetic isotope fractionation between CO2 and HCO3- during precipitation of speleothem calcite, as observed for CaCO3/HCO3-. In the previous section, we have shown a strong dependence of 13CaCO3/HCO3- on precipitation rate. Thus, 13CaCO3/HCO3- is not constant along the plates, but becomes more positive with increasing residence time. However, using a Rayleigh approach, tot, is constant by definition (Eq. (11)). As a result, the values for 13 CO2/HCO3- calculated with Eq. (13) are not constant, but become more negative with increasing residence time. However, it is likely that 31

ACCEPTED MANUSCRIPT 13

CO2/HCO3-

also depends on precipitation rate. Thus, the values calculated for

13

CO2/HCO3-

should be

considered as an estimate rather than a precise determination.

5.4 Implications for the interpretation of speleothem isotope records The results of this study suggest that quantitative reconstruction of temperature and meteoric precipitation from speleothem stable isotope values remains difficult. This is not only due to the

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complex interplay of processes occurring in the atmosphere, the soil and the karst (Lachniet, 2009), but also due to disequilibrium isotope fractionation on the speleothem surface. Progressive precipitation of speleothem calcite leads to a strong enrichment in the 18O and 13C values of both DIC

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and calcite. This may also have a strong effect on speleothem 18O and 13C values. For instance, if the

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solution entering a cave precipitated CaCO3 prior to dripping onto the stalagmite (referred to as PCP, e.g., while flowing down a stalactite), the 18O and 13C values of the DIC are driven out of isotopic equilibrium with the water. As a result, the isotope signal that is incorporated into speleothem calcite

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does not reflect the 18O value of the drip water, and can, thus, not directly be interpreted in terms of climate change above the cave.

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Since we show that oxygen and carbon isotope fractionation between HCO3- and CaCO3 is negative and depends on the precipitation rate, the degree of enrichment in 18O and 13C does not only depend on the degree of PCP, but also on temperature and precipitation rate. Varying conditions

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in cave and drip water parameters, such as temperature, drip rate, degree of supersaturation with

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respect to calcite and, as a consequence, precipitation rate, as well as residence time on a stalactite thus have a varying effect on the speleothem isotope values. These signals may be considered as noise distorting the actual climate signal, but also contain important information about karst and in-cave processes, which may itself be related to climate. In order to better understand these proxy signals and

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to make the most use of them in terms of reconstructing past climate variability, further experiments better constraining the individual isotope fractionations and their dependence on temperature and

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precipitation rate are required. If, for example, the growth rate of a speleothem is well known, the use of an appropriate fractionation factor could provide more reliable estimates of the temperature during its formation. This could then be further validated by measurements of 18O of fluid inclusions. In addition, monitoring the present-day cave conditions as well as measuring the 18O and 13C values of the drip water and of in-situ precipitated calcite (e.g., Meyer et al., 2014; Riechelmann et al., 2013; Riechelmann et al., 2011; Van Rampelbergh et al., 2014) are still valuable to estimate the fractionation factors for the corresponding cave site. This could potentially provide very important information on the underlying mechanisms for the interpretation of paleoclimate records.

32

ACCEPTED MANUSCRIPT 6. Conclusions The experiments presented in this study, conducted under controlled, cave-analogue conditions, allow for the first time to directly investigate oxygen and carbon isotope fractionation between the precipitated CaCO3 and all other involved species (HCO3-, H2O, CO2) in a thin water film, comparable to the surface of speleothems. All chemical parameters, including precipitation rate, the time constants of precipitation and pH are in agreement with previously published theoretical studies (Baker et al., 1998; Buhmann and Dreybrodt, 1985; Dreybrodt et al., 1997) and show the expected temperature

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dependence. We observed a strong enrichment of the 13C values of +2.2 to +9.6 ‰ in both the DIC and the

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CaCO3 experiments. The temporal evolution of the 13CDIC values can be explained by a Rayleigh distillation model as suggested by Scholz et al. (2009). The total carbon isotope fractionation,

13

tot,

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was much larger than expected from isotope equilibrium, with values up to -13.7 ‰. All experiments show a large negative fractionation between CaCO3 and DIC, 13CaCO3/HCO3-, which strongly depends on

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precipitation rate. With increasing residence time and, thus, decreasing supersaturation and precipitation rate, the fractionation becomes smaller and eventually even positive approaching chemical equilibrium. This clearly shows that isotope fractionation in speleothems is kinetically

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controlled even if absolute values and their dependence on temperature and precipitation rate cannot be determined. This implies that the assumption of a constant fractionation factor (Dreybrodt, 2008; Dreybrodt and Scholz, 2011; Scholz et al., 2009) is not correct. In order to investigate these

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mechanisms in more detail it will be necessary to perform experiments with a longer duration and

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solutions closer to chemical equilibrium.

The 18O values of DIC and water are initially in equilibrium as calculated using equilibrium fractionation factors by Beck et al. (2005). As a result of CaCO3 precipitation the system is forced out

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of isotopic equilibrium, because the time required to re-equilibrate the DIC with the water is substantially longer than the time scale of precipitation and the residence time on the plate. The total fractionation, 18tot, ranges from -0.38 to -3.3 ‰. The observed fractionation between CaCO3 and HCO3-

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, 18CaCO3/HCO3-, is in good agreement with the fractionation factors observed in natural cave systems (Johnston et al., 2013; Tremaine et al., 2011). With increasing residence time on the plate, and, thus, decreasing supersaturation and precipitation rate, the fractionation between CaCO3 and HCO3becomes smaller, approaching the predictions by Coplen (2007) and Watkins et al. (2014; 2013). The initial fractionation (i.e., at the beginning of the experiments) between CaCO3 and water, 1000ln18, is in good agreement with the values determined in natural cave systems (Johnston et al., 2013; Tremaine et al., 2011) and shows a very similar temperature dependence. However, with progressive precipitation of CaCO3, the system is forced out of isotopic equilibrium with the water, and 1000ln18 increases. These findings show (i) that our laboratory experiments closely resemble a cave and (ii) reaction kinetics have to be taken into account for the interpretation of speleothem 18O records. 33

ACCEPTED MANUSCRIPT The results of this study imply that quantitative reconstruction of paleotemperatures and past precipitation from speleothem isotope values remains difficult. This is not only due to the complex interplay of processes occurring in the atmosphere, the soil and the karst (Lachniet, 2009), but also because of disequilibrium isotope fractionation on the speleothem surface. Varying conditions in cave and drip water parameters will have a varying effect on the speleothem isotope values and thus further complicate their interpretation. Thoroughly conducted cave monitoring programs studying the present-day isotope fractionation processes in-situ may provide important constraints on the most

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suitable fractionation factors for a given cave site.

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Acknowledgements

M. Hansen and D. Scholz acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG)

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through grants SCHO 1274/8-1 and SCHO 1274/9-1 and the ‘QUEST’ funding from the European Union’s Horizon 2020 Research and Innovation program under the Marie Skłodowska-Curie grant

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agreement No 691037. We also thank Marie Froeschmann for her support as a student assistant during the experiments and preparation of samples for stable isotope analyses. Furthermore, we are thankful to the workshop of the Institutes for Geosciences and Physics of the Atmosphere, University of Mainz,

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especially S. Klumb, for very helpful technical support during the experiments and for keeping the climate box running. We thank Jens Fohlmeister and two anonymous reviewers for their thoughtful

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editorial work of Michael Böttcher.

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and detailed comments, which helped to improve the manuscript. Finally, we highly appreciate the

List of Figures

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Fig. 1: Sketch of the experimental setup of the DIC experiment. Degassing of dissolved CO2 and adjustment of the new pH take place on the upper “equilibration plate”. Precipitation of CaCO 3 occurs on the lower plate.

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Fig. 2: Schematic sketch of the experimental setup for the CaCO3 experiment. Fig. 3: Chemical and isotopic evolution on the equilibration plate for 13C and 18O (reported vs VPDB) for an experiment conducted at 1000 ppmV CO2, with a 5 mmol/L CaCO3-solution at 20 °C. “Beginning Eq” corresponds to the impact of the bulk solution from the peristaltic pump on the equilibration plate. “Exit equilibration plate” corresponds to the end of the equilibration plate after degassing of excess CO2 and establishment of high supersaturation with respect to calcite. Fig. 4: Temporal evolution of electrical conductivity on the marble plates for experiments conducted using a CaCO3 concentration of 5 mmol/L and an ambient pCO2 of 1000 (a) and 3000 ppmV (b). The solid lines are exponential fits of the experimental data according to Eq. (6).

34

ACCEPTED MANUSCRIPT Fig. 5: Temporal evolution of the 13CDIC for experiments conducted using a 5 mmol/L CaCO3 solution and an ambient pCO2 of 1000 (a) and 3000 ppmV (b). Fig. 6: Temporal evolution of the 18ODIC values on the marble plate for the experiments conducted with a 5 mmol/L CaCO3 solution and a pCO2 of 1000 (a) and 3000 ppmV CO2 (b). 18ODIC values are shown on the VPDB scale. Fig. 7: Transmitted-light photomicrographs of CaCO3 precipitated on glass plates in four different experiments: (a) 5 mmol/L CaCO3 solution at 30 °C and an ambient pCO2 of 3000 ppmV; (b)

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5 mmol/L CaCO3 solution at 20 °C and an ambient pCO2 of 1000 ppmV; (c) 5 mmol/L CaCO3 solution at 10 °C and an ambient pCO2 of 3000 ppmV; (d) 3 mmol/L CaCO3 solution at 20 °C and

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an ambient pCO2 of 1000 ppmV.

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Fig. 8: Temporal evolution of the 13C values of the precipitated CaCO3 on the glass plates for experiments conducted using a 5 mmol/L CaCO3 solution and an ambient pCO2 of 1000 (a) and 3000 ppmV (b).

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Fig. 9: Temporal evolution of 18O values of CaCO3 precipitated on the glass plates. As an example, we show the data from the experiments conducted with a 5 mmol/L CaCO3 solution and an ambient

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pCO2 of 1000 (a) and 3000 ppmV (b).

Fig. 10: Evolution of 13CDIC (a and b) and 18ODIC (c and d) values plotted versus the remaining fraction of [Ca2+] in solution for the experiments performed with a Ca2+ concentration of 5 mmol/L at

D

10, 20, 30 °C and a pCO2 of 1000 (a, c) and 3000 ppmV (b, d). The solid lines are the

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corresponding fits according to Eq. (11). Note that in (b) and (d), the last two points of the 30 °C (blue symbols) experiment were excluded from the fit. Fig. 11: Temporal evolution of the 13CDIC and 18ODIC values for the experiments conducted using a

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5 mmol/L CaCO3 solution at 10, 20 and 30 °C and a pCO2 of 1000 (a, c) and 3000 ppmV (b, d). The solid lines show the modeled evolution according to Eq. (9). The dashed lines are the

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corresponding uncertainties, which were calculated by error propagation of the uncertainties obtained from the fits of the experimental data (Figs. 4 and 8). Fig. 12: (a) Temporal evolution of the 18O values of the precipitated CaCO3 and the water for the experiment conducted with a 5 mmol/L CaCO3 solution at 20°C and 1000 ppmV (b) 1000ln18 for the experiment conducted with a 5 mmol/L CaCO3 solution at 20 °C and 1000 ppmV CO2 plotted against the residence time on the plate. Also shown are the 1000ln18 values determined by laboratory experiments (Kim and O'Neil, 1997) and observations from natural (cave) systems (Coplen, 2007; Johnston et al., 2013; Tremaine et al., 2011). Fig. 13: 1000ln18 values plotted as a function of temperature. The different lines show different fractionation factors from the literature. The blue symbols denote the experimentally determined values of this study for 5 mmol/L solutions, whereas the ruby and purple colored 35

ACCEPTED MANUSCRIPT squares denote the values for the experiments conducted at 2 and 3 mmol/L. The orange symbols are the observations of Day and Henderson (2011). The water sample of the experiment conducted with a 5 mmol/L CaCO3 solution at 30° C and 1000 ppmV CO2 was lost during shipping. Thus, for 30 °C, only the data point for the corresponding 3000 ppmV CO2 experiment is shown. However, since the 18O values of the water remained almost constant along the plate it is reasonable to assess the initial value by using an average 18OH20 value. The data point (not shown) plots very close to the value for the 3000 ppmV CO2 experiment

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(1000ln18 = 28.6 ‰ for 3000 ppmV and 28.8 ‰ for 1000 ppmV CO2). Also shown are different literature values as well as the results of the cave-analogue experiments of Day and

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Henderson (2011).

Fig. 14: Experimentally observed 1000ln18 values plotted against 103/T. The red line is a linear

SC

fit of the experimental data.

Fig. 15: Comparison of the 13C values of the DIC (black) and the precipitated CaCO3 (red). Also shown

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are the 13C values expected for CaCO3 precipitated under conditions of carbon isotope equilibrium (blue). Shown are the results for experiments conducted using (a) a 5 mmol/L CaCO3 solution at 10 °C and 1000 ppmVCO2; (b) a 5 mmol/L CaCO3 solution at 10 °C and

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3000 ppmV CO2; (c) a 3 mmol/L at 20 °C and 1000 ppmV CO2; and (d) a 2 mmol/L CaCO3 solution at 30 °C and 1000 ppmV. Error bars for the 13C values of the DIC were calculated by

values are reported vs. VPDB.

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error propagation using Eq. (9) and the errors from the fits of the experimental data. All 13C

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Fig. 16: Carbon isotope fractionation between CaCO3 and HCO3-,

13CaCO3/HCO3-,

as a function of

precipitation rate. Shown are the results of the experiments conducted using (a) a 5 mmol/L CaCO3 solution at 10 °C and 1000 ppmV CO2; (b) a 5 mmol/L CaCO3 solution at 10 °C and

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3000 ppmV CO2; (c) a 3 mmol/L at 20 °C and 1000 ppmV CO2; and (d) a 2 mmol/L CaCO3 solution at 30 °C and 1000 ppmV.

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Fig. 17: Carbon isotope fractionation between CaCO3 and HCO3-,

13CaCO3/HCO3-,

as a function of

precipitation rate. The results of the experiments conducted using a 5 mmol/L CaCO3 solution at 10 °C and 1000 ppmV CO2 are compared with values obtained in a cave monitoring program by Riechelmann et al. (2013) as well as with the laboratory experiments of Romanek et al. (1992). Fig. 18: Comparison of the 18O values of the DIC (black symbols) and CaCO3 (red symbols). (a) 5 mmol/L CaCO3 solution, 10°C, 1000 ppmV CO2; (b) 5 mmol/L CaCO3 solution, 20°C, 1000 ppmV CO2; (c) 5 mmol/L CaCO3 solution, 30°C, 1000 ppmV CO2; (d) 5 mmol/L CaCO3 solution, 10°C, 3000 ppmV CO2; (e) 5 mmol/L CaCO3 solution, 20°C, 3000 ppmV CO2; (f) 5 mmol/L CaCO3 solution, 30°C, 3000 ppmV CO2; (g) 2 mmol/L CaCO3 solution, 30°C,

36

ACCEPTED MANUSCRIPT 1000 ppmV CO2; (h) 3 mmol/L CaCO3 solution, 20°C, 1000 ppmV CO2. All 18O values calibrated vs. VPDB. Fig. 19: Oxygen isotope fractionation between CaCO3 and HCO3-,

18

CaCO3/HCO3-,

plotted against the

precipitation rate for the experiments conducted using a (a) 5 mmol/L CaCO3 solution, 10°C, 1000 ppmV CO2, (b) 5 mmol/L CaCO3 solution, 20°C, 1000 ppmV CO2, (c) 5 mmol/L CaCO3 solution, 30°C, 1000 ppmV CO2, (d) 5 mmol/L CaCO3 solution, 10°C, 3000 ppmV CO2, (e) 5 mmol/L CaCO3 solution, 20°C, 3000 ppmV CO2, (f) 5 mmol/L CaCO3 solution, 30°C, 3000 ppmV

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CO2, (g) 2 mmol/L CaCO3 solution, 30°C, 1000 ppmV CO2, (h) 3 mmol/L CaCO3 solution, 20°C, 1000 ppmV CO2. Also shown are the 18O values expected for isotope equilibrium between

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CaCO3 and HCO3- using different fractionation factors from the literature by Coplen (2007) (green dashed line), Tremaine et al. (2011) (blue dashed line), Johnston et al. (2013) (orange

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dashed) and Kim and O’Neil (1997) (purple dashed line. Note that these fractionation factors

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were not determined in dependence of the precipitation rate).

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Dreybrodt, W. and Scholz, D. (2011) Climatic dependence of stable carbon and oxygen isotope signals recorded in speleothems: From soil water to speleothem calcite. Geochimica et Cosmochimica Acta 75, 734-752. Emrich, K., Ehhalt, D.H. and Vogel, J.C. (1970) Carbon isotope fractionation during the precipitation of calcium carbonate. Earth and Planetary Science Letters 8, 363-371.

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Fairchild, I.J. and Baker, A. (2012) Speleothem science: from process to past environments. John Wiley & Sons.

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Fantidis, J. and Ehhalt, D.H. (1970) Variations of the carbon and oxygen isotopic composition in stalagmites and stalactites: Evidence of non-equilibrium isotopic fractionation. Earth and Planetary Science Letters 10, 136-144.

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ACCEPTED MANUSCRIPT Table 1: Summary of experimental data. Experiment No. 1

DIC

DIC

pCO2 [ppmV]

rH [%]****

Film thickness [mm]

5

10 ± 0.5

1038 ± 21

80.5 ± 2

0.11

10.1 ± 0.02

1029 ± 48

89.2 ± 1

0.11

19.9 ± 0.3

1030 ± 18

91.1 ± 1.5

0.16

- 44.8 - - 42.9

19.7 ± 0.1

1053 ± 42

98.7 ± 1.2

0.1

- 46.5 - - 45.5 -27.3 - -9.4***

30.6 ± 0.2

1033 ± 38

96.5 ± 1.6

0.1

- 46.0 - - 43.9

-10.22 - -9.89

30.7 ± 0.3

1007 ± 42

97.5 ± 1.2

0.1

- 45.4 - - 43.2

-11.5 - -9.4

9.9 ± 0.1

2980 ± 28

82.1 ± 1.2

0.11

- 47.6 - - 44.8

-7 - -5.7

9.7 ± 0.1

3020 ± 28

89.8 ± 1.2

0.12

- 46.0 - - 45.5

20.3 ± 0.2

3046 ± 27

88.0 ± 1.3

0.12

- 39.2 - - 39.7

-8 - -7.8

20.0 ± 0.1

3060 ± 35

95.6 ± 0.7

0.11

- 40.3 - - 40.0

-9.5 - -6.4

31.0 ± 0.2

3069 ± 29

98.4 ± 2.7

0.1

- 38.1 - - 38.9

30.7 ± 0.1

3076 ± 56

99.9 ± 0.6

0.11

- 39.9 - - 39.3

-8.5 - -8.2

10.0 ± 0.1

1042 ± 13

77.7 ± 1.7

0.12

- 38.1 - - 38.9

-7 - -6.3

9.9 ± 0.2

1030 ± 18

86.4 ± 1.6

0.14

- 39.9 - - 39.3

-7.4 - -4.7

20.3 ± 0.1

1099 ± 16

99.7 ± 0.3

0.13

- 40.3 - - 39.3

-10.3 - -9.4

20 ± 0.1

1062 ± 14

100 ± 0.0

0.11

30.8 ± 0.1

1075 ± 13

95.2 ± 2.2

0.11

- 35.4 - - 34.8

1066 ± 17

99.0 ± 0.6

0.11

- 35.2 - - 31.4

1071 ± 10

100 ± 0

0.14

- 39.7 - - 37.6

1065 ± 20

100 ± 0

0.12

- 40.5 - - 38.5

5

CaCO3 3

DIC

5

CaCO3 4

DIC

5

CaCO3 5

DIC

5

CaCO3 6

DIC

5

CaCO3 7*

DIC

2

CaCO3 8*

DIC

2

CaCO3 9

DIC

2

CaCO3 10

DIC CaCO3

18OCO2 [‰] (VPDB)

T [°C]

CaCO3 2

13CCO2 [‰] (VPDB)

[CaCO3] [mmol/L] ****

30.6 ± 0.1 3

20.3 ± 0.1 20.2 ± 0.1

C A

- 46.1 - - 48.5

-8.2 - -7.2

M

- 40.6 - - 36.7

13tot [‰]

1054 ± 543

- 11.92 ±0.15

244 ± 24

- 13.67 ± 0.67

T P

-3.3 ± 0.19

29.87

182 ± 17

- 10.48 ± 0.65

-1.78 ± 0.3

**

644 ± 161

- 7.38 ± 0.83

-2.5 ± 0.34

32.24

410 ± 50

- 12.08 ± 0.61

-2.61 ± 0.22

30.12

270 ± 17

- -9.2 ± 1.24

-1.44 ± 0.22

28.55

----

---

---

---

----

---

---

---

270 ± 33

- 4.73 ± 0.44

-3.26 ± 0.3

26.61**

436 ± 51

- 9.8 ± 3.18

-0.38 ± 1.48

29.16**

-6.4 - -5.5 -7.4 - -6.9

I R

C S U

N A

D E

PT

E C

- 45.8 - - 44.4

pr [s]

18tot [‰]

-1.81 ± 0.5

1000ln18

32.34

-14.9 - -6***

-8.4 - -8.1

-11.4 - -9.3 ----

-7.7 - -7.4 -8.7 - -7.5

* The experiments conducted using 2 mmol/L CaCO3 at 10 and 20 °C did not yield enough calcite to determine the 13C and 18O values. Therefore, pr, tot and 1000ln are not provided for these experiments.

**Note that the 18O values of the water of these experiments were probably affected by evaporation. Thus, these values are systematically too low. See text for details. ***The amount of pre-equilibrated CO2 was too low to establish the required pCO2 in the climate box. Therefore, small amounts of non-equilibrated CO2 were added. Note that within a few hours of the experimental run, the 18O value of the CO2 approached an equilibrium value. ****[CaCO3] corresponds to the initial concentration of the solution and rH is the relative humidity.

43

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19