Ca

Journal Pre-proofs Constraining multiple controls on planktic foraminifera Mg/Ca Kate Holland, Oscar Branson, Laura L. Haynes, Bärbel Hönisch, Katherine A. Allen, Ann D. Russell, Jennifer S. Fehrenbacher, Howard J. Spero, Stephen M. Eggins PII: DOI: Reference:

S0016-7037(20)30027-2 https://doi.org/10.1016/j.gca.2020.01.015 GCA 11595

To appear in:

Geochimica et Cosmochimica Acta

Received Date: Revised Date: Accepted Date:

14 December 2018 18 December 2019 9 January 2020

Please cite this article as: Holland, K., Branson, O., Haynes, L.L., Hönisch, B., Allen, K.A., Russell, A.D., Fehrenbacher, J.S., Spero, H.J., Eggins, S.M., Constraining multiple controls on planktic foraminifera Mg/Ca, Geochimica et Cosmochimica Acta (2020), doi: https://doi.org/10.1016/j.gca.2020.01.015

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Constraining multiple controls on planktic foraminifera Mg/Ca. Kate Hollanda, Oscar Bransona,b, Laura L. Haynesc, Bärbel Hönischd, Katherine A. Allene, Ann D. Russellf, Jennifer S. Fehrenbacherg, Howard J. Sperof, Stephen M. Egginsa Research School of Earth Sciences, The Australian National University, Canberra, ACT, Australia Department of Earth Sciences, University of Cambridge, Downing St, Cambridge, UK c Institute of Earth, Ocean and Atmospheric Sciences, Rutgers University, NJ, USA d Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY, USA e School of Earth and Climate Sciences, University of Maine, Orono, ME, USA f Department of Earth and Planetary Sciences, University of California Davis, Davis, CA, USA g College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, OR, USA a

b

Abstract

The Mg/Ca of planktic foraminifera is widely used to determine past surface ocean temperatures but temperature is not the only factor that controls test Mg/Ca. Here we quantify the combined influence of seawater temperature, carbon chemistry, and cation chemistry on Orbulina universa Mg/Ca, based on experimental cultures where these factors were varied independently and simultaneously. We fit a new empirical multi-parameter model that quantifies the effects of each of these variables on the Mg/Ca of O. universa: ( ) Mg/CaO. universa = Mg/Casw𝐴 ∙ 𝐷𝐼𝐶𝐵sw ∙ 𝑒𝑥𝑝 𝐶 ∙ [𝐶𝑎]𝑠𝑤 + 𝐷 ∙ 𝑇 + 𝐸 We extend our approach to published Mg/Ca from cultured and sediment trap collected Globigerinoides ruber, and show that a similar equation can be used to describe test Mg/Ca, using [CO32-]sw or pH in place of DIC. The cause of this difference is unknown, but the sensitivity of these two ecophysiologically similar species to different carbon chemistry parameters highlights the uncertainty inherent in applying modern Mg/Ca calibrations to uncalibrated and/or extinct species. In both O. universa and G. ruber, Mg/Casw, [Ca]sw and carbon chemistry (DIC, [CO32-]sw or pH) each modulate the sensitivity of Mg/Ca to temperature. These variables are not constant in the ocean over time-scales relevant to palaeotemperature reconstructions, and must be accounted for when deriving temperature from foraminiferal Mg/Ca. Over time-scales longer than the residence times of Mg and Ca, secular changes in Mg/Casw and [Ca]sw will exert a primary influence on foraminiferal Mg/Ca and its sensitivity to temperature. On shorter timescales, covariance between temperature and seawater carbon chemistry will influence Mg/Ca-derived temperature estimates. This is particularly relevant to transient hyperthermal events, where the Mg/Ca palaeothermometer is used to evaluate the relationship between atmospheric CO2 and ocean temperature. We explore the potential impact of these effects in an illustrative reinterpretation of Mg/Ca records across the Paleocene-Eocene Thermal Maximum.

1. Introduction

Our capacity to predict the sensitivity of Earth’s climate to anthropogenic CO2 emissions depends on the accuracy of estimates of past temperature change in response to climate forcing. One of the best-established tools for estimating past ocean temperature is the Mg/Ca ratio of fossil foraminifera tests (Lea et al. 1999; Elderfield & Gassen, 2000; Anand et al. 2003). This palaeothermometer is based on the endothermic substitution of Mg for Ca in calcite (CaCO3), where thermodynamic laws predict that the partitioning of Mg into the solid from solution (DMg = Mg/Casolid / Mg/Casolution) will increase exponentially with temperature (Garrels and Christ, 1965; Katz, 1973; Lea et al., 1999), according to: 𝐷Mg = exp

(ΔS𝑅)

⋅ exp

(ΔH RT )

where 𝐵1 = exp

= 𝐵1 ⋅ exp

(ΔS𝑅)

and 𝐴 =

(𝐴𝑇)

∆𝐻 𝑅,

(1) ΔS is the change in entropy, R is the gas constant, ΔH is the

change in enthalpy or heat of the reaction, and T is the temperature in Kelvin. This predicts an exponential increase in Mg/Ca with temperature, which is well-established in inorganic precipitates (e.g. Katz, 1973). Laboratory culture, sediment-trap, and sediment core-top studies confirm that foraminiferal Mg/Ca also increases exponentially with temperature: Mg/Caforam = 𝐵 ⋅ exp𝐴 ⋅ 𝑇

(2)

where T (in °C) is temperature, the exponential constant A is the ‘sensitivity’ of Mg/Caforam to temperature and the pre-exponential constant B is a species-specific constant (Lea et al., 1999; Anand et al., 2003). Considerations of the ‘sensitivity’ of this relationship are traditionally restricted to the A term of this equation, but it is important to note the slope of the Mg/Caforam vs. temperature relationship (i.e. sensitivity) is given by:

∂Mg/Caforam ∂T

= 𝐴 ∙ 𝐵 ⋅ exp𝐴 ⋅ 𝑇

(3)

Thus, the sensitivity of the proxy depends on both the pre-exponential and exponential parts of the equation. Where B is constant this is inconsequential, but on multi-million-year time scales the pre-exponent has been shown to vary as a function of seawater composition (e.g. Evans & Müller, 2012), and the consideration of proxy ‘sensitivity’ becomes more complex. The exponential nature of Equation 2 makes foraminiferal Mg/Ca a sensitive seawater thermometer, but the divergence of measured Mg/Caforam from thermodynamic predictions (Equation 1) indicates the response of foraminiferal Mg/Ca to temperature is influenced by additional non-thermal factors. The term ‘vital effects’ is often used to describe all processes that drive differences in the composition of foraminiferal calcite from that predicted for inorganic calcite formed under similar conditions (e.g. Urey et al., 1951). The specifics of vital effects remain poorly constrained, but we do know that foraminifers exert substantial control over the amount of Mg incorporated into their calcite shells (e.g. Zeebe and Sanyal, 2002; Bentov and Erez, 2006), and that Mg is enriched in the organic mineral templates used in shell formation by the planktic foraminifer Orbulina universa (Branson et al., 2016). Foraminiferal Mg/Ca therefore cannot be considered analogous to inorganic calcite, and identifying and quantifying nontemperature controls on foraminiferal Mg/Ca is needed to ensure the proxy can be used as a robust palaeothermometer. Foraminifera culturing studies have been essential for isolating non-temperature controls on foraminiferal Mg/Ca that are otherwise obscured by covariation with temperature in nature. Studies of planktic foraminifera have identified a positive linear relationship between Mg/Caforam and salinity (Kısakürek et al., 2008; Dueñas-Bohórquez et al., 2009; Hönisch et al., 2013), a negative relationship between Mg/Ca and seawater pH and/or [CO32-]sw which is more

pronounced at lower pH (<8.2) and [CO32-]sw (<200 µmol/kg) (Lea et al., 1999; Russell et al., 2004; Kısakürek et al., 2008; Allen et al., 2016; Evans et al., 2016a), and a positive non-linear dependence of Mg/Caforam on the seawater Mg/Ca ratio (Mg/Casw) when [Mg]sw is modified (Delaney et al., 1985; Evans and Müller, 2012; Evans et al., 2016b). Studies of shallow benthic species have found the Mg/Caforam of both low- and high-Mg calcite secreting foraminifera to depend strongly on Mg/Casw (Segev and Erez, 2006; Raitzsch et al., 2010; Dissard et al., 2010; Dueñas-Bohórquez et al., 2011; Mewes et al., 2014; Evans et al., 2015). In high-Mg calcite producing species (e.g., Amphistegina lobifera, Amphistegina lessonii, Heterostegina depressa, Operculina ammonides), Mg/Caforam varies with Mg/Casw irrespective of whether [Mg]sw or [Ca]sw is modified (Segev and Erez, 2006; Raitzsch et al., 2010; Dueñas-Bohórquez et al., 2011; Mewes et al., 2014; Evans et al., 2015), whereas in the low-Mg calcite forming Ammonia tepida the Mg/Caforam vs. Mg/Casw relationship changes depending on whether [Mg]sw or [Ca]sw is modified (Dissard et al., 2010; Raitzsch et al., 2010; Dueñas-Bohórquez et al., 2011; Table 1). Attempts to correct the Mg/Ca palaeothermometer for non-temperature influences have focused on Mg/Casw as a modifier of the pre-exponential term (B) in Equation 2. In the absence of detailed experimental evidence, the influence of Mg/Casw on Mg/Caforam was initially assumed to be linear (e.g., Lear et al. 2000, 2002). After dedicated culturing work to identify the form of this relationship, it was later defined as a power-law function (Hasiuk and Lohmann, 2010; Evans & Müller, 2012), and subsequently revised to include a quadratic dependence on Mg/Casw in the exponential term (Evans et al. 2016b). These corrections have been applied to palaeotemperature reconstructions where Mg/Casw differs from modern (e.g., Dunkley Jones et al., 2013; Kozdon et al., 2013; O’Brien et al., 2014; Martínez-Botí et al., 2015). They do not, however, capture the full range of other influences on Mg/Caforam (Gray & Evans, 2019).

Accounting for the combined influences of seawater temperature, carbon and cation chemistry on Mg/Caforam has so far been impossible because their respective effects have been quantified only in isolation. Quantifying non-thermal influences on Mg/Ca is essential if palaeothermometry is to be applied in deep geological time where temperature, seawater composition, pH and carbon content have varied in ways that are not found in the modern ocean. Here, we develop a new empirical model for the Mg/Ca palaeothermometer. Our model is based on a combination of previously published Mg/Ca data and new Mg/Ca measurements of Orbulina universa cultured in conditions where [Ca]sw, [Mg]sw, dissolved inorganic carbon (DIC), pH and temperature were varied independently and simultaneously (Figure 1). Together, these data reveal O. universa Mg/Ca is best predicted by temperature, Mg/Casw, [Ca]sw and DIC. We expand this model to explore its applicability to other foraminifer species and evaluate its implications for applying the Mg/Ca palaeothermometer in deep time, using the PaleoceneEocene Thermal Maximum as an illustrative example.

2. Methods 2.1. Foraminifera culturing

Foraminifera were hand-collected by SCUBA divers and cultured following established methods (e.g. Russell et al, 2004; Allen et al. 2011, 2012) at the Wrigley Institute for Environmental Studies (WIES) on Santa Catalina Island, California over several field seasons (2008, 2011, 2013 and 2014) in chemically manipulated seawater (online supplement, “Data/Compiled_Mg_data.xlsx”). Individual foraminifera were grown in 120 ml Wheaton jars, isolated from the laboratory atmosphere by Parafilm™ and tight-fitting lids, and incubated in constant-temperature water baths under a 12hr/12hr light/dark cycle at PAR irradiance level >300 µmol photons m-2 s-1 for the duration of the experiments. Experimental seawater with compositions different from modern seawater was prepared either by combining natural and artificial seawater to reduce the concentration of cations (e.g., 0.5x Mg/Casw, 0.5x [Ca]sw) and/or anions (0.5x DIC), or by adding salts to increase their concentration (e.g., 2x Mg/Casw, 2x [Ca]sw, 2x DIC). Natural seawater was collected at the dive site and filtered through a 0.8 µm cellulose nitrate membrane. Artificial seawater was synthesised by dissolving high purity (Analytical Reagent grade) salts into MilliQ water (18 ; see Supplementary Material, “Seawater_Recipe.xlsx” for details; Millero, 1974). [Mg]sw and [Ca]sw were varied by dissolving MgCl2 and/or CaCl2 into artificial seawater, and mixing with natural seawater, or by adding aliquots of a stock CaCl2 solution to natural seawater. Salinity was held constant in all treatments by adjusting the amount of NaCl added to the artificial seawater. Low DIC seawater (~ 1000 µmol kg-1) was made by combining equal portions of natural and DIC-free seawater, which was made by acidifying natural seawater to pH ~4 and bubbling with N2 gas to remove CO2. High DIC seawater (~ 4000 and 8000 µmol kg-1) was made by dissolving NaHCO3 into natural seawater. Twenty experiments included in this study contained 5x [B]T of

modern seawater, produced by the addition of B(OH)3. The pH of all treatments was determined with a pH electrode (Metrohm combined pH glass electrode) calibrated to NBS buffers and titrated to the target experimental pH with either 0.1M NaOH or 0.1M HCl. 2.2. Seawater chemistry analysis

Samples of experimental seawater were taken at the beginning and end of each experiment for trace element analysis. Aliquots were filtered using 0.2 µm syringe filters and then acidified (pH < 3) using OptimaTM grade HNO3 or HCl to preserve trace metals for analysis and prevent microbial activity in the sample container. Trace metal compositions in experimental seawater were determined using a Varian Vista Pro Axial ICP-AES and a Varian 820 Quadrupole ICP-MS at the Research School of Earth Sciences (RSES), Australian National University (ANU). Seawater samples were diluted 10x with 2% HNO3 prior to ICP-AES analysis and 100x prior to ICP-MS analysis. The reproducibility of measured Mg/Ca ratios in seawater reference material CASS-4 was ±2.0% (2σ) by ICP-MS and ±0.8% (2σ) by ICP-AES. Instrument drift during ICPOES analysis was corrected for using a standard-sample-standard bracketing protocol. Internal element and enriched isotope standards (9Be, 45Sc, 141Pr and 235U) were added to diluted sample solutions were used to monitor and correct for instrument drift and sample-specific mass bias changes during ICP-MS analysis. 2.3. Seawater carbon chemistry analysis and calculation

Total alkalinity and pH of seawater were measured at the beginning and end of each experiment. Alkalinity was measured using a Metrohm open cell auto-titrator which was calibrated daily to Dickson certified alkalinity standards or an in-house standard of filtered ambient seawater that was calibrated against the Dickson standard. Seawater pH was measured using a Metrohm combined glass electrode calibrated against NIST NBS buffer solutions. All

carbonate system measurements were conducted at 25 °C. The pHNBS at measurement temperature is provided in the supplemental data file, but throughout the manuscript and model fitting all carbon system parameters are at experimental temperatures, and pH is reported on the Total scale (pHT). Conversion from measured to culture conditions and between pH scales was achieved following standard methods (e.g. Zeebe & Wolf-Gladrow, 2001), whereby measured pHNBS and alkalinity are used to calculate pHT and DIC at measurement conditions (salinity, temperature and cation composition), then DIC and alkalinity are used to calculate pHT and carbon speciation at the experimental temperature. The chemical composition of seawater affects the stoichiometric equilibrium constants (K*s) by changing the activity of carbonate species through ion-pairing interactions (Garrels & Thompson, 1962; Ben-Yaakov & Goldhaber, 1973; Zeebe & Wolf-Gladrow, 2001; Tyrell & Zeebe, 2004; Hain et al., 2015; Zeebe & Tyrell, 2018; Hain et al., 2018). It is therefore necessary to account for these variations when calculating carbon parameters in our modified seawater conditions. Hain et al. (2015, 2018) developed MyAMI, a specific ion interaction model to adjust modern K* values (the ‘conditional equilibrium constants’, cf. K the equilibrium constant) for modified [Ca]sw and [Mg]sw. However, some concerns have been raised over the accuracy of this approach (Zeebe & Tyrrell, 2018). To overcome this uncertainty, we employ both MyAMI (Hain et al., 2015) and the Pitzer ion interaction model within PHREEQC (Parkhurst and Appelo, 2013). In both cases, each model was used to calculate a solution-specific correction factor, fcond, for the K* in our experiment condition (Kexp), following: Kexp = Ksw*fcond

(4)

fcond = cKcond / cKsw

(5)

In each experimental condition Kexp is derived from the empirically determined seawater value (Ksw) and correction factors (fcond) calculated from modelled K*s at the experimental (cKcond) and ambient seawater (cKsw) conditions by both MyAMI and PHREEQC. The full carbon system was then calculated from measured alkalinity, pHNBS and these adjusted K*s using the cbsyst Python module (doi:10.5281/zenodo.1402261). Carbon system parameters estimated using the two approaches differ slightly (Figure S1), but are generally within the analytical uncertainty of pHT and alkalinity (which are on average < ± 0.05 pH units and < ± 15 µmol kg-1) and varied less than the differences between experimental conditions. Reported carbon speciation values are the mean of the two estimates, and the reported uncertainty is the larger of either the measurement uncertainty, or the difference between the two carbon speciation calculation methods (see electronic supplement, ‘Complete Data Analysis (as published)’). 2.4. Foraminifera preparation and analysis

Orbulina universa tests were cracked open, oxidatively cleaned following Pak et al. (2004), and mounted on carbon tape for analysis by laser ablation ICP-MS (LA-ICP-MS) using a Varian 820 Quadrupole ICP-MS coupled to an ArF excimer laser (λ = 193 nm, pulse length FWHM = 25 ns) via an ANU Helex laser ablation system at the Research School of Earth Sciences (RSES, ANU), following Eggins et al. (2003). Laser ablation sampling was undertaken with uniform laser fluence of ~2 J cm-2, a 3 Hz pulse rate and a 70 µm spot. Isotopes 24Mg, 25Mg, 43Ca and 44Ca

were measured simultaneously using a rapid peak hopping protocol with dwell times

between 10 and 30 ms for each analyte. Three depth profile analyses were acquired through the test wall of each fragment.

Data were reduced using well established procedures for time resolved analyses (Longerich et al., 1996) following Eggins et al. (2003, 2004). Background noise measured with the laser off is subtracted from analyte intensities. The NIST SRM 610 glass is used as a calibration standard and variation in ablation yield and instrument drift were corrected for using 43Ca as an internal standard (Eggins et al., 2003, 2004). Average shell Mg/Ca is calculated by integrating the entire laser-ablation depth profile, excluding regions where the 43Ca signal is below a threshold value and the trace-element enriched pulse at the start of an ablation. The three measured profiles are averaged to report the mean Mg/Ca of each individual foraminifer. Reported Mg/Ca for each experiment is an average of Mg/Ca from all specimens grown in the same conditions (n = 4-28). 2.5. Data compilation

To establish a comprehensive and comparable dataset for evaluating the controls on O. universa Mg/Ca, we combined the new data from cultured O. universa from our experiments with those of Lea et al. (1999), Russell et al. (2004) and Spero et al. (2015). We observe a 15% offset between Mg/CaO. universa between our data and the data of Russell et al. (2004), but a similar temperature sensitivity. This is likely attributable to small differences in inter-lab sample preparation and/or analytical offsets between solution-ICPMS and LA-ICPMS. To make these datasets comparable, we account for this offset by applying a constant multiplier of 1.15 to our Mg/CaO. universa measurements, which quantitatively reconciles the Mg/Ca-temperature relationship at ambient conditions in the two datasets. Similarly, the data of Lea et al. (1999) are ~17% higher than that of Russell et al. (2004), but show a similar sensitivity to temperature at ambient conditions. We therefore apply a correction factor of 0.83 to their raw data to make these data directly comparable. Additionally, Lea et al. (1999) do not report alkalinity data, so we estimate this from the measured salinity of their cultures and a typical summer alkalinity

value for Santa Catalina Island seawater, calculated from the mean alkalinity of our ambient cultures (2219 mol kg-1 at a salinity of 33). We do not include O. universa Mg/Ca data from Allen et al. (2016) or Hönisch et al. (2013) in our aggregate dataset. Excluding these data does not alter the form of our model, but increases the uncertainties in the best fit parameters and the resulting predictions. A full replication of our analysis including the data of Allen et al. (2016) and Hönisch et al. (2013) is given in the online supplement (‘Complete Data Analysis (including all published data)’). We link this to an unusually large portion (>50%) of the reported variance that is not accounted for by controlled experimental variables in the Allen et al. (2016) or Hönisch et al. (2013) studies (Figure S2). While it is not possible to definitively attribute the cause of this anomalous unexplained variance, it could stem from systematic differences in test thickness associated with how long individual foraminifers survived in different treatments. Individuals that live longer in culture have thicker tests with more diurnal bands (Eggins et al., 2004; Spero et al., 2015) that tend to increase in Mg/Ca composition with age. This hypothesis is supported by systematic differences in shell diameter and longevity between treatments recorded in the culture logs for these experiments. In excluding the data of Hönisch et al. (2013) and Allen et al. (2016), we emphasise that the high unexplained variance in these datasets is restricted to Mg/Ca in O. universa, is not observed for species reported by Hönisch et al. (2013) and Allen et al. (2016), and does not appear to effect other trace element data in O. universa. We recalculate the carbon chemistry for all studies from two of pHNBS, DIC or alkalinity reported by each study, and present all data on the pHT scale at experimental conditions, following the method described in the seawater carbon chemistry calculations section.

All data (both included and excluded from the model) is provided in the online supplement (‘Data Directory/Compiled_Mg_Data.xlsx’). 2.6. Data processing and analysis

Data processing, analysis and visualisation was performed in Python 3.7 (Copyright ©20012017, Python Software Foundation), making extensive use of the NumPy (van der Walt et al., 2011), SciPy (Jones et al., 2001), Pandas (McKinney, 2010) and Matplotlib (Hunter, 2007) packages. Uncertainty propagation was handled using the ‘uncertainties’ package (Lebigot, 2019). Uncertainties on our model parameters were calculated by Monte Carlo sampling of uncertainties (Hall, 1992; Davison and Hinkley, 1997) in both independent and dependent variables over 10,000 iterations. 2.6.1. Foraminiferal Mg/Ca Uncertainty Estimation

Past studies of foraminiferal Mg/Ca report different uncertainty metrics. Studies of individual foraminifera (e.g. by LA-ICPMS) tend to report the standard deviation calculated from N individual tests, which is a good estimate of true intra-population variance when N is large. However, measurements by solution ICPMS typically report uncertainty based on repeat measurements of sample aliquots, or the long-term analytical precision. Both can considerably underestimate true intra-population variance, so cannot be interpreted as an estimate of how accurately a measurement represents the true population mean. This is particularly true for sample-limited culture studies, where the number of analysed tests is small. These uncertainty metrics are fundamentally different, and cannot be used interchangeably, making it hard to compare measurements between studies when considering aggregate data. To represent the uncertainty of our aggregate data within a consistent framework, we derive an estimated standard deviation based on analyses of multiple individual O. universa shells by

LA-ICPMS. These analyses exhibit a consistent relative standard deviation (the ratio of the standard deviation over the mean, RSD =  /  of ~0.26, which we use to estimate the standard deviation of each measurement in the dataset, then calculate the standard error of that measurement based on the number of individual tests analysed (𝑆𝐸 = 𝜎 √𝑁). Wherever the reported uncertainty for an analysis is smaller than our estimated SE, we use our estimated SE value instead of the reported value. We then calculate the 95% confidence interval for each measurement from this value using a t-distribution (95% CIIFA). Thus, the estimated SE uncertainties used in our model fits and the 95% confidence intervals represented in our figures are directly comparable between studies, and provide a consistent metric that represents the confidence that a given data point reflects the true population mean. 2.6.2. Model Selection

To identify the functional form that best describes patterns in our data, we considered temperature, DIC, [H+], [Ca]sw, [Mg]sw and Mg/Casw as potential independent variables. We tested the ability of all possible linear combinations of these variables and their logtransformations to explain the patterns in Mg/CaO. universa. Each model was evaluated using a Bayes Factor, which provides an estimate of the relative probability of the data given two candidate models based on the goodness-of-fit (R2), the number of observations, and the model degrees of freedom (Rouder & Morey, 2013). For example, the Bayes Factor (BA-B) gives the relative probability of observing the data if model A is correct, relative to if model B is correct. In simple terms, BA-B value of 5 would indicate that the data are five times more likely if model A is true, relative to if model B is true. We report Bayes Factors of any model (N) relative to the best-performing model, BN-best, and interpret these relative probabilities using the guideline criteria of Kass & Raftery (1995), which are comprised of the target model being ‘decisively less

probable’ (BN-best < 0.01), ‘strongly less probable’ (0.01 < BN-best < 0.1), ‘substantially less probable’ (0.1 < BN-best < 0.3125) and ‘not worth more than a bare mention’ (0.3125 < BN-best < 1) relative to the reference model. This evaluation was performed using the ‘brutefit’ python package (doi:10.5281/zenodo.3364898). A full description of this method is available in the online supplement (‘Model Selection Methodology’).

3. Results

Previous studies of O. universa Mg/Ca have identified systematic relationships with individual chemical and physical variables. To evaluate whether these relationships are present in our multi-variate dataset, we consider the response of our data to single experimental variable when all other variables are held constant (Figure 2). In experiments conducted at constant modern seawater [Mg]sw and [Ca]sw concentrations (referred to as our ambient condition; i.e. [Mg]sw = 50 ± 5 mmol kg-1, [Ca]sw = 10 ± 1 mmol kg-1) we observe increasing test Mg/Ca with temperature (Figure 2A), consistent with previous studies (e.g. Lea et al., 1999; Russell et al., 2004). This relationship holds for seawater with higher and lower than ambient Mg/Casw (Mg/Casw  1.3 to 10; Figure 2A). We observe systematic increases between test Mg/Ca and DIC at three different Mg/Casw conditions (Mg/Casw  1.3, 5 and 10; Figure 2B). In contrast to previous studies of O. universa (Lea et al., 1999; Russell et al., 2004; Spero et al. 2015; Allen et al., 2016), we observe no clear relationship between Mg/Ca and pHT at any Mg/Casw (Figure 2C). A number of our low-pH experiments were conducted in seawater with elevated (5x) ambient [B]T (~ 2 mmol kg-1) which might act to suppress the influence of pH through buffering effects at the site of calcification (Hönisch et al., 2003; Zeebe et al., 2003). If significant, this could obscure relationships between Mg/CaO. universa and seawater pH, however, we observe no systematic effect of [B]T on Mg/CaO. universa (Figure S3), suggesting elevated [B]T does not bias our results. In experiments where temperature, DIC and pH are held at ambient conditions (T = 22 °C, DIC = 2100 ± 200 µmol mol-1, pHT = 8.1 ± 0.2) we observe clear trends between the Mg/CaO. universa and [Mg]sw at ambient [Ca]sw (Figure 2D), with [Ca]sw for a range of [Mg]sw

concentrations (Figure 2E), and with Mg/Casw (Figure 2F). This is consistent with results from G. ruber where seawater [Mg]sw was varied (Evans et al. 2016b). Across the range of experimental conditions investigated, Mg/Casw exhibits the largest influence on test Mg/Ca. This is evident in the relatively small residual around the relationship between Mg/Casw and Mg/CaO. universa (Figure 2F) and in most data obtained outside ambient conditions lying within the envelope defined by the high-Mg/Casw and low-Mg/Casw trends (Figure 2A-C). To identify secondary controls on test Mg/Ca, we normalise our data to Mg/Casw, and consider DMg (DMg = Mg/Casolid / Mg/Casolution). We find DMg to be influenced by temperature (Figure 3A), DIC (Figure 3B) and [Ca]sw (Figure 3E). The way Mg/Casw is changed, either by [Mg]sw or [Ca]sw, has a significant effect on Mg partitioning, as can be seen in the large change in DMg that occurs when [Ca]sw is varied (Figure 3E) compared to the small change when [Mg]sw is varied (Figure 3D). Seawater pHT and [Mg]sw (Figure 3C-D) show no clear systematic influence on DMg, although we do tend to observe greater variability in DMg at lower pHT. Our analysis to this point has focused on identifying the influence of individual parameters on Mg/CaO. universa and DMg in univariate subsets of the data. While conceptually useful, this approach neglects the multi-variate nature of our data, and provides limited insights into controls over Mg/Ca. To fully explore controls on foraminiferal Mg/Ca, we employ a multi-variate model which simultaneously accounts for all observed variables on Mg/CaO. universa.

4. Discussion 4.1. A new model for foraminiferal Mg/Ca

Our data reveal that O. universa Mg/Ca is modulated by Mg/Casw, temperature, [Ca]sw and DIC. Contrary to previous studies, the data do not support the inclusion of pH or [CO32-]sw as significant terms in the model fit. Mg/Casw exerts a primary control on foraminiferal Mg/Ca (Figure 2), and temperature, [Ca]sw and DIC exert secondary influences on the partitioning of Mg into the test (DMg; Figure 3). The functional form that best describes these influences, is: (

)

Mg/CaO. universa = Mg/Casw𝐴 ∙ 𝐷𝐼𝐶𝐵sw ∙ 𝑒𝑥𝑝 𝐶 ∙ [𝐶𝑎]𝑠𝑤 + 𝐷 ∙ 𝑇 + 𝐸

(6)

The A and B terms describe the dependence of the pre-exponential term on Mg/Casw and DIC (Figure 2D and F) as power-law functions. In the case of Mg/Casw this behaviour is consistent with Freundlich adsorption isotherm behaviour (Hasiuk and Lohmann, 2010). The exponential terms, C and D describe the dependence of the exponential term on temperature and [Ca]sw. This equation provides an empirical description of the combined influences of biological and crystal growth processes on Mg incorporation, which are yet to be fully described. Equation (6) was found to be the best of 729 candidate models composed of linear combinations of the candidate independent variables temperature, Mg/Casw, [Ca]sw, [Mg]sw, [H+] and DIC. All other models ranged from ‘substantially’ to ‘decisively’ less probable (Kass & Raftery, 1995) than our best models. The best-performing model which includes pH as a variable is less probable than our best model, with BN-best = 0.39. This indicates that there is likely a minor pH-effect present in the data, but its inclusion in the model is not justified by the aggregate dataset comprising Lea et al. (1999), Russell et al. (2004), Spero et al. (2015) and this study. The outcome is substantively unchanged by the inclusion of data from Allen et al. (2016) and Hönisch et al. (2013), although when these data are included the best-performing model with a pH term obtained a BN-best = 0.12, indicating that these data do not add evidence to support the

inclusion of a pH-term. The absence of a significant pH effect is in line with the results of Tierney et al. (2019), who report the inclusion of a pH term degrades the performance of the BAYMAG model. We also calculate Bayes Factors for previously proposed model forms (Anand et al., 2003; Evans and Müller, 2012; Evans et al., 2015; Gray & Evans, 2019), all of which were decisively less probable than our best model (Figure S5). The best previously proposed model is that of Evans & Müller (2012; BN-best = 2x10-11), although a modification of Gray & Evans (2019) to include Mg/Casw in the pre-exponent performed marginally better (BN-best = 4x10-11). To assess the skill of our model, we present predicted Mg/CaO. universa calculated using our best model vs. measured Mg/CaO. universa (Figure 4A), and the predicted temperature using the best model fit parameters vs. measured temperature (Figure 4B). Uncertainties represent the 95% confidence interval derived from inter-individual variability of O. universa, providing an internally-consistent reference for determining the goodness-of-fit of the model to data with low n. Some parameters in our model exhibit substantial covariance, particularly between terms A and C and between B and E. In the case of A and C this is intuitive, as these terms relate to Mg/Casw and [Ca]sw which by definition covary, but the inclusion of both terms is clearly supported by the data, as evident in the influence of [Ca]sw on DMg (Figure 3E). The existence of parameter covariance is not a problem, given the relative strength of our model established by our exhaustive evaluation of all possible candidate models. However, the covariance between these parameters means that individual parameter confidence intervals cannot be propagated linearly to provide an uncertainty estimate of foraminiferal Mg/Ca given a particular set of environmental conditions. The parameter covariance matrix (Table S1) must be used to correctly

estimate the uncertainty associated with a model prediction. We provide functions to do this in a freely available online python module (https://foramgeochem.readthedocs.io/en/latest/). The relative magnitude and the functional form of each controlling variable on Mg/CaO. universa can be observed by using our best model fit to remove the influence of other variables (Figure 5A-D). Similarly, we may examine the influence of variables not included in the model by removing the influence of Mg/Casw, DIC, [Ca]sw and temperature to examine the effects of salinity, pH, [CO32-]sw and [Mg]sw (Figure 5E-H). For this exercise we include data from all studies (i.e. including those that were originally excluded from model fitting). Overall, the model and data show good agreement. There is a weak, significant trend between pH and normalised Mg/CaO. universa (-0.92, p=0.04), although the magnitude of this effect is smaller than the scatter in the data (SD = ±0.99 mmol/mol; Figure 5F). This trend suggests that pH exerts a relatively minor influence on Mg/CaO. universa, although the size of this trend relative to scatter in the data do not support inclusion of pH in our model formulation, as indicated by the poor BN-best of models that include pH. 4.2. Comparison to previously observed influences on O. universa Mg/Ca

At ambient seawater conditions (DIC = 2100 ± 200 µmol mol-1, pHT = 8.1 ± 0.2, [Mg]sw = 50 ± 5 mmol kg-1 and [Ca]sw = 10 ± 1 mmol kg-1) our model (Equation 6) produces a temperatureMg/CaO. universa calibration curve equivalent to that reported by Russell et al. (2004; Figure 6). Although not included in our best model fit, the majority of Mg/CaO. universa data from Allen et al. (2016) and Hönisch et al. (2013) are also consistent with the model at the 95% confidence level (Figure S6). We find limited evidence for a significant influence of pH on Mg/CaO. universa, contrary to findings reported in several previous studies (Russell et al., 2004; Spero et al., 2015; Allen et al.,

2016). Our best model fit suggests a residual pH effect that is small relative to the influence of temperature, DIC, Mg/Casw and [Ca]sw. Alternatively, it is possible that the identification of a more significant pH effect in previous studies might be biased by the large uncertainties associated with the smaller numbers of tests grown in low-pH cultures. For example, the pH effect reported by Russell et al. (2004) arises from 3 data points obtained from two low-pH treatments that comprise only 1-3 shells each. At the time when those data were published, it was not yet clear how large the inter-shell Mg/Ca variability is in planktic foraminifera, and the most ‘anomalous’ values were considered outliers and excluded from reported averages (Russell et al., 2004). We now know that intra-shell Mg/Ca variability is significant and when all points are included the data of Russell et al. (2004) are within uncertainty of our model prediction. The aggregate data show increased Mg/Ca variance at low pH (Figures 2C and 3C), consistent with the higher variability observed in the low-pH cultures and the lack of a pH effect on Mg/Ca above pHT 8.07 found in Russell et al. (2004). Allen et al. (2016) also report a pH trend in O. universa, but the large unaccountable variance in their data make this trend difficult to interpret. However, note that the DIC variability in our cultures is significantly larger than that found in the natural ocean. While this large range allows us to clearly identify a DIC-effect, it may also act to mask a more subtly pH effect which may become apparent over a narrower DIC range. Constraining the relative significant of the pH effect will require further high-N culture experiments at low pH to overcome the current limitations of intra-population variability and the increased variance observed at low pH in the data. Our best model fit does not reproduce the relationship between Mg/Ca and salinity observed by previous studies (Figure 5E; Lea et al., 1999; Hönisch et al., 2013). In our parameterisation,

the influence of salinity manifests via a change in [Ca]sw, which describes patterns in our data well (Figure S4). 4.3.

Beyond Orbulina: Mg/Ca in Globigerinoides ruber

Studies of O. universa have underpinned our understanding of foraminiferal geochemistry, biology and biomineralization, but O. universa is seldom used in palaeoceanography. To assess whether our best model fit applies to other species, we use it to estimate the Mg/Ca of Globigerinoides ruber observed in culture experiments (Kısakürek et al., 2008; Henehan et al. 2013; Hönisch et al. 2013; Evans et al., 2016a; Allen et al., 2016) and sediment trap/plankton tow samples from the Pacific, Atlantic and Indian Oceans (Gray et al., 2018; Figure 7). We exclude the temperature and salinity experiments of Kısakürek et al. (2008), where the carbon system was not measured and equilibration with atmospheric CO2 cannot be excluded as a confounding factor in the carbon system. We show fits including these data in Figure S9. We find large differences between predicted and measured G. ruber Mg/Ca values a clear residual trend with [CO32-]sw (Figure 7A). As noted by Evans et al. (2016a), pH and [CO32-]sw are tightly coupled in all G. ruber culture experiments to date, so are functionally interchangeable in these data. Accordingly, we have fit models using [CO32-]sw (Figure 7B-D) and [H+] as an alternative (Figure S7) to the data, and find these perform with similar skill. We use [H+] instead of pH to avoid the non-linearity inherent in the pH scale. Kısakürek et al. (2008), Hönisch et al. (2013) and Gray et al. (2018) report a small salinity effect on Mg/CaG. ruber, which is accounted for in our model by variations in [Ca]sw as a function of salinity, as we observe no significant trends with salinity in the model residuals (Figure S8). Previously proposed model forms for G. ruber (white; Anand et al., 2003; Evans and Müller, 2012; Evans et al., 2015; Gray & Evans, 2019) are decisively less probable compared to our best model (Figure S10). A modification of the Gray & Evans (2019) model to account for Mg/Casw performs marginally better than our model (BFN-best

= 0.81), although there is insufficient evidence to discriminate between these two top models. The exponential temperature coefficient of our model is 0.057-0.086, depending on which subset of data is considered (Fig. 7), roughly consistent with Gray and Evans (2019). The lack of significant DIC dependence in G. ruber could result from the limited DIC range, which varies only 30% in available culture experiments (Kısakürek et al., 2008; Henehan et al., 2013; Hönisch et al., 2013; Evans et al., 2016a; Allen et al., 2016). Alternatively, it could reflect a biophysical and/or biochemical difference between O. universa and G. ruber. Culture experiments designed to explicitly isolate the effects of DIC from [CO32-]sw and pH in G. ruber are required to further investigate and resolve the apparent differences between these species. 4.4. Implications for Mg/Ca seawater thermometry

The relationship between Mg/Caforam and temperature is modified by Mg/Casw and DIC (or [CO32-]sw or pH) in the pre-exponent, and by [Ca]sw in the exponent. This requires foraminiferal Mg/Ca seawater thermometry to account for past changes in these variables to recover quantitative estimates of absolute or relative seawater temperature. The [Mg]sw and [Ca]sw of the ocean have changed significantly over long timescales (tens of My; Sandberg, 1983; Hardie, 1996) and must be taken into account to reconstruct long-term absolute trends in temperature. Carbon in the atmosphere and ocean can vary on shorter timescales and may be coupled with temperature excursions (e.g. Petit et al., 1999; Hönisch and Hemming, 2005; Henehan et al., 2013), the sizes of which are a target for constraint using Mg/Ca palaeothermometry. This requires both estimates of [Mg]sw and [Ca]sw at the time of the excursion, and the change in carbon chemistry across the excursion to be well-characterised, as these factors modify the sensitivity of Mg/Caforam to temperature.

For palaeoceanographic applications, it is useful to consider the relative sensitivity of Mg/CaO. universa to individual environmental variables that have changed in the past (Figure 8). For modern seawater with Mg/Casw of 5.17 mmol kg-1, [Ca]sw of 10.2 mmol kg-1 and DIC of 2100 µmol kg-1, a temperature increase from 22 to 23 °C will increase Mg/CaO. universa from 7.24 to 7.90 mmol mol-1; an increase of 0.66 mmol mol-1 or ~9.1%. This is consistent with the temperature sensitivity reported by Lea et al. (1999) and Russell et al. (2004), but higher than the temperature sensitivities of ~6% for other species of planktic foraminifera reported in recent studies (Gray & Evans, 2019; Tierney et al., 2019). An equivalent change in Mg/CaO. universa could be caused by a 3.84 mmol kg-1 (38%) increase in [Ca]sw, a 590 µmol kg-1 (29%) increase in DIC or a 0.6 mol mol-1 (12%) increase in Mg/Casw relative to modern seawater. If two or more of these variables change simultaneously, a similar increase in Mg/CaO. universa could be caused by smaller changes in each contributing variable. The magnitudes of these changes are within the range of the long-term natural variation of these variables, such that any observed change in Mg/Caforam in a palaeoceanographic record should carefully consider the changes in and relative influence of these variables. 4.4.1. The influence of [Mg]sw and [Ca]sw

Variation in Mg/Casw over millions of years is driven by changes in rates of seafloor spreading, dolomite formation, and changes to weathering inputs (Hardie, 1996). Model and carbonate proxy estimates indicate a decrease in [Ca]sw and an increase in Mg/Casw over the last ~120 My (Figure 9A-B; Dickson, 2002, 2004; Horita et al., 2002; Lowenstein et al., 2003; Fantle and DePaolo, 2005, 2006; Timofeeff et al., 2006; Coggon et al., 2010; Brennan et al., 2013; Rausch et al., 2013; Gothmann et al., 2015; Evans et al., 2018). Reconstructed Mg/Casw is significantly lower in the past than the modern value of ~5.1 mol mol-1, reaching ~1.3 mol mol-1

at ~100 Mya (Sandberg, 1983; Coggon et al., 2010). Our model indicates lower Mg/Casw drives lower Mg/CaO. universa and produces a shallower Mg/Ca- temperature relationship, meaning a larger temperature change is required to cause an equivalent change in Mg/CaO. universa (Figure 2A, Figure 8A and Figure 9C). This is consistent with the findings of previous studies (O’Brien et al. 2014; Evans et al. 2016b). Estimates of past [Ca]sw decrease linearly from ~30 mmol kg-1 to 10.2 mmol kg-1 over the past 120 million years (Horita et al., 2002; Lowenstein et al., 2003, 2005; Brennan et al., 2004, 2013; Figure 9A). All else being equal, the relationship between Mg/CaO. universa and temperature is steeper at higher [Ca]sw. This allows smaller changes in temperature to be recorded by the proxy (Figure 8B), and higher [Ca]sw in the past partly cancels out the effect of lower Mg/Casw (i.e. Figure 2F and Figure 3E). However, [Ca]sw change also modifies Mg/Casw which exerts a stronger influence on Mg/Caforam (Figure 8A) and results in a lower overall sensitivity of Mg/Caforam to temperature (Figure 9C). In ancient oceans, foraminiferal Mg/Ca will therefore change less for a given temperature change than in the modern ocean. This works to reduce the signal to analytical uncertainty ratio and our ability to resolve smaller temperature variations in the past. Conversely, an equivalent change in Mg/Caforam in the past translates into a larger temperature change than in the modern ocean. 4.4.2. The influence of DIC

Temperature excursions in the past often co-vary with changes in pCO2, and can be associated with ocean pH, [CO32-]sw or DIC change (e.g. across glacial/interglacial cycles, Sigman & Boyle (2000), or during transient hyperthermal events, Penman et al. (2014)). Elevated seawater DIC results in higher Mg/CaO. universa at a given temperature and our model predicts O. universa growing in seawater with higher DIC will record a smaller temperature

change for a specific change in Mg/CaO. universa (Figure 8C). Thus, in an excursion where warming and DIC co-vary positively (e.g., the PETM; Zachos et al., 2010; Penman et al., 2014), both will contribute to increased Mg/CaO. universa, and the size of the calculated temperature excursion across a hyperthermal will be reduced by accounting for the contribution of DIC. 4.4.3. Uncertainty in temperature predictions

Constraining the influence of Mg/Casw, [Ca]sw and carbon chemistry on Mg/Caforam allows uncertainties in these parameters to be included in temperature reconstructions. In general, this increases the uncertainty of the palaeothermometer, and reduces its power to resolve small temperature excursions. While inconvenient, these previously unconstrained uncertainties can now be quantified and deliver improved confidence in past temperature estimates. The uncertainty in temperature reconstructions can only be reduced by better constraining the input parameters: Mg/CaO. universa, Mg/Casw, [Ca]sw, carbon chemistry and the model coefficients. To focus future efforts, we have conducted an uncertainty analysis (Figure 10), to identify how uncertainties propagate through our new temperature equation:

(

𝑙𝑛

𝑇=

)

Mg Ca O. universa Mg Ca𝐴 ∙ DIC𝐵 sw

― 𝐶 ∙ [𝐶𝑎]𝑠𝑤 ― 𝐸

𝐷

(7)

Uncertainties in Mg/Casw exert the strongest influence on estimated temperature uncertainties, particularly when Mg/Casw is low (Figure 10A), making it the primary target for reducing the uncertainty of temperature estimates for ancient oceans. Uncertainty in [Ca]sw, which modifies the exponent, exerts a relatively minor influence on propagated temperature uncertainty (Figure 10B), such that gains achieved by reducing [Ca]sw uncertainty will primarily come from concomitant reductions in Mg/Casw uncertainty. There are relatively large uncertainties in both the [Ca]sw and Mg/Casw through time (Figure 9A-B), requiring both to be included where the goal is to reconstruct long-term temperature changes. However, for

reconstructions over periods shorter than the residence times of Mg and Ca in seawater, an argument can be made to use constant [Mg]sw and [Ca]sw, as the large propagated uncertainties from [Mg]sw and [Ca]sw would otherwise obscure temperature excursions. In such cases, the most important sources of temperature uncertainty derive from DIC (Figure 10C) and Mg/Caforam (Figure 10D), although it is also essential to include estimates of Mg/Casw and [Ca]sw, as these interact with DIC to alter the slope of the Mg/CaO. universa-temperature relationship (Equation. 7; e.g. Modern vs. PETM in Figure 10C-D). We further note that the Mg/Caforam value alters how uncertainties propagate through the model, as it is a non-linear term in Equation 7. Collectively, the uncertainties of our model coefficients produce a minimum uncertainty of ~±1°C, evident in the y-intercept values in Figure 10. Reducing these uncertainties for O. universa, or estimating them accurately for other species, will require substantial further culturing and calibration work, spanning the entire matrix of conditions considered in this study. 4.5. Case Study: Assessment of PETM seawater temperature change

The PETM (~56 Ma) is a transient hyperthermal period in Earth history caused by a massive release of isotopically light carbon into the ocean and atmosphere resulted in global warming (Dickens et al., 1997). It is marked by a large negative excursion in terrestrial and marine δ13C records, termed the carbon isotope excursion (CIE; Bralower et al., 1997; Kennett and Stott, 1991; Koch et al., 1992; Zachos et al., 2005). The PETM has been widely studied as a natural analogue for anthropogenic fossil carbon release, as it provides an opportunity to examine climate feedbacks and responses to rapid increases in atmospheric carbon dioxide (e.g. Zachos et al., 2003, 2005, 2010; Dunkley-Jones et al., 2013; Penman et al., 2014; Gutjahr et al., 2017). Foraminiferal Mg/Ca records across the PETM are restricted to extinct species of foraminifera, which have been interpreted to date using modern multi-species calibrations, such as that of Anand et al. (2003), to estimate temperature changes (e.g. Zachos et al., 2003; Dunkley Jones et

al., 2013; Penman et al. 2014, Babila et al., 2016; Frieling et al., 2017). This approach produces an estimated low-latitude temperature increase of ~5 °C at the PETM (e.g. Penman et al., 2014). However, it does not account for Mg/Casw and [Ca]sw at the time, which were substantially different from modern (Mg/Casw = 1.90 ± 0.25 and [Ca]sw = 20.9 ± 0.8; Figure 9A-B), nor the excursion in seawater DIC, which is estimated to have increased by between 300 and 3000 µmol kg-1 across the PETM (Zeebe et al., 2009; Gutjahr et al., 2017; Haynes et al., 2017). To evaluate the potential impact of seawater Mg/Casw, [Ca]sw and DIC on PETM temperature estimates, we use our new Mg/Ca-temperature relationship to re-interpret the PETM Mg/Ca record of the mixed layer dwelling planktic foraminifer Morozovella velascoensis (Ocean Drilling Program (ODP) site 1209; Figure 11A; Penman et al., 2014). To facilitate the application of our model to this illustrative example we scale our O. universa model to match the lower Mg/Ca of other planktic foraminifera species. To do this, we modify the constant offset term (E in Equation 6) to -0.27 ± 0.5 such that our model reproduces the trend in the multispecies data of Anand et al. (2003). This modification reduces the absolute Mg/Ca predicted by our model while retaining the sensitivity of Mg/Ca to environmental parameters determined from O. universa (parameters A, B, C and D), which are not constrained in the Anand et al. (2003) data set, or in extinct species. We opt to use the DIC sensitivity of O. universa because it is better constrained than the influence of pH or [CO32-]sw on G. ruber. However, we emphasise the shortfalls of this approach, as the sensitivity of M. velascoensis and other extinct species to environmental variables remains largely unknown, rendering our approach arbitrary and this example purely illustrative. The carbon system sensitivities of extinct species may be constrained in future by combinations of Mg/Ca with other tracers. We do not attempt a pH or [CO32-]sw

correction, or a dissolution correction to the Mg/Ca data. Our evaluation method and all corresponding data are provided in the online supplements. Applying the multi-species calibration of Anand et al. (2003) to the M. velascoensis data yields a temperature change of 4.4 ± 0.7 °C. Incorporating the [Mg]sw and [Ca]sw of PETM seawater, we calculate a temperature change across the PETM of 4.2 ± 0.6 °C (Figure 11B). This is within error of the temperature excursion estimated using the calibration of Anand et al. (2003), but our absolute temperature estimate is ~5 °C higher (Figure 11B). These results are similar to those calculated using the equation of Evans & Müller (2012), which predicts a warming of 4.1 ± 0.6°C and similar higher absolute temperatures (Figure 11B). Accounting for changes in [Mg]sw and [Ca]sw substantially modifies our absolute temperature estimates, but has a negligible effect on relative temperature change across the PETM. Our peak temperature estimates of ~34°C are consistent with values up to 36°C reported using a variety of proxies (see Dunkley-Jones et al. (2013) for a review). However, the analysis so far neglects DIC, which also changes across the PETM, and acts to increase Mg/Caforam. Existing estimates for the size of the seawater DIC excursion across the PETM range from ~350 µmol kg-1 to ~2500 µmol kg-1 (Figure 11C). The lowest value is based on the LOSCAR carbon cycle model of Zeebe et al. (2009) and is estimated from deep-sea carbonate dissolution records. A higher value of ~700 µmol kg-1 has been derived using the cGENIE Earth System Model constrained by paired foraminiferal 11B and 13C (Gutjahr et al. 2017), and the highest estimate comes from Haynes et al. (2017) who used paired 11B and B/Ca to estimate DIC. We note that Haynes et al. (2017) recognized this estimate to be too high given it results in positive carbonate saturation anomalies when paired with ocean pH estimates from boron isotopes. We

evaluate the impact of each candidate DIC scenario on the estimated PETM temperature excursion (Figure 11D). The magnitude of the DIC excursion has a substantial effect on the PETM warming estimated from Mg/CaM. velascoensis (Figure 11D). The DIC excursions of ~350 and ~700 µmol kg-1 (Zeebe et al., 2009; Gutjahr et al., 2017) reduce the PETM warming from +4.2 ± 0.6 °C (Figure 9B) to +3.9 ± 1.0 °C and +3.1 ± 0.9 °C, respectively (Figure 11D). The much larger ~2500 µmol kg-1 excursion (Haynes et al., 2017) produces an initial negative temperature change of -1.7 ± 2.4 °C and delays warming until much later in the CIE (Figure 11D). This high DIC result is inconsistent with multiple strands of evidence for early and even pre-PETM warming at the PETM (Sluijs et al., 2007; Dunkley-Jones et al., 2013), and suggests the DIC change estimated by Haynes et al. (2017) is indeed too large. Nonetheless, it highlights the potential important influence of carbon chemistry on Mg/Ca-derived temperature records, and that the size of temperature excursion calculated from Mg/Caforam is increasingly damped by the size of the DIC excursion. Placing accurate constraints on the size and evolution the PETM temperature excursion clearly requires precise knowledge of the timing and magnitude of DIC change. If the temperature change across the PETM can be independently constrained, it may be possible to use our new model to constrain DIC from Mg/Caforam. The oxygen isotopic composition of foraminifera provides an independent constraint on the temperature excursion across the PETM. The δ18O of M. velascoensis measured at ODP site 1209 suggests a temperature change of only 2.5°C, which is inconsistent with larger Mg/Ca-derived temperature excursion estimates. This inconsistency has been attributed to poor foraminifera shell preservation (Dunkley-Jones et al., 2013) or to accompanying changes in surface ocean δ18O

and salinity (Zachos et al., 2003; Harper et al. 2017). Our model provides an alternative explanation, namely that the DIC rise magnified the Mg/Ca change relative to the actual temperature change. To explore this possibility, we combine the temperature change constrained by M. velascoensis δ18O with Mg/Ca records of both Zachos et al. (2003) and Penman et al. (2014) from ODP site 1209 to estimate DIC across the PETM (Figure 12). It is important to note the δ18O record used here is not corrected for possible pH effects (Uchikawa and Zeebe, 2010), nor is it corrected for δ18Osw changes across this event. We assume a constant δ18Osw value of 0.47 ‰, as in Dunkley-Jones et al. (2013). The observed changes in δ18O and Mg/Caforam across the PETM combine to provide an initial DIC excursion estimate of 1151 ± 675 µmol kg-1, and evidence for a second DIC pulse of 1464 ± 1290 µmol kg-1 beginning ~50 Kyr after onset of the CIE (Figure 12B). The initial excursion is higher than modelled estimates for the DIC release across the PETM (Zeebe et al., 2009; Gutjahr et al., 2017) and about half the proxy data-based estimate (Haynes et al., 2017). The second DIC pulse larger than the first, but aligns well with secondary peaks in both the DIC estimates of Zeebe et al. (2009) and Haynes et al. (2017). However, it could be caused by an artefact of other influences on the δ18O and Mg/Caforam records, for example diagenetic alteration. Considerable uncertainties aside, this example further serves to demonstrate the importance of accounting for the influences of both DIC and temperature on Mg/Caforam.

5. Conclusions

In addition to temperature, the Mg/Ca of Orbulina universa tests is sensitive to seawater Mg/Casw, [Ca]sw and DIC. The influence of Mg/Casw is consistent with earlier studies, but the contributions of DIC and [Ca]sw have not been previously constrained. Contrary to earlier studies, we find limited evidence for the influence of pH on O. universa Mg/Ca, although our ability to resolve this relatively minor effect may have been limited by the large DIC range of our study. The Mg/Ca of G. ruber can be explained using a similar functional form, but requires that [CO32-]sw or [H+] is used in place of DIC. Our new empirical models describe the majority of the published data within the uncertainty limits that arise from the analysis of small numbers of tests in culture experiments. Across periods where seawater Mg/Ca, [Ca]sw and carbon chemistry deviate from modern conditions, these variables must be constrained to accurately estimate temperature from foraminiferal Mg/Ca. This has three main implications for the use of the Mg/Ca palaeothermometer: (1) Reconstruction of long-term absolute temperature trends must account for secular variations in [Ca]sw and [Mg]sw. (2) For reconstructions across climate perturbations where carbon system and temperature changes are correlated, carbon chemistry must be constrained to reconstruct temperature, or temperature must be known to calculate carbon system excursions, in addition to accounting for [Ca]sw and [Mg]sw, which modify the sensitivity of the temperature proxy. (3) The uncertainty associated with a temperature reconstruction can be more accurately estimated by propagating the uncertainties associated with Mg/Casw, [Ca]sw and carbon chemistry in past oceans.

We illustrate the importance of seawater carbon system and cation chemistry controls upon Mg/Ca thermometry by evaluating Mg/Caforam temperature estimates across the PETM using our new model. Lower Mg/Casw and higher [Ca]sw at the time of the PETM result in higher overall temperature estimates, consistent with previous studies. Larger estimates for the size of the DIC excursion at the PETM reduce the size of the calculated warming. This exercise serves to illustrate the potentially substantial effects of non-temperature influences on Mg/Caforam, and highlights the need to consider them in palaeothermometry. Online Supplementary Material

https://github.com/oscarbranson/ForamGeochem/tree/master/Supplementary/Holland_MgCa Acknowledgements

We thank Les Kinsley, Graham Nash, and Linda McMorrow for supporting chemical analysis of foraminifera tests and seawater at the RSES, ANU. We thank Malcolm Sambridge, David Heslop and Andrew Valentine for invaluable discussions of statistical methods throughout our analysis. We are grateful to the staff at USC Wrigley Institute for Environmental Studies, and over many field seasons the efforts from Caroline Baptist, Tom Bergamaschi, Elisa Bonnin, Edward Chu, Kate Davis, Steve Doo, Alex Gagnon, Brittany Grimm, Anthony Menicucci, Eric Naumann, Elliot Schoenig, Jordan Snyder, Spider Vetter, and Bill Wagman, without whom this work would not have been possible. We also thank Andy Ridgwell for access to GENIE model DIC output. Finally, we thank Will Gray and one anonymous reviewer for their constructive and helpful comments on our manuscript. This research was supported by ARC Discovery grants DP0880010, DP110103158, DP160102081, and ANU Vice Chancellors funds to SE, NSF OCE 12-32987 to BH, and NSF OCE 1261519 to ADR and JSF.

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Table 1. Summary of controls on foraminiferal Mg/Ca aside from temperature identified in culture studies. Parameter

Mg/Caforam response

Comment

Salinity

Positive linear increase

Small influence

pH or [CO32-]

Negative relationship, or no relationship (species-specific)

Most pronounced below pHT 8.07 or [CO32-] < 200 µmol kg-1

Positive non-linear increase in planktic foraminifera

Mg/Casw

Positive non-linear increase in benthic foraminifera

Characterised for increases in [Mg]sw only For high-Mg calcite species DMg responds to Mg/Casw rather than [Mg]sw or [Ca]sw For low-Mg calcite species DMg responds to [Mg]sw and [Ca]sw

Species G. ruber, O. universa, T. sacculifer

Reference Kısakürek et al., 2008 Dueñas-Bohórquez et al., 2009; Hönisch et al., 2013

G. bulloides, G. ruber, T. sacculifer, O. universa

Lea et al., 1999; Russell et al., 2004; Kısakürek et al., 2008; Allen et al., 2016; Evans et al., 2016a Delaney et al., 1985; Evans and Müller, 2012; Evans et al., 2016b Segev and Erez, 2006; Dissard et al., 2010; Raitzsch et al., 2010; Dueñas-Bohórquez et al., 2011; Mewes et al., 2014; Evans et al., 2015 Dissard et al., 2010; Raitzsch et al., 2010; Dueñas-Bohórquez et al., 2011

G. ruber, T. sacculifer A. lobifera, A. lessonii, H. depressa, O. ammonides A. tepida

Figure Captions Figure 1. A simple exponential relationship Mg/CaO. universa = 𝐵 ⋅ exp𝐴 ⋅ 𝑇 describes the increase in test Mg/Ca with temperature after correction of biases between the different culture studies to the study of Russell et al (2004; see text for details). The shaded grey bands show 95% confidence interval for the fit, and the blue line shows the exponential relationship reported by Russell et al. (2004) for reference. These fits fail to capture the full extent of test Mg/Ca variability observed with variation in [Mg]sw, [Ca]sw, DIC and pH. Coloured symbols compile data from culture experiments conducted where [Mg]sw, [Ca]sw, DIC and pH, have been varied in addition to temperature. Red symbols show experiments where seawater [Mg]sw and/or [Ca]sw was varied; blue symbols show where DIC and/or pH was varied; and purple symbols show where both [Mg]sw and/or [Ca]sw were varied concurrently with pH and/or DIC. Figure 2. Relationships between test Mg/CaO. universa and the independently varied parameters. Red and blue symbols in A, B, C and E are data cultured at Mg/Casw of 10 and 1.3, respectively. Open symbols indicate ambient Mg/Casw of 5, where aside from the parameter of interest on the x-axis, other parameters fixed at ambient conditions (temperature = 22 ± 0.2°C, DIC = 2000 ± 200 µmol mol-1, pHT = 8.1 ± 0.2). Increasing trends in test Mg/CaO. universa are observed with temperature (A) and DIC (B), no trends with pH (C), and decreasing trends with [Ca]sw (E), respectively. The trends have been fit with simple weighted linear regression using the uncertainty of each data point (see section 2.6.1). All other data for cultures beyond ambient conditions are shown as pale grey background points in each panel. The dominant influence of Mg/Casw is evident in (F). Crosses in panel (B) are results for low pH cultures, but otherwise ambient conditions, and are included to highlight the positive trend with DIC. Symbol are the same as in Figure 1, and size increases with the number (n) of foraminifera tests comprising each sample point. Figure 3. Relationships between O. universa DMg and various independent variables. Coloured points highlight differences in [Ca]sw, temperature or DIC in experiments with all other parameters fixed at ambient conditions (i.e. temperature = 22 ± 0.2°C, DIC = 2000 ± 200 µmol mol-1, pHT = 8.1 ± 0.2). Other data including all data outside the range of ambient conditions are shown as pale grey background points in each panel. Increases in DMg are observed with temperature (A), DIC (B), and with [Ca]sw (E), but there is no consistent trend with pH (C), and no change with [Mg]sw (D). The response of DMg to temperature (A), DIC (B) and pH (C) is modified by [Ca]sw. Crosses in panel (B) have low pH yet otherwise ambient conditions, and are included to highlight the trend with DIC. Symbols and symbol sizes are as in Figures 1-2. Figure 4. Plots of measured and predicted Mg/CaO. universa (A) and measured and predicted seawater temperature (B) by our best model fit. Parameter fits used to generate the predicted data are shown in (A) for units of mol mol-1 (Mg/Casw), mol kg-1 ([Ca]sw and DIC) and °C (temperature). Error bars on measured Mg/CaO. universa (A) are the larger of either the reported uncertainty or the estimated 95% confidence interval based on Mg/Ca variability in O. universa with test population sample size (see online supplement ‘Complete Data Analysis (as published’). Error bars on predicted Mg/CaO. universa (A) are propagated from model fit parameter uncertainties. Error envelopes either side of the 1:1 line in (A) represent the 95% confidence interval for the mean of pooled analyses of 4, 10 and 30 individual tests. Error bars in (B) are

propagated from Mg/CaO. universa measurement uncertainties and model parameter uncertainties. Error envelopes either side of the 1:1 line in (B) represent the 95% confidence interval of a temperature reconstruction based on Mg/CaO. universa measured from 4, 10 and 30 individual tests. The temperature uncertainty associated with measuring the Mg/Ca of 4 O. universa tests is ~ ±2.5 °C and decreases with larger n (B). There is no pattern in the model-data residual as a function of any measured seawater parameter (Figure S4). Symbols are as in Figures 1-2. Figure 5. Plot of isolated effects of different seawater variables on Mg/CaO. universa. To reveal the effect of each individual seawater variable, we subtract the influence of all other variables on measured Mg/CaO. universa using the model. The influence attributable to each variable is presented as a line with 68% and 95% confidence intervals. The scatter around this line represents the residual difference between the data and the model, incorporating both the misfit of the model and scatter in the data. Any systematic pattern in these residuals indicates an effect that is not captured by the model. All published Mg/CaO. universa culture data (both included and excluded from our model fit) are shown and used in the calculation of residuals. The top row shows parameters that are included in the model, and illustrates the power law influence of Mg/Casw and DIC on Mg/CaO. universa and the exponential influence of [Ca]sw and temperature on Mg/CaO. universa. The bottom row shows seawater variables that are not represented in the model, and reveals small but significant trend with pH and [CO32-]. Symbols are as in Figures 1-2. Figure 6. Plot of measured O. universa Mg/Ca versus seawater temperature, compared to predicted Mg/CaO. universa from our best model fit (black line) for Mg/Casw = 5 mol mol-1, [Ca]sw = 10 x 10-3 mol kg-1 and DIC = 2000 x 10-6 mol kg-1). Parameter values used to generate the predicted curve are shown in Figure 4. Error bars on Mg/CaO. universa are the larger of either the reported uncertainty or the estimated 95% confidence interval based on Mg/Ca variability in O. universa with test population sample size (see online supplement ‘Complete Data Analysis (as published)’). Error bars on the predicted temperature-Mg/CaO. universa curve fit are propagated from model fit parameter uncertainties. Figure 7. Measured and predicted G. ruber Mg/Ca. The best model fit using DIC (A), shows a strong residual trend in [CO32-]sw (or pH). This suggests Mg/Ca of G. ruber responds differently to seawater carbon chemistry than O. universa, with G. ruber potentially more sensitive to [CO32-]sw (or pH which co-varies with [CO32-]sw in the data set, as illustrated by an alternative version of this figure using [H+]sw instead of [CO32-]sw, Figure S7). When either [CO32-]sw or [H+]sw is used in place of DIC, patterns in cultured (B) and combined cultured and sediment-trap (C) G. ruber (white) and cultured G. ruber (pink) (D) are predicted well by our model, and there are no trends in the residuals with other seawater parameters (Figure S8). The model A term is unconstrained for the sediment trap data due to invariance of Mg/Casw in the modern ocean, so was set to the value obtained for cultured G. ruber (white), allowing values for B, C, D and E to be fit. Parameter fit values and 95% confidence intervals are shown in panels B, C and D. Error bars show uncertainties reported in the original studies (± 2 standard deviations of the long-term instrument measurement error). It was not possible to estimate 95% confidence intervals for measured data (as with O. universa), as the within population variability of G. ruber has not yet been determined. Error bars for predicted values have been propagated from model parameter uncertainties. Units used in the model are mol mol-1 (Mg/Casw), mol kg-1 ([Ca]sw and [CO32-]sw) and C (temperature).

Figure 8. Plots illustrating the influence of (A) Mg/Casw, (B) [Ca]sw and (C) DIC on the relationship between Mg/Ca and temperature calculated using the best-fit parameters for O. universa. Each panel shows how the relationship between temperature and Mg/CaO. universa varies with a particular variable as all other input variables are kept constant at values specified in each panel. Thicker black lines indicate the relationship for modern seawater, and the grey areas indicate seawater compositions that lie outside the geological record for the past 120Ma. Figure 9. Changes in [Ca]sw and Mg/Casw ratio over the past 120 My, and their corresponding influence on how Mg/CaO. universa records temperature. [Ca]sw is notable for having decreased following an approximately linear trend (A) interpolated from ranges of reconstructed [Ca]sw indicated by the grey boxes. Mg/Casw has increased (B), and together with [Ca]sw modifies both the absolute Mg/CaO. universa at a given temperature, and the sensitivity of Mg/CaO. universa to temperature change (C). Assuming constant DIC, an O. universa with ~4 mmol mol-1 Mg/Ca growing in the modern ocean with (Mg/Casw = 5 mol mol-1 and [Ca]sw = 10 mmol kg-1) would correspond to a seawater temperature of ~15C, whereas the same Mg/Ca value 60 My ago would correspond to a temperature of ~21C. [Ca]sw changes are linearly interpolated between data points and Mg/Casw changes are calculated with a Gaussian weighted moving average. Figure 10. Plots illustrating how uncertainties in the input variables Mg/Casw (A), [Ca]sw (B), DIC (C) and Mg/CaO. universa (D) propagate into uncertainties in reconstructed temperature. Uncertainties are calculated for foraminifers with Mg/CaO. universa of 5 and 7 mmol mol-1 in modern seawater conditions (Mg/Casw = 5 mol mol-1, [Ca]sw = 10 mmol kg-1 and DIC = 2000 µmol kg-1) and for Paleocene seawater conditions (Mg/Casw = 1.5 mol mol-1, [Ca]sw = 20 mmol kg-1 and DIC = 2000 µmol kg-1). Model coefficient uncertainties are incorporated in each case, and produce the non-zero intercept in each scenario. The difference in y-axis scales should be noted for panels A-B and C-D. Figure 11. Evaluation of reconstructed temperature change across the PETM based on the M. velascoensis Mg/Ca record of Penman et al. (2014) (A) for three different proposed DIC scenarios. In the absence of DIC variation across the PETM, our model produces absolute temperatures similar to the Evans & Müller (2012) Mg/Casw calibration and a similar warming of 4.1 ± 1.0°C vs. 4.4 ± 1.8°C (B). When previously proposed DIC increases (C) are included in our model, the size of the temperature excursion is progressively reduced (D) with the size of the DIC excursion. The high +2500 µmol kg-1 DIC excursion estimates of Haynes et al. (2017) results in a negative temperature change at the PETM. Constant Mg/Casw (1.9 mol mol-1) and [Ca]sw (20.9 mmol kg-1) have been assumed for all calculations, and uncertainties have been calculated from on model parameter uncertainties and the uncertainty envelope around the smoothed Mg/Caforam record (A). Figure 12. The DIC excursion at the PETM estimated from M. velascoensis δ18O and Mg/Ca from the same core intervals. Using our model, the temperature difference calculated from δ18O (blue symbols and line in A) and Mg/Caforam (orange symbols and line in A) can be used to estimate the size and evolution of the DIC excursion across the PETM (B). The resulting calculated initial increase in DIC is larger than, but within error of previous estimates of DIC release. It is followed by a second DIC increase ~50 kyr after the CIE onset. This is compared to

previous DIC estimates for the PETM which are coloured as red, purple and brown (see Figure 11; Zeebe et al. 2009; Gutjahr et al. 2017 and Haynes et al. 2017 respectively). Our calculations incorporates multiple caveats, and are illustrative rather than quantitatively correct. For example, in contrast previous studies, the second DIC increase (marked by paler shading) is larger than the first in our analysis. This may be an artefact of diagenetic effects on the δ18O record (Zachos et al., 2003).

Mg/Ca

.

(mmol mol 1)

14 12 10 8

This Study Spero et al. (2015) Russell et al. (2004) Lea et al. (1999) Variable T C only Variable [Mg] and [Ca] Variable pH and DIC Multiple Variables Russell Fit

6 4 2 16

18

20

22

Temperature ( C)

24

26

(mmol mol 1)

15

A

10

W Mg/Ca S nt Ambie

10 5

C

B nt AmwbiepH) (lo

Mg/Ca

.

3 Mg/CaSW 1.

0

20

25

2500 5000 7500

(mmol mol 1)

Temperature ( C)

15

DIC ( mol kg 1)

E

D

10

[Ca]

10

[Mg] 100 [Mg] 50

50

[Mg]SW (mmol kg

100

1)

8.5

4 11 41

[Mg] 25

.

Mg/Ca

8.0

pH (Total)

F

5 0

7.5

10

20

[Ca]SW (mmol kg

1)

5

Mg/CaSW

10

DMg × 1000

4 3

A

B 20 [Ca] SW 15 [Ca]SW t n ie Amb

2

[Ca] SW

1 20

25

4 3

D

nt AmwbiepH) lo ( 5

2500 5000 7500

Temperature ( C)

DMg × 1000

C

DIC ( mol kg 1)

E

DIC p Tem

2

400

0

26

DIC

100

[Ca] 10

1 50

[Mg]SW (mmol kg

100 1)

10

20

[Ca]SW (mmol kg 1)

0

7.5

8.0

pH (Total)

8.5

95% CI

N=4

10

Predicted Mg/Ca

5

A: 0.785+/-0.060 B: 0.338+/-0.061 C: 22.762+/-7.491 D: 0.087+/-0.013 E: 0.636+/-0.501 Mg/Caforam = Mg/CaASW DICB eC [Ca]SW + DT + E

5

Measured Mg/Ca

10 .

(mmol mol

15

1)

30

B

30 N=10 N=

25

4

N=

8.4 8.2 pHTotal

30 N= 0 1 N=

Predicted Tempterature ( C)

A

.

(mmol mol 1)

15

8.0

20 4 10 30

15 15

20

25

Measured Temperature ( C)

7.8 30

(mmol mol 1) .

Mg/Ca (mmol mol 1) .

Mg/Ca

15

A

B

C

D

10 Included Data Excluded Data Model 68% CI 95% CI

5 0 15

2.5

5.0

7.5 10.0

2000 4000 6000 8000

Mg/CaSW

DIC ( mol kg

10

1)

20

[Ca]SW (mmol kg

1)

15

20

25

Temperature ( C)

E

F

G

H

Slope: 0.13 (p=0.89) Res. Mean: 0.09 (p=0.39) Res. Std: 0.99 (Normal, p=0.19)

Slope: -0.92 (p=0.04)

Slope: -3.29e-03 (p=0.06)

Slope: -1.04e-03 (p=0.23)

10 5 0

30

35

Salinity

7.5

8.0

pHTotal

8.5

200

400

[CO23 ] ( mol kg 1)

50

[Mg]SW (mmol kg 1)

100

This Study Spero et al. (2015) Russell et al. (2004) Lea et al. (1999) Predicted Model 95% CI

12 10 8

Mg/Ca

.

(mmol mol 1)

14

6 4 14

16

18

20

22

Temperature ( C)

24

26

(mmol mol 1)

6

Predicted Mg/Ca

8

.

10

A culture - white (DIC)

3

4

(mmol mol 1)

8

.

6

Mg/Caforam = Mg/CaASW [CO3]B eC [Ca]SW + DT + E A: 0.837+/-0.167 B: -0.409+/-0.070 C: 400.5+/-142.7 D: 0.086+/-0.028 E: -9.721+/-1.997

[CO23 ]

Evans et al. (2016) Henehan et al. (2013) K sakürek et al. (2008)

100 300 500

2 10

Predicted Mg/Ca

B culture - white (CO )

Mg/Caforam = Mg/CaASW DICB eC [Ca]SW + DT + E

C sed. trap & culture - white

D culture - pink

A: 0.838+/-0.105 B: -0.409+/-0.037 C: 184.6+/-19.4 D: 0.068+/-0.002 E: -6.870+/-0.462

B: -0.157+/-0.033 C: 166.9+/-34.1 D: 0.057+/-0.012 E: -4.368+/-0.656

4 2

Allen et al. (2016) Hönisch et al. (2013)

Gray et al. (2018)

2

4

Measured Mg/Ca

6 .

8

(mmol mol

1)

2

4

Measured Mg/Ca

6 .

8

(mmol mol 1)

T ( C)

3

A

B

2

Modern Paleocene Mg/Ca . = 5 mmol mol Mg/Ca . = 7 mmol mol

1 1

1 0.0

T ( C)

1.25

0.2

0.4

Mg/CaSW (mol mol 1)

C

0.0

0.5

1.0

1.5

0.1

0.2

0.3

2.0

[Ca]SW (mmol kg 1)

D

1.00 0.75 0.50 0.25

0

200

400

DIC ( mol kg

1)

600 0.0

Mg/Ca

.

(mmol mol

1)

0.4

Mg/Ca (mmol mol 1) Temperature ( C)

5.5 5.0 4.5 4.0 3.5 3.0 40 35

Penman et al. (2014)

B

Our Model (constant DIC) Evans & Müller (2012) Anand et al. (2003)

30 25

5000 DIC ( mol kg 1)

A

4000

C

Zeebe et al. (2009) Gutjahr et al. (2017) Haynes et al. (2017)

3000

Temperature ( C)

2000 36 34 32 30 28 26 200

D

150

100

50

0

Time Relative to CIE Onset (Kyr)

50

A

6 5 4 3

B

Calculated DIC

[DIC] ( molkg 1)

Mg/Ca (mmol mol 1)

T C ( 18O)

4 3 2 1 0 1

Zachos et al. (2003) Penman et al. (2014)

5000 4000 3000 2000 1000 200 150 100 50

0

Time Relative to CIE Onset (Kyr)

50