# On the combination of the planktonic foraminiferal Mg/Ca, clumped (Δ47) and conventional (δ18O) stable isotope paleothermometers in palaeoceanographic studies

Marion Peral, Franck Bassinot, Mathieu Daëron, Dominique Blamart, Jérôme Bonnin, Frans Jorissen, Catherine Kissel, Elisabeth Michel, Claire Waelbroeck, Helene Rebaubier, et al.

► To cite this version:

Marion Peral, Franck Bassinot, Mathieu Daëron, Dominique Blamart, Jérôme Bonnin, et al. On the combination of the planktonic foraminiferal Mg/Ca, clumped (Δ47) and conventional (δ18O) stable isotope paleothermometers in palaeoceanographic studies. Geochimica et Cosmochimica Acta, 2022, 339, pp.22-34. 10.1016/j.gca.2022.10.030. hal-04291869

HAL Id: hal-04291869

https://hal.science/hal-04291869v1

Submitted on 17 Nov 2023

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC0 1.0 - Universal - International License
1 On the combination of the planktonic foraminiferal Mg/Ca, clumped ($\Delta_{47}$) and

2 conventional ($\delta^{18}$O) stable isotope paleothermometers in palaeoceanographic studies

3

4 Marion Peral¹,², Franck Bassinot¹, Mathieu Daëron¹, Dominique Blamart¹, Jérôme Bonnin³,

5 Frans Jorissen⁴, Catherine Kissel¹, Elisabeth Michel¹, Claire Waelbroeck⁵, Helene

6 Rebaubier¹ and William R Gray¹

7

8 (1) Laboratoire des Sciences du Climat et de l'Environnement, LSCE/IPSL, CEA-CNRS-UVSQ, Université

9 Paris-Saclay, France

10 (2) Now at Analytical-Environmental and Geo-Chemistry, Vrije Universiteit Brussel, Belgium

11 (3) Université de Bordeaux, CNRS, Environnements et Paléoenvironnements Océaniques et
12 Continentaux (EPOC), UMR 5805, Allée Geoffroy St Hilaire, 33615 Pessac Cedex, France

13 (4) UMR CNRS 6112 LPG-BIAF Bio-Indicateurs Actuels et Fossiles, Université d'Angers, 2, Boulevard

14 Lavoisier, 49045 Angers Cedex, Franc

15 (5) LOCEAN/IPSL, Sorbonne Université-CNRS-IRD-MNHN, UMR7159, Paris, France

16

17 Abstract

18

19 Assuming that foraminiferal clumped isotope ($\Delta_{47}$) values are independent of seawater salinity
20 and pH, the combination of Mg/Ca, $\delta^{18}$O and $\Delta_{47}$ values, may in theory allow us to disentangle
21 the temperature, salinity/$\delta^{18}$Osw and pH signals. Here, we present a new Mg/Ca-$\Delta_{47}$ dataset
22 for modern planktonic foraminifera, from various oceanographic basins and covering a large
23 range of temperatures (from 0.2 to 25.4 °C). These measurements were performed on the
24 same samples and species as the ones used for the foraminiferal $\Delta_{47}$ calibration of Peral et al.

25 (2018), allowing comparison between both Mg/Ca and $\Delta_{47}$ paleothermometers (excluding the
26 two benthic foraminiferal data points). There is a good agreement between these two
27 paleothermometers when the Mg/Ca-temperature is corrected for seawater salinity and pH,
28 suggesting that foraminiferal $\Delta_{47}$ may not be influenced by salinity or pH. However, our results
29 show that $\Delta_{47}$ temperature uncertainties still limit our ability to reconstruct pH and $\delta^{18}$Osw
30 from the combination of Mg/Ca, $\delta^{18}$O and $\Delta_{47}$ in a useful manner. We also find that
31 disagreements between Mg/Ca and $\Delta_{47}$ values in G. *bulloides* persist after correction for vital,
32 salinity and pH effects, suggesting that other process(es) may also influence Mg/Ca in this
33 species.

34 This study also provides an updated I-CDES version of the previously published planktonic and
35 benthic foraminiferal $\Delta_{47}$ calibration of Peral et al. (2018), covering a range of temperature
36 from -2 to 25.4 °C.
# 1. INTRODUCTION

The reconstruction of key physical and chemical ocean water parameters, like seawater temperature, salinity and pH, is critical to understand the processes driving past ocean and climate variations. However, precisely quantifying these parameters remains extremely challenging. Several proxies have been developed to reconstruct paleo-temperatures, but they all suffer from various limitations and biases. In his seminal work on isotopes, Harold Urey suggested that the extent by which $^{18}$O was enriched in marine calcium carbonates relative to the water from which it is precipitated, could be used as a past ocean thermometer (Urey, 1947). However, later studies showed that this paleo-thermometer is biased by the isotopic composition of the global ocean ($\delta^{18}$O$_{sw}$) that does not remain constant but reflects the waxing and waning of large continental ice sheets over glacial and interglacial cycles. This signal associated with global changes in continental ice volume strongly imprints $^{18}$O records obtained from marine carbonates (Shackleton, 1967), with additional contributions from regional modifications of evaporation/precipitation to a lesser degree. Thus, it is impossible to accurately reconstruct past ocean temperature using the carbonate $^{18}$O-thermometer without an independent knowledge of seawater $\delta^{18}$O$_{sw}$. Furthermore, interspecies differences in the $\delta^{18}$O-temperature relationship testify to the importance of physiological processes, also called "vital" effects (e.g. Urey et al., 1951). In order to take into account these effects, several authors developed species-specific calibrations (e.g., Bemis et al., 1998; Mulitza et al., 2003).

More recently, several studies showed that the Mg/Ca elemental ratio of foraminiferal calcite can be used to reconstruct paleo-seawater temperatures (Rosenthal et al., 1997; Lea et al., 1999; Elderfield and Ganseen, 2000). Most foraminiferal species build their shells from magnesium-poor calcite, in which the minor amount of Mg that can be substituted to Ca is temperature dependent (Oomori et al, 1987). The paleoclimatology community had great expectations regarding the combination of foraminiferal $\delta^{18}$O and the Mg/Ca-thermometer, which could be measured from the same material allowing theoretically to disentangle temperature and $\delta^{18}$O$_{sw}$ signals. However, the Mg/Ca-thermometry proved to be more complex and challenging than originally expected. First, it appeared that the partitioning coefficient between Mg in seawater and Mg in the crystal matrix is not only
thermodynamically controlled by temperature, but also reflects physiological or ecological processes (Rosenthal et al., 1997; Lea et al., 1999; Elderfield and Ganseen, 2000; Lea, 2014), prompting several authors to develop species-specific, empirical Mg/Ca-temperature calibrations (Nürnberg et al., 1996; Rosenthal et al., 1997; Lea et al., 1999; Erez, 2003). From the first development of the Mg/Ca paleothermometer it was shown that foraminiferal Mg/Ca is influenced by physico-chemical variables other than temperature such as bottom-water carbonate ion concentration (Elderfield et al., 2006; Rosenthal et al., 2006), as well as surface salinity (Nürnberg et al., 1996; Lea et al., 1999; Kisakürek et al., 2008; Mathien-Blard and Bassinot; 2009, Gray et al., 2018; Gray and Evans, 2019) and pH (Lea et al., 1999; Gray et al., 2018; Gray and Evans 2019), and - on time-scales longer than ~1 Ma - the Mg/Ca ratio of seawater (Evans et al., 2016). In addition, analytical procedures must be carefully considered since cleaning protocols have an effect on the measurement of Mg/Ca within foraminiferal shells (Barker et al 2003; Pang et al., 2020 and references therein). These secondary influences on foraminiferal Mg/Ca complicate its use as a temperature proxy.

The carbonate clumped isotope method (noted Δ<sub>47</sub> hereafter) is one of the most recent paleothermometers, which has been developed over the last decade (Eiler, 2007, 2011). The Δ<sub>47</sub> approach is based on the quantification of subtle statistical anomalies in the abundance of doubly substituted carbonate isotopologues (¹³C¹⁸O¹⁶O¹⁶O²⁻) relative to the random distribution of isotopes (Eiler, 2007, 2011). A slightly higher abundance of ¹³C-¹⁸O bonds is, for thermodynamical reasons, a function of temperature (Eiler, 2011; Passey and Henkes, 2012; Stolper and Eiler, 2016) and this relationship is independent of the δ¹⁸O of water in which the calcification occurs (Schauble et al., 2006). Clumped isotope methodological studies have shown no evidence of vital effects (Tripati et al., 2010; Grauel et al., 2013; Peral et al., 2018; Piasecki et al., 2019; Meinicke et al., 2020) nor salinity effects (Grauel et al., 2013; Peral et al., 2018) on foraminiferal Δ<sub>47</sub>. Moreover, studies dealing with non-foraminiferal carbonates (Tripati et al., 2015; Watkins and Hunt, 2015) showed a lack of pH effect (or its negligible influence) on clumped isotope. The absence of major biases would make Δ<sub>47</sub> one of the most promising paleo-thermometers. However, its use is still limited because of its low temperature sensitivity and the large sample size required to significantly reduce the analytical uncertainties. Obtaining precise and high-resolution Δ<sub>47</sub> records remain a challenge.
Because of non-thermal effects on Mg/Ca from foraminifer shells, recent comparisons
revealed discrepancies between Mg/Ca- and Δ₄₇-derived temperatures (Peral et al., 2020;
Leutert et al., 2020; Meinecke et al., 2021). These discrepancies are not linked to any specific
foraminifer species (different species were used in the three studies), nor are they associated
to a given oceanic basin (samples from three different regions were studied, the
Mediterranean Sea, the Southern Ocean, and the Indian Ocean) or to a time period (the
studies covered from the late Pleistocene to 5 million years ago). We believe that these
discrepancies can be extremely informative as they may chiefly reflect vital effects and the
impact of salinity and pH on the Mg/Ca-thermometer, offering theoretically the opportunity
to disentangle temperature, salinity, and pH from the combination of δ¹⁸O, Mg/Ca and Δ₄₇ in
planktonic foraminifera. Planktonic foraminiferal δ¹⁸O depends on temperature and δ¹⁸Osw,
the latter being correlated with the salinity. Carbonate δ¹⁸O may be combined with Δ₄₇-
derived temperature to reconstruct the δ¹⁸Osw (Peral et al., 2020). As Mg/Ca is influenced by
salinity and pH, pH may be obtained by paring the Mg/Ca ratio with the reconstructed
temperature from Δ₄₇ and salinity estimates from sea-level or from the combination of δ¹⁸O-
Δ₄₇, following the equations described in Gray et al. (2018 and 2019). Combining δ¹⁸O, Mg/Ca
and Δ₄₇ in foraminifera may therefore prove highly useful in palaeoceanographic studies.

The relationship between Mg/Ca and Δ₄₇ in modern planktonic foraminifera has been
previously studied to investigate our ability to detect the potential biases associated to Fe-Mn
oxide coatings, contamination and/or dissolution of foraminiferal tests (Breitenbach et al.,
2018) in order to extract the best paleo-temperature estimates from non-biased
measurements. However, the sensitivity of foraminiferal Δ₄₇ to salinity and pH has not been
given much attention so far and still needs to be examined since a potential dependence of
Δ₄₇ on these chemo-physical parameters would potentially explain part of the differences
observed between the Δ₄₇ and the Mg/Ca paleothermometers.

For the present paper, we measured Mg/Ca on the same set of samples and
foraminiferal species used in the Δ₄₇ calibration of Peral et al. (2018). These data make it
possible to explore the sensitivity of foraminiferal Δ₄₇ to salinity and pH and evaluate the
potential interest and limits of combining δ¹⁸O, Mg/Ca- and clumped-temperatures to
disentangle temperature, salinity-δ¹⁸Osw, and pH effects. In the process, we took advantage
of re-calibrated clumped isotope data following cutting-edge methodological developments
to provide a revised version of the planktonic and benthic foraminiferal clumped isotope calibration of Peral et al. (2018), that could be used for future paleoceanographic studies.

## 2. MATERIALS AND METHODS

### 2.1. Samples

We used the same samples as those used in Peral et al. (2018), which are core-tops from twelve marine sedimentary cores from different oceanographic basins in the North Atlantic, Southern, Indian and Pacific Oceans (Fig. 1). All core-tops were chronologically constrained and are from the late Holocene (Peral et al., 2018). The location of samples, the water depths of the cores, the studied species and the ages are given in Table 1. We assume no changes in temperature, salinity, and pH over the late Holocene at our core sites and use modern hydrological atlases to estimate these data, at the location of our sites and at the living depths of the planktonic species studied here (see paragraph 2.4.). As discussed later, the recent warming and the addition of anthropogenic CO₂ to the surface ocean likely complicate the comparison of instrumental carbonate system measurements with core-top foraminiferal samples.

The core sites cover a wide range of seawater physico-chemical conditions, with temperatures ranging from 0.2 to 25 °C (for the planktonic only) and from -2 to 25 °C (including the benthic foraminifera), and with salinity ranging from 33.7 to 36.2 and pH from 7.7 to 8.1 (both for planktonic only). The top 1 cm of each sediment core-top was collected and dried overnight at 50°C. The samples were wet sieved to collect the size fraction larger than 150 µm, and the residues were dried. To limit the potential size effects on Mg/Ca, we picked the planktonic foraminifera in narrow size ranges centered around the optimal size of each species (i.e., the size corresponding to the maximum abundance of adult shells). The optimal sizes are divided every ~50 µm (e.g., 200-250, 250-315, 315-355, 355-400, 400-450 and 450-500 µm). Each species have their size ranges (see details in Table 2).

Nine species of planktonic foraminifera and two species of benthic foraminifera were hand-picked under a binocular. For the Mg/Ca-Δ₄₇ comparison, because of the differing carbonate chemistry controls on Mg/Ca in planktonic and benthic foraminifera (Lea, 1999; Elderfield et al 2006) we exclude the two benthic samples and only provide and discuss Mg/Ca
162
163
164
165

data from the planktonic foraminifera samples at the optimal size fractions. For the clumped-isotope calibration, we include the benthic foraminifera data, and a large range of size as was originally done in Peral et al. (2018).

<figure><img src="image_2.png" /></figure>

166
167
168
169

<caption>**Figure 1:** Map showing the location of core-tops used in this study, with the mean annual SST from WOA13</caption>

170
171

## 2.2. Clumped isotopes

172
173
174
175
176
177
178
179
180
181
182
183

The clumped-isotope data were previously published in Peral et al. (2018). The methodology (from the cleaning protocol to the measurement) is described in Daëron et al. (2016) and Peral et al. (2018). A summary of the cleaning protocol steps is presented in the supplementary material (Fig. S1). In the present paper, we reprocessed our Δ<sub>47</sub> data in accordance with the new InterCarb - Carbon Dioxide Equilibrium Scale (I-CDES) and the associated data processing methods (Bernasconi et al., 2021; Daëron, 2021).

In previous studies, discrepancies between clumped isotope calibrations had been observed (e.g., Tripati et al., 2010; Grauel et al., 2013). Thanks to an international effort, several laboratories conducted an intercalibration exercise in order to determine clumped isotope values of carbonate standards (ETH 1-4, IAEA-C1&2 and MERK; Bernasconi et al., 2021). This new standardization approach (I-CDES reference frame) results in internationally agreed calibrations (Anderson et al., 2021; Fiebig et al., 2021).
The $\Delta_{47}$ values of our modern foraminifera (Peral et al., 2018) were normalized to the I-CDES reference frame (Bernasconi et al., 2021) using the carbonate standards ETH-1/2/3/4. Data processing was performed using the $\Delta_{47}$ crunch library and the new pooled standardization approach, as described in Daëron (2021). The reprocessed $\Delta_{47}$ calibration is now compared with the new and/or other recalculated calibrations and used for future paleoceanographic studies. The full dataset is provided in the supplementary material (Table S1).

The $\Delta_{47}$ values were converted to temperatures using the Peral et al. re-calculated calibration. The temperature uncertainties were estimated by propagating (i) the external $\Delta_{47}$ reproducibility of our analytical sessions of measurements, based on repeated analyses of standards and samples and (ii) the uncertainties associated with respective calibrations. Recently, Anderson et al. (2021) have shown that when using the same standardization and data processing, re-evaluated $\Delta_{47}$-temperature calibrations obtained on various carbonate materials agree within the range of uncertainty. In terms of $\Delta_{47}$-temperature reconstructions, using Peral et al. (2018) re-calculated calibration (this paper), or using the unified calibration from Anderson et al. (2021), yield the same results. We found it important to provide in the present paper a revised calibration equation that is based on cutting-edge approaches of $\Delta_{47}$ standardization and processing methods (Bernasconi et al. 2021; Daëron, 2021) to serve for future studies based on the state-of-the-art standard values.

## 2.3. Mg/Ca analyses and derived temperatures

### 2.3.1. Mg/Ca measurements

A total of 93 Mg/Ca analyses on 9 species of planktonic foraminifera were performed at the Laboratoire des Sciences du Climat et de l'Environnement (LSCE) using a PlasmaQuant ELITE Inductively coupled plasma mass spectrometry (ICP-MS) from Analytik Jena. One milligram of foraminiferal shells was hand-picked for each sample allowing to perform 3 to 4 replicate analyses. We followed the cleaning protocol of Barker et al. (2003). Shells were crushed between two glass plates and the resulting fragments were put into acid-leached micro-vials. Fine material (i.e. clay) was removed through repeated ultrasonic cleaning with 18.2 MΩ water and then ethanol. In order to remove potential organic contaminants, the
216

samples were then oxidized with alkali-buffered 1% H₂O₂ solution for 10 minutes at 100°C.

217

The final cleaning treatment consists in a rapid leaching with 0.001 M HNO₃, before dissolution
in 0.15 M HNO₃. Samples are centrifuged immediately after dissolution and transferred to a
new acid-leached centrifuge tube, leaving a residual ~ 10 µl, which helps exclude any
remaining undissolved contaminants. Trace metal grade (NORMATOM) acids are used
throughout.

218

219

220

221

222

A 10 µl aliquot of each sample was first analyzed in order to determine calcium
concentrations. The samples were then diluted to a calcium concentration of 1mM Ca, to
match that of the bracketing standards. Mg/Ca ratios were measured using a modified version
of the method of Yu et al. (2005) against in-house standards prepared from single elementary
solutions. Mg/Ca instrumental precision was determined based on multiple replicates of a
standard solution of known Mg/Ca composition, with a long-term precision of 2% (2RSD).
Analysis of external standard NIST RM 8301 (Foraminifera) using our method gives a value of
2.65 ± 0.02 (1SE), in excellent agreement with its published value of 2.62 ± 0.14 (Stewart et
al., 2020). The data are summarized in Table 2 and the full data set is provided in
supplementary material (Table S2).

223

224

225

226

227

228

229

230

231

232

233

2.3.2. Correction of Mg/Ca for the effects of salinity and pH

234

235

236

We corrected our Mg/Ca values for pH and salinity effects based on the following
procedure: 1) using species-dependent calibrations, we calculated at each core location the
Mg/Ca values which are expected given the atlases-derived pH and salinity, and the δ¹⁸O-
derived temperature, 2) at all the sites, we also calculated a pH- and salinity- normalized
Mg/Ca values (Mg/Ca normalized) by setting pH=8 and salinity=35, and using the sample-
specific oxygen isotopic-derived temperature; 3) the difference between the expected and
normalized Mg/Ca values provide correction values at each site and for each species, (4) these
correction values are then substracted from our measured Mg/Ca values to cancel out the
salinity and pH effects from our data, thus leaving only temperature as a control parameter.

237

238

239

240

241

242

243

244

245

Practically, for the first step of this procedure, we used the species-specific equations
(Table 3) from Gray and Evans (2019) for *Globigerinoides ruber* and *Globigerina bulloides* to
estimate the “expected” Mg/Ca values. For the species for which a specific calibration is not

246

247
available, we used the generic equation of Gray and Evans (2019). To the best of our knowledge, N. pachyderma is not pH sensitive (Tierney et al., 2019). Thus, no pH correction was applied to the Mg/Ca of this species, and it is corrected for salinity only.

The multi-parameter regression equations of Gray and Evans (2019) provide Mg/Ca as a function of the temperature, the salinity, and the pH of the sea water in which the foraminifera have grown:

$$ \text{Mg/Ca} = \exp ( a \times ( S - a ) + c \times T + d \times ( \text{pH} - e ) + f ) $$

Where a, b, c, d, e and f are constants, and T, S and pH are the temperature (in °C), the salinity and the pH of seawater during calcification. As said above, for each site and each species, we solved the regression equations using modern, atlas-derived pH and salinities, and the foraminifer $\delta^{18}$O-derived temperature (see details in section 2.4), and then proceed to steps 2 to 4 (see above).

260

261

### 2.3.3. Mg/Ca-derived temperatures

263

#### 2.3.3.1 Multi-species calibration equation from Anand et al. (2003)

265

In order to compare Mg/Ca and clumped-isotope-derived temperatures, we first calculated the Mg/Ca-derived temperatures using the multi-species calibration of Anand et al. (2003) solved using our pH- and salinity- corrected Mg/Ca values. The estimated-Mg/Ca temperatures show a large difference when compared with the clumped-isotope-derived temperatures (see supplementary material, Fig. S2). We recalculated the multi-species Anand et al. (2003) calibration using the temperatures from the oxygen isotopic calibration of Kim and O'Neil (1997). This equation may provide a more robust basis for reconstructing temperature effects (Roche et al., 2018) than the modified, benthic-derived equation of Shackleton (1974) originally used in the Anand et al. (2003) study (see details in section 2.4.1). Following the same strategy as Anand et al. (2003), we only included the data from the 350 – 500 µm size-range and excluded the data from *Orbulina universa* and *Globigerinella*. We note that, as shown in Anand et al. (2003), the measured $\delta^{18}$Ocalcite is up to ~1 per mil too light in the wintertime compared to the value predicted using the measured sea surface temperature- and salinity-based $\delta^{18}$Osw estimates at the Sargasso Sea sediment trap site. This is likely due to

266

267

268

269

270

271

272

273

274

275

276

277

278

279
280

a seasonal change in the δ¹⁸Osw-salinity relationship at this site, which potentially introduces
a substantial bias to the resulting Mg/Ca equation (Gray et al, 2018). The recalculated equation
is presented in Table 3 and shown in supplementary material (Data Processing file).

281

282

283

284

2.3.3.2 Mono species-specific equations

285

286

We first used calibration equations that were derived by linking Mg/Ca to temperature
only. To the best of our knowledge, we chose the most adequate calibrations, considering the
species, the size fraction, the oceanic region, and the cleaning protocol. For seven of the
planktonic species studied in the present manuscript, we used the mono-specific equations of
Anand et al. (2003). Unfortunately, the only available calibration for *Globorotalia menardii*
was established using a cleaning protocol with a reductive step (Regenberg et al., 2010), which
is known to lower the Mg/Ca ratio of foraminifera compared to the cleaning approach of
Barker et al. (2003) that we used for the present paper (e.g., Pang et al., 2020). In the absence
of a calibration for *Neogloboquadrina pachyderma* (dextral), we used the same calibration as
the one developed for *N. pachyderma* (sinistral) (Vázquez Riveiros et al., 2016). The
uncertainties were calculated by propagating the analytical errors, based on the long-term
standard deviation of our standards and the uncertainties associated with the respective
calibrations.

287

288

289

290

291

292

293

294

295

296

297

298

299

It is important to underline that, for internal consistency, the mono-species calibrations were
corrected for local pH and salinity effects, as described in section 2.3.2. (i.e. species-specific
equation of Gray and Evans (2019) with isotopic temperature, and salinity and pH from the
atlases). For the Anand et al. (2003) calibrations, we used the *in situ* salinities available in
Deuser and Ross (1989). The calibration of Regenberg et al. (2010) based on *G. menardii* was
not corrected because we could not find the raw Mg/Ca data.

300

301

302

303

304

305

306

2.4. Independent constraints on temperatures, salinity and pH from Δ47 and Mg/Ca ratios

307

308

2.4.1. Estimation of calcification temperatures

309

310

In order to limit uncertainties associated to the imperfect knowledge of planktonic
foraminifera ecology, numerous authors have used δ¹⁸O-derived temperatures instead of

311
312 atlas temperatures for the calibration of geochemical proxies (e.g. Anand et al., 2003; 313 Mathien-Blard and Bassinot, 2009; Peral et al., 2018; Meinicke et al., 2020). Comparing 314 WOA13 atlas temperatures and foraminifer δ¹⁸O-derived temperatures obtained using 315 various calibration equations, Peral et al. (2018) suggested the use of the calibration equation 316 of Kim and O'Neil (1997), modified for consistency by using an acid fractionation factor 317 (difference of oxygen isotope ratio between the mineral (calcite) and the CO₂ gas evolved from 318 acidification with phosphoric acid) of 1.01025 (Eq. 1). The Kim and O'Neil (1997) calibration is 319 then used to calculate the δ¹⁸O-derived temperatures in this study: 320

$$321 \qquad 1000 \ln(\alpha_{CC/W}) = 18.03 \times 1000 / T - 32.17 \quad (\text{Eq. 1}) \qquad 322$$

323 Where T is the isotopic temperature in Kelvin and αCC/W is the oxygen-18 fractionation factor 324 between calcite and water, with: 325

$$326 \qquad \alpha_{CC/W} = (1 + \delta^{18}\text{O}_{C/\text{SMOW}} / 1000) / (1 + \delta^{18}\text{O}_{\text{SW/SMOW}} / 1000) \quad (\text{Eq. 2}) \qquad 327$$

328 Where δ¹⁸Oc/SMOW and δ¹⁸Osw/SMOW correspond to foraminiferal calcite and seawater δ¹⁸O 329 relative to VSMOW. Following the recommendation of Marchitto et al. (2014), δ¹⁸Oc values 330 for *Uvigerina* were adjusted by subtracting 0.47 ‰. 331

Seawater δ¹⁸O values at each core site were extracted from the gridded data set of 331 LeGrande and Schmidt (2006). The same approach as the WOA-temperature extraction is 332 followed (as described in Peral et al., 2018). Because one still does not know well the exact 333 habitat depth and growth season of planktonic species and their spatial variability in relation 334 to nutrient availability and physico-chemical conditions (i.e., Retailleau et al., 2011; Schiebel 335 and Hemleben, 2017), we followed the same approach as Peral et al. (2018). We calculated 336 the δ¹⁸Osw of seawater in which foraminifera calcified by averaging at each site the gridded 337 δ¹⁸Osw of LeGrande and Schmidt (2006) over species-specific living depth ranges. These depth 338 ranges may vary across ocean basins. According to Tolderlund and Be´ (1971) and Durazzi 339 (1981), living depths in the North Atlantic Ocean range between 0 – 50 m for *G. ruber* and *O. 340 universa*, and the depth range is 0-100m for *G. bulloides*, *G. truncatulinoides*, *G. menardii* and 341 *G. inflata* (Steinke et al., 2005; Numberger et al., 2009, Rebotim et al 2017). For *N.* 342
pachyderma, the living depth is estimated from 0 to 200 m depth (Rebotim et al., 2017). In the Indian Ocean, Duplessy et al. (1981) placed the depth of calcification for all these species within and below the mixed layer, except for G. ruber and G. menardii which are believed to remain respectively at the surface and within the mixed layer (0–100 m). In the South China Sea, G. ruber and G. menardii are described as living near the surface and in the top 100 m, respectively (Pflaumann and Jian, 1999). Finally, the living depth of O. universa being very poorly constrained to the best of our knowledge, we assume that it lives everywhere at the same depth as in the North Atlantic Ocean (Rebotim et al., 2017). For benthic foraminifera (re-calibration of clumped isotope versus temperature), we must use the bottom $\delta^{18}$O$_{sw}$ values. For the planktonic foraminifera, the mean $\delta^{18}$O$_{sw}$ values averaged for the living depth of each species for each oceanic basin is considered. The uncertainty of $\delta^{18}$O$_{sw}$ at each site was estimated as the quadratic sum of the site-specific standard deviation of $\delta^{18}$O$_{sw}$ within the corresponding water depth and a constant error of 0.20 ‰ assigned to the GISS grid interpolation. Final uncertainties of the oxygen isotopic temperatures are propagated based on the $\delta^{18}$O$_{sw}$ uncertainties and the external analytical error on $\delta^{18}$O values.

For G. bulloides and O. universa, we could also compare the reconstructed Mg/Ca-temperatures to $\delta^{18}$O-temperatures obtained using the species-specific $\delta^{18}$O calibrations from Bemis et al. (1998). This comparison is presented in Figure S3 and discussed in paragraph 4.2.

361

### 2.4.2. Estimation of seawater salinity and pH

363

The seawater salinity values at each core-top location were extracted from the WOA13 gridded data set (Zweng et al., 2013). As for the GISS $\delta^{18}$O$_{sw}$ values (see above), for each ocean basin, we computed the seawater salinity in which the foraminifera calcified by averaging the atlas salinities over the living depth range known for each species. Uncertainties were estimated at each site as the quadratic sum of a nominal error of 0.20 arbitrarily assigned to the WOA13 data set and the site-specific standard deviation of salinity.

The seawater pH values at each core-top location and for each species living depth were extracted from the GLODAP 2020 data set (Olsen et al., 2020). Similarly, following the same strategy as for the GISS $\delta^{18}$O$_{sw}$ and WOA13 salinity, we averaged the available GLODAP 2020 data over the living depth-range published for each species. A pH uncertainty of 0.02

370

371

372

373
374 was assigned to GLODAP pH data (Olsen et al., 2020). We note that this only represents a
375 'climatological' error. The use of climatological pH data is far from ideal because, due to the
376 release of anthropogenic CO2, the surface ocean has acidified considerably since 1850. This
377 has lowered the pH relative to the pre-industrial value, whereas the vast majority of
378 foraminifera retrieved in the core top samples are likely to be of preindustrial age or older.
379 This pH uncertainty represents a major source of uncertainty in our analysis and is a major
380 hindrance to usefully constraining the sensitivity of foraminiferal proxies to the carbonate
381 system using coretop material.

382

383 **3. RESULTS**

384

385 **3.1. Clumped isotope dataset**

386

387 The clumped-isotope calibration using the same data set as Peral et al. (2018) is
388 recalculated following the latest methodological developments (see section 2.2 for details).
389 The recalculated clumped-isotope data range from 0.6976 ‰ to 0.5917 ‰ and cover a range
390 of temperatures from -2.3 to 25.4 °C (oxygen isotopic temperatures from eq. 1 are used in the
391 whole section; Table 2). As expected, the Δ47 values increase with decreasing temperatures;
392 the benthic foraminifera sample from the artic (C. wuellerstorfi - MOCOSED-St1) shows the
393 highest Δ47 value, while planktonic foraminifer sample from one of the warmest sites G. ruber
394 - MD00-2360) shows the lowest Δ47 value.

395

396 **3.2. Raw Mg/Ca dataset**

397

398 We only measured Mg/Ca for the planktonic foraminifera. Our raw Mg/Ca dataset
399 ranges from 0.8 to 7.7 mmol/mol (Table 2 for the whole section) and covers a range of
400 temperatures from -0.7 to 25.4 °C (temperatures for the whole section; Table 2). As expected,
401 the cold-water dwelling foraminifera (N. pachyderma s. - MOCOSED st 1) show the lowest
402 Mg/Ca values and the warm-water surface dwellers such as G. ruber and O. universa show the
403 highest Mg/Ca values. Note the particularly high value (Mg/Ca =7.7 mmol/mol) obtained for
404 O. universa . This species likely calcifies at a lower temperature than G. ruber, which
405 nevertheless shows a raw Mg/Ca value of only 4.3 mmol/mol (sample of MD00-2360). Our
406

data therefore support previous observations that *O. universa* is characterized by unusually
high Mg/Ca ratios (Lea, 1999; Anand et al., 2003).

407

408

The raw Mg/Ca ratios measured on the same samples and species, but for different
size fractions, show a maximum difference of 0.4 mmol/mol between all the size fractions.

409

410

411

**3.3. Corrected Mg/Ca**

412

413

The raw Mg/Ca values are corrected for salinity and pH from atlas data, using the
method as described in section 2.3.2. The corrected Mg/Ca, excluding *N. pachyderma*
samples, ranges from 1.6 mmol/mol (Table 2) for *G. bulloides*-MD12-3401 that calcified at 5
°C (isotopic temperatures, Table 2), to 4.9 for *G. ruber*-MD00-2360 that calcified at 24.8 °C
(isotopic temperatures, Table 2). It is also noticeable that *G. bulloides* species still records high
Mg/Ca values, as discussed in part 4.3. For a better comparison between our Δ₄₇ and Mg/Ca
values, we test all subsequent analysis with and without G. bulloides in the dataset. The
corrected Mg/Ca values for the species coming from the same core tops display a consistent
relationship with calcification temperatures.

414

415

416

417

418

419

420

421

422

423

**3.4. Comparison of Mg/Ca-derived temperatures (multi-species and mono-species equations) with δ¹⁸O and Δ₄₇-derived temperatures**

424

425

426

The Mg/Ca-derived temperatures were estimated using the recalculated multi-species
calibration of Anand et al. (2003) and compared to the δ¹⁸O-temperatures (Fig. 2.a) estimated
using Kim and O'Neil (1997) equation (eq. 1), as described in section 2.4.1. The Mg/Ca-
temperatures for the species *G. bulloides* are systematically higher than the δ¹⁸O-derived
temperatures, while most of the other species display lower Mg/Ca-derived temperatures
(Fig. 2.a). A linear regression only explains 57 % of co-variance between the two thermometers
(Fig. 2.a).

427

428

429

430

431

432

433

Then, the Mg/Ca-derived temperatures reconstructed using the multi-species
calibration of Anand et al. (2003) are compared to the Δ₄₇-derived temperatures obtained
using the recalculated version of the foraminifer calibration equation of Peral et al. (2018; see
section 2.3; Fig. 2.b). As was observed with the δ¹⁸O-temperatures, the *G. bulloides* species

434

435

436
437

show higher Mg/Ca-derived temperatures than those derived from $\Delta_{47}$ and a linear regression only explains 52 % of co-variance between the two thermometers (Fig. 2.b).

438

439

We then computed Mg/Ca-derived temperatures using mono-species calibrations. These Mg/Ca-temperatures are in better agreement with $\delta^{18}$O-derived temperatures (Table 3; Fig. 2.c) and $\Delta_{47}$-derived temperatures (Fig. 2.d.), with regression equations explaining 80 % and 76 % of co-variance. However, Mg/Ca-derived temperatures are always warmer than the isotopic temperatures.

440

441

442

443

<figure><img src="image_3.png" /></figure>

444

445

**Figure 2:** Comparison of temperature estimates obtained on 9 planktonic species. Top panels: reconstructed Mg/Ca temperatures using the recalculated multi-species calibration of Anand et al. (2003) compared to reconstructed $\delta^{18}$O temperatures, using Kim and O'Neil (1997) (a) and $\Delta_{47}$-derived temperatures, using the recalculated calibration equation of Peral et al. (2018) (this paper) (b). Bottom panel: reconstructed Mg/Ca derived temperatures using the most adequate mono-specific calibrations compared to reconstructed $\delta^{18}$O temperatures, using Kim and O'Neil (1997) (c) and $\Delta_{47}$-derived temperatures, using recalculated Peral et al.

446

447

448

449

450

451
452

(2018) calibration (d). Dotted black lines are linear regressions, the black solid lines are the 1:1 line. Uncertainties are at 2SE.

453

454

455

**3.5. Δ₄₇ values versus raw, corrected Mg/Ca values**

456

457

The Δ₄₇ values (recalculated from the raw data of Peral et al., 2018) are compared to (1) the raw Mg/Ca values (Fig. 3.a – without *O. universa*), (2) the Mg/Ca values corrected for seawater salinity only (i.e. setting d constant to zero in the correction equations from Gray and Evans, 2019) (Fig. 3.b), and (3) the Mg/Ca values corrected for both seawater salinity and pH salinity (Fig. 3.c).

458

459

460

461

462

The raw Mg/Ca data (without corrections) show a poor agreement with the Δ₄₇ values (Fig. 3.a; R² = 0.52). Similarly, poor agreement is observed using either "salinity" corrected Mg/Ca or "salinity + pH" corrected Mg/Ca. " (R² = 0.51 in Fig. 3.b & c). However, it should be noted that without the *G. bulloides* samples, the agreements for the three comparisons improve significantly with an R² of 0.90, 0.90 and 0.89, respectively (Fig. 3.a&b&c).

463

464

465

466

467

<figure><img src="image_4.png" /></figure>

468

469

**Figure 3:** Comparison of our recalculated foraminiferal Δ₄₇ values with raw Mg/Ca values (uncorrected) (a), with corrected Mg/Ca for salinity only (b), and with corrected Mg/Ca for pH (c). The Mg/Ca values are corrected using the equations from Gray and Evans (2019), the salinity and pH from the atlas and the oxygen isotopic temperatures. The red dotted logarithmic regressions are plotted for all the plots, including *G. bulloides* and the black regressions are without *G. bulloides*. All the uncertainties are at 2SE.

470

471

472

473

474

475
4. DISCUSSION

477

4.1. Updated foraminiferal clumped-isotope calibration

479

The efforts of the clumped-isotope community have led to the establishment of an international standardization and a uniform measurement data processing, allowing robust/accurate comparisons between Δ₄₇ measurements performed in different laboratories (Bernasconi et al., 2021, and Fig. 4 therein). Following the newest methodological advancements in clumped isotope – new standard values and data processing (see details in section 3.2) - (Bernasconi et al., 2021; Daëron, 2021), we recomputed the multi-foraminiferal species calibration from Peral et al. (2018) (Fig. 4). The total least squares regression yields the following relationship:

488

$$ \Delta_{47} = A \times 10^3 / T^2 + B \quad \text{eq. 3} $$

490

Where A = 37.0 and B = 0.181

To compute the formal standard errors for this regression, we reformulate the equation 3 in terms of the barycenter of our (1/T²₀) values, so that parameters A and B₀ are statistically independent:

495

$$ \Delta_{47} = A*(T^{-2} - T_{0}^{-2}) + B_{0} \quad \text{eq. 4} $$

497

Where A = 37.0 (SE = 2.0), B₀ = 0.636 (SE = 0.0025) and T₀ = 285.1 K

499

The conclusions drawn by Peral et al. 2018) based on the original data, are still valid – i.e. no apparent species-specific foraminiferal size and salinity effects (cf. Peral et al., 2018 for more details). The updated calibration established in the present paper is compared with the unified calibration of Anderson et al. (2021) and the precise inorganic calibration of Fiebig et al. (2021) (Fig. 4). A good agreement (in the range of 0.3 – 1.3 °C, within the calibration uncertainties) is observed between the three calibrations. This agreement between biogenic carbonates (this study) and inorganic carbonates (Anderson et al., 2021; Fiebig et al., 2021 and the slow-growing Laghetto Basso and Devils Hole calcite (Daëron et al., 2019; Anderson et al.,
2021)) confirms that using standardized protocols (Bernasconi et al., 2021; Daëron, 2021) solves the large discrepancy between the calibrations (Anderson et al., 2021; Fiebig et al., 2021). Also, this calibration constitutes the more precise equation based on foraminifera. These observations allow a direct application of this calibration to foraminifera for palaeoceanographic studies; this recalculated version of the calibration by Peral et al. (2018) should be used instead of the original version for future paleoceanographic studies.

<figure><img src="image_5.png" /></figure>

**Figure 4:** Recalculated Δ₄₇ values (mean and 2SE) compared to oxygen isotopic temperatures (mean and 2SE) obtained with Kim and O'Neil (1997) for planktonic (circle) and benthic (square) foraminifera samples, combining all size fractions (modified from Peral et al., 2018). The new calibration regression corresponds to the black line (Peral et al., 2018 recalculated). The recalculated foraminiferal calibration is compared to the slow-growing calcite from Laghetto Basso and Devils Hole (from Anderson et al., 2021) and to calibrations of Anderson et al. (2021) and Fiebig et al. (2021)

**4.2. Species specific effects on Mg/Ca-temperatures vs Δ₄₇-temperatures comparison**
525

By comparing various paleothermometers we are able to better constrain the
limitations of each of the methods and, within the framework of these limitations, try to
extract as much meaningful climatic information as possible by combining those proxies.

526

527

528

The plot of Mg/Ca-temperatures vs Δ₄₇-derived temperatures (Fig. 2.b) shows a larger
scattering around the 1:1 line than the plot displaying Mg/Ca-temperatures vs δ¹⁸O-derived
temperatures (Fig. 2.a). This larger scattering likely results from the higher uncertainties in the
clumped-isotope-derived temperatures. The use of species-specific calibrations for Mg/Ca-
derived temperatures improves the fit with the Δ₄₇-derived temperatures, compared to the
use of a multi-species calibration (Fig. 2.d vs Fig. 2.b). No species-specific calibration is
necessary for clumped isotope as Δ₄₇ thermometer does not appear to be affected by species-
specific effects (Tripati et al., 2010; Grauel et al., 2013; Peral et al., 2018; Meinicke et al., 2020).

529

530

531

532

533

534

535

536

Although R² values significantly increase when using species-specific Mg/Ca
calibrations, the Mg/Ca-derived temperatures are systematically warmer than δ¹⁸O- and Δ₄₇-
derived temperatures (Fig. 2.b&d – linear regression lines). This is coherent with previous
observations (Peral et al., 2020; Leutert et al., 2020).

537

538

539

540

No significant improvement is observed when species-specific calibrations are used to
reconstruct temperatures from *G. bulloides* and *O. universa* δ¹⁸O (Bemis et al., 1998) (Figure
S3). *G. bulloides* Mg/Ca data result in temperatures as high as 20 °C, showing up to 12 °C
difference with the two isotopic thermometers (see discussion below in section 4.3.). One
second explanation would be the dependance of Mg/Ca values on salinity and pH (Nürnberg
et al., 1996; Kisakürek et al., 2008; Mathien-Blard and Bassinot, 2009, Gray et al., 2018; Gray
and Evans, 2019). It has been shown that the Δ₄₇ in foraminifera is not affected by salinity
(Tripati et al., 2010; Peral et al., 2018), however, the pH dependence of the foraminiferal Δ₄₇
thermometer has never been studied to this date. By comparing both foraminiferal-Δ₄₇ and
corrected-Mg/Ca temperatures, the potential effect of pH on clumped isotopes can be
deciphered.

541

542

543

544

545

546

547

548

549

550

551

552

4.3. *G. bulloides* species in Mg/Ca

553

554

The relatively poor correlation between raw or corrected Mg/Ca and clumped isotope
(Fig. 3a&b&c) chiefly results from particularly high *G. bulloides* Mg/Ca values and the high
variability of *G. bulloides* data over a narrow Δ₄₇ range (Fig. 3a&b&c). The correlations

555

556
significantly improve when *G. bulloides* samples are excluded. The high Mg/Ca ratios measured in *G. bulloides* and their important variability are not explained by anomalous, local salinity or pH values. High *G. bulloides* Mg/Ca values could be likely explained by 1) diagenesis or metal coating, 2) pH effect on δ¹⁸O measurements or 3) the existence of different *G. bulloides* morphotypes and/or genotypes characterize by different temperature-driven Mg/Ca incorporation mechanisms.

1) Diagenesis or metal coating: The relationship between foraminiferal $\Delta_{47}$ and raw Mg/Ca has been previously examined by Breitenbach et al. (2018). These authors suggested that the clumped isotope-Mg/Ca comparison could help identify potential problems and biases of the Mg/Ca-thermometer resulting from Fe-Mn oxide coatings, clay contamination and/or foraminiferal test dissolution. Our foraminifera samples are in a good state of preservation and do not suffer from dissolution (SEM pictures available in Peral et al., 2018). Additionally, the Fe/Ca and Mn/Ca values are low in our dataset, below the thresholds that lead to suspect a contamination problem (Boyle and Keigwin (1985); see supplementary material Table S2). Nevertheless, the *G. bulloides* sample showing the highest Mg/Ca value (sample from core MD95-2014) displays also an anomalously high Al/Ca content of 7337 mmol/mol compared to the other samples for which Al/Ca values are below 100 mmol/mol. For this sample, contamination by clay minerals is likely. Our observations suggest that the Fe-Mn oxide coatings, clay contamination (except for one sample) and/or foraminiferal test dissolution do not explain the too high Mg/Ca values of *G. bulloides* and the higher range of variability when compared with $\Delta_{47}$ values.

2) pH effect on the δ¹⁸O measurements: δ¹⁸O-derived temperatures are used to correct the Mg/Ca; but the δ¹⁸O of *G. bulloides* may be affected by pH effect (Spero et al., 1997; Spero et al., 1999; Zeebe, 1999). As a result, the high corrected Mg/Ca may be due to not considering the pH effect on δ¹⁸O. However, if the Mg/Ca is corrected using the temperature from the WOA rather than by the δ¹⁸O-derived temperature, the conclusion is similar: high corrected Mg/Ca is obtained. The pH effect on *G. bulloides* δ¹⁸O cannot explain the high Mg/Ca ratio.

3) *G. bulloides* has been shown to present different morphotypes and also different genotypes (sometime with a similar morphotype), these cryptic species can potentially live at different depths and have specific ecological niches (Osborne et al., 2020). The $\Delta_{47}$ values of *G. bulloides* are in very good agreement with the other species used and do not show systematic biases (Fig. 3), suggesting that the singularity of *G. bulloides* data in the Mg/Ca. vs.
Δ₄₇ only occur in Mg/Ca ratio. The Δ₄₇ SD of the *G. bulloides* measurements are good, suggesting that in any given sample, *G. bulloides* with the same morphotype and/or genotype were picked. However, we cannot exclude the possibility that different genotypes (with similar morphotype) were analyzed at different sites. More detailed studies on *G. bulloides* are essential to better understand the potential cryptic variability of this species and its impact on Mg/Ca incorporation.

In the rest of the article, *G. bulloides* samples are removed from the dataset to better compare the corrected Mg/Ca and the clumped isotope-derived temperatures.

## 4.4. Salinity and pH effects on reconstructed Mg/Ca vs Δ₄₇ temperatures

Considering that the Δ₄₇ is independent of salinity and pH, and by correcting the Mg/Ca temperatures for each of these parameters, the observations made on figure 2 may be explained. In figure 5, we redraw the Mg/Ca-temperature.vs.Δ₄₇-temperature comparison of Figure 2d (i.e. obtained using the mono-specific calibration equations) but without *G. bulloides*. The mono-species Mg/Ca calibrations are corrected for salinity and pH (section 2.3.3). Using this corrected-mono-species calibrations for Mg/Ca-derived temperature, the comparison with Δ₄₇-derived temperatures is better; the regression line is close to the 1:1 line and explains 86% of the co-variance between both thermometers (Fig. 5). Thus, our results concur with observations from the geological record (Leutert et al, 2020; Meinecke et al 2021), that improved agreement between Δ₄₇-derived and Mg/Ca-derived temperatures is observed when the influences of pH and salinity on Mg/Ca are accounted. This emphasizes the importance of correcting Mg/Ca values for non-thermal influences. However, it is noticeable that cold Mg/Ca-derived temperatures still show a slight difference with Δ₄₇-derived temperatures. This could result from the small number of samples available and/or specific problems (e.g., effects of species, CO₃²⁻). More data is requested on the cold end member to better understand this potential difference.

The good agreement between the Δ₄₇-derived temperatures and corrected Mg/Ca-derived temperatures provides further support that Δ₄₇ is not affected by salinity (Tripati et al., 2010; Peral et al., 2018) and pH (or that the effect of pH is negligible).
<figure><img src="image_6.png" /></figure>

**Figure 5:** Mg/Ca-derived temperatures using mono-species calibrations, compared to the Δ₄₇-derived temperatures using the recalculated Peral et al. (2018) calibration (a) and the Mg/Ca-derived temperatures using the corrected Mg/Ca mono-species calibrations for salinity and pH compared to the Δ₄₇-derived temperatures using the recalculated Peral et al. (2018) calibration (b). The dotted linear regression, excluding *O. universa* and *G. bulloides*, is plotted. A line 1:1 is plotted in black; uncertainties are at 2 SE.

**4.5. The potential of combining Mg/Ca ratio, δ¹⁸O and Δ₄₇ for palaeoceanographic studies**

The combination of δ¹⁸O and Δ₄₇ in foraminifera has been previously studied to accurately reconstruct the signal of δ¹⁸Oₗw even during glacial-interglacial scales (Rodriguez-Sanz et al., 2021; Peral et al., 2020). Next, the comparison between Mg/Ca and Δ₄₇
632

systematically shows differences between the two thermometers in modern and fossil
foraminifera. Breitenbach et al. (2018) showed that combining Mg/Ca and clumped isotopes
data may help to detect possible dissolution and metal coating biases on the Mg/Ca-
thermometer. When samples are not biased by contamination, dissolution or diagenesis, the
combination of these two proxies has been used to estimate long-term variations in seawater
Mg/Ca (Evans et al., 2018; Meinecke et al., 2021).

633

634

635

636

637

638

In the present study, we showed that salinity and pH lead to discrepancies between clumped isotope and Mg/Ca in planktonic foraminifera frequently used for paleoceanographic reconstructions (however, further work is needed for O. universa and G. bulloides). Because of the multi-parameter dependency of foraminiferal δ¹⁸O, Δ₄₇ and Mg/Ca, the combination of these paleo-thermometers could provide us with more than just the estimates of past ocean temperatures. Theoretically, based on the Gray and Evans equation (2019), the pH could be reconstructed by (i) solving the Mg/Ca dependency to temperature using Δ₄₇-derived temperatures and (ii) correcting for salinity using either the salinity estimated from sea level variations (Gray et al., 2019) or the salinity estimated from the combination of a thermometer (Δ₄₇-temperature or TEX₈₆ as in Leutert et al. (2020)) and δ¹⁸O (to obtain the δ¹⁸O₈ₙ).

639

640

641

642

643

644

645

646

647

648

We tested such an approach with our core-top dataset. Firstly, δ¹⁸Osw was reconstructed by pairing δ¹⁸O and Δ₄₇ and using the equation 1 (Kim and O'Neil, 1997). Then salinity was reconstructed using modern salinity-δ¹⁸Osw relationships (section 2.4; supplementary material Fig. S4, at our site locations). Finally, we used our raw Mg/Ca, the estimated salinities and the clumped isotope temperatures to reconstruct pH values from the equations of Gray and Evans (2019). The reconstructed pH is compared to the pH extracted from the GLODAP 2020 data set (Olsen et al., 2020), by plotting their differences against the different species (Fig. 6). For each species, the differences between estimated- and atlas-pH (ΔpH) present a relatively good agreement, within the error bars, especially for G. ruber (Fig. 6). Part of the differences can be explained by the inaccurate assumptions regarding the depth of life and the optimal developmental season of foraminifera species, thus leading to incorrect pH being extracted from the atlases. Additionally, another limitation of this approach is the salinity reconstruction that we applied. It requires to assume that, in the past, the regional relationships between δ¹⁸Osw and salinity were the same as today. It is likely that in past climates, regional changes of evaporation/precipitation and isotopic fractionation during

649

650

651

652

653

654

655

656

657

658

659

660

661

662
atmospheric transport of water vapor, lead to changes in the δ¹⁸Osw – salinity relationship. On a global scale, these changes may have also altered the impact of ice sheet waxing/waning on the seawater δ¹⁸Osw-salinity relationship. The extent and amount of sea ice may have also decoupled this δ¹⁸Osw- salinity relationship (LeGrande and Schmidt, 2011). A direct application of the δ¹⁸O and Δ47 combination is therefore not straightforward and other methods of salinity reconstruction should be used (Gray and Evans, 2019; Leutert et al., 2020).

Thus, despite the theoretical potential of the approach described above, it should be noted that the uncertainties in pH are large (at 2SE in Fig. 6), making the application of this approach challenging. It is important to note that these uncertainties are particularly large with respect to expected pH changes in the geological past (see discussion below). The uncertainties in the reconstructed pH range between 0.23 and 0.39, which is too high for useful paleoceanographic reconstruction and conversion to atmospheric CO₂ concentration, since it has been estimated that pH variations over G-IG cycles are on the order of 0.15 (e.g. Hönisch and Hemming, 2005; Henehan et al., 2013), and by 0.2 units over the Miocene (Leutert et al., 2020)). In terms of propagation of errors, the estimated pH uncertainties are dominated by the uncertainties in the clumped isotope-derived temperatures. The Δ47 uncertainties need to be reduced by measuring more replicates or by improvements in mass spectrometry.

Further studies and technical improvements are needed to improve species-specific equations and better understand the dependence of Mg/Ca on salinity and pH, and to reduce the amount of material needed for Δ47 measurements and decrease temperature uncertainties. It is also mandatory to improve our knowledge about past relationships between δ¹⁸Osw and salinity. While we are not able yet to fully benefit from the combination of Mg/Ca, δ¹⁸O and Δ47 ratios, the systematic use of these proxies is nonetheless useful to better understand these proxies, their biases and thus help their interpretations in paleoceanographic studies. Pairing these paleothermometers with the boron isotope pH proxy (e.g., Foster and Rae, 2016), which requires knowledge of temperature to calculate K<sub>B</sub> and pH, would allow for multiple independent constraints on past variations in pH and temperature.

692
<figure><img src="image_7.png" /></figure>

**Figure 6:** the difference for all the species from our dataset (excluding *O. universa*, *G. bulloides* and *N. pachyderma*) between the extracted pH from the atlas (GLOPAD 2020) and the reconstructed pH, using the equations from Gray and Evans (2019) with the raw Mg/Ca, the Δ₄₇-derived temperatures, and the combination of δ¹⁸O and Δ₄₇-derived temperatures to reconstruct the δ¹⁸Osw. The uncertainties correspond to the uncertainties associated with the reconstructed pH (2SE)

**5. CONCLUSION**

The Mg/Ca in 7 planktonic foraminifer species is affected by species, salinity and pH effects (Gray et al., 2018). A strong correlation exists between Δ₄₇ and Mg/Ca data when the later are corrected for salinity and pH effects with the Δ₄₇ values. The *G. bulloides*-Mg/Ca ratio appear to show anomalously high values compared to the Mg/Ca-Δ₄₇ relationship observed for the other seven planktonic species. Another process(es) may affect Mg/Ca in this species and additional investigation is needed to better understand what controls high Mg/Ca we observe in this species.

The improved agreement observed between Mg/Ca- and Δ₄₇-derived temperatures when Mg/Ca values are corrected for salinity and pH suggests that the foraminiferal clumped isotopes may only be temperature dependent. As such, the combination of the foraminiferal Mg/Ca, δ¹⁸O and Δ₄₇, could allow the temperature (Δ₄₇ thermometer), salinity (by combining δ¹⁸O and Δ₄₇, to reconstruct the δ¹⁸Osw and then, the salinity) and pH (the only remaining unknown) of the past seawater to be determined. However, at present, the application of this
716 later approach is nontrivial. In particular, the $\Delta_{47}$-temperature uncertainties result in pH
717 uncertainties higher than the expected pH changes in the geological record. Furthermore, the
718 estimation of past salinity is also not straightforward. Finally, the species-specific Mg/Ca-pH
719 sensitivity (Gray and Evans, 2019) adds an additional complication when applying the
720 approach to extinct species.

721 This paper is also present an update of the foraminiferal clumped-isotope calibration
722 of Peral et al. (2018), that benefits from the latest methodological developments (data
723 processing and standardization) and can be directly applied to palaeoceanographic studies.

724

725 References
726

726

727 Anand P., Elderfield H. and Conte M. H. (2003) Calibration of Mg/Ca thermometry in
728 planktonic foraminifera from a sediment trap time series. *Paleoceanography*, 18(2).

729 Anderson, N. T., Kelson, J. R., Kele, S., Daëron, M., Bonifacie, M., Horita, J., T. J. Mackey, C. M.
730 John, T. Kluge, P. Petschnig, A. B. Jost, K. W. Huntinton, S. M. Bernasconi, Bergmann, K.
731 D. (2021). A unified clumped isotope thermometer calibration (0.5–1100° C) using
732 carbonate-based standardization. *Geophysical Research Letters*, e2020GL092069.

733 Barker S., Greaves M. and Elderfield H. (2003) A study of cleaning procedures used for
734 foraminiferal Mg/Ca paleothermometry. *Geochemistry, Geophys. Geosystems* 4, 1–20.

735 Bemis, B. E., Spero, H. J., Bijma, J., & Lea, D. W. (1998). Reevaluation of the oxygen isotopic
736 composition of planktonic foraminifera: Experimental results and revised
737 paleotemperature equations. *Paleoceanography*, 13(2), 150-160.

738 Bernasconi, S. M., Daëron, M., Bergmann, K. D., Bonifacie, M., Meckler, A. N., Affek, H. P.,
739 (n.d.). InterCarb: A community effort to improve inter-laboratory standardization of the
740 carbonate clumped isotope thermometer using carbonate standards. *Geochemistry,
741 Geophysics and
742 Geosystems*. https://doi.org/10.1002/essoar.10504430.410.1002/essoar.10504430.3e
743 ms

744 Bernasconi S. M., Müller I. A., Bergmann K. D., Breitenbach S. F. M., Fernandez A., Hodell D.
745 A., Jaggi M., Meckler A. N., Millan I. and Ziegler M. (2018) Reducing uncertainties in
746 carbonate clumped isotope analysis through consistent 3 carbon- ate-based
747 standardization. *Geochem. Geophys, Geosyst*.

748 Boyle, E. and Keigwin, L. (1985). Comparison of Atlantic and Pacific Paleochemical Records for
749 the Last 215,000 Years - Changes in Deep Ocean Circulation and Chemical Inventories.
750 Earth and Planetary Science Letters, 76:135-150.

751 Brand W. A., Assonov S. S. and Coplen T. B. (2010) Correction for the 17O interference in
752 $\delta(13C)$ measurements when analyzing CO2 with stable isotope mass spectrometry
753 (IUPAC Technical Report). Pure Appl. Chem. 82, 1719-1733. Available at:
754 https://www.degruyter.com/view/j/pac.2010.82.issue-8/pac-rep-09-01-05/pac-rep-09-01-05.xml.

756 Breitenbach S. F. M., Mleneck-Vautravers M. J., Grauel A.-L., Lo L., Bernasconi S. M., Müller I.
757 A., Rolfe J., Greaves M. and Hodell D. A. (2018) Coupled Mg/Ca and clumped isotope
758 analyses of foraminifera provide consistent water temperatures. *Geochim. Cosmochim. Acta* 236, 283-296.

759

760 Daëron, M., Blamart, D., Peral, M., & Affek, H. P. (2016). Absolute isotopic abundance ratios and the accuracy of Δ47 measurements. *Chemical Geology*, *442*, 83-96.

761 Daëron, M., Drysdale, R. N., Peral, M., Huyghe, D., Blamart, D., Coplen, T. B., ... & Zanchetta, G. (2019). Most Earth-surface calcites precipitate out of isotopic equilibrium. *Nature communications*, *10*(1), 1-7.

762 Daëron, M. (2021). Full propagation of analytical uncertainties in Δ47 measurements. *Geochemistry, Geophysics, Geosystems*, *22*(5), e2020GC009592.

763 Daëron, M., Drysdale, R. N., Peral, M., Huyghe, D., Blamart, D., Coplen, T. B., ... & Zanchetta, G. (2019). Most Earth-surface calcites precipitate out of isotopic equilibrium. *Nature communications*, *10*(1), 1-7.

764 Daëron, M. (2021). Full propagation of analytical uncertainties in Δ47 measurements. *Geochemistry, Geophysics, Geosystems*, *22*(5), e2020GC009592.

765 Deuser, W. G., and E. H. Ross. 1989. Seasonally abundant planktonic foraminifera of the Saragossa Sea: Succession, deep-water fluxes, isotopic compositions, and paleoceanographic implications, J. Foraminiferal Res., 19, 268-293.

766 Eiler, J.M. (2007) "Clumped-isotope" geochemistry-the study of naturally-occurring, multiply-substituted isotopologues. Earth Planet. Sci. Lett. 262, 309-327.

767 Eiler, J.M. (2011) Paleoclimate reconstruction using carbonate clumped isotope thermometry. Quat. Sci. Rev. 30 (25-26), 3575-3588. https://doi.org/10.1016/j.quascirev.2011.09.001

768 Elderfield H., Gansen G. (2000). Past temperature and δ¹⁸O of surface ocean waters inferred from foraminiferal Mg/Ca ratios. *Nature*, 405, pp. 422-445

769 Elderfield, H., Vautravers, M., & Cooper, M. (2002). The relationship between shell size and Mg/Ca, Sr/Ca, δ¹⁸O, and δ¹³C of species of planktonic foraminifera. *Geochemistry, Geophysics, Geosystems*, 3(8), 1-13.

770 Elderfield H., Yu J., Anand P., Kiefer T. and Nyland B. (2006) Calibrations for benthic foraminiferal Mg/Ca paleothermometry and the carbonate ion hypothesis. Earth Planet. Sci. Lett. 250, 633-649.

771 Elderfield H., Greaves M., Barker S., Hall I. R., Tripati A., Ferretti P., Crowhurst S., Booth L. and Daunt C. (2010) A record of bottom water temperature and seawater d 18 O for the Southern Ocean over the past 440 kyr based on Mg / Ca of benthic foraminiferal Uvigerina spp. Quat. Sci. Rev. 29, 160-169. Available at: http://dx.doi.org/10.1016/j.quascirev.2009.07.013.

772 Evans, D., Brierley, C., Raymo, M. E., Erez, J., & Müller, W. (2016). Planktic foraminifera shell chemistry response to seawater chemistry: Pliocene-Pleistocene seawater Mg/Ca, temperature and sea level change. *Earth and Planetary Science Letters*, *438*, 139-148.

773 Evans, D., Sagoo, N., Renema, W., Cotton, L. J., Müller, W., Todd, J. A., ... & Affek, H. P. (2018). Eocene greenhouse climate revealed by coupled clumped isotope-Mg/Ca thermometry. *Proceedings of the National Academy of Sciences*, *115*(6), 1174-1179.

774 Erez, J. (2003). The source of ions for biomineralization in foraminifera and their implications for paleoceanographic proxies. *Reviews in mineralogy and geochemistry*, *54*(1), 115-149.

775 Fiebig, J., Daëron, M., Bernecker, M., Guo, W., Schneider, G., Boch, R., Bernasconi, S., Jautzy, J., & Dietzel, M. (2021). Calibration of the dual clumped isotope thermometer for carbonates. *Geochimica et Cosmochimica Acta*, *312*, 235-256.
804 Foster, G. L., & Rae, J. W. (2016). Reconstructing ocean pH with boron isotopes in
805 foraminifera. *Annual Review of Earth and Planetary Sciences*, **44**, 207-237.

806 Grauel A. L., Schmid T. W., Hu B., Bergami C., Capotondi L., Zhou L. and Bernasconi S. M. (2013)
807 Calibration and application of the “clumped isotope” thermometer to foraminifera for
808 high-resolution climate reconstructions. *Geochim. Cosmochim. Acta* **108**, 125–140.
809 Available at: http://dx.doi.org/10.1016/j.gca.2012.12.049.

810 Gray, W. R., Weldeab, S., Lea, D. W., Rosenthal, Y., Gruber, N., Donner, B., & Fischer, G. (2018).
811 The effects of temperature, salinity, and the carbonate system on Mg/Ca in
812 Globigerinoides ruber (white): A global sediment trap calibration. *Earth and Planetary
813 Science Letters*, **482**, 607–620. https://doi.org/10.1016/j.epsl.2017.11.026

814 Gray, W. R., & Evans, D. (2019). Nonthermal influences on Mg/Ca in planktonic foraminifera:
815 A review of culture studies and application to the last glacial
816 maximum. *Paleoceanography and Paleoclimatology*, **34**(3), 306-315.

817 Hönisch, B., & Hemming, N. G. (2005). Surface ocean pH response to variations in pCO2
818 through two full glacial cycles. *Earth and Planetary Science Letters*, **236**(1-2), 305-314.

819 Henehan, M. J., Rae, J. W., Foster, G. L., Erez, J., Prentice, K. C., Kucera, M., ... & Elliott, T.
820 (2013). Calibration of the boron isotope proxy in the planktonic foraminifera
821 Globigerinoides ruber for use in palaeo-CO2 reconstruction. *Earth and Planetary Science
822 Letters*, **364**, 111-122.

823 Kim S.-T. and O'Neil J. R. (1997) Equilibrium and nonequilibrium oxygen isotope effects in
824 synthetic carbonates. *Geochim. Cosmochim. Acta* **61**, 3461–3475. Available at:
825 http://linkinghub.elsevier.com/retrieve/pii/S0016703797001695.

826 Kisakürek, B., A. Eisenhauer, F. Böhm, D. Garbe-Schönberg, and J. Erez (2008), Controls on
827 shell Mg/Ca and Sr/Ca in cultured planktonic foraminiferan, Globigerinoides ruber
828 (white), *Earth Planet. Sci. Lett.*, **273**, 260–269, doi:10.1016/j.epsl.2008.06.026.

829 Kissel C., Laj C., Mulder T., Wandres C. and Cremer M. (2009) The magnetic fraction: A tracer
830 of deep water circulation in the North Atlantic. *Earth Planet. Sci. Lett.* **288**, 444–454.
831 https://doi.org/10.1016/j.epsl.2009.10.005.

832 Kissel C., Van Toer A., Laj C., Cortijo E. and Michel E. (2013) Variations in the strength of the
833 North Atlantic bottom water during Holocene. *Earth Planet. Sci. Lett.* **369**, 248–259.

834 Lea, D., T. Mashiotta, and H. Spero (1999), Controls on magnesium and strontium uptake in
835 planktonic foraminifera determined by live culturing, *Geochim. Cosmochim. Acta*, **63**,
836 2369-2379, doi:10.1016/S0016-7037(99)00197-0.

837 Lea DW (2014) Elemental and isotopic proxies of past ocean temperatures. Treatise on
838 Geochemistry, eds Holland HD, Turekian KK (Elsevier, Amsterdam), 2nd Ed, pp 373–397.

839 Lear, C. H., Rosenthal, Y., & Slowey, N. (2002). Benthic foraminiferal Mg/Ca-
840 paleothermometry: A revised core-top calibration. *Geochimica et Cosmochimica
841 Acta*, **66**(19), 3375-3387.

842 LeGrande A. N. and Schmidt G. A. (2006) Global gridded data set of the oxygen isotopic
843 composition in seawater. *Geophys. Res. Lett.* **33**, 1–5.

844 LeGrande, A. N., and Schmidt G. A. (2011), Water isotopologues as a quantitative paleosalinity
845 proxy, *Paleoceanography*, **26**, PA3225, doi:10.1029/2010PA002043

846 Leutert, T. J., Auderset, A., Martínez-García, A., Modestou, S., & Meckler, A. N. (2020). Coupled
847 Southern Ocean cooling and Antarctic ice sheet expansion during the middle
848 Miocene. *Nature Geoscience*, **13**(9), 634-639.
849 Marchitto, T. M., Bryan, S. P., Curry, W. B., & McCorkle, D. C. (2007). Mg/Ca temperature
850 calibration for the benthic foraminifer Cibicidoides
851 pachyderma. *Paleoceanography*, **22**(1).

852 Marchitto T. M., Curry W. B., Lynch-Stieglitz J., Bryan S. P., Cobb K. M. and Lund D. C. (2014)
853 Improved oxygen isotope temperature calibrations for cosmopolitan benthic foramini-
854 fera. *Geochim. Cosmochim. Acta* 130, 1–11. https://doi.org/10.1016/j.gca.2013.12.034.

855 Mathien-Blard E. and Bassinot F. (2009) Salinity bias on the foraminifera Mg/Ca thermometry:
856 Correction procedure and implications for past ocean hydrographic reconstructions.
857 Geochemistry, Geophys. Geosystems 10.

858 Meckler A. N., Ziegler M., Millán M. I., Breitenbach S. F. M. and Bernasconi S. M. (2014) Long-
859 term performance of the Kiel carbonate device with a new correction scheme for
860 clumped isotope measurements. Rapid Commun. Mass Spectrom. 28, 1705–1715.

861 Meinicke, N., Ho, S. L., Hannisdal, B., Nürnberg, D., Tripati, A., Schiebel, R., & Meckler, A. N.
862 (2020). A robust calibration of the clumped isotopes to temperature relationship for
863 foraminifers. *Geochimica et Cosmochimica Acta*, **270**, 160-183.

864 Meinicke, N., Reimi, M. A., Ravelo, A. C., & Meckler, A. N. Coupled Mg/Ca and clumped isotope
865 measurements indicate lack of substantial mixed layer cooling in the Western Pacific
866 Warm Pool during the last~ 5 million years. *Paleoceanography and Paleoclimatology*,
867 e2020PA004115.

868 Mulitza, S., Boltovskoy, D., Donner, B., Meggers, H., Paul, A., Wefer, G. (2003) Temperature:
869 δ18O relationships of planktonic foraminifera collected from surface waters.
870 Palaeogeography, Palaeoclimatology, Palaeoecology, **202**(1–2), 143-152.
871 https://doi.org/10.1016/S0031-0182(03)00633-3.

872 Numberger, L., Hemleben, C., Hoffmann, R., Mackensen, A., Schulz, H., Wunderlich, J. M., &
873 Kucera, M. (2009). Habitats, abundance patterns and isotopic signals of morphotypes of
874 the planktonic foraminifer Globigerinoides ruber (d'Orbigny) in the eastern
875 Mediterranean Sea since the Marine Isotopic Stage 12. Marine Micropaleontology, **73**(1-
876 2), 90-104.

877 Nürnberg, D., J. Bijma, and C. Hemleben (1996), Assessing the reliability of magnesium in
878 foraminiferal calcite as a proxy for water mass temperatures, Geochim. Cosmochim.
879 Acta, 60, 803–814, doi:10.1016/0016-7037(95)00446-7.

880 Olsen, A., Lange, N., Key, R M., Tanhua, T., Bittig, H C., Kozyr, A., Álvarez, M., Azetsu-Scott, K.,
881 Becker, S., Brown, P J., Carter, B R., da Cunha, L., Feely, R A., van Heuven, S., Hoppema,
882 M., Ishii, M., Jeansson, E., Jutterström, S., Landa, C S., Lauvset, S K., Michaelis, P., Murata,
883 A., Pérez, F F., Pfeil, B., Schirnick, C., Steinfeldt, R., Suzuki, T., Tilbrook, B., Velo, A.,
884 Wanninkhof, R., Woosley, R. J. (2020). An updated version of the global interior ocean
885 biogeochemical data product, GLODAPv2. 2020. *Earth System Science Data*, **12**(4), 3653–3678.

887 Pang, X., Bassinot, F., & Sepulcre, S. (2020). Cleaning method impact on the Mg/Ca of three
888 planktonic foraminifer species: A downcore study along a depth transect. *Chemical
889 Geology*, **549**, 119690.

890 Oomori, T., Kaneshima, H., Maezato, Y., Kitano, Y., 1987. Distribution coefficient of Mg2+ ions
891 between calcite and solution at 10–50°C. Marine Chemistry 20, pp. 327-336.

892 Osborne, E. B., Umling, N. E., Bizimis, M., Buckley, W., Sadekov, A., Tappa, E., ... & Thunell, R.
893 C. (2020). A sediment trap evaluation of B/Ca as a carbonate system proxy in asymbiotic
894 and nondinoflagellate hosting planktonic foraminifera. *Paleoceanography and
895 Paleoclimatology*, **35**(2), e2019PA003682.
896

Passey, B. H., & Henkes, G. A. (2012). Carbonate clumped isotope bond reordering and geospeedometry. *Earth and Planetary Science Letters, 351*, 223-236.

897

898

Peral M., Daëron M., Blamart D., Bassinot F., Dewilde F., Smialkowski N., Isguder G., Jorissen F., Kissel C., Michel E., Vázquez Riveiros, N. and Waelbroeck C. (2018) ScienceDirect Updated calibration of the clumped isotope thermometer in planktonic and benthic foraminifera. 239, 1-16.

899

900

901

902

Peral, M., Blamart, D., Bassinot, F., Daëron, M., Dewilde, F., Rebaubier, H., Nomade, S., Girone, A., Marimo, M., Maiorano, P., & Ciaranfi, N. (2020). Changes in temperature and oxygen isotopic composition of Mediterranean water during the Mid-Pleistocene transition in the Montalbano Jonico section (southern Italy) using the clumped-isotope thermometer. *Palaeogeography, Palaeoclimatology, Palaeoecology*, 544, 109603.

903

904

905

906

907

Petersen, S. V., Defliese, W.F., Saenger, C., Daëron, M., John, C. M., Huntington, K. W., Kelson, J. R., Bernasconi, S. M., Colman, A. S., Kluge, T., Olack, G. A., Schauer, A. J., Bajnai, D., Bonifacie, M., Breitenbach, S. F. M., Fiebig, J., Fernandez, A. B., Henkes, G. A., Hodell, D., Katz, A., Kele, S., Lohmann, K. C., Passey, B. H., Peral, M., Petrizzo, D. A., Rosenheim, B. E., Tripati, A., Venturelli, R., Young, E. D., Wacker U., Winkelstern, I. Z. 2019. *Effects of Improved ¹⁷O Correction on Inter-Laboratory Agreement in Clumped Isotope Calibrations, Estimates of Mineral-Specific Offsets, and Acid Fractionation Factor Temperature Dependence*. Special Issue of Geochemistry, Geophysics, Geosystems, 20, 3495-3519

908

909

910

911

912

913

914

915

916

Piasecki, A., Bernasconi, S. M., Grauel, A., Hannisdal, B., Ho, S. L., Leutert, T. J., et al. (2019). Application of clumped isotope thermometry to benthic foraminifera. *Geochemistry, Geophysics, Geosystems*, 2018GC007961. https://doi.org/10.1029/2018GC007961

917

918

919

920

Regenberg, M., Steph, S., Nürnberg, D., Tiedemann, R., & Garbe-Schönberg, D. (2009). Calibrating Mg/Ca ratios of multiple planktonic foraminiferal species with δ18O-calcification temperatures: Paleothermometry for the upper water column. *Earth and Planetary Science Letters*, 278(3-4), 324-336.

921

922

923

924

Rebotim, A., Voelker, A. H., Jonkers, L., Waniek, J. J., Meggers, H., Schiebel, R., ... & Kucera, M. (2017). Factors controlling the depth habitat of planktonic foraminifera in the subtropical eastern North Atlantic. *Biogeosciences*, 14(4), 827-859.

925

926

927

Retailleau, S., Schiebel, R., & Howa, H. (2011). Population dynamics of living planktic foraminifers in the hemipelagic southeastern Bay of Biscay. *Marine Micropaleontology*, 80(3-4), 89-100.

928

929

930

Roche, D.M., C. Waelbroeck, B. Metcalfe, T. Caley, 2018. FAME (v1.0): a simple module to simulate the effect of planktonic foraminifer species-specific habitat on their oxygen isotopic content. Geoscientific Model Development 11(9), 3587-3603.

931

932

933

Rodríguez-Sanz, L., Bernasconi, S.M., Marino, G. et al. Author Correction: Penultimate deglacial warming across the Mediterranean Sea revealed by clumped isotopes in foraminifera. *Sci Rep* **11**, 17511 (2021). https://doi.org/10.1038/s41598-021-96895-3

934

935

936

Rosenthal, Y., Boyle, E. A., & Slowey, N. (1997). Temperature control on the incorporation of magnesium, strontium, fluorine, and cadmium into benthic foraminiferal shells from Little Bahama Bank: Prospects for thermocline paleoceanography. *Geochimica et Cosmochimica Acta*, **61**(17), 3633-3643.

937

938

939

940

Schauble E. A., Ghosh P. and Eiler J. M. (2006) Preferential formation of 13C-18O bonds in carbonate minerals, estimated using first-principles lattice dynamics. *Geochim. Cosmochim. Acta* 70, 2510-2529.

941

942
943 Shackleton N. (1967) Oxygen isotope analyses and Pleistocene temperatures re-assessed.
944 Nature 215, 15-17.

945 Shackleton N.J. (1974) Attainment of isotopic equilibrium between ocean water and
946 benthonic foraminifera genus *Uvigerina*: isotopic changes in the ocean during the last
947 glacial. Les méthodes quantitatives d'étude des variations du climat au cours du
948 Pleistocène, Gif-sur-Yvette. Colloque international du CNRS, 219, pp. 203-210

949 Spero H.J., Bijma J., Lea D.W., Bermis B.E. (1997) Effect of seawater carbonate concentration
950 on foraminiferal carbon and oxygen isotopes. *Nature*, 390, 497-500.

951 Spero H.J., Bijma J., Lea D.W., Russell, A.D. (1999) Deconvolving glacial ocean carbonate
952 chemistry from the planktonic foraminifera carbon isotope record.
953 F. Abrantes, A.C. Mix (Eds.), Reconstructing Ocean History: A Window into the
954 Future, Kluwer Academic/Plenum Publishers, New York, 329-342

955 Steinke, S., Chiu, H. Y., Yu, P. S., Shen, C. C., Löwemark, L., Mii, H. S., & Chen, M. T. (2005).
956 Mg/Ca ratios of two Globigerinoides ruber (white) morphotypes: Implications for
957 reconstructing past tropical/subtropical surface water conditions. Geochemistry,
958 Geophysics, Geosystems, 6(11).

959 Stewart, J. A., Christopher, S. J., Kucklick, J. R., Bordier, L., Chalk, T. B., Dapoigny, A., Douville,
960 E., Foster, G. L., Gray, W. R., Greenop, R., Gutjahr, M., Hemsing, F., Henehan, M. J.,
961 Holdship, P., Hsieh, Y., Kolevica, A., Lin, Y., Mawbey, E. M., Rae, J. W. B., Robinson, L. F.,
962 Shuttleworth, R., You, C., Zhang, S., & Day, R. D. (2021). NIST RM 8301 boron isotopes in
963 marine carbonate (simulated coral and foraminifera solutions): inter-laboratory δ11B
964 and trace element ratio value assignment. *Geostandards and Geoanalytical
965 Research*, 45(1), 77-96.

966 Stolper D. A. and Eiler J. M. (2016) Constraints on the formation and diagenesis of
967 phosphorites using carbonate clumped isotopes. *Geochim. Cosmochim. Acta* 181, 238-
968 259.

969 Tierney, J. E., Malevich, S. B., Gray, W., Vetter, L., & Thirumalai, K. (2019). Bayesian calibration
970 of the Mg/Ca paleothermometer in planktic foraminifera. *Paleoceanography and
971 Paleoclimatology*, 34, 2005-2030. https://do.i.org/10.1029/2019PA003744

972 Tripati A. K., Eagle R. A., Thiagarajan N., Gagnon A. C., Bauch H., Halloran P. R. and Eiler J. M.
973 (2010) 13C-18O isotope signatures and "clumped isotope" thermometry in foraminifera
974 and coccoliths. *Geochim. Cosmochim. Acta* 74, 5697-5717. Available at:
975 http://dx.doi.org/10.1016/j.gca.2010.07.006.

976 Tripati, A. K., Hill, P. S., Eagle, R. A., Mosenfelder, J. L., Tang, J., Schauble, E. A., ... & Henry, D.
977 (2015). Beyond temperature: Clumped isotope signatures in dissolved inorganic carbon
978 species and the influence of solution chemistry on carbonate mineral
979 composition. *Geochimica et Cosmochimica Acta*, 166, 344-371.

980 Urey, H.C., Lowenstam, H.A., Epstein, S. and McKinney, C.R. (1951): Measurements of
981 paleotemperatures and temperatures of the Upper Cretaceous of England, Denmark
982 and the southeastern United States. Bull. Geo. Soc. of Am., 62: 399-416.

983 Vázquez Riveiros N., Govin A., Waelbroeck C., Mackensen A., Michel E., Moreira S., Bouinot T.,
984 Caillon N., Orgun A. and Brandon M. (2016) Mg/Ca thermometry in planktic foraminifera: improving paleotemperature estimations for G. bulloides and N. pachyderma left.
985 Geochem. Geophy. Geosy. 17, 1249-1264. https://doi.org/10.1002/2015GC006234

987 Watkins, J. M., & Hunt, J. D. (2015). A process-based model for non-equilibrium clumped
988 isotope effects in carbonates. *Earth and Planetary Science Letters*, 432, 152-165.
989 Whitaker J., Khrulev C., Huard D., Paulik C., Hoyer S., Mohr F. A., Marquardt C., Couwenberg
990 B., Bohnet M., Brett M., Hetland R., Korenčiak M., Onu K., Helmus J. J., Hamman J.,
991 Barna A., Koziol B., Kluyver T., May R., Smrekar J., Barker C., Davar G., Cournapeau
992 D., da Silva D., Gohlke C., Kinoshita B. P. (2019). Unidata/netcdf4-pythin: version
993 1.4.3.2 release (v1.4.3.2). Zenodo. https://doi.org/10.5281/zenodo.2592291

994 Yu, J.M., Day, J., Greaves, M., Elderfield, H., 2005. Determination of multiple element/calcium
ratios in foraminiferal calcite by quadrupole ICP-MS. Geochem. Geophys. Geosyst. 6,
996 Q08P01. doi:10.1029/2005GC000964.

997 Zeebe R.E. (1999). An explanation of the effect of seawater carbonate concentration on
998 foraminiferal oxygen isotopes. Geochim. Cosmochim. Acta, 63, 2001-2007.

999 Zweng, M.M, J.R. Reagan, J.I. Antonov, R.A. Locarnini, A.V. Mishonov, T.P. Boyer, H.E. Garcia,  
1000 O.K. Baranova, D.R. Johnson, D.Seidov, M.M. Biddle, 2013. *World Ocean Atlas 2013*,  
1001 *Volume 2: Salinity*. S. Levitus, Ed., A. Mishonov Technical Ed.; NOAA Atlas NESDIS 74, 39  
1002 pp.
1003 **Author contributions**

1004 MP and FB have designed the study. MP wrote the manuscript, and all co-authors help in the
1005 writing. MD provided the python code to reprocess the clumped-isotope calibration. FB, DB,
1006 MD and WG provided assistance in the interpretation of the clumped-isotope and/or Mg/Ca
1007 data. JB, FJ, CK, EM and CW helped in the selection of the marine sediment cores and
1008 foraminifer species. MP hand-picked the foraminiferal samples. MP and HR cleaned the
1009 samples for the Mg/Ca measurements and HR and WG performed the Mg/Ca measurements.

1010

1011 **Acknowledgements**

1012 All authors thank the editor for his patience in the lengthy process of reviewing this article and
1013 the 3 anonymous reviewers for their really useful comments that significantly improve the
1014 manuscript. MP thanks the CEA for the financially support during her 3-years PhD fellowship
1015 2015-2018.
<table><caption>**Table 1:** Core top locations and water depth with species considered in this study and chronological.</caption><thead><tr><th>Cores</th><th>Latitude (°)</th><th>Longitude (°)</th><th>Water depth (m)</th><th>Species</th><th>Core-top cal. yrs BP (95% CL)</th><th>References</th></tr></thead><tbody><tr><td>MOCOSEDst1</td><td>73.04</td><td>-11.93</td><td>1839</td><td>Cibicides wuellerstorfi; N. pachyderma s</td><td>6317 (+150/-94) *</td><td>(1)</td></tr><tr><td>MD04-2720</td><td>-49.13</td><td>71.36</td><td>750</td><td>N. pachyderma d</td><td>n.a.</td><td></td></tr><tr><td>MD12-3401</td><td>-44.69</td><td>80.4</td><td>3445</td><td>G. bulloides</td><td>&lt; 4000 **</td><td>(2)</td></tr><tr><td>MD95-2014</td><td>60.59</td><td>-22.08</td><td>2397</td><td>G. bulloides</td><td>715 (+94/-149) *</td><td>(1)</td></tr><tr><td>MD08-3182Q</td><td>52.71</td><td>-35.94</td><td>1355</td><td>N. pachyderma s; G. bulloides</td><td>500 (+40/-53) *</td><td>(3)</td></tr><tr><td>MD03-2680Q</td><td>61.06</td><td>-24.55</td><td>1812</td><td>N. pachyderma d</td><td>402</td><td>(4)</td></tr><tr><td>2FPA1</td><td>43.67</td><td>-2.00</td><td>664</td><td>Uvigerina mediterranea</td><td>&lt; 4000 ***</td><td>(1)</td></tr><tr><td>SU90I-03</td><td>40.05</td><td>-30</td><td>2475</td><td>G. bulloides</td><td>2013 (+125/-120) *</td><td>(1)</td></tr><tr><td>MD08-3179Q</td><td>37.86</td><td>-30.3</td><td>2036</td><td>G. ruber; G. inflata; G. truncatulinoides s; G. truncatulinoides d</td><td>4403 (+153/-121) *</td><td>(1)</td></tr><tr><td>MD12-3426Q</td><td>19.73</td><td>114.61</td><td>3630</td><td>G. menardii; O. universa</td><td>1755 (+159/-139) *</td><td>(1)</td></tr><tr><td>MD00-2360</td><td>-20.08</td><td>112.67</td><td>980</td><td>G. menardii; O. universa; G. ruber</td><td>3622 (+135/-137) *</td><td>(1)</td></tr><tr><td>MD02-2577Q</td><td>28.84</td><td>-86.67</td><td>4076</td><td>G. menardii; O. universa; G. ruber</td><td>1107 (+110/-105) *</td><td>(1)</td></tr></tbody></table>

* Age determined by radiocarbon dating

** Age determined by stratigraphic control

*** Age determined by presence of Rose Bengal

(1) Peral et al., 2018; (2) Vazquez Riveiros et al., 2016; (3) Kissel et al., 2013 and (4) Kissel et al., 2009
<table><caption>**Table 2:** Summary of the main results used in this study. The samples/species are represented with the optimal size fraction. The raw Mg/Ca values are presented, as well as the δ¹⁸Oc and the recalculated Δ₄₇ values with their associated uncertainties at 1SE. We also present the corrected Mg/Ca values for salinity and pH. Seawater salinity from WOA and pH from GLODAP 2020 (Olsen et al., 2020), are reported.</caption><thead><tr><th>Core</th><th>Species</th><th>Optimal Size</th><th>δ18Oc SE VPDB (‰)</th><th>Δ47 SE (‰)</th><th>Mg/Ca SE raw</th><th>Mg/Ca SE corrected</th><th>pH SE reconstructed</th></tr></thead><tbody><tr><td>MD08-3182</td><td>G. bulloides</td><td>250-315</td><td>1.77 0.1</td><td>0.6489 0.0074</td><td>2.10 0.006</td><td>2.24 0.309</td><td>7.941 0.27</td></tr><tr><td>MD08-3182</td><td>G. bulloides</td><td>315-355</td><td>1.87 0.1</td><td>0.665 0.0074</td><td>2.06 0.006</td><td>2.20 0.300</td><td>7.571 0.28</td></tr><tr><td>MD12-3401</td><td>G. bulloides</td><td>250-315</td><td>2.04 0.1</td><td>0.6626 0.0075</td><td>1.45 0.006</td><td>1.64 0.144</td><td>8.041 0.23</td></tr><tr><td>MD95-2014</td><td>G. bulloides</td><td>315-355</td><td>2.13 0.1</td><td>0.6492 0.0074</td><td>4.69 0.006</td><td>4.86 0.211</td><td>7.044 0.39</td></tr><tr><td>SU90-03</td><td>G. bulloides</td><td>250-315</td><td>1.59 0.1</td><td>0.6429 0.0063</td><td>3.30 0.006</td><td>3.44 0.427</td><td>7.570 0.30</td></tr><tr><td>MD08-3179</td><td>G. inflata</td><td>355-400</td><td>1.19 0.1</td><td>0.6286 0.0074</td><td>2.03 0.008</td><td>2.10 0.328</td><td>8.283 0.31</td></tr><tr><td>MD08-3179</td><td>G. inflata</td><td>400-450</td><td>1.08 0.1</td><td>0.6219 0.0073</td><td>1.68 0.008</td><td>1.76 0.339</td><td>8.747 0.29</td></tr><tr><td>MD08-3179</td><td>G. inflata</td><td>450-500</td><td>1.24 0.1</td><td>0.6247 0.0085</td><td>2.00 0.008</td><td>2.08 0.323</td><td>8.429 0.35</td></tr><tr><td>MD00-2360</td><td>G. menardi menardi</td><td>355-400</td><td>-0.37 0.1</td><td>0.5977 0.0075</td><td>2.85 0.004</td><td>3.15 0.354</td><td>8.741 0.37</td></tr><tr><td>MD00-2360</td><td>G. menardi menardi</td><td>400-450</td><td>-0.29 0.1</td><td>0.619 0.0074</td><td>2.55 0.004</td><td>2.84 0.346</td><td>8.170 0.34</td></tr><tr><td>MD00-2360</td><td>G. ruber</td><td>250-315</td><td>-1.76 0.1</td><td>0.5917 0.0058</td><td>4.34 0.008</td><td>4.88 0.643</td><td>8.262 0.32</td></tr><tr><td>MD02-2577</td><td>G. ruber</td><td>250-315</td><td>-1.33 0.1</td><td>0.5959 0.0073</td><td>4.59 0.008</td><td>4.71 0.813</td><td>8.099 0.37</td></tr><tr><td>MD02-2577</td><td>G. ruber</td><td>315-355</td><td>-1.46 0.1</td><td>0.5977 0.0073</td><td>4.63 0.008</td><td>4.75 0.847</td><td>8.029 0.37</td></tr><tr><td>MD08-3179</td><td>G. ruber</td><td>250-315</td><td>-0.08 0.1</td><td>0.6167 0.0073</td><td>3.21 0.008</td><td>3.37 0.597</td><td>7.988 0.33</td></tr><tr><td>MD08-3179</td><td>G. truncatulinoides (d.)</td><td>355-400</td><td>1.05 0.1</td><td>0.6424 0.0074</td><td>1.97 0.006</td><td>2.05 0.345</td><td>7.926 0.25</td></tr><tr><td>MD08-3179</td><td>G. truncatulinoides (d.)</td><td>400-450</td><td>1.14 0.1</td><td>0.6251 0.0074</td><td>2.09 0.006</td><td>2.16 0.336</td><td>8.331 0.34</td></tr><tr><td>MD08-3179</td><td>G. truncatulinoides (d.)</td><td>450-500</td><td>1.07 0.1</td><td>0.6278 0.0074</td><td>2.06 0.006</td><td>2.14 0.342</td><td>8.268 0.33</td></tr><tr><td>MD08-3179</td><td>G. truncatulinoides (s.)</td><td>355-400</td><td>1.08 0.1</td><td>0.638 0.0074</td><td>1.91 0.006</td><td>1.99 0.341</td><td>8.080 0.28</td></tr><tr><td>MD08-3179</td><td>G. truncatulinoides (s.)</td><td>400-450</td><td>1.07 0.1</td><td>0.6343 0.0074</td><td>1.90 0.006</td><td>1.98 0.342</td><td>8.184 0.30</td></tr><tr><td>MD08-3179</td><td>G. truncatulinoides (s.)</td><td>450-500</td><td>1.17 0.1</td><td>0.6342 0.0074</td><td>1.72 0.006</td><td>1.79 0.332</td><td>8.312 0.31</td></tr><tr><td>MD03-2680</td><td>N. pachyderma (d.)</td><td>200-250</td><td>1.73 0.1</td><td>0.647 0.0074</td><td>1.16 0.008</td><td>1.184 0.008</td><td></td></tr><tr><td>MD04-2720</td><td>N. pachyderma (d.)</td><td>200-250</td><td>3.24 0.1</td><td>0.676 0.0075</td><td>0.76 0.008</td><td>0.87 0.008</td><td></td></tr><tr><td>MD08-3182</td><td>N. pachyderma (s.)</td><td>200-250</td><td>1.76 0.1</td><td>0.6504 0.0074</td><td>1.09 0.006</td><td>1.17 0.006</td><td></td></tr><tr><td>MOCOSED</td><td>N. pachyderma (s.)</td><td>200-250</td><td>2.86 0.1</td><td>0.6678 0.0074</td><td>0.90 0.006</td><td>1.15 0.006</td><td></td></tr></tbody></table>
<table><caption>**Table 3:** Summary of all the Mg/Ca calibration used in this study: mono-specific species calibrations, calibration with salinity and pH corrections and the salinity and pH corrected multi-species calibration</caption><thead><tr><th colspan="5">Recalculated multi-species calibration from Anand et al., 2003</th></tr><tr><th colspan="5">Mg/Ca = B*exp(A*T)</th></tr></thead><tbody><tr><td></td><td>Values</td><td>SE</td><td></td><td></td></tr><tr><td>A</td><td>0.0913</td><td>0.003</td><td></td><td>Recalculated in this study</td></tr><tr><td>B</td><td>0.6109</td><td>0.002</td><td></td><td></td></tr><tr><th colspan="5">Mono-specific calibrations</th></tr><tr><th colspan="5">Mg/Ca = B*exp(A*T)</th></tr><tr><td></td><td>Values</td><td>SE</td><td>Size fraction</td><td></td></tr><tr><td>G. menardii</td><td>A<br>B</td><td>0.091<br>0.36</td><td>0.012<br>0.31</td><td>355-400</td><td>Regenberg et al., 2009</td></tr><tr><td>O. universa</td><td>A<br>B</td><td>0.085<br>1.38</td><td>0.002<br>0.05</td><td>NA</td><td>Lea et al., 1999</td></tr><tr><td></td><td>A<br>B</td><td>0.09<br>0.595</td><td>0.042</td><td>350-500</td><td></td></tr><tr><td>G. ruber</td><td>A<br>B</td><td>0.09<br>0.449</td><td>0.006</td><td>250-350</td><td>Anand et al., 2003</td></tr><tr><td></td><td>A<br>B</td><td>0.09<br>0.395</td><td>0.009</td><td>350-500</td><td></td></tr><tr><td>N. pachyderma s</td><td>A<br>B</td><td>0.084<br>0.58</td><td>0.006<br>0.084</td><td>200-250</td><td>Vasquez Riveiros et al., 2016</td></tr><tr><td>G. inflata</td><td>A<br>B</td><td>0.09<br>0.299</td><td>0.005</td><td>350-500</td><td></td></tr><tr><td>G. truncatulinoides d.</td><td>A<br>B</td><td>0.09<br>0.359</td><td>0.008</td><td>350-500</td><td>Anand et al., 2003</td></tr><tr><td>G. truncatulinoides s.</td><td>A<br>B</td><td>0.09<br>0.359</td><td>0.008</td><td>350-500</td><td></td></tr><tr><td>G. bulloides</td><td>A<br>B</td><td>0.081<br>0.81</td><td>0.005<br>0.04</td><td>250-315</td><td>Elderfield and Ganssen. 2000<br>North Atlantic</td></tr><tr><td></td><td>A<br>B</td><td>0.061<br>0.996</td><td>0.005<br>0.038</td><td>250-315</td><td>Elderfield and Ganssen. 2000<br>Southern Ocean</td></tr><tr><th colspan="5">Mono-specific calibrations with SSS and pH corrections</th></tr><tr><th colspan="5">Mg/Ca=exp(A*(S - B) + C*T + D*(pH - E) + F)</th></tr><tr><td></td><td>Values</td><td>SE</td><td></td><td></td></tr><tr><td>G. ruber</td><td>A<br>B<br>C<br>D<br>E<br>F</td><td>0.036<br>35<br>0.061<br>-0.87<br>8<br>0.03</td><td>0.006<br>0.005<br>0.1<br>0<br>0.03</td><td></td><td></td></tr><tr><td>G. bulloides</td><td>A<br>B<br>C<br>D<br>E<br>F</td><td>0.036<br>35<br>0.061<br>-0.88<br>8<br>0.21</td><td>0.006<br>0.005<br>0.12<br>0<br>0.04</td><td>Gray and Evans. 2019</td><td></td></tr><tr><td>O. universa</td><td>A<br>B<br>C<br>D<br>E<br>F</td><td>0.036<br>35<br>0.061<br>-0.51<br>8<br>0.77</td><td>0.006<br>0.005<br>0.11<br>0<br>0.48</td><td></td><td></td></tr><tr><td>Multi-species</td><td>A<br>B<br>C<br>D<br>E<br>F</td><td>0.036<br>35<br>0.061<br>-0.73<br>8<br>0</td><td>0.006<br>0.005<br>0.07<br>0<br>0</td><td></td><td></td></tr></tbody></table>
Step 1

<figure><img src="image_8.png" /></figure>

Step 2

<figure><img src="image_9.png" /></figure>

Step 3

<figure><img src="image_10.png" /></figure>

Cleaning protocol for clumped
isotope in foraminifera

**Step 1: Crush the foraminifera**

Gently crush foraminifera between
two glass slides to open all chambers

**Step 2: remove clay**

Add milliQ water

Remove the water

Ultrasonic bath for 30s

Repeat 3 times or more until water
remains clear and colourless

Add methanol

Ultrasonic bath for 30s

Remove the methanol

Repeat 2 time or more until the
methanol remains clear and colourless

Remove the maximum of the
methanol

**Step 3: Dry**

Dry at room temperature under a
fume hood. Microtubes should be
open but covered with aluminum foil
to avoid dust contaminants

Equipment:

Microtubes, gloves, fume hood, microscope, 4 beaker (for water & dirty water and for methanol & dirty methanol), pipette and pipette tip (change for each sample or each step)

4
5

6

**Figure S1:** summary of the cleaning protocol steps for clumped isotope in foraminifera
7

<figure><img src="image_11.png" /></figure>

<table><thead><tr><th>Species list:</th><th>● G. bulloides</th><th>♦ O. universa</th><th>■ N. pachyderma s.</th><th>▽ G. truncatulinoides s.</th></tr></thead><tbody><tr><td>○ G. ruber</td><td>◇ G. menardi</td><td>△G. inflata</td><td>☐ N. pachyderma d.</td><td>▼ G. truncatulinoides d.</td></tr></tbody></table>

8

9

10

11

12

13

14

15

**Figure S2:** reconstructed Mg/Ca temperatures using the original multi-species calibration of Anand et al. (2003) compared to reconstructed δ¹⁸O temperatures, using Kim and O'Neil (1997) (a) and Δ₄₇-derived temperatures, using recalculated Peral et al. (2018) (b) for 9 planktic foraminifera. The linear regressions are the dotted black lines, a line 1:1 is in black, and the uncertainties are at 2 SE. The Mg/Ca-derived temperatures are systematically higher than the isotopic-derived temperatures.
<figure><img src="image_12.png" /><figcaption>**Figure S3:** reconstructed Mg/Ca temperatures using the recalculated multi-species calibration of Anand et al. (2003) compared to reconstructed δ¹⁸O temperatures, using Kim and O'Neil (1997) (a) and reconstructed Mg/Ca derived temperatures using the most adequate mono-specific calibrations compared to reconstructed δ¹⁸O temperatures, using Kim and O'Neil (1997) and Bemis et al. (1998) calibration for *G. bulloides* (b). The linear regressions are the dotted black lines, the 1:1 line is the black solid line, and the uncertainties are at 2 SE.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Figure S4:** relationship between the seawater salinity from WOA 13 and the δ¹⁸O of the seawater from GISS atlas for all our samples defined as core/species. For benthic foraminifera we used the available bottom data and planktonic foraminifera we integrated data withing the column water corresponding to the known living depths of each specie (see details in Peral et al., 2018). The linear regressions are the dotted black lines, a line 1:1 is in black, and the uncertainties are at 2 SE.</figcaption></figure>
**Figure 1:** Map of core-top location used in this study, with the mean annual SST from WOA13

**Figure 2:** Comparison of temperature estimates obtained on 9 planktonic species. Top panels: reconstructed Mg/Ca temperatures using the recalculated multi-species calibration of Anand et al. (2003) compared to reconstructed $\delta^{18}$O temperatures, using Kim and O'Neil (1997) (a) and $\Delta_{47}$-derived temperatures, using recalculated Peral et al. (2018) (b). Bottom panel: reconstructed Mg/Ca derived temperatures using the most adequate mono-specific calibrations compared to reconstructed $\delta^{18}$O temperatures, using Kim and O'Neil (1997) (c) and $\Delta_{47}$-derived temperatures, using recalculated Peral et al. (2018) calibration (d). Dotted black lines are linear regressions, the black solid lines are the 1:1 line. Uncertainties are at 2SE.

**Figure 3:** Comparison of our recalculated foraminiferal $\Delta_{47}$ values with raw Mg/Ca values (uncorrected) (a), with corrected Mg/Ca for salinity only (b), and with corrected Mg/Ca for salinity and pH (c). The Mg/Ca values are corrected using the equations from Gray and Evans (2019), the salinity and pH from the atlas and the oxygen isotopic temperatures. The red dotted logarithmic regressions are plotted for all the plots, including *G. bulloides* and the black regressions are without *G. bulloides*. All the uncertainties are at 2SE.

**Figure 4:** Recalculated $\Delta_{47}$ values (mean and 2SE) compared to oxygen isotopic temperatures (mean and 2SE) obtained with Kim and O'Neil (1997) for planktonic (circle) and benthic (square) foraminifera samples, combining all size fractions (modified from Peral et al., 2018). The new calibration regression corresponds to the black line (Peral et al., 2018 recalculated). The recalculated foraminiferal calibration is compared to the slow-growing calcite from Laghetto Basso and Devils Hole (from Anderson et al., 2021) and to calibrations of Anderson et al. (2021) and Fiebig et al. (2021).

**Figure 5:** Mg/Ca-derived temperatures using mono-species calibrations, compared to the $\Delta_{47}$-derived temperatures using the recalculated Peral et al. (2018) calibration (a) and the Mg/Ca-derived temperatures using the corrected Mg/Ca mono-species calibrations for salinity and pH compared to the $\Delta_{47}$-derived temperatures using the recalculated Peral et al. (2018) calibration (b). The dotted linear regression, excluding *O. universa* and *G. bulloides*, is plotted. A line 1:1 is plotted in black; uncertainties are at 2 SE.
64

65

66

67

68

69

70

**Figure 6:** the difference for all the species from our dataset (excluding *O. universa*, *G. bulloides* and *N. pachyderma*) between the extracted pH from the atlas (GLOPAD 2020) and the reconstructed pH, using the equations from Gray and Evans (2019) with the raw Mg/Ca, the $\Delta_{47}$-derived temperatures, and the combination of $\delta^{18}$O and $\Delta_{47}$-derived temperatures to reconstruct the $\delta^{18}$Osw. The uncertainties correspond to the uncertainties associated with the reconstructed pH (2SE)