Boron Isotopes in Foraminifera: Systematics, Biomineralisation, and CO2 Reconstruction

Rae, James W. B.

doi:10.1007/978-3-319-64666-4_5

James W. B. Rae⁴

Part of the book series: Advances in Isotope Geochemistry ((ADISOTOPE))

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Abstract

The boron isotope composition of foraminifera provides a powerful tracer for CO₂ change over geological time. This proxy is based on the equilibrium of boron and its isotopes in seawater, which is a function of pH. However while the chemical principles underlying this proxy are well understood, its reliability has previously been questioned, due to the difficulty of boron isotope (δ¹¹B) analysis on foraminferal samples and questions regarding calibrations between δ¹¹B and pH. This chapter reviews the current state of the δ¹¹B-pH proxy in foraminfera, including the pioneering studies that established this proxy’s potential, and the recent work that has improved understanding of boron isotope systematics in foraminifera and applied this tracer to the geological record. The theoretical background of the δ¹¹B-pH proxy is introduced, including an accurate formulation of the boron isotope mass balance equations. Sample preparation and analysis procedures are then reviewed, with discussion of sample cleaning, the potential influence of diagenesis, and the strengths and weaknesses of boron purification by column chromatography versus microsublimation, and analysis by NTIMS versus MC-ICPMS. The systematics of boron isotopes in foraminifera are discussed in detail, including results from benthic and planktic taxa, and models of boron incorporation, fractionation, and biomineralisation. Benthic taxa from the deep ocean have δ¹¹B within error of borate ion at seawater pH. This is most easily explained by simple incorporation of borate ion at the pH of seawater. Planktic foraminifera have δ¹¹B close to borate ion, but with minor offsets. These may be driven by physiological influences on the foraminiferal microenvironment; a novel explanation is also suggested for the reduced δ¹¹B-pH sensitivities observed in culture, based on variable calcification rates. Biomineralisation influences on boron isotopes are then explored, addressing the apparently contradictory observations that foraminifera manipulate pH during chamber formation yet their δ¹¹B appears to record the pH of ambient seawater. Potential solutions include the influences of magnesium-removal and carbon concentration, and the possibility that pH elevation is most pronounced during initial chamber formation under favourable environmental conditions. The steps required to reconstruct pH and pCO₂ from δ¹¹B are then reviewed, including the influence of seawater chemistry on boron equilibrium, the evolution of seawater δ¹¹B, and the influence of second carbonate system parameters on δ¹¹B-based reconstructions of pCO₂. Applications of foraminiferal δ¹¹B to the geological record are highlighted, including studies that trace CO₂ storage and release during recent ice ages, and reconstructions of pCO₂ over the Cenozoic. Relevant computer codes and data associated with this article are made available online.

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5.1 Introduction

The boron isotope composition of marine carbonates has been widely shown to reflect ocean pH (Vengosh et al. 1991; Hemming and Hanson 1992; Sanyal et al. 1996; Foster 2008; Rae et al. 2011; Henehan et al. 2013). Boron isotope measurements on fossil carbonates thus have the potential to constrain changes in pH and CO₂ over geological time (Pearson and Palmer 2000; Hönisch et al. 2009; Rae et al. 2014; Penman et al. 2014; Greenop et al. 2014; Martínez-Botí et al. 2015a). The shells, or “tests”, of foraminifera, which are single-celled protists, provide a convenient host for the δ¹¹B-pH proxy, being widely distributed throughout the world’s oceans, relatively well-preserved in marine sediment cores, and having chemistry that closely reflects surrounding seawater conditions (Wefer et al. 1999; Erez 2003). Foraminifera have thus become key agents in geochemical reconstructions of past climates, and boron isotope analyses on foraminifera may be readily compared to tracers of various other conditions determined on the same samples (Katz et al. 2010).

5.1.1 Aqueous Boron Isotope Systematics

The ability of boron isotopes in foraminifera to record seawater pH stems from the acid-base equilibrium between boric acid (B(OH)₃) and borate ion $ \left( {{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } } \right) $:

$$ {\text{B}}\left( {\text{OH}} \right)_{3} + {\text{H}}_{2} {\text{O}} \rightleftharpoons {\text{B}}\left( {\text{OH}} \right)_{4}^{ - } + {\text{H}}^{ + } . $$

(5.1)

The equilibrium constant of this reaction (K_B) is 10^−8.6 (Dickson 1990), giving pK_B of 8.6, close enough to typical ocean pH (~8) to give large changes in the relative abundance of these molecules as a function of seawater pH (Fig. 5.1a):

$$ K_{B} = \frac{{[{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } ][{\text{H}}^{ + } ]}}{{[{\text{B}}\left( {\text{OH}} \right)_{3} ]}} ;\quad pK_{B} \approx 8.6. $$

(5.2)

Boron has two stable isotopes, ¹¹B (~80%) and ¹⁰B (~20%), and an equilibrium fractionation of 27.2‰ (Klochko et al. 2006) exists between boric acid and borate ion, due to the stronger bonding environment of boron in the trigonal boric acid molecule:

$$ \alpha_{B} = \frac{{^{{\frac{11}{10}}} R_{{{\text{B}}\left( {\text{OH}} \right)_{3}^{{}} }} }}{{^{{\frac{11}{10}}} R_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} }} = 1.0272. $$

(5.3)

The boron isotope composition of seawater (δ¹¹B_SW) is 39.61‰ (Foster et al. 2010). As boron in seawater is overwhelmingly made up of boric acid and borate,^{Footnote 1} the combined boron nuclides within these molecules must give ¹¹B/¹⁰B equal to that in seawater. Therefore as the abundance of these molecules vary, so too must their isotopic composition (Fig. 5.1b). At low pH, where seawater boron is dominantly present as boric acid, this molecule must have δ¹¹B = δ¹¹B_SW, with an infinitesimal quantity of borate ion offset below this by a function of the fractionation factor:

$$ \updelta^{11} {\text{B}}_{{{\text{B}}\left( {\text{OH}} \right)_{3} }} =\updelta^{11} {\text{B}}_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} \cdot \alpha_{B} +\upvarepsilon_{B} , $$

(5.4)

where ε_B = 1000 · (α_B − 1). The opposite is true at high pH, while at intermediate pH the isotopic composition of these molecules will vary as a predictable function of pH. This is commonly expressed as the mass balance:

$$ \begin{aligned}^{{\frac{11}{10}}} R_{SW} \times \left[ B \right]_{SW} & = ^{{\frac{11}{10}}} R_{{{\text{B}}\left( {\text{OH}} \right)_{3} }} \times \left[ {{\text{B}}\left( {\text{OH}} \right)_{3} } \right] \\ & \quad + \, ^{{\frac{11}{10}}} R_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} \times \left[ {{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } } \right], \\ \end{aligned} $$

(5.5)

from which, rearranging and substituting Eq. (5.4), the following expression for borate isotopic composition as a function of pH can be derived:

$$ \updelta^{11} {\text{B}}_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} = \frac{{\updelta^{11} {\text{B}}_{{\left( {sw} \right)}} \left[ B \right]_{sw} - \varepsilon_{B} \left[ {{\text{B}}\left( {\text{OH}} \right)_{3} } \right]}}{{\left[ {{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } } \right] + \alpha_{B} \left[ {{\text{B}}\left( {\text{OH}} \right)_{3} } \right]}} . $$

(5.6)

However note that this is an approximation, as mass balance cannot accurately be formulated in terms of isotope ratios. More strictly, we must write the mass balance for each nuclide and then combine these equations to obtain the isotope ratio mass balance. This gives the formula:

$$ \begin{aligned} & \frac{{^{{\frac{11}{10}}} R_{SW} \cdot \left( {\left[ {{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } } \right] + \left[ {{\text{B}}\left( {\text{OH}} \right)_{3}^{{}} } \right]} \right)}}{{^{{\frac{11}{10}}} R_{SW} + 1}} \\ & \quad = \,\frac{{^{{\frac{11}{10}}} R_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} \cdot \alpha_{B} \cdot \left[ {{\text{B}}\left( {\text{OH}} \right)_{3} } \right]}}{{^{{\frac{11}{10}}} R_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} \cdot \alpha_{B} + 1}} \\ & \quad + \, \frac{{^{{\frac{11}{10}}} R_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} \cdot \left[ {{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } } \right]}}{{^{{\frac{11}{10}}} R_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} + 1}}. \\ \end{aligned} $$

(5.7)

which can be rearranged and solved (best done by computer; see supplementary code) for the isotopic composition of borate. This is given by the root:

$$ \begin{aligned} R_{{{\text{B}}({\text{OH}})_{4}^{ - } }} & = ((H^{2} \cdot R_{SW}^{2} + 2H^{2} \cdot R_{SW} \cdot \alpha_{B} \\ & \quad + \,H^{2} \cdot \alpha_{B}^{2} + 2H \cdot K_{B} \cdot R_{SW}^{2} \cdot \alpha_{B} \\ & \quad - \,2H \cdot K_{B} \cdot R_{SW} \cdot \alpha_{B}^{2} \\ & \quad + \;8 \cdot H \cdot Kb \cdot R_{SW} \cdot \alpha_{B} \\ & \quad - \,2 \cdot H \cdot K_{B} \cdot R_{SW} \\ & \quad + \,2H \cdot K_{B} \cdot \alpha_{B} + K_{B}^{2} \cdot R_{SW}^{2} \cdot \alpha_{B}^{2} \\ & \quad + \,2K_{B}^{2} \cdot R_{SW} \cdot \alpha_{B} + K_{B}^{2} )^{(1/2)} \\ & \quad - \,H \cdot \alpha_{B} - K_{B} + H \cdot R_{SW}^{{}} \\ & \quad + \,K_{B} \cdot R_{SW} \cdot \alpha_{B} )/(2 \cdot \alpha_{B} \cdot (H + K_{B} )); \\ \end{aligned} $$

(5.8)

where R is the ¹¹B/¹⁰B ratio and H is the hydrogen ion concentration. Equation (5.4) can then be used to calculate the composition of boric acid. The error in calculated boron isotopic compositions resulting from the use of the approximation in Eq. (5.6) compared to the accurate formula in Eq. (5.8) is illustrated in Fig. 5.1c, and may be up to 0.15‰. Matlab codes and an Excel spreadsheet that carry out these calculations are provided in the supplementary online materials.

5.1.2 The Carbonate δ¹¹B-pH Proxy

Marine carbonates have boron isotopic compositions of ~15–25‰, substantially lower than that of seawater (39.61‰). This is explained by the dominant incorporation of borate ion into growing carbonate (Vengosh et al. 1991; Hemming and Hanson 1992). As the boron isotopic composition of borate varies with pH, so too should δ¹¹B of marine carbonate.

Early calibrations of boron isotopes in foraminifera showed strong control by pH (Sanyal et al. 1996, 2001), leading to several applications to reconstruct past CO₂ system change and its causes (Sanyal et al. 1995; Pearson and Palmer 2000; Palmer and Pearson 2003). However the reliability of this proxy has been challenged, notably by Pagani et al. (2005a). Concerns with the δ¹¹B-pH proxy have centered on: (1) boron isotope fractionation; (2) mechanisms of boron incorporation into carbonate; (3) vital effects in foraminifera; (4) analytical uncertainties; (5) the evolution of δ¹¹B_SW. While several of these topics remain the subject of considerable ongoing research, significant progress has been made on each of these fronts.

Box 1: A quick primer on the ocean carbonate system

The behaviour of boron isotopes in foraminifera discussed in this chapter is intimately linked to the chemistry of CO₂ in seawater, so a brief review of this topic may be helpful. For more detailed treatment see Zeebe and Wolf-Gladow (2001) and Sarmiento and Gruber (2006).

CO₂ reacts with water to form bicarbonate (HCO₃ ⁻) and carbonate ion (CO₃ ²⁻):

$$ {\text{CO}}_{2 } + {\text{H}}_{2} {\text{O}} \mathop \Leftrightarrow \limits^{{K_{1} }} {\text{H}}^{ + } + {\text{HCO}}_{3}^{2 - } \mathop \Leftrightarrow \limits^{{K_{ 2} }} 2{\text{H}}^{ + } + {\text{CO}}_{3}^{2 - } $$

where K ₁ and K ₂ are the first and second dissociation constants for carbonic acid, and have values of ~10⁻⁶ and ~10⁻⁹ respectively (varying with temperature, salinity, pressure, and major ion chemistry).

pH (and thus δ¹¹B of borate) is a sensitive tracer of the equilibrium state of this acid-base system. However this state is actually controlled by the balance between the master variables alkalinity (ALK) and dissolved inorganic carbon (DIC). DIC is simply the total concentration of inorganic carbon molecules. ALK is analytically defined as the number of moles of strong acid required to drive seawater to the equivalence point of bicarbonate. More intuitively, ALK is equivalent to the charge imbalance between strong bases and strong acids in seawater (see inset figure based on Broecker 2005). The requirement for charge balance is taken up largely by variable dissociation of weak acids and bases, predominantly those of CO₂ and boron.

Therefore if alkalinity is large and the pool of DIC to balance it is relatively small, the carbonate system must be pulled toward doubly charged CO₃ ²⁻; vice versa, if a large pool of DIC exists but alkalinity is small, much of the DIC must be present as uncharged CO₂. pCO₂, [CO₃ ²⁻], pH (and $ \left[ {{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } } \right] $) are thus primarily controlled by the balance of ALK and DIC, and as a result are tightly coupled and closely traced by δ¹¹B of borate. This is well illustrated by a ALK-DIC contour plot (inset figure, plotted for 25 °C, 35 psu, and 0 m water depth).

A final important concept is calcium carbonate mineral saturation (Ω):

$$ \Omega = \frac{{[{\text{Ca}}^{2 + } ] \times [{\text{CO}}_{3}^{ - } ]}}{{K_{\text{sp}} }} $$

where K _sp is the equilibrium solubility product, ~10^−6.4 for calcite and ~10^−6.2 for aragonite in the surface ocean. Undersaturated conditions correspond to Ω < 1, supersaturated conditions to Ω > 1. Ω_calcite ranges from ~4–6 in most of the modern surface ocean, dominantly as a function of [CO₃ ²⁻], and decreases to <1 at depth.

5.2 Methods of Boron Isotope Analysis in Foraminifera

The analysis of boron isotopes is discussed in detail by Foster et al. (2013) for carbonates, and in Chap. 2 of this volume for a broad range of natural samples. Below I provide a brief overview of the specifics of δ¹¹B analysis of foraminifera, which is challenging due to the small sample sizes and complex matrix involved, and has been a topic of considerable discussion (Ni et al. 2010; Foster et al. 2013; Farmer et al. 2016).

5.2.1 Samples

5.2.1.1 Sample Size and Preparation

Foraminiferal samples are taken from ocean sediment cores, plankton tows, and culture experiments. For solution analyses between ~2 and 20 ng boron are typically used. Boron concentrations and shell masses vary considerably between different species of foraminifera (Yu and Elderfield 2007; Henehan et al. 2016), dictating the number of foraminifera required: for low mass (5–20 μg) low B/Ca (40–60 μmol/mol) planktic species such as G. bulloides and N. pachyderma, ~400 specimens are typically required; for bulkier (10–30 μg) or higher B/Ca (80–120 μmol/mol) planktic species such as T. sacculifer and G. ruber, ~100 specimens are required; for higher B/Ca epifaunal benthic species such as C. wuellerstorfi and C. mundulus (~30–100 μg; 100–250 μmol/mol) it is possible to analyze ~2–20 specimens. Note that analytical uncertainty increases as sample sizes are reduced (Rae et al. 2011).

For sediment core samples, standard 10 cm³ volumes of pelagic sediment are often sufficient, though this may vary considerably depending on setting. As with any foraminifera-based work, sediment disaggregation and sieving is required; detergents and disaggregation agents (Feldmeijer et al. 2013) may have high levels of boron and should be avoided.

5.2.1.2 Preservation and Diagenesis

Preservation state of foraminifera is not currently thought to exert major influence on boron isotope ratios. For instance, no change in δ¹¹B with partial dissolution is seen in recent G ruber (Ni et al. 2007; Seki et al. 2010; Henehan et al. 2013) or C. wuellerstorfi (Rae et al. 2011). Although changes in δ¹¹B have been noted with partial dissolution in recent T. sacculifer, this is thought to be due to the presence of dissolution resistant and anomalously low-δ¹¹B gametogenic calcite in this species (Hönisch and Hemming 2004; Ni et al. 2007; Seki et al. 2010).

Edgar et al. (2015) show similar δ¹¹B between well-preserved “glassy” and partially recrystallized “frosty” planktic foraminifera of Eocene age, despite lower B/Ca in the recrystallized samples. This may result from only partial exchange with pore waters during foraminiferal recrystalisation and from low partitioning of boron into inorganically (re)precipitated calcite (Uchikawa et al. 2015) compared to the original foraminiferal carbonate, especially under low-pH (and thus low borate) conditions (Edgar et al. 2015). Mass balance may thus help minimize the influence of diagensis on foraminiferal δ¹¹B.

5.2.2 Cleaning of Foraminiferal Samples

Samples of foraminifera for δ¹¹B analysis are typically subjected to physical and chemical cleaning, of the type developed for trace element determinations (Boyle 1981; Barker et al. 2003; Ni et al. 2007). This involves gentle crushing to open chambers, repeat ultrasonication in deionized water to remove clays, and oxidation of organic matter in bleach or buffered hydrogen peroxide. Extensive tests of the influence of cleaning on B/Ca ratios suggest that reductive cleaning, commonly employed for Cd/Ca, has little effect on B/Ca, but can result in substantial loss of shell material (Yu et al. 2007). This step is thus typically omitted when cleaning foraminifera for δ¹¹B (though may still be used if certain other trace element analyses on the same sample are required). Note that given the high contents of organic matter in cultured and towed foraminifera, these samples are typically subjected to a more thorough oxidative cleaning (Russell et al. 2004; Henehan et al. 2013). To check for sample cleanliness and obtain complementary proxy data, several laboratories analyse trace element ratios (e.g. Al/Ca) on aliquots of the same samples prior to boron isotope analyses. No strict cut-off value for contamination exists, as the boron to aluminium ratio and the boron isotope composition of the leachate will vary between samples, but samples with Al/Ca of a few hundred μmol/mol or more may be treated with suspicion (see also Deyhle and Kopf 2004).

5.2.3 Chemical Purification

Chemical purification of boron from the sample matrix is required prior to analysis by Multi-Collector Inductively-Coupled-Plasma Mass Spectrometry (MC-ICPMS; see Wei et al. 2014). Some Negative Thermal Ionisation Mass Spectrometry (NTIMS) methods also employ chemical purification, whereas others load samples in their dissolved carbonate matrix (compare Duke and Lamont methods in Foster et al. (2013) and see discussion in Farmer et al. 2016).

5.2.3.1 Column Chromatography

Boron purification is typically carried out using column chromatography, taking advantage of the Amberlite 743 boron-specific resin (Kiss 1988; Lemarchand et al. 2002). Dissolved samples are buffered to elevate pH, which allows borate to complex with the resin’s N-methyl-glucamine groups (Yoshimura et al. 1998). CaCO₃ matrix is then removed using deionized water, and boron is eluted using dilute acid. Some laboratories use a cation column to reduce major ion concentrations prior to Amberlite purification (Paris et al. 2010a; Trotter et al. 2011); and see Paris and Duke methods in Foster et al. 2013). As boron is volatile in acidic conditions (Gaillardet et al. 2001) it is not possible to pre-concentrate samples by evaporation, so column volumes must be minimized to concentrate boron for analysis. The column chromatography approach is common in isotope geochemistry and can provide data with reproducibility of ~0.2‰ (2SD; e.g. Rae et al. 2011). However the relatively long exposure time of samples purified by this technique requires laboratory contamination (“blank”) to be carefully controlled. This likely accounts for poor inter-laboratory reproducibility between MC-ICPMS techniques at small sample sizes (see discussion in Foster et al. 2013). Control of laboratory blank is a unique challenge for boron, due to the common use of boro-silicate fibers in HEPA filters, lab insulation, and fire-retardants (Rosner et al. 2005). However as boron contamination is also a problem for the semi-conductor industry, boron-free alternatives are available, allowing total procedural blanks to be kept to <100 pg under carefully controlled conditions (Wang et al. 2010; Rae et al. 2011).

5.2.3.2 Microsubliation

Boron purification has also been carried out by “micro-sublimation” (Gaillardet et al. 2001; Wang et al. 2010; Misra et al. 2014). This takes advantage of the volatility of boron to evaporate it from the sample matrix. The dissolved sample is loaded onto the upturned lid of a Teflon beaker, which is then closed and placed on a hotplate, allowing boron to evaporate from the matrix and condense along with water in the beaker’s upturned base. This method has the advantage of being totally enclosed, minimizing contamination. Microsublimation has yielded promising results for solution standards, seawater, and multiple aliquots of dissolved carbonate samples (Gaillardet et al. 2001; Wang et al. 2010; Misra et al. 2014). However results on foraminifera are more limited and, to date, show poorer reproducibility; for instance Misra et al. (2014) show that multiple solid splits of a foraminiferal sample have variability of ~1.7‰ (2SD). This is significantly larger than replicate aliquots of a single solution by this method (~0.5‰, 2SD), and cannot be attributed to sample heterogeneity, as the same levels of scatter are seen in subsamples of 25 and 50 foraminiferal tests (Misra et al. 2014). This may suggest variable mass fractionation during boron evaporation as a function of subtle differences in sample matrix.

5.2.4 Mass Spectrometry

5.2.4.1 NTIMS

The pioneering early work on boron isotopes in foraminifera was carried out by Negative Thermal Ionisation Mass Spectrometry (Hemming and Hanson 1994; Sanyal et al. 1995; Pearson and Palmer 2000). By switching polarity from typical positive TIMS and analyzing boron as BO₂ ⁻ beams instead of Cs₂B₂ ⁺, sample sizes were reduced to levels permitting analysis of small foraminiferal samples (Hemming and Hanson 1994). As described in greater detail in Chap. 2, the carbonate matrix promotes ionization of boron, so dissolved foraminifera are typically loaded directly onto filaments with no further purification (Kasemann et al. 2009; Farmer et al. 2016). However this sensitivity to matrix has the potential to introduce inaccuracies, with NTIMS analyses deviating from MC-ICPMS values in samples with low boron/matrix ratios (see inter-laboratory comparison by Foster et al. (2013) and intra-laboratory comparison by Farmer et al. 2016), though the exact cause of these offsets remains unknown.

5.2.4.2 MC-ICPMS

MC-ICPMS is increasingly used for analysis of boron isotopes on marine carbonates. As described above and in Chap. 2, this technique requires careful separation of boron from the carbonate matrix, and has further challenges including memory effects in the sample introduction system due to boron’s volatility (Al-Ammar et al. 2000), large mass bias (~15% per amu) requiring stable-enough conditions for accurate correction by sample-standard bracketing (Foster 2008), and relatively low sensitivity (~10 mV/ppb using a 50 μl/min nebuliser). Recent inter-laboratory comparison shows good agreement (~0.5‰ 2SD) between MC-ICPMS analyses for relatively large samples (Foster et al. 2013; Gutjahr et al. 2014). However reproducibility is notably poorer for smaller samples, of the size typically used in foraminiferal analyses (Foster et al. 2013), highlighting the need for careful control of laboratory blank.

5.2.4.3 In Situ Analysis

Laser-Ablation MC-ICPMS (LA-MC-ICPMS) and Secondary Ionisation Mass Spectrometry (SIMS) can be used to make in situ analyses of δ¹¹B in foraminifera (Rollion-Bard and Erez 2010; Fietzke et al. 2010; Kaczmarek et al. 2015). Until recently, the precision of these methods has been relatively low, due to low count rates. However recent technical developments, along with pooling of multiple spots have considerably improved LA-MC-ICPMS precision (Fietzke et al. 2015; Sadekov et al. 2016). Accurate correction for mass bias in situ analyses requires homogenous and carefully characterized standards, and matrix matching is important for SIMS (Kasemann et al. 2009), though less so for LA-MC-ICPMS (Fietzke et al. 2015). While in situ analysis is unlikely to replace bulk/solution techniques for generating foraminiferal δ¹¹B records, it may provide valuable insights into the distribution of boron isotopes within foraminiferal carbonate, and the statistical spread of δ¹¹B values of individuals within a sample population (Rollion-Bard and Erez 2010; Kaczmarek et al. 2015; Sadekov et al. 2016).

5.3 Boron Isotope Systematics in Modern Foraminifera

A particular attraction of the δ¹¹B-pH proxy is its underlying chemical framework: pH controls δ¹¹B of borate, and as borate is thought to be incorporated in foraminifera, foraminiferal δ¹¹B should track pH. However it is possible that equilibrium or kinetic isotopic fractionations occur on boron incorporation into carbonate, and/or that foraminiferal physiology may impart further offsets from inorganic systematics (known as “vital effects”). Thus it is crucial to test the relationship between δ¹¹B of borate, calculated from measured seawater pH, and foraminiferal δ¹¹B. This has been achieved with measurements of natural modern samples taken from sediment core-tops, plankton tow nets and sediment traps, and using culturing experiments, where foraminifera are taken from the wild and grown in controlled laboratory conditions over a range of pH.

As δ¹¹B proxy calibration studies aim to test the relationship between δ¹¹B in foraminifera and borate—on which this proxy is based—presenting calibration data on cross-plots of foram δ¹¹B versus δ¹¹B of borate is recommended. This also has the advantage over presentation on δ¹¹B-pH figures that different environmental conditions may be readily plotted together, whereas δ¹¹B-pH figures may only be constructed for a single set of environmental conditions (T, S, P, and resulting K_B). However given that several previous studies have shown calibration data on δ¹¹B-pH figures, these are also shown here for reference, with data plotted at the pH of the original growth conditions and δ¹¹B re-calculated for standard surface water conditions of 25 °C and 35 psu. This is achieved by applying the offset between foraminiferal and borate δ¹¹B found at the original growth conditions to the δ¹¹B of borate calculated with K_B for 25 °C, 35 psu, and 0 m depth, at the original growth pH, i.e.

1.
calculate δ¹¹B offset at in situ conditions: Δδ¹¹B = δ¹¹B_foram − δ¹¹B_{borate-in situ};
2.
calculate K_B at the T, S, P conditions of the desired pH-δ¹¹B plot, using Eq. (5.11) (and 5.12 and 5.13 if plotting at non-zero water depths);
3.
calculate δ¹¹B of borate for the desired plot conditions using Eq. (5.8), with K_B from step 2 above, and pH from the original measurement at in situ conditions;
4.
apply the δ¹¹B offset from step 1 to δ¹¹B of borate calculated in step 3, to give the adjusted foram δ¹¹B: δ¹¹B_{foram-adjusted} = δ¹¹B_borate-plot + Δδ¹¹B.

Other approaches to this adjustment are possible (for instance using pH rather than δ¹¹B offsets), but the assumptions and steps in the approach above are the most straightforward.

Boron isotope data on modern foraminifera are discussed below, from deep sea calcitic benthic, planktic, and other benthic foraminifera in turn. The implications of these data for δ¹¹B-pH systematics are then synthesized, including modes of boron incorporation into foraminiferal carbonate, isotopic fractionation and physiological influences, and constraints on pH during biomineralisation.

5.3.1 Results of Boron Isotope Calibration Studies on Modern Foraminifera

5.3.1.1 Deep Sea Benthic Foraminifera—A Model System?

The low-Mg calcite hyaline benthic foraminifera found in deep ocean environments provide a useful starting point for assessing foraminiferal boron isotope systematics. This grouping includes a wide range of genera, lacks symbionts, is thought to have relatively low metabolic rate, and inhabits stable deep-sea environments that span a wide range of conditions (pH, T, S, P, ∆CO₃ ²⁻ etc.).

Deep sea benthic foraminifera appear to record the δ¹¹B of borate ion—and thus pH—of the surrounding water with little or no modification. This is most readily demonstrated for the epifaunal taxa Cibicides and Planulina (Rae et al. 2011; Yu et al. 2010), which inhabit the sediment surface and thus have the closest association with bottom water conditions (Figs. 5.2 and 5.3). In a set of 45 foraminiferal δ¹¹B samples spanning 17 different sites in the Atlantic, C. wuellerstorfi, C. mundulus, C. lobatus, C. ungerianus, and P. ariminensis all have δ¹¹B that closely matches δ¹¹B of borate at bottom water pH (Rae et al. 2011). There are no systematic differences in δ¹¹B values with different foraminiferal test size nor between species (Rae et al. 2011). C. wuellerstorfi appears to track bottom water pH conditions with least scatter, as previously observed for other geochemical tracers (δ¹³C, δ¹⁸O, element/calcium ratios), likely due to its elevated epifaunal habitat (Lutze and Thiel 1987).

Infaunal benthic foraminifera also appear to record δ¹¹B of borate, but at conditions reflecting their pore water environment (Fig. 5.2). Infaunal species analysed to date include C. robertsonianus, Oridorsalis umbonatus, Gyroidina soldanii, Uvigerina peregrine, Melonis zaandamae, Ammonia beccarii, and Lenticulina vortex, inhabiting the top few cm of deep sea sediment. Infaunal foraminifera have δ¹¹B up to 2‰ lower than δ¹¹B of borate in bottom waters. However pH may be lowered in pore waters by oxidation of organic matter, and δ¹¹B of pore water itself may be lowered by interaction with light boron from clays, carbonate, opal, and organic matter (Rae et al. 2011). These factors combine to decrease δ¹¹B of borate by around −0.5 to −2.0‰ in the top 5 cm of pore waters compared to overlying bottom waters (Fig. 5.2b), similar to the δ¹¹B offsets seen in infaunal benthic foraminifera (Fig. 5.2a). More detailed comparison of pore-water chemistry and infaunal δ¹¹B is limited by knowledge of sedimentary habitat depths; nonetheless, the most simple explanation of δ¹¹B in infaunal foraminifera is that it follows the same systematics as in epifaunal species, incorporating borate ion but at the conditions of the surrounding pore water (Corliss 1985).

The close match between δ¹¹B of benthic foraminifera and δ¹¹B of borate at the pH of the surrounding water, across a wide range of environmental conditions and different taxa, provides support for simple models of δ¹¹B-pH proxy systematics (e.g. Hemming and Hanson 1992 and see Sect. 3.2.1).

5.3.1.2 Planktic Foraminifera—Key Proxy Carriers

Planktic foraminifera have been the focus of much of the development work on foraminiferal boron isotopes, due to the importance of surface ocean δ¹¹B-derived pH records in studies of past atmospheric CO₂. Modern planktic foraminifera evolved from benthic species (Hemleben et al. 2012), and have relatively simple low-Mg calcite tests compared to the variety found in benthic taxa. However despite their low taxonomic diversity, planktic foraminifera span a wide range of ecological niches and lifestyles, ranging from shallow-dwelling taxa with photosynthetic symbionts, to deep-dwelling taxa lacking symbionts. The life span of most planktic species is relatively short (weeks to months), so metabolic rates are high: compared to benthic foraminifera, planktics tend to live fast and die young. Some species have preferences for certain seasons, and some may migrate through different water depths during their life cycle. However individual species tend to occupy a relatively limited set of environmental (e.g. pH and temperature) conditions (Bijma et al. 1990). These factors, along with limited depth and seasonally-resolved water-column pH data, may complicate proxy calibration in planktic foraminifera from the wild (e.g. core-tops, tows, sediment traps). Culturing experiments have thus been employed in δ¹¹B calibrations to provide an expanded pH range with controlled environmental conditions, but do not necessarily provide analogous conditions to the open ocean.

Boron isotope data from all planktic foraminifera analysed to date lie within a few permil of δ¹¹B of borate and show sensitivity to seawater pH (Fig. 5.3). However while δ¹¹B values lie close to δ¹¹B of borate (compared to δ¹¹B of seawater or boric acid), there are notable offsets. Species lacking photosynthetic symbionts (including G. bulloides and N. pachyderma) have δ¹¹B below that of borate ion (i.e. an offset to lower pH), while symbiont-bearing species (e.g. G. ruber and T. sacculifer) tend to have δ¹¹B above borate at seawater pH (i.e. an offset to higher pH; Hönisch et al. 2003).

These offsets may be explained by the physiological influences of photosynthesis, respiration, and calcification on the foraminiferal microenvironment (Zeebe et al. 2003; Fig. 5.4a). Photosynthesis draws down CO₂, raising microenvironmental pH, while respiration releases CO₂, lowering pH (Wolf-Gladrow et al. 1999). Calcification draws down two moles of alkalinity (via Ca²⁺) per one mole of dissolved inorganic carbon (either as HCO₃ ⁻ or CO₃ ²⁻), resulting in a net lowering of pH (see Box 1 for a quick review of carbonate chemistry). The influence of these processes on the microenvironment of planktic foraminifera has been demonstrated using microelectrodes (Rink et al. 1998; Köhler-Rink and Kühl 2000), which reveal pronounced gradients in pH and O₂ in the diffusive boundary layer surrounding planktic foraminifera. Culturing studies demonstrate that these processes are reflected in boron isotope composition (Hönisch et al. 2003), with an increase in δ¹¹B of O. universa grown at increasing light levels, due to enhanced photosymbiont activity. These offsets have also been reproduced in a diffusion-reaction model of the foraminiferal microenvironment (Zeebe et al. 2003; and see further discussion below). Physiological alteration of foraminiferal microenvironment may also account for the influence of size on δ¹¹B in symbiont-bearing planktic foraminifera (Zeebe et al. 2003). Increases in δ¹¹B with shell size are seen in G. ruber and T. sacculifer (Henehan et al. 2013; Ni et al. 2007; Hönisch and Hemming 2004), which may result from documented increases in photosynthetic rates relative to respiration with increasing test size (Lombard et al. 2010; Hemleben and Bijma 1994).

Given the influence of physiological processes on planktic foraminiferal δ¹¹B, it is crucial for proxy calibration to test how these are realized in modern ocean settings. This is well-illustrated by recent open ocean δ¹¹B data from O. universa (Henehan et al. 2016), which are offset below δ¹¹B of borate at seawater pH, despite the presence of dinoflagellate symbionts. This may be explained by the fact that O. universa tends to inhabit water depths where light attenuation may limit photosynthetic activity (Morard et al. 2009; Jorgensen et al. 1985). Respiration and calcification thus exert a greater net influence than photosynthesis at the habitat depth of O. universa, leading to an offset to lower δ¹¹B and pH. Indeed Hönisch et al. (2003) note that their culture experiments that used low light levels lie closest to their O. universa data from plankton tows (though not core-tops).

Early culture work (Sanyal et al. 1996) suggested that δ¹¹B in O. universa showed a lower sensitivity to pH than δ¹¹B of borate (Fig. 5.3c, d). However this is not seen in the wild data of Henehan et al. (2016), which closely follow δ¹¹B of borate with a small constant offset (see further discussion in Sect. 3.2.2). Indeed despite the influence of physiology on planktic foraminiferal δ¹¹B, Henehan et al. (2016)’s open ocean O. universa data—from plankton tows and core tops—demonstrate that these vital effects may be remarkably stable, or closely coupled, over a wide range of environmental conditions.

5.3.1.3 Other Benthic Foraminifera—Enigmatic Signals in High-Mg Calcite and Aragonite

Large, high-Mg calcite, reef-dwelling benthic foraminifera of the genus Amphistegina are commonly used in culture studies of biomineralisation, being relatively robust to environmental change, easy to collect, and large enough to image effectively. However boron isotope data on Amphistegina from different studies are currently somewhat conflicting. While Rollion-Bard and Erez (2010)’s SIMS data, when averaged, give bulk δ¹¹B values lying ~5–12‰ above δ¹¹B borate, Kaczmarek et al. (2015)’s recent laser ablation data range from values ~2‰ above borate to ~7‰ below. Kaczmarek et al. (2015) also find a range of ~6‰ between different specimens cultured under the same environmental conditions, with the lowest δ¹¹B values in these specimens lying below the lower limit for δ¹¹B of borate ion.

The cause of these offsets between specimens and studies is currently unknown. However the range of δ¹¹B in specimens taken from the same environmental conditions suggests strong but variable internal control of δ¹¹B by individual foraminifera of this species under these conditions. Internal control of δ¹¹B in Amphistegina was also suggested by Rollion-Bard and Erez (2010), who found a notable change in the spread of δ¹¹B values from individual SIMS spots in a given specimen as a function of pH (see Sect. 3.2.3 on Biomineralisation).

Enigmatic boron isotope results have also been obtained from the only common modern aragonitic foraminifera, Hoeglundina elegans. Indeed the life style of this species is in itself an enigma, being widely distributed in the deep ocean at depths and conditions where aragonite is highly undersaturated. Boron isotope values from this epifaunal species lie below ambient borate by ~0.5–3.5‰ (Rae et al. 2011), notably different to low-Mg epifaunal benthic foraminifera. Indeed the lowest δ¹¹B values from this species (11.97‰; Rae et al. 2011) lie below the lower limit of seawater borate ion, suggesting further isotopic fractionation during biomineralisation in this species.

5.3.2 Discussion of Boron Isotope Calibration on Modern Foraminifera

The synthesis of boron isotope data on modern foraminifera presented above provides a basis to re-evaluate the assumptions underlying the δ¹¹B-pH proxy, and provides powerful constraints on models of calcification.

5.3.2.1 Boron Incorporation in Foraminifera

A key assumption in the use of boron isotopes in marine carbonates to reconstruct pH is that only borate ion is incorporated into carbonate (for more detailed discussion see Chap. 3 by Branson and recent paper by Balan et al. 2016). Given the physiological influences on planktic foraminiferal δ¹¹B, the deep sea benthic foraminifera provide a useful model system to test this assumption. The close match between epifaunal benthic δ¹¹B and δ¹¹B of borate (Figs. 5.2 and 5.3) strongly supports the exclusive incorporation of borate ion from seawater into foraminiferal carbonate: incorporation of just 4% boric acid would offset benthic δ¹¹B from borate ion by more than 1‰, in contrast with the close match observed. Indeed across a wide range of life styles and environments, and despite physiological influences, almost all foraminiferal δ¹¹B data lie relatively close to δ¹¹B of borate, and are substantially below δ¹¹B of seawater or boric acid.

Although NMR data have shown the presence of both tetrahedrally and trigonally coordinated boron in biogenic carbonates (Sen et al. 1994; Klochko et al. 2009; Rollion-Bard et al. 2011; Noireaux et al. 2015; Mavromatis et al. 2015), this does not necessarily reflect the coordination of the molecule incorporated from solution (Klochko et al. 2009; Balan et al. 2016). Indeed some re-coordination of tetrahedral borate is to be expected upon incorporation into trigonal calcite (Hemming et al. 1995; Klochko et al. 2009), with recent quantum mechanical modelling showing that boron is structurally substituted for carbonate groups in the calcite lattice, being found as partially deprotonated trigonal BO₂(OH)²⁻ and minor B(OH) ⁻₄ (Balan et al. 2016). Although under equilibrium conditions isotopic fractionation may be expected between borate and BO₂(OH)²⁻, if this re-coordination occurs during incorporation without further exchange with seawater, it may not be expressed. Indeed recent synchrotron work (Branson et al. 2015) suggests that boron may be exclusively present in trigonal form in calcitic benthic foraminifera. If this trigonal boron were to reflect boric acid incorporation, foraminiferal δ¹¹B values should lie ~28‰ above borate. However δ¹¹B data on these samples lie within a few ‰ of δ¹¹B of borate ion (Kaczmarek et al. 2015), supporting exclusive addition of borate ion to growing calcite, with re-coordination to trigonal form upon incorporation into foraminiferal calcite with no further isotopic exchange (Hemming and Hanson 1992).

Although some recent experimental work has suggested that boric acid may be incorporated into inorganically precipitated calcites, results from different studies are conflicting. Based on boron concentration data, Uchikawa et al. (2015) suggest that partitioning of boron into calcite is best described in terms using total boron in solution rather than borate ion, especially at high precipitation rates. However preliminary δ¹¹B data on these same precipitates lie close to borate ion (Farmer et al. 2015), inconsistent with substantial incorporation of boric acid. Noireaux et al. (2015) provide δ¹¹B data on inorganic aragonite and calcite precipitates (as used in Mavromatis et al. 2015). While Noireaux et al. (2015)’s aragonites have δ¹¹B within error of borate ion, the calcites have δ¹¹B up to ~10‰ higher than borate, and these authors suggest incorporation of boric acid may account for this offset. However in a separate study, Kaczmarek et al. (2016) give δ¹¹B values for inorganic calcite precipitates within 1.5‰ of borate ion, supporting the predominant incorporation of borate. Further work is required to reconcile these conflicting results and this will doubtless lead to improved understanding of the fundamental mechanisms of boron incorporation into carbonate (Balan et al. 2016). However it should be noted that inorganic experiments do not provide a perfect analogue to precipitation of calcite by foraminifera, and that foraminiferal δ¹¹B data are currently most easily explained by exclusive incorporation of borate ion at pH close to that in surrounding seawater.

5.3.2.2 Boron Isotope Fractionation in Foraminifera

The boron isotope fractionation factor between boric acid and borate ion was, for a long time, poorly constrained (see further discussion in Chap. 8). Early studies frequently used a value of 1.0194, based on calculations by Kakihana and Kotaka (1977) using vibrational frequency data from Kotaka and Kakihana (1977). However it was later shown that a major vibrational frequency mode had been improperly assigned in these calculations (Rustad and Bylaska 2007), and recalculation using various methods yields higher values, though with considerable range (~1.020–1.050; Oi 2000; Liu and Tossell 2005; Zeebe 2005). Experimental determination of the fractionation factor was thus crucial. Klochko et al. (2006) achieved this with an elegant experiment that takes advantage of the fact that pure ¹⁰B boric acid and pure ¹¹B boric acid have subtly different dissociation constants, which can be linked to the fractionation factor. This yields an isotopic fractionation of 1.0272 ± 0.0006 (95% confidence) between borate and boric acid in seawater, which has been widely adopted. This has recently been corroborated using an independent experimental set-up, based on separation of boric acid from borate ion (and associated ion pairs) using reverse osmosis, and isotopic measurement of these solutions (Nir et al. 2015). This yields a value of 1.0260 ± 0.001, within error of the Klochko et al. (2006) value.

Although the aqueous fractionation factor is now well constrained, there has been continued discussion about fractionation of boron into carbonates (for instance see supplementary information of Hönisch et al. 2009). While inorganic precipitate data might be hoped to provide constraints on inorganic equilibrium and/or kinetic fractionation, the unexplained discrepancies between different studies (discussed in Sect. 3.2.1) currently make it difficult to derive unambiguous fractionation factors from this work. Much of the discussion of boron fractionation during carbonate formation has thus been based on δ¹¹B in biogenic carbonates.

As discussed above, benthic foraminifera appear to follow δ¹¹B of borate with no significant offset (Figs. 5.2 and 5.3). However planktic foraminifera show a range of offsets (Fig. 5.3), some of which vary as a function of pH (i.e. the δ¹¹B data have a different “slope” or sensitivity to pH compared to borate). In corals, large offsets above δ¹¹B of borate are commonly attributed to internal pH elevation (Hönisch et al. 2004; Krief et al. 2010; McCulloch et al. 2012b; Allison and Finch 2010; Allison et al. 2014 and see Chap. 5 by McCulloch), but this appears not to exert major influence in most foraminifera (see further discussion below). In foraminifera, the physiological processes of photosynthesis, respiration, and calcification are well-documented to cause pH modification in the microenvironment (Rink et al. 1998; Köhler-Rink and Kühl 2000). Zeebe et al. (2003)’s reaction-diffusion model suggested that boron isotope offsets due to these processes may stay constant across a range of pH, making the variable offsets hard to explain. However variable offsets may occur if the nature of carbonate precipitation changes over the range of culture conditions.

Variable δ¹¹B offsets may be expected to arise due to changes in the buffering capacity of the carbonate system at different pH. At low pH, a given change in DIC (for instance via photosynthesis) will drive a larger change in pH than at higher absolute pH values (Fig. 5.4a; and see Allison and Finch 2010). This appears at first to provide a possible explanation for the larger offsets from δ¹¹B of borate observed in foraminifera cultured at low pH. However the effect of this on the boron isotope system is countered by the reduced sensitivity of δ¹¹B of borate at lower pH (the flattening of the δ¹¹B of borate curve in Fig. 5.2b). Thus although the size of the pH offset resulting from a constant photosynthetic DIC-drawdown may change at different bulk solution pH, the offset in δ¹¹B remains relatively constant. This is illustrated by the schematic in Fig. 5.4a: the photosynthesis DIC-drawdown vectors cross 0.1 pH units at high pH and 0.2 at low pH, but in both cases cross ~2 permil in δ¹¹B of borate. This is also shown with simple steady state calculations in Fig. 5.4b, c: the offset between δ¹¹B of borate in the bulk solution and the green dashed lines (depicting a constant DIC-drawdown or addition) stays relatively constant with solution pH, as shown more comprehensively in Zeebe et al. (2003)’s diffusion-reaction model.

Variable δ¹¹B offsets may instead be explained by changes in physiology as a function of pH. Photosynthesis and respiration rates are not thought to be substantially impacted by changes in the carbonate system of this magnitude (Glas et al. 2012a). (Though a potential exception to this is noted by Henehan et al. (2013), who observe that cultured G. ruber holds its symbionts closer to its test under low pH conditions, which may increase the intensity of photosynthetic elevation of pH and δ¹¹B at low pH.) Calcification rate, on the other hand, is expected to vary substantially as a function of changes in carbonate saturation (Ω) over the range of pH values used in culture studies (e.g. Bijma et al. 2002). For instance calcite saturation state varies from ~1.5 to 20 over the pH_tot range of 7.6–8.9 used in Sanyal et al. (1996); a generalized calcite precipitation rate law of R = 2(Ω−1)^1.9, gives a factor of 1000 change in precipitation rate over this range. Carbonate precipitation draws down local pH by removing 2 mol of ALK for every 1 of DIC (Fig. 5.4a). Rapid CaCO₃ precipitation at high saturation states may thus drive large decreases in microenvironment pH (Glas et al. 2012b; Toyofuku et al. 2017), compared to slower CaCO₃ precipitation at lower saturation states giving smaller local pH decrease (Fig. 5.4a). This may act to decrease δ¹¹B values in foraminiferal carbonate in cultures at high pH and saturation state, and thus give δ¹¹B in cultured foraminifera a relatively “shallow slope” or reduced sensitivity to δ¹¹B of borate as a function of pH.

The potential influence of variable calcification rates on foraminiferal microenvironment is illustrated with the simple steady state calculation in Fig. 5.4b, c. This calculation alters the carbonate system for a modelled microenvironment compared to the bulk solution by ALK and DIC drawdown in a 2:1 ratio as a function of saturation state, along with a constant net DIC-drawdown due to net respiration. This equilibrium treatment is a (gross!) simplification of variable rates of carbonate precipitation, and it should also be noted that foraminifera may not follow this precipitation rate law (see Allen et al. 2016, though note that crystal growth rate may vary substantially from mass added in culture). However this calculation does illustrate the potential for the extremely large range of saturation states experienced in culture to cause reduced sensitivity of foraminiferal δ¹¹B to pH (“shallow slopes”), as observed in culture (Fig. 5.4b, c).

The reduced sensitivity of planktic foraminiferal δ¹¹B to pH displayed in culture is not readily observed in wild samples of planktic or benthic foraminifera (Figs. 5.3 and 5.4b, c), although it should be noted that few wild calibration studies span a large-enough pH range to precisely constrain this sensitivity. Nonetheless, the recent wild O. universa data of Henehan et al. (2016) follow the pH sensitivity of δ¹¹B of borate more closely than previous O. universa cultures (Sanyal et al. 1996). This might be explained by the different character of carbonate system changes under culture versus natural conditions. While many culture experiments make large alkalinity changes at constant DIC, resulting in an extremely large range of carbonate saturation states (Ω_calcite of ~1.5–20), in natural conditions alkalinity and DIC changes are often coupled, and changes in saturation state are muted by carbonate compensation. Furthermore on long timescales, changes in ocean carbonate saturation are buffered compared to changes in pH (Tyrrell and Zeebe 2004; Hönisch et al. 2012). Therefore if the large range of carbonate saturation is the chief cause of reduced sensitivity of cultured δ¹¹B to pH, then calibration data obtained from wild samples may be more applicable to the geological record. Further work is required to test this idea and to further improve calibrations of foraminiferal δ¹¹B to pH under both culture and wild conditions.

5.3.2.3 Boron Isotope Constraints on Biomineralisation

The sensitivity of boron isotopes to pH makes them a powerful constraint on mechanisms of calcification in foraminifera. Here I briefly discuss the influence of some potential calcification processes on boron isotopes in foraminifera, and speculate on models that may match the constraints from δ¹¹B. Note that as the timescale of boron isotope equilibration is extremely fast (~125 μs; Zeebe et al. 2001), kinetic processes are unlikely to exert a primary influence, simplifying interpretations compared to δ¹⁸O and δ¹³C (Zeebe and Wolf-Gladow 2001).

A common feature of many models of calcification is the elevation of pH in a somewhat isolated volume of seawater (de Nooijer et al. 2014). pH elevation of ~0.5–1 units above ambient seawater has indeed been observed during calcification in foraminifera (de Nooijer et al. 2009; Bentov et al. 2009) and corals (Venn et al. 2011) using fluorescent dyes. However while high δ¹¹B in corals appears to reflect this pH elevation (see Chap. 6 and McCulloch et al. 2012a; Krief et al. 2010; Anagnostou et al. 2012; Allison et al. 2014), δ¹¹B in most foraminifera does not: pH elevation of 1 pH unit should give δ¹¹B ~7–14‰ above seawater borate (Fig. 5.5), but most foraminifera lie within a few permil of borate ion at seawater pH (Figs. 5.3 and 5.5).

The impact of pH elevation on foraminiferal δ¹¹B may be even greater if boric acid is able to diffuse from seawater to the site of pH elevation, where it would re-equilibrate and elevate the total (or “seawater”) δ¹¹B of the calcifying solution above 39.61‰. Rayleigh fractionation also has the potential to elevate δ¹¹B in an isolated volume of seawater, due to progressive drawdown of borate into carbonate, but the low partitioning of boron into calcite negates this effect (Rae et al. 2011; Stewart et al. 2016).

To date, substantial influence of pH elevation on foraminiferal δ¹¹B has only been suggested from one study, based on SIMS analyses of cultured Amphistegina lobifera (Rollion-Bard and Erez 2010). In these specimens the lowest δ¹¹B values from individual SIMS spots fall close to δ¹¹B of borate at ambient culture water pH, while the highest δ¹¹B values reach an upper limit of ~30‰, equivalent to a pH of ~8.9. Notably, this is similar to pK₂, the second equivalence point of carbonic acid, above which the overwhelming majority of DIC is present as CO₃ ²⁻. pH elevation above this point would thus give no further increase in carbonate saturation and may also impact carbon concentration mechanisms. Whatever the causal mechanism, these data thus appear to suggest well-regulated pH elevation up to a chemically-determined limit (see also Gagnon et al. 2013 and Toyofuku et al. 2017), with calcification at pHs between this limit and ambient seawater (Rollion-Bard and Erez 2010; and see green lines in Fig. 5.5a). However in a separate study using LA-MC-ICPMS, Kaczmarek et al. (2015) find large negative δ¹¹B offsets in cultured Amphistegina, which are hard to reconcile with pH elevation (though one possible explanation is discussed below). The results from these high Mg foraminifera thus remain somewhat enigmatic.

As the low-Mg benthic and planktic foraminifera have δ¹¹B values close to δ¹¹B of borate at seawater pH, the majority of the boron incorporated into these genera seems unlikely to have been derived directly from a seawater pool that experienced large pH elevation (Fig. 5.5). However this must be reconciled with the observations that at least some seawater is present during chamber formation (de Nooijer et al. 2009; Bentov et al. 2009; Nehrke et al. 2013) and that pH elevation does occur in a range of genera (de Nooijer et al. 2009; Bentov et al. 2009). Possible mechanisms that may satisfy these apparently contradictory observations include:

(1)
borate that reaches the calcifying space being (selectively) removed from seawater at seawater pH;
(2)
notable pH elevation occurring only during initial chamber formation, while the bulk of the shell is precipitated at a pH close to seawater, perhaps aided by Mg-removal;
(3)
initial pH elevation being countered by carbon concentration and/or carbonate precipitation;
(4)
pH elevation being less pronounced in the wild than during culture observations.

If borate ion is selectively transported from seawater to the calcifying space, without input of bulk seawater or boric acid, then pH could vary without impacting shell δ¹¹B, provided that all of the borate in this pool is incorporated (Rae et al. 2011). Selective transport could potentially be achieved by trans-membrane ion channels, which have been proposed by some authors to deliver significant portions of calcium (Nehrke et al. 2013; de Nooijer et al. 2009; Toyofuku et al. 2008), and potentially also DIC (de Nooijer et al. 2014), to the calcifying space. It has been suggested that Ca²⁺ channels might be “leaky” to Mg²⁺, given its similar size and charge (Raitzsch et al. 2010; de Nooijer et al. 2009); likewise it is possible that HCO₃ ⁻ transporters could be leaky to B(OH) ⁻₄ . However the presence of membrane-impermeable dyes and beads at the site of calcification (Bentov and Erez 2006; Nehrke et al. 2013; de Nooijer et al. 2009) and in calcite itself (Bentov and Erez 2006) shows that bulk seawater—and not just channel-derived ions—must reach the site of calcification. Given the high concentration of boron in seawater this would likely dominate the total boron in the calcification space, so pH elevation would elevate foraminiferal δ¹¹B. Selective transport of borate is thus unlikely to offer a silver bullet to explain the match between seawater borate and foraminiferal δ¹¹B. However if borate transport does occur, it could potentially help counter elevation of δ¹¹B due to pH elevation, by reducing δ¹¹B of bulk boron in the calcification space.

Alternatively the lack of an obvious signal of pH elevation in low-Mg foraminifera could be explained if pH elevation only occurs during initial chamber formation, with the majority of calcification taking place at pH closer to seawater. Bulk shell δ¹¹B could be kept within 0.5‰ of seawater borate if pH elevation of 0.5 units is only experienced by ~5–25% of the boron incorporated into foraminiferal calcite (depending on environmental conditions; Fig. 5.5b). The rest of the boron could be sourced from borate ion adsorbed and incorporated during thickening of calcite onto existing chambers, if this process takes place at pH close to ambient seawater. The challenge to such a scenario is finding mechanisms to drive calcification under these conditions.

Calcification at pH close to ambient may perhaps be facilitated by active magnesium removal (Bentov and Erez 2006). Mg-removal acts to increase the activity of carbonate ions and reduce Mg “poisoning” of calcite growth (Zeebe and Sanyal 2002), and has been suggested to occur via mitochondrial activity in pseudopods surrounding the shell (Spero et al. 2015). Mg-removal has particular relevance to boron isotopes because reduced Mg concentrations notably increase K_B (Fig. 5.1d), reducing the sensitivity of δ¹¹B to changes in pH (Fig. 5.5b). For instance reducing Mg concentrations at the site of calcification to ~3 mol/kg (as predicted using inorganic partition coefficients and Mg concentrations in low-Mg foraminifera) may reduce the impact of 0.5 units pH elevation on δ¹¹B from ~5 to ~3‰ depending on initial conditions (Fig. 5.5b). Mg-removal would also reduce the impact of local pH decrease during calcification (see below). Different degrees of Mg removal from the calcifying space may also partially explain the contrasting δ¹¹B offsets between taxa with different Mg/Ca (Fig. 5.5): extensive Mg-removal in low-Mg benthic and planktic species would minimise the impact of local pH changes on δ¹¹B; in contrast minimal Mg-removal in high-Mg taxa such as Amphistegina renders their boron isotope composition highly sensitive to pH changes during biomineralisation.

The influence of pH elevation during initial chamber formation on δ¹¹B may also be countered by local reductions in pH due to DIC concentration or during calcification. Bentov et al. (2009) demonstrate the presence of low-pH vacuoles during calcification, which they suggest may drive carbon concentration via CO₂ diffusion to low-CO₂/high-pH seawater vacuoles (see Allison et al. 2014 for analogous process in corals). Indeed were CO₂ diffusion infinitely efficient, DIC addition would keep pace with pH elevation, resulting in minimal net elevation in pH or δ¹¹B. The fact that high pH vacuoles are observed demonstrates that DIC addition is not as efficient as in this end member scenario. Nonetheless, concentration of CO₂ seems likely to play a role in minimizing offsets in δ¹¹B.

Acidification of the calcifying microenvironment may also occur due to net alkalinity drawdown during calcification (Fig. 5.4a), and indeed could act as a negative feedback on calcification. To combat this, foraminifera have been shown to actively extrude H + from the calcifying space into surrounding seawater (Glas et al. 2012b), using a V-ATPase “proton-pump” (Toyofuku et al. 2017). Nonetheless, depending on the efficiency of this pump, some degree of acidification at the site of calcification may still occur. Acidification of the seawater surrounding the foraminifera is also likely to drive further CO₂ diffusion to the site of calcification, increasing DIC and countering some of the initial pH elevation (Toyofuku et al. 2017). Furthermore, if this low-pH water is vacuolised and transported to the site of calcification, it could not only counter the influence of initial pH elevation, but may even produce negative offsets between foraminiferal δ¹¹B and seawater borate (Fig. 5.4). The magnitude of these influences will be highly dependent on calcification rate and diffusion in the shell’s microenvironment, which may differ between settings, and could perhaps provide a mechanism to explain differences in Amphistegina δ¹¹B between studies (Rollion-Bard and Erez 2010; Kaczmarek et al. 2015).

Finally it is possible that active pH manipulation may be most pronounced under the warm and energy-rich conditions in lab cultures, and less pronounced in the wild, in particular in cold deep-sea environments with low food. The reduced sensitivity of δ¹¹B to pH in cold, low-pH environments (Fig. 5.5b) may also contribute to the absence of a pH elevation signal in wild Cibicidoides from the deep ocean, despite the fact that pH elevation has been observed in this genera under culture conditions (de Nooijer et al. 2009). Higher turbulence in the wild may also help minimize pH gradients in the microenvironments surrounding calcifying foraminifera (Glas et al. 2012b; Toyofuku et al. 2017).

In summary, the close correspondence between δ¹¹B of foraminifera and seawater borate provides useful constraints on pH during calcification. Trans-membrane transport of borate ion is unlikely to explain this signal (in contrast to the suggestion of Rae et al. 2011), as it will be overwhelmed by boron from the seawater that is present at the site of calcification. DIC concentration and acidification during calcification could in part counter pH elevation; however at least some of this acidification is a result of actively extruded protons, which will maintain elevated pH at the site of chamber formation. Furthermore although scenarios that balance extremely high and low pH influences are possible, it seems unlikely that they could consistently produce small δ¹¹B offsets if they account for the majority of the shell’s boron. One possible scenario is that the majority of the shell’s boron is incorporated at pH close to seawater during chamber thickening, with pH elevation only employed during initial chamber formation and partially offset by concentration of DIC. Magnesium removal may help drive this secondary thickening, and would also reduce the sensitivity of δ¹¹B to further change in pH. Indeed variable Mg-removal, along with environmental influences on pH-δ¹¹B sensitivity, foraminiferal energy budgets, and variable efficiency of DIC concentration, may contribute to variable δ¹¹B offsets between taxa. Further observations are required to test this model, including better estimates of the mass balance of calcite and boron from primary chamber formation versus secondary thickening (Allen et al. 2011; Raitzsch et al. 2011). Nonetheless, it is interesting to consider that pH elevation may only be used to promote rapid initial chamber formation, with foraminifera expending energy to quickly overcome the thermodynamic barriers and physiological vulnerabilities of this process, whereas the bulk of the shell—and its boron—may be precipitated onto an existing calcite template at pH closer to seawater.

5.4 δ¹¹B-Derived pH and CO₂

Interest in the boron isotope composition of foraminifera stems largely from its application as a tracer of the CO₂ system in the geological past (Fig. 5.6). Below I describe the processes and assumptions that allow foraminiferal δ¹¹B to be converted to pH and CO₂. However it should be noted that even without further conversion, δ¹¹B of borate, as tracked by foraminiferal δ¹¹B, provides a powerful tracer of carbonate system changes in its own right. Indeed, over much of the ALK-DIC space in the modern ocean, δ¹¹B of borate is a more linear tracer of ALK/DIC ratio—and [CO₃ ²⁻] and pCO₂—than is pH (see inset figure in Box 1). Thus provided timescales are short enough that δ¹¹B_sw can be assumed to have remained relatively constant (<10 Myr; see below), foraminiferal δ¹¹B alone provides a valuable tracer of relative changes in past CO₂ system conditions, and plotting raw δ¹¹B data is a valuable first step in any record. Indeed this is somewhat analogous to foraminiferal δ¹⁸O, which reflects both temperature and δ¹⁸O_sw, but is typically provided with no further conversion, and provides a valuable tracer of past oceanographic conditions in this raw form. Furthermore, it should be noted that despite uncertainties in absolute pH and CO₂ values arising from estimates of δ¹¹B_sw and a second carbonate system parameter, relative changes in pH and CO₂ may still be well constrained. Indeed Foster and Rae (2016) demonstrate that estimates of climate sensitivity in the past, based on comparison of δ¹¹B-derived CO₂ to sea surface temperature, are relatively insensitive to uncertainties in δ¹¹B_sw and estimates of alkalinity.

5.4.1 pH from δ¹¹B

5.4.1.1 δ¹¹B of Borate and pH

The first step in obtaining pH from foraminiferal δ¹¹B is conversion to δ¹¹B of borate. This is achieved using the calibrations described above and shown in Fig. 5.3 (see also Foster and Rae 2016). Ideally the calibration used would be based on foraminifera collected under wild conditions, as these should most accurately reflect the combination of influences felt by open ocean foraminifera taken from samples “down-core”. However in many cases these wild calibrations do not span a wide range of pH and so culture calibrations are also commonly applied. As discussed above, some culture calibrations have lower sensitivity to δ¹¹B borate changes than wild calibrations, and more work is required to determine which is most appropriate for the geological record. Careful micropalaeontoloty is also required to assess the most appropriate calibrations to use for extinct species (Anagnostou et al. 2016).

With δ¹¹B of borate determined, conversion to pH is typically achieved using Eq. (5.9), which is based on the approximation provided by Eq. (5.6).

$$ \begin{aligned} pH & = pK_{B} \\ & \quad - \,{ \log }\left( { - \frac{{\updelta^{11} {\text{B}}_{SW} -\updelta^{11} {\text{B}}_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} }}{{\updelta^{11} B_{SW} - \alpha_{B} .\updelta^{11} B_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} -\upvarepsilon_{B} }}} \right) \\ \end{aligned} $$

(5.9)

More accurately, using Eqs. (5.2) and (5.7), we obtain the expression in Eq. (5.10) below.

$$ pH = - \log_{10} \frac{{K_{B} \cdot^{{^{{\frac{11}{10}}} }} R_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} - K_{B} \cdot^{{^{{\frac{11}{10}}} }} R_{SW} + \alpha_{B} \cdot K_{B} \cdot^{{^{{\frac{11}{10}}} }} R^{2}_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} - \alpha_{B} \cdot K_{B} \cdot^{{^{{\frac{11}{10}}} }} R_{SW} \cdot^{{^{{\frac{11}{10}}} }} R_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} }}{{^{{^{{\frac{11}{10}}} }} R_{SW} +^{{^{{\frac{11}{10}}} }} R_{SW} \cdot^{{^{{\frac{11}{10}}} }} R_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} - \alpha_{B} \cdot^{{^{{\frac{11}{10}}} }} R_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} - \alpha_{B} \cdot^{{^{{\frac{11}{10}}} }} R_{{{\text{B}}\left( {\text{OH}} \right)_{4}^{ - } }} }} $$

(5.10)

Conversion of δ¹¹B borate to pH thus requires knowledge of K_B and δ¹¹B_sw.

5.4.1.2 K_B

The equilibrium constant of boric acid, K_B, is a well-defined function of temperature, salinity, and pressure, given by the expression (Dickson 1990):

$$ \begin{aligned} {\text{K}}_{\text{B}} & = {\text{exp[((}} - 8966.9 - 2890.53*{\text{S}}^{1/2} \\ & \quad - \,77.942*{\text{S}} + 1.728*{\text{S}}^{3/2} - 0.0996*{\text{S}}^{2} ))/{\text{Tk}} \\ & \quad + \, 148.0248 + 137.1942*{\text{S}}^{1/2} + 1.62142*{\text{S}} \\ & \quad + \,( - 24.4344 - 25.085*{\text{S}}^{1/2} - 0.2474*{\text{S}})*{\text{ln(Tk)}} \\ & \quad + \, 0.053105*{\text{S}}^{1/2} *{\text{ Tk]}} \\ \end{aligned} $$

(5.11)

with the formula below giving the correction for different pressures:

$$ \begin{aligned} {\text{P}}_{\text{factor}} & = (29.48 - 0.1622 * {\text{Tc}} \\ & \quad + 0.002608 * {\text{Tc}}^{2})/({\text{R*Tk) * P}} \ldots \\ & \quad + 0.5 * (-0.00284)/({\text{R*Tk) * P}}^{2} \\ \end{aligned} $$

(5.12)

$$ {\text{K}}_{\text{B}} {\text{ = exp }}\left( {{\text{lnK}}_{\text{B}} {\text{ + P}}_{\text{factor}} } \right) $$

(5.13)

where S is salinity, Tk is temperature in Kelvin, Tc is temperature in Celcius, P is pressure in bars (equivalent to depth in meters divided by 10), and R is the gas constant (83.14472 cm³ bar K⁻¹ mol⁻¹; Dickson et al. 2007). Note that the influence of these environmental parameters on the conversion of δ¹¹B of borate to pH is relatively minor over the conditions likely to be found at a given site: changes of ±5 °C, ±1 psu, and ±100 m result in differences in δ¹¹B borate of ~0.35‰, 0.05‰, and 0.03‰ respectively, for δ¹¹B borate of ~15‰ at 25 °C, 35 psu and 100 m water depth (Fig. 5.1c). Matlab codes and an Excel spreadsheet that carry out these calculations are provided in the supplementary online materials.

The composition of seawater can also influence K_B, in particular due to ion pairing of Ca and Mg ions with borate (Hershey et al. 1986; Nir et al. 2015; Hain et al. 2015). Hain et al. (2015)’s MyAMI ion pairing model shows that pK_B is relatively insensitive to the changes in [Ca] seen over the Cenozoic, though more sensitive to [Mg] (Fig. 5.1d). For instance δ¹¹B of borate of 16‰, at 25 °C, 35 psu, 0 m water depth, and with modern δ¹¹B_sw, yields pH of 7.82 under modern [Ca] of 10 M and [Mg] of 52 M, 7.84 under Miocene [Ca] of 14 M and [Mg] of 48 M, and 7.94 under Eocene [Ca] of 20 M and [Mg] of 30 M (Horita et al. 2002; Hain et al. 2015). Note that equivalent calculations using the Pitzer ion pairing model available with PHREEQ give slightly larger changes in pK_B (Nir et al. 2015).

5.4.1.3 δ¹¹B of Seawater

The boron isotope composition of modern seawater is 39.61 ± 0.04‰ (Foster et al. 2010). Boron has a long residence time in seawater of ~10 Myr, and modelling suggests that typical rates of change for δ¹¹B_sw over the last ~100 Myr are of the order 0.1‰/Myr (Lemarchand et al. 2000). δ¹¹B_sw may thus be assumed to have remained within analytical error of modern values for the last ~3 Myr, and δ¹¹B records spanning a few million years should be dominantly a function of change in pH rather than δ¹¹B_sw. However for accurate reconstruction of absolute pH values beyond ~3 Ma and for interpretation of δ¹¹B records spanning multiple millions of years, constraints on past δ¹¹B_sw are required (see Figs. 5.6 and 5.8).

Three general approaches have been used to reconstruct δ¹¹B_sw:

(1)
box modelling, using estimates of oceanic input and output fluxes over time;
(2)
measurement of substances, such as pore waters and halites, with δ¹¹B close to that of ancient seawater;
(3)
measurement of carbonate δ¹¹B where independent constraints can be placed on pH.

Box models of δ¹¹B_sw must take account of source terms, including weathering flux in rivers (Lemarchand et al. 2000), hydrothermal venting (Smith et al. 1995), and fluids from accretionary prisms (You et al. 1993), and sink terms, including oceanic crust alteration (Spivack and Edmond 1987), adsorption onto clays (Spivack et al. 1987), and incorporation in carbonates (Hemming and Hanson 1992). These terms are not well constrained over geological time, but may be proxied by more general geological processes, such as seafloor spreading rates (Simon et al. 2006) and total carbonate deposition (Lemarchand et al. 2000). Despite the uncertainties in how each of these fluxes has changed, this approach may be valuable when paired with constraints on the secular evolution of seawater chemistry from other isotopic systems (e.g. ⁸⁷Sr/⁸⁶Sr, δ⁷Li).

Measurement of archives with δ¹¹B close to ancient seawater is appealing, but it is hard to find settings where these signatures are pristine. Paris et al. (2010b) use δ¹¹B measurements on halites in evaporite deposits to reconstruct δ¹¹B_sw at 3 intervals over the last 40 Myr (Fig. 5.6b). This approach takes advantage of the fact that halites are one of the only solid materials with δ¹¹B similar to seawater rather than borate ion, likely due to the trapping of brine inclusions of fluid inclusions during halite growth. However δ¹¹B_sw determined by this method lies ~3–6‰ below other estimates, and it is possible that evaporite δ¹¹B may be influenced by fractionation during evaporation or incorporation into halite (Vengosh et al. 1992) or by riverine input in the partially isolated conditions of evaporite formation. Spivack et al (1993) used pore fluid δ¹¹B data from a carbonate-rich ODP core to estimate changes in δ¹¹B_sw. However given the notable changes in δ¹¹B_sw seen in even the top few cm of pore fluids (Rae et al. 2011), use of this approach requires careful constraints on boron desorption from clays and dissolution of carbonates. Some deep pore fluids have also been shown to have quite exotic boron isotope compositions (Brumsack and Zuleger 1992), which further complicates this approach.

If pH can be independently constrained, then measurements of δ¹¹B in carbonates can be used to estimate δ¹¹B_sw. Raitzsch and Hönisch (2013) assume a linear increase in deep ocean pH over the last 50 Myr, and combined this with δ¹¹B measurements of benthic foraminifera to estimate δ¹¹B_sw (Fig. 5.6). However, it is unlikely that pH change has been linear through time, as evidenced by the unrealistically rapid changes in δ¹¹B_sw; in this record, given boron’s ~10 Myr residence time. Furthermore, use of this δ¹¹B_sw record with benthic δ¹¹B data would only ever reproduce the original assumption of linear change in pH.

An alternative approach instead uses measurements of carbonate δ¹¹B across an assumed or estimated pH gradient. This takes advantage of the curved relationship between δ¹¹B of borate and pH, which means that for a given change in pH, a measured δ¹¹B difference will be a function of δ¹¹B_sw. This approach was first proposed by Palmer et al. (1998), who assumed that the pH gradient between surface and thermocline-dwelling planktic foraminifera has remained constant, and made δ¹¹B measurements on a suite of these species over the Cenozoic. Pagani et al. (2005a) point out the influence of uncertainty in habitat depth on this calculation. However Anagnostou et al. (2016) have recently shown the power of this method to give bounds on possible changes in δ¹¹B_sw, when supported by measurements of δ¹⁸O and δ¹³C, and underpinned by conservative assumptions with fully propagated uncertainties. Foster et al. (2012) and Greenop et al. (2017) have also proposed a variant of this approach based on comparison of planktic and benthic δ¹¹B measurements, with the pH gradient between them constrained by measurements of δ¹³C.

Thus while accurate determination of δ¹¹B_sw remains a challenge for δ¹¹B-based reconstructions of the carbonate system, progress is being made—and should continue—on a number of fronts.

5.4.2 CO₂ from pH

While records of pH may be used to study the history and impact of ocean acidification, much of the interest in foraminiferal boron isotope records stems from the ability of a paleo-pH meter to reconstruct CO₂. pH and aqueous CO₂ concentrations are closely coupled in seawater, both being governed by the primary carbonate system variables alkalinity and dissolved inorganic carbon (Box 1 and Fig. 5.7). From knowledge of aqueous [CO₂], along with estimates of temperature and salinity, Henry’s law allows calculation of the partial pressure of atmospheric CO₂ in equilibrium with this water. Measurement of δ¹¹B in planktic foraminifera may thus be used to reconstruct atmospheric CO₂ in regions such as subtropical gyres (e.g. Figs. 5.6, 5.8 and 5.9), where oceanic and atmospheric CO₂ are close to equilibrium, or constrain the strength of CO₂ sources and sinks at high latitudes or in upwelling regions (Fig. 5.10).

The ocean carbonate system is most simply described by the 6 components alkalinity, DIC, CO₂, HCO₃ ⁻, CO₃ ²⁻, and pH, which are linked by 4 independent equations; the carbonate system thus has two degrees of freedom, so knowledge of two components allows the system to be completely determined (Box 1 and Fig. 5.7). The next most important acid-base system in seawater after CO₂ is boron, which adds 3 extra components $ \left( {{\text{B}}_{\text{SW}} , {\text{ B}}\left( {\text{OH}} \right)_{ 3} , {\text{ and B}}\left( {\text{OH}} \right)_{ 4}^{ - } } \right) $ and 2 independent equations. Thus with knowledge of B_SW, the system continues to have 2 degrees of freedom. Complete determination of the carbonate system from δ¹¹B-derived pH therefore requires a second carbonate system parameter to be known.

In any determination of the carbonate system it is crucially important to consider the relationships—and associated error propagation—between different carbonate system components (Fig. 5.7). For instance due to the sub-parallel relationship between pH and [CO₃ ²⁻] in ALK-DIC space, the use of these parameters to determine a less closely-related component of the system (such as DIC) results in large propagated uncertainties. Rae et al. (2011) show that even with errors of only ~0.03 in pH from δ¹¹B and ~10 μmol/kg in [CO₃ ²⁻] from benthic B/Ca, propagated uncertainty on DIC is ~300 μmol/kg, so although the DIC determination is accurate, the uncertainty spans a larger range than the whole modern ocean! However these carbonate system relationships also present opportunities, particularly in the determination of CO₂ from pH. As pH and CO₂ are very closely coupled, a well-constrained pH value will largely control the calculated CO₂ (Fig. 5.7). Therefore a reasonable estimate of a second carbonate system parameter, with generous error bars, should still result in a relatively accurate and precise determination of CO₂. Indeed it is far preferable to estimate a second carbonate system parameter with low precision that is likely to encompass the right value, than to use an estimate that is precise but inaccurate: provided the pH determination is accurate, the former approach will yield the correct CO₂ within error, while the latter will produce spurious results with the impression of high precision.

The two most commonly used second carbonate system parameters in δ¹¹B-based CO₂ reconstructions are alkalinity and Ω-derived [CO₃ ²⁻]. Alkalinity estimates in early studies (Hönisch and Hemming 2005; Foster 2008) were based on the close relationship between alkalinity and salinity in modern surface seawater: reconstructions of salinity, either from paired δ¹⁸O and Mg/Ca measurements or from scaling with global sea level change, were thus used to estimate alkalinity. However alkalinity may vary independently of salinity due to changes in CaCO₃ cycling (Broecker and Peng 1987). Recent studies have thus used modern alkalinity but with a large range (e.g. ±175 µmol/kg; Martínez-Botí et al. 2015a) and a uniform rather than normal distribution. CO₂ is then determined via Monte-Carlo simulations, and the resulting CO₂ estimates include every possible alkalinity within the given range with equal likelihood.

On timescales beyond the last ~3 Myr the assumption that alkalinity has remained close to modern values is unlikely to hold. On these timescales several studies have used assumptions or models of calcite saturation state (Ω_ca)

$$ \Omega _{\text{ca}} = \frac{{\left[ {\text{Ca}} \right]\left[ {{\text{CO}}_{3}^{2 - } } \right]}}{{K_{spc} }} $$

(5.13)

to estimate [CO₃ ²⁻] (Pearson et al. 2009; Anagnostou et al. 2016). It is thought that carbonate compensation maintains the global mean surface Ω_ca in the range 4–6 on long timescales (Ridgwell 2005; Hönisch et al. 2012; Hain et al. 2015), so given estimates of [Ca] (Horita et al. 2002) and K_sp (from temperature and major ion composition; Hain et al. 2015), [CO₃ ²⁻] can be estimated.

The ultimate test of any proxy-based reconstruction of atmospheric CO₂ is comparison to the ice core CO₂ record. This is illustrated in Fig. 5.9, demonstrating that despite the various potential sources of uncertainty, foraminiferal boron isotopes are able to provide accurate CO₂ reconstruction, with fully propagated uncertainty of ~20 ppm (2SD). Although application further back in the geological may present other challenges, the close match to ice core CO₂ demonstrates the potential of foraminiferal δ¹¹B for pH and CO₂ reconstruction.

5.5 Proxy Application: Examples

Spurred on by the development work described above, application of boron isotopes in foraminifera to the geological record has grown rapidly in recent years. Here I give a brief overview of some highlights from this work.

5.5.1 Glacial-Interglacial CO₂

Over the glacial cycles of the last 800 kyr, atmospheric CO₂ levels are well known, but the cause of CO₂ change between glacial and interglacial periods remains a mystery (EPICA 2004; Kohfeld and Ridgwell 2009). All leading hypotheses invoke changes in CO₂ partitioning between the deep ocean and the atmosphere, likely mediated by changes in circulation and productivity at high latitudes where deep waters are ventilated (Sigman et al. 2010). Boron isotope records can be used to test these hypotheses, by constraining CO₂ (dis)equilibrium between the surface ocean and the atmosphere, and CO₂ storage and release in deep waters.

A notable first application of δ¹¹B over glacial cycles was provided by Sanyal et al. (1995), who used planktic foraminifera and mixed benthic foraminifera to suggest that the pH of the ocean was ~0.3 units higher during the last glacial maximum compared to the Holocene. This was taken as support for glacial CO₂ drawdown by elevated ocean alkalinity (e.g. Archer and Maier-Reimer 1994). However reconciling this with changes in CaCO₃ preservation in the deep ocean is problematic (Sigman et al. 1998), and more recent work from monospecific benthics suggests much smaller changes in pH in the deep glacial ocean (Hönisch et al. 2008; Yu et al. 2010; Rae et al. 2014).

Several studies have used δ¹¹B in planktic foraminifera to reconstruct the extent of disequilibrium (∆pCO₂) between CO₂ in surface waters and the atmosphere (Sanyal et al. 1997; Sanyal and Bijma 1999; Palmer and Pearson 2003; Foster and Sexton 2014; Naik et al. 2015; Martínez-Botí et al. 2015b; see Fig. 5.10). Recent work shows a pronounced increase in CO₂ outgassing in the East Equatorial Atlantic during the LGM (Foster and Sexton 2014), indicative of enhanced upwelling, while surface water CO₂ in the West Equatorial Atlantic stays close to equilibrium with the atmosphere, suggesting that the upwelled CO₂ and nutrients from the East are progressively drawn-down by biological productivity. In the East (Martínez-Botí et al. 2015b) and West (Palmer and Pearson 2003) Equatorial Pacific, ∆pCO₂ is similar to or slightly lower than modern during the LGM, then shows a dramatic increase during the deglaciation, interpreted as an increase in the CO₂ content of upwelled waters. In the Indian Ocean, δ¹¹B records have been used to show variability in CO₂ outgassing related to different monsoon conditions (Naik et al. 2015; Palmer et al. 2010), with a peak in outgassing in the Bølling-Allerød interstadial, associated with an invigorated SW/Summer monsoon.

At high latitudes Yu et al. (2013) show that North Atlantic surface waters remained a sink of CO₂ from the atmosphere for the last 18 kyr. In contrast Southern Ocean surface waters saw pulses of high CO₂ during the last deglaciation (Martínez-Botí et al. 2015b), coincident with increases in atmospheric CO₂. This provides the first direct evidence for the role of the Southern Ocean in driving deglacial CO₂ rise, likely as a result of enhanced upwelling of CO₂-rich deep waters; the advection of these waters to the subsurface of the East Equatorial Pacific may also explain the pulses of CO₂ outgassing seen in this region (Martínez-Botí et al. 2015b; Fig. 5.10).

Boron isotope records from benthic foraminifera have also been used to examine the deep ocean carbonate system over the last deglaciation. These might be expected to show a pattern of increased deep ocean pH during intervals of CO₂ release from the deep ocean to the atmosphere. However Rae et al. (2014)’s data from the deep North Pacific show the opposite (Fig. 5.10d), with pulses of low pH during CO₂ rise in HS1 and the Younger Dryas. These are interpreted to result from mixing of CO₂-rich water from mid depths through the water column during pulses of local deep water formation (supported by comparison to radiocarbon and δ¹³C data). This emphasizes the importance of considering changes in circulation, as well biogeochemistry, in interpreting benthic δ¹¹B records.

5.5.2 pH and CO₂ Beyond the Ice Cores

The reconstruction of atmospheric CO₂ change beyond the reach of the ice cores has been a major goal for studies using foraminiferal δ¹¹B. Applications of such data include understanding the major climate transitions as Earth evolved from greenhouse to icehouse over the Cenozoic (Pearson et al. 2009; Bartoli et al. 2011; Fig. 5.6), to determining climate sensitivity in a warmer world (Anagnostou et al. 2016; Martínez-Botí et al. 2015a).

Early applications of foraminiferal δ¹¹B to reconstruct long term changes in surface ocean pH and atmospheric CO₂ indicated substantial decrease in CO₂ over the Cenozoic (Spivack et al. 1993; Pearson and Palmer 1999, 2000). However Pearson and Palmer (2000)’s iconic δ¹¹B-CO₂ record also shows high amplitude spikes in the Palaeogene, and low and constant values in the Neogene (Fig. 5.6), leading to some suggestions that CO₂ and climate were decoupled (Shevenell et al. 2004; Pagani et al. 2005b; Mosbrugger et al. 2005).

More recent work shows high CO₂ values (~1500 ppm) during the early Eocene climatic optimum (EECO), which then decrease through the rest of the Eocene (Anagnostou et al. 2016). At higher resolution, Penman et al. (2014) use δ¹¹B to provide the first direct evidence of ocean acidification during the PETM, while Pearson et al. (2009) show decreasing CO₂ levels over the Eocene-Oligocene boundary, though with an intriguing re-bound following Antarctic ice growth in the early Oligocene. In the Miocene, Foster et al. (2012) show a close coupling between atmospheric CO₂ and global climate and sea level (Fig. 5.8), which is also observed at higher temporal resolution (Fig. 5.6; Greenop et al. 2014; Badger et al. 2013).

A strong link between CO₂ and climate has also been shown using foraminiferal δ¹¹B in the Pliocene and early Pleistocene (Fig. 5.6). Seki et al. (2010), Bartoli et al. (2011) and Martínez-Botí et al. (2015a) show that the Pliocene warm period had CO₂ levels of ~400 ppm, similar to modern day anthropocene values. Martínez-Botí et al. (2015a) further quantify the relationship between CO₂ and climate at high resolution over this interval, and show that Earth System climate sensitivity in this warmer climate was half that of the Pleistocene. This can be attributed to a reduced ice-albedo feedback in the Pliocene, with equilibrium climate sensitivity found to be the same in both intervals when ice volume changes are considered. Between the Pliocene and the Pleistocene CO₂ falls (Seki et al. 2010; Bartoli et al. 2011), and Honisch et al. (2009) show that further intensification of glaciation during the mid-Pleistocene transition was linked to lower CO₂ in glacial periods, while CO₂ in interglacials remained relatively similar (Fig. 5.6).

5.6 Summary and Outlook

Recent developments in boron isotope analyses have spurred on an exciting era in the development and application of the boron isotope pH proxy in foraminifera. Boron isotope analysis by column chromatography and MC-ICPMS now gives reproducibility of ~0.2‰, equivalent to ~0.02 pH units, on around 5–20 benthic or 50–200 planktic foraminifera. Calibration studies show that foraminiferal δ¹¹B lies close to that of borate ion at seawater pH, consistent with simple models of δ¹¹B-pH systematics based on sole incorporation of the borate ion into foraminiferal carbonate. Offsets between foraminifera and borate ion are largely attributable to modification of the local microenvironment by photosynthesis, respiration, and calcification. pH elevation during biomineralisation might be expected to drive substantial elevation of foraminiferal δ¹¹B above seawater borate, but this is not observed in the majority of species. The majority of the boron incorporated into foraminiferal calcite appears to be derived from borate ion at or close to seawater pH, providing an important constraint on models of biomineralisation.

Given the close coupling between seawater pH and CO₂, foraminiferal δ¹¹B measurements may provide relatively precise constraints on past CO₂ change, even with conservative estimates of a second carbonate system parameter. Boron isotope-based CO₂ reconstructions show a close match to the ice core CO₂ record where these overlap. On glacial-interglacial timescales, δ¹¹B records from regions of CO₂ disequilibrium in the surface ocean and in the deep ocean provide evidence of deglacial CO₂ release from the Southern Ocean and North Pacific, and changes in upwelled CO₂ in the tropics. Beyond the reach of the ice cores, foraminiferal δ¹¹B records increasingly demonstrate coupling between CO₂ and climate over key intervals of the last 60 Myr.

Future work should continue to refine boron isotope calibration in foraminifera, capitalize on boron’s constraints on biomineralisation, and further constrain the evolution of seawater δ¹¹B to improve long-term pH and CO₂ reconstructions.

Notes

1.
Minor polynuclear species of aqueous boron exist, such as $ {\text{B}}_{3} {\text{O}}_{3} \left( {\text{OH}} \right)_{4}^{ - } $, but are only present in negligible quantities at boron concentrations <25 mmol/kg (Su and Suarez 1995), and can thus safely be ignored at seawater concentrations of ~0.4 mmol/kg.

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Acknowledgements

This chapter was greatly improved thanks to detailed and thoughtful reviews by Marcus Gutjahr and an anonymous reviewer, editorial comments by Gavin Foster, and informal reviews by David Evans and Rosanna Greenop. Other members of the STAiG lab boron group, including Will Gray, Ben Taylor, Jessica Crumpton-Banks, Eloise Littley, and Matt Kaminski, along with the “B-team” at Southampton, are thanked for their hard work developing boron isotopes in foraminifera. Discussions over the last ten years with Michael Henehan, Gavin Foster, Richard Zeebe, Tim Elliott, Wally Broecker, Andy Ridgwell, Daniela Schmidt, Bärbel Hönisch, Kat Allen, Jess Adkins, and Jonathan Erez have all greatly contributed to my thinking about boron isotopes in foraminifera and CO₂ reconstruction; though any omissions or mistakes are mine alone. This work was partially supported by a research fellowship from the University of St Andrews, $100 (pending) from Richard Zeebe, and NERC grants NE/N003861/1 and NE/N011716/1.

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James W. B. Rae

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Gavin Foster

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Rae, J.W.B. (2018). Boron Isotopes in Foraminifera: Systematics, Biomineralisation, and CO₂ Reconstruction. In: Marschall, H., Foster, G. (eds) Boron Isotopes. Advances in Isotope Geochemistry. Springer, Cham. https://doi.org/10.1007/978-3-319-64666-4_5

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