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 The North Atlantic and Norwegian Sea are prominent sinks of atmospheric CO2 today, but their roles in the past remain poorly constrained. In this study, we attempt to use B/Ca and δ11B ratios in the planktonic foraminifera Neogloboquadrina pachyderma (sinistral variety) to reconstruct subsurface water pH and pCO2 changes in the polar North Atlantic during the last deglaciation. Comparison of core-top results with nearby hydrographic data shows that B/Ca in N. pachyderma (s) is mainly controlled by seawater B(OH)4−/HCO3− with a roughly constant partition coefficient of 1.48 ± 0.15 × 10−3 (2σ), and δ11B in this species is offset below δ11B of the borate in seawater by 3.38 ± 0.71‰ (2σ). These values represent our best estimates with the sparse available hydrographic data close to our core-tops. More culturing and sediment trap work is needed to improve our understanding of boron incorporation into N. pachyderma (s). Application of a constant KD of 1.48 × 10−3 to high resolution N. pachyderma (s) B/Ca records from two adjacent cores off Iceland shows that subsurface pCO2 at the habitat depth of N. pachyderma (s) (~50 m) generally followed the atmospheric CO2 trend but with negative offsets of ~10–50 ppmv during 19–10 ka. These B/Ca-based reconstructions are supported by independent estimates from low-resolution δ11B measurements in the same cores. We also calibrate and apply Cd/Ca in N. pachyderma (s) to reconstruct nutrient levels for the same down cores. Like today's North Atlantic, past subsurface pCO2 variability off Iceland was significantly correlated with nutrient changes that might be linked to surface nutrient utilization and mixing within the upper water column. Because surface pCO2 (at 0 m water depth) is always lower than at deeper depths and if the application of a constant KD is valid, our results suggest that the polar North Atlantic has remained a CO2 sink during the calcification seasons of N. pachyderma (s) over the last deglaciation.
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 Natural variations in atmospheric CO2 are primarily governed by gas exchange with the land biosphere and ocean, whose carbon reservoirs are respectively ~3 and ~50 times that of the atmosphere [Sigman and Boyle, 2000]. Mapping of surface seawater partial pressure of CO2 (pCO2) in the modern ocean [Takahashi et al., 2009] shows that low-latitude regions, such as the eastern equatorial Pacific and Arabian Sea, serve as CO2 sources to the atmosphere due to upwelling and warming of nutrient- and CO2-rich subsurface mode waters primarily sourced from Southern Ocean [Sarmiento et al., 2003]. As the upwelled waters flow to high latitudes, cooling and nutrient utilization draw down surface water pCO2, producing prominent CO2 sinks at subtropical/subpolar confluence regions that absorb CO2 from the atmosphere in both hemispheres [Takahashi et al., 2009]. On centennial to millennial timescales, which are sufficiently long to complete the shallow mode water circulation, CO2 degassing at low-latitude upwelling regions roughly balances CO2 absorption at subtropical/subpolar convergence zones, resulting in little net effect on atmospheric CO2 content [Hain et al., 2013; Sarmiento et al., 2003]. Therefore, the most likely regions that could have significant impacts on atmospheric CO2 on millennial or longer timescales are the polar oceans [Sigman and Boyle, 2000]. These regions are crucial for carbon exchange between the deep ocean and the surface ocean and the atmosphere, due to their tight link to the deep ocean circulation, which occurs on the timescale of ~1000 years [Broecker, 1982].
 The cause of the rapid rise of 75 parts per million in volume (ppmv) in atmospheric CO2 during the last deglaciation has been suggested to be CO2 release by intensified upwelling in the Southern Ocean [e.g., Anderson et al., 2009]. Release of CO2 from the Southern Ocean to the atmosphere also occurred during the most recent pre-industrial period [Keeling and Heimann, 1986]. However, no rise in atmospheric CO2 was observed [Etheridge et al., 1996], as CO2 released from the Southern Ocean was largely balanced by CO2 uptake in the North Atlantic [Broecker and Peng, 1992]. This highlights the point that, in addition to constraining variation in potential CO2 source regions (e.g., Southern Ocean), quantification of CO2 flux in oceanic sinks (e.g., North Atlantic) is critical to understanding past atmospheric CO2 changes.
 Direct constraints on past changes in CO2 source-fluxes and sink-fluxes in the polar oceans are lacking, primarily due to the shortage of surface water pCO2 reconstructions in cold high-latitude waters. Surface water pCO2 in the North Atlantic has been reconstructed using organic matter within planktonic foraminifera, but this method is complicated by having to use planktonic δ13C to obtain a surface water value and gives unreasonably high sea-air pCO2 gradients (ΔpCO2) of up to approximately −100 ppmv based on core-top samples from the North Atlantic [Jasper et al., 1995; Maslin et al., 1997]. It is also unclear which seasons are represented by these pCO2 reconstructions. Although yielding more reasonable results, the recent estimation method based on planktonic foraminifera weight [Barker and Elderfield, 2002] has been challenged [e.g., Beer et al., 2010]. As a result, we do not know whether the polar North Atlantic has served as a sink or a source of CO2 to the atmosphere in the past. In this study, we explore the feasibility of using B/Ca and δ11B in the planktonic foraminifera Neogloboquadrina pachyderma (sinistral) as novel proxies for cold polar subsurface water pCO2 reconstructions. We present the first high-resolution B/Ca-based estimates of subsurface water pCO2 during the last deglaciation (19–10 ka) in the subpolar/polar North Atlantic, using two cores south of Iceland. We have also examined Cd/Ca in N. pachyderma (s) to investigate possible links between subsurface water nutrient changes and pCO2 in the past.
2 B/Ca and δ11B Methodology
 The use of foraminiferal B/Ca and δ11B for seawater pH and pCO2 reconstructions has been discussed previously [Foster, 2008; Hemming and Hanson, 1992; Hönisch and Hemming, 2005; Palmer et al., 2010; Rae et al., 2011; Sanyal et al., 1996; Yu et al., 2007b]. Briefly, dissolved boron in seawater exists primarily as a mixture of the mononuclear species B(OH)3 (boric acid) and B(OH)4− (borate), the proportions of which are highly pH dependent. Boron has two stable isotopes, 11B and 10B, and an equilibrium isotope fractionation occurs between B(OH)3 and B(OH)4− [Klochko et al., 2006]. The 11B/10B ratio, expressed in delta notation as δ11B, of each molecular species is thus also pH dependent. δ11B data from modern marine carbonates suggest that B(OH)4− is the dominant species incorporated into carbonates [Hemming and Hanson, 1992]:
 Both the boron concentration and isotopic ratio in carbonates will thus be a function of the ocean carbonate system. δ11B in carbonates (δ11Bcc) can be used to calculate seawater pH by
where pKB* is the pK value for boric acid at the in situ temperature and salinity, δ11Bsw = 39.61‰ [Foster et al., 2010], α = 27.2‰ [Klochko et al., 2006], and δ11Bcc-B4 is the offset between δ11Bcc and δ11B of seawater B(OH)4−. The partition coefficient, KD, of boron between calcium carbonate and seawater is defined as
 Provided that the KD in equation ((2)) is constant or can be quantified, carbonate B/Ca ratios can be used to estimate seawater [B(OH)4−/HCO3−]. Coupled with an estimate of surface water alkalinity (ALK), B/Ca-derived [B(OH)4−/HCO3−] ratios and δ11B-derived pH provide constraints on seawater pCO2. Given the close relationships in the carbonate system between pH, [B(OH)4−/HCO3−], and [CO2], these pCO2 estimates are relatively insensitive to the alkalinity estimate and will be mainly driven by the B/Ca and δ11B data [Foster, 2008; Hönisch et al., 2008; Palmer and Pearson, 2003].
 Previous measurements of B/Ca in Globigerina bulloides, Globigerina inflata, Globigerinoides ruber, and Globigerinoides sacculifer suggest that KD varies within and between these planktonic species as a result of secondary controls by temperature or carbonate ion concentration [Foster, 2008; Yu et al., 2007b]. Approaches have been suggested to estimate seawater [B(OH)4−/HCO3−] and hence pH and pCO2, although corrections for temperature or carbonate ion effect inevitably introduce errors in the calculated pCO2 values and compromise interpretations [Yu et al., 2007b]. Recent work [Allen and Hönisch, 2012] has also suggested that the variability of KD associated with some species such as G. bulloides, G. ruber, and G. sacculifer could mainly be driven by the denominator in equation ((3)), not by B/Ca itself, casting doubt on previous paleo-reconstructions [e.g., Palmer et al., 2010; Yu et al., 2007b]. Allen and Hönisch  also stressed the potential risk of using down-core samples to calibrate KD.
 In this study, we first explore the variability of KD in the planktonic foraminifera N. pachyderma (s) using core-tops from the North Atlantic. We then apply the core-top derived KD to two down-core records and check the credibility of our estimates of KD for paleo-pH and pCO2 reconstructions by comparing reconstructions from a second pH proxy, δ11B, from the same cores.
3 Species, Materials, and Methods
 During cold time intervals, the dominant species in polar and subpolar waters is N. pachyderma (s). Other planktonic foraminifera species are therefore either absent or very low in abundance (≲2% of the total foraminiferal assemblage) in subpolar and polar North Atlantic cores throughout the LGM and cold intervals of the deglacial. N. pachyderma (s) is thus widely used for paleoceanographic studies to obtain continuous glacial-interglacial records in this region. Here, we explore the possibility of using B/Ca and δ11B ratios in N. pachyderma (s) for past subsurface water pH and pCO2 reconstructions. Core-top samples include three locations from the southern Norwegian Sea, two locations from the South Iceland Basin, and 12 locations from the Labrador Sea (Figure 1 and Table 1). These core-tops are verified to be of recent age (≲3000 years), mostly based on 14C dates [Kristjánsdóttir et al., 2011]. Two nearby cores RAPiD-10-1P (62°58.53'N, 17°35.37W; 1237 m water depth) and RAPiD-15-4P (62°17.58'N, 17°08.04W; 2133 m water depth) (hereafter 1P and 4P, respectively) from the South Iceland Rise were used for down-core B/Ca and δ11B measurements. The chronology of these cores is from Thornalley et al. . The sedimentation rates for the two cores are 10–50 cm/1000 years during the last deglacial period. These cores are bathed in deep waters supersaturated with respect to calcite [Yu et al., 2010], and therefore dissolution of foraminiferal tests is minimal.
Table 1. Core-top N. pachyderma (s) B/Ca, Cd/Ca and δ11B, together with estimated habitat hydrographic data and calculated partition coefficients and δ11Bcc-B4.
Lat., Long., Water Depth (°N, °W, m)
Hydrographic Data (50m water depth)
δ11B B(OH)4− (‰)
14C age (years)
aHabitat depths (55 m at 15 MCA and 16MCA, and 35 m at 19MCA) are assigned at σt = 27.65 kg/m3, according to Simstich et al. .
 Approximately, 100–200 tests (~1 mg) of N. pachyderma (s) were picked from the 150–250 µm size fraction and then cleaned following the “Mg-cleaning” procedure [Barker et al., 2003]. Analysis of trace element concentrations followed the method described in Yu et al. . The long-term relative precisions (2σ) for B/Ca and Cd/Ca are 5.2% and 10% based on duplicate measurements of in-house standards with B/Ca = 150 µmol/mol (n = 638, 1SD = 3.9 µmol/mol) and Cd/Ca = 0.024 µmol/mol (n = 233, 1SD = 0.001 µmol/mol), respectively.
 A comparison of different cleaning methods showed little effect on foraminiferal B/Ca [Yu and Elderfield, 2007]. Although previous studies on foraminiferal Cd/Ca have typically used reductive cleaning [Boyle and Keigwin, 1985/86], we employed the “Mg-cleaning” method [Barker et al., 2003] for both core-top and down-core samples. We do so for the following reasons: (i) Yu et al. [2007a] discovered a significant decrease in benthic foraminiferal Cd/Ca in core-tops during the reductive cleaning step in the laboratory. The decreases are not caused by hydrazine, the reagent originally employed to remove Fe-Mn oxides [Boyle and Keigwin, 1985/86], but are due to dissolution of carbonates by citrate [Yu et al., 2007a]. A similar phenomenon has also been observed for planktonic foraminifera [Bian and Martin, 2010]. Due to the very low Mn/Ca of these samples (down to ~2 µmol/mol, even without reductive cleaning) [Bian and Martin, 2010], decreases in Cd/Ca are unlikely to be caused by removal of any Mn coatings and are more likely due to preferential leaching of Cd from foraminiferal carbonate or dissolution of high-Cd carbonate phases [Yu et al., 2007a], although we acknowledge that further work is necessary to pin down the exact reasons. (ii) Mn/Ca values for core-top samples are <20 µmol/mol, well below the generally accepted threshold of 100 µmol/mol [Boyle, 1983], suggesting the absence of, or minimal, coatings associated with these samples. (iii) No correlation is observed between Cd/Ca and Mn/Ca (Fe/Ca) for our two down-core records, either separately or combined together (r < 0.1, P > 0.28) (Figures 2 and S1 in the auxiliary material). Down-core samples at deeper depths generally show higher Mn/Ca and Fe/Ca ratios. These increasing trends in Mn/Ca and Fe/Ca are in stark contrast to decreasing Cd/Ca down-core. One would expect to observe increasing Cd/Ca down-core and positive correlations with Mn/Ca and Fe/Ca, were Cd from Fe-Mn-containing coatings significant. (iv) The two down-cores show consistent Cd/Ca ratios, despite their different Mn/Ca ranges of 21–285 µmol/mol for 1P and 108–495 µmol/mol for 4P and very large contrast in Mn/Ca up to ~300 µmol/mol at some time intervals (Figure 2), which may be associated with various degrees of diagenesis in sediments under different sedimentation environments at different water depths (1P: 1237 m; 4P: 2133 m). Similarly, large Fe/Ca ratios are observed between the two cores. These provide strong evidence for insignificant contribution of Cd from Fe-Mn coatings [Boyle, 1983], if any, in our core sites. (v) At 10.5–12 ka and 15.2–16.1 ka (Figure 2), Mn/Ca in 1P are below the commonly used threshold of 100 µmol/mol and one would expect Cd/Ca from these time intervals are not significantly compromised by Mn coatings [Boyle, 1983]. Over the same time intervals, Mn/Ca in 4P range from 174 to 332 µmol/mol but Cd/Ca in 4P are similar to those from 1P, implying that Mn coatings are Cd-absent or Cd-depleted in our cores. (vi) Our Cd/Ca are fully consistent with a low resolution Cd/Ca in N. pachyderma (s), cleaned by the full reductive cleaning protocol [Boyle and Keigwin, 1985/86], for a nearby core NEAP 4K (61.5°N, 24.2°W, 1627 m; Figure 2b) [Rickaby and Elderfield, 2005], confirming that our Cd/Ca data are not contaminated by any Fe-Mn coating contamination. (vii) We use the same cleaning method for both our core-top and down-core samples, for consistency in this paper. Based on the above, we assert that it is unlikely that our Cd/Ca are compromised by the influence of any Fe-Mn coating contamination due to the exclusion of the reductive cleaning step. Instead, our results suggest that high Mn/Ca and Fe/Ca ratios do not necessarily indicate Cd contamination from Fe-Mn coatings at all times. We recommend that a comparison of Cd/Ca in shells from adjacent cores, bathed in the same water masses but experienced different diagenesis histories, could provide a useful approach to evaluate influences from Fe-Mn coatings. Possible cleaning effects on foraminiferal Cd/Ca may vary for samples from different environments and further studies are warranted in the future.
 The δ11B ratios were measured on a Neptune MC-ICP-MS according to the method of Foster  with an average uncertainty (2SD external reproducibility equivalent) of ±0.25‰ [Foster, 2008; Rae et al., 2011]. Each sample for δ11B had ~400–700 shells (equivalent to ~3–5 mg) from the 150–250 µm size fraction and was also cleaned following the “Mg-cleaning” procedure [Barker et al., 2003]. Because of large sample size requirements, significantly more laboratory effort, and the availability of shells, we measured δ11B for only eight samples from core-tops and seven samples down-core. Foraminiferal Mg/Ca and δ18O are from Thornalley et al. [2011b].
 Hydrographic variables used in our core top calibration are estimated from nearby Global Ocean Data Analysis Project (GLODAP) sites [Key et al., 2004]. For sites in the South Iceland Basin and Labrador Sea, we estimate hydrographic conditions at a habitat depth of 50 m and between March and September, as a nearby sediment trap study in the Irminger Sea shows that spring and late summer blooms account for >95% of the total annual flux in the 150–250 µm size fraction [Jonkers et al., 2010]. In the Norwegian Sea, N. pachyderma (s) shows a single blooming during the summer at water depths with a constant density of σt = ~27.65 kg/m3 [Simstich et al., 2003]. Water depths with σt = 27.65 kg/m3 correspond to 55 m at core-top sites GS06-144-15MCA/16MCA, and 35 m at site GS06-144-19MCA (Table 1). Owing to the paucity of hydrographic sites, we used the two closest hydrographic sites (July) available in GLODAP to estimate seawater [B(OH)4−/HCO3−] and δ11B of B(OH)4− for three core-tops from the Norwegian Sea, which could introduce large uncertainties. However, we stress that exclusion of Norwegian Sea core-tops from our calibration does not affect our conclusions.
 Hydrographic conditions at the habitat depth of N. pachyderma (s) at our core sites were interpolated from GLODAP data using the 3-D estimation function in Ocean Data View (ODV) [Schlitzer, 2006]. We only select hydrographic sites which have the complete set of variables used in CO2 system calculations (i.e., sites with all T, S, P, Si, TCO2, ALK, and anthropogenic CO2; Figure 1a), as calculated [B(OH)4−/HCO3−] may be biased if sites containing complete CO2 variables are combined with those having only some of these variables. The only exception to this is for anthropogenic CO2 data in the Norwegian Sea: no anthropogenic CO2 estimates are available at these two sites, and so we assumed a constant value of 45 µmol/kg (the value observed for hydrographic sites in the Labrador Sea [Key et al., 2004]) for 0–100 m in the water column. The anthropogenic CO2 contribution was subtracted from TCO2, and pre-industrial seawater [B(OH)4−/HCO3−] are calculated using CO2sys.xls (Ver. 12) [Pelletier et al., 2005]. The equilibrium constants K1 and K2 are those from Mehrbach et al. , refit by Dickson and Millero , KB according to Department of Energy (DOE) ], KSO4 is from Dickson , and we use the recently redetermined total boron value of Lee et al. . Core-top results are reported in Table 1 and down-core results are tabulated in the auxiliary material.
4 Core-Top Data
 The N. pachyderma (s) from core-top samples shows B/Ca ratios ranging from 56 to 67 µmol/mol (Figure 3a), similar to those observed in this species from the Southern Ocean [Hendry et al., 2009]. Comparison of B/Ca ratios with seawater [B(OH)4−/HCO3−] shows that B/Ca and seawater [B(OH)4−/HCO3−] are positively correlated (r = 0.66, P < 0.0001) and KD into N. pachyderma (s) is normally distributed with a mean of 1.48 ± 0.15 × 10−3 (2σ) (Figures 3a and 3b).
 Core-top N. pachyderma (s) δ11B displays a range of 13.19–14.33‰, significantly lower than the estimated δ11B of seawater B(OH)4− of 16.88–17.37‰ at these sites (Table 1 and Figures 3c and 3d). The δ11B offset between shell carbonate and seawater B(OH)4−, δ11Bcc-B4, shows a range of −2.7‰ to −3.8‰ with an average of −3.38 ± 0.71‰ (2σ). Negative δ11Bcc-B4 offsets as seen in N. pachyderma (s) have previously been observed in another symbiont-barren planktonic foraminifera Neogloboquadrina dutertrei (δ11Bcc-B4 ≈ −1.5‰), and contrast with the positive δ11Bcc-B4 offsets associated with symbiont-bearing species G. ruber and G. sacculifer [Foster, 2008]. δ11Bcc-B4 offsets have previously been attributed to incorporation of boric acid (which has δ11B ~ 27‰ higher than borate), pH elevation during calcification, or alteration of microenvironment pH by CO2 released during foraminifera and symbiont respiration, or CO2 taken up by symbiont photosynthesis [e.g., Foster, 2008; Hönisch et al., 2003; Klochko et al., 2009; Zeebe et al., 2003]. The negative offsets we observe in N. pachyderma (s) cannot be simply related to boric acid incorporation, nor to pH elevation during calcification, both of which would raise foraminifera δ11B above that of seawater borate. One explanation for these offsets, which is applicable to all the species mentioned above, is alteration of the foraminiferal microenvironment by respiration and photosynthesis [e.g., Hönisch et al., 2003; Zeebe et al., 2003]. This may cause negative δ11Bcc-B4 in the symbiont-barren species due to respiration and positive δ11Bcc-B4 in the symbiont-bearing species due to photosynthesis. Alternatively, the offset may be due to some unknown vital effects. As with previous studies [e.g., Foster, 2008; Zeebe et al., 2003], this offset is assumed to be constant.
 To explore possible links between upper ocean pCO2 and nutrients in the past, we use N. pachyderma (s) Cd/Ca ratios to reconstruct past subsurface water P contents, following the approach described by Rickaby and Elderfield . We use core-top Cd/Ca data to define a partition coefficient between N. pachyderma (s) calcite and seawater Cd (DCd) appropriate for our sites. Seawater P and temperature were estimated using the same approach as for B/Ca calibration, except that we used all hydrographic sites with P and T during the spring-summer season rather than only selecting sites with all the carbonate system parameters. Seawater P is related to seawater Cd using Cd = Cdt/[α×(Pt/P − 1) + 1], where Cdt = 1.2 nmol/kg, Pt = 3.3 µmol/kg, and α = 2 from Elderfield and Rickaby . A constant Ca concentration of 0.01 mol/kg is used to calculate seawater Cd/Ca. Then the partition coefficient of Cd into calcite of N. pachyderma (s) is obtained from DCd = (Cd/Ca)foram/(Cd/Ca)sw. Similar to what is observed for G. bulloides [Rickaby and Elderfield, 1999], DCd for N. pachyderma (s) shows an exponential dependence on the calcification temperature (Figure 4).
5 Variability of KD and δ11Bcc-B4 and Complications with Core-Top Calibrations
 We observe considerable variability in KD and δ11Bcc-B4 associated with core-top N. pachyderma (s) (Figure 3), which is significantly greater than our analytical uncertainties and may be largely due to weak constraints related to paucity of our hydrographic data. As can be seen in Figure 1a, suitable hydrographic sites in this region are sparse and are from a limited number of cruises (in 1981, 1997, and 1998) [Key et al., 2004], especially for the Norwegian Sea samples. This inevitably introduces errors in estimates of hydrographic conditions for core-top shell samples which likely represent the average carbonate system conditions over many years. It is probably an oversimplification to use an average habitat depth for calibration. The calcification depth of N. pachyderma (s) may vary significantly in different ocean regions. For example, this species has been found to live at depths varying between ~30 m and 250 m in the Arctic and Nordic Seas [e.g., Bauch et al., 1997; Hillaire-Marcel and de Vernal, 2008; Nyland et al., 2006; Simstich et al., 2003]. N. pachyderma (s) also migrates vertically in the water column through its life cycle, experiences encrustation, and cements secondary calcites at depth [e.g., Simstich et al., 2003]. Error bars in Figure 3 show the influences from potential changes in the habitat depth between 40 and 60 m. At the depth of the thermocline where large gradients in seawater pCO2 occur (Figures 1b and 1c), even a small variation in water depth (especially to shallow depths) is accompanied with large changes in seawater [B(OH)4−/HCO3−] and δ11B of B(OH)4− (Figure 3). Furthermore, the blooming season of this species may vary [Kuroyanagi et al., 2011]. In addition, our core-top samples are from locations that span relatively narrow ranges in seawater [B(OH)4−/HCO3−] and δ11B. We cannot include N. pachyderma (s) B/Ca data from the Southern Ocean [Hendry et al., 2009] in our calibration, because there is no seawater [B(OH)4−/HCO3−] for those samples. We encourage high-quality core-top samples from other regions with sufficiently different carbonate chemistry to extend the calibration (Figure 3).
 The range of ages characterizing our core-tops and the change in atmospheric CO2 during this period may also add to the observed variability. Although our core-top samples are from relatively high sedimentation rate box cores, radiocarbon dates show an age range of 0 to ~3000 years (conventional radiocarbon age) (Table 1 and Figure 5). N. pachyderma (s) B/Ca shows a significant decrease since industrialization, mirroring the rising atmospheric CO2 (Figure 5); only one δ11B measurement falls within this period and also shows a slight decrease. Due to low temperatures and relatively low TCO2, surface water CO2 content in the North Atlantic is highly sensitive to atmospheric CO2 increases [Feely et al., 2004]. With increasing atmospheric CO2, surface water pH, [B(OH)4−/HCO3−], and δ11B of B(OH)4− will decrease. Thus, it is inappropriate to use pre-industrial CO2 values to calculate KD for very young core-tops (≲500 years radiocarbon age). If we use modern TCO2 (measured in June 1998, the only cruise available in GLODAP) [Key et al., 2004] for these young samples, the calculated KD would be ~1.79–1.87 × 10−3 and δ11Bcc-B4 would be approximately −2.95‰, slightly higher than the averages using all core-tops (Table 1 and Figure 3). However, the hydrographic data (mainly TCO2) from this single cruise are unlikely to accurately represent the conditions over the time interval when these core-top shells calcified (presumably a few decades to a hundred years), in the face of a very rapid rise in atmospheric CO2 during the past century (Figure 5).
 Altogether, the above factors would contribute to KD and δ11Bcc-B4 variations observed in our core-top samples. It is a problem that will beset all such calibration attempts given the timescale mismatch between sediment and water data. However, core-top samples serve as the closest analogue to down-core samples as they both have calcified in natural marine environments and experienced various processes including growth at surface, secondary encrustation during vertical migration in the water column, and subsequent burial in sediments. The calibrations in Figure 3 represent our best estimates based on currently available hydrographic data and our understanding about the habitat of N. pachyderma (s) in the North Atlantic. Below, we assumed constant KD of 1.48 × 10−3 and δ11Bcc-B4 of −3.38‰ for our down-core calculations. We strongly encourage further studies such as laboratory culturing [e.g., Allen et al., 2011] and plankton tows combined with simultaneous measurements of hydrographic data to improve our understanding about boron incorporation into N. pachyderma (s).
 When applying N. pachyderma (s)-based proxies to down-core data, we must bear in mind the uncertainty in assigning a specific depth habitat for N. pachyderma (s). Our down-core proxy data should therefore be interpreted simply in terms of our best estimate of past subsurface pCO2. However, because surface pCO2 at 0 m water depth is always lower than at greater depths (Figures 1b and 1c), our subsurface pCO2 reconstructions also provide a constraint for the maximum possible value of surface pCO2. As will be shown, our subsurface pCO2 reconstructions are lower than atmospheric pCO2, enabling us to suggest that the polar North Atlantic has remained a CO2 sink during the calcification seasons of N. pachyderma (s) over the last deglaciation.
6 Down-Core Data
 The N. pachyderma (s) from 1P and 4P shows a similar trend and a comparable range in B/Ca of 64–97 µmol/mol during the last deglacial period (Figure 6a). B/Ca ratios decreased by ~45% since the last glacial. The higher glacial B/Ca cannot be explained by an ~3% increase in seawater B concentration caused by ice growth during the glacial period (note the incorporation of boron into calcite does not involve Ca2+ according to equations ((1)) and ((3))). The decrease of B/Ca during the last deglacial is not linear, displaying rapid decreases in B/Ca from 97 to 77 µmol/mol during Heinrich Stadial 1 (HS1) and from 77 to 64 µmol/mol during the Younger Dryas (YD), interrupted by a plateau during the Bølling/Allerød (B/A). This temporal change in N. pachyderma (s)B/Ca roughly mirrors that of atmospheric CO2 (Figure 6d) [Monnin et al., 2001]. From the last glacial to early Holocene, N. pachyderma (s) δ11B decreased from 16.25‰ to 14.84‰ (a change of −1.41‰) and followed the B/Ca trend (Figure 6a).
 We used a constant KD of 1.48 × 10−3 (Figure 3b) to calculate past seawater [B(OH)4−/HCO3−] from N. pachyderma (s) B/Ca (Figure 6a). In this case, any reconstructed changes in pH and pCO2 should be driven by changes in B/Ca, not by KD [Allen and Hönisch, 2012] (Figure S2). In addition to seawater [B(OH)4−/HCO3−], a second variable is needed to fully constrain the seawater CO2 system, and ALK is often used. The history of seawater ALK is poorly constrained and here we follow the previous approach of Foster . We estimate surface seawater ALK in which N. pachyderma (s) calcified using the equation of ALK = 2305 + 53.97 × (S − 35) + 2.74 × (S − 35)2 − 1.16 × (T − 20) − 0.040 × (T − 20)2 from Lee et al. , assuming that this relationship has remained unchanged since the last glacial maximum (Figure 7). However we note that given the close relationship between [B(OH)4−/HCO3−], pH and [CO2], our pCO2 estimates are mainly driven by our δ11B and B/Ca data; in other words, a large uncertainty of ±3% or approximately ±100 µmol/kg for ALK (arbitrarily assigned, compared to approximately ±50 µmol/kg in Palmer and Pearson ) produces relatively small errors in pCO2 (Figure 6) [Foster, 2008; Hönisch et al., 2008; Palmer and Pearson, 2003]. Calcification temperatures for N. pachyderma (s) are reconstructed using Mg/Ca(TMg/Ca) [Thornalley et al., 2011b]. With N. pachyderma (s) δ18Occ and TMg/Ca, the seawater δ18Osw is calculated using the equation: δ18Osw = (δ18Occ + 0.27) − [4.64 − (4.642 − 4 × 0.09*(16.1 − TMg/Ca))0.5]/(2 × 0.09) [Kim and O'Neil, 1997]. To estimate salinity from δ18Osw, rather than use the modern S − δ18Osw relationship which is unlikely to be robust during the deglaciation when meltwater input was high, we employ a simple mixing model, with a freshwater end-member δ18Osw value of −30‰, based on typical values for ice melt in this region [Azetsu-Scott and Tan, 1997; Rasmussen et al., 2006]. It is possible to use other models to calculate S (such as the modern Norwegian Sea S − δ18Osw relationship [LeGrande and Schmidt, 2006]), but these do not yield S values outside the estimated error assigned to S of 1‰ and would have little effect on the calculated pH, CO32−, and pCO2. Furthermore, while 1P and 4P showed very different S during the late HS1 (Figure 7c), which may be associated with more intense local surface freshening and/or brine rejection at 1P [Thornalley et al., 2011a; Thornalley et al., 2010], the two cores show very similar carbonate system and pCO2 trends (Figures 6b–6d). This suggests that the B/Ca methodology is relatively insensitive to S changes. With TMg/Ca, S, ALK, and [B(OH)4−/HCO3−], we calculate seawater pH, CO32−, and pCO2 (Figures 6b–6d) using CO2sys.xls by iteration in Excel [Pelletier et al., 2005]. We applied a constant δ11Bcc-B4 of −3.38‰ (Figures 3c and 3d) to convert N. pachyderma (s) δ11B to seawater pH using equation ((2)), and combined this with ALK, to obtain surface CO32− and pCO2, following the approach in Foster  (Figure 6). Error sourced from individual input variables is given in Figure 6. The average integrated reconstruction uncertainties for B/Ca and δ11B are similar, at ±0.04 units in pH, ±15 µmol/kg in CO32−, and ±20 ppmv in pCO2 (2σ), respectively.
7 Comparison of CO2 Variables Derived from B/Ca and δ11B
 As N. pachyderma (s) B/Ca and δ11B were measured in shells from the same depths, they should yield similar pH, CO32−, and pCO2 values, if the KD and δ11Bcc-B4 values obtained from core-top samples are correct. All seawater pH, CO32−, and pCO2 values from B/Ca and δ11B agree within their reconstruction uncertainties, though δ11B-based values mainly (five out of seven cases) lie below those from B/Ca (Figure 6). This suggests a systematic offset that could be removed with only a slight adjustment of KD and/or δ11Bcc-B4. For example, if the δ11Bcc-B4 is adjusted from −3.38‰ to −3.1‰, which is still within the range of δ11Bcc-B4 (Figure 3d), δ11B-derived pH, CO32−, and pCO2 would entirely match those from B/Ca.
 Using a different habitat depth would shift both δ11B and B/Ca derived values upward or downward in the same direction, with little effect on the temporal pattern (Figure S3). The discrepancy between B/Ca and δ11B-derived values becomes slightly larger down core, if 100 m habitat depth is chosen for the core-top calibration. This favors a shallow habitat depth for N. pachyderma (s). If we use a habitat depth of 30 m for core-tops, the down-core pH and pCO2 results remain similar to those using 50 m habitat depth, and the match of pH, CO32−, and pCO2 based on B/Ca and δ11B does not improve compared to that using 50 m habitat depth (Figure S3).
 The slight mismatch in absolute estimates in pH, CO32−, and pCO2 from B/Ca and δ11B cannot be attributed to secondary influences on KD from seawater CO32− or calcification temperature, because KD in N. pachyderma (s) from core-tops and down-cores show no relationship with the calcification temperature or ambient CO32− (Figure S4). At this time, we use constant KD of 1.48 × 10−3 and δ11Bcc of −3.38‰ in N. pachyderma (s) (Figure 3) for down-core reconstructions. Considering complications associated with our core-top calibrations (Section 5) as well as reconstruction uncertainties from the two independent methods, the agreement within uncertainty between the B/Ca and δ11B-based reconstructions is encouraging (Figure 6). We will show that using results from B/Ca and δ11B independently would not affect our final conclusions regarding the CO2 uptake history of the northern North Atlantic in the past.
8 Deglacial Subsurface pCO2 Variation in the Northern North Atlantic
 Given its high temporal resolution, we focus on B/Ca derived pH, CO32−, and pCO2 in the discussion below. The last glacial (17.5–21 ka) to early Holocene (10.5–11 ka) changes in surface water pH, CO32−, and pCO2 at 1P and 4P are −0.13 units, −41 µmol/kg, and +70 ppmv, respectively (Figures 6b–6d). These changes are similar to those observed in the tropical and subtropical regions over the same time interval [Foster, 2008; Hönisch and Hemming, 2005; Palmer and Pearson, 2003; Sanyal et al., 1997; Yu et al., 2007b]. Our reconstructed subsurface pCO2 is close to and generally follows the trend of atmospheric CO2 [Lemieux-Dudon et al., 2010; Monnin et al., 2001], showing rapid rises during the HS1 and YD, interrupted by a pause during the B/A (Figure 6d). A few samples centered at 11.65, 12.66, and 14.20 ka showed pCO2 values higher than the contemporary atmospheric CO2. Typically, however, subsurface pCO2 was lower than the contemporary atmospheric CO2. During the last deglacial, the sea-air pCO2 gradient (ΔpCO2) between the habitat depth of N. pachyderma (s) and the atmosphere remained largely negative with an average value of −26 ± 35 ppmv (2σ variability of all data during the last deglacial) (Figure 8a), compared to the preindustrial offset of approximately −20 ppmv during spring-summer at 50 m water depth in this area [Key et al., 2004; Takahashi et al., 1993; Takahashi et al., 2002].
 A close inspection of our pCO2 and ΔpCO2 records also reveals considerable millennial timescale variability (Figures 6d and 8a). For example, the ΔpCO2 variability during the HS1, shown in both 1P and 4P, reached a maximum magnitude of ~40 ppmv between 15 and 16 ka. Changes in seawater pCO2 off Iceland are affected by a combination of factors, including the pCO2 of source waters from the Gulf Stream/North Atlantic Current and gradients in temperature, salinity/alkalinity, and nutrients from the source region to the core location. Reconstruction of surface water pCO2 for core ODP 999 in the Caribbean Sea shows that surface water at low latitudes of the Atlantic has remained roughly in equilibrium with the atmosphere since the last glacial [Foster, 2008]. The temperature gradient between ODP 999 [Schmidt et al., 2004] and 1P/4P [Thornalley et al., 2011b] was only slightly greater (by <2°C) during the last glacial period than the early Holocene (Figure 8c) and shows no correlation with ΔpCO2 (Figure 8a). These observations suggest that changes in source water pCO2 and temperature gradients (ODP 999 versus 1P/4P) are not major reasons for past ΔpCO2 variations observed at our sites.
 In contrast, similar trends are observed between ΔpCO2 and the raw Cd/Ca (Figures 8a and 8b). We have used N. pachyderma (s) Mg/Ca derived TMg/Ca to account for the temperature effect on DCd, based on the core-top calibration to reconstruct seawater P (Figures 4 and 9). Reconstructed seawater P and raw Cd/Ca are highly correlated (Figure 9D), suggesting that changes in down-core P are mainly caused by changes in Cd/Ca. Therefore, ΔpCO2 and seawater P have covaried during the last deglaciation (r = 0.46, P < 0.0001, n = 114, all date from 19 to 10 ka; r = 0.84, P < 0.0001, n = 44, early deglacial from 17.5 to 14 ka; Figure S5). This covariation is not an artifact induced by (i) conversions from B/Ca to seawater pCO2 because changes in pCO2 are mainly driven by those in B/Ca, as reflected by the tight correlation between subsurface pCO2 and B/Ca (r2 = 0.924, P < 0.0001; Figure S2), or (ii) the age model uncertainty associated with our cores (Figure S6). A comparison of raw data suggests that the covariation between ΔpCO2 and P is largely driven by the correlation between B/Ca and Cd/Ca (Figure S7). The covariation between ΔpCO2 and P suggests that biological processes and/or mixing waters from above and below have played an important role in the observed variability of ΔpCO2 (Figures 8a and 8b), as it does today [Takahashi et al., 1993]. Using Redfield ratio stoichiometry and the Revelle factor to estimate pCO2 changes from our reconstructed seawater P change gives shifts in pCO2 on the order of ~60 ppmv (Figure S5), supporting a significant control on ΔpCO2 by changes in seawater nutrient concentration. The δ13C of N. pachyderma (s) (Figure S8) may also be sensitive to changes in seawater nutrient content. However, it is likely that many additional factors affect planktonic δ13C, but not Cd/Ca [Duplessy et al., 1988; Kohfeld et al., 2000; Lynch-Stieglitz et al., 1995], preventing an obvious correlation between Cd/Ca and δ13C.
9 The Role of the Polar North Atlantic in Atmospheric CO2 During the Last Deglaciation
 Today, the polar North Atlantic serves as one of the major sinks of CO2 in the global oceans [Takahashi et al., 2002]. A change in the strength with which CO2 is absorbed in the North Atlantic Ocean would influence atmospheric CO2. The air-sea exchange of CO2 is affected by sea-air ΔpCO2 at 0 m water depth. Our reconstructed pCO2 cannot be treated directly as past sea surface pCO2, but represent values at the subsurface habitat depth (~50 m) of N. pachyderma (s) during the calcification seasons. However, subsurface pCO2 is always higher than that at the surface due to regeneration of sinking biogenic matter and mixing with high-pCO2 waters from deeper depths. Today, the offset in pCO2 between 50 m and 0 m in the polar North Atlantic is about 40–90 ppmv during the summer (Figures 1b and 1c). If our application of a constant KD from our core-top calibration is correct, the negative sea-air ΔpCO2 based on N. pachyderma (s) indicates that even considering our reconstruction uncertainties of ±20 ppmv, surface pCO2 remained lower than contemporary atmospheric CO2 during 19–10 ka. Therefore, like today, regions off Iceland in the polar North Atlantic served as a sink of CO2 to the atmosphere during the calcification seasons of N. pachyderma (s) (spring to summer, if the modern observation in Irminger Sea applies to the past) during the last deglaciation. The same conclusion can be drawn from our low-resolution δ11B record independently (Figure 6d).
 Our work does not fully constrain the role of the polar North Atlantic on CO2 uptake during the last deglaciation, because N. pachyderma (s) only lives in certain seasons, if the modern observation in the North Atlantic applies to the past. To obtain the annual mean values of surface mixed layer properties, a perfect situation requires that (i) the species lives in the surface mixed layer during its entire life cycle, (ii) the species grows year round, (iii) the flux of shells of the species is evenly distributed during different seasons throughout the year and does not change through time, and (iv) the shells of the species calcified in each season are equally/proportionally preserved in the sediment. Unfortunately almost no species fulfills these criteria, and certainly not one found in the polar North Atlantic. Much work is therefore still needed to fully constrain the role of the polar North Atlantic in controlling atmospheric CO2 in the past. However, we note that sediment trap studies from the northwestern North Pacific [Kuroyanagi et al., 2011] found that N. pachyderma (s) appears to calcify year-around with roughly equal shell fluxes from contrasting seasons (spring versus autumn and summer versus winter) and non-flux-normalized δ18O of shells matches the modern annual mean water value. This has led these authors to suggest that δ18O of this species could represent the annual mean environments around the pycnocline under certain circumstances. We therefore encourage future studies to investigate the possible use of N. pachyderma (s) B/Ca and δ11B to obtain estimates of past annual mean surface pCO2 in the (sub) polar North Pacific.
 We have investigated B/Ca and δ11B in N. pachyderma (s) as proxies to constrain changes in CO2 uptake in the polar North Atlantic Ocean during the last deglaciation. We use N. pachyderma (s) as it is the only species from which we could obtain continuous deglacial B/Ca and δ11B records. Our core-top results suggest roughly constant KD and δ11Bcc-B4 associated with the incorporation of boron into N. pachyderma (s), with some scatter possibly attributable to the scarcity of suitable hydrographic data in the study region. Using KD = 1.48 × 10−3 and δ11Bcc-B4 = −3.38‰, seawater pH, CO32−, and pCO2 values derived from B/Ca and δ11B in down-core records show similar trends and agree within reconstruction uncertainties. Both methods show subsurface pCO2 has been lower than contemporary atmospheric CO2 during 19–10 ka. The variability in down-core pCO2 is significantly correlated with nutrient based on Cd/Ca. As surface pCO2 are inevitably lower than subsurface values, our reconstructions suggest that the polar North Atlantic has remained a sink of CO2 over the growth seasons of N. pachyderma (s) during the last deglaciation. Reconstructing past surface water pCO2 is challenging and we suggest future studies such as culturing and sediment trap work to improve our understanding of boron incorporation into N. pachyderma (s).
 We thank T. Takahashi, R. Ryderson, H. Elderfield, and F. He for very helpful discussions, O. Hyams-Kaphzan, Z. Jin, M. Greaves, and Chris Coath for excellent lab assistance, and T. Dokken for providing three core-tops from the Norwegian Sea. We also thank constructive comments from two anonymous reviewers. This research is funded by Lamont-Doherty Postdoctoral Fellowship, Lawrence Livermore Fellowship and the Australian National University (J.Y.), by NERC RAPID grant NER/T/S/2002/00436 (N. M. and D. T.), and by a NERC PhD studentship (J.R.). The cores examined in this study were obtained during cruise CD-159 of RRS Charles Darwin funded by the RAPID Climate Change programme of NERC (UK).