# Extra environment friendly North Atlantic carbon pump through the Final Glacial Most

### CO2 system calculations

For each the preindustrial ocean and down-core CO2 system calculations, seawater carbonate system variables had been calculated utilizing the CO2sys.xls program28 with dissociation constants K1 and K2 in line with Mehrbach et al.55 and (Okay_) in line with Dickson56. Seawater whole boron focus was calculated from the boron–salinity relationship of Lee et al.57. For the GLODAP dataset, the anthropogenic CO2 contribution was subtracted from the measured DIC to acquire preindustrial DIC values2.

### Preindustrial Atlantic DICas and [CO32−]as

The GLODAP dataset2 is used to calculate preindustrial ocean CO2 system variables. Following the established methodology of Broecker and Peng3, we account for DIC anomalies created by (1) freshwater addition or removing based mostly on S, (2) soft-tissue carbon creation and respiration based mostly on PO4, and (three) CaCO3 formation and dissolution based mostly on ALK and nitrate (NO3). See Fig. 1 for the simplified idea. We undertake the time period DICas to signify web air–sea alternate element DIC signatures from:

$$hskip-10pt = _ – (_ – {_4^rm}) instances mathrmC/PO_4 – ^ hbox _instances left( {mathrmALK_mathrms-mathrmALK^ + mathrmNO_-_3^rm} proper)-_mathrmfixed$$

(1)

the place the subscript “s” represents values normalized to S of 35 (e.g., DICs = DIC × 35/S); the superscript “mo” denotes imply ocean values at S = 35 (PO4mo = 2.2 μmol/kg, ALKmo = 2383 μmol/kg, DICmo = 2267 μmol/kg, and NO3mo = 31 μmol/kg)29; C/PO4 represents the soft-tissue stoichiometric Redfield ratio; and the arbitrary DICconstant ( = 2285 μmol/kg) is designed to convey zero DICas near the NADW–AABW boundary (Fig. 2). The time period (PO4s − PO4mo) × C/PO4 corrects for DIC modifications because of photosynthesis and soft-tissue degradation, and the time period ½ × (ALKs − ALKmo + NO3s − NO3mo) accounts for DIC modifications brought on by CaCO3 formation and dissolution. To be according to earlier work3,30, we used C/PO4 = 127 to calculate DICas and [CO32−]as in Fig. 2. Utilizing different C/PO4 values10 doesn’t considerably have an effect on spatial DICas and [CO32−]as patterns (Supplementary Figs. 11 and 12). Neither are their patterns affected by utilizing different PO4–ALK–NO3 values to switch world imply values in Eq. (1) (Supplementary Figs. 13 and 14). Ideally, DICconstant could be the imply DIC worth of an abiotic ocean (Fig. 1), however this worth can’t be merely decided from trendy observations. As a result of our curiosity lies in spatial DICas contrasts as a substitute of absolute values, the selection of DICconstant has no impact on our interpretation.

To acquire [CO32−]as, we first calculate [CO32−]PO4–T–S–P utilizing (DICas + DICconstant), ALKmo, and PO4mo at T = three °C, S = 35, and P = 2500 dbar. [CO32−]as is then calculated by [CO32−]as = [CO32−]PO4–T–S–P − [CO32−]fixed, the place [CO32−]fixed ( = 78 μmol/kg, calculated utilizing DICconstant and ALKmo) is designed to convey zero [CO32−]as near the NADW–AABW boundary. In essence, the [CO32−]as distribution displays the variation of [CO32−] when normalized to the identical PO4−T−S−P situations.

### CO2 system sensitivities and calculation of [CO32−]Norm

As a result of the seawater CO2 system is nonlinear, there may be at present no easy approach to derive these sensitivities based mostly on CO2 system equations16. We use GLODAP preindustrial data2 to calculate numerically [CO32−] sensitivities to numerous physiochemical parameters. Use of LGM outputs from the LOVECLIM mannequin58 yields comparable sensitivities. We first use hydrographic knowledge, together with T, S, P, DIC, ALK, PO4, and SiO3 to calculate [CO32−]. We then change S to 35‰ and different chemical concentrations proportionally. For instance, ALK and DIC will change as follows:

$$mathrmALK_=,$$

(2)

$$_ = ; instances .$$

(three)

We use S = 35‰, ALKS=35, DICS=35, [PO4]S=35, and [SiO3]S=35 together with hydrographic T and P to calculate [CO32−]S=35. The [CO32−] to S sensitivity (Sen_S) is calculated by:

$$__ = left( {left[ right]-left[ right]_} proper)/left( – proper).$$

(four)

To estimate temperature results, we calculate [CO32−]S=35, T=three °C utilizing S = 35‰, ALKS=35, DICS=35, [PO4]S=35, [SiO3]S=35, T = three °C, and hydrographic P. The sensitivity of [CO32−]S=35 to temperature (Sen_T) is outlined by:

$$__mathrmT,,left( {left[ right]_,mathrmT = ^ circ -left[ right]_} proper)/left( -T proper).$$

(5)

Relating to stress results, we calculate [CO32−]S=35, T=three °C, P=2500 dbar utilizing S = 35‰, ALKS=35, DICS=35, [PO4]S=35, [SiO3]S=35, T = three°C, and P = 2500 dbar. The sensitivity of [CO32−]S=35, T=three°C to P (Sen_P) is outlined by:

$$__ = ,left( {left[ right]_,mathrmT = ^ circ , = ,mathrmdbar} proper. left. {-left[ right]_ = ,mathrmT = ^ circ } proper)/left( proper).$$

(6)

To estimate the affect on [CO32−] from within-ocean ALK–DIC redistributions by organic processes, we assume a zero.1 μmol/kg enhance in PO4 (i.e., ΔPO4 = zero.1 μmol/kg) because of organic respiration (photosynthesis has an reverse impact). The resultant ALK (ALKS=35+respiration) and DIC (DICS=35+respiration) can then be calculated from:

$$mathrmALK_ = , mathrmALK_ + _ instances mathrmC/PO_ div , R instances -_ instances _.$$

(7)

$$_ = _ + _ instances mathrmC/PO_ + _ instances mathrmC/PO_ div R.$$

(eight)

Resultant [CO32−] ([CO32−]Norm+respiration) values are calculated utilizing DICS=35+respiration, ALKS=35+respiration, and ([PO4]S=35 + ΔPO4) at fixed bodily situations of T = three °C, S = 35, and P = 2500 dbar. The sensitivity of [CO32−]Norm to PO4 is outlined by:

$$left[ right]_mathrmNorm_,mathrmsensitivity = left( {left[ right]_mathrm- left[ right]_mathrmNorm} proper)/_.$$

(9)

We contemplate 4 Redfield stoichiometric eventualities: C/PO4 = 127, R = four (the reference composition; Fig. 4d); C/PO4 = 140, R = four; C/PO4 = 127, R = eight; and C/PO4 = 140, R = eight (Supplementary Fig. 15). In all circumstances, sturdy exponential correlations exist between [CO32−]Norm/PO4 sensitivities and [CO32−]Norm. The correlations could replicate the buffering impact of the seawater CO2 system: for seawater with excessive DIC (low [CO32−] and excessive buffering functionality), [CO32−] could be comparatively much less delicate to organic DIC and ALK disturbances. The entire above sensitivity calculations assume no web air–sea CO2 change.

To calculate air–sea alternate sensitivities, we assume a 10 μmol/kg enhance in DICS=35 because of atmospheric CO2 invasion (i.e., ΔDICas = 10 μmol/kg). We calculate [CO32−]Norm+as utilizing S = 35‰, ALKS=35, DICS=35+as ( = DICS=35 + ΔDICas), [PO4]S=35, [SiO3]S=35, T = three °C, and P = 2500 dbar. The sensitivity of [CO32−]as to DICas is outlined by:

$$left[ right]_mathrm/DIC_,mathrmsensitivity = left( {left[ right]_-left[ right]_mathrmNorm} proper)/Delta _.$$

(10)

Utilizing sensitivities proven in Fig. four, [CO32−]Norm could be calculated by:

$$left[ right]_mathrmNorm ,= ,left[ right] + left( – proper) instances + left( -T proper) instances , + left( proper)mathrm/100 hskip1ptinstances .$$

(11)

Excel spreadsheets are offered in Supplementary Knowledge 7–eight to calculate [CO32−]Norm and the organic curves proven in Fig. 5.

### LGM–Holocene North Atlantic carbon funds

The overall further carbon enhance (Δ∑CLGM−Holocene) in Fig. 6 is calculated by Δ∑CLGM−Holocene = V × density × %GNAIW × ([CO32−]as_ODP999-BOFSLGM/zero.61) × 12 − V × density × %NADW × ([CO32−]as_ODP999-BOFSHolocene/zero.59) × 12, the place V is the worldwide deep ocean quantity (>1 km water depth) at 100.eight × 1016 m3, density = 1027.eight kg/m3 (ref. 29), %GNAIW and %NADW, respectively, signify their quantity fractions within the deep ocean, [CO32−]as_ODP999-BOFSHolocene = 56 μmol/kg, [CO32−]as_ODP999-BOFSLGM = 114 μmol/kg (Fig. 5), phrases zero.61 and zero.58, respectively, signify absolutely the LGM and Holocene [CO32−]as/DICas sensitivities (Fig. 4e) used to switch [CO32−]as_ODP999-BOFS into ODP999–BOFS DICas contrasts (LGM: 186 μmol/kg; Holocene: 95 μmol/kg), and the quantity 12 converts C from moles into weight. Based mostly on earlier estimates, %NADW is considered ~50% (refs. 38,39), whereas %GNAIW remained roughly much like %NADW or shrank (refs. 35,36). These estimates are debated and have giant uncertainties, and we thus calculate Δ∑CLGM−Holocene for a variety of %NADW and %GNAIW values (Fig. 6). Any affect from AAIW is ignored due to its related [CO32−]as indicators to Gulf Stream through the Holocene (Supplementary Fig. three) and far diminished northward advection through the LGM23,31,32,33. We tentatively deal with Δ∑CLGM-Holocene of ~100 PgC utilizing %NADW = 50% and %GNAIW = 30% as our greatest estimate. Assuming no Holocene–LGM DICas gradient change (i.e., the identical CO2 uptake effectivity) and the whole lot else being equal, Δ∑CLGM–Holocene could be −240 PgC at %NADW = 50% and %GNAIW = 30%.

### Cores, age fashions, samples, and analytical strategies

We used ODP Web site 999 for Gulf Stream surface-water reconstructions (Fig. 2). The age mannequin is from Schmidt et al.59. Planktonic foraminiferal Globigerinoides ruber (sensu stricto, white selection) δ18O, Mg/Ca, and δ11B knowledge are from refs. 21,22,59. Briefly, about 25 and 55 shells from the 250–350 μm dimension fraction had been used for δ18O and Mg/Ca analyses, respectively. Samples for δ18O analyses had been sonicated in methanol for five–10 s, roasted below vacuum at 375 oC for 30 min, and analyzed on a Fisons Optima IRMS with a precision of

Three cores (BOFS 17, BOFS 11, and BOFS 14 Okay) from the polar North Atlantic Ocean are used for deep-water reconstructions (Fig. three). Their age fashions are based mostly on printed chronologies24,63,64,65. For every pattern (~2 cm thickness), ~10–20 cm3 of sediment was disaggregated in de-ionized water and was moist sieved by way of 63 μm sieves. To facilitate analyses, we picked essentially the most plentiful species for measurements. For every B/Ca evaluation, ~10–20 monospecific shells of the benthic foraminifera C. mundulus (BOFS 17 Okay) and C. wuellerstorfi (BOFS 14, 11 Okay) had been obtained from 250 to 500 μm dimension fraction. The shells had been double checked below a microscope earlier than crushing to make sure that constant morphologies had been used all through the core. On common, following this cautious screening the beginning materials for every pattern was ~eight–12 shells, which is equal to ~300–600 μg of carbonate. For benthic B/Ca analyses, foraminiferal shells had been cleaned with both the “Mg-cleaning” methodology61 or the “Cd-cleaning” protocol61, to analyze cleansing results on hint ingredient/Ca in foraminiferal shells62,66. No discernable B/Ca distinction is noticed between the 2 cleansing strategies25,62. Benthic B/Ca ratios had been measured on an ICP–MS utilizing procedures outlined in ref. 67, with an analytical error higher than ~5%.

For every benthic Cd/Ca evaluation, ~10–20 shells of the benthic foraminiferal taxa C. mundulus (BOFS 17 Okay), C. wuellerstorfi (BOFS 14 Okay, 11 Okay), and Uvigerina spp. (BOFS 17 Okay) had been picked from the 250–500 μm dimension fraction. Earlier research26,27,68 confirmed related Cd/Ca ratios between infaunal Uvigerina spp. and epifaunal Cibicidoides, and we thus mixed Cd/Ca knowledge from these taxa to acquire steady downcore PO4 information. We used the “Cd-cleaning” methodology60,69 to scrub benthic shells for Cd/Ca measurements. Cd/Ca ratios had been measured on an ICP–MS with an analytical error higher than ~5% (ref. 67)

For δ11B measurements, about 20 benthic shells from the 250–500 μm dimension fraction had been picked for every pattern. Shells used for δ11B analyses had been cleaned utilizing the “Mg-cleaning” methodology, to attenuate lack of shell materials61. After cleansing, shells had been dissolved and pure boron was extracted utilizing column chemistry as described by Foster21. Benthic δ11B was measured on a Neptune multi-collector (MC)–ICP–MS following ref. 21. The analytical error in δ11B is about ± zero.25‰. As a result of comparatively giant pattern dimension requirement, shell availability, and prolonged chemical remedies for δ11B, we current low-resolution δ11B for C. mundulus from BOFS 17 Okay and for C. wuellerstorfi from BOFS 11 Okay. Be aware that constant [CO32−] outcomes from B/Ca and δ11B strengthen the reliability of our reconstructions (Fig. three).

Revealed benthic Cd/Ca and B/Ca outcomes are included in Fig. three. Altogether, we generated 180 new measurements of benthic δ11B, B/Ca, and Cd/Ca. All knowledge are listed in Supplementary Knowledge 1–9.

### ODP 999 reconstructions

ODP Web site 999 was used to constrain previous bodily situations and carbonate chemistry of the Gulf Stream (Supplementary Fig. four). Following earlier approaches21,22, floor water temperature (Tsurface) and salinity (Ssurface) had been estimated based mostly on G. ruber Mg/Ca (ref. 59) and sea degree modifications21,22,59, respectively. We first convert G. ruber δ11B to borate δ11B (δ11Bborate), following the conversion methodology of ref. 22. Floor water pH (pHsurface) was calculated from seawater δ11Bborate together with Tsurface and Ssurface. To constrain the CO2 system, two CO2 system variables are essential16. Along with δ11B-derived pH, literature research21,22,41 usually estimate previous surface-water ALK (ALKsurface) modifications. Following refs. 21,22, we estimate ALKsurface from Ssurface utilizing the fashionable Ssurface–ALKsurface relationship (ALKsurface = 59.19 × Ssurface + 229.08, R2 = zero.99)21. Along with Tsurface and Ssurface, pHsurface, and ALKsurface had been used to calculate different CO2 system variables together with surface-water [CO32−] ([CO32−]floor) and DIC (DICsurface) utilizing the CO2sys program28. Floor-water PO4 focus at ODP 999 is assumed to be zero during the last 27 ka.

Following refs. 21,22,59, errors are estimated to be 1 °C, 1‰, 100 μmol/kg, and ~zero.43‰ for Tsurface, Ssurface, ALKsurface, and δ11Bborate, respectively. Built-in common uncertainties in [CO32−]floor and DICsurface for a single reconstruction are, respectively, ~20 (Holocene: ~18, LGM: ~24) and ~90 μmol/kg, based mostly on quadratic addition of all particular person errors sourced from Tsurface ([CO32−]floor: 2 μmol/kg, DICsurface: three μmol/kg), Ssurface ([CO32−]floor: 2 μmol/kg, DICsurface: 5 μmol/kg), ALKsurface ([CO32−]floor: 14 μmol/kg, DICsurface: 86 μmol/kg), and δ11Bborate ([CO32−]floor: 16 μmol/kg, DICsurface: 24 μmol/kg; notice that δ11Bborate results in an error in [CO32−] by way of pH). Uncertainties for calculated CO2 system variables at ODP 999 are tabulated in Supplementary Knowledge 1. Use of different strategies to estimate ALK would have little impression on our conclusions (Supplementary Figs. 16 and 17).

### From pH to [CO32−]

For palaeo-studies, surface-water pH is usually obtained from planktonic foraminiferal δ11B. To calculate [CO32−], a second CO2 system variable is required16. Following the earlier strategy21,22, previous ALKsurface at ODP 999 have been estimated from S utilizing the Ssurface–ALKsurface relationship. As a result of restricted information in regards to the previous Ssurface–ALKsurface relationship, a beneficiant uncertainty has been assigned to ALKsurface at ±100 μmol/kg (ref. 21,22), which is about half of your complete ALK vary within the current world ocean2. Utilizing ALKsurface and pHsurface together with Tsurface and Ssurface, [CO32−]floor and DICsurface could be calculated utilizing the CO2sys program28. Due to the big uncertainty in ALKsurface, giant errors in DICsurface could be anticipated (Supplementary Fig. four). Nevertheless, given the constraint from pHsurface, seawater ALKsurface and DICsurface variations should not random however should range systematically inside ALK–DIC area (Supplementary Fig. 5). Due to the shut relationship between pH and [CO32−] (i.e., roughly parallel patterns of pH and [CO32−] inside ALK−DIC area; Supplementary Fig. 5), this systematic ALK−DIC variation permits us to restrict [CO32−] with acceptable uncertainty. For a given pH at ODP 999, an error of 100 μmol/kg in ALK solely results in an error of about ±14 μmol/kg in [CO32−] (Supplementary Fig. 5).

For readability, Supplementary Fig. 5a, b solely contemplate the impact of ALK errors on [CO32−] estimates assuming fixed pH and T–S–P situations. To completely propagate errors from numerous sources together with Tsurface, Ssurface, ALKsurface, and pHsurface, we use a Monte Carlo strategy (n = 10,000) to calculate the built-in error in [CO32−] (ref. 70). As could be seen from Supplementary Fig. 5c–f, the ultimate errors (~20–25 μmol/kg) in a person [CO32−] reconstruction based mostly on the Monte-Carlo are much like these (~18–24 μmol/kg) based mostly on quadratic addition of particular person errors, justifying our main error estimation strategy (i.e., quadratic addition).

### Subtropical western North Atlantic floor [CO32−]

As a result of most of North Atlantic subtropical gyre waters flow into by way of the Caribbean Sea earlier than being transported to the subpolar North Atlantic by way of the Gulf Stream, ODP 999 from Caribbean Sea is used to constrain previous Gulf Stream carbonate chemistry20. To additional check the feasibility of utilizing ODP 999 to signify the first-order Gulf Stream [CO32−] modifications through the Holocene and LGM, we’ve got estimated surface-water [CO32−] for 4 websites from the broader subtropical western Atlantic area (latitude: 12–33°N, longitude: 61–91°W). Amongst these websites, KNR140–51GGC (33°N, 76°W) is positioned inside the Gulf Stream at this time71. As a result of subtropical floor waters cycle a number of instances by way of the higher ocean gyre circulations, it’s attainable that floor waters have been near equilibrium with previous atmospheric pCO2 (refs. 21,22). Due to this fact, we assume surface-water pCO2 of 270 and 194 ppm for the Holocene and LGM, respectively72. We assign a ±15 ppm error to surface-water pCO2 to account for any potential air–sea CO2 disequilibrium. For these websites, we use floor temperature and salinity reconstructions from earlier publications71,73,74,75. ALK is calculated based mostly on the identical strategy for ODP 999. The reconstructed in situ [CO32−] values present some variations between cores, because of native T–S situations. Since we’re desirous about air–sea CO2 alternate indicators, we convert reconstructed in situ [CO32−] into [CO32−]Norm utilizing Eq. (11). As could be seen from Supplementary Fig. 6 and Supplementary Knowledge 2, these cores present related [CO32−]Norm values for the Holocene (~260 μmol/kg) and LGM (~300 μmol/kg) as ODP 999. Due to this fact, we argue that ODP 999 sufficiently information first-order Gulf Stream air–sea alternate carbonate chemistry for the Holocene and LGM. As a result of we goal to acquire a proxy-based estimates, we use ODP 999 knowledge for calculations in the principle textual content.

### Benthic B/Ca and δ11B to deep-water [CO32−]

Most deep-water [CO32−] values are reconstructed utilizing benthic B/Ca (refs. 25,47) from [CO32−]downcore = [CO32−]PI + ΔB/Cadowncore–coretop/ok, the place [CO32−]PI is the preindustrial (PI) deep-water [CO32−] worth estimated from the GLODAP dataset2, ΔB/Cadowncore–coretop represents the deviation of B/Ca of down-core samples from the core-top worth, and ok is the B/Ca–[CO32−] sensitivity of C. wuellerstorfi (1.14 μmol/mol per μmol/kg) or C. mundulus (zero.69 μmol/mol per μmol/kg)25. We use a reconstruction uncertainty of ±10 μmol/kg in [CO32−] based mostly on world core-top calibration samples25,76.

For cores BOFS 17 Okay and BOFS 11 Okay, new monospecific epifaunal benthic δ11B values had been transformed into deep-water [CO32−] following the strategy detailed in ref. 77. Briefly, benthic δ11B is assumed to instantly replicate deep-water borate δ11B, as recommended by earlier core-top calibration work78. Deep-water pH is calculated utilizing benthic δ11B together with Tdeep and Sdeep, much like the strategy to calculate surface-water pH at ODP 999 (refs. 21,22). We assume fixed ALK on the studied websites (2313 μmol/kg at BOFS 17 Okay and 2310 μmol/kg at BOFS 11 Okay) up to now. Following ref. 77, a beneficiant error of 100 μmol/kg is assigned to ALK estimates. We then calculate deep-water [CO32−] from pH and ALK utilizing the CO2sys program28. The built-in common uncertainty in deep-water [CO32−] is ~±10 μmol/kg, based mostly on quadratic addition of particular person errors of ~±2 μmol/kg sourced from Tdeep (±1 °C), ~±2 μmol/kg from Sdeep (±1‰), ~±5 μmol/kg from ALK (±100 μmol/kg), and ~±eight μmol/kg from δ11Bborate (~±zero.25‰). As demonstrated by Supplementary Fig. 5, the big ALK error solely contributes a small uncertainty to the ultimate [CO32−] estimate. As proven in Fig. three, benthic B/Ca and δ11B yield constant deep-water [CO32−] reconstructions for the Holocene and LGM.

### Benthic Cd/Ca to deep-water PO4

We comply with the established strategy26,46,79 to transform benthic (C. wuellerstorfi, C. mundulus, and Uvigerina spp.) foraminiferal Cd/Ca into deep-water Cd concentrations. Partition coefficients (DCd) are used to calculate deep water Cd from: Cd (nmol/kg) = [(Cd/Ca)foram/DCd] × 10. Bertram et al.65 used empirical DCd values of two.three, 2.2, and a couple of.7 for BOFS 17, 14, and 11 Okay, respectively. Nevertheless, these DCd values would end in Holocene Cd of zero.three–zero.four nmol/kg, greater than the noticed worth of ~zero.25 nmol/kg from trendy hydrographic measurements (Supplementary Fig. 7)80. This offset could counsel greater DCd values for the North Atlantic Ocean, which has been acknowledged just lately81. We thus modify DCd (~25% enhance) in order that the calculated Holocene deep-water Cd concentrations match trendy measurements. This adjustment is supported by constant Cd reconstructions from this examine and former reconstructions based mostly on Cd/Ca measurements for Hoeglundina elegans. In comparison with Cibicidoides, DCd into H. elegans is much much less variable79. As could be seen from Supplementary Fig. eight, for cores with related benthic δ13C from related water depths (i.e., bathed in related water lots), our Cd reconstructions match favorably with these based mostly on H. elegans measurements82. Deep water Cd is transformed into PO4 utilizing the connection based mostly on the most recent North Atlantic Ocean measurements (Supplementary Fig. 7)80. Utilizing older printed Cd–PO4 relationships26,83 solely marginally impacts our PO4 estimates.

Uncertainties related to Cd and PO4 reconstructions are estimated as follows. Error for Cd is estimated utilizing 2σCd = (sqrt), the place (2sigma _) and (2sigma _mathrm/mathrm) (=5%) are errors for DCd and Cd/Ca, respectively. As a result of poorly outlined uncertainty for DCd from the literature, we assume an error of 50%, after which examine our ultimate errors with literature estimates to evaluate the appropriateness of our calculations. Seawater PO4 is calculated from Cd utilizing: PO4 = (frac), the place 2σa and 2σb, respectively, signify 95% confidence errors related to a and b (Supplementary Fig. 7b). The PO4 uncertainty was calculated from: (2sigma _rm_4 = sqrt {left( {partial _rm_4partial _a cdot 2sigma _a} proper)^2 + left( {partial _rm_4partial _b cdot 2sigma _b} proper)^2 + left( {partial _rm_4/partial _ cdot 2sigma _} proper)^2}), the place (partial _rm_4/partial _a) = (frac), (partial _rm_4/partial _b) = (fraca), and (partial_rm_4/partial _) = (fraca). Our ultimate errors on particular person Cd and PO4 are ~zero.12 nmol/kg (~55%) and ~zero.5 μmol/kg (~50%), respectively. When put next with beforehand printed uncertainties (~zero.08 nmol/kg for Cd and ~zero.17 μmol/kg for PO4)46,68, our error estimates are presumably too beneficiant. Right here we use ~50% error to be conservative. We encourage future work to enhance uncertainty estimates for the benthic Cd/Ca proxy.

The oceanic residence time of PO4 is ~100,000 years84. The LGM deep ocean was presumably extra decreasing85, which could have facilitated sediment natural matter preservation, and, thus, PO4 removing from the ocean. Nevertheless, this impact might need been compensated by decreased natural burial on continental slopes because of shallower LGM sea ranges86,87. Contemplating the brief (~10,000 years) final deglacial84, we assume that world PO4 and Cd reservoirs remained fixed between the Holocene and LGM. Our reconstructions (Fig. three) are according to excessive benthic δ13C and low benthic Cd/Ca at quite a few glacial North Atlantic mid-depth websites23,31,46,65,88,89.

### Deep-water temperature and salinity estimates

Deep-water temperature (Tdeep) is estimated from the ice quantity corrected benthic δ18O (δ18OIVC) and the δ18O-temperature equation of Marchitto et al.90 from Tdeep = 2.5 − (δ18OIVC − 2.eight)/zero.224, the place δ18OIVC = δ18Obenthic − δ18Oglobal_sealevel. δ18Oglobal_sealevel was estimated from sea degree curves86,87 with a worldwide δ18Oseawater−sea degree scaling of zero.0085‰/m (ref. 91). Deep-water salinity (Sdeep) is calculated by: Sdeep = Score_top + 1.11 × δ18Oglobal_sealevel, the place Score_top is the fashionable Sdeep (35.06, 34.926, and 34.893 at BOFS 17 , 11 , and 14 Okay, respectively2) and the time period 1.11 is the scaling time period for a worldwide S−δ18Oglobal_sealevel relationship29,91. We assume ±1 °C and ±1‰ uncertainties in Tdeep and Sdeep, respectively. Use of different strategies to estimate Tdeep and Sdeep negligibly impacts our conclusions, because of comparatively weak sensitivities of [CO32−]Norm to T and S modifications (Fig. four).

### Uncertainties and statistical analyses

Uncertainties related to [CO32−] and PO4 had been evaluated utilizing a Monte-Carlo strategy92,93. Errors related to the chronology (x-axis) and [CO32−] and PO4 reconstructions (y-axis) are thought of throughout error propagation. Age errors are assumed to be ±3000 years for the three BOFS cores. Strategies to calculate errors related to particular person [CO32−] and PO4 reconstructions (y-axis) are given above. All knowledge factors had been sampled individually and randomly 5000 instances inside their chronological and [CO32−] or PO4 uncertainties and every iteration was then interpolated linearly. At every time step, the chance most and knowledge distribution uncertainties of the 5000 iterations had been assessed. Determine three reveals chance maxima (daring curves) and ±95% (mild grey; 2.5−97.fifth percentile) chance intervals for the info distributions, together with chronological and proxy uncertainties. For particulars, see refs. 92,93.

For a time interval (e.g., Holocene) the place a number of analyses can be found, uncertainties are calculated following the strategy from ref. 94 by 2σ = (sqrt [mathop nolimits_i = 1^n (2sigma _i)^2]/n), the place n is the variety of reconstructions and 2σi is the error related to particular person reconstruction. For [CO32−] or [CO32−]Norm offsets between the Holocene and LGM, 2σ = (sqrt ), the place (2 _) and (2 _mathrmLGM) are 2σ of Holocene and LGM values, respectively. Different strategies (e.g., weighted imply)95 would give related outcomes.

When utilizing Eq. (11) to calculate [CO32−]Norm, errors from numerous sensitivities are <1.5 μmol/kg (see Supplementary Knowledge eight for crosschecking). As a result of [CO32−] is normalized to a continuing situation (i.e., no error with ultimate T–S–P), the error in [CO32−]Norm is basically sourced from [CO32−] reconstruction uncertainties. For floor water [CO32−]Norm calculations, T and S errors are already included in floor [CO32−] reconstructions. For calculations related to deep waters, [CO32−]Norm errors are ~zero.5, ~three.5, and ~zero.1 μmol/kg from ± 1 °C in T, ±1‰ in S, and ±50 dbar in P, respectively. Due to this fact, these uncertainties (already included in error calculations) are comparatively much less essential in comparison with the reconstruction error of ±10 μmol/kg for deep water [CO32−].