Volume 33, Issue 2 p. 128-151
Research Article
Free Access

A Synthesis of Deglacial Deep-Sea Radiocarbon Records and Their (In)Consistency With Modern Ocean Ventilation

Ning Zhao

Corresponding Author

Ning Zhao

Massachusetts Institute of Technology-Woods Hole Oceanographic Institution Joint Program in Oceanography, Woods Hole, MA, USA

Now at Climate Geochemistry Department, Max Planck Institute for Chemistry, Mainz, Germany

Correspondence to: N. Zhao,

[email protected]

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Olivier Marchal

Olivier Marchal

Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA, USA

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Lloyd Keigwin

Lloyd Keigwin

Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA, USA

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Daniel Amrhein

Daniel Amrhein

School of Oceanography and Department of Atmospheric Sciences, University of Washington, Seattle, WA, USA

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Geoffrey Gebbie

Geoffrey Gebbie

Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA, USA

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First published: 08 January 2018
Citations: 33


We present a synthesis of 1,361 deep-sea radiocarbon data spanning the past 40 kyr and computed (for 14C-dated records) from the same calibration to atmospheric 14C. The most notable feature in our compilation is a long-term Δ14C decline in deep oceanic basins over the past 25 kyr. The Δ14C decline mirrors the drop in reconstructed atmospheric Δ14C, suggesting that it may reflect a decrease in global 14C inventory rather than a redistribution of 14C among different reservoirs. Motivated by this observation, we explore the extent to which the deep water Δ14C data jointly require changes in basin-scale ventilation during the last deglaciation, based on the fit of a 16-box model of modern ocean ventilation to the deep water Δ14C records. We find that the fit residuals can largely be explained by data uncertainties and that the surface water Δ14C values producing the fit are within the bounds provided by contemporaneous values of atmospheric and deep water Δ14C. On the other hand, some of the surface Δ14C values in the northern North Atlantic and the Southern Ocean deviate from the values expected from atmospheric 14CO2 and CO2 concentrations during the Heinrich Stadial 1 and the Bølling-Allerød. The possibility that deep water Δ14C records reflect some combination of changes in deep circulation and surface water reservoir ages cannot be ruled out and will need to be investigated with a more complete model.

Key Points

  • Published and new deep ocean radiocarbon records for the past 40 kyr are compiled
  • A 16-box model of modern ventilation is fit to the deglacial data
  • The residuals of the fit can generally be explained by data uncertainties

1 Introduction

Variations in the exchange of CO2 between the ocean and the atmosphere have long been postulated to have contributed to the preindustrial changes in the concentration of atmospheric CO2 documented in Antarctic ice core records (e.g., Knox & McElroy, 1984; Sarmiento & Toggweiler, 1984; Siegenthaler & Wenk, 1984). Among the processes that could modify air-sea CO2 fluxes on centennial and longer time scales resolved by these records are changes in ocean circulation, particularly in the transport between surface and deep waters. These changes could modify the temperature, salinity, dissolved inorganic carbon, and alkalinity of surface waters, thereby altering surface water CO2 partial pressure and air-sea CO2 flux (Sarmiento & Gruber, 2006). In particular, the Southern Ocean, where transport of deep waters to the surface would be favored by upwelling along density surfaces, has been suggested to be an important region for understanding past changes in atmospheric pCO2 (for recent reviews, see Fischer et al., 2010; Sigman et al., 2010) and climate (Marshall & Speer, 2012). Indeed, circulation changes in the Southern Ocean have been inferred from a variety of paleoclimatic indicators (e.g., Anderson et al., 2009; Jaccard et al., 2016; Schmitt et al., 2012; Skinner et al., 2010).

In paleoceanography, quantitative information about the exchange between surface and deep waters is often deduced from the “age” of deep waters relative to that of the surface waters or the atmosphere (for recent studies, see, e.g., Burke & Robinson, 2012; Chen et al., 2015; Freeman et al., 2016; Keigwin & Lehman, 2015; Rae et al., 2014; Sikes et al., 2016; Skinner et al., 2015). The age of deep ocean waters over the past 40 kyr or so is typically estimated from measurements of the radiocarbon (half-life of 5,700 ± 30 years; Audi et al., 2003) activity of fossil samples of benthic foraminifera or deep-dwelling corals. Many studies relied on such measurements to draw inferences about deep ocean “ventilation” during the last deglaciation, a period during which the atmospheric CO2 concentration is estimated to have increased by about 80 ppmv (e.g., Monnin et al., 2001). Notably, Marchitto et al. (2007) and Bryan et al. (2010) suggested that Antarctic Intermediate Water (AAIW) was significantly older than today during the Heinrich Stadial 1 (HS1, circa 17.6–14.7 kyr B.P.) and the Younger Dryas (YD, circa 12.9–11.7 kyr B.P.) using sediment cores from the eastern North Pacific and the northern Indian Ocean, respectively. Both studies argued that the inferred presence of low 14C concentration in AAIW during these two intervals was due to increased ventilation of Southern Ocean deep waters that would have released carbon accumulated at abyssal depths during the last glacial period into the overlying AAIW and the atmosphere.

This interpretation, however, has not gone unchallenged. Samples from the eastern South Pacific (De Pol-Holz et al., 2010) and western South Pacific (Rose et al., 2010) do not support an aging of AAIW during the HS1 and the YD. Moreover, there is debate over whether an isolated, deep ocean reservoir existed during the Last Glacial Maximum (LGM), a time interval centered at circa 21 kyr B.P. On the one hand, samples from several ocean basins suggest the presence of relatively old deep waters during the LGM, for example, in the eastern Equatorial Pacific (Keigwin & Lehman, 2015), the western South Pacific (Sikes et al., 2016), and the Atlantic sector of the Southern Ocean (Skinner et al., 2010). On the other hand, some studies concluded that the ages of deep ocean waters during the LGM were not substantially different from today (e.g., Broecker et al., 2004; Broecker & Clark, 2010; Lund et al., 2011). In the same vein, model calculations tend to challenge the notion that exchange with an isolated deep ocean reservoir produced the 14C activity drop observed at intermediate depths during the last deglaciation (e.g., Hain et al., 2011).

Many factors can influence a particular deep ocean radiocarbon record in addition to basin-scale changes in bottom water age. For instance, estimating the initial radiocarbon concentration (usually expressed as Δ14C, the 14C/12C ratio referred to a preindustrial atmospheric value and corrected for isotopic fractionation) of a fossil sample of benthic foraminifera or deep-sea coral requires accurate knowledge about the calendar age of the sample. The calendar ages of such samples, however, can suffer from various uncertainties due, for example, to the post-depositional movement of foraminiferal shells along the sedimentary column (bioturbation), changes in the difference in 14C ages between the ocean surface water and the atmosphere (reservoir age), and gains or losses of U-series isotopes in corals (open-system behavior; e.g., Robinson et al., 2006). Each of these sources of uncertainty can lead to a sizeable error in the reconstructed value of bottom water Δ14C. In general, the errors in calendar chronology and hence in bottom water Δ14C tend to be larger for older samples.

Other factors compound the interpretation of deep-sea radiocarbon records in terms of bottom water age. For example, changes in the radiocarbon age of ocean bottom water may not necessarily reflect changes in the true age of the water, since the radiocarbon concentration of waters entering the deep sea may vary with time (e.g., Wunsch, 2003). Mixing between different water masses is also likely to bias age estimates deduced from radiocarbon ages, as radiocarbon concentration is a nonlinear function of radiocarbon age. Finally, inferences made from single records, which constitute the majority of the literature on the subject, often assume that changes observed in the record are representative of a large oceanic region. However, single records may not represent basin-scale changes of bottom water age in a straightforward manner, especially if they originate from a region characterized by large gradients in radiocarbon concentration. The above considerations suggest that an analysis of multiple records which gives due consideration to errors is needed for a rigorous interpretation of deep-sea radiocarbon data in terms of paleoceanographic events.

In this study, we report a compilation of deep water Δ14C estimates for the last 40 kyr and examine the compiled data in the presence of a simple (box) model of modern ocean ventilation. Specifically, we explore the extent to which deglacial radiocarbon records from different oceanic basins jointly require changes in basin-scale ventilation during this period, given their errors and their scarcity (by modern standards). To this end, the model of modern ocean ventilation is fit to the deep water Δ14C records, and we examine whether (i) the differences between the observed and fitted values of deep water Δ14C are larger than the uncertainties and (ii) the surface water Δ14C values implied by the fit lie outside of upper or lower bounds. The upper bound is provided by the reconstructed value of contemporaneous atmospheric Δ14C (Reimer et al., 2013): since 14C, a cosmogenic radionuclide, is produced in the atmosphere, Δ14C in surface water is expected to be always smaller than atmospheric Δ14C, although pathological cases where surface ocean Δ14C is higher than atmospheric Δ14C could be constructed. The lower bound is provided by the contemporaneous Δ14C values that are found in the deep ocean. Although factors such as a larger sea ice extent could increase reservoir ages and decrease surface water Δ14C in high-latitude regions (e.g., Bard, 1988), the lowest Δ14C values in the ocean are expected to occur at depth rather than near the surface.

This paper is organized as follows. In section 2, we describe (i) our compilation of published and new deep water radiocarbon data, (ii) the treatment of these data for the present analysis, (iii) the box model of modern ocean ventilation, and (iv) the method used to fit the model to the data. The results of our analysis are presented in section 3. In section 4, we discuss their sensitivity to various assumptions about the data and the model. We clarify their paleoceanographic implications in section 5. Finally, possible perspectives of research are mentioned in section 6.

It is worth being explicit about the limitations of this study. One obvious limitation arises from the spatial distribution and scarcity (by modern standards) of deep water Δ14C data. The spatial distribution and scarcity of the data may bias inferences of past ocean conditions, although an effort is made to account for the resulting uncertainties (section 2.1). Likewise, the temporal resolution of radiocarbon records is relatively poor, implying that centennial and higher frequency variability is typically not resolved and may alias onto longer-period changes. Also, as alluded to above, estimates of paleo-Δ14C of deep ocean waters suffer from significant uncertainties, such as due to chronological errors. In this study, we rely on the sediment and coral chronologies reported in the original publications and conduct recalibration according to IntCal13 (Reimer et al., 2013), if needed. It is thus expected that unrecognized errors in the chronologies and in the IntCal13 calibration, in particular, systematic errors, would influence our results to some extent. Another limitation resides in the very coarse resolution of the model that is used to interpret the data. Although use of a very coarse resolution model is consistent with our research question and benefits from simplicity of interpretation, it implies that the paleodata be averaged over large oceanic volumes and that the errors in the volume averages be properly estimated. Support for our approach to derive basin-scale Δ14C from Δ14C measurements on fossil carbonates from a few sites is reported in section 3.1. Despite the aforementioned limitations, the present investigation appears justified given the postulated role of basin-scale ocean circulation changes in deglacial variations of atmospheric pCO2 and climate.

2 Methods

2.1 Deep Water Radiocarbon Data

The sources of the deep water radiocarbon data compiled for this study are listed in Table 1, where the data appear in order of decreasing latitude. Our compilation (available at the National Climatic Data Center of NOAA; https://www.ncdc.noaa.gov/paleo/study/21390) includes data published until December 2016 as well as our new data (Table 1). Overall, it comprises a total number of 1,361 deep water 14C age estimates for the past 40 kyr based on 14C measurements on fossil samples of benthic foraminifera (76.0% of the data), deep-dwelling corals (23.0%), deep-dwelling planktonic foraminifera (0.6%), and bivalves and spiral shells (0.4%). The geographic distribution of the data is very irregular: most of the samples originate from near the oceanic margins, and large oceanic regions are devoid of any data (e.g., the South Indian Ocean; Figure 1). The depths of the samples vary from about 250 m to 5,000 m (Figure S1 in the supporting information). Approximately 55% of the samples come from depths greater than 1,500 m, and only about 25% of the samples come from depths greater than 2,500 m. Factors contributing to the depth distribution include the difficulty in obtaining carbonate material for paleoceanographic reconstruction in deep, corrosive water, and the small number of corals dredged below about 2,500 m.

Table 1. List of Deep Water Δ14C Data Compiled in This Study (BF: Benthic Foraminifera; DC: Deep-Dwelling Coral; PF: Planktonic Foraminifera)
Latitude Longitude Sediment core/coral name Modern water depth (m) Substrate References
63.0 −17.6 RAPiD-10-1P 1,237 BF Thornalley et al. (2011)
62.3 −17.1 RAPiD-15-4P 2,133 BF Thornalley et al. (2011)
61.5 −19.5 RAPiD-17-5P 2,303 BF Thornalley et al. (2011)
60.1 −179.4 SO202-18-6 1,100 BF Max et al. (2014)
59.6 −144.2 EW0408-84TC 682 BF Davies-Walczak et al. (2014)
58.9 170.7 SO201-2-101KL 630 BF Max et al. (2014)
57.5 170.4 SO201-2-85KL 968 BF Max et al. (2014)
56.3 170.7 SO201-2-77KL 2,135 BF Max et al. (2014)
55.5 −15.7 2706 724 DC Schroder-Ritzrau et al. (2003)
54.6 −148.8 ODP887 3,647 BF Galbraith et al. (2007)
54.5 144.8 LV27-2-4 1,305 BF Gorbarenko et al. (2010)
54.4 −148.9 MD02-2489 3,640 BF Gebhardt et al. (2008); Rae et al. (2014)
54.0 162.4 SO201-2-12KL 2,145 BF Max et al. (2014)
53.7 165.0 VINO19-4 GGC17 3,960 BF Cook and Keigwin (2015)
52.7 144.7 SO178-13-6 713 BF Max et al. (2014)
52.2 −12.8 2307 686 DC Schroder-Ritzrau et al. (2003)
51.3 167.7 MD01-2416 2,317 BF Sarnthein et al. (2006, 2007)
51.2 167.8 ODP883 2,385 BF Sarnthein et al. (2006)
51.1 167.9 RNDB GGC5 2,804 BF Cook and Keigwin (2015)
51.1 169.0 RNDB PC11 3,225 BF Cook and Keigwin (2015); Keigwin and Lehman (2015)
51.1 168.1 RNDB GGC15 3,700 BF Cook and Keigwin (2015)
51.0 148.3 936 1,305 BF Gorbarenko et al. (2004)
50.4 −46.4 Orphan Knoll deep-sea corals 1,600 DC Cao et al. (2007)
50.4 167.7 VINO19-4 GGC37 3,300 BF Cook and Keigwin (2015)
50.1 153.2 V34-98 1,175 BF Gorbarenko et al. (2002)
49.7 168.3 RNDB PC13/PG13 2,329 BF Cook and Keigwin (2015); Keigwin and Lehman (2015)
49.6 150.2 Nesmeyanov25-1 GGC27 995 BF Keigwin (2002); Cook and Keigwin (2015)
49.4 152.9 LV29-114-3 1,765 BF Max et al. (2014)
49.1 150.3 B34-91 1,227 BF Keigwin (2002)
48.9 −126.9 JT96-09 920 BF McKay et al. (2005)
48.9 150.4 Nesmeyanov25-1 GGC20 1,510 BF Keigwin (2002); Cook and Keigwin (2015)
48.8 150.4 Nesmeyanov25-1 GGC18 1,700 BF Keigwin (2002); Cook and Keigwin (2015)
48.6 150.4 Nesmeyanov25-1 GGC15 1,980 BF Keigwin (2002); Cook and Keigwin (2015)
47.6 −7.3 2774 490 DC Schroder-Ritzrau et al. (2003)
47.0 −5.5 1471 and 2631 240 DC Schroder-Ritzrau et al. (2003)
44.5 145.0 MR0604 PC04A 1,215 BF Okazaki et al. (2014)
43.5 −54.9 OCE326 GGC26 3,975 BF; Bivalve This study
43.5 −54.8 KNR197-10 CDH42 3,870 BF Keigwin and Swift (2017)
43.4 −60.2 KNR197-10 CDH46 965 BF This study
43.1 −49.0 KNR197-10 GGC36 1,520 BF This study
43.1 −55.8 OCE326 GGC14 3,525 BF Robinson et al. (2005); this study
43.0 −55.3 HU73031-7 4,055 BF Robinson et al. (2005)
43.0 −59.9 HU72021-3 2,470 BF Robinson et al. (2005)
42.2 144.2 GH02-1030 1,212 BF Ikehara et al. (2006)
42.1 −125.8 W8709A-13PC 2,710 BF Mix et al. (1999); Lund et al. (2011)
42.0 −29.0 JFA deep-sea corals 1,684–1,829 DC Adkins et al. (1998)
41.7 142.6 CH84-14 978 BF Duplessy et al. (1989)
41.7 −124.9 ODP1019 980 BF Mix et al. (1999)
41.1 142.4 MR01-K03-PC4/5 1,366 BF Ahagon et al. (2003)
40.4 143.5 KR02-15-PC6 2,215 BF Minoshima et al. (2007)
40.0 −69.0 KNR198 CDH36 1,828 BF This study
39.2 −68.0 KNR198 GGC15 3,308 BF This study
34.0–40.0 −66.0 – −57.0 New England Seamount deep-sea corals 1,176–2,529 DC Adkins et al. (1998); Robinson et al. (2005); Eltgroth et al. (2006); Thiagarajan et al. (2014)
38.0 −31.1 MD08-3180 3,064 BF Sarnthein et al. (2015)
38.0 −25.6 Smithsonian deep-sea coral 1,069–1,235 DC Eltgroth et al. (2006)
37.8 −10.2 MD99-2334K 3,146 BF Skinner and Shackleton (2004); Skinner et al. (2010); Skinner et al. (2014)
37.8 −9.7 JC89-SHAK-14-4G 2,063 BF Freeman et al. (2016)
37.8 −9.5 JC89-SHAK-10-10K 1,127 BF Freeman et al. (2016)
37.7 −10.5 JC89-SHAK-03-6K 3,735 BF Freeman et al. (2016)
37.6 −10.7 JC89-SHAK-05-3K 4,670 BF Freeman et al. (2016)
37.6 −10.4 JC89-SHAK-06-4K 2,642 BF Freeman et al. (2016)
37.2 −123.2 F8-90-G21 1,605 BF van Geen et al. (1996)
37.1 −31.9 KNR197-10 GGC5 2,127 BF This study
36.4 −48.5 KNR197-10 GGC17 5,011 BF Keigwin and Swift (2017)
36.1 −72.3 KNR178 GGC2 3,927 BF Keigwin and Swift (2017)
36.1 141.8 MD01-2420 2,101 BF Okazaki et al. (2012)
36.0 −74.7 KNR178 JPC32 1,006 BF This study
35.6 −121.6 F2-92-P3 799 BF van Geen et al. (1996)
34.4 −30.5 660 795–830 DC Schroder-Ritzrau et al. (2003)
34.3 −120.0 ODP893A 576.5 BF; Bivalve; Spiral Shell Ingram and Kennett (1995); Sarnthein et al. (2007); Magana et al. (2010)
34.2 137.7 BO04-PC11 1,076 BF Ikehara et al. (2011)
34.0 −63.0 Muir Seamount deep-sea corals 2,026–2,441 DC Robinson et al. (2005); Eltgroth et al. (2006); Thiagarajan et al. (2014)
33.7 −57.6 HU89038-8PC 4,600 Bivalve Keigwin and Boyle (2008)
33.7 −57.6 OCE326 GGC5 4,600 Bivalve Keigwin and Boyle (2008)
33.7 −57.6 KNR31 GPC5 4,583 BF This study
33.2 −29.0 654 695 DC Schroder-Ritzrau et al. (2003)
32.9 −76.3 KNR140 GGC56 1,400 BF Robinson et al. (2005)
32.8 −76.3 KNR140 GGC51 1,790 BF Keigwin (2004); Robinson et al. (2005)
32.8 −76.2 KNR140 GGC50 1,903 BF Keigwin (2004); this study
32.8 −13.3 2657 1,284–1,350 DC Schroder-Ritzrau et al. (2003)
32.5 −76.3 KNR140 GGC66 2,155 BF Keigwin (2004)
32.4 −76.4 KNR140 JPC01 2,243 BF Keigwin (2004)
32.2 −76.3 KNR140 PG02 2,394 BF Keigwin (2004)
32.2 133.9 KT89-18-P4 2,700 BF Okazaki et al. (2010)
32.0 −76.1 KNR140 GGC43 2,590 BF Keigwin (2004)
31.7 −75.4 KNR140 JPC37 2,972 BF Keigwin and Schlegel (2002)
31.7 −75.4 KNR140 GGC39 2,975 BF Keigwin and Schlegel (2002)
30.7 −74.5 KNR140 GGC30 3,433 BF Robinson et al. (2005)
29.8 −12.7 2088 652–986 DC Schroder-Ritzrau et al. (2003)
29.7 −73.4 KNR140 GGC26 3,845 BF Keigwin (2004)
29.1 −72.9 KNR140 JPC12 4,250 BF Keigwin (2004); Robinson et al. (2005); this study
28.3 −74.4 KNR140 JPC22 4,712 BF Keigwin (2004)
27.9 −111.7 DSDP 480 655 BF Keigwin and Lehman (2015)
27.5 −112.1 AII125-8 GGC55/JPC56 818 BF Keigwin (2002)
23.6 −111.6 MV99-MC17/GC32/PC10 430 BF Lindsay et al. (2016)
23.5 −111.6 MV99-MC19/GC31/PC08 705 BF Marchitto et al. (2007)
23.2 −111.1 MV99-GC38 1,270 BF Lindsay et al. (2016)
20.1 117.4 GIK17940 1,727 BF Sarnthein et al. (2007); Sarnthein et al. (2015)
19.5 116.3 MD05-2904 2,066 BF Wan and Jian (2014)
18.9 115.8 50-37KL 2,695 BF Broecker, Peng, et al. (1990)
18.3 57.7 RC27-14 596 BF Bryan et al. (2010)
18.0 57.6 RC27-23 820 BF Bryan et al. (2010)
15.4 −51.1 Gramberg Seamount deep-sea corals 1,492–1,544 DC Chen et al. (2015)
14.9 −48.2 Vayda Seamount deep-sea corals 795–1,827 DC Chen et al. (2015)
11.9 −78.7 Vema 28-122 1,800 BF Broecker, Klas, et al. (1990)
10.7 −44.6 Vema Fracture Zone deep-sea corals 1,097–1,657 DC Chen et al. (2015)
9.2 −21.3 Carter Seamount deep-sea corals 973–2,100 DC Chen et al. (2015)
8.8 111.4 MD05-2896 1,657 BF Wan and Jian (2014)
7.2 112.1 V35-05 1,953 BF Andree et al. (1986); Broecker, Andree, et al. (1988); Broecker, Klas, et al. (1988)
7.2 112.2 V35-06 2,030 BF Andree et al. (1986)
6.0 126.0 MD98-2181 2,100 BF Broecker et al. (2004)
5.6 −26.9 Knipovich Seamount deep-sea corals 749–2,814 DC Chen et al. (2015)
4.9 −43.2 KNR110 50GGC 3,995 BF Broecker, Klas, et al. (1990)
4.6 −43.4 KNR110 66GGC 3,547 BF Broecker, Klas, et al. (1990)
4.3 −43.5 KNR110 82GGC 2,816 BF Broecker, Klas, et al. (1990)
4.0 −114.2 KNR73 6PG 3,806 BF Keigwin and Lehman (2015)
2.3 −30.6 GeoB 1503-1 2,306 DC Mangini et al. (1998)
1.8 −110.3 KNR73 4PC 3,681 BF Keigwin and Lehman (2015)
1.0 160.5 V28-238 3,120 BF Broecker, Klas, et al. (1988)
1.0 130.0 MD01-2386 2,800 BF Broecker et al. (2008)
0.0 −86.5 ME0005-24JC 2,941 BF Keigwin and Lehman (2015)
0.0 −86.5 ODP1240 2,921 BF de la Fuente et al. (2015)
−0.4 −106.2 KNR73 3PC 3,606 BF Keigwin and Lehman (2015)
−1.0 146.0 MD97-2138 1,900 BF Broecker et al. (2004)
−1.2 −89.7 VM21-30 617 BF Stott et al. (2009)
−1.3 −11.9 RC24-08 600 Deep-Dwelling PF Cléroux et al. (2011)
−1.6 162.6 S67 FFC15 4,250 BF Keigwin and Lehman (2015)
−2.0 −140.0 TTN013-18 4,400 BF Broecker and Clark (2010)
−3.3 −102.5 PLDS 7G 3,253 BF Keigwin and Lehman (2015)
−3.5 −35.4 MD09-3256Q 3,537 BF Freeman et al. (2016)
−3.6 −84.0 TR163-31 3,210 BF Shackleton et al. (1988)
−4.2 −37.1 GS07-150-17/1GC-A 1,000 BF Freeman et al. (2015)
−4.2 −36.4 MD09-3257 2,344 BF Freeman et al. (2016)
−4.5 −102.0 VNTR01-10GGC 3,410 BF Keigwin and Lehman (2015)
−10.3 −111.3 TT154-10 3,225 BF Broecker, Andree, et al. (1988); Broecker, Klas, et al. (1988)
−13.1 121.7 MD01-2378 1,783 BF Sarnthein et al. (2011)
−22.4 −40.0 ENG-111 621 DC Mangini et al. (2010)
−24.2 −43.3 21210009 781 DC Mangini et al. (2010)
−27.5 −46.3 KNR159-5-78GGC 1,829 BF Lund et al. (2015)
−27.5 −46.5 KNR159-5-36GGC 1,268 BF Sortor and Lund (2011)
−35.3 176.6 S794 2,406 BF Sikes et al. (2016)
−36.2 −73.7 SO161-SL22 1,000 BF De Pol-Holz et al. (2010)
−36.7 176.6 RR0503-TC83/JPC83 1,627 BF Sikes et al. (2016)
−37.0 176.6 RR0503-JPC79 1,165 BF Sikes et al. (2016)
−37.0 177.2 H213 2,065 BF Sikes et al. (2000)
−37.2 177.7 H209 1,675 BF Sikes et al. (2000)
−37.4 177.0 RR0503-JPC64 651 BF Rose et al. (2010)
−39.5 −176.4 S931 4,097 BF Sikes et al. (2016)
−39.9 −177.7 RR0503-JPC41 3,836 BF Sikes et al. (2016)
−39.9 −176.2 RR0503-JPC36 4,389 BF Sikes et al. (2016)
−40.4 178.0 MD97-2121 2,314 BF Skinner et al. (2015)
−41.1 7.8 TNO57-21 4,981 BF Barker et al. (2010)
−43.5 174.9 MD97-2120 1,210 BF Rose et al. (2010)
−44.1 −14.2 MD07-3076 3,770 BF Skinner et al. (2010); Gottschalk et al. (2016)
−44.8 174.5 PS75/104-1 835 BF Ronge et al. (2016)
−45.0 148.0 Tasmania deep-sea corals 1,428–1,947 DC Hines et al. (2015)
−45.1 174.6 SO213-84-1 972 BF Ronge et al. (2016)
−45.1 179.5 U938 2,700 BF Sikes et al. (2000)
−45.8 177.1 SO213-84-1 2,498 BF Ronge et al. (2016)
−45.8 176.6 SO213-82-1 2,066 BF Ronge et al. (2016)
−45.8 179.6 SO213-79-2 3,140 BF Ronge et al. (2016)
−46.0 −75.0 MD07-3088 1,536 BF Siani et al. (2013)
−46.2 −178.0 SO213-76-2 4,339 BF Ronge et al. (2016)
−54.2 −125.4 PS75/059-2 3,613 BF Ronge et al. (2016)
−54.5 −62.2 Burdwood Bank deep-sea corals1 318 DC Burke and Robinson (2012)
−55.0 −62.0 Burdwood Bank deep-sea corals2 816–1,516 DC Burke and Robinson (2012); Chen et al. (2015)
−59.4 −68.5 47396 1,125 DC Robinson and van de Flierdt (2009)
−59.7 −68.7 47396B 1,125 DC Goldstein et al. (2001)
−60.0 −69.0 Sars Seamount deep-sea corals 695–1,750 DC Burke and Robinson (2012); Chen et al. (2015)
−60 −58 Shackleton Fracture Zone deep-sea corals 806–823 DC Burke and Robinson (2012); Chen et al. (2015)
−61.0 −66.0 Interim seamount deep-sea corals 983–1,196 DC Burke and Robinson (2012); Chen et al. (2015)
Details are in the caption following the image
Locations of coring and dredging sites where samples have been collected to estimate deep water Δ14C according to our compilation (red dots). Yellow dashed lines delineate the lateral boundaries of the intermediate and deep boxes of the model (CYCLOPS). The interface between the Circumpolar Deep Water box and the intermediate and deep boxes in the Atlantic, Pacific, and Indian Oceans is sloping down northward, which is not rendered in the figure (only the southernmost latitude of the interface is shown).

In contrast to most other paleoceanographic indicators, the magnitude of a Δ14C estimate is a function of the sample calendar age, as this is used to correct for radioactive decay until the time of sample collection. In our compilation, the calendar ages of benthic foraminiferal samples used to reconstruct bottom water Δ14C are generally based on (i) 14C dates of co-occurring planktonic foraminifera in the core, (ii) estimates of surface water reservoir age, and (iii) the relationship between atmospheric 14C and calendar ages (14C calibration; e.g., Reimer et al., 2013). Samples associated with apparent age reversal or loose age constraints are excluded from our compilation (e.g., planktonic foraminiferal or ash age from an asynchronous deposition layer could introduce significant dating errors for cores with low sedimentation rates). For some other benthic foraminiferal samples, calendar ages have been determined from assumptions about phase relationships with other, relatively well-dated records (“wiggle matching”). The calendar ages of deep-dwelling corals, on the other hand, are typically established from 234U/230Th dates and the assumption of closed system. Calendar ages of the samples considered in this study come from the literature (Table 1), with one notable exception: for the samples whose calendar age is determined from radiocarbon dating, we recalibrate all radiocarbon ages to calendar ages with the most recent relationship of IntCal13 (Reimer et al., 2013), if this was not done in the original publications. For this calculation, we use the surface reservoir ages from the publications (Table 1). Note that about 71% of the compiled radiocarbon data fall within the time interval from 10 to 20 kyr B.P. (Figure 2), which is the interval of interest in this study. Note also that all data in our compilation have been recalculated to be consistent with the revised estimate of the 14C half-life (Audi et al., 2003).

Details are in the caption following the image
Distribution of the calendar ages of the published and new deep-sea 14C age data compiled in this study.

2.1.1 Estimation of Δ14C Values Within Ocean Volumes

We partition the compiled deep water Δ14C data into 10 different oceanic volumes corresponding to the 10 intermediate and deep boxes of the model used for this study (Figure 1 and section 2.2). The global sea level during the LGM is estimated to have been about 130 m lower than today (Clark et al., 2009; Lambeck et al., 2014), which implies that the depths of the glacial and deglacial samples should have been shallower than today by 130 m or less. However, the deglacial changes in global sea level have only a minor effect on the repartition of the samples among the intermediate and deep ocean boxes (Figure S1). As a result, the modern depths of the samples are used. Data from the Arctic Ocean and the Nordic Seas are not included in our study, for these regions are not covered by the 10 subsurface boxes of the model (section 2.2).

To increase the robustness of Δ14C estimates for the model boxes, estimates of deep water Δ14C in each box are averaged in temporal bins. The bins are adjacent, have uniform duration (see below), and span together the interval from 10 to 20 kyr B.P. In order to prevent single-core Δ14C values from dominating our results, bins containing deep water Δ14C estimates originating from only one record are excluded from our analysis.

The width (duration) of the bins is selected on the basis of the uncertainties in the calendar ages of the compiled data (Figure 3). The median error (two standard deviations) of the calendar ages between 10 and 20 kyr B.P. amounts to ~ 300 years. This value is probably a lower estimate due to some factors that were not considered in the original publications, such as sedimentation rate changes between chronological tie points (interpolation errors), reservoir age changes, and open-system behavior for deep-dwelling corals. Nevertheless, based on this value, a bin width of 600 years is chosen for the calculation of deep water Δ14C values, unless stipulated otherwise. For the bin duration of 600 years, the Δ14C estimates are averaged in the bins [20.1–19.5] kyr B.P., [19.5–18.9] kyr B.P., …, [10.5–9.9] kyr B.P. The bin Δ14C values are defined at the center of the bins and occur at the same times for all boxes, for example, the Δ14C values for the bin [15.3–14.7] kyr B.P. are all defined at 15.0 kyr B.P. The effect of bin width is discussed in section 4.1.

Details are in the caption following the image
Published errors (two standard deviations) in the calendar ages of the deep-sea 14C age data compiled in this study. The median error for the time interval between 10 and 20 kyr B.P. amounts to ~ 300 years.

2.1.2 Estimation of Time-Average Binned Δ14C Errors

The bin Δ14C values have various sources of uncertainty arising from (i) errors in the original Δ14C data (e.g., instrumental and chronological errors), (ii) the assumption that site-specific data reflect basin-scale averages, and (iii) temporal variability of deep water Δ14C within a bin.

In our analysis, the error in a bin Δ14C value is set equal to urn:x-wiley:25724517:media:palo20476:palo20476-math-0001, where σa is the standard error of the mean of deep water Δ14C data falling in that bin and σb is the mean of the Δ14C errors in that bin calculated from published analytical and calendar age uncertainties (for samples whose calendar age uncertainty is not reported, a value of 300 years is used based on the bin width). This approach has the benefit of accounting for not only the error from the data themselves but also for the spatial (e.g., intercore) variability and temporal (e.g., intracore) variability. The temporal mean of the bin Δ14C errors estimated using our method varies from 29‰ to 53‰, depending on the box.

2.2 Box Model

The model used in this study is a 16-box model of the world oceans (excluding the Arctic Ocean), called CYCLOPS. This model was initially developed by Keir (1988), has been the subject of different extensions (e.g., Hain et al., 2010; Sigman et al., 1998), and has been applied in a variety of paleoceanographic studies (for recent works see, e.g., Galbraith et al., 2015; Hain et al., 2011, 2014b). It includes 6 surface boxes, and 10 intermediate and deep boxes (Figure 4). The lateral boundaries of the surface boxes coincide with latitude and longitude lines, except in the North Atlantic (Keir, 1988). Lateral boundaries of subsurface boxes are not everywhere the same as those of surface boxes (Figure 1): whereas the zonal boundaries of Southern Hemisphere surface boxes are latitude lines, the interfaces between the Circumpolar Deep Water box and the intermediate and deep boxes in the Atlantic, Indian, and Pacific Oceans are sloping in the meridional direction in order to reflect the southward uplift of density surfaces in the Southern Ocean (Keir, 1988).

Details are in the caption following the image
Schematic diagram of the box model CYCLOPS (after Keir, 1988; Sigman et al., 1998). The numbers in black indicate the volume fluxes between the boxes in units of Sv (1 Sv = 106 m3 s−1).

The volume transports in the box model (Figure 4) were estimated from measurements of a variety of tracers in the modern ocean, including dissolved phosphorous, dissolved oxygen, dissolved inorganic carbon (DIC), alkalinity, and the 13C/12C ratio and Δ14C of DIC (Keir, 1988). They depict conventional features of the modern circulation, such as the formation of deep waters in the northern North Atlantic (at a rate of 9.5 sverdrup (Sv), where 1 Sv = 106 m3 s−1), the upwelling in the Southern Ocean (21.5 Sv), and the transports of waters to the rest of the ocean (Figure 4). The model analogue of the Atlantic meridional overturning circulation amounts to 21.5 Sv, broadly consistent with more recent observational estimates (e.g., Lumpkin & Speer, 2003, 2007; Lumpkin et al., 2008; Rayner et al., 2011).

2.2.1 Definition of Radiocarbon Concentration

The radiocarbon concentrations in the model are defined as follows. Consider the conventional definition of Δ14C,
Here Fm is the “fraction modern” reported from the instrument, that is, the 14C/12C ratio (normalized to δ13C of −25‰) of the sample divided by that of a standard (McNichol et al., 2001), “cal age” is the calendar age of the sample, and the mean life of 8,223 years is based on the 5,700 year half-life (Audi et al., 2003). From 1, we define the radiocarbon concentrations in the model as

Thus, C (dimensionless) represents the 14C/12C ratio of the sample when the carbonate was formed, normalized to that of the standard. For example, a Δ14C value of −200‰, such as observed in the modern deep Pacific (e.g., Broecker & Peng, 1982), would correspond to a radiocarbon concentration C = 0.8, whereas a Δ14C value of −1,000‰ (equivalent to infinite calendar age) would correspond to C = 0.

Notice that radiocarbon concentration, instead of 14C age, is used in our analysis, because 14C concentration as represented by Δ14C is a straightforward variable to implement in a tracer transport model, in contrast to age-related concepts. On the other hand, time series of Δ14C do not place changes in deep ocean 14C content in the context of atmospheric changes. For this reason, in this paper, the variations in deep water Δ14C are illustrated jointly with those of atmospheric Δ14C as reconstructed by IntCal13.

2.2.2 Governing Equation for Radiocarbon

The radiocarbon concentration in each deep and intermediate box of the model evolves according to the governing equation:

Here Ci is the radiocarbon concentration in box i, Vi is the volume of box i, Jji is the volume transport from box j to box i, and λ = (1/8,223) year−1 is the 14C radioactive decay constant. Thus, Ci is the concentration in an intermediate or deep box, and Cj is the concentration in an intermediate, deep, or surface box. Although Ci is a concentration ratio, its governing equation can be cast in the form of a governing equation for a concentration with at least first-order accuracy (Fiadeiro, 1982). On the right-hand side of 3, the first term represents the supply of 14C due to water transport from the surrounding boxes, the second describes the removal of 14C from water export to the surrounding boxes, and the last is the rate of disappearance of 14C due to radioactive decay within the box. Since our study aims to evaluate the (in)consistency of the paleodata with modern ventilation rates, the volume transports (Jij) are fixed to their modern values (Figure 4). Other effects such as due to organic matter remineralization and carbonate dissolution (negligible at least to first order; Fiadeiro, 1982), hydrothermal processes, and water-sediment fluxes are neglected. The omission of the effect of organic C remineralization (the major biological carbon flux from the surface to deep ocean (Hain et al., 2014a)) is further motivated by a previous study showing that changes in this effect have a minor influence on the oceanic Δ14C distributions simulated in experiments of ocean circulation change with a zonally averaged circulation-biogeochemistry model (maximum difference ranging from −9‰ to 7‰, depending on the oceanic basin and the experiment; Marchal et al., 1999). Details about the model used in this study are reported in Text S1.

2.3 Inverse Method

2.3.1 Statement of the Problem

The box model described in section 2.2 is fit to the deep water Δ14C data summarized in section 2.1 (for details see Text S1). Briefly, we use an inverse method that relies on a whole-domain approach (e.g., Amrhein et al., 2015; Wunsch, 2006). In this approach, the finite difference forms of the radiocarbon governing equation 3 for the different subsurface boxes and different time steps, with the unsteady term dCi/dt retained, are combined so as to reduce the fitting problem to the solution of a set of linear algebraic equations (equation 4 below). The model fit to the data is achieved by adjusting the Δ14C values in the surface boxes of the model. These values are obtained by solving a system of linear algebraic equations,

Here urn:x-wiley:25724517:media:palo20476:palo20476-math-0006 is a vector of the deep water 14C concentration data binned in space and time and expressed as anomalies from the initial time step (Text S1), urn:x-wiley:25724517:media:palo20476:palo20476-math-0007 is a matrix that represents the effect of ocean circulation, urn:x-wiley:25724517:media:palo20476:palo20476-math-0008 is a vector including the surface water 14C concentrations, and urn:x-wiley:25724517:media:palo20476:palo20476-math-0009 is a vector including the errors of the data in urn:x-wiley:25724517:media:palo20476:palo20476-math-0010. The system 4 includes one equation for each subsurface box and for each bin for which a deep water Δ14C estimate is available. It provides a formal statement of the inverse problem: the inference of surface water 14C concentrations ( urn:x-wiley:25724517:media:palo20476:palo20476-math-0011) from deep water 14C concentration data ( urn:x-wiley:25724517:media:palo20476:palo20476-math-0012) under modern circulation conditions ( urn:x-wiley:25724517:media:palo20476:palo20476-math-0013) and in the presence of observational errors ( urn:x-wiley:25724517:media:palo20476:palo20476-math-0014). In other words, time series of surface water 14C concentrations are inferred from a fit of the box model of modern ocean ventilation to the deep water Δ14C data records, given the presence of errors in the data.

2.3.2 Method of Solution

Time series of 14C concentration in each surface box are inferred using a three-step approach. First, each equation in 4 is divided by the error in the corresponding bin Δ14C in order to give more weight to the bin Δ14C values with smaller uncertainties (row scaling; Wunsch, 2006). Each quantity in 4 affected by row scaling is referred below to with an asterisk; for example, the scaled vector urn:x-wiley:25724517:media:palo20476:palo20476-math-0015 is referred to as urn:x-wiley:25724517:media:palo20476:palo20476-math-0016. Second, a first guess of the solution, urn:x-wiley:25724517:media:palo20476:palo20476-math-0017, is obtained from (i) the atmospheric Δ14C reconstruction (Reimer et al., 2013), (ii) observational estimates of modern (preindustrial) reservoir ages for the six surface boxes (Bard, 1988), and (iii) the effect of atmospheric pCO2 on sea surface reservoir age (Galbraith et al., 2015). Specifically, modern reservoir age is set equal to 1,000 years for the Antarctic box and 400 years for the other surface boxes, which values are consistent with observational estimates reported by Bard (1988), and the reservoir age is set to increase with decreasing atmospheric pCO2 (Galbraith et al., 2015), yielding an offset of ~ 250 years from today at the LGM. Finally, the solution urn:x-wiley:25724517:media:palo20476:palo20476-math-0018 is expressed as the sum of the first guess and a deviation, that is, urn:x-wiley:25724517:media:palo20476:palo20476-math-0019. The deviation urn:x-wiley:25724517:media:palo20476:palo20476-math-0020 is obtained from the solution of a new set of equations (for a similar approach, see Gebbie, 2012),
where urn:x-wiley:25724517:media:palo20476:palo20476-math-0022. Thus, we are solving for deviations of 14C concentration in each surface box from a hypothetical value based on atmospheric Δ14C and pCO2 changes and modern (preindustrial) reservoir ages.
The system 5 is solved for urn:x-wiley:25724517:media:palo20476:palo20476-math-0023 using singular value decomposition, SVD (e.g., Wunsch, 2006). To this end, the coefficient matrix urn:x-wiley:25724517:media:palo20476:palo20476-math-0024 is decomposed as
where U (V) is an orthonormal matrix containing the left (right) singular vectors of urn:x-wiley:25724517:media:palo20476:palo20476-math-0026 and Λ is a nonsquare diagonal matrix with the singular values of urn:x-wiley:25724517:media:palo20476:palo20476-math-0027 ranked in order of decreasing magnitude along the diagonal. The SVD solution of 5 is
where ui and vi are singular vectors (the ith column of U and V, respectively), λi is a singular value (the ith element along the diagonal of Λ), K is the number of singular values different from zero, and αi is an unknown expansion coefficient. On the right-hand side of 7, the first term represents the contribution due to structures in urn:x-wiley:25724517:media:palo20476:palo20476-math-0029 that can be determined from the data (the range of urn:x-wiley:25724517:media:palo20476:palo20476-math-0030) and the second term represents the contribution due to structures that cannot be determined from the data (the null-space of urn:x-wiley:25724517:media:palo20476:palo20476-math-0031). It can be shown that the SVD solution 7 is a weighted least squares solution when this exists, that is, in the absence of a null-space for which K = N (e.g., Wunsch, 2006). The “particular SVD solution” includes only the first term and is biased for K < N.
The error covariance matrix, or uncertainty, of the SVD solution urn:x-wiley:25724517:media:palo20476:palo20476-math-0032 is
where urn:x-wiley:25724517:media:palo20476:palo20476-math-0034 is the error covariance matrix for the observational estimates of 14C concentration in urn:x-wiley:25724517:media:palo20476:palo20476-math-0035 and 〈·〉 denotes the expected value. The diagonal elements of urn:x-wiley:25724517:media:palo20476:palo20476-math-0036 are equal to 1 (since equation 4 has been scaled) and the off-diagonal elements of urn:x-wiley:25724517:media:palo20476:palo20476-math-0037 are set equal to zero, assuming negligible error covariances; that is, urn:x-wiley:25724517:media:palo20476:palo20476-math-0038 is an identity matrix. The first term on the right-hand side of 8 represents the contribution due to the observational errors, whereas the second is the contribution due to presence of a null-space in the solution (if any). Since the expansion coefficients αi (i = K + 1, …, N) are unknown, the second term in 8 is sometimes set to zero. In this case, the uncertainties in the elements of the solution ( urn:x-wiley:25724517:media:palo20476:palo20476-math-0039) should be viewed as lower estimates.

3 Results

In this section, we first describe our compilation of deep ocean Δ14C data for the past 40 kyr. The box model of modern ocean ventilation is then fit to the deep ocean Δ14C data (bin values) by allowing Δ14C to vary in the model surface boxes.

3.1 Synthesis of Deep Water Δ14C Data

The compiled Δ14C data attributed to different intermediate and deep oceanic volumes are shown in Figure 5. As expected, the oceanic Δ14C values are lower than the reconstructed Δ14C in the contemporaneous atmosphere, with a few exceptions presumably due to chronological errors.

Details are in the caption following the image
Compiled deep water Δ14C data for the 10 intermediate and deep boxes of the model (cyan circles). Magenta circles show data potentially influenced by hydrothermal processes (Ronge et al., 2016; Stott et al., 2009). The atmospheric Δ14C reconstruction is shown in red for reference (Reimer et al., 2013). Vertical dotted lines delineate the time interval 10–20 kyr B.P. The order in which the different panels appear is arbitrary, although it is intended to broadly correspond to the sense of the estimated movement of deep waters from the northern North Atlantic (leftmost top panel) to the deep North Pacific in the modern ocean (rightmost bottom panel).

Particularly large variations in deep water Δ14C are observed in the Intermediate South Pacific, the Deep South Pacific, and the Circumpolar Deep Water boxes (magenta circles in Figure 5). The Δ14C record from 617 m water depth near the Galapagos Archipelago (Stott et al., 2009) shows very low values compared to other Δ14C records for the Intermediate South Pacific. These very low values have been suggested to reflect a supply of old carbon from hydrothermal activity (e.g., Lund & Asimow, 2011; Stott & Timmermann, 2011). Likewise, two records close to plate boundaries in the South Pacific (in the Deep South Pacific and Circumpolar Deep Water boxes of the model) display very low Δ14C values during the LGM and early deglaciation which have been suggested to reflect hydrothermal processes (Ronge et al., 2016). In this section, we exclude the three foregoing records since the model does not include the effect of hydrothermalism; the influence of these records on the model fit to the data is documented in section 4.2.

The most conspicuous feature in the assembled deep water Δ14C data (Figure 5) is a long-term decrease from about 25 kyr B.P. to the present, similar to the decrease in reconstructed atmospheric Δ14C over the same time interval (Reimer et al., 2013). In order to quantify the apparent decrease in the assembled data set, we use the rank correlation coefficient Kendall tau (Kendall & Gibbons, 1990). Kendall tau measures the amount of monotonic relationship between two random variables (in the present case, deep water Δ14C and time), making weaker assumptions about their underlying distributions than more conventional measures of correlation, such as the Pearson correlation coefficient. We find that Kendall tau is negative with p < 0.05 in all oceanic basins (Table 2), indicating that the apparent decrease in deep water Δ14C is significant and ubiquitous in our compilation.

Table 2. Kendall Tau Coefficient and Its p Value for the Relationship Between Deep Ocean Δ14C and Calendar Age (25–0 kyr B.P.)
Box NCW Int Atl Deep Atl CDW Int Ind Deep Ind Int S Pac Deep S Pac Int N Pac Deep N Pac
Kendall tau −0.63 −0.61 −0.45 −0.48 −0.65 −0.68 −0.49 −0.32 −0.59 −0.65
p value <0.01 <0.01 <0.01 <0.01 <0.01 0.04 <0.01 <0.01 <0.01 <0.01
  • Note. A negative value indicates a decrease of deep ocean Δ14C with time.

The mean of deep water Δ14C in the different oceanic regions and in different climatic intervals is calculated to reveal possible spatiotemporal patterns of deep ocean Δ14C over the deglaciation (Table 3). The climatic intervals include the LGM (defined here as 24–17.6 kyr B.P.), the HS1 (17.6–14.65 kyr B.P.), the Bølling-Allerød (BA, 14.65–12.85 kyr B.P.), the YD (12.85–11.65 kyr B.P.), the early Holocene (EH, 11.65–8 kyr B.P.), and the late Holocene (LH, 4–0 kyr B.P.). Importantly, the LH values agree within two standard errors with basin-scale averages in the modern ocean based on water column Δ14C measurements corrected for bomb-14C (data synthesis of Key et al., 2004; Table 3 and Figure 6). The agreement supports our working assumption that averages of Δ14C of fossil carbonates from a few sites can constrain Δ14C of large oceanic volumes. The Δ14C decrease from the LGM to the EH would have ranged from 110‰ to 330‰, depending on the oceanic region (Table 3). Interestingly, some spatial patterns seem to have been maintained over time. For example, the Δ14C of the deep Atlantic appears to have remained higher than that of the deep North Pacific by 100 ± 18‰ to 145 ± 19‰, depending on the climatic interval. For reference, the prebomb Δ14C averages in these two regions differ by 106‰ according to the data synthesis of Key et al. (2004) (Table 3).

Table 3. Mean ± One Standard Error of the Mean of Δ14C Data for Different Climatic Intervalsa and Different Subsurface Boxes
Box NCW Int Atl Deep Atl CDW Int Ind Deep Ind Int S Pac Deep S Pac Int N Pac Deep N Pac
LGM 178 ± 14 (10) 287 ± 17 (23) 198 ± 15 (61) 81 ± 26 (22) 206 ± 25 (10) 187 ± 13 (4) 211 ± 20 (16) 102 ± 20 (27) 167 ± 16 (34) 93 ± 13 (59)
HS1 159 ± 43 (3) 162 ± 11 (38) 115 ± 15 (75) 85 ± 16 (27) 1 ± 25 (8) 75 ± 46 (2) 179 ± 14 (23) 68 ± 25 (20) 91 ± 14 (53) 14 ± 10 (45)
BA 119 ± 9 (14) 75 ± 19 (24) 93 ± 15 (30) 42 ± 10 (19) 8 ± 20 (9) NA (1) 83 ± 20 (3) 51 ± 21 (33) 0 ± 9 (51) −52 ± 12 (47)
YD 86 ± 14 (5) 71 ± 21 (23) 59 ± 13 (35) 53 ± 14 (8) −50 ± 20 (4) NA (0) 50 ± 26 (4) 70 ± 49 (3) −43 ± 14 (26) −67 ± 7 (14)
EH 22 ± 16 (6) 26 ± 17 (32) 10 ± 16 (16) −27 ± 17 (20) −124 ± 22 (13) NA (0) −38 ± 48 (2) −105 ± 23 (7) −50 ± 9 (47) −109 ± 9 (47)
LH NA (1) −92 ± 9 (11) −114 ± 14 (8) −168 ± 19 (7) NA (0) NA (0) NA (0) −224 ± 20 (2) −156 ± 13 (21) −214 ± 13 (9)
MODERNb −74 −87 −112 −151 −111 −183 −107 −188 −142 −218
  • Note. The number of data in each interval is between parentheses.
  • a The dates for the onset of the BA, the onset of the YD, and the termination of the YD are from Rasmussen et al. (2006) (their Table 4). The date for the onset of HS1 is based on an interpretation by de la Fuente et al. (2015) of Greenland ice core [Ca2+] records compiled in Rasmussen et al. (2008).
  • b Mean of water column Δ14C data corrected for bomb 14C (GLODAP; Key et al., 2004).
Details are in the caption following the image
Comparison between late Holocene (LH, 0–4 kyr B.P.) Δ14C derived from seafloor carbonates (vertical axis, mean ± one standard error) and water column Δ14C corrected for bomb 14C derived from GLODAP (horizontal axis; Key et al., 2004). The values displayed are basin-mean averages of Table 3 (from left to right in the figure): Deep N Pac, Deep S Pac, CDW, Int N Pac, Int Ind, and Int Atl. The dashed line is the line of perfect agreement. Notice that the second point (off the diagonal line by more than one standard error) corresponds to the Deep South Pacific, where only two LH data are available (Table 3).

In order to present the evolution of deep water radiocarbon in the context of atmospheric Δ14C changes, we show the averaged ventilation ages of different records for each box (Figure 7). Here ventilation age is simply defined as the 14C age difference between seawater and the contemporaneous atmosphere. A number of features emerge. The mean 14C ventilation age for the LGM is often the largest, but the differences with subsequent intervals are not always significant. It is tempting to identify different trends in ventilation age between different basins, although it should be stressed that many of the changes from one time interval to the next are not significant even at the level of one standard error. Nonetheless, some of the changes do seem significant (at the level of two standard errors), such as the reduction in ventilation age from the LGM to the Holocene in the northern North Atlantic (NCW), the Deep Atlantic, the Southern Ocean (CDW), and the Deep North Pacific.

Details are in the caption following the image
Mean ± one standard error of mean radiocarbon ventilation ages for different oceanic volumes and different climatic intervals: LGM (red), HS1 (yellow), BA (green), YD (cyan), EH (blue), and LH (black) (see text).

3.2 (In)Consistency With Modern Ocean Ventilation

In this section, we test whether the deep water Δ14C data (bin Δ14C values) for the time interval from 20 to 10 kyr B.P. can be explained in terms of modern ocean ventilation. First, we examine the extent to which the modern ocean ventilation model can be fitted to the deep water Δ14C data; the surface Δ14C values that lead to the fit are considered next.

3.2.1 Evolution of Deep Water Δ14C

The deep water Δ14C values obtained from the model fit to the data are computed by propagating inferred surface Δ14C values through the box model, as
where urn:x-wiley:25724517:media:palo20476:palo20476-math-0041.

The model fit to the data depends on the number K of singular vectors that are retained to construct the solution of the inverse problem (equations 7 and 8). Among the 96 singular values of the coefficient matrix urn:x-wiley:25724517:media:palo20476:palo20476-math-0043, six are numerically vanishing (Figure S2a), suggesting the presence of a solution null-space (section 2.3.2). A solution obtained from all the singular vectors associated with a nonvanishing λi (K = 90) produces deep water Δ14C values that overfit the data (Figure 8a); that is, the solution with K = 90 includes structures that are not justifiable given the data errors (Text S1).

Details are in the caption following the image
Distribution of the difference between fitted and observed (bin) deep water Δ14C values, normalized to the error in the observed deep water Δ14C, for two different solutions: (a) K = 90 and (b) K = 20. In each panel, the red curve is the normal (Gaussian) distribution shown for reference.

We therefore consider a model fit obtained with a smaller number of singular vectors (K = 20). In this case, we find that the overfit to the deep water Δ14C data is largely mitigated (Figure 8b). Despite the reduced number of structures allowed in the solution, a good fit to the deep water Δ14C data is still achieved (Figure 9). In particular, the deep Δ14C values derived from the fit capture the generally negative trend with time that is suggested both in the original data and in the bin records. Some of these values, mainly in the Intermediate Indian where records come from only one location (Bryan et al., 2010), tend to present systematic differences with the data. However, the model fit to the data overall appears satisfactory, particularly in the light of the data errors (Figure 8b): we find that 87% of the data are fit by the model within two standard deviations (Table 4), a fraction which increases to 91% when residuals from Intermediate Indian are excluded from the calculation.

Details are in the caption following the image
Deep water Δ14C data (cyan circles), deep water bin Δ14C ± one standard deviation (dark blue lines), and deep water Δ14C resulting from the model fit for K = 20 (magenta squares). The atmospheric Δ14C reconstruction (Reimer et al., 2013) is shown for reference (red line). The acronyms at the bottom of each panel refer to different climatic intervals (see text).
Table 4. Fraction of Deep Water Δ14C Data Which Are Not Explained by Modern Ventilation
Main solution (section 3) Bin width 400 year (section 4.1) Low-Δ14C records included (section 4.2) Two horizontal deep Atlantic boxes (section 4.3) Two vertical deep Atlantic boxes (section 4.4)
13% 9% 11% 13% 12%
  • Note. Fraction of data that are not fit to within two standard deviations in the data errors.

Differences between the deep water Δ14C values derived from the fit and the deep water Δ14C data are worth discussing in more detail (Figure 9). As already mentioned, some of the derived values in the Intermediate Indian tend to systematically deviate from the data, although it should be emphasized that these data originate from a single location. Perhaps more relevant, deep water Δ14C values derived from the fit are systematically lower than the observed values in the Intermediate Atlantic, particularly during HS1. A similar offset is suggested in the Intermediate South Pacific during HS1. These results illustrate that the model fit to the whole data set is achieved to the detriment of large and sometimes significant differences with individual data at some locations and during some time intervals. Thus, whereas most of the deep water Δ14C data can be explained by modern ventilation rates as described in the model, it is also clear that these rates cannot account for all the data. Although consideration of a larger number of structures in the solution (K > 20) would reduce the misfits to individual data, such solutions would also tend to overfit the data and thus disregard the data uncertainties, as shown in Text S1.

3.2.2 Evolution of Surface Water Δ14C

We find that the surface Δ14C values inferred from the fit with K = 20 are all within the bounds set by the atmospheric and deep ocean observations, in spite of the relatively small error variance of the solution (Figure 10). Notable in the K = 20 solution are relatively large deviations of surface water Δ14C estimated in the boreal Atlantic Ocean and near Antarctica. It thus appears that most of the deep water Δ14C data could be explained by modern basin-scale circulation, provided that changes in surface water Δ14C took place at high latitudes. These changes correspond to changes in surface water reservoir age, as indicated by the variable difference between the surface water Δ14C implied by the fit and the atmospheric Δ14C reconstructed by IntCal13 (Figure 10). The corresponding reservoir ages increase or decrease with time, depending on the time interval and the surface region (boreal or Antarctic box). However, taking uncertainties into account, most of the surface reservoir age changes are not significant: in the boreal and Antarctic boxes, only 4 over 32 of the surface water Δ14C values implied by the fit differ from the values expected from the atmospheric Δ14C and pCO2 records (first guess) by more than two standard deviations (see green stars in Figure 10).

Details are in the caption following the image
Surface water Δ14C estimated for K = 20 (green, with error bar showing ± one standard deviation). The red line is the reconstructed atmospheric Δ14C (Reimer et al., 2013) and the blue dots are bin Δ14C values in all the subsurface boxes. Magenta line is the surface water Δ14C calculated from atmospheric Δ14C (Reimer et al., 2013) and estimates of preindustrial reservoir ages (Bard, 1988), with the influence of atmospheric pCO2 considered (Galbraith et al., 2015). It is the first guess of the solution as defined in section 2.3.2. The values that differ from this first guess by more than two standard deviations are noted with green stars.
The large (relative to other regions) variations in surface water Δ14C estimated in the boreal Atlantic and near Antarctica arise from the fact that the deep ocean is mostly ventilated from these regions. Changes in these two regions can be relatively well resolved from deep water data. To demonstrate this, consider the relationship between the actual and estimated time series of surface water Δ14C values,
where Tv is the solution resolution matrix defined by (e.g., Wunsch, 2006)

Equation 10 shows that each element of the solution, urn:x-wiley:25724517:media:palo20476:palo20476-math-0046, can be regarded as a linear combination of the actual values in urn:x-wiley:25724517:media:palo20476:palo20476-math-0047. Departures of urn:x-wiley:25724517:media:palo20476:palo20476-math-0048 from urn:x-wiley:25724517:media:palo20476:palo20476-math-0049 can thus be investigated from the matrix Tv. One approach for such investigation is to repeatedly calculate urn:x-wiley:25724517:media:palo20476:palo20476-math-0050 from 10 for a number of vectors urn:x-wiley:25724517:media:palo20476:palo20476-math-0051, where each vector has the elements corresponding to a given surface box set to 1 for all times while the elements corresponding to other surface boxes are set to 0 (Amrhein et al., 2015). The elements of urn:x-wiley:25724517:media:palo20476:palo20476-math-0052 calculated in this way provide a measure of the ability of the deep water Δ14C data to resolve Δ14C in the different surface boxes of the model, with a value near 0 indicating poor resolvability and a value near 1 indicating high resolvability.

We find that for K = 20, the elements of urn:x-wiley:25724517:media:palo20476:palo20476-math-0053 averaged over the time interval from 20 to 10 kyr B.P. indicate the highest resolvability in the boreal Atlantic and Antarctic boxes (Table 5), which both directly ventilate the deep ocean in the model (Figure 4). The resolvability for the other boxes is close to zero, suggesting that the estimated surface Δ14C values in those boxes should be interpreted with particular caution. Amrhein et al. (2015) obtained a similar result in an analysis of deglacial benthic δ18O records using a much more detailed tracer transport model.

Table 5. Resolvability of Δ14C in the Surface Boxes for the K = 20 Solution
Boreal Atlantic Antarctic Indian South Pacific North Pacific
0.50 0.02 0.89 0.01 0.01 0.02

4 Sensitivity to Data and Model Assumptions

In section 3.2, we have fitted a model of modern ocean ventilation to a compilation of deep water Δ14C data for the time interval 10–20 kyr B.P. We have found that the residuals of the fit can generally be explained by data errors and that most of the surface water Δ14C values which produce the fit are oceanographically consistent, in the sense that these values are in general neither significantly larger than atmospheric Δ14C nor significantly lower than deep sea Δ14C. In this section, we assess the robustness of these results against several assumptions in the analysis. In all cases, model fits to the data obtained with K = 20 are considered for a consistent comparison with the solution presented in section 3.2.

4.1 Effect of Bin Width

Bin width influences how the deep-sea radiocarbon data are grouped in time within each of the intermediate and deep boxes of the model. It thereby determines the magnitude, uncertainty, and timing of the observational estimates of deep water Δ14C. With a median error of 300 years for the sample calendar ages (Figure 3), a bin width larger than 600 years (the value assumed in section 3.2) does not seem to be generally justified. Here we consider the case where the data are grouped in narrower bins of 400 years.

As expected, the fraction of bins for which deep water Δ14C data are available decreases in this case: for a bin width of 400 years, about 38% of the bins are empty, compared to 28% for a bin width of 600 years. Consequently, the number of singular values of urn:x-wiley:25724517:media:palo20476:palo20476-math-0054 that are numerically vanishing is larger for a bin width of 400 years (Figure S2b) than for a bin width of 600 years (Figure S2a). Besides, the bin Δ14C values tend to portray more variability for a bin width of 400 years (Figure S3) than for a bin width of 600 years (Figure 9). This result stems from the fact that for a bin width of 400 years, bin Δ14C values are derived from a reduced number of data.

We find that the inversion produces similar results to those presented in section 3 (Table 4). The model fit to the deep water Δ14C data is generally good (Figure S3), with 91% of the data fit within two standard deviations. This fraction is larger than for the case with a bin width of 600 years (87%), because bin errors generally increase with a smaller number of data falling in each bin (larger σa). No values of surface water Δ14C significantly transgress the bounds set by atmospheric and deep-sea Δ14C (Figure S4).

4.2 Effect of Records With Very Low Δ14C

In this section, we repeat our analysis by adding the three records with particularly low Δ14C values (Ronge et al., 2016; Stott et al., 2009). The major changes are the appearance of higher-frequency variability in the bin Δ14C and the presence of larger bin Δ14C errors in the Intermediate South Pacific, the Deep South Pacific, and the Circumpolar Deep Water boxes (Figure S5). The inverse solution is very similar to that obtained when the three low-Δ14C records are excluded (Figures S2c, S5, and S6 and Table 4). Thus, data from regions where these records originate appear to have a relatively small influence on the solution.

The relative influence on the solution of data from different regions can be illustrated from the data resolution matrix, which is defined as (e.g., Wunsch, 2006)
where UK is a matrix containing the first K left singular vectors of urn:x-wiley:25724517:media:palo20476:palo20476-math-0056. The diagonal elements of the matrix Tu reflect the relative importance of different Δ14C data (bin values) in determining the surface water Δ14C. These elements are plotted in Figure 11. It is seen that data from the high-latitude North Atlantic boxes are generally more important than those from other regions in determining the solution. The importance of data from the Intermediate South Pacific and Deep South Pacific is relatively small, consistent with the modest effect on the solution of the data originating from these regions.
Details are in the caption following the image
Data importance of the subsurface boxes for the case where low-Δ14C records are included in the analysis. Each circle corresponds to a bin.

4.3 Effect of Model Architecture: Northern and Southern Deep Atlantic Boxes

Box models such as the one used in this study represent the world oceans with a small number of regions with very large volumes (Figure 1). As a result, and despite the apparent ability of Δ14C data from a few sites to constrain the volume-averaged Δ14C (section 3.1), the adequacy of box models to analyze data from a few locations can legitimately be questioned. For instance, most of the data for the Atlantic Ocean are from the northern hemisphere (Figure 1). In this section, we consider a slightly more detailed model, where the deep Atlantic box in the original model is split into two boxes: a northern box and a southern box.

Volume transports in the modified model are derived from those in the original model (Figure 4). Thus, in the modified model, the northern box receives a flux of 21.5 Sv from Northern Component Water, exchanges 3.5/2 = 1.75 Sv with the Intermediate Atlantic, and loses 21.5 Sv of water to the southern box. The southern box receives a flux of 21.5 Sv from the northern box, exchanges 1.75 Sv with the Intermediate Atlantic, and loses 21.5 Sv to, and exchanges 8 Sv with, Circumpolar Deep Water. The other volume transports of the modified model are the same as in the original model. With this circulation scheme, volume is conserved in all boxes, as in the original model.

The modified model of modern ocean ventilation is fit to the deep water Δ14C data using the same assumptions as for the original model (section 3.2). The fit to the deep water data is generally good (Figure S7 and Table 4), and all of the surface Δ14C values are within two standard deviations of the bounds provided by the atmosphere and deep ocean data (Figure S8). Thus, the modified model displays a similar aptitude to explain the data as the original model.

4.4 Effect of Model Architecture: Deep and Bottom Atlantic Boxes

Recent studies have inferred the presence of 14C age maxima at water depths of 3,500–4,500 m in the deep Atlantic during the LGM (Burke et al., 2015; Keigwin & Swift, 2017; Skinner et al., 2017). Age extrema at these depths cannot be captured by the ventilation model used in this study, as this model represents the entire Atlantic below 1,500 m with a single box. In this section, we consider another slightly more detailed model, where the Atlantic Ocean below 1,500 m is subdivided into two juxtaposed boxes: a deep box extending from 1,500 m to 3,000 m and a bottom box extending from 3,000 m to 4,000 m, the bottom depth of CYCLOPS (Figure S9).

In this modified model, the volume transports in the deep Atlantic are established as follows. The transports from NCW to the deep and bottom boxes are set to 13 Sv and 8.5 Sv, respectively, in proportion to their thicknesses. The exchange flux of 8 Sv between CDW and the bottom box represents the combined effect of (i) the northward flux of Antarctic Bottom Water (AABW) and (ii) the southward flux of the lowest components of North Atlantic Deep Water (NADW) and of entrained AABW (Lumpkin & Speer, 2007). Water flows at the rate of 8.5 Sv from the bottom box to the deep box to represent the upwelling driven by mixing below the crest of the Mid-Atlantic Ridge (Ganachaud & Wunsch, 2000; St Laurent et al., 2002; Waterhouse et al., 2014). Finally, the water flux from the deep box to CDW, set to 21.5 Sv, accounts for the main components of southward deep water export (Ganachaud & Wunsch, 2000). As for the other model versions considered in this paper, volume is conserved in all boxes.

We find that with the modified model comprising two layers in the deep Atlantic, (i) the deep water Δ14C values produced from the fit still explain most of the deep water data (Figures S10 and S11 and Table 4) and (ii) the inferred surface Δ14C values are all within the bounds provided by deep water and atmospheric Δ14C (Figure S12). Although this model appears to overestimate some of the deep water data in the bottom Atlantic, a closer inspection of the results shows that only 1 of the 10 fitted values differ from the bin values by more than two standard deviations (Figure S10).

5 Paleoceanographic Implications

Radiocarbon measurements on fossil samples recovered from the seafloor have been used over the past two decades to draw inferences about changes in deep ocean ventilation during the last deglaciation. The study of ocean paleoventilation is a particularly active field of research, often motivated by its postulated effect on atmospheric CO2 concentration and climate. However, interpretations of deep-sea 14C records remain challenging, given in particular the multiple sources of error that can affect these records and the paucity of the current database (by modern standards).

In this study, we present a compilation of 1,361 deep water Δ14C data originating from different oceanic basins and spanning the past 40 kyr. Notable in the compilation is the observation of a decline in deep water Δ14C over the past 25 kyr in different basins, particularly if deep water Δ14C records previously interpreted as reflecting seafloor processes are discarded. The deep water Δ14C decline is similar to that observed in the atmospheric Δ14C reconstruction over the same time interval and appears significant (Table 2).

Motivated by this result, we explore the extent to which the deep water Δ14C records jointly require changes in basin-scale ventilation rates from 20 to 10 kyr B.P., a time interval characterized by a relative abundance of data. A quantitative model of modern ocean ventilation is fit to deglacial data, and the results of the fit are analyzed. These results are the fitted values of deep water Δ14C and the implied values of surface water Δ14C. We find that most of the fit residuals (87%) are consistent with the estimated data uncertainties and that the implied values of surface water Δ14C are reasonable given the bounds provided by contemporaneous values of atmospheric Δ14C and deep water Δ14C. None of our sensitivity tests, bearing on bin width (section 4.1), consideration of low-Δ14C records (section 4.2), and model architecture (sections 4.3 and 4.4), provide strong evidence that the deglacial data are incompatible with modern ocean ventilation as represented in the box model (Table 4).

Nonetheless, whereas most of the deep water Δ14C data appear consistent with basin-scale ventilation rates in the modern ocean, these rates cannot account for all the data. Moreover, some of the surface water Δ14C values implied by the deep water Δ14C data under the assumption of modern ventilation significantly deviate from the values expected from variations in atmospheric Δ14C and pCO2. Four out of 32 of the implied values in the northern North Atlantic (boreal box) and the Southern Ocean (Antarctic box) differ from the expected values by more than two standard deviations (Figure 10). It is tempting to notice that a number of implied values that most strongly deviate from the expected values, albeit not always significantly so (at the level of two standard deviations), cluster in some intervals, most notably during the BA and HS1 both in the northern North Atlantic and in the Southern Ocean (Figure 10).

Estimates of deep ocean 14C age have been used to infer variations in deep ocean carbon storage and atmospheric CO2 level during the last (de)glacial periods (e.g., Sarnthein et al., 2013; Skinner et al., 2010). Our results, on the other hand, show that deep water Δ14C records do not generally require basin-scale ventilation rates that are different from modern, provided that changes in surface reservoir ages occurred, particularly at high latitudes. Changes in sea ice cover at high latitudes could reconcile the inferences above with our results, because these changes can impact both air-sea CO2 exchange (e.g., Stephens & Keeling, 2000) and surface reservoir ages (e.g., Bard, 1988). For example, during the BA (Antarctic Cold Reversal), sea ice in the Southern Ocean might have expanded (e.g., Ferry et al., 2015) and ice-free conditions might have existed in the northern North Atlantic (e.g., Müller et al., 2009), which could have influenced the surface 14C disequilibria with the atmosphere (Figure 10). Whether these changes could operate without a commensurate change in basin-scale ventilation, detectable from 14C measurements on fossil carbonates, remains to be investigated. The possibility that deep water Δ14C records reflect some combination of changes in deep circulation and surface water reservoir ages cannot be ruled out based on the kinematical model used in this study.

Many studies using different proxies have concluded for deglacial changes in ocean circulation (e.g., Bryan et al., 2010; McManus et al., 2004; Rae et al., 2014; Siani et al., 2013; Skinner et al., 2014). While such conclusions are clearly plausible, it should also be stressed that quantitative estimates of the inferred circulation changes and of their uncertainties are typically not reported. Absent such estimates, the degree of (in)consistency of inferences between different studies, and between prior studies and the present study, is difficult to assess.

Importantly, our results do not imply that changes in basin-scale ocean ventilation did not take place during the deglaciation. Our approach may not have the skill to differentiate modest changes in basin-scale ventilation rates, although it should be adequate to test large changes in radiocarbon inventory (Hain et al., 2014b) and ocean circulation (e.g., Broecker & Barker, 2007; McManus et al., 2004). Furthermore, whether our results will still hold as additional deep water Δ14C data become available remains to be seen. Additional data would be helpful, not only for better constraining basin-scale ventilation changes (if any) but also for identifying changes on time scales shorter than those considered in this analysis. Finally, our results do not rule out the possibility of deglacial changes in ventilation at horizontal scales smaller than O(1,000 km) and vertical scales smaller than O(1,000 m), as these scales are not resolved by the ocean model used in this study.

6 Perspectives

Besides the need for more data, especially in regions with currently poor spatial and (or) temporal coverage, we feel that other lines of research should be pursued in order to enhance the value of deep water radiocarbon records in the study of paleocirculations. First and foremost, accurate estimates of core and coral chronologies are critical for the reconstruction of deep water Δ14C, since Δ14C depends sensitively on calendar age (e.g., Davies-Walczak et al., 2014). The chronological errors arising from varying sedimentation rate and reservoir age are poorly understood and generally not reported in the publications. Second, a common procedure to obtain Δ14C measurements on fossil samples appears highly desirable for the construction of an internally consistent data set. For example, 14C measurements on benthic shells could be restricted to samples originating from peaks in benthic shell abundance (e.g., Keigwin & Schlegel, 2002) and (or) to cores with high sedimentation rates, so as to minimize bioturbation effects. Finally, studies are needed to establish the relationship between Δ14C of benthic foraminifera or deep-sea corals sampled from the seafloor and the Δ14C of ambient bottom water (e.g., Figure 6). In particular, more research should be done on the potential of seafloor processes, such as hydrothermal activities and methane seeps, to affect the 14C/12C ratios of fossil biogenic carbonates (e.g., Ronge et al., 2016; Stott & Timmermann, 2011).

On the other hand, it is clear that progress in the use of radiocarbon data to extract information about paleoventilation should not come exclusively from the data. Use of more complete models than the one considered here is clearly desirable. In particular, models that have sufficient spatial resolution to properly represent ocean ventilation in marginal regions where most of the paleodata lie would alleviate the need for estimating large-scale averages and increase the power of these data to constrain past ocean conditions. Use of an ocean circulation model—with an explicit representation of the equations of motion—would allow inferences to be made that are both dynamically and observationally consistent (e.g., Burke et al., 2011; Gebbie & Huybers, 2006; LeGrand & Wunsch, 1995; Marchal & Curry, 2008). Consideration of sea ice dynamics and C cycle processes, particularly at the seafloor, might also be needed for interpreting at least some of the deep water 14C records.

Besides, other approaches of data analysis can offer complementary insights. The approach adopted in this paper does not lead to quantitative inferences about past ventilation rates but to an assessment of the changes in surface water Δ14C that the deep water Δ14C data imply under the assumption of modern ventilation. Alternative approaches, such as based on Lagrange multipliers (adjoint methods) and sequential methods of optimal estimation theory (Kalman filters and related smoothers), could be used to make such inferences from the quantitative combination of a model with the data (e.g., Wunsch, 2006). Each of these approaches has strengths and weaknesses. Whereas adjoint methods can be used to fit an ocean general circulation model to ocean data, they do not generally produce error estimates (e.g., Dail & Wunsch, 2014). Sequential methods do lead to the production of error estimates but are more difficult to apply given their high computational cost. As a result, sequential methods have generally been used to combine ocean data with simplified models (e.g., Marchal et al., 2016).


O. M. thanks Edouard Bard for sharing preindustrial estimates of radiocarbon reservoir ages. Discussions with Dave Lund and Laura Robinson helped the authors to stay updated with the paleo-Δ14C database and with potential issues in some Δ14C records. Carl Wunsch and two referees provided useful comments on an early version of the manuscript. The authors are grateful to Mathis Hain and an anonymous reviewer for their thoughtful and constructive comments on the present manuscript. This research was supported by a grant from the U.S. National Science Foundation (OCE-1301907). Data used in this study are archived at the NOAA National Climatic Data Center (https://www.ncdc.noaa.gov/paleo/study/21390).