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

Abstract

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)

Figure 1

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).

Figure 2

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.

Figure 3

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 , where σ_a is the standard error of the mean of deep water Δ¹⁴C data falling in that bin and σ_b 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).

Figure 4

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,

(1)

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

(2)

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:

(3)

Here C_i is the radiocarbon concentration in box i, V_i is the volume of box i, J_ji is the volume transport from box j to box i, and λ = (1/8,223) year⁻¹ is the ¹⁴C radioactive decay constant. Thus, C_i is the concentration in an intermediate or deep box, and C_j is the concentration in an intermediate, deep, or surface box. Although C_i 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 (J_ij) 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 dC_i/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,

(4)

Here 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), is a matrix that represents the effect of ocean circulation, is a vector including the surface water ¹⁴C concentrations, and is a vector including the errors of the data in . 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 ( ) from deep water ¹⁴C concentration data ( ) under modern circulation conditions ( ) and in the presence of observational errors ( ). 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 is referred to as . Second, a first guess of the solution, , 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 is expressed as the sum of the first guess and a deviation, that is, . The deviation is obtained from the solution of a new set of equations (for a similar approach, see Gebbie, 2012),

(5)

where . 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 using singular value decomposition, SVD (e.g., Wunsch, 2006). To this end, the coefficient matrix is decomposed as

(6)

where U (V) is an orthonormal matrix containing the left (right) singular vectors of and Λ is a nonsquare diagonal matrix with the singular values of ranked in order of decreasing magnitude along the diagonal. The SVD solution of 5 is

(7)

where u_i and v_i are singular vectors (the ith column of U and V, respectively), λ_i is a singular value (the ith element along the diagonal of Λ), K is the number of singular values different from zero, and α_i is an unknown expansion coefficient. On the right-hand side of 7, the first term represents the contribution due to structures in that can be determined from the data (the range of ) and the second term represents the contribution due to structures that cannot be determined from the data (the null-space of ). 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 is

(8)

where is the error covariance matrix for the observational estimates of ¹⁴C concentration in and 〈·〉 denotes the expected value. The diagonal elements of are equal to 1 (since equation 4 has been scaled) and the off-diagonal elements of are set equal to zero, assuming negligible error covariances; that is, 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 α_i (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 ( ) 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.

Figure 5

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).

Figure 6

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.

Figure 7

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

(9)

where .

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 , 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 λ_i (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).

Figure 8

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.

Figure 9

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-Δ^14C 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).

Figure 10

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,

(10)

where T_v is the solution resolution matrix defined by (e.g., Wunsch, 2006)

(11)

Equation 10 shows that each element of the solution, , can be regarded as a linear combination of the actual values in . Departures of from can thus be investigated from the matrix T_v. One approach for such investigation is to repeatedly calculate from 10 for a number of vectors , 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 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 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 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 σ_a). 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)

(12)

where U_K is a matrix containing the first K left singular vectors of . The diagonal elements of the matrix T_u 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.

Figure 11

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).

Acknowledgments

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).