# Rejuvenating the ocean: mean ocean radiocarbon, CO 2 release, and radiocarbon budget closure across the last deglaciation

Luke Skinner, Francois Primeau, Aurich Jeltsch-Thömmes, Fortunat Joos,

Peter Köhler, Edouard Bard

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Luke Skinner, Francois Primeau, Aurich Jeltsch-Thömmes, Fortunat Joos, Peter Köhler, et al. Rejuvenating the ocean: mean ocean radiocarbon, CO 2 release, and radiocarbon budget closure across the last deglaciation. Climate of the Past, 2023, 19 (11), pp.2177-2202. 10.5194/cp-19-2177-2023 hal-04910639

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# Rejuvenating the ocean: mean ocean radiocarbon, CO₂ release, and radiocarbon budget closure across the last deglaciation

Luke Skinner<fnref n="1" />, Francois Primeau<fnref n="2" />, Aurich Jeltsch-Thömmes<fnref n="3" />,<fnref n="4" />, Fortunat Joos<fnref n="3" />,<fnref n="4" />, Peter Köhler<fnref n="5" />, and Edouard Bard<fnref n="6" />

**Correspondence:** Luke Skinner (lcs32@cam.ac.uk)

Received: 14 April 2023 – Discussion started: 4 May 2023
Revised: 1 September 2023 – Accepted: 5 September 2023 – Published: 3 November 2023

**Abstract.** Radiocarbon is a tracer that provides unique insights into the ocean's ability to sequester CO₂ from the atmosphere. While spatial patterns of radiocarbon in the ocean interior can indicate the vectors and timescales for carbon transport through the ocean, estimates of the global average ocean–atmosphere radiocarbon age offset (B-Atm) place constraints on the closure of the global carbon cycle. Here, we apply a Bayesian interpolation method to compiled B-Atm data to generate global interpolated fields and mean ocean B-Atm estimates for a suite of time slices across the last deglaciation. The compiled data and interpolations confirm a stepwise and spatially heterogeneous “rejuvenation” of the ocean, suggesting that carbon was released to the atmosphere through two swings of a “ventilation seesaw” operating between the North Atlantic and both the Southern Ocean and the North Pacific. Sensitivity tests using the Bern3D model of intermediate complexity demonstrate that a portion of the reconstructed deglacial B-Atm changes may reflect “phase-attenuation” biases that are unrelated to ocean ventilation and that arise from independent atmospheric radiocarbon dynamics instead. A deglacial minimum in B-Atm offsets during the Bølling–Allerød could partly reflect such a bias. However, the sensitivity tests further demonstrate that when correcting for such biases, ocean “ventilation” could still account for at least one-third of deglacial atmospheric

CO₂ rise. This contribution to CO₂ rise appears to have continued through the Younger Dryas, though much of the impact was likely achieved by the end of the Bølling–Allerød, indicating a key role for marine carbon cycle adjustment early in the deglacial process. Our global average B-Atm estimates place further new constraints on the long-standing mystery of global radiocarbon budget closure across the last deglaciation and suggest that glacial radiocarbon production levels are likely underestimated on average by existing reconstructions.

## 1 Introduction

The evolving spatial distribution of marine radiocarbon provides unique constraints on air–sea gas exchange at the sea surface, and the ocean dynamics that convey surface ocean–atmosphere pCO₂ differences into the ocean interior (Koewe et al., 2015). These transports of carbon in turn set constraints on the ability of the ocean to store CO₂, away from the atmosphere, in the form of either “disequilibrium” or “respired” dissolved inorganic carbon (Galbraith and Skinner, 2020). A slower overturning circulation enhances the accumulation of respired carbon in the ocean interior, in parallel with greater radiocarbon decay (Menviel et al., 2017;

<footnote n="1">¹Godwin Laboratory for Palaeoclimate Research, Earth Sciences Department, University of Cambridge,
Downing Street, CB2 3EQ Cambridge, UK</footnote>

<footnote n="2">²Department of Earth System Science, University of California, Irvine, CA 92697, California, USA</footnote>

<footnote n="3">³Climate and Environmental Physics, Physics Institute, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland</footnote>

<footnote n="4">⁴Oeschger Centre for Climate Change Research, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland</footnote>

<footnote n="5">⁵Alfred-Wegener-Institut Helmholtz-Zentrum für Polar-und Meeresforschung (AWI),
P.O. Box 12 01 61, 27515 Bremerhaven, Germany</footnote>

<footnote n="6">⁶CEREGE, Aix Marseille Univ., CNRS, IRD, INRAE, College de France, Technopole de l'Arbois,
BP 80, 13545, Aix-en-Provence, France</footnote>
Eggleston and Galbraith, 2018; Tschumi et al., 2011). Reduced air-sea exchange impedes the release of respired carbon from upwelled water to the atmosphere while also impeding radiocarbon input from the atmosphere to the ocean (e.g. Khatiwala et al., 2019; Stocker and Wright, 1996). Both processes enhance carbon sequestration in the ocean (Galbraith and Skinner, 2020; Eggleston and Galbraith, 2018) while depleting the ocean's average radiocarbon activity relative to the atmosphere (Skinner and Bard, 2022). Therefore, estimates of the global average ocean-atmosphere radiocarbon age offset (B-Atm) may provide powerful constraints on the evolving carbon exchange between the ocean and atmosphere (Siegenthaler et al., 1980). This in turn has implications for the closure of the radiocarbon budget of the atmosphere, given that the atmospheric radiocarbon inventory is largely set by the radiocarbon production rate and ocean-atmosphere radiocarbon exchange (Siegenthaler, 1989).

Few estimates of global average B-Atm prior to the instrumental record currently exist. This largely relates to the difficulty of estimating the “volumetric representativity” of sparse data points, in order to weight their contribution to the global mean. Using a simple unweighted arithmetic mean of existing data from the Last Glacial Maximum (LGM, ~20 ka), Sarnthein et al. (2013) demonstrated an increase in the mean ocean-atmosphere radiocarbon age offset (B-Atm) by ~600 ¹⁴C yr. A subsequent study instead made use of a Bayesian interpolation method, over a 4° resolution global grid, to generate a global field of B-Atm offsets from which to derive a volume-weighted global average (Skinner et al., 2017). This alternative approach again showed that the glacial ocean was significantly more radiocarbon depleted relative to the atmosphere, especially in the deep Atlantic and the Southern Ocean (Sikes et al., 2016a; Skinner et al., 2021, 2010; Gottschalk et al., 2020). This study inferred a mean ocean B-Atm increase of 689 ± 53 ¹⁴C yr as compared with the pre-industrial ocean. Using yet another approach, whereby individual data points were weighted according to their location (and their current offset from modern regional and/or basin averages), Rafter et al. (2022) have again confirmed an “ageing” of the deep ocean at the LGM. The study of Rafter et al. (2022) was restricted to the deep ocean > ~1000 m water depth and therefore did not yield global mean estimates. Nevertheless, the ~1050 ± 150 ¹⁴C yr increase inferred by Rafter et al. (2022) for the deep ocean (approximately equivalent to > 2 km water depth) almost certainly implies a significant increase in the global mean B-Atm at the LGM. Note that Rafter et al. (2022) incorrectly identified the global mean estimate of Skinner et al. (2017) as referring to the deep ocean > 3 km water depth, and that consequently the estimates of Rafter et al. (2022) and Skinner et al. (2017) may be more consistent with each other than initially apparent.

Overall, a consistent picture has therefore emerged of a relatively “aged” dissolved inorganic carbon (DIC) pool in the LGM ocean. A recent review of the existing data has fur-

ther demonstrated coherent patterns in marine radiocarbon evolution since the LGM, across the last deglaciation (Skinner and Bard, 2022). Several key observations have so far emerged from the compiled data: (1) at the onset of deglaciation, during Heinrich Stadial 1 (HS1, ~17.5–14.7 ka), and to a lesser extent the Younger Dryas (YD, ~12.9–11.7 ka), B-Atm offsets increased in the deep and intermediate North Atlantic, while they decreased in the Southern Ocean and North Pacific (particularly in the intermediate North Pacific, suggesting a “ventilation seesaw”) (e.g. Broecker, 1998; Skinner et al., 2013, 2014; Menviel et al., 2018; Ahagon et al., 2003; Menviel et al., 2014; Freeman et al., 2015; Max et al., 2014; Okazaki et al., 2010; Walczak et al., 2020). (2) B-Atm offsets decreased significantly throughout the global ocean at the Bølling–Allerød (BA, ~14.7–12.9 ka), in places suggesting an overshoot to values younger than pre-industrial (e.g. Barker et al., 2010). (3) Surface reservoir ages in the high latitudes of the North Atlantic and the Southern Ocean tend to track B-Atm changes at intermediate depths (Skinner et al., 2019), suggesting limited changes in transport < 2 km water depth (and therefore a significant contribution from restricted gas-exchange efficiency instead). This contrasts with the deep ocean > 2 km, where stronger evidence for transport changes is apparent (Skinner et al., 2021; Marchal and Zhao, 2021a). Encouragingly, similar observations have recently been reported based on a complex approach to data screening, averaging, and weighting (Rafter et al., 2022). The latter study emphasized the influence of transport changes on B-Atm offsets: enhanced mid-depth ventilation was inferred in the North Pacific at the LGM; and reduced transport rates were inferred in the deep Pacific at the LGM, and in the deep North Atlantic during HS1 and the YD.

Several questions arise in light of the existing body of deglacial marine radiocarbon data. First, what do the existing data imply for global average (i.e. rather than regional or deep ocean) B-Atm offsets across the last deglaciation? Second, can we determine the degree to which observed changes in the mean ocean B-Atm offset reflect changes in “ventilation” specifically (i.e. circulation rates and gas exchange), as opposed to, for example, independent changes in atmospheric radiocarbon (Franke et al., 2008)? Third, can we quantify the likely impact of past radiocarbon ventilation effects (regardless of their origin) on ocean-atmosphere carbon partitioning and, therefore, atmospheric CO₂ (Skinner and Bard, 2022)? Finally, can the temporal evolution of mean ocean B-Atm offsets be reconciled with past atmospheric radiocarbon activities and past radiocarbon production rates; and do they resolve the long-standing “mystery” of deglacial radiocarbon budget closure (Broecker and Barker, 2007; Köhler et al., 2022, 2006)?

Here, we attempt to address each of these questions in turn. We update a previously deployed Bayesian interpolation technique (Skinner et al., 2017), which we apply to an updated compilation of radiocarbon data spanning the last deglaciation, to derive estimates of global average B-Atm
offsets. These estimates are interpreted against a suite of
new sensitivity tests and transient simulations conducted us-
ing the Bern3D model of intermediate complexity (Müller et
al., 2006; Ritz et al., 2011; Roth et al., 2014). The new sim-
ulations are aimed at constraining the potential magnitude
of “ventilation” versus “non-ventilation” effects in global
mean B-Atm offsets, as well as associated changes in ocean-
atmosphere CO₂ partitioning.

## 2 Methods

### 2.1 Radiocarbon data

Our data compilation is based on the work of Zhao et
al. (2018) as presented in Skinner and Bard (2022). The com-
pilation has been reconciled with a similar collection of data
that has recently emerged (Rafter et al., 2022). A key differ-
ence in our compilation is that we include warm water (near
surface) coral data and surface reservoir age data (e.g. Skin-
ner et al., 2019) where direct estimates exist. Our compilation
adopts revised chronologies and radiocarbon age offsets con-
sistent with the latest *Intcal20* (Reimer et al., 2020) and *Ma-
rine20* (Heaton et al., 2020) calibration curves. To update the
chronologies of the collected time series, where the only age
control derives from planktonic radiocarbon dates, we have
used the *Marine20* calibration curve (Heaton et al., 2020),
in conjunction with modern local deviations from the global
average surface reservoir age (Δ*R* values ~ local R-age mi-
nus 550 ¹⁴C yr) (Heaton et al., 2020), to generate “reservoir-
age” corrected calibrated calendar ages, using the R package
*Bchron* (Parnell et al., 2008). While this approach has the ad-
vantage of remaining as faithful as possible to the original
published age scale for each record, it also has the notable
drawback of neglecting potential changes in Δ*R*, which are
known to have occurred in mid-to-high latitudes (e.g. Skin-
ner et al., 2019) and have been directly estimated in some
of the studies included in the compilation. For records up-
dated in this way, where the density and/or down-core vari-
ability of planktonic radiocarbon dates in a sediment core
is sufficient to result in age reversals (i.e. older dates strati-
graphically above younger dates), we have generated new
sediment depth-age models using the MCMC approach of
*Bchron*, from which maximum likelihood calendar age es-
timates and 95% uncertainty intervals (~2σ) are obtained
for each sample depth. For time series that have made use
of U-series dating (e.g. Robinson et al., 2005; Burke and
Robinson, 2012; Chen et al., 2015; Hines et al., 2015), or
stratigraphic alignments (including stratigraphic alignments
that have provided time-varying surface reservoir age correc-
tions; e.g. Skinner et al., 2010; Gottschalk et al., 2020; Austin
et al., 2011; Peck et al., 2006), as well as a priori assignment
of down-core changes in reservoir ages (e.g. Ronge et al.,
2020), we adopt the published calendar ages, as these do not
depend on the atmospheric radiocarbon calibration curve.

For all compiled data, we have recalculated radiocarbon
reservoir age offsets relative to the *Intcal20* (Reimer et al.,
2020) atmospheric reference curve using the *radcal* func-
tion in the *R* package *ResAge* (Soulet, 2015). This approach
yields 95% uncertainty limits for the resulting radiocarbon
age offsets based on the joint calendar age and radiocar-
bon age uncertainties. The resulting probabilistic B-Atm es-
timates differ from simple differences between marine and
atmospheric radiocarbon values to some extent (Rafter et al.,
2022). Estimates of the relative (radiocarbon) isotopic en-
richment of the ocean versus the atmosphere are expressed
as radiocarbon age offsets between the ocean and the con-
temporary atmosphere (i.e. in ¹⁴C yr), which are equivalent
to -8033 × ln(α<sub>O-Atm</sub>), where α<sub>O-Atm</sub> represents the ratio
of marine radiocarbon activity versus the contemporary at-
mospheric radiocarbon activity at time *T*, i.e. Fm<sub>O</sub><sup>*T*</sup>/Fm<sub>Atm</sub><sup>*T*</sup>
(Soulet et al., 2016). We do not refer to offsets between ma-
rine and atmospheric Δ¹⁴C (i.e. Δ¹⁴C<sub>O</sub> minus Δ¹⁴C<sub>Atm</sub>),
since this metric does not relate to the isotopic depletion
of the marine reservoir relative to the atmosphere in a pre-
dictable way without knowledge of the absolute atmospheric
and marine radiocarbon activities (e.g. Cook and Keigwin,
2015).

Data quality flags are assigned to anomalous values or
datasets, including those that yield negative ventilation ages,
negative reservoir ages, or negative benthic–planktonic off-
sets (B–P), or that exhibit significant down-core age rever-
sals (e.g. Rose et al., 2010). In addition, datasets that deviate
significantly from regional trends, for example due to alterna-
tive age models, are also flagged. The latter category includes
records based on “plateau tuned” (PT) chronologies (Sarn-
thein et al., 2015, 2007, 2020, 2013; Ausín et al., 2021) that
differ significantly from alternative reconstructions using the
same data, or from reconstructions at proximal sites (Skinner
and Bard, 2022). Such differences may relate to identifiable
drawbacks of the “plateau tuning” methodology (Bard and
Heaton, 2021). Datasets that are interpreted as being influ-
enced by hiatuses are also flagged (e.g. Ronge et al., 2020,
2019), as are data that are interpreted as having been influ-
enced by localized geological or sedimentary carbon sources
(Rafter et al., 2019, 2018; Lindsay et al., 2016, 2015; Ronge
et al., 2016; Bova et al., 2018; Stott et al., 2009; Marchitto
et al., 2007). A similar selection was effectively made in the
recent study of Rafter et al. (2022), where all data from wa-
ter depths less than ~ 1000 m were omitted from consider-
ation, and where individual data points were removed from
binned regional water-depth groupings based on their devia-
tion (by > 3σ) from the group’s weighted arithmetic mean.

Although the data compiled in this study have all been
published, including the vast majority in a previous compi-
lation (Zhao et al., 2018), it remains possible that some data
have been affected by as yet undetected biases arising from
bioturbation (Bard et al., 1987; Dolman et al., 2021) and/or
diagenesis (Wycech et al., 2016). Unless obviously anoma-
lous signals are produced (Missiaen et al., 2020), such bi-
ases can be extremely difficult to positively identify but could
have profound impacts (Lougheed et al., 2020; Stott, 2023).
Although sites with very low sedimentation rates may be
particularly prone to bioturbation effects (Bard et al., 1987;
Dolman et al., 2021), the avoidance of all data from such
locations might also introduce a sampling bias due to their
prevalence at greater water depths. This presents a signif-
icant challenge. In order to limit the potential impacts of
anomalies caused by bioturbation (Dolman et al., 2021), we
apply data flags to all sediment cores with average accumu-
lation rates < 2 cm kyr⁻¹ (rounded to the nearest digit). Of
the remaining data, 75 % derive from sites with accumulation
rates > 10 cm kyr⁻¹ and 95 % derive from sites with accu-
mulation rates > 4 cm kyr⁻¹. A comparison of late Holocene
data (< 6 ka BP) with pre-industrial observations (Key et al.,
2004) serves to demonstrate the general fidelity of B-Atm
offsets derived from fossil substrates as compared with mod-
ern seawater values (R² = 0.81; see Fig. 1). However, this
comparison also illustrates the significant scatter that exists
in the fossil data (RMSE ~ 273 years; or an “inverse pre-
diction interval”, which is more appropriate if considering
a “calibration” of fossil data, ~ RMSE × 1.96 = 535 years;
McClelland et al., 2021). A similar result has recently been
demonstrated for sub-modern B-Atm offsets by Rafter et
al. (2022). The observed scatter is expected to derive primar-
ily from sedimentary and sampling issues, rather than ana-
lytical uncertainty, and calls for caution when interpreting
the subtler features that emerge from the collected data. Ac-
cordingly, an underlying premise of our work (as for previ-
ous compilations) is that the temporal trends and spatial pat-
terns that emerge from a large body of independent data are
far less likely to be dominated by sedimentary or diagenetic
biases that can more readily influence individual sediment
cores (Ronge et al., 2019; Stott, 2020).

In order to assess the implications of applying the
data flags described above, three alternative interpolations
were performed: (1) the baseline interpolation, where all
flagged data were excluded (Table 1, “Baseline”); (2) as
for the baseline but with low sedimentation rate sites
(< 2 cm kyr⁻¹) retained (Table 1, “Low sedimentation”); and
(3) as for the baseline but retaining only high sedimenta-
tion rates > 10 cm kyr⁻¹ (mainly affecting sites in the 2500–
4000 m water depth range). In keeping with a similar assess-
ment made by Rafter et al. (2022), we find that the inclusion
of very low sedimentation rate sites (< 2 cm kyr⁻¹) has no
major effect on our findings, particularly for the global av-
erages (Table 1). The same is true when only retaining sites
with very high sedimentation rates > 10 cm kyr⁻¹ (Figs. S2
and S3 in the Supplement), though global averages are bi-
ased to slightly lower values (Stott, 2023), particularly at the
LGM (Table 1, “High sedimentation”). This apparent lack
of sensitivity arises here due to the averaging of a relatively
large number of data points (thereby reducing the influence
of statistical outliers); however, it should be borne in mind
that the inclusion or exclusion of individual data points from

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Comparison of modern seawater (corrected for the effects of atomic bomb testing) B-Atm radiocarbon age offsets (Key et al., 2004) versus proxy-based B-Atm reconstructions using material deposited during the past ~6000 years (open black circles) and the past ~1500 years (filled red circles). Dashed grey line indicates the 1:1 trend. The linear fit to the data is indicated by the red line (dashed red lines show 95% confidence limits), with the following equation: $y = (1.1 \pm 0.1)x + (89 \pm 98)$, $R^2 = 0.81$, $p = 1.77 \times 10^{-17}$.</figcaption></figure>

sparsely sampled regions (e.g. for the Indian Ocean) can in-
fluence the detail of inferred spatial patterns.

## 2.2 Time slices

We isolate data associated with six key time slices based on
their calendar ages and associated uncertainties: the LGM
(19–21.8 ka BP), Heinrich Stadial 1 (15–17.5 ka BP), the
Bølling-Allerød (12.8–14.8 ka BP), the Younger Dryas (YD,
11.8–12.7 ka BP), the early Holocene (EHOL, 9–11 ka BP),
and the late Holocene (HOL, < 6 ka BP). Note that the
boundaries of these time intervals are informed by, but do not
correspond precisely to, their respective ice-core chronozone
definitions (Rasmussen et al., 2014). This is due to the gen-
erally lower resolution of the marine records and the need to
be pragmatic in avoiding, as much as possible, misattributing
data to an adjacent chronozone. Where calendar age uncer-
tainties result in an ambiguous assignation of a single time
slice, no time slice is assigned.

## 2.3 Radiocarbon “ventilation” metrics

The term “ventilation” is defined here as comprising the
processes that influence physical and chemical property ex-
changes between the ocean interior and the atmosphere
(Skinner and Bard, 2022). Accordingly, the term “(radiocar-
<table><caption>**Table 1.** Time-slice global average B-Atm values and their offset from the modern global average B-Atm value, based on 3D interpolations, for three different data flagging approaches, as described in the text: baseline (all flagged data are excluded); low sedimentation (as for baseline but with low sedimentation rate sites included, < 2 cm kyr⁻¹); high sedimentation (as for baseline but retaining only high sedimentation rate sites, > 10 cm kyr⁻¹). Hypothetical corrections for maximum “attenuation biases” and inferred atmospheric CO₂ impacts are shown compared with observed mean atmospheric CO₂ levels. For each data flag scenario, the total number of deglacial data points and average recorded water depth is shown as a rough indication of the impact of the data flags: as more stringent flags are applied, the data are biased to fewer points at shallower depths.</caption><thead><tr><th rowspan="3">Time slice</th><th colspan="3">Baseline (n = 2579, avg. z = 1407 m)</th><th colspan="3">Low sedimentation (n = 2688, avg. z = 1472 m)</th><th colspan="3">High sedimentation (n = 2036, avg. z = 1244 m)</th><th rowspan="3">err</th><th rowspan="3">Obs Δ(pCO₂) vs. Pl</th><th rowspan="3">ppmv</th><th rowspan="3">ppmv</th></tr><tr><th rowspan="2">Mean ocean B-Atm</th><th rowspan="2">Δ(B-Atm) vs. Pl</th><th rowspan="2">err</th><th rowspan="2">Mean ocean B-Atm</th><th rowspan="2">Δ(B-Atm) vs. Pl</th><th rowspan="2">err</th><th rowspan="2">Max. attenuation bias in model (CONST)</th><th rowspan="2">'Corrected' Δ(B-Atm), impact, baseline</th><th rowspan="2">Estimated pCO₂ baseline</th><th rowspan="2">ppmv</th></tr><tr><th>Mean ocean B-Atm</th><th>Δ(B-Atm) vs. Pl</th><th>err</th><th>Max. attenuation bias in model (CONST)</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th><th>14Cyr</th></tr></thead><tbody><tr><td>HOL</td><td>1335</td><td>-24</td><td>22</td><td></td><td>1328</td><td>-31</td><td>24</td><td>1350</td><td>-9</td><td>20</td><td></td><td>25</td><td>-49</td><td></td><td>3</td><td>281.9</td><td>-3.6</td><td>0.5</td></tr><tr><td>EHOL</td><td>1359</td><td>0</td><td>26</td><td></td><td>1360</td><td>1</td><td>39</td><td>1329</td><td>-30</td><td>31</td><td></td><td>-52</td><td>-52</td><td></td><td>-3</td><td>268.2</td><td>-17.3</td><td>0.4</td></tr><tr><td>YD</td><td>1484</td><td>125</td><td>37</td><td></td><td>1515</td><td>156</td><td>37</td><td>1478</td><td>119</td><td>41</td><td></td><td>28</td><td>-6</td><td></td><td>-6</td><td>253.7</td><td>-31.8</td><td>0.7</td></tr><tr><td>BA</td><td>1435</td><td>76</td><td>32</td><td></td><td>1487</td><td>128</td><td>37</td><td>1432</td><td>73</td><td>32</td><td></td><td>-217</td><td>-18</td><td></td><td>293</td><td>241.5</td><td>-43.9</td><td>0.5</td></tr><tr><td>HS</td><td>1877</td><td>518</td><td>40</td><td></td><td>1981</td><td>621</td><td>55</td><td>1793</td><td>434</td><td>55</td><td></td><td>-107</td><td>625</td><td></td><td>-39</td><td>219.7</td><td>-65.8</td><td>1.5</td></tr><tr><td>LGM</td><td>2123</td><td>764</td><td>32</td><td></td><td>2185</td><td>825</td><td>36</td><td>1993</td><td>634</td><td>46</td><td></td><td>-26</td><td>789</td><td></td><td>-50</td><td>194.7</td><td>-90.8</td><td>0.6</td></tr></tbody></table>

bon) ventilation age” is not used to refer to “ideal ages” or “transit times” (England, 1995; Marchal and Zhao, 2021b), but rather to the degree of isotopic (¹⁴C/C) disequilibrium between the ocean and atmosphere, as determined by gas-exchange efficiency and water transport rates (Koeve et al., 2015). In this context “gas-exchange efficiency” is a catch-all term that refers primarily to the gas transfer piston velocity and includes the influence of the mixed layer equilibration time, which in turn depends on, for example, the mixed layer depth.

“Radiocarbon ventilation” must in turn be differentiated from measures of relative isotopic enrichment, such as B-Atm age offsets (Soulet et al., 2016). While ‘ventilation’ refers to a set of processes (principally gas-exchange efficiency and water transport), observation-based metrics such as B-Atm reflect measurements of radiocarbon isotopic disequilibrium, typically between the ocean interior and the atmosphere or mixed layer (Skinner and Bard, 2022). This terminology mirrors a standard geological principle of separating descriptive names (e.g. diamicton) from the inference of process (e.g. glacial till).

In summary, B-Atm should not be used to directly imply transit times or ideal ages, which are not equivalent to “radiocarbon ventilation ages”. Furthermore, metrics such as B-Atm offsets are influenced by a wider variety of processes than just ventilation (i.e. more than just gas exchange and transport), including, for example, atmospheric radiocarbon production changes (Heaton et al., 2021). Therefore, B-Atm offsets should only be used to refer to ventilation (i.e. gas exchange and transport) with caution, as we explore in this study.

## 2.4 Interpolation

We use the interpolation method described in Skinner et al. (2017), updated to weight input data according to their reported uncertainties. The method interpolates the observed ocean-atmosphere radiocarbon age offset anomalies onto the grid of an ocean model with 24 vertical levels and 2° × 2° horizontal resolution. The anomalies are defined relative to the modern GLODAP radiocarbon ages (Key et al., 2004). The interpolating function is constructed using a weighted superposition of radial basis functions centred at the sediment-core locations. These basis functions are built here using an exponential basic function, $\varphi(r) = e^{-\varepsilon r}$, with shape parameter, $\varepsilon$. The distance $r$ is defined as the time for tracer impulses to spread out from the core locations to the rest of the grid, based on the modern transport and density stratification. The basis-function weights, the shape parameter, and two hyper-parameters that scale the relative size of the precisions in the prior and likelihood functions are inferred using a three-level Bayesian procedure. (Further details are given in Skinner et al., 2017.) The interpolation process is repeated independently for each time slice so that the data from one
time slice do not influence the interpolation for the other time
slices.

This interpolation method is somewhat conservative be-
cause it is based on the distribution of relative tracer transport
and diffusion timescales in the modern ocean. This choice
is premised on the need to obtain an interpolated solution
in three dimensions that is physically sensible and informed
by large-scale oceanographic requirements, including verti-
cal stratification, basin margins/topographic boundaries, and
dominant transport pathways (e.g. the Antarctic Circumpolar
Current, Deep Western Boundary currents, etc.). It is impor-
tant to note that the interpolation method does not impose
the modern transport on the resulting interpolated fields, nor
does it assume strict adherence to the modern density field.
Rather, it represents a physically guided and data-constrained
anomaly relative to the modern state. The inferred anomalies
relax to zero in the absence of data constraints, though some
locations in the ocean can have far reaching influence. This
method represents a counterpoint to the approach recently
taken by Rafter et al. (2022), for example, where spatial in-
terpolations were illustrated for data projected onto 2D sec-
tions. In their study, averages were also produced for time se-
ries grouped and weighted according to their position within
the modern density- and B-Atm distributions (i.e. locations
closest to the modern mean for a given basin and density
class were weighted to dominate the mean in the past). With
this approach, the spatial distribution of density classes is as-
sumed invariant over time, despite the inference of circula-
tion changes. This mirrors to some extent our use of a modern
transport field as a guide to the volumetric representativity of
individual sample locations. Interpolating a sparsely sampled
3D field is a difficult problem, and a diversity of approaches
is surely useful; however, it should be noted that Rafter et
al. (2022) did not consider the upper ~1000 m of the ocean
and did not produce or discuss global averages.

In order to assess the accuracy of the interpolation method
of Skinner et al. (2017), and its ability to represent different
circulation states, we apply it to a range of modelled radio-
carbon fields. For this we use new outputs from the Bern3D
model (see below) and pre-existing outputs from the LOVE-
CLIM model (Menviel et al., 2017, 2018). We extract data
from the modelled fields at the same locations as the avail-
able proxy data (e.g. for the LGM) and attempt to reproduce
the modelled global field using the interpolation method. As
shown in Fig. 2, the interpolation method is generally suc-
cessful in reproducing the simulated radiocarbon fields for
altered circulation states. The interpolation does best for cir-
culation states characterized by altered wind, diffusivity, and
gas exchange, yielding average errors for 1000 randomly se-
lected individual grid cell estimates of RMSE ~276 years
(INT_ALL60; this study), RMSE ~244 years (INT_ALL80;
this study), RMSE ~398 years (V3LNAw; Menviel et al.,
2017), and RMSE ~511 years (V3LNAwSOwSHWw; Men-
viel et al., 2017) (see Figs. 2 and 3). The interpolation per-
forms slightly less well for extremely different circulation

states, e.g. yielding RMSE ~457 years for the HS1 sim-
ulation of Menviel et al. (2018) and RMSE ~577 years
for the collapsed Atlantic Meridional Overturning Circula-
tion (AMOC) simulation of Menviel et al. (2017), both of
which yielded reversed radiocarbon gradients in the Atlantic
as compared with today (Fig. 3). Encouragingly, the inter-
polation method reproduces the modelled fields more accu-
rately than model simulations of the LGM are typically able
to match observations (Muglia et al., 2018; Menviel et al.,
2017).

In the present study, the interpolation is primarily in-
tended for calculating global average B-Atm offsets using a
relatively sparse dataset (N = 124–476). It is therefore no-
table that the interpolation reproduces modelled global aver-
ages even more accurately than the spatial distributions, with
RMSE ~ 53 years (Fig. 4, circles). In contrast, simple arith-
metic means of B-Atm values drawn from a sub-set of lo-
cations in the modelled fields consistently underestimate the
true global mean by ~ 274 years on average (Fig. 4, trian-
gles). This comparison underlines the importance of apply-
ing a spatially resolved volumetric weighting to the observa-
tions for the derivation of accurate global averages. While
our interpolation approach leaves room for improvement,
it complements alternative data-constrained modelling ap-
proaches that have been applied to, for example, the LGM
and the YD (Pöppelmeier et al., 2023), and it represents
a first step towards addressing the problem of deriving 3D
global fields, and appropriately weighted global averages,
from sparsely sampled proxy data, without (as yet) the use
of forward or inverse models.

2.5 Modelling

The intermediate complexity Bern3D v2.0 Earth system
model (Ritz et al., 2011; Roth et al., 2014) has been used
to explore a series of idealized scenarios that aim to probe
the parallel sensitivities of atmospheric CO2 and marine ra-
diocarbon, subject to changes in global vertical diffusivity,
Southern Ocean winds, and/or Southern Ocean gas-exchange
efficiency. The implementation of radiocarbon in the Bern3D
model is described elsewhere (Müller et al., 2006; Müller
et al., 2008; Dinauer et al., 2020), and the simulations pre-
sented here extend those performed by Jeltsch-Thömmes et
al. (2019) and Dinauer et al. (2020), as well as those per-
formed using an earlier version of the Bern3D model by
Tschumi et al. (2011). The applied version of the Bern3D
model comprises a single-layer energy-moisture balance at-
mosphere with a thermodynamic sea-ice component (Ritz
et al., 2011), coupled to a 3D geostrophic-frictional balance
ocean model (Edwards et al., 1998; Müller et al., 2006), and a
four-box representation of the land biosphere that simulates
the dilution of an atmospheric isotopic perturbation by the
land biosphere but here does not address changes in land car-
bon stocks (Siegenthaler and Oeschger, 1987). Furthermore,
marine sediments were not implemented in the model set-up
<figure><img src="image_4.png" /></figure>

**Figure 2.** Testing the interpolation method using numerical model outputs. Interpolations for the Bern3D and LOVECLIM models, from top to bottom: INT_ALL60 (this study), INT_ALL80 (this study), and V3LNAw (Menviel et al., 2017). Cross plots at left show “true” versus interpolated B-Atm offsets (black circles for input data, red circles for 1000 randomly sampled locations in the ocean interior), with $R^2$ and RMSE shown. Contoured panels show zonally averaged B-Atm offsets (i.e. $^{14}$C-age relative to the atmosphere), for the Pacific (left) and Atlantic (right), for both the model output (upper panels) and the interpolated reconstructions (lower panels), with input data used for the interpolations indicated by the filled circles.

used here, as we sought to isolate the impacts of ventilation processes (i.e. ocean gas exchange and transport).

A first set of sensitivity tests (PI-), performed under “pre-industrial” conditions, and run out for 10 000 years with a fully interactive climate-carbon cycle system (minus sediments), consisted of step changes in (1) global vertical diffusivity in the ocean ($K_v$), (2) Southern Ocean wind stress

(SW), (3) Southern Ocean gas-exchange efficiency or piston velocity (SG), or (4) a combination of $K_v$, SW, and SG (ALL). In each case the relevant parameter was reduced by 20%, 40%, 60%, or 80% relative to its baseline value, and impacts were evaluated after 2000 years. (Impacts after 500 and 5000 years are illustrated in Fig. S1.)
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Testing the interpolation method using numerical model outputs, as for Fig. 2. Interpolations for simulations using the LOVECLIM model, from top to bottom: V3LNAwSOwSHWw (Menviel et al., 2017), V3LNAoff (Menviel et al., 2017), and HS1 (Menviel et al., 2018). Cross plots at left show “true” versus interpolated B-Atm offsets (black circles for input data, red circles for 1000 randomly sampled locations in the ocean interior), with $R^2$ and RMSE shown. Contoured panels show zonally averaged B-Atm offsets (i.e. $^{14}$C-age relative to the atmosphere), for the Pacific (left) and Atlantic (right), for both the model output (upper panels) and the interpolated reconstructions (lower panels), with input data used for the interpolations indicated by the filled circles.</figcaption></figure>

In an additional set of simulations, we employed a range of glacial/deglacial scenarios, similar to those of Jeltsch-Thömmes et al. (2019), where each is again defined by idealized adjustments to vertical diffusivity, wind stress, Southern Ocean gas exchange, or a combination of these, as described for the above PI- sensitivity tests. For these simulations, the model was “spun up” into equilibrium over 35 000

model years under pre-industrial (1700 CE) boundary conditions. The model was then ramped linearly over 5000 years from the resulting PI equilibrium state into “glacial” boundary conditions (i.e. representative of 50 ka BP) for ice sheet albedo, greenhouse gas radiative forcing, and insolation, as well as prescribed values for diffusivity, wind stress, and Southern Ocean gas-exchange efficiency as described above.
<figure><img src="image_6.png" /><figcaption>**Figure 4.** Comparison of global average B-Atm offsets based on interpolated fields (circles, with estimated interpolation error), and geometric averages of the input data used for the interpolations (triangles, with standard error), versus the true values for the model simulations shown in Figs. 2 and 3 plus an additional simulation (NAw) from (Menviel et al., 2017). The $R^2$ correlation coefficient, RMSE, and 1 : 1 line (dashed red line) are indicated.</figcaption></figure>

After this, ice-sheet albedo, greenhouse gas radiative forcing, and insolation were varied based on observations since 50 ka BP, with diffusivity, Southern Ocean wind stress, and Southern Ocean gas-exchange efficiency remaining constant for 32 000 years and then relaxing linearly back to PI control values from 18 to 14.6 ka BP, after which PI control values were maintained.

In one set of “glacial/deglacial” model simulations (INT-), atmospheric radiocarbon was prescribed from 50 ka BP based on the *Intcal20* reference curve (Reimer et al., 2020). Radiocarbon concentrations in the model were therefore required to be consistent with the observed atmospheric radiocarbon concentration, via changes in the global radiocarbon inventory (which are equivalent to ad hoc changes in radiocarbon production). In a second set of simulations (FIX-) atmospheric radiocarbon activity was held constant at 140‰, while in a third set of simulations (CONST-) atmospheric radiocarbon production rates were held constant at the PI value. In each case a control simulation was performed with evolving boundary conditions as described above. A series of additional simulations were then performed with altered global vertical diffusivity ($K_v$), Southern Ocean wind stress (SW), Southern Ocean gas-exchange efficiency (SG), or a combination of these (see Table S1 in the Supplement). The goal of these transient simulations is not to reproduce the last deglaciation but to assess the sensitivity of both marine radiocarbon and atmospheric $CO_2$ to a variety of changes in ocean ventilation (in terms of both the type of forcing and its magnitude), specifically where concurrent radiocarbon pro-

duction rate changes are either minimized (CONST-/FIX-) or maximized (INT-).

## 3 Results

Figure 5 illustrates zonally averaged radiocarbon age offsets (B-Atm) for the LGM, HS1, BA, and YD, in the Atlantic and Pacific basins, based on global interpolations of the compiled data (using the “baseline” data flags). Differences between each successive time-slice interpolation are shown in Fig. 6. Zonal averages and time-slice offsets for the Indian Ocean are shown in Fig. 7. Zonal averages for the EHOL and HOL, which differ only slightly from the modern field (Key et al., 2004), are shown in Fig. 8 and compared with the interpolated fields for the BA and LGM. As noted elsewhere (Skinner and Bard, 2022; Rafter et al., 2022), the current paucity of data from the Indian Ocean makes interpolations for this basin somewhat tentative and more strongly dependent on individual data points (Fig. 7). This highlights the Indian basin as an important target for future work reconstructing past B-Atm changes. Across all the time-slice interpolations, correlations between observed and interpolated values for the same locations yield $R^2$ values in the range 0.59–0.86. Because the interpolation is not performed on a 2D zonal plane, local B-Atm estimates may deviate from the zonal average where zonal gradients exist. Furthermore, the interpolations necessarily provide an average “snapshot” for an entire time slice and therefore will mask variability within the time slice. These aspects appear to be particularly relevant for HS1 in the Atlantic, as discussed below.

The global interpolations illustrated in Fig. 5 capture the main features of deglacial B-Atm evolution that have previously been identified in individual time series and in compiled time series that were grouped by basin and region, or water depth (Skinner and Bard, 2022). Broadly similar patterns have also been identified in averaged time series and 2D zonal projection contour plots of compiled data (Rafter et al., 2022). The main features include the following:

1. increased B-Atm offsets throughout the global ocean at the LGM as compared with the modern state (Fig. 8a, b, g, h), in particular > 2000 m water depth as demonstrated previously (Skinner et al., 2017) but with a slightly larger anomaly ~ 760 $^{14}$C yr;

2. a stepwise “rejuvenation” of the ocean interior across the last deglaciation;

3. evidence for positive B-Atm anomalies in the deep North Atlantic, from the LGM to HS1 and, again, from the BA to the YD, occurring in parallel with changes of broadly opposite sign in the Southern Ocean and the intermediate depth North Pacific (boxed areas in Fig. 6c, d, g, h);
<figure><img src="image_7.png" /></figure>

**Figure 5.** Zonally averaged interpolated B-Atm radiocarbon age offsets for the LGM, HS1, BA, and YD (Pacific zonal averages at left, Atlantic at right). Filled circles and shading indicate input data and values.

4. a marked “rebound” to lower B-Atm offsets throughout the ocean, from HS1 to the BA (Fig. 6e, f); and

5. a further rebound to lower B-Atm offsets in the deep North Atlantic, from the YD to the EHOL, again with evidence for changes of opposite sign in the Southern Ocean and intermediate depth North Pacific (boxed areas in Fig. 6a, b).

Perhaps the most striking aspect of the successive time-slice reconstructions is the marked drop in B-Atm offsets that coincides with the transition from HS1 to the BA (Fig. 6e, f), which involved positively correlated changes in B-Atm in the deep Southern Ocean and deep North Atlantic (Skinner et al., 2013), and which has been linked to an “overshoot” in B-Atm offsets at some locations (Barker et al., 2010; Hines et al., 2015). Notably, as shown in Fig. 8, the step change at the BA resulted in a global B-Atm distribution very similar to that

<figure><img src="image_8.png" /></figure>

**Figure 6.** Offsets between spatial B-Atm interpolations for successive time-slice reconstructions. Boxed areas highlight regions of the deep North Atlantic (> 0° N, > 2.5 km), deep Southern Ocean (> 30° S, > 2 km), and intermediate North Pacific (> 0° N, 0.9–2 km) and deep North Pacific (> 0° N, > 2 km), for which regional time-series splines are illustrated in Fig. 9. Broadly antiphased anomalies are indicated between the North Atlantic and Southern Ocean (especially the Atlantic sector), and between the North Atlantic and intermediate North Pacific.

of the late Holocene, despite representing the approximate temporal midpoint of deglaciation.

The features identified above can also be discerned in regional time-series averages (Skinner and Bard, 2022; Rafter et al., 2022). We show this here using cubic splines for North Atlantic, Southern Ocean, and North Pacific data grouped according to the boxed areas highlighted in Fig. 6. The resulting regional average splines are illustrated in Fig. 9b–d compared with global average B-Atm values derived for each successive time slice (Fig. 9d, filled circles; Table 1). During HS1 and the YD, the regional splines exhibit broadly antiphased trends in B-Atm between the deep North Atlantic and the deep Southern Ocean and intermediate North Pacific (Fig. 9, shaded vertical bars). The collected time series thus support
<figure><img src="image_9.png" /></figure>

**Figure 7.** Zonally averaged interpolated B-Atm radiocarbon age offsets in the Indian Ocean for the LGM, HS1, BA, and YD. Sparse data coverage is notable. Left: interpolated time-slice reconstructions (as for Fig. 5). Right: offsets between spatial B-Atm interlocations for successive time-slice reconstructions (as for Fig. 6).

the antiphase patterns apparent in the zonal averages shown in Fig. 6 (boxed areas). The averaged time series only tentatively support the suggestion of a “flipped” vertical radiocarbon gradient between the intermediate- and deep North Pacific at the LGM (Rafter et al., 2022), and more emphatically demonstrate this for the deglacial period that includes the YD, BA, and HS1. Indeed, during the BA, the North Pacific, North Atlantic, and Southern Ocean all exhibit B-Atm offsets at least as low as modern, resulting in global average B-Atm that also approaches the modern value and slightly “overshoots” relative to the subsequent YD (see Fig. 9d). Consistent with the fact that the Pacific accounts for ~50% of the global ocean volume and the Southern Ocean ventilates ~58% of the ocean interior (Primeau, 2005), Fig. 9 also shows that global average B-Atm estimates generally track the deep North Pacific and the deep Southern Ocean. Different patterns of variability are expressed in the North Atlantic

<figure><img src="image_10.png" /></figure>

**Figure 8.** Zonally averaged interpolated B-Atm offsets for the LGM, BA, EHOL, and HOL (Pacific zonal averages at left, Atlantic at right). Filled circles and shading indicate input data and values.

and the intermediate North Pacific, where more rapid and regionally important fluctuations are apparent (Freeman et al., 2015).

## 4 Discussion

In principle, evolving large-scale patterns of ocean-atmosphere radiocarbon age offsets (B-Atm) will primarily reflect the combined influences of (1) radiocarbon production, (2) ocean transports, (3) air-sea gas-exchange efficiency (especially in the regions of deep-water export), and (4) the changing contributions of different source regions to locations in the ocean interior. While the influence of atmospheric radiocarbon production changes on evolving B-Atm offsets is often ignored, it may in principle influence deep ocean B-Atm offsets through relatively rapid (i.e. sub-millennial) changes in atmospheric radiocarbon activity that are only conveyed to the deep ocean on the millennial timescale of ocean turnover (Adkins and Boyle, 1997). This can produce
<figure><img src="image_11.png" /></figure>

**Figure 9.** “Ventilation seesaws” across the last deglaciation based on cubic spline fits to compiled ocean–atmosphere radiocarbon age offsets (Skinner and Bard, 2022). Cubic splines with a stiffness factor of $10^{-9}$ are fit to all existing data, using updated age models and taking into account B-Atm uncertainties, and applying the same “baseline” data flags as for the time-slice interpolations. (a) Greenland temperature proxy (Svensson et al., 2008). (b) northeast Atlantic shallow sub-surface reservoir ages (dashed red line; Skinner et al., 2019); B-Atm from the North Atlantic 0.2–2 km (grey line, shaded red area); B-Atm from the deep North Atlantic > 2.5 km (blue line, shaded blue area). (c) B-Atm from the intermediate North Pacific 0.9–2 km (grey line, shaded red area); B-Atm from the deep North Pacific > 2 km (blue line, shaded blue area). (d) Mean ocean B-Atm estimates (black line and circles; see Table 1 “baseline” data flags) and compiled shallow sub-surface reservoir ages from the Southern Ocean (dashed red line; Skinner et al., 2019); B-Atm from the Southern Ocean < 2 km (grey line and shaded red area); B-Atm from the deep Southern Ocean > 2 km (blue line and shaded blue area). (e) Antarctic temperature proxy (EPICA Community Members, 2004; Lemieux-Dudon et al., 2010). Vertical lines and shaded bars indicate the timing of the LGM, HS1, BA, YD EHOL, and HOL time slices.

a convergence or divergence of marine and atmospheric radiocarbon ages, due to atmospheric radiocarbon changing quickly and the deep ocean remaining relatively invariant (Franke et al., 2008; Heaton et al., 2021).

Below, we discuss how all these processes have influenced marine radiocarbon cycling across the last deglaciation. Accordingly, we address (1) evidence for the operation of a “ventilation seesaw” that we emphasize was linked to *both* gas-exchange and transport anomalies emanating from the

main regions of deep- and intermediate water formation (i.e. the North Atlantic, Southern Ocean, and North Pacific); and (2) the potential for atmospheric radiocarbon dynamics (independent of ocean ventilation) to bias B-Atm offsets by ~hundreds of $^{14}$C yr, in particular during the apparent BA “overshoot”. We further seek to quantify the likely carbon cycle impacts associated with the observed global average B-Atm changes, and to reconcile these impacts with the evolution of the global radiocarbon budget since the last glacial period.

## 4.1 Ventilation “seesaws”: gas-exchange and transport effects

A survey of the modern ocean’s transport pathways indicates that ~86% of the ocean interior is sourced by water that last made contact with the atmosphere in three key regions: the Southern Ocean (contributing ~58%), the high latitude North Atlantic (contributing ~21%), and the North Pacific (contributing ~7%) (Primeau, 2005). These three regions account for ~31% of the ocean’s surface and “ventilate” ~86% of the ocean’s interior (Primeau, 2005). Although the long equilibration time for dissolved $\Delta^{14}$C(DIC) means that a water parcel’s point of last contact with the atmosphere will not necessarily be equivalent to its point of “radiocarbon equilibration” (high latitude sources are typically characterized by distinct levels of disequilibrium (Bard, 1988; Matsumoto, 2007), changes in the three main regions of deep-water export will exert a strong influence on temporal variations in the ocean interior’s radiocarbon distribution.

This expectation is clearly borne out in the global interpolations shown in Figs. 5 and 6, and in the regional stacks illustrated in Fig. 9. Deglacial changes in marine radiocarbon distribution were apparently dominated by anomalies extending from the North Atlantic (affecting the deep Atlantic in particular), coordinated with anomalies of broadly opposite sign originating in the Southern Ocean and North Pacific (Figs. 6 and 9). The time-slice interpolations and regional averages therefore cohere with numerous previous proposals for “ventilation seesaws” operating between the North Atlantic and the Southern Ocean (Broecker, 1998; Skinner et al., 2013, 2014; Menviel et al., 2018), and between the North Atlantic and North Pacific (Menviel et al., 2014; Freeman et al., 2015; Max et al., 2014; Okazaki et al., 2010; Walczak et al., 2020).

As suggested previously (Skinner et al., 2019; Skinner and Bard, 2022), Fig. 9 also shows that B-Atm offsets in the deep (> 2 km) North Atlantic (Fig. 9b, blue line and shaded area) exhibit a similar pattern of variability to that of the upper ocean (0.2–2 km) and surface “reservoir ages” in the region (Fig. 9b grey lines with shaded area, and dashed red lines). The same is apparent in the Southern Ocean (Fig. 9d). These relationships, and their further link to polar climate variability (Fig. 9a, e), suggest a mechanistic link between the observed deglacial B-Atm variability and the “thermal bipolar seesaw” (Stocker and Johnsen, 2003; EPICA Community
Members, 2006). This association most likely operated via coordinated changes in North Atlantic and Southern Ocean convection and advection (Broecker, 1998; Menviel et al., 2015; Skinner et al., 2014, 2020) associated with regional changes in sea ice (Skinner et al., 2019; Rae et al., 2018), winds (Sikes et al., 2016b; Menviel et al., 2018), and/or buoyancy forcing (Ferrari et al., 2014; Hines et al., 2019; Watson et al., 2015). The further coupling between the Southern Ocean and North Pacific has been proposed to relate to freshwater balance in the Pacific basin (Menviel et al., 2014), possibly influenced by changing moisture transports across the Isthmus of Panama (Leduc et al., 2007), and/or Cordilleran ice mass balance (Walczak et al., 2020).

While the “ventilation seesaws” noted above may reflect changes in ocean circulation to some extent, it is important to note that they also reflect changes in gas-exchange efficiency. This is demonstrated by the fact that

the amplitude of B-Atm variability in the shallow Atlantic 0.2–2 km water depth (e.g. Freeman et al., 2015; Chen et al., 2015) differs very little from that of surface “reservoir ages” in the northeast Atlantic (Fig. 9b, grey line and dashed red line). This implies a muted contribution from flow speed changes in the upper Atlantic < 2 km (Bradtmiller et al., 2014) and a dominant influence on radiocarbon signatures from gas-exchange (i.e. “pre-formed ages”) instead. Again, the same is true for the Southern Ocean, where B-Atm offsets from the shallow ocean (0.2–2 km) generally overlap with surface reservoir age reconstructions (Fig. 9d, grey line and dashed red line). Accordingly, B-Atm values at the LGM in mid-deaths may indeed have been consistent with the modern transport (Marchal and Zhao, 2021a).

In contrast, however, “pre-formed ages” cannot account for the amplitude of B-Atm changes observed in the deep Atlantic (Fig. 9b, blue line) and the deep Southern Ocean (Fig. 9d, blue line), indicating a more significant contribution from water sourcing and/or transport changes > 2 km, and perhaps between 2 and 3 km water depth in particular (Skinner et al., 2021; Lund et al., 2015; Rafter et al., 2022). The patchy response seen in the zonal average anomaly for the North Atlantic between HS1 and the LGM (Fig. 6h) contrasts with the clearer signal seen in individual and collected time series (Fig. 9b). In part, this likely reflects a spatially heterogeneous hydrographic response, both in the depth domain (Skinner et al., 2021; Lund et al., 2015) and in the eastern versus western North Atlantic (Gherardi et al., 2005; Ng et al., 2018). This interpretation is supported by the less ambiguous positive B-Atm anomaly seen in the deep North Atlantic regional time-series spline during HS1 (Fig. 9b, blue line and shaded area; see also Rafter et al., 2022).

The patchy spatial interpolation outcome for HS1 may also reflect a more complex pattern of ventilation during HS1 than is captured by a “collapsed AMOC” scenario that lasted until the onset of the BA, as indicated by a recent multi-proxy and modelling study (Pöppelmeier et al., 2023). Furthermore, in addition to tentative evidence for a “mid-HS1 B-Atm mini-

mum” (Skinner and Bard, 2022), there is evidence for a drop in B-Atm offsets at intermediate depths (< 2.5 km) in the western Atlantic late in HS1 (Robinson et al., 2005; Thigarajan et al., 2014), and evidence for declining B-Atm offsets in the Nordic Seas ~ 400 years prior to the onset of the BA (Muschitiello et al., 2019). Any such changes during HS1 will have been averaged out in our time-slice interpolation for 15–17.8 ka BP. These observations underline the need for further detailed reconstruction of the spatial expression and temporal evolution of ocean–atmosphere radiocarbon offsets across the North Atlantic during HS1, particularly with a view to disentangling transport and gas-exchange impacts.

Overall, the message that emerges from the collected data is that deglacial marine B-Atm changes throughout the global ocean were significantly influenced by *both* air–sea gas-exchange effects and mass transport effects (Koeve et al., 2015), with the latter primarily affecting parts of the deep ocean > 2 km, but with evidence for a complex response during HS1. The inferred spatial expression and coordination of both gas-exchange and transport effects in the Atlantic may have been related to changes in the spatial extent of different water masses in the deep ocean. This would be consistent with previous work where B-Atm offsets have been found to place stronger constraints on water mass “geometry” than, for example, AMOC strength per se (Muglia and Schmittner, 2021; Pöppelmeier et al., 2023). The influence of further non-ventilation effects at each time-slice is taken up in the following section.

## 4.2 “Attenuation biases” in B-Atm offsets at the BA

As noted above, global average B-Atm changes can occur independently of ventilation effects, due to rapid atmospheric radiocarbon variability to which the deep ocean is too slow to respond. We refer to such effects as “attenuation biases”, as they reflect the phase and attenuation response of a slowly adjusting reservoir (the global ocean interior), subject to continuous exchange with a more rapidly changing reservoir (the atmosphere) (Maier-Reimer and Hasselmann, 1987). The primary external (i.e. non-marine) driver for rapid atmospheric radiocarbon variability is likely to be changes in radiocarbon production (Köhler et al., 2022), though transient terrestrial carbon sources (e.g. from permafrost) might also be hypothesized (Köhler et al., 2014; Wu et al., 2022).

For attenuation biases in mean ocean B-Atm offsets to occur, atmospheric radiocarbon activity would have to change rapidly, that is, on a timescale that is shorter than the mean mixing time of the ocean (i.e. < 1000 years). Accordingly, gradual long-term trends in radiocarbon production are unlikely to produce significant attenuation biases, as is confirmed by model simulations where atmospheric radiocarbon production is based on relatively smooth trends in mean relative (geomagnetic) palaeointensity (RPI) (Dinauer et al., 2020). However, given the scatter amongst existing reconstructions of past radiocarbon production (e.g.
Laj et al., 2004; Adolphi et al., 2018; Nowaczyk et al., 2013; Channell et al., 2018), particularly on (sub-) millennial timescales, it remains unclear to what extent rapid (centennial or millennial) radiocarbon production variability and/or other non-marine carbon sources might have biased B-Atm offsets via their impact on the atmosphere. Therefore, to explore the maximum possible contribution of externally driven atmospheric radiocarbon variability to mean ocean B-Atm changes, we compare transient simulations using the Bern3D model where radiocarbon production rates or atmospheric radiocarbon are held constant (i.e. FIX- and CONST-, respectively) with simulations where nearly all variability in atmospheric radiocarbon is assumed to have occurred independently of ocean ventilation change (i.e. INT-, where atmospheric radiocarbon is prescribed according to *Intcal20*). The difference between the INT- simulations and their CONST/FIX- counterparts yields the *maximum* amplitude of B-Atm changes that could be produced independently of ocean ventilation change, for each idealized scenario. Indeed, as discussed below, these estimates are likely overestimates as they are premised on the assumption that all atmospheric radiocarbon variability occurred independently of ocean-atmosphere radiocarbon exchange, which is unlikely.

As illustrated in Fig. 10 (and summarized in Table S1), our idealized scenarios demonstrate three key points regarding the emergence of “attenuation biases” in B-Atm offsets:

1. These biases depend on the occurrence of rapid atmospheric variability that is not forced by ocean ventilation change, but they can in principle result in persistent long-term biases via an accumulation of centennial or millennial perturbations (e.g. as for a “random walk” process).

2. Such biases are time varying and may be positive relative to a given reference time (e.g. at the Laschamps event; Fig. 10a), negative (e.g. notably, at the BA onset; Fig. 10c), or nil (e.g. at the LGM; Fig. 10b), thus enhancing, diminishing, or not affecting the B-Atm changes that are expressed between time periods (Fig. 10d).

3. The relative contribution of such biases will be diminished and potentially eliminated to the extent that they coincide with large abrupt ocean ventilation changes (not included in our idealized model simulations), though it is apparent that their magnitude depends mainly on the amplitude of atmospheric radiocarbon production changes, as they yield a relatively invariant offset between the INT- and CONST/FIX- simulations for any given time slice; Fig. 10a–d).

It is important to stress that the true magnitude of such attenuation biases cannot be determined without prior detailed knowledge of the history and magnitude of both ocean ventilation changes and non-marine carbon and/or radiocarbon

inputs to the atmosphere. Nevertheless, two observations are worth underlining: the first is that maximum estimates of the attenuation biases that could hypothetically affect deglacial B-Atm offsets would only result in relatively minor biases in the incremental B-Atm changes between time slices (ranging from –227 to +25 $^{14}$C yr). Even if maximal attenuation biases are hypothesized, the observed deglacial mean ocean B-Atm trends must include a significant ventilation contribution. Indeed, such changes are directly attested to by proxy evidence for ocean transport and sea-ice change (McManus et al., 2004; Schüpbach et al., 2018), as well as the spatially heterogeneous patterns in marine B-Atm offsets that we present here (e.g. Figs. 6 and 9).

A second key observation is that correcting for such biases would tend to diminish the apparent “ventilation surge” that might be inferred from the change in B-Atm between HS and the BA (and more so between the LGM and the BA). Thus, if the rapid atmospheric radiocarbon decline across HS1 and at the onset of the BA were entirely driven by radiocarbon production changes and/or non-marine carbon inputs to the atmosphere, then the change in global average B-Atm between the LGM and the BA would be biased by at most ~227 $^{14}$C yr. In this case, radiocarbon ventilation ages during the BA would be ~227 $^{14}$C yr older than inferred from observed B-Atm offsets, resulting in a smaller radiocarbon ventilation change between the LGM and the BA. Non-ventilation biases affecting global average B-Atm differences between the LGM and the BA could therefore imply a smaller contribution from gas-exchange and transport rate changes to the apparent radiocarbon “ventilation surge” suggested for the BA in Fig. 6e and f. In this case, the “rejuvenation” of the marine radiocarbon pool may not in fact have been completed midway through deglaciation as initially apparent (Rafter et al., 2022). This inference would be more consistent with stable carbon isotope ($^{13}$C/$^{12}$C) evidence (Sikes et al., 2016b), which suggests an ongoing contribution to ocean-atmosphere carbon exchange well beyond the BA. Indeed, a significant portion of the convergence between marine and atmospheric radiocarbon observed at the BA may have been driven by “old” carbon release to the atmosphere, e.g. from melting permafrost (Köhler et al., 2014; Wu et al., 2022).

Although they remain difficult to accurately quantify, “attenuation biases” unrelated to ventilation are important to acknowledge, as these may exert a subtle yet potentially significant influence on our interpretation of transient changes in B-Atm offsets and their quantification, as illustrated above for the BA. These effects will need to be explored in greater detail in the future, a task that will inevitably require the use of numerical models and also require accurate knowledge of past radiocarbon production changes (Köhler et al., 2022; Dinauer et al., 2020). The accuracy of our existing radiocarbon production records is discussed further in Sect. 4.4.
<figure><img src="image_12.png" /></figure>

**Figure 10.** Model outputs from idealized “deglacial” scenarios illustrating hypothetical attenuation biases that are unrelated to ocean “ventilation” effects (indicated by horizontal offsets between similar symbol colours; horizontal arrow in panel (a)). Panel (a) shows 41 ka BP (coinciding with the Laschamps geomagnetic excursion), (b) the LGM, (c) the BA, and (d) the offset between the LGM and the BA. Data are expressed as 1000-years average anomalies relative to the pre-industrial period 4–5 ka BP, when atmospheric radiocarbon was relatively stable and therefore plausibly approached a pseudo-equilibrium state. In all panels, crosses indicate model experiments carried out with prescribed atmospheric radiocarbon as given by *Intcal20* (Reimer et al., 2020) (INT), circles are for atmospheric radiocarbon fixed at 140‰ (FIX), and triangles are for constant pre-industrial radiocarbon production rates (CONST). Symbol colours distinguish experiments carried out with altered Southern Ocean winds (purple), vertical diffusivity (red), Southern Ocean gas-exchange efficiency (green), or all combined (black). Four symbol sizes indicate the extent of parameter reduction: 0% (control, smallest symbols), 20%, 40%, 60%, and 80% (largest symbols). For CONST, only two sets of experiments were run: for control conditions and for all tuning variables reduced by 60%. Note that the impact on B-Atm due to reduced Southern Ocean winds (purple circles) is attenuated in well-equilibrated states (e.g. 41 ka and LGM), because of, for example, slow adjustments in the distribution of North Atlantic sourced deep water (see text).

## 4.3 Ventilation-related atmospheric CO₂ change

In theory, a broadly linear relationship between atmospheric CO₂ change and global average marine radiocarbon age anomalies is to be expected when these are driven by gas-exchange and/or transport rates (Skinner and Bard, 2022; Skinner et al., 2017). This is because (1) longer residence times in the ocean interior result in greater respired carbon accumulation along with greater radiocarbon decay, and (2) restricted gas exchange in regions of “upwelling” and/or deep mixing impede the conversion of respired and/or disequilibrium carbon to equilibrium carbon (Eggleston and Galbraith, 2018) while also impeding the invasion of radiocarbon into the ocean.

Our model sensitivity tests, involving shifts in vertical diffusivity, Southern Ocean winds, and/or gas exchange, cohere with a number of existing simulations using box models and Earth system models of intermediate complexity (e.g. Tschumi et al., 2011; Kwon et al., 2011; Skinner and

Bard, 2022), confirming a broad relationship between B-Atm anomalies and associated atmospheric CO₂ change (Fig. 11a, Table 2), despite large differences in model experiment setup. These experiments include the effects of pCO₂ changes on air–sea ¹⁴C exchange (Galbraith et al., 2015; Bard, 1988). Our sensitivity tests indicate consistent sensitivities for individual suites of experiments, e.g. for varying Southern Ocean winds, vertical diffusivity, or Southern Ocean gas-exchange rates. However, depending on the processes responsible for altering deep ocean ventilation, modelled sensitivities span a range of approximately ±50% for a given magnitude of B-Atm change. Furthermore, the sensitivities may vary with perturbation timescale, with different impacts on millennial timescales than on glacial-interglacial or longer timescales (Jeltsch-Thömmes and Joos, 2020). For example, a reduction in Southern Ocean winds draws down atmospheric CO₂ and increases global average B-Atm on a timescale of ~2000 years via impacts on gas-exchange
rates and upper ocean turnover (Fig. 11a). However, after ~5000 years (see Fig. S1) the mean ocean B-Atm response is diminished, primarily due to the spin up of North Atlantic deep water, which replaces southern sourced water in the deep Atlantic. A muted B-Atm response can therefore be seen for stronger Southern Ocean wind forcing in the 50 ka simulations illustrated in Fig. 10a (purple symbols). Despite their potential role in transient millennial scale pulses, Southern Ocean winds are therefore unlikely to account for long-term glacial-interglacial B-Atm changes, at least in the absence of further forcing to suppress North Atlantic ventilation (Menviel et al., 2018).

The broadly linear scaling apparent in the suite of PI model sensitivity tests is consistent with basic theory (Skinner et al., 2017; Skinner and Bard, 2022), based on a two-box ocean connected to an atmosphere to form a closed system (Fig. 11a, solid line). This simple inventory theory predicts a higher sensitivity for higher global export productivity and/or a higher “Revelle buffer factor” (i.e. higher background atmospheric $pCO_2$), all else being equal. Clearly, the marine carbon cycle response to the variety of ventilation processes that can affect radiocarbon cannot be reduced to a single linear scaling. However, the degree of consistency in the parallel sensitivities of atmospheric $CO_2$ and marine B-Atm offsets implies that the wide range of modelled sensitivities may be approximated by a theoretical prediction using an arbitrary ±50% range in export productivity as a tuning parameter in the two-box ocean model (Fig. 11a, dashed lines). This theoretical scaling, arbitrarily tuned to the range of more complex model outputs, would suggest ~6.3 ± 3.2 ppm $CO_2$ change per 100 $^{14}$C yr of global mean B-Atm change. Such a sensitivity would tentatively imply a drawdown of atmospheric $CO_2$ by ~50 ± 27 ppm associated with an increase in global average B-Atm by ~789 ± 32 $^{14}$C yr, as reconstructed for our “baseline” data flag scenario at the LGM and assuming a maximum “attenuation bias correction” (Table 1). Estimates based on uncorrected B-Atm offsets and/or on alternative data flagging scenarios (Table 1) differ by up to ~8 ppm. These estimates should be interpreted as indicating a non-negligible contribution to deglacial $CO_2$ rise, perhaps equivalent to over a third of the total glacial-interglacial atmospheric $CO_2$ change.

Interestingly, observed global average B-Atm estimates also loosely correlate with observed atmospheric $CO_2$ changes across the last deglaciation (Fig. 11b, open triangles). The correlation with observed $pCO_2$ anomalies, particularly for the BA, is improved when global average B-Atm is “corrected” for maximal possible attenuation biases as discussed above (Fig. 11b, filled triangles). The similarity of the observed correlation and the modelled $CO_2$ sensitivity (Fig. 11b, dashed and solid red lines) again merely suggests that a significant portion of the incremental changes in atmospheric $CO_2$, stepping through the deglaciation from the LGM to the early Holocene, could in principle be accounted for by ocean ventilation changes that influenced

<figure><img src="image_13.png" /></figure>

**Figure 11.** Panel (a) shows theoretical and modelled sensitivity of atmospheric $CO_2$ anomalies and mean ocean radiocarbon ventilation age (B-Atm) anomalies to air-sea gas-exchange and transport changes. Filled diamonds indicate model sensitivity tests from this study, based on step changes under PI conditions and 2000 years of equilibration time (purple: Southern Ocean wind, red: vertical diffusivity, green: Southern Ocean gas-exchange efficiency). Open diamonds are Southern Ocean wind experiments (Tschumi et al., 2011). Filled squares are wind and/or diffusivity experiments using an idealized radiocarbon-like tracer (Kwon et al., 2011). As terisks and open circles represent two- and three-box model experiments, with varying overturning rates ($F$) and “high latitude” gas-exchange rates (gas), respectively. A median theoretical sensitivity is indicated by the solid and dashed red lines, derived for the two-box model results (Skinner and Bard, 2022), equivalent to ~6.3 ± 3.2 ppm $CO_2$ change per 100 $^{14}$C yr of global radiocarbon ventilation age change. Panel (b) shows observed values of coincident global average B-Atm and atmospheric $pCO_2$, expressed as time-slice anomalies versus pre-industrial values. Open triangles show paired observations of mean ocean B-Atm (this study) and atmospheric $CO_2$ (Monnin et al., 2001; Marcott et al., 2014). Filled triangles show observed B-Atm age offsets corrected for hypothetical “non-ventilation” biases (see text). Solid and dashed red lines in (b) show the same theoretical sensitivities as for (a), offset by ~30 ppm to aid comparison with observed trends.
<table><caption>**Table 2.** B-Atm and atmospheric CO₂ results for sensitivity experiments carried out using the Bern3D model with varying Southern Ocean (SO) wind, gas exchange, or global vertical diffusivity (illustrated in Fig. 10). Results are evaluated 2000 years after forcing is applied (see text).</caption><thead><tr><th>Scenario</th><th>Ventilation parameter changed</th><th>Reduction (%)</th><th>B-Atm</th><th>pCO<sub>2</sub></th><th>Δ(B-Atm)</th><th>Δ(pCO<sub>2</sub>)</th></tr></thead><tbody><tr><td>PI (ctrl)</td><td>none</td><td>0</td><td>1428</td><td>276.5857</td><td>0</td><td>0</td></tr><tr><td rowspan="4">PI</td><td rowspan="4">SO wind</td><td>20</td><td>1495</td><td>270.2083</td><td>67</td><td>-6</td></tr><tr><td>40</td><td>1548</td><td>264.4817</td><td>120</td><td>-12</td></tr><tr><td>60</td><td>1577</td><td>260.3277</td><td>150</td><td>-16</td></tr><tr><td>80</td><td>1588</td><td>259.9954</td><td>160</td><td>-17</td></tr><tr><td rowspan="4">PI</td><td rowspan="4">SO gas exchange</td><td>20</td><td>1472.1</td><td>275.7578</td><td>44</td><td>-1</td></tr><tr><td>40</td><td>1523.3</td><td>274.6609</td><td>96</td><td>-2</td></tr><tr><td>60</td><td>1585.5</td><td>272.8658</td><td>158</td><td>-4</td></tr><tr><td>80</td><td>1662.4</td><td>269.6315</td><td>235</td><td>-7</td></tr><tr><td rowspan="4">PI</td><td rowspan="4">Vertical diffusivity</td><td>20</td><td>1480.3</td><td>273.7565</td><td>53</td><td>-3</td></tr><tr><td>40</td><td>1523.6</td><td>271.5337</td><td>96</td><td>-5</td></tr><tr><td>60</td><td>1564.6</td><td>269.6152</td><td>137</td><td>-7</td></tr><tr><td>80</td><td>1597.5</td><td>268.211</td><td>170</td><td>-8</td></tr></tbody></table>

global average B-Atm offsets. Although the steeper dashed line in Fig. 11b would imply a maximal ~80 ppm contribution to deglacial atmospheric CO₂ rise due to ocean ventilation alone, we believe this is unlikely. Rather, the observed correlation between atmospheric CO₂ and global average B-Atm offsets more likely implies a mixture of direct and indirect causal connections that may have been coordinated by the thermal bipolar seesaw. Direct impacts of ocean ventilation on atmospheric CO₂ (e.g. Fig. 11a) would therefore have coincided with contributions from linked processes, such as ocean temperature change, export productivity anomalies, and others (Marchal et al., 1998; Menviel et al., 2008; Jochum et al., 2022; Gottschalk et al., 2019; Menviel et al., 2012), or indeed long-term Southern Ocean wind changes that have had little effect on mean ocean B-Atm.

In any event, if mean ocean B-Atm changes scale in a consistent manner with marine CO₂ sequestration changes (as suggested by simple inventory theory and the relationships in Fig. 11a), then the ocean ventilation contribution to deglacial atmospheric CO₂ rise would have been primarily associated with HS1, the BA, and the YD. The magnitude of ocean ventilation impacts on CO₂ after ~15 ka BP appear to hinge crucially on attenuation biases that may have affected B-Atm offsets during the BA. Nevertheless, the increase in atmospheric CO₂ observed across the Holocene coincided with rather muted changes in global average B-Atm and low potential for significant attenuation biases. This suggests a minor role for ocean ventilation in CO₂ rise from the onset of the Holocene, which would be consistent with the inference that CO₂ rise from ~6 ka BP was primarily linked to changes in ocean temperature, the terrestrial biosphere, coral reef formation and carbonate preservation (i.e. ocean alkalinity), and/or the solid earth (i.e. volcanism) (Joos et al., 2004; Broecker and Clark, 2007). This observation might also res-

onate with the speculative proposal of a “natural tendency” for atmospheric CO₂ decline across an interglacial due to ocean ventilation processes (Barker et al., 2019).

## 4.4 Towards a closure of the global carbon and radiocarbon cycles since the LGM

The reconciliation of past radiocarbon production changes with records of atmospheric pCO₂ and Δ¹⁴C (hereafter Δ¹⁴C_atm) across the last deglaciation represents a long-standing puzzle that remains unresolved (Bard, 1998). This puzzle has a direct bearing on our understanding of past atmospheric pCO₂ change, as well as our understanding of geomagnetic and solar variability (Heaton et al., 2021). The record of atmospheric radiocarbon variability indicates a significant decrease across the last deglaciation, equivalent to a change in Δ¹⁴C_atm of just over ~400‰ (Reimer et al., 2020) (Fig. 12b, blue line). If there were no change in the steady state global radiocarbon inventory, the 90 ppm increase in atmospheric pCO₂ that occurred since the last glacial period would alone account for only ~25‰ of this change (Bard, 1998; Siegenthaler et al., 1980). This implies a dominant role for changes in the global radiocarbon budget (i.e. radiocarbon production) and/or the distribution of radiocarbon between atmosphere and other carbon reservoirs (i.e. the carbon cycle).

Model simulations of deglacial radiocarbon production and atmospheric radiocarbon and pCO₂ consistently indicate that past Δ¹⁴C_atm cannot be accounted for by existing reconstructions of changing radiocarbon production alone (e.g. Hain et al., 2014; Köhler et al., 2006; Dinauer et al., 2020; Köhler et al., 2022). Earth system model simulations applying mean relative palaeomagnetic intensity- (RPI) based radiocarbon production rate changes (Dinauer et al., 2020),
<figure><img src="image_14.png" /></figure>

**Figure 12.** Observed and modelled atmospheric and marine radiocarbon, compared with radiocarbon production rates, and atmospheric CO₂. Panel (a) shows relative radiocarbon production rates. Shaded area: full range of reconstructed values (Laj et al., 2000, 2004; Adolphi et al., 2018; Channell et al., 2018; Nowaczyk et al., 2013); solid black line: mean RPI (Laj et al., 2000, 2004; Channell et al., 2018; Nowaczyk et al., 2013); thick blue line: as inferred from an idealized model scenario to match *Intcal20*, INT_ALL60 (1 kyr moving average; this study). Panel (b) shows atmospheric Δ¹⁴C anomalies normalized to modern values: prescribed in the INT_ALL60 model scenario (i.e. *Intcal20*, Reimer et al., 2020; solid dark blue line; this study); driven only by inferred production rates that match *Intcal20* (INT_ALL60-CONST_ALL60; dashed blue line; this study); driven only by mean RPI production rates (solid black line; Dinauer et al., 2020); driven only by carbon cycle and ventilation changes in the CONST-ALL60 model scenario (dashed grey line; this study); simulated with the BICYCLE box model (Köhler et al., 2006) using ¹⁰Be-based (Muscheler et al., 2005) radiocarbon production estimates and a full carbon cycle scenario (dashed orange line). Panel (c) shows B-Atm radiocarbon age offset anomalies relative to modern values: Bern3D and BICYCLE model outputs as for (b); and inferred from time-slice interpolations (filled black circles and line; this study), including a maximal correction for “attenuation biases” (open black circles and dashed line), with the full range of reconstructed values (shaded area) due to uncertainties, corrections, and alternative data flagging scenarios (see Table 1). Panel (d) shows atmospheric CO₂ normalized to LGM values: from EDC (red line; Monnin et al., 2001); inferred from observed mean “corrected” ocean B-Atm using a sensitivity of ~-6.3 ± 3.2 ppm per 100 ¹⁴C yr (open black circles and line with shaded range; this study); and simulated in the Bern3D model for the INT_ALL60 scenario that is also illustrated in (a)–(c).

yield only a small increase (~150‰) in Δ¹⁴C_atm at the LGM relative to the late Holocene (Fig. 12b, black line). Similar Δ¹⁴C_atm changes are obtained using alternative radiocarbon production histories (Hain et al., 2014; Köhler et al., 2006; Dinauer et al., 2020; Köhler et al., 2022). The widely recognized implication of these results is that additional carbon cycle changes (i.e. altered rates of carbon exchange with other reservoirs) and/or different radiocarbon production changes are required in order to account for the observed Δ¹⁴C_atm amplitude.

Turning to carbon cycle changes first, given the tight coupling of the marine and atmospheric carbon pools, altered exchange rates between the ocean and atmosphere are likely to have played a leading role in deglacial Δ¹⁴C_atm variability (Muscheler et al., 2004). Arguably for the first time, our global average B-Atm estimates confirm such a role. Indeed, our mean ocean B-Atm estimates indicate a lower average exchange rate of radiocarbon (and likely CO₂) between the ocean and atmosphere during the last glacial period, and an increase in this exchange rate across the deglaciation (Fig. 12c, black line and circles). All else being equal, an increase in ocean-atmosphere radiocarbon exchange would result in a drop in Δ¹⁴C_atm during deglaciation, in parallel with a decrease in marine B-Atm offsets, as observed in Fig. 12b and c. Such changes would have also contributed to deglacial atmospheric CO₂ rise (e.g. Muglia et al., 2018; Khatiwala et al., 2019; Brovkin et al., 2012; Ganopolski and Brovkin, 2017). As discussed above, a tentative quantification of this contribution to atmospheric CO₂ rise can be derived from the observed mean ocean B-Atm (Table 1) and modelled sensitivities (Fig. 11a), as illustrated in Fig. 12d (open circles and shaded region). This tentative contribution compares well with simulated CO₂ effects in the Bern3D model (INT_ALL60), bearing in mind that the simulated ageing of the global ocean is only ~50% of that observed (Fig. 12c, blue line and dashed grey line) and that ~50% of the simulated CO₂ signal derives from ocean ventilation impacts alone.

While the observed mean ocean B-Atm estimates suggest a significant impact on the carbon cycle, the observed changes are still too small to account for the observed ~400‰ drop in Δ¹⁴C_atm across the deglaciation. This is demonstrated by model simulations that produce a mean ocean ageing of ~500 ¹⁴C yr (~63% of the observed value; Table 1) and yield a Δ¹⁴C_atm increase of only ~56‰, or ~14% of observed (Fig. 12b, dashed grey line). Similar results have been obtained using the BICYCLE box model (Köhler et al., 2006), which produced a Δ¹⁴C_atm increase of only ~200‰ at the LGM (~50% of observed), despite yielding mean ocean B-Atm offsets that match our observed values (Fig. 12b, c, dashed orange line). A mismatch was also obtained for the LGM using the CLIMBER intermediate complexity model (Ganopolski and Brovkin, 2017), where a 20% higher radiocarbon production rate, combined with reduced ocean ventilation causing a global mean B-Atm in-
crease of ~800 years (again in line with our LGM estimate), coincided with a $\Delta^{14}$C$_{atm}$ increase of only ~280‰ (~70% of observed).

Therefore, existing radiocarbon production records cannot account for past atmospheric radiocarbon variability, either alone or in conjunction with ocean ventilation changes that are consistent with global mean B-Atm estimates (Fig. 12b, c). While there remain uncertainties in atmospheric radiocarbon reconstructions, these are likely on the order of ~1% (Reimer et al., 2020), and it seems highly unlikely that $\Delta^{14}$C$_{atm}$ variability over the last glacial cycle has been significantly overestimated. Similarly, it seems implausible (though clearly not impossible) that existing marine radiocarbon data significantly underestimate the magnitude of mean ocean B-Atm change since the last glacial period. The problem of closing the global radiocarbon budget since the last glacial period becomes even more difficult if volcanic/metal-morphic CO$_2$ inputs are invoked as a significant contributor to the global carbon pool during the last glacial period (Stott et al., 2019, 2009) or if no change in ocean ventilation is inferred (Stott et al., 2021).

Given the wide range of existing radiocarbon production estimates (e.g. as compiled by Dinauer et al., 2020; Fig. 12a, shaded area), it seems reasonable to postulate that existing production reconstructions might, on average, underestimate the amplitude of radiocarbon production rate change between the last glacial and the late Holocene, as suggested by a recent box-model study (Köhler et al., 2022). A “po-lar bias” in radiocarbon production records derived from ice-core $^{10}$Be fluxes has indeed been recently quantified sepa-rately for the geomagnetic and heliomagnetic modulations of cosmogenic production (Adolphi et al., 2023). Neverthe-less, it has also been noted that correcting for the identified long-term geomagnetic bias in $^{10}$Be would not eliminate the mismatch between observed and modelled $\Delta^{14}$C$_{atm}$ at the LGM (Adolphi et al., 2023). Our idealized simulations with prescribed $\Delta^{14}$C$_{atm}$ allow us to infer the radiocarbon pro-duction changes that would be needed to reconcile imposed ventilation and carbon cycle changes with observed atmo-spheric $\Delta^{14}$C$_{atm}$ (Fig. 12b, blue line. The rapid deglacial fluctuations in production that are inferred in this way (e.g. across HS1, the BA, and YD) almost certainly reflect biases due to transient carbon cycle and ocean ventilation changes that have not been implemented in our idealized simulations (see Sect. 2.5). However, the longer-term trend in inferred production rates indicates levels at the LGM that are close to the high end of the existing range of estimates (Fig. 12a, shaded area). A similar result has recently been obtained using the BICYCLE box model (Köhler et al., 2022). The higher radiocarbon production rates that are inferred at the LGM would have had a significant impact, possibly account-ing for the majority of the deglacial atmospheric radiocarbon signal (Fig. 12b, dashed blue line). The implication of these results is that a parallel closure of the radiocarbon and carbon cycles since the last glacial period might yet be obtained by

exploiting the plausible range of reconstructed radiocarbon production rates (Köhler et al., 2022). Our global average B-Atm estimates provide a useful new constraint for achieving this goal.

## 5 Conclusion

We present spatial interpolations of compiled radiocarbon data for a suite of time slices spanning the last deglaciation. The primary purpose of these interpolations is to derive global average B-Atm estimates. A clear trend in global average B-Atm offsets is apparent since the LGM (when B-Atm was ~760 $^{14}$C yr higher than today on average), demonstrat-ing unambiguous changes in the partitioning of radiocarbon between the ocean and atmosphere across the last deglaciation.

The spatial interpolations cohere with previous studies in indicating a stepwise and spatially heterogeneous rejuvena-tion of the ocean interior across the last deglaciation, and in suggesting the operation of a “ventilation seesaw” between the North Atlantic and both the North Pacific and Southern Ocean, especially during HS1 the YD.

A comparison of surface-, shallow-, and deep-water B-Atm trends indicates that transport changes in the upper ocean across the last deglaciation were likely modest (Mar-chal and Zhao, 2021a) and that B-Atm changes in the up-per ocean (<2 km) were more strongly influenced by gas-exchange efficiency changes at high latitudes. In contrast, a more significant contribution from transport and/or water mass geometry is apparent in the deeper ocean (> 2 km).

The time-slice reconstructions emphasize a widespread drop in B-Atm at the onset of the BA, resulting in a global average B-Atm within ~100 $^{14}$C yr of modern global average. However, model sensitivity tests indicate that a portion of this B-Atm drop could have resulted from atmospheric ra-diocarbon dynamics that were independent of ocean ventila-tion (radiocarbon production, terrestrial carbon release, etc.). The exact magnitude of this effect cannot yet be quantified, but a maximum bias of ~-190 $^{14}$C yr relative to the LGM is estimated. Such a bias would imply that mean ocean B-Atm at the BA underestimates the true “ventilation age” of the ocean.

Model sensitivity tests further suggest a direct relation-ship between global average B-Atm anomalies and atmo-spheric CO$_2$ change, with a tentative average sensitivity of ~-6.3 ppm CO$_2$ per 100 $^{14}$C yr. On this basis, our global average B-Atm estimates would imply a non-negligible con-tribution to atmospheric CO$_2$ change across the last deglaciation (perhaps as much as > 30% of the total observed). Global average B-Atm estimates also suggest that any venti-lation contribution to atmospheric CO$_2$ change was concen-trated during HS1, the BA, and the YD, and was largely ex-hausted by the onset of the Holocene.
While our results serve to underline, and tentatively to quantify, the ocean's role in deglacial carbon cycle change, they also demonstrate that a complete closure and reconciliation of the radiocarbon and carbon cycles since the last glacial remains to be achieved. Our results point to the possibility that, on average, existing reconstructions may tend to underestimate radiocarbon production rates during the last glacial period. Further work to improve the accuracy of past radiocarbon production rate estimates therefore emerges as a priority.

**Data availability.** Data lodged with PANGAEA include the compiled radiocarbon data and regional splines (https://doi.org/10.1594/PANGAEA.960693, Skinner et al., 2023a), netCDF files of zonally averaged time-slice interpolations (https://doi.pangaea.de/10.1594/PANGAEA.962525, Skinner et al., 2023b), and global average B-Atm estimates derived for each time slice from the global interpolations (https://doi.pangaea.de/10.1594/PANGAEA.962526, Skinner et al., 2023c).

**Video supplement.** Animation of zonal average time-slices spanning the last deglaciation, derived from global interpolations of compiled radiocarbon data (https://doi.org/10.5446/63113, Skinner, 2023).

**Supplement.** The supplement related to this article is available online at: https://doi.org/10.5194/cp-19-2177-2023-supplement.

**Author contributions.** LS designed the study, compiled and processed the radiocarbon data, and performed the interpolations with the assistance of FP. FP developed the interpolation code, and LS and FP analysed the interpolation outputs. Numerical model runs using Bern3D were performed by AJT and analysed by AJT, FJ, and LS. LS wrote the manuscript with input from all co-authors.

**Competing interests.** The contact author has declared that none of the authors has any competing interests.

**Disclaimer.** Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

**Acknowledgements.** This work benefited from discussions during the INQUA IPODS working group meeting held in Cambridge, UK, in 2018. Luke Skinner acknowledges support from the Royal Society, the Cambridge Isaac Newton Trust, and the NERC

OCEAN-14 and ROGUE-14 projects. Aurich Jeltsch-Thömmes and Fortunat Joos acknowledge funding from the Swiss National Science Foundation. The authors are particularly grateful to Laurie Menviel for assistance with accessing the LOVECLIM results used to test the interpolation method, as well as Patrick Rafter, Ning Zhao, Dan Amrhein, and Olivier Marchal for helpful discussions. This study was initiated in 2019 and initially submitted for review in 2021, and we are grateful for the constructive comments of one anonymous reviewer at that stage and the comments of Juan Muglia and an anonymous reviewer at a later stage, all of which helped to improve the manuscript.

**Financial support.** This research has been supported by the Natural Environment Research Council (grant no. NE/L006421/1), the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (grant no. SNF 200020_200511) and NERC (grant no. NE/V011464/1).

**Review statement.** This paper was edited by Qiuzhen Yin and reviewed by Juan Muglia and one anonymous referee.

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