2.1 Marine20 vs. LSG OGCM

Marine20 uses a transient application of the BICYCLE carbon cycle box model (Köhler et al. Reference Köhler, Muscheler and Fischer2006, Reference Köhler, Fischer and Schmitt2010). While Marine20 does incorporate the major changes in the global carbon cycle that occurred during the glacial, it only aims to summarize their wide-scale effect on large ocean areas. The resultant Marine20 curve, and its ${R^{Global}}\left( \theta \right)$ , should therefore only be viewed as providing a global-scale estimate of changes over time in oceanic ¹⁴C levels (Heaton et al. Reference Heaton, Köhler, Butzin, Bard, Reimer, Austin, Bronk Ramsey, Grootes, Hughen and Kromer2020, Reference Heaton, Bard, Bronk Ramsey, Butzin, Hatte, Hughen, Köhler and Reimer2022). If there are additional localized effects in a study location that are temporally varying, for example, if regional sea-ice was not present during the Holocene but likely extensive during the glacial, then a Marine20 user must incorporate those effects through adjustments to the regional ${\rm{\Delta }}R\left( \theta \right)$ .

The LSG OGCM (Butzin et al. Reference Butzin, Heaton, Köhler and Lohmann2020) is able to provide more localized ocean modeling, generating estimates of ¹⁴C levels and MRA at specific marine locations on a 2.5º by 2.5º grid (see Figure 2). However, the LSG OGCM is much slower to run than BICYCLE. The LSG OGCM estimates are run under fixed climate scenarios as well as being model-specific. This currently makes it difficult to use the LSG OGCM to fully understand the uncertainties in local MRAs since knowledge regarding the appropriate glacial climate and carbon cycle to apply is highly imprecise. LSG OGCM estimates of overall MRA are available, forced by the IntCal20 posterior mean for atmospheric ¹⁴C concentrations (Reimer et al. Reference Reimer, Austin, Bard, Bayliss, Blackwell, Ramsey, Butzin, Cheng, Edwards and Friedrich2020), under three specific climate scenarios (Butzin et al. Reference Butzin, Prange and Lohmann2005):

• PD—a climate scenario intended to be very similar to the present day.

• GS—a glacial climate scenario representing the Last Glacial Maximum (LGM), featuring a shallower AMOC weakened by about 30% compared to PD.

• CS—a more extreme glacial climate scenario aiming to mimic cold stadials with further AMOC weakening by about 60% compared with PD.

Figure 2 Location-specific estimates, at 0 cal yr BP, of the overall MRA, ${R^{Location}}\left( \theta \right)$ , obtained by the LSG OGCM under the PD scenario. The plotting color represents the MRA value with scale shown on RHS (in ¹⁴C yrs); white represents land. Three line transects are shown passing through the South Pacific (purple 160ºW), North Pacific (yellow 170ºW), and North Atlantic and Arctic (green 20ºW). We highlight sample sites on each transect which are used later (in Figure 3) to illustrate the potential changes in surface-water ¹⁴C depletion under various glacial scenarios as we extend into higher-latitude oceans.

While designed to incorporate more of the localized variations in surface-ocean ¹⁴C depletion, the LSG OGCM estimates do not incorporate every potential influence and are model specific. Consequently, they still require a regional correction $\Delta {R^{LSG}}$ (equivalent to a ${\rm{\Delta }}{R_{20}}$ ) if they are to be used for calibration. This $\Delta {R^{LSG}}$ would typically be obtained by comparing known-age ¹⁴C samples from the recent past against the corresponding PD scenario output from the nearest open-ocean LSG OGCM location (analogous to the calculation of a ${\rm{\Delta }}{R_{20}}$ ). Using the LSG OGCM outputs directly for calibration is therefore non-trivial; and since they are run under fixed climate scenarios, calibration against any one scenario will still give overprecise calendar ages. However, we believe that the constant-state GS scenario provides a reasonable upper bound for the level of oceanic ¹⁴C depletion during the glacial. More detail on both construction of the BICYCLE/Marine20 and the LSG OGCM estimates can be found in Supplementary Information A.

To justify our proposed approach to polar calibration using Marine20, we demonstrate that a user can approximately recreate the regional LSG OGCM estimates while maintaining use of the global-scale Marine20 through a simple modification, or boost, to their ${\rm{\Delta }}{R_{20}}\left( \theta \right)$ . Our approach relies on three key elements. Firstly, that each climate scenario of the LSG OGCM output can be approximated by applying a constant (not time dependent) shift to Marine20’s $R_{20}^{Global}\left( \theta \right)$ . Consequently, we can effectively transition to the different LSG OGCM scenarios, while retaining the use of Marine20, just by applying a static (constant) shift to a present-day estimate of ${\rm{\Delta }}{R_{20}}$ . Secondly, in low-latitude locations (within 40ºS to 40ºN) the uncertainty bands on Marine20 already encapsulate the LSG OGCM scenarios. Thirdly, that by latitudinally averaging the boost required to match the LSG OGCM scenario, we reduce the influence of the model specificity of the LSG OGCM (for example, the precise location and dynamics of sea-ice and freshwater balance) and simplify the application of our proposed calibration approach.

We propose using the GS scenario of the LSG OGCM as the upper bound for surface ocean ¹⁴C depletion in the glacial. However, should a user decide that they wish to bound their glacial climate with the more extreme CS scenario, a similar set of findings hold. The corresponding CS-based upper bound on the glacial boost to ${\rm{\Delta }}{R_{20}}$ can be found in Table A2 (Appendix) and the Supplementary Information (Figures S3–S6 in Supplementary Info C, and accompanying spreadsheet in Supplementary Info D).

2.2 Illustrative Regional Estimates of MRA

The LSG OGCM surface-water estimates are provided every 50 cal yrs for open ocean regions. For both the GS and CS scenarios, the Pacific was disconnected from the Arctic Ocean because the Bering Strait (which is currently shallower than 50 m in depth) was closed during the glacial sea-level lowstand (Jakobsson et al. Reference Jakobsson, Pearce, Cronin, Backman, Anderson, Barrientos, Björk, Coxall, de Boer and Mayer2017). Global sea-levels during the glacial are believed to have been in the order of 130m lower than those of the present day (Lambeck et al. Reference Lambeck, Rouby, Purcell, Sun and Sambridge2014).

To illustrate our proposed approach, we consider three transects (Figure 2). The first (in purple) passes through the Southern Pacific Ocean at a longitude of 160ºW. The second (in yellow) through the Northern Pacific at a longitude of 170ºW. During the glacial period this transect becomes cut-off from the Arctic Ocean further North by closure of the Bering Strait. The third transect (in green) passes through the Atlantic and into the Arctic at a longitude of 20ºW. The estimates along these transects are typical of the LSG OGCM outputs. In Figure 2, we plot the spatial MRA estimates provided by the LSG OGCM under the PD scenario at 0 cal yr BP (i.e., 1950 CE).

To enable comparison of the LSG OGCM estimates with Marine20 we must account for the shifts (denoted ${\rm{\Delta }}{R^{LSG}}$ and ${\rm{\Delta }}{R_{20}}$ respectively) that would need to be applied to each estimate. For each location, we have calculated the difference between the mean (in ¹⁴C yrs) of the PD scenario of the LSG OGCM from 11,500–0 cal yr BP and the mean of the $R_{20}^{GlobalAv}\left( \theta \right)$ in the same period. This difference has then been used to shift both the PD and GS outputs of the LSG OGCM for that location. Figure 3 presents these shifted location-specific estimates of the MRA over time along the three selected transects under both the PD and GS scenario of the LSG OGCM; and the equivalent estimates with Marine20. For each location, the mean over the 11,500–0 cal yr BP period of $R_{20}^{GlobalAv}\left( \theta \right)$ and the shift-adjusted PD outputs of the LSG OGCM are equal. Applying such a shift to both the PD and GS outputs of the LSG OGCM enables comparison between the calibration one would achieve using Marine20 (with a constant estimate of ${\rm{\Delta }}{R_{20}}$ based on recent-past/Holocene ¹⁴C data), and that obtained using the LSG OGCM outputs (with a constant $\Delta {R^{LSG}}$ based on the same recent-past/Holocene ¹⁴C data). We do not show the GS estimates from 11,500–0 cal yr BP as this climate scenario is inappropriate for the Holocene.

Figure 3 Comparing the Marine20, PD and GS estimates for the MRA at marine locations along the line transects shown in Figure 2 passing through the: (a) South Pacific Ocean; (b) North Pacific Ocean; (c) North Atlantic and Arctic Oceans. Shown in black is the estimate of ${\rm{R}}_{20}^{{\rm{GlobalAv}}}\left( {\rm{\theta }} \right)$ used in Marine20 together with its 2 ${\rm{\sigma }}$ interval (gray shaded region). The GS and PD estimates from the LSG OGCM have been shifted so that the mean of the plotted PD scenario in each location agrees with the mean of ${\rm{R}}_{20}^{{\rm{GlobalAv}}}\left( {\rm{\theta }} \right)$ from 11,500–0 cal yr BP. The shifted PD scenario for each latitude on the transect is shown as a (variously colored) solid line and the shifted GS scenario as a matched dashed line. The vertical line represents 11,500 cal yr BP. GS estimates from the LSG OGCM are not provided for calendar ages more recent than this.

Figure 3 effectively illustrates the difference, at a specific location, in overall MRA one would obtain using Marine20 compared with the PD and GS scenarios of the LSG OGCM. The difference between the PD (colored solid lines) and GS (dashed lines) estimates between 55,000–11,500 cal yr BP show how much additional ¹⁴C depletion, according to the LSG OGCM, is modeled at that ocean location by changing from a Holocene-type (PD) scenario to a glacial (GS) scenario. The difference between the $R_{20}^{GlobalAv}\left( \theta \right)$ of Marine20 (solid black line) and the adjusted GS estimates show how much additional localized ¹⁴C depletion might have occurred, beyond that already incorporated within the global-scale estimate of Marine20, under a GS glacial scenario. These location-dependent increases from $R_{20}^{GlobalAv}\left( \theta \right)$ must be incorporated into ${\rm{\Delta }}{R_{20}}\left( \theta \right)$ if we wish to represent the GS scenario with Marine20. Similar plots for the more extreme CS scenario of the LSG OGCM can be found in the Supplementary Information C (Figures S3 and S4).

2.3 Comparing the LSG OGCM and Marine20

Several observations are immediately apparent from Figure 3. Firstly, during the Holocene, once we have estimated both a ${\rm{\Delta }}{R_{20}}$ and a ${\rm{\Delta }}{R^{LSG}}$ regional/coastal adjustment based on modern ¹⁴C samples, the PD scenario from the LSG OGCM provides very similar MRA estimates to Marine20 for all the ocean locations on our sample transects. As we extend into the very high latitudes in the Southern Pacific and Arctic Ocean, the PD scenario does perhaps suggest slightly greater variations in MRA, in terms of the change from the levels of ¹⁴C depletion seen at the beginning of the Holocene compared to the present day, than Marine20. However, these changes are minor and generally lie within the uncertainty bands of Marine20. Intuitively, the uncertainty bands of Marine20 result from considering multiple potential climate and carbon cycle scenarios. It is likely that, during the Holocene, one of these (BICYCLE-based) scenarios lies extremely close to the PD scenario of the LSG OGCM. Consequently, for samples between 11,500–0 cal yr BP, there should be little difference between calibrating at sites along our transects using the PD output from LSG OGCM (with a ${\rm{\Delta }}{R^{LSG}}$ adjustment) and using Marine20 (with a regional ${\rm{\Delta }}{R_{20}}$ ). This is the case for both polar and equatorial regions.

Secondly, from 55,000–11,500 cal yr BP, we can see that (after the ${\rm{\Delta }}{R_{20}}$ and ${\rm{\Delta }}{R^{LSG}}$ shift/adjustment) the PD scenario of the LSG OGCM (colored solid lines) tends to generate estimates of the overall MRA along our transects that are lower than those of Marine20 (solid black line). This highlights that, while not able to resolve regionally, Marine20 does incorporate global effects of climatic and carbon cycle changes during the glacial. In this pre-Holocene period, the PD scenario of the LSG OGCM is unlikely to be appropriate as we know there were substantial global changes in the climate and carbon cycle between the glacial and the present day (Böhm et al. Reference Böhm, Lippold, Gutjahr, Frank, Blaser, Antz, Fohlmeister, Frank, Andersen and Deininger2015; Henry et al. Reference Henry, McManus, Curry, Roberts, Piotrowski and Keigwin2016; Kageyama et al. Reference Kageyama, Harrison, Kapsch, Lofverstrom, Lora, Mikolajewicz, Sherriff-Tadano, Vadsaria, Abe-Ouchi and Bouttes2021; Oka et al. Reference Oka, Abe-Ouchi, Sherriff-Tadano, Yokoyama, Kawamura and Hasumi2021; Petit et al. Reference Petit, Mourner, Jouzel, Korotkevich, Kotlyakov and Lorius1990). We expect that, from 55,000–11,500 cal yr BP, the true level of oceanic ¹⁴C depletion at a site will therefore be bounded below by the ( ${\rm{\Delta }}{R_{20}}$ -adjusted) Marine20 rather than the ( ${\rm{\Delta }}{R^{LSG}}$ -adjusted) PD scenario of the LSG OGCM.

Thirdly, if we consider the ( ${\rm{\Delta }}{R^{LSG}}$ -adjusted) GS scenario estimates (dashed lines) as providing an upper bound on the overall level of ¹⁴C depletion at any marine site then, for the more equatorial locations, these are encapsulated in Marine20’s 2 $\sigma $ uncertainty bands (shaded gray). Only once we extend beyond approximately 40ºS or 40ºN do the ( ${\rm{\Delta }}{R^{LSG}}$ -adjusted) GS scenario of the LSG OGCM provide location-specific estimates of overall MRA that are not covered by the tail estimates one would obtain with (a ${\rm{\Delta }}{R_{20}}$ -adjusted) Marine20. This suggests that on our transects, for calibration of marine samples from regions within ∼ 40ºS–40ºN, the use of Marine20 (with a modern day ${\rm{\Delta }}{R_{20}}$ ) can be justified back to 55,000 cal yr BP as its inbuilt uncertainty will cover the upper (GS-scenario) limit for regional ¹⁴C depletion. However, at higher latitudes, the GS scenarios indicate the possibility of substantial additional localized ¹⁴C oceanic depletion during glacial periods that is not captured in the global scale Marine20. Under the GS scenario, along our transects, the overall MRA in high-latitude polar regions may be increased by up to 1000 ¹⁴C yrs during the glacial compared to the global Marine20 values. To recreate this GS scenario, these polar-specific increases would need to be accounted for by a corresponding change to ${\rm{\Delta }}{R_{20}}\left( \theta \right)$ if Marine20 is used for calibration.

Fourthly, Figure 3 suggests that from 40,000–11,500 cal yr BP the increase in a particular location from the Marine20-based estimate of overall MRA to the LSG OGCM under its GS scenario (after the initial ${\rm{\Delta }}{R_{20}}$ and $\Delta {R^{LSG}}$ adjustments) is approximately constant over time. This can be seen very clearly in Figure S1 of the Supplementary Information B where we present the increase for each location along our three selected ocean transects. For a given location, we can therefore get a good approximation of the overall MRA estimate under the GS scenario of the LSG OGCM (at least between 40,000–11,500 cal yr BP) with Marine20 by applying a constant (albeit location-specific) increase to ${\rm{\Delta }}{R_{20}}$ . These increases (latitudinally averaged rather than along single transects) will become our ${\rm{\Delta }}R_{20}^{Hol\; \to \;GS}$ .

3.1 Summarizing the High-Latitude Increases in Regional ¹⁴C Depletion for a Glacial Scenario

To provide an upper (maximum) bound on the additional regional ¹⁴C depletion that may need to be incorporated into Marine20’s ${\rm{\Delta }}{R_{20}}\left( \theta \right)$ at high-latitudes during glacial periods, we have calculated latitudinal-average ${\rm{\Delta }}R_{20}^{Hol\; \to \;GS}$ adjustments. These adjustments take the form described in Section 2 where, for every marine location on the 2.5º by 2.5º grid of the LSG OGCM grid, we have:

• Shifted the LSG OGCM estimates so that the PD scenario in that location has a mean during the period from 11,500–0 cal yr BP that matches Marine20’s $R_{20}^{GlobalAv}\left( \theta \right)$ .

• Calculated the difference in the mean, during the glacial period from 40,000–11,500 cal yr BP, between $R_{20}^{GlobalAv}\left( \theta \right)$ and the (shifted) GS scenario.

This difference indicates by how much the level of ¹⁴C depletion must be increased from the global-only $R_{20}^{GlobalAv}\left( \theta \right)$ to recreate the regional GS scenario of the LSG OGCM. At a given latitude, we summarize the mean (and 95% quantiles) of these increases to obtain the latitude-dependent ${\rm{\Delta }}R_{20}^{Hol\; \to \;GS}$ values shown in Figure 1 (and Figure 4 showing the adjustment required at a particular latitude).

Figure 4 The latitudinal-average increase $\Delta R_\;^{Hol\; \to \;GS}\;$ needed to recreate the GS scenario of the LSG OGCM from Marine20 during the glacial time period (reproducing earlier Figure 1). To estimate the adjustment needed at a particular location, e.g., core site MD02-2496 at 49ºN, we read the value for the corresponding latitude. Here, the required boost $\Delta R_{MD02 - 2496}^{Hol\; \to \;GS}$ to recreate the GS scenario using Marine20 (to be added to an initial Holocene $\Delta R_{20\;}^{Hol}$ estimate) is ca. 390 ¹⁴C yrs.

Note that we perform latitudinal averaging, rather than providing latitude and longitude dependent adjustments, to reduce the effect of model specificity in the LSG OGCM estimates regarding precise sea-ice location/dynamics and freshwater balance. We also do not provide, or suggest using, the variance on the shifts at a given latitude. The set of modeled values provided by the LSG OGCM at a given latitude are not well approximated by a normal distribution. To recreate the GS scenario, we propose simply applying the mean shift ${\rm{\Delta }}R_{20}^{Hol\; \to \;GS}$ at a given latitude and leaving the uncertainty as for the Holocene-based ${\rm{\Delta }}{R_{20}}$ .

We also calculate the shift needed based on the period from 40,000–11,500 cal yr BP, to avoid the non-constancy in the differences from the LSG OGCM outputs to Marine20 at high latitudes from 55,000–40,000 cal yrs BP when atmospheric ¹⁴C levels increased very rapidly (Reimer et al. Reference Reimer, Austin, Bard, Bayliss, Blackwell, Ramsey, Butzin, Cheng, Edwards and Friedrich2020). We suggest our calculated shifts can however be applied back to 55,000 cal yr BP, although at very high latitudes, users should recognize additional adjustments may be needed for ¹⁴C samples of such great age.

For more equatorial ocean locations, the increase ${\rm{\Delta }}R_{20}^{Hol\; \to \;GS}$ is seen to overlap with the uncertainty bands on $R_{20}^{GlobalAv}\left( \theta \right)$ . For these low-latitude regions, within ca. 40ºS–40ºN, we therefore suggest that no artificial boosting of (a Holocene-based) ${\rm{\Delta }}{R_{20}}$ in glacial periods is required. A user can (cautiously) calibrate ¹⁴C samples into the glacial period using an estimate of ${\rm{\Delta }}{R_{20}}$ from the recent past. Outside these regions, at higher latitudes, the boosting needed to represent the GS scenario of the LSG OGCM increases rapidly.

The boost ${\rm{\Delta }}R_{20}^{Hol\; \to \;GS}$ does not however increase monotonically with latitude: it rises to a maximum around 60ºS/70ºN but then drops at the very poles. This is perhaps understandable since the greatest glacial boost will be needed when the local oceanic conditions in the GS scenario have changed most substantially from those seen in the Holocene/PD scenario. This occurs not at the poles themselves (where both the PD and GS scenarios have sea-ice) but rather slightly below the poles (where the GS scenario has sea-ice, but the PD does not). The extent of sea-ice in the different LSG OGCM scenarios can be found in Figures 3 and 10 of Butzin et al. (Reference Butzin, Prange and Lohmann2005). At its greatest, around 60ºS and 70ºN, the GS scenario of the LSG OGCM suggests that glacial period ${\rm{\Delta }}{R_{20}}\left( \theta \right)$ may be 1000 to 1500 ¹⁴C yrs greater than in the recent past. If we fail to recognize the potential for such an increase in polar depletion when calibrating such high latitude samples against Marine20, then we may obtain calibrated ages that are ca. 1000 cal yrs too old.

An equivalent investigation of the changes required to a modern-day ${\rm{\Delta }}{R_{20}}\left( \theta \right)$ to recreate the more extreme CS scenario of the LSG OGCM, while still using Marine20, can be found in the Supplementary Information C (Figures S3–S6). As for the GS scenario, the differences in modeled MRA between Marine20 and the CS scenario remain approximately constant over time, at least from 40,000–11,500 cal yr BP, at a given location. We can therefore obtain an approximate CS scenario with Marine20 by applying a constant, latitude-dependent, boost ${\rm{\Delta }}R_{20}^{Hol\; \to \;CS}$ to a modern-day ${\rm{\Delta }}{R_{20}}$ estimate (Figure S5). The latitudinal ${\rm{\Delta }}R_{20}^{Hol\; \to \;CS}$ shifts needed to be applied to recreate the CS scenario from Marine20 are, as expected, somewhat larger than the shifts required to recreate the GS scenario (Table A2, Appendix). A user wishing to be more cautious in calibration of samples during the glacial period may choose to select an upper bound for the polar ¹⁴C depletion using this CS scenario.

3.2 Comparison with Independent Estimates of Surface MRA over Time

To provide an independent assessment of our proposed bracketing approach, we provide an illustration of the high- and low- depletion estimates of the overall MRA, ${\rm{R}}_{20}^{{\rm{Location}}}\left( {\rm{\theta }} \right)$ , that we would obtain from 40,000–0 cal yr BP at the location of deep-sea core MD04-2829 (59.0ºN, 9.5ºW; Skinner et al. Reference Skinner, Muschitiello and Scrivner2019). This is a high-latitude site (59ºN) within the Northern Atlantic where we might expect additional, localised, variations in ${\rm{\Delta }}R_{20}^\;\left( \theta \right)$ during the glacial period. We then compare our suggested bounding ¹⁴C depletion scenarios against estimates of surface MRA obtained directly from this core’s planktonic ¹⁴C measurements. MD04-2829 has a calendar age-depth timescale based upon the alignment of changes in the abundance of planktonic foraminifer species N. pachyderma to the NGRIP δ¹⁸O ice record (Svensson et al. Reference Svensson, Andersen, Bigler, Clausen, Dahl-Jensen, Davies, Johnsen, Muscheler, Parrenin, Rasmussen, Röthlisberger, Seierstad, Steffensen and Vinther2008). Measurements of planktic ¹⁴C within the core can therefore be compared against IntCal20 to provide independent, and direct, estimates of the overall surface-atmospheric MRA.

Our bracketed estimates for $R_{20}^{Location}\left( \theta \right)$ are based on adjusting the global-scale $R_{20}^{GlobalAv}\left( \theta \right)$ of Marine20, just as would be implemented by a user of our approach. We first estimate a ${\rm{\Delta }}R_{20}^{Hol}$ based upon the single most recent ¹⁴C measurement within the MD04-2829 core. When combined with Marine20’s $R_{20}^{GlobalAv}\left( \theta \right),\;$ this ${\rm{\Delta }}R_{20}^{Hol}$ fixes the estimate for the overall MRA throughout the Holocene and determines the lower bound for the overall depletion in the glacial period. The resultant Holocene, and low-depletion glacial, estimate for $\;R_{20}^{Location}\left( \theta \right)$ is plotted in blue (with 1 ${\rm{\sigma }}$ intervals). The location-specific upper bound for the glacial period is then calculated by applying the appropriate latitudinal shift ${\rm{\Delta }}R_{20}^{Hol\; \to \;GS}$ . In the case of MD04-2829 (at 59ºN) this is 1000 ¹⁴C yrs (see Table A2, Appendix). These shifted upper-bound glacial estimates are shown in red (with 1 ${\rm{\sigma }}$ intervals).

We would hope that the directly observed MRA estimates obtained from planktonic ¹⁴C measurements within the core (shown as black dots, with 1 ${\rm{\sigma }}$ intervals) would lie between the two bounding (high- and low-) $R_{20}^{Location}\left( \theta \right)$ curves. Figure 5 shows this to generally be the case. We note that, during the Holocene, the blue ${\rm{\Delta }}R_{20}^{Hol}$ -adjusted estimate appears a good fit. This suggests that Marine20’s $R_{20}^{GlobalAv}\left( \theta \right)$ is capturing the main global-scale effects on the MRA; and that temporal variations in ${\rm{\Delta }}R_{20}^\;\left( \theta \right)$ are small during the Holocene (even at high latitudes). This supports our recommendation that, even at high-latitudes, users can continue using Marine20 (with a constant ${\rm{\Delta }}R_{20}^\;$ ) during the Holocene.

Figure 5 Plot of the upper and lower bounds on the overall MRA, $R_{20}^{Location}\left( \theta \right)$ obtained using our proposed bracketing approach compared against estimates of MRA calculated directly from planktic foraminifera (black dots) in the deep-sea core (MD04-2829, 59ºN 9ºW; Skinner et al. Reference Skinner, Muschitiello and Scrivner2019). The high (red) and low (blue) depletion estimates shown are calculated by applying the appropriate latitudinal-shift to the global-scale $R_{20}^{GlobalAv}\left( \theta \right)$ of Marine20. Both the curves and the observations are shown with 1 $\sigma $ intervals. Heinrich events are overlain as shaded intervals.

Once we enter the glacial period however, we see that the observed MRAs in our high-latitude location vary significantly away from the low-depletion scenario. There are periods when ${\rm{\Delta }}R_{20}^\;\left( \theta \right)$ has clearly increased substantially in this polar marine location, and calibrating using the low-depletion scenario would not be appropriate. However, the directly observed estimates still lie within the upper- and lower-depletion curves, indicating that our bracketing approach is able to bound the variability in ${\rm{\Delta }}R_{20}^\;\left( \theta \right)$ . As might be expected for a North Atlantic core such as MD04-2829, the regional ${\rm{\Delta }}R_{20}^\;\left( \theta \right)$ appears to increase during/around the Heinrich events and around the LGM with the overall MRA moving towards its upper (red) limits, and then reduce away from these periods dropping back towards the lower (blue) limit.

4.1 Calibration of Single ¹⁴C Samples from Polar Regions

Suppose we wish to calibrate two individual ¹⁴C samples taken from the deep-sea core site MD02-2496 at 49.0ºN, 127.0ºW:

1. 1. Holocene Sample A (at depth 412 cm) with a ¹⁴C age of 9215 ± 25 ¹⁴C yrs BP (1 $\sigma )$

2. 2. Glacial Sample B (at depth 2057cm) with a ¹⁴C age of 25190 ± 150 ¹⁴C yrs BP (1 $\sigma )$

Readers should note that these examples of individual calibration are intended as illustrations only. In practice, we would always suggest calibrating ¹⁴C samples within a core together as part of an age-depth model rather than individually. By calibrating jointly, we can usually add strength to our calendar age estimation.

4.1.1 Calibration during the Holocene (9215 ± 25 ¹⁴C yrs BP—Sample A)

Since the marine ¹⁴C sample (sample A) that we wish to calibrate is from the Holocene, we do not need to incorporate a glacial increase in localized depletion. We can therefore calibrate the ¹⁴C determination directly against Marine20 with the single value of ${\rm{\Delta }}{R_{20}}$ calculated from the (recent past) samples shown in Figure 6. This calibration is shown in Figure 7 and provides a mean calibrated age estimate of 9570 cal yr BP, with a 95.4% confidence interval of [9340, 9840] cal yr BP.

Figure 7 Calibration of marine sample A from the Holocene (9215 ± 25 ¹⁴C yrs BP) taken from deep-sea core MD02-2496 (ca. 49.0ºN, 127.0ºW). We use a value of $\Delta {R_{20}} = \;178 \pm 73$ ¹⁴C yrs. Calibration is performed using OxCal v4.4.4 (Bronk Ramsey Reference Bronk Ramsey2009) using the Marine20 calibration curve (Heaton et al. Reference Heaton, Köhler, Butzin, Bard, Reimer, Austin, Bronk Ramsey, Grootes, Hughen and Kromer2020). The Gaussian curves on the y-axis represent the raw ¹⁴C-age (lighter) and the $\Delta {R_{20}}$ -adjusted ¹⁴C-age (darker) of the marine sample. We calibrate the $\Delta {R_{20}}$ -adjusted ¹⁴C-age against the Marine20 curve. The posterior calendar age estimate is shown along the x-axis. Note that, the OxCal calendar age scale runs from left (oldest) to right (youngest/more recent).

Note that we can be confident that Sample A arises from the Holocene as the 95.4% calendar age range obtained under the calibration does not extend into the glacial. If the calendar age interval did extend beyond 11,500 cal yr BP, then we would advise that the dual approach of Section 4.1.2 is required.

4.1.2 Calibration during the Glacial (25190 ± 150 ¹⁴C yrs BP—Sample B)

To calibrate a sample from the glacial period at the site of core MD02-2496, we must first calculate the increase, from the Holocene/recent-past ${\rm{\Delta }}{R_{20}}$ , that is required to emulate the GS scenario of the LSG OGCM. At a latitude of 49ºN, Figure 4 and Table A2 suggests an increase of 390 ¹⁴C yrs is needed. We then calibrate against Marine20 under two different glacial scenarios. We hope these scenarios will bracket the ¹⁴C depletion at the deep-sea site and time of the sample.

Calibrating in a low-depletion glacial scenario (oldest calendar age limit): To estimate the calendar age of the MD02-2496 ¹⁴C determination ( $25,\!190 \pm 150$ ¹⁴C yrs BP) in a low-depletion glacial scenario, we calibrate against Marine20 using the level of regional ¹⁴C depletion seen in the present day, i.e., ${\rm{\Delta }}R_{MD02 - 2496}^{Hol} = {\rm{\Delta }}{R_{20}} = 178\; \pm 73$ ¹⁴C yrs. This calibration still incorporates global-scale glacial conditions (e.g., the increase in ¹⁴C concentrations, changes in CO₂, and large-scale carbon cycle changes over the Holocene/pre-Holocene boundary that is included in Marine20) but does not incorporate the potential for regional sea-ice to temporally affect the site-specific ${\rm{\Delta }}{R_{20}}\left( \theta \right)$ .

Calibrating in a high-depletion glacial scenario (youngest calendar age limit): To calibrate in a high-depletion scenario that assumes regional/localized polar conditions similar to those modeled in the GS scenario of the LSG OGCM, we add our latitudinal boost ${\rm{\Delta }}R_{20}^{Hol\; \to \;GS}$ to the modern-day estimate of ${\rm{\Delta }}{R_{20}}$ :

$${\rm{\Delta }}R_{MD02 - 2496}^{GS} = {\rm{\Delta }}R_{MD02 - 2496}^{Hol} + {\rm{\Delta }}R_{MD02 - 2496}^{Hol\; \to \;GS} = \;178 + 390 = 568\;{}_\;^{14}C\;yrs.$$

We retain the same ( $1\sigma )$ uncertainty of ± 73 ¹⁴C yrs taken from the value of ${\rm{\Delta }}{R_{20}}$ . We then calibrate against Marine20 with this boosted ${\rm{\Delta }}R_{MD02 - 2496}^{GS}$ estimate of regional depletion.

Obtaining bracketing calendar ages: The calendar age estimates obtained from calibrating the glacial sample ( $25,\!190 \pm 150$ ¹⁴C yrs BP) with the bracketing low- and high-depletion scenarios are shown in Figure 8 and Table 1. The overall calibrated age range covering both limiting depletion scenarios (running from the overall minimum calendar age to the maximum calendar age) is [27560, 28750] cal yr BP (Table 1). This combined interval aims to cover the maximum potential calendar age range for the ¹⁴C sample. If we expect the true value of regional depletion ${\rm{\Delta }}R\left( \theta \right)$ at the time the sample was exchanging with its environment to lie somewhere between the two extreme low- and high-depletion scenarios, the calendar age of the sample will also lie between the two scenario estimates. If no external knowledge is available regarding whether the low- or high- depletion glacial scenario is more appropriate for the sample, this extremely broad bracketing may be all we can provide. However, if independent information on the extent of sea-ice in the location is available, a calibration user may wish to make an argument that either the low- or high-depletion calibration scenarios (and hence calibrated ages) are more appropriate (or indeed argue for an intermediate level of depletion).

Figure 8 Calibration of glacial sample B with a ¹⁴C determination of $25,\!190 \pm 150$ ¹⁴C yrs BP from deep-sea core MD02-2496 (49ºN 127ºW). The top distribution shows the calibrated age under a low-depletion marine scenario (no additional changes in ¹⁴C depletion over those seen in Equatorial waters). The bottom plot, the calibrated age under a high-depletion polar scenario (intended to represent conditions similar to the LGM). Note that the low-depletion glacial scenario (top) provides an older calendar age estimate—the OxCal calendar age scale runs from left (oldest) to right (youngest/more recent).

Table 1 95.4% credible intervals for the calendar age of sample B (a glacial-period marine ¹⁴C sample with a ¹⁴C determination of $25,\!190 \pm 150$ ¹⁴C yrs BP) from core MD02-2496 (∼49ºN) under a low- and high-depletion glacial scenario.

We stress that the combined (bracketed) interval of [27560, 28750] cal yr BP should have a coverage that is considerably greater than 95.4% (since it covers the two extremes). However, we do not provide any probability distribution on it, and no such distribution should be inferred as we expect that the true level of ¹⁴C depletion may transition relatively rapidly between scenarios (spending less time at intermediate values) as sea-ice appears and disappears. Additionally, while in principle, there is no guarantee that the 95.4% quantiles for the calibrated age of a ¹⁴C date decrease monotonically with increasing MRA/depletion levels (i.e., there might be an intermediate level of depletion which has 95.4% calendar age quantiles outside the range above) in practice, due to the smoothness of the current Marine20 estimate, there are no such cases pre-Holocene.

4.2 Calibrating Multiple ¹⁴C Polar Determinations and Age Modeling

Polar ¹⁴C calibration is also required when creating age-depth models for sediment cores based upon multiple ¹⁴C determinations (e.g., McClymont et al. Reference McClymont, Bentley, Hodgson, Spencer-Jones, Wardley, West, Croudace, Berg, Gröcke, Kuhn, Jamieson, Sime and Phillips2022; Taylor et al. Reference Taylor, Hendy and Pak2014). For such age-depth models, ¹⁴C calibration is typically done internally to the creation of the chronology. We recommend an analogous approach to that of Section 4.1. For those Holocene ¹⁴C samples that are used to inform the overall chronology, we suggest a user apply a single ${\rm{\Delta }}R_{20}^{Hol}$ ; while for older samples we suggest creating separate age-depth models under the low- and high-depletion scenarios. Then, when estimating the age at any specific depth, a user can read off the calendar age estimate for each age-depth model (low- and high-depletion) and use the same bracketing approach described in Section 4.1.2. Alternatively, they may wish to use independent palaeoclimatic/proxy evidence to support an age-depth model based on the level of ¹⁴C depletion under one scenario (or to justify an intermediate level of depletion). As for the calibration of single ¹⁴C samples, this can all be achieved within standard calibration software simply by adjusting, e.g., DeltaR, during age-depth model construction (see Supplementary Information F).

We consider an age-depth model fitted to the 40 ¹⁴C determinations in core MD02-2496 using OxCal’s p-sequence (Bronk Ramsey Reference Bronk Ramsey2008; Bronk Ramsey and Lee Reference Bronk Ramsey and Lee2013). To create this model, we have averaged the two measurements (9215 ± 25 and 10,065 ± 45 ¹⁴C yrs BP) at 412cm into a single ¹⁴C date of 9415 ± 22 ¹⁴C yrs BP. For the low-depletion glacial scenario, we use a regional correction of ${\rm{\Delta }}R_{MD02 - 2496}^{Hol} = 178\; \pm 73{\rm{\;}}$ ¹⁴C yrs as justified in the previous section; while for the high-depletion glacial scenario, we use a ${\rm{\Delta }}R_{MD02 - 2496}^{GS} = 568 \pm 73$ ¹⁴C yrs. In this location, the transition between the Holocene and glacial corresponds to approximately 10,000 ¹⁴C yrs BP, i.e., a sample with a determination of 10,000 ¹⁴C yrs BP calibrates to being just older than 11,500 cal yr BP using a non-glacial ${\rm{\Delta }}R_{MD02 - 2496}^{Hol} = 178\; \pm 73{\rm{\;}}$ ¹⁴C yrs. For both our high and low-depletion age-depth models, we therefore apply a Holocene value of ${\rm{\Delta }}R\left( \theta \right)$ when constructing the age-depth model for all ¹⁴C samples at depths from 0–412 cm. Deeper in the core, we apply the appropriate high- and low-depletion glacial ${\rm{\Delta }}R\left( \theta \right)$ .

When fitting our OxCal p-sequence, we have selected a variable k, P_Sequence(“”,100,5,U(-2,2)), with core depths provided in m. There is one clear outlier with the sample at depth 5.52m (14,025 ± 50 ¹⁴C yrs BP) being significantly older than the next five samples upcore at 5.92, 6.72, 7.57, 8.37, and 8.52m (ca. 13,300–13,900 ¹⁴C yrs BP). We have therefore used an outlier model with a prior probability of 0.05 of a sample being an outlier: Outlier_Model(“General”,T(5),U(0,4),"t”).

The resultant models (with their uncertainty bands) are shown in Figure 9. The green age-depth model represents the chronology had core MD02-2496 been in a high-depletion ${\rm{\Delta }}R_{MD02 - 2496}^{GS}$ polar scenario throughout the glacial period before shifting to ${\rm{\Delta }}R_{MD02 - 2496}^{Hol}$ in the Holocene. In the blue age-depth model, ${\rm{\Delta }}R\left( \theta \right) = \;{\rm{\Delta }}R_{MD02 - 2496}^{Hol}$ throughout. This represents the chronology if the climate at site MD02-2496 had followed a low-depletion polar scenario throughout the glacial where no additional regional changes in oceanic ¹⁴C depletion were seen beyond those large-scale effects captured in Marine20.

Figure 9 Age-depth models of deep-sea core MD02-2496 (49ºN 127ºW) under a low (blue) and high (green) depletion polar scenario using an OxCal p-sequence (with a variable k and general outlier model). Changes in depletion can be achieved by modification of DeltaR within OxCal’s p-sequence model. Core depths are given in m. We consider the age of a hypothetical event at 15.2 m within the core. Again, the OxCal calendar age scale runs from left (oldest) to right (youngest/more recent).

If we are interested in the calendar age of a hypothetical event at depth of 15.2m in the core (as illustrated in Figure 9), then we can obtain calendar age estimates from the separate age-depth models under the low- and high-depletion glacial polar scenarios. These calendar ages are shown in Table 2. Again, these can be combined by selecting the most extreme calendar ages to create a wide age-bracketing that hopefully includes the true calendar age.

Table 2 Calendar age estimates of the MD02-2496 (49ºN) sediment core at a depth of 15.2 m based on OxCal’s p-sequence age-depth modeling (with a variable k and general outlier model) under the low- and high-depletion polar scenarios.

We note that it is possible that the true ${\rm{\Delta }}R\left( \theta \right)$ flips between the high- and low-depletion polar glacial scenarios over time throughout the core as we move from stadials to interstadials. Our suggested bracketing age-depth models assume a constant ${\rm{\Delta }}R\left( \theta \right)$ depletion scenario (either high or low). Such scenario flips could change the age-depth model substantially. However, preliminary testing suggests that even with changes from high- to low-depletion within the core, the calendar ages from the fixed, bounding, glacial scenarios bracket the calendar ages of the scenario-changing model at any given depth. Users of age-depth models may also wish to place a uniform prior on their estimate of ${\rm{\Delta }}R\left( \theta \right)$ with upper- and lower-bounds taken from the low- and high-depletion scenarios. Such a model would provide a single age-depth model. However, if the climate flips rapidly between climate scenarios, with the appropriate ${\rm{\Delta }}R\left( \theta \right)$ also flipping between its upper and lower limits, this approach may give over-confident estimates.

4.3 Incorporating Paleoclimatic and Proxy Evidence on the Sea-Ice Extent into Calibration

We recommend that all those calibrating glacial period ¹⁴C samples from polar regions present the results from both bracketing scenarios, with the belief that the true calendar ages should lie between the values obtained under the two limiting scenarios. However, we recognize that some users may have expert knowledge from independent palaeoclimatic/proxy evidence as to which scenario is more appropriate. Such users might therefore, quite reasonably, wish to argue one option is more plausible than the other; or indeed they may believe that an intermediate ¹⁴C depletion scenario (which would result in intermediate calendar ages) is most suitable. We leave such interpretation up to the individual expert and would encourage them to do so if it is felt appropriate, provided their reasoning is fully documented.

Further into the future, it may be possible to determine more precise ${\rm{\Delta }}R\left( \theta \right)$ regional adjustments in polar regions using paleoclimatic and proxy evidence to infer the extent of sea-ice. Such proxy information might allow one to scale, for any individual ¹⁴C sample, the ${\rm{\Delta }}R\left( \theta \right)$ between the present-day ${\rm{\Delta }}{R_{20}}$ value and that representing the GS/CS values of the LSG OGCM. If such a procedure was shown to improve our estimation of polar ${\rm{\Delta }}R\left( \theta \right)$ , then it would also provide more precise calendar dating when calibrating polar ¹⁴C samples. Reconstructing sea-ice variation is possible but challenging. Several proxies have been proposed. These include micropaleontological transfer functions based on diatoms (e.g., Gersonde et al. Reference Gersonde, Crosta, Abelmann and Armand2005) and dinocysts (de Vernal et al. Reference de Vernal, Henry, Matthiessen, Mudie, Rochon, Boessenkool, Eynaud, Grøsfjeld, Guiot and Hamel2001); molecular abundance of a particular hydrocarbon (IP25) synthesized by diatoms living at the bottom of sea-ice (Belt and Müller Reference Belt and Müller2013); and stomach-oil deposits from snow petrels (McClymont et al. Reference McClymont, Bentley, Hodgson, Spencer-Jones, Wardley, West, Croudace, Berg, Gröcke, Kuhn, Jamieson, Sime and Phillips2022; Thatje et al. Reference Thatje, Hillenbrand, Mackensen and Larter2008). Several authors have used these proxies to show systematic changes of sea-ice that are linked to abrupt climate changes (Hoff et al. Reference Hoff, Rasmussen, Stein, Ezat and Fahl2016; Méheust et al. Reference Méheust, Stein, Fahl and Gersonde2018; Stein et al. Reference Stein, Fahl, Gierz, Niessen and Lohmann2017). To investigate whether such a sliding, sea-ice proxy-informed, ${\rm{\Delta }}R(\theta $ ) correction improves calendar dating would require suitable independent testing: either by comparing the resultant core chronology against absolute chronologies; or with downcore evidence of local MRA changes (e.g., using tephra). Such work goes beyond that possible here but would be a valuable further avenue of study.