Re-evaluating 14 C dating accuracy in deep-sea sediment archives.

The current geochronological state-of-the-art for applying the radiocarbon ( 14 C) method to deep-sea sediment archives lacks key information on sediment bioturbation. Here, we apply a sediment accumulation model that simulates the sedimentation and bioturbation of millions of foraminifera, whereby realistic 14 C activities (i.e. from a 14 C calibration curve) are assigned to each single foraminifera based on its simulation timestep. We find that the normal distribution of 14 C age typically used to represent discrete-depth sediment intervals (based on the reported laboratory 14 C age and measurement error) is unlikely to be a faithful reflection of the actual 14 C age distribution for a specific depth interval. We also find that this deviation from the actual 14 C age distribution is greatly amplified during the calibration process. Specifically, we find a systematic underestimation of total geochronological error in many cases (by up to thousands of years), as well as the generation of age-depth artefacts in downcore calibrated median age. Even in the case of “perfect” simulated sediment archive scenarios, whereby sediment accumulation rate (SAR), bioturbation depth, reservoir age and species abundance are all kept constant, the 14 C dating and calibration process generates temporally dynamic median age-depth artefacts, on the order of hundreds of years – whereby high SAR scenarios (40 cm kyr -1

previously incorrectly attributed to changes in SAR coinciding with global climate.Our study highlights the need for the development of improved deep-sea sediment 14 C calibration techniques that include an a priori representation of bioturbation for multi-specimen samples.

Background and rationale
For over half a century, radiocarbon ( 14 C) dating has been applied to deep sea sediment archives.The material that is typically analysed from these archives consists of the calcareous tests of foraminifera.
The minimum amount of material required for viable 14 C analysis has meant that researchers have had to pick tens to hundreds of individual foraminifera specimens (depending on specimen size) from a single discrete-depth core interval (typically 1 cm of core depth) and combine these into a single sample for analysis.Such multi-specimen samples are likely to be heterogeneous in 14 C activity (i.e.combine individual specimens of varying true age).The 14 C laboratory measurement (and reported machine error) applied to such an amalgamated multi-specimen sample will simply represent the mean 14 C activity of the total carbon of all individual specimens.Consequently, the true intra-sample 14 C age heterogeneity of a sample is concealed from the researcher.Failure to consider the actual 14 C age heterogeneity of multi-specimen samples can lead to downcore 14 C age artefacts when postdepositional processes mix foraminifera with differing 14 C activities, especially during periods coinciding with periods of dynamic Δ 14 C history of the Earth.Furthermore, one must also take into consideration that younger specimens within a sample contribute exponentially more to the sample's mean 14 C activity than older specimens do, a process referred to as the isotope mass balance effect (Erlenkeuser, 1980;Keigwin and Guilderson, 2009), due to 14 C being a radioactive isotope (specimen 14 C activity decreases exponentially with the passing of time).Systematic bioturbation has long been recognised as an inherent feature of deep-sea sediment archives (Bramlette and Bradley, 1942;Arrhenius, 1961;Olausson, 1961).Long-established mathematical models of bioturbation in deep-sea sediment archives consider the uppermost ~10 cm of a sediment archive to be uniformly mixed due to active bioturbation -the bioturbation depth (BD) (Berger and Heath, 1968;Berger and Johnson, 1978;Berger and Killingley, 1982).The presence of such a BD has been supported by the detection of a uniform mean age in the uppermost intervals of sediment archives (Peng et al., 1979;Trauth et al., 1997;Boudreau, 1998;Teal et al., 2008) and by the 14 C analysis of single foraminifera (Lougheed et al., 2018).The total range of single specimen ages mixed within the BD is dependent upon two main factors: the depth of the BD itself, and the sediment accumulation rate (SAR), both of which can exhibit spatiotemporal variation due to environmental and biological factors (Müller and Suess, 1979;Trauth et al., 1997).The presence of uniform mixing within the BD throughout the sedimentation history of a deep-sea sediment archive ultimately results, in the case of temporally constant SAR and BD, in the single specimen population of discrete sediment intervals being characterised by an exponential probability density function (PDF) for true age, with a maximum probability for younger ages and a long tail towards older ages.The existence of such a distribution has been supported by the post-depositional mixing of tephra layers (Bramlette and Bradley, 1942;Nayudu, 1964;Ruddiman and Glover, 1972;Abbott et al., 2018) and the smoothing out of the downcore mean signal (Guinasso and Schink, 1975;Pisias, 1983;Schiffelbein, 1984;Bard et al., 1987;Löwemark et al., 2008;Trauth, 2013), the smoothing of which can change downcore in tandem with foraminiferal abundance changes (Ruddiman et al., 1980;Peng and Broecker, 1984;Paull et al., 1991;Löwemark et al., 2008).If SAR, BD and the Δ 14 C history of the planet were all to be temporally constant, then the idealised 14 C activity PDF of each discrete depth (expressed as, e.g., the 14 C/ 12 C ratio or normalised as fraction modern [F 14 C]) would, therefore, exhibit the combination of two exponential functions (the exponential PDF of true age plus the exponential PDF of 14 C activity vs time predicted by the half-life of 14 C).However, the distribution of the 14 C activity PDF is made complicated by the fact that 14 C activity vs time is not always the exact exponential function that would be predicted by the radioactive half-life of 14 C, seeing as the Earth's carbon reservoir exhibits a dynamic Δ 14 C history, as demonstrated by temporal changes in atmospheric 14 C activity (Suess, 1955(Suess, , 1965;;de Vries, 1958;Reimer et al., 2013).These changes are brought about by changes in 14 C production in the atmosphere in combination with climatic and oceanic influence upon the carbon cycle (Craig, 1957;Damon et al., 1978;Siegenthaler et al., 1980).Furthermore, non-uniform mixing of the oceans can contribute to temporal changes in local water 14 C activity at a given coring site, further affecting the idealised PDF shape.
When applying the 14 C method to sediment core material, researchers represent the 14 C activity of a discrete-depth interval using a normal (Gaussian) distribution, based on the conventional mean 14 C age (a reporting convention for 14 C activity) and measurement error reported by the 14 C laboratory (Stuiver and Polach, 1977).In some cases, this 14 C age normal distribution is widened by researchers to also incorporate a reservoir age uncertainty, but it remains a normal distribution.This normal distribution of 14 C age is subsequently calibrated using a suitable reference record of past Δ 14 C (e.g.those produced by the IntCal group), allowing researchers to arrive at an estimation of the discrete depth interval's true (i.e.calendar) age.Such an approach inherently excludes the effects of bioturbation, because one would not expect a normal 14 C age distribution to be representative of a discrete depth interval, for the reasons described in the previous paragraph.Currently, systematic investigation is lacking into whether neglecting to include the effects of bioturbation has significant impact upon the interpretative accuracy of 14 C dating as it is currently applied in palaeoceanography, i.e. if it may ultimately lead to spurious geochronological interpretations.

Experimental design
Here, we we take advantage of computer modelling to construct an ideal experimental design whereby we can evaluate how the current 14 C state-of-the-art within palaeoceanography would work in the case of best-case sediment conditions.Such best-case conditions do not exist in in the field, meaning that a computer modelling environment can uniquely be used to create such a best-case scenario, which is ideal for testing the current state-of-the-art.We use the Δ 14 C-enabled, single-specimen SEdiment AccuMUlation Simulator (SEAMUS) (Lougheed, 2020).This model uses the long-established understanding of bioturbation as included in existing bioturbation models (Trauth, 2013;Dolman and Laepple, 2018), but differs in that it explicitly simulates the accumulation and bioturbation of single foraminifera, each with individually assigned 14 C activities, to create a synthetic sediment archive history.Subsequently, current palaeoceanographic subsampling and 14 C dating practices are virtually applied to the 1 cm discrete-depth sediment intervals of the model's outputted synthetic archive, resulting in discrete-depth 14 C ages and calibrated ages that are representative of the existing palaeoceanographic state-of-the-art.These results are subsequently compared to the actual discretedepth true age distributions within the model, allowing us to quantitatively evaluate contemporary palaeoceanographic 14 C dating and calibration techniques.By keeping multiple model input parameters constant, we can construct an experimental environment whereby we have full control over the degrees of freedom.This modelling approach allows us to test, at a most fundamental level, the accuracy of the current 14 C dating state-of-the-art as applied to deep-sea sediments.

The synthetic core simulation
The SEAMUS model (Lougheed, 2020) synthesises n number of single foraminifera raining down from the water column per simulation timestep, whereby n is the capacity of the synthetic sediment archive being simulated (analogous to sediment core radius) scaled to the SAR of the timestep as predicted by an inputted age-depth relationship (Lougheed, 2020).To provide good statistics, all simulations use a timestep of 5 years and 10 4 synthetic foraminifera per cm core depth.An abundance of 10 4 specimens per cm is also similar to a best-case scenario value for a particular sample in the field (Broecker et al., 1992).
In each timestep, all newly created single foraminifera are assigned an age (corresponding to the timestep), a sediment depth (according to the age-depth input), as well as a 14 C age (in 14 C yr BP) and normalised 14 C activity (in F 14 C) based on Marine13 (Reimer et al., 2013) after the application of a prescribed reservoir age for the timestep.For older sections of the Marine13 calibration curve, where only 10 year timesteps are available, linear interpolation is used to provide a 5 year 14 C activity timestep resolution.Within SEAMUS, all single foraminifera older than the oldest available age within the chosen calibration curve (in this case Marine13) are assigned the same 14 C activity: that of the analytical blank, which must be set in the simulation.In this way, the model incorporates the principles of 14 C dating, whereby individual very old foraminifera contained within a sample will contribute a 14 C signal equivalent to the analytical blank.Here, we choose to set the the simulation's analytical blank value to 46806 14 C yr BP (more precisely the F 14 C equivalent thereof), which corresponds to the lowest activity level in the Marine13 calibration curve.The analytical blank activity in most laboratories is somewhat lower (e.g., >50000 14 C yr BP), but we have no way of accurately applying an activity to single foraminifera older than the oldest value contained within Marine13.Rather than infer a Δ 14 C history beyond the limit of Marine13, we simply set the analytical blank in our simulation to 46806 14 C yr BP.In some scenarios we wish to investigate parameters within an experimental construct with temporally constant Δ 14 C, and in such scenarios we assign 14 C activity (as F 14 C) as follows: F 14 C(t) = e ( [t+R(t)] / -8267 ) , where t is the single foraminifera age in years before 1950 CE, and R(t) is the reservoir age for age t.
After the creation of all new single foraminifera within the synthetic core for a specific timestep, bioturbation is simulated.Specifically, for each timestep the depth values corresponding to all simulated foraminifera within the contemporaneous BD are each assigned a new depth by way of uniform random sampling of the BD interval.In this way, uniform mixing of foraminifera within the BD is simulated following established understanding of bioturbation (Berger and Heath, 1968;Trauth, 2013).All of the aforementioned processes are repeated for every simulation timestep until such point that the end of the age-depth input (i.e. the final core top) is reached.All simulations are initiated at 70 ka (in true age) in order to confidently exclude the influence of model spin-up effects upon our period of interest (0 -45 ka), given the possibility of a given cm of sediment to have a long-tail of older foraminifera specimens.While SEAMUS can in principle be run on a local machine, to save time multiple simulations were run in parallel on a computing cluster provided by the Swedish National Infrastructure for Computing (SNIC) at the Uppsala Multidisciplinary Centre for Advanced Computational Science (UPPMAX).

Virtual discrete-depth analysis
After the completion of the synthetic core simulation, synthetic foraminifera (and corresponding values for true age, F 14 C, and 14 C age) are picked from each discrete 1 cm interval of the sediment core.In this study, we assume best-case scenarios where it is possible to pick all whole foraminifera contained within the sediment intervals.Subsequently, each of these picked 1 cm samples also undergoes a synthetic 14 C determination analogous to a perfect accelerator mass spectrometry (AMS) measurement, whereby it is assumed that the AMS determination perfectly reproduces the mean 14 C activity (in F 14 C) of the sample.Within the discrete-depth subsampling simulation, this mean 14 C activity is calculated by taking the mean of all F 14 C values of all the single foraminifera contained within the picked sample.As mentioned in Section 2.1, the analytical blank is already included when assigning 14 C to single foraminifera, meaning that the influence of the analytical blank upon sample AMS measurements is incorporated.
Using the Libby half-life, a sample's mean F 14 C value is also reported as a conventional 14 C age determination (in 14 C yr).All such synthetic determinations are assigned a synthetic 1σ measurement error analogous to a best-case scenario laboratory counting error for a large sample.The prescribed synthetic measurement error ranges from 30 14 C yr in the case of near-modern samples to 500 14 C yr in the case of samples nearing the blank value.Specifically, when assigning measurement errors to synthetic AMS determinations, a 14 C determination of 1.0 F 14 C is assumed to have a measurement error of 30 14 C yr, and a determination with the F 14 C value e (blankvalue-1)/-8033 (i.e. one 14 C yr younger than the blank value) is assumed to have a measurement error of 500 14 C yr. Errors (in 14 C yr) for intermediate dates are linearly interpolated to F 14 C.
The synthetic laboratory 14 C determinations and associated measurement uncertainties for each 1 cm discrete-depth sample are subsequently converted to calibrated years within SEAMUS using the embedded MatCal (v 2.6) 14 C calibration software (Lougheed and Obrochta, 2016), the Marine13 calibration curve (Reimer et al., 2013) and a prescribed reservoir age (according to the scenario -see following sections), to produce a calibrated age probability density function (PDF) and 95.4% highest posterior density (HPD) credible interval(s) for every cm core depth, i.e. analogous to what would be typically produced using contemporary palaeoceanography methods in the case of every discrete cm of core depth being exhaustively 14 C dated.The MatCal software calibrates ages in F 14 C space, resulting in an accurate calibration, especially in the case of older samples or samples with large uncertainty.

Best-case scenario simulations
In order to investigate the baseline accuracy when applying 14 C dating to deep-sea sediment cores, the first simulations in this study consider a number of best-case scenarios.Essentially, we seek to test how well the current application of 14 C within palaeoceanography would function in the case of such a best-case scenario, thus testing the current state-of-the-art at a most fundamental level.In such simulations, we assume that Marine13 constitutes a perfect reconstruction of past surface-water 14 C activity at the synthetic core site, and we therefore employ a temporally constant reservoir age (ΔR = 0 14 C yr).Furthermore, we assume a scenario involving synthetic sediment cores with temporally constant SAR and BD, and we also assume that the synthetic core is made up of a single planktonic foraminiferal species with a temporally constant abundance (10 4 cm -1 ) and specimen size.A total of five best case scenarios are carried out, with five different SAR scenarios (5, 10, 20, 40 and 60 cm kyr -1 ).The BD is set to 10 cm in all cases, following established understanding of global BD (Trauth et al., 1997;Boudreau, 1998).In this scenario, we also assume perfection in sub-sampling, i.e. the possibility to exhaustively sample all foraminifera material from each 1 cm discrete-depth interval when picking for multi-specimen samples, thus excluding noise due to small sample sizes.The results of these five scenarios are visualised in Fig. 1 and Fig. S1-S5.
A second set of best-case scenarios takes into account that relatively older foraminifera contained within a given discrete depth of core sediment will have accumulated a longer residence time in the active bioturbation depth.Due to their longer residence time in the active bioturbation depth, these foraminifera are more likely to be broken and/or partially dissolved (Rubin and Suess, 1955;Ericson et al., 1956;Emiliani and Milliman, 1966;Barker et al., 2007), and are thus less likely to be picked by palaeoceanographers who preferentially pick whole/unbroken foraminifera specimens for analysis.In this way, palaeoceanographers exclude the oldest, least-well preserved fraction of the sediment.An indication of the BD residence time of single specimens for a given 1 cm discrete depth is shown in Fig. 2 for all five simulated SAR scenarios, along with the median and 90 th percentile residence time.
The percentage of broken specimens within the sediment archive is chiefly governed by the aforementioned BD residence time, bottom water chemistry (Bramlette, 1961;Berger, 1970;Parker and Berger, 1971), and the susceptibility of a particular foraminifera species to dissolution/breakage (Ruddiman and Heezen, 1967;Boltovskoy, 1991;Boltovskoy and Totah, 1992).Previous studies have indicated that the percentage of foraminifera exhibiting test breakage for typically analysed species at locations above the lysocline can hover around 10% (Le and Shackleton, 1992).In the second set of best-case scenarios we, therefore, exclude from the picking process for each 1 cm discrete depth all foraminifera with a number of bioturbation cycles greater than the 90 th percentile for that particular discrete depth.This broken foraminifera percentage of 10% is applied to all five SAR scenarios (5, 10, 20, 40, 60 cm kyr -1 ) in a second set of best case scenarios, shown in Fig. 3 and Fig. S6-S10.One should be aware, however, that BD residence time likely varies with SAR itself: when sediment accumulation is slower, single specimens remain in the BD for relatively longer than in the case of faster SAR (Bramlette, 1961).

14 C age artefacts
Radiocarbon analysis focuses on determining the mean 14 C activity of a particular sample, which is reported together with an associated analytical error.This mean activity of samples is often considered in the literature as conventional 14 C age in 14 C yr BP.Conventional 14 C age, a unit of convenience, is linear vs time, whereas 14 C activity is actually exponential vs time, due to 14 C being a radioactive isotope.Therefore, with increasing age heterogeneity of a sample, we can expect increased offset between the AMS conventional 14 C age of a sample (the mean measured activity of the homogenised sample reported as conventional age) and the idealised mean of the conventional 14 C ages of all single foraminifera within the sample.In Fig. 1, we compare the simulated AMS mean conventional 14 C age calculated for each discrete depth to the idealised mean 14 C age (based on the mean value of all single foraminifera conventional 14 C ages contained within a sample).The resulting offset can help shed light upon how the measurement of age-heteregenous material is inherently biased towards younger (higher 14 C activity) specimens contained within the sample.We find that the AMS mean 14 C age is generally younger than the idealised mean 14 C age in all cases.This effect can be attributed to the fact that younger foraminifera within a heterogeneous sample contribute exponentially more to a sample's mean 14 C activity (what the measurement process is actually analysing) than older foraminifera do.This bias towards younger foraminifera is most apparent in cases with large intra-sample heterogeneity, such as in scenarios with lower SAR (Fig. 1a), and is also reduced somewhat in the case of more broken foraminifera (Fig. 3a), due to lesser older foraminifera being picked, thus reducing the age heterogeneity.In the case of the highest SAR scenarios (> 40 cm kyr -1 ) the aforementioned bias is insignificant in a practical sense, in that it falls within the typical 14 C measurement error.For all scenarios, superimposed upon the general bias are artefacts of the Earth's dynamic Δ 14 C history, caused by foraminifera from times of markedly differing Δ 14 C to be mixed together into a single sample, thus altering a sample's 14 C activity distribution and causing downcore dynamic offsets between AMS mean 14 C age and idealised mean 14 C age.The most pronounced example of these artefacts can be seen during known periods of dynamic Δ 14 C, such as during the Laschamps geomagnetic event (ca.40~41 ka) (Guillou et al., 2004;Laj et al., 2014), when a large spike in atmospheric 14 C production occurred (Muscheler et al., 2014).We note that our simulations assign single foraminifera 14 C activity using the Marine13 calibration curve, while newer records of Δ 14 C (Cheng et al., 2018) suggest that the Laschamps Δ 14 C excursion may have been of greater magnitude than was previously thought.A larger excursion would generate even more pronounced 14 C artefacts in the downcore, multi-specimen, discrete-depth record.Furthermore, there may exist as yet undiscovered, past short-lived excursions in Δ 14 C (Miyake et al., 2012(Miyake et al., , 2017;;Mekhaldi et al., 2015).
We can also visualise how well a sample's 14 C activity probability distribution function (PDF) is represented by a distribution based on its mean AMS-measured 14 C activity and 1σ measurement error.This visualisation is shown on the vertical axes of Fig. 1d-i and Fig. 2d-i for a number of simulated discrete depths for the different SAR scenarios with a BD of 10 cm.It can be clearly seen that that the normal distribution derived from a sample's AMS mean measurement and associated uncertainty is a poor representation of a sample's actual 14 C activity distribution.

Calibration amplifies 14 C age distribution mischaracterisation
When estimating a true age distribution for a particular sample, researchers calibrate a normal distribution of 14 C age using suitable calibration curve (in this case Marine13).As discussed in the previous section, the aforementioned normal distribution of 14 C activity derived from the measurement mean and machine error is not a faithful representation of the actual 14 C activity distribution for a particular discrete depth.Such a misrepresentation has the potential to be further amplified during the calibration process itself, potentially resulting in a poor estimation of a discrete depth's 95.4% age range and/or median age, the latter of which is often used to calculate e.g.sedimentation rates, or represents the region of highest probability which will steer age-depth modelling routines.In Fig. 1b (0% broken foraminifera) and Fig. 3b (10% broken foraminifera), we show the offset between each discrete depth's true median age, and the corresponding median age derived from 14 C calibration process.We find large offsets for all constant SAR scenarios, ranging from ~200 years in the case of the the 60 cm kyr -1 scenario, to up to ~700 years in the case of the 5 cm kyr -1 scenario.In certain low SAR scenarios that coincide intervals of the calibration curve that are highly resolved (e.g. the late Holocene), the discrete-depth true median age can consistently fall outside the 68.2% age range predicted by the 14 C dating and calibration process.A 68.2% certainty suggests that, statistically, the true median will fall outside of the 68.2% calibrated age range in only 31.8% of cases, but in the case of the 5 cm kyr -1 scenario (Fig. S1), the true median falls outside of the 68.2% calibrated age range for 84% of the discrete depths spanning the 5 to 0 cal ka period.In the case of 10% broken foraminifera, this effect is reduced.
All offsets for all scenarios vary dynamically downcore, meaning that they can potentially cause spurious interpretations of changes in SAR.Furthermore, as these offsets occur during periods of dynamic Δ 14 C, which can be caused by large-scale changes in the carbon cycle caused by climate shifts (such as during the last deglaciation), it is possible that some apparent changes in SAR in the palaeoceangraphic literature may have been erroneously attributed to climate processes, when they may be (partially) an artefact of the current application of 14 C dating and calibration within palaeoceanography.
Using the simulation output, it is also possible to quantitatively estimate how well the current 14 C dating and calibration state-of-the-art applied within palaeoceanography estimates the true age range contained within discrete-depth sediment intervals.The offset between the calibrated 95.4% age range and the true 95.4% age range for each discrete depth for all SAR scenarios is shown in Fig. 1c (0% broken foraminifera) and Fig. 3c (10% broken foraminifera) and is further visualised for all scenarios in Fig. S1-S10.For the lower SAR scenarios, the current application of 14 C dating within palaeoceanography significantly underestimates the total age range contained within each discretedepth, by many thousands of years.The underestimation is less in the case of the scenario with 10% broken foraminifera.In the case of higher SAR scenarios, the discrete-depth 95.4% age range predicted by the 14 C calibration process is similar to that of the discrete depth 95.4% age range of the sediment itself.In some cases with very high SAR, the 14 C calibration process actually overestimates the 95.4% age range (e.g.Fig. 1e, Fig. 3e, Fig. S5 and Fig. S10).

The influence of the analytical blank
A general consequence of bioturbation and the subsequent mixing of single foraminifera specimens is that older foraminifera become systematically mixed upwards throughout the sedimentation history of a sediment archive.This general mixing can have a particular consequence near the analytical limit of the 14 C method, in that foraminifera with a 14 C activity that is lower than a laboratory's analytical sensitivity can become mixed into samples. 14C determinations with a 14 C age that is older than the established 14 C blank value (i.e. they fall below the detection limit of the analytical process) are commonly referred to as " 14 C-dead".Within older intervals of heterogeneous deep-sea sediment archives, it is possible that a sample with an apparent measured 14 C age younger than the 14 C blank value can already contain a significant proportion of 14 C-dead foraminifera.The presence of these 14 Cdead specimens within a sample will bias the sample's apparent measured 14 C age towards a too young value, because they will contribute a 14 C activity to the sample that is equivalent to the laboratory's analytical blank.Such artefactually young 14 C ages could ultimately erroneously be interpreted as age-depth features.In Table 1, the very first downcore occurrence of at least one simulated 14 C-dead foraminifer is detailed for each of the aforementioned constant SAR scenarios introduced in Section 3.0.In the case of low SAR scenarios with 0% broken foraminifera, 14 C-dead foraminifera are already present in discrete-depth samples with apparent AMS ages that would normally be considered well above the 14 C blank value, e.g. an apparent AMS age of 22647 14 C yr BP in the case of 5 cm kyr -1 , and 33747 14 C yr BP in the case of 10 cm kyr -1 .However, the contribution of 14 C-dead foraminifera at these levels may still be insignificant.The exact percentage contribution of 14 C-dead foraminifera to discrete depth AMS determinations is, therefore, detailed in Fig. 4a, 4c, 4e, 4g and 4i.From this analysis, it transpires that the first occurrence of at least 1% contribution of 14 Cdead foraminifera to discrete-depth AMS determinations occurs in the case of AMS ages of 39158 14 C yr BP and 43601 14 C yr BP, respectively for the 5 cm kyr -1 and 10 cm kyr -1 scenarios.The percentage increases quickly further downcore.In the case of scenarios involving 10% broken foraminifera, older foraminifera within discrete-depth sediment intervals are no longer whole, and therefore not picked for samples by a palaeoceanographer preferring whole specimens.The consequence of this effect is that the first occurrence of picked 14 C-dead whole foraminifera occurs much further downcore (Table 1, Fig. 4b,4d,4f,4h and 4j).This finding further underlines the importance of understanding foraminifera preservation conditions for particular species and/or water chemistry, and the associated consequences for 14 C dating.
As motivated in the method section, for practical reasons we have set the 14 C analytical blank value at 46806 14 C yr BP within our model simulations.The laboratory blank value in most laboratories is around ~50000 14 C yr BP, or even greater, depending on sample size, preparation conditions and measurement capability.For such greater blank values, essentially the same curves as shown in Fig. 4 would apply (i.e.assuming there are no as of yet undiscovered, large Δ 14 C excursions around the period of the blank age), but shifted further to the right on the x-axis.In other words, researchers interested in interpreting Fig. 4 in the case of an analytical blank of 50000 14 C yr BP should simply shift the curves to the right such that the 100% 14 C-dead contribution exactly coincides with 50000 14 C yr BP on the x-axis.

Dynamic sediment core scenarios
The multiple sediment archive scenarios carried out in Section 3.0 all involved best-case input parameters with constant SAR.In Fig. 5, we carry out four scenarios to investigate the influence of stepwise changes in the following four input parameters: (1) SAR; (2) BD; (3) species abundance and; (4) reservoir age (ΔR).In each of the four scenarios, one of the aforementioned input parameters is varied at a certain time while the other three are kept constant (Figs.5a-d).In this way, the influence of one of the dynamic input parameters can be independently judged.To further ensure the ability to independently judge the dynamic sediment input parameters, in these scenarios we do not employ a dynamic Δ 14 C history using Marine13, but instead assign 14 C activities to foraminifera using a constant Δ 14 C history (with an added constant 400 yr reservoir age).This constant Δ 14 C history is assigned as detailed in the method (Section 2.1).For the calibration process, we also constructed a calibration curve with same aforementioned constant Δ 14 C (also with an added constant 400 yr reservoir age), whereby the confidence interval sizes of Marine13 are copied for incorporating a realistic calibration uncertainty.The scenario with dynamic ΔR (Fig. 5d) is simulated upon the foraminifera by additionally subtracting (ΔR = -100) or subtracting (ΔR = +100) to/from the 14 C age of simulated foraminifera respectively younger or older than 20 ka.During the simulated picking and calibration processes, it is assumed that the researcher is aware of the change in ΔR and, during calibration, applies a ΔR of -100 to all discrete depths shallower than 204 cm, and a ΔR of +100 to all discrete depths deeper than 204 cm.
The simulations using dynamic parameter inputs demonstrate that temporal changes in any of the four main input parameters (SAR, BD, species abundance, ΔR) can result in the generation of 14 C-induced age-depth artefacts in the discrete-depth domain, due to the median calibrated age dynamically deviating from the true median age downcore (Fig. 5f).We also note that the changes in the input parameters can cause the 14 C dating and calibration process to generate artefacts in the over-or underestimation of the true 95.4% age range of the sample by the calibration process, artefacts which are superimposed upon a long-term change in the underestimation of the true age range of the sample caused by a long term change in the confidence intervals in the calibration curve (Fig 5g).Specifically regarding ΔR, the current method for correcting for reservoir age during calibration, which we apply in this simulation, involves subtracting the ΔR from the the AMS date just prior to calibration.This method poses a particular challenge for periods near temporal changes in ΔR, where multi-specimen samples will incorporate single foraminifera with varying individual ΔR values.The blanket application of a single ΔR correction to the entire sample fails to adequately represent the ΔR heterogeneity of the foraminifera population.
The influence of the various dynamic parameters upon the 14 C dating and calibration process, as outlined in Fig. 5, represent further sources of age-depth bias in addition to the large biases caused by dynamic Δ 14 C history previously outlined in Section 3.0.Furthermore, as has been detailed in previous studies, changes in abundance and bioturbation depth can in themselves also cause additional general age-depth artefacts, no matter what geochronological method is being used (independent of the 14 C method), (Bard, 2001;Löwemark and Grootes, 2004;Löwemark et al., 2008;Lougheed, 2020).Such effects can be seen in age-depth artefacts also visible in the true median age for the dynamic BD scenario (Fig. S12) and the dynamic abundance scenario (Fig. S13).Such artefacts occur in addition to the artefacts related to the 14 C dating and calibration process outlined in this study.
Researchers should be aware that periods of long-term climate change can cause many input parameters to change in concert.For example, the last deglaciation in the North Atlantic is known to be characterised by highly dynamic Δ 14 C (Stuiver et al., 1986;Reimer et al., 2013), dynamic reservoir age (Austin et al., 1995;Waelbroeck et al., 2001;Butzin et al., 2020) and dynamic foraminiferal abundance (Ruddiman and McIntyre, 1981).It is possible that all of these parameters can combine at once to produce very large age-depth artefacts, which could lead to spurious interpretations regarding the relationship between, e.g., the last deglaciation and the perceived magnitude of associated SAR change.

Conclusion
This study demonstrates the possibility for the current 14 C dating and calibration method, as it is applied to multi-specimen samples within palaeoceanography, to produce age-depth artefacts, even in the case of best-case sediment archives where SAR, BD, species abundance and reservoir age are all constant.We also find that high SAR sediment archives (40 cm kyr -1 and 60 cm kyr -1 ) are not immune to the generation of age-depth artefacts during the 14 C dating and calibration process.Additional agedepth artefacts can be generated in the case of real-world sediment archives where the aforementioned SAR, BD, species abundance and reservoir age processes are inherently dynamic.Researchers should be aware, therefore, of the possible existence of such artefacts when interpreting deep-sea sediment geochronologies developed using 14 C methods applied to multi-specimen samples.Key to understanding the possible existence of such artefacts is a good quantification of the possible magnitude of temporal change in both foraminiferal abundance and preservation conditions, as well as awareness of the possibility of changes in local 14 C activity due to the influcence of dynamic Δ 14 C and reservoir age.It may also be necessary to revisit existing studies and re-evaluate the magnitude of changes in deep-sea sediment SAR inferred from 14 C-based geochronologies, especially close to periods of dynamic Δ 14 C and/or dynamic foraminiferal abundance.These 14 C-specific artefacts should be considered in addition to previously highlighted general age-depth artefacts that can occur in sedimentary records (Bard, 2001;Löwemark and Grootes, 2004;Löwemark et al., 2008;Lougheed, 2020).One should also consider that paired analysis of mulispecimen samples for both 14 C and another proxy could lead to a signal offset between the two proxies due to the 14 C method, as currently applied within palaeoceanography, being prone to the generation of age artefacts as outlined in this study.

Outlook and future research
We demonstrate that the failure to take into account the effect of bioturbation upon the ( 14 C) age distribution of foraminifera in multi-specimen samples sourced from deep-sea archives can lead to spurious age interpretations, especially during the 14 C calibration process.We propose, therefore, that the 14 C calibration process for deep-sea sediment archives could be improved in future studies through the development of a new 14 C calibration method including bioturbation a priori, seeing that no information regarding bioturbation is included in the current palaeoceanographic state-of-the-art.This new approach would involve constructing a representative distribution for 14 C age that includes a priori information regarding the approximate SAR and BD of the sediment archive, while also taking into account some basic information regarding possible temporal changes in species abundance and ΔR.Such a future development would go some way to providing more realistic uncertainties (i.e.95.4% age range) to 14 C-derived age-depth geochronologies in deep-sea sediment archives.
Finally, we note that increased automation and cost-effectiveness in 14 C analysis of ultra-small carbonate samples (Ruff et al., 2010;Lougheed et al., 2012;Wacker et al., 2013bWacker et al., , 2013a) ) can allow for the parallel measurement of δ 18 O, δ 13 O and 14 C on a single foraminifer of suitable size (Lougheed et al., 2018), thereby allowing for the extraction of both age and palaeoclimate data from single foraminifera in a manner that is independent of the sediment depth and bioturbation aspects of deepsea sediment archives.
First downcore occurrence of " 14 C-dead" foraminifera Table 1.The first downcore discrete-depth where " 14 C-dead whole" foraminifera occur (i.e.ndead ≥ 1) for the various constant SAR and broken foraminifera scenarios discussed in Section 3 of this study.
Also shown are the simulated median true ages, AMS 14 C ages and median 14 C calibrated ages corresponding to the discrete depth.The simulation analytical blank value is set at 46806 14 C yr BP (see Section 2.1), thus any single foraminifera with a 14 C age older than that blank value are assumed " 14 C-dead".corresponds to its mean.The pink probability distribution on the x-axis represents the calibrated age PDF arising from the calibration of the aforementioned AMS 14 C determination using Marine13 (Reimer et al, 2013) and MatCal (Lougheed and Obrochta, 2016), where the pink square represents the median calibrated age.Also shown, for reference, are the Marine13 calibration curve 1σ (dark grey) and 2σ (light grey) confidence intervals.corresponds to its mean.The pink probability distribution on the x-axis represents the calibrated age PDF arising from the calibration of the aforementioned AMS 14 C determination using Marine13 (Reimer et al, 2013) and MatCal (Lougheed and Obrochta, 2016), where the pink square represents the median calibrated age.Also shown, for reference, are the Marine13 calibration curve 1σ (dark grey) and 2σ (light grey) confidence intervals.and 10% broken foraminifera, (c) SAR of 10 cm kyr -1 and 0% broken foraminifera (d) SAR of 10 cm kyr -1 and 10% broken foraminifera, (e) SAR of 20 cm kyr -1 and 0% broken foraminifera, (f) SAR of 20 cm kyr -1 and 10% broken foraminifera, (g) SAR of 40 cm kyr -1 and 0% broken foraminifera, (h) SAR of 40 cm kyr -1 and 10% broken foraminifera, (i) SAR of 60 cm kyr -1 and 0% broken foraminifera, (j) SAR of 60 cm kyr -1 and 10% broken foraminifera.

Figure 1 .
Figure1.Overview of results of simulations using Marine13 Δ 14 C involving multiple constant SAR scenarios(5, 10, 20, 40  and 60 cm kyr -1 ) with constant BD of 10 cm, constant species abundance of 100% and 0% broken foraminifera.All discrete-depth results are plotted against their true median age on the x-axes.(a) The discrete-depth offset between mean AMS (i.e.laboratory) conventional 14 C age and the idealised mean 14 C age.(b) The discrete-depth offset between the true median age and the calibrated median age (i.e. that derived from the 14 C dating and calibration process).(c) The discretedepth difference between the calibrated highest posterior density (HPD) 95.4% age range (i.e that derived from the 14 C dating and calibration process) and the true 95.4% age range of the sediment.(d, e, f, g, h, i) A visualisation of 14 C calibration skill for select discrete-depth samples from various scenarios indicated on the figure panels.The blue histograms represent the actual single-foraminifera simulation output: on the x-axis the true age distribution of the single foraminifera (with the blue diamond corresponding to the median true age), and on the y-axis the corresponding true 14 C age distribution of the single foraminifera (with the blue diamond corresponding to the mean 14 C age of all individual foraminifera).All histograms are shown using 30 ( 14 C) year bins.The pink distributions represent the current state-of-the art in 14 C dating.The pink normal distribution on the y-axis represents an AMS 14 C determination carried out upon the single specimens, where the pink square

Figure 2 .
Figure 2.An overview of residence time of single foraminifera within the active BD for the various simulation scenarios detailed in Fig. 1, i.e. with a constant BD of 10 cm and a SAR of (a) 5 cm kyr -1 (b) 10 cm kyr -1 (c) 20 cm kyr -1 (d) 40 cm kyr -1 (e) 60 cm kyr -1 .

Figure 3 .
Figure3.Overview of results of simulations using Marine13 Δ 14 C involving multiple constant SAR scenarios(5, 10, 20, 40  and 60 cm kyr -1 ) with constant BD of 10 cm, constant species abundance of 100% and 10% broken foraminifera.All discrete-depth results are plotted against their true median age on the x-axes.(a) The discrete-depth offset between mean AMS (i.e.laboratory) conventional 14 C age and the idealised mean 14 C age.(b) The discrete-depth offset between the true median age and the calibrated median age (i.e. that derived from the 14 C dating and calibration process).(c) The discretedepth difference between the calibrated highest posterior density (HPD) 95.4% age range (i.e that derived from the 14 C dating and calibration process) and the true 95.4% age range of the sediment.(d, e, f, g, h, i) A visualisation of 14 C calibration skill for select discrete-depth samples from various scenarios indicated on the figure panels.The blue histograms represent the actual single-foraminifera simulation output: on the x-axis the true age distribution of the single foraminifera (with the blue diamond corresponding to the median true age), and on the y-axis the corresponding true 14 C age distribution of the single foraminifera (with the blue diamond corresponding to the mean 14 C age of all individual foraminifera).All histograms are shown using 30 ( 14 C) year bins.The pink distributions represent the current state-of-the art in 14 C dating.The pink normal distribution on the y-axis represents an AMS 14 C determination carried out upon the single specimens, where the pink square

Figure 4 .
Figure 4.An estimation of the contribution of " 14 C-dead" (i.e.activity below the analytical blank value) foraminifera to discrete-depth sample activity plotted against the apparent AMS 14 C mean age of the discrete-depth sample.Based on the simulation scenarios detailed in Fig. 1 and Fig 3 with a constant BD of 10 cm and (a) SAR of 5 cm kyr -1 and 0% broken foraminifera, (b) SAR of 5 cm kyr -1

0 % broken foraminifera scenario 10% broken foraminifera scenario
BD, (c) species abundance, (d) reservoir age (ΔR).A constant broken foraminifera percentage of 10% is applied in all cases.(e)For each scenario, the resulting discrete-depth offset between mean AMS (i.e.laboratory) conventional 14 C age and the idealised mean 14 C age.(f)For each scenario, the discrete-depth offset between the true median age corresponding to the median true age), and on the y-axis the corresponding true 14 C age distribution of the single foraminifera (with the blue diamond corresponding to the mean 14 C age of all individual foraminifera).All histograms are shown using 30 ( 14 C) year bins.The pink distributions represent the current state-of-the art in 14 C dating.The pink normal distribution on the yaxis represents an AMS 14 C determination carried out upon the single specimens, where the pink square corresponds to its mean.The pink probability distribution on the x-axis represents the calibrated age PDF arising from the calibration of the aforementioned AMS 14 C determination using a custom-made calibration curve with constant Δ 14 C (see Section 4.0) and MatCal(Lougheed and and the calibrated median age (i.e. that derived from the 14 C dating and calibration process).(g) For each scenario, the difference between the calibrated highest posterior density (HPD) 95.4% age range (i.e that derived from the 14 C dating and calibration process) and the true 95.4% age range of the sediment.(h, i, j, k) A visualisation of 14 C calibration skill for select discrete-depth samples from various scenarios indicated on the figure panels.The blue histograms represent the actual singleforaminifera simulation output: on the x-axis the true age distribution of the single foraminifera (with the blue diamond