No Consistent Simulated Trends in the Atlantic Meridional Overturning Circulation for the Past 6,000 Years

The Atlantic Meridional Overturning Circulation (AMOC) is a key feature of the North Atlantic with global ocean impacts. The AMOC's response to past changes in forcings during the Holocene provides important context for the coming centuries. Here, we investigate AMOC trends using an emerging set of transient simulations using multiple global climate models for the past 6,000 years. Although some models show changes, no consistent trend in overall AMOC strength during the mid-to-late Holocene emerges from the ensemble. We interpret this result to suggest no overall change in AMOC, which fits with our assessment of available proxy reconstructions. The decadal variability of the AMOC does not change in ensemble during the mid-and late-Holocene. There are interesting AMOC changes seen in the early Holocene, but their nature depends a lot on which inputs are used to drive the experiment.

A large amount of different proxies have been used to reconstruct AMOC during the Holocene.These have been assessed to show a relatively stable overall AMOC strength (excepting several abrupt events) until a weakening during the Industrial period (Gulev et al., 2021).It can often be unclear whether individual reconstructions are tracking the integrated flow throughout overturning circulation or just a particular, local component.Reconstructions from both vertical density gradient (Lynch-Stieglitz et al., 2009) or based on Pa/Th ratios (e.g., Hoffmann et al., 2018;Lippold et al., 2019;Ng et al., 2018) suggest little change in the overall AMOC strength since 9,000 years ago.Data assimilation approaches similarly suggest little long-term AMOC change in the Holocene (Osman et al., 2021;Ritz et al., 2013).Higher temporal resolution reconstructions for the past 2,000 years also show little change in overall AMOC, but exhibit uncertainty about the timing and nature of the Industrial Era decline (Caesar et al., 2021;Thornalley et al., 2018;Valley et al., 2022).Reconstructions exist that propose different temporal behavior; combining all the existing records to provide a complete picture of all aspects of the AMOC remains an ongoing effort.
Snapshot equilibrium simulations for 6,000 years ago (6 ka) have been performed for the midHolocene experiment of the Palaeoclimate Modeling Intercomparsion Project (PMIP, Kageyama et al., 2018).Brierley et al. (2020) found that the AMOC strength in the midHolocene ensemble is not markedly different.These results are supported by associated simulations of the last interglacial (Jiang et al., 2023).There is known to be a resolution dependency (Shi & Lohmann, 2016;Shi et al., 2020), which itself could vary by model (Jackson et al., 2020).
Currently there is an effort in the community to undertake transient Holocene simulations, which focus on analyzing the time-dependent interactions between different components in the Earth system and the long-term climate evolution.Here we collate the emerging set of Holocene transient simulations from different modeling groups to further investigate whether there is a consistent message from the ensemble about trends in (a) AMOC strength, (b) its spatial structure, and (c) its internal decadal variability since 6,000 years ago.Summary information about the different transient simulations is given in Section 2, along with an explanation of the analysis procedures.Further information about each of the individual simulations can be found in Supporting Information S1.The results of the AMOC trends in Holocene transient runs are presented in Section 3, followed by discussion and conclusions in the last section.

Data and Methods
We use nine transient model simulations from eight different coupled climate models (summarized in Table 1).All of the simulations are run continuously toward the present day from 6 ka or earlier.Not all of the models are truly independent: EC-Earth3-veg-LR, KCM, and IPSL-CM5 use NEMO ocean model at different resolutions (Crosta et al., 2018;Madec et al., 2008); AWI-ESM-2, MPI-ESM, and KCM have versions of the ECHAM atmosphere (Mauritsen et al., 2019;Roeckner et al., 2003;Shi et al., 2020;Sidorenko et al., 2019).
All simulations incorporate changes in the orbital configuration, and their associated changes in the seasonal distribution of incoming solar radiation across Earth (Otto-Bliesner et al., 2017).Also varying concentrations of well-mixed greenhouse gases are specified in every simulation using ice-core records, although the precise reconstructions used do differ.Those simulations that start in the early Holocene generally incorporate changes in ice-sheet topography and their associated changes in the land-sea mask (Hopcroft & Valdes, 2021;Otto-Bliesner et al., 2006;Tian et al., 2022).Only the simulations with CCSM3 impose meltwater fluxes implied by changes in ice-sheet topography.Reconstructions of volcanic forcing and variations in total solar irradiance introduce forced variability into the simulations, although this has only been done in a single simulation (Dallmeyer et al., 2021).Anthropogenic impacts on global vegetation started with the development of farming in the early Holocene, but became much more substantial approaching the industrial period (Smith & Zeder, 2013).These are incorporated by MPI-ESM using the reconstructions after Hurtt et al. (2011) and Lawrence et al. (2016), but only for the last millennium (850-1850 CE).
The zonal-averaged meridional overturning streamfunction in the Atlantic basin is computed for each decade.Given that the data are decadally averaged, calendar adjustments to account for variations in the month lengths (Shi et al., 2022) should not matter.Therefore, they have not been applied.The strength of the AMOC is taken as the maximum streamfunction at 30°N below 500 m after Brierley et al. (2020).The computation of the standard deviation of the AMOC at 30°N below 500 m is based on a sliding 100-year time window, starting from at earliest 7 ka BP.

Trends in Maximum AMOC Strength
The evolution of maximum AMOC strength in each transient simulation is shown in Figure 1.Changes in AMOC since industrialization are not captured through a combination of the varying simulation end dates and the 100-year running mean used to smooth the time series.Absolute AMOC strength differs substantially between the models (Figure 1), which is mainly due to the model physics.Two simulations-AWI-ESM-2 (Shi et al., 2022) andCCSM3 (Otto-Bliesner et al., 2006)-show an overall increasing trend throughout their simulation years, but they differ in timing: AWI-ESM-2 sees an enhancement of the AMOC by 10% during 6-4 ka BP, after which the AMOC remains relatively stable and a slight decreasing trend is shown in the late Holocene.The increasing trend in CCSM3 is dominated by the strengthening of AMOC in the early to mid-Holocene, with only a subtle trend from 6 ka BP onwards.Conversely three simulations show an overall decreasing AMOC trend for the maximum AMOC: IPSL-CM5 (∼2 Sv), EC-Earth3-veg-LR (∼1 Sv) and KCM.In KCM there is a decrease of approximately 10% in the early portion, but after roughly 6 ka it remains relatively stable with a marginal increase in the late Holocene (Segschneider et al., 2018).The other simulations do not show any obvious trends in the overall maximum AMOC strength at 30°N through the Holocene (MPI-ESM, HadCM3 and CESM1.2.1).Both transient runs with the MPI-ESM (SLO0043 and SLO0050) do display a slightly higher maximum AMOC strength at 8 to 6 ka BP compared to later periods in the Holocene.In HadCM3, the AMOC strength before and after the 8.2 ka event remain relatively stable at ∼19.5-21 Sv.CESM1.2.1 exhibits a step-change at 7.5 ka BP, but the AMOC is very stable afterward.
All the simulations that start in the early Holocene (CCSM3, HadCM3, KCM, and CESM1.2.1) show stronger changes in AMOC prior to 8 ka than afterward.The early Holocene saw the 8.2 ka event with a large amount of meltwater entering into the Labrador Sea (e.g., Barber et al., 1999;Matero et al., 2017) through three possible freshwater sources: the sudden discharge of Lake Agassiz, the altered route of the continental freshwater in the North America due to the Laurentide ice sheet melting, and the continuous retreat of Laurentide ice sheet and meltwater release from 9 to 6 ka BP (Aguiar et al., 2021).However, the different forcings imposed in the simulations (Table 1) mean that only CCSM3 responds directly to a changed meltwater flux.The early Holocene decline in KCM arises primarily from model drift (Segschneider et al., 2018), but may include an AMOC response to increasing Greenhouse gases (as the lack of a continued trend into the late Holocene rules out an orbital influence).The sudden reduction in AMOC strength in HadCM3 around 8 ka BP arises from the opening of Hudson Bay, when the land sea mask is updated.This connected a large volume of freshwater to the Atlantic and weakened the AMOC for around 250 years.The run with CESM1.2.1 demonstrates an abrupt decrease in AMOC strength by 18% at 7.7-7.5 ka BP, after which the AMOC recovered and stabilized, but never returned to the same intensity as that in the early Holocene.The accumulated effect of the rapid retreat of the Laurentide ice sheet from 9 to 7 ka BP (Tian et al., 2022) could be the main cause for the abrupt weakening of AMOC at around 7.7 ka BP in this run.
In conclusion, the transient simulations do not show any AMOC changes over the past 6,000 years that are "consistent" (i.e., with a majority of models showing statistically significant changes in the same direction).They do not have a consistent message about the small changes in the overall AMOC strength, as they show trends in different directions (Table S1 in Supporting Information S1) that are roughly three orders of magnitude less than those projected over the coming century (Fox-Kemper et al., 2021;Weijer et al., 2020).Several models simulate changes of roughly ±10%, but these are not of the same sign across models, nor do they exhibit similar temporal behaviors.The few simulations that start in the early Holocene all exhibit stronger changes prior to 6 ka BP than afterward.This is likely related to the loss of the remnant glacial ice through either meltwater or sea-level changes.

Trends in Spatial Structure of Streamfunction
There could be robust changes in the spatial structure of the AMOC, even if the ensemble members show little change in its overall strength.We investigate this possibility by mapping the trend in overturning streamfunction at each grid box from 6 ka BP to present (Figure 2).Different forms of AMOC evolution emerge-some models show the whole circulation spinning up (or down) together, whilst others demonstrate more complex structure (such as a subsurface warming at 30°N with cooling on either side of it).
Four simulations show broadly coherent changes in streamfunction especially visible in the deep southward return flow at 30°-50°N, 1,700-3,000 m (Figures 2b, 2e, and 2g show coherent decreasing trends; Figure 2h shows coherent increasing trends).IPSL-CM5, EC-Earth3-veg-LR, and KCM show an opposite direction of trend compared to CCSM3, as might be expected given their opposite trends in maximum AMOC strength (Figure 1).A tripole pattern in the mid-latitudes, extending down to ∼1,200 m, is seen in the simulations by HadCM3 (Figures 2c,2d,and 2f).Variations in the Mediterranean outflow could potentially be one of the causes lead to this pattern, given the latitude.Ivanovic et al. (2013) explore the impact of the Mediterranean outflow parameterization in one of the models used here, HadCM3, and demonstrate that it can create changes in AMOC of a similar spatial pattern (Ivanovic et al., 2014).Swingedouw et al. (2019) show the pattern of Mediterranean outflow changes are model dependent though.AWI-ESM-2 (Figure 2a) shows a pattern that combines both this upper-ocean mid-latitude tripole and a broad shift below 1,700 m.The CESM1.2.1 transient run has the weakest trend among all the simulations (Figure 2i), with almost no trend at any individual sites for the North Atlantic basin from 6 to 0.1 ka BP.
Taken as an ensemble, the simulations do not demonstrate a consistent trend in meridional streamfunction from 6 to 0 ka BP at any individual locations.Rather they highlight a range of possible behavior-from coherent changes throughout the basin or more nuanced patterns showing both strengthening and weakening at different locations.

Trends in AMOC Variability
The key difference between the two MPI-ESM simulations is the inclusion of externally forced variability (Bader et al., 2020).This motivates us to explore the AMOC variability throughout the Holocene, which we assess using the standard deviation of the decadally averaged, maximum overturning streamfunction at 30°N calculated over a sliding 100-year time window (Figure 3).However, there is clearly a strong role for internal variability in AMOC, as MPI-ESM SLO0050 shows roughly the same standard deviations as SLO0043 despite the addition of volcanic and solar forcing.
The magnitude of the (internal) variability varies substantially between simulations (Figure 3).The run with CESM1.2.1 has the smallest magnitude of the internal variability and indicates its simulated AMOC is very stable since 7 ka BP.Meanwhile, the transient runs with CCSM3, IPSL and KCM model also demonstrate relatively smaller magnitude compared to all other runs.Other simulations typically show a magnitude of the internal variability ranging from 1 to 1.5 Sv, with the strongest fluctuations in AWI-ESM2, IPSL, and EC-Earth3-veg-LR. 10.1029/2023GL103078 6 of 12 The CCSM3 simulation also demonstrates a millennium internal variability for the maximum AMOC at 30°N in the Holocene-this not seen in any other model (Figure 1), nor in other simulations with the same model (He & Clark, 2022).
None of the simulations show a large trend in the standard deviations (Figure 3).Over the past 6,000 years, only CCSM3 shows a small trend that is statistically significant (Table S1 in Supporting Information S1), and even that becomes insignificant if the analysis is extended back to 7 ka.Therefore, the ensemble as a whole shows no trend in the decadal variability of the maximum AMOC at 30°N (Figure 3; similarly for multi-decadal variability, Figure S2 in Supporting Information S1).We conclude that the internal variability of the AMOC remained constant during mid-and late Holocene, at least in models.

Discussion and Conclusions
Overall, there is little support from this ensemble of simulations for major changes in AMOC over the past 6,000 years.This is true for long-term trends in overall AMOC strength: although individual models may show small trends, there is no consistency in the direction of their changes.It is also true for internal variability of the AMOC.The different experimental set-ups used in the simulations did not appear to play a large role in AMOC evolution since 6,000 years ago, but there were clear consequences from the choice of imposed forcings in the early Holocene.This conclusion fits well with results from PMIP, which performed snapshot simulations for 10.1029/2023GL103078 9 of 12 6,000 years ago.They also found no consistent changes in AMOC strength (Brierley et al., 2020).Combining those mid-Holocene snapshot simulations alongside last interglacial simulations suggests that variations in precession would not be expected to alter AMOC (Jiang et al., 2023).
Our interpretation of the ensemble of Holocene transient model simulations as indicating no changes in AMOC agrees with various reconstructions of the overall AMOC (Figure 4).These include Pa/Th reconstructions, which have the benefit of (at least potentially) recording the integrated strength of AMOC from a few key sites (Lippold et al., 2019).Multiple independent AMOC reconstructions based upon data assimilation are also now available (Osman et al., 2021;Ritz et al., 2013).Additionally, the winter SST index of Caesar et al. (2018) can be applied to Holocene reconstructions of temperature anomalies (in this instance from Erb et al., 2022) to reconstruct past Holocene AMOC strength.Because this reconstruction represents annual mean temperature instead of November-May SST, the correlation to AMOC is likely slightly weakened and a direct conversion to absolute AMOC changes is not appropriate.Nonetheless this SST fingerprint approach should retain the timing and directions of any AMOC deviations and trends.Collectively these reconstructions also show little change in the AMOC during the mid-to-late Holocene (Figure 4).
Although the IPCC assessment of reconstructions suggest little change in AMOC during most of the past 6,000 years (Gulev et al., 2021), there are several proxy reconstructions that posit a late Holocene decline (Ayache et al., 2018;Valley et al., 2022).It may be that these reflect changes in individual components of the AMOC, such as Iceland-Scotland overflow water.Prior research suggests that strengthened deep water formation in the Labrador Sea could be compensated for by decreased deep water formation in the Nordic Seas, resulting in no change in overall AMOC (Renssen et al., 2005).All the data assimilation efforts (Figures 4b-4d) seem to show AMOC tail off toward the end of their respective records.These drops are not captured by the transient simulations, nor do proxy reconstructions show a strong long-term decrease over the last 2,000 years (Figure S1 in Supporting Information S1, Rahmstorf et al., 2015;Thornalley et al., 2018).Further work combining simulations and proxy reconstructions to explore possible compensation between different sub-components of the AMOC may provide useful additional information on future AMOC projections.
It has been suggested that the AMOC may play a role in Holocene centennial events, such as the 4.2 ka and 2.8 ka BP events (e.g., Denton & Broecker, 2008;Jalali et al., 2019;Keigwin & Boyle, 2000;Oppo et al., 2003).None of the individual transient simulations capture an event around 4.2 or 2.8 ka (Figure 1), nor do the assimilation products (Figure 4, although it is questionable whether they have sufficient temporal resolution to detect them).Nonetheless the weakest two centennial-scale periods of ensemble mean AMOC occur at ∼4.2 and 2.8 ka (Figure 4a), which warrants further investigation.This is especially intriguing as explanations involving volcanic or solar forcing seem unlikely as the majority of simulations do not include these forcings.
In summary, this research implies that the overall AMOC maintained its strength over the past 6,000 years until the recent changes.The evidence for this conclusion comes from an ensemble of transient simulations using fully coupled general circulation models, supported by snapshot simulations and data assimilation products.Additionally, we find no consistent trend in the internal variability of the overall AMOC, as the amplitude of decadal variations does not change noticeably between 6 ka to present in any of the simulations.Neither did this research show any consistent support for zonal mean streamfunction trends at particular latitudes or depths.This suggests that AMOC changes are unlikely to contribute to long-term (multi-millennial) global trends since the mid-Holocene (Kaufman & Broadman, 2023).We emphasize that this does not rule out AMOC playing an important role in ongoing and future climate changes (Fox-Kemper et al., 2021;Weijer et al., 2020).

Figure 1 .
Figure 1.Evolution of the Atlantic Meridional Overturning Circulation (AMOC) in nine climate model simulations.The AMOC strength is tracked by the maximum meridional overturning streamfunction at 30°N below 500 m (at a decadal resolution, smoothed by a 100-year running mean).Note the different vertical scales.

Figure 3 .
Figure 3. Running standard deviations of the maximum Atlantic Meridional Overturning Circulation strength at 30°N below 500 m from 7 ka BP to present (based on a sliding 100-year time window).

Figure 4 .
Figure 4. Comparison of Atlantic Meridional Overturning Circulation (AMOC) simulations with reconstructions.(a) Ensemble mean of the nine transient simulations' maximum AMOC at 30°N, after each simulation has been standardized by conversion to a z-score over the period 6-0 ka BP.(b) The AMOC reconstruction identified in the reanalysis ofOsman et al. (2021).This reanalysis combines marine geochemical data with climate model experiment using proxy system models and data assimilation.Dark and lighter shading on the timeseries indicate ±1σ and 95% confidence intervals, respectively.(c) AMOC variations reconstructed byRitz et al. (2013) using data assimilation with priors based on either LOVECLIM or Bern3D simulations.Gray dots are Pa/Th proxy data fromLippold et al. (2019), on the right axis.(d) AMOC variations resulting from applying an annualized SST index (afterCaesar et al. (2018)) to the surface air temperature anomalies reconstructed byErb et al. (2022) using data assimilation of the temperature 12k database(Kaufman et al., 2020).

Table 1
Bader et al. (2020)ocene Transient Simulations, Their Experimental Design and Primary Publication About the Individual Model Description Two simulations of MPI-ESM are used here: SLO50 is the main focus ofBader et al. (2020)and includes volcanic and solar forcing variations, SLO43 does not include them and is only considered as a sensitivity run inBader et al. (2020).cInthis study, we use the simplest of the HadCM3-M2.1densemble members, which is the "xokm" simulation.