Freshwater Routing In Eddy-permitting Simulations Of The Last Deglacial : Impact Of Realistic Freshwater Discharge

. Freshwater, in the form of glacial runoff, is hypothesized to play a critical role in centennial to millennial scale climate variability such as the Younger Dryas and Dansgaard-Oeschger Events, but this relationship is not straightforward. Large-scale glacial runoff events, such as Meltwater Pulse 1A, are not always temporally proximal to subsequent large-scale cooling. As well, the typical design of hosing experiments that support this relationship tends to artiﬁcially amplify the climate response. This study explores the impact that limitations in the representation of runoff in conventional hosing simulations has 5 on our understanding of this relationship by examining where coastally released freshwater is transported when it reaches the ocean. We focus particularly on the impact of: 1) the injection of freshwater directly over sites of deep-water formation (DWF) rather than at runoff locations (i.e. Hosing), 2) excessive freshwater injection volumes (often by a factor of 5), and 3) the use of present-day (rather than paleo) ocean gateways. We track the routing of glaciologically-constrained freshwater volumes from four different inferred injection locations in 10 a suite of eddy-permitting glacial ocean simulations using MITGCM under both open and closed Bering Strait conditions. Restricting freshwater forcing values to realistic ranges results in less spreading of freshwater across the North Atlantic and indicates that the freshwater anomalies over DWF sites depend strongly on the geographical location of meltwater input. In particular, freshwater released into the Gulf of Mexico generates a very weak freshwater signal over DWF regions as a result of entrainment by the turbulent Gulf In contrast, released into the with an open Bering or from the Eurasian Ice sheet is found to generate the largest salinity anomalies over DWF regions in the North Atlantic and GIN Seas respectively. Experiments show that when the Bering Strait is open, the Mackenzie River source exhibits more than twice as much freshening of the North Atlantic deep water deep-water (cid:58) formation regions as when the Bering Strait is closed. Our results illustrate that applying a freshwater ‘hosing’ directly into the North Atlantic with even “realistic” freshwater amounts still over-estimates the amount of terrestrial runoff reaching DWF regions. Given the simulated freshwater (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) salinity (cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58)(cid:58) anomaly and the lack of reconstructed impact on deepwater formation during the Bølling-Allerød, our results support (cid:58)(cid:58)(cid:58) that the majority of the MWP1A

cooling. As well, the typical design of hosing experiments that support this relationship tends to artificially amplify the climate response. This study explores the impact that limitations in the representation of runoff in conventional hosing simulations has 5 on our understanding of this relationship by examining where coastally released freshwater is transported when it reaches the ocean. We focus particularly on the impact of: 1) the injection of freshwater directly over sites of deep-water formation (DWF) rather than at runoff locations ::: (i.e. ::::::: Hosing), 2) excessive freshwater injection volumes (often by a factor of 5), and 3) the use of present-day (rather than paleo) ocean gateways.
We track the routing of glaciologically-constrained freshwater volumes from four different inferred injection locations in the Eurasian Ice sheet is found to generate the largest salinity anomalies over DWF regions in the North Atlantic and GIN Seas respectively. Experiments show that when the Bering Strait is open, the Mackenzie River source exhibits more than twice as much freshening of the North Atlantic deep water :::::::: deep-water : formation regions as when the Bering Strait is closed. Our results illustrate that applying a freshwater 'hosing' directly into the North Atlantic with even "realistic" freshwater amounts still over-estimates the amount of terrestrial runoff reaching DWF regions. Given the simulated freshwater :::::: salinity :::::::: anomaly 1 Introduction The most recent deglacial and glacial intervals are punctuated by large-scale centennial to millennial scale climate variability, 25 including the Bølling-Allerød, Younger Dryas, and Dansgaard-Oeschger events. Changes in freshwater discharge into the ocean and subsequent transport are thought to play a significant role in this variability through their resultant impact on deepwater formation (DWF) in the North Atlantic (Broecker et al., 1989;Manabe and Stouffer, 1997;Teller et al., 2002). However, recent earth system modelling (Peltier and Vettoretti, 2014;Zhang et al., 2014;Kleppin et al., 2015;Brown and Galbraith, 2016;Vettoretti and Peltier, 2016;Zhang et al., 2017;Klockmann et al., 2018) has also demonstrated that changing freshwater inputs 30 into the oceans is not required to get such transitions.
Furthermore, there are clear intervals during the last deglaciation when strongly enhanced net freshwater injection into the oceans resulted in no temporally proximal cooling (see Fig. 1). In the case of Meltwater Pulse (MWP) 1-A, current best estimates of its timing indicate that, within dating uncertainties, the freshwater injection aligns with the Bølling-Allerød (Deschamps et al., 2012) warm interval. This is consistent with the physical reasoning that a warm interval coinciding with 35 continental-scale ice sheets should result in enhanced glacial runoff. The more than millennial time interval to the onset of the subsequent cold Younger Dryas interval ::::: occurs ::::: more :::: than : a :::::::::: millennium ::::: later, ::::: which : is longer than would be consistent with a direct physical linkage. These ideas are further supported by the glacial systems modelling of Tarasov et al. (2012), whose runoff time series for the North American Ice Sheet complex is shown in the bottom panel of Fig. 1. North American runoff shows no significant increase prior to the Younger Dryas interval. Therefore, understanding the ::::::::::: Understanding ::: the : factors that 40 control the impact of freshwater on climate is an important step toward understanding these past climate changes and predicting those in the future.
Climate models have generally supported the ability of freshwater to generate abrupt climate transitions in hosing experiments, where large volumes of freshwater (1 − 10dSv 1 ) are imposed over sites of DWF (Kageyama et al., 2013). Such hosings are meant to reproduce the effect of changing freshwater input into the oceans from regional ice sheet melt and iceberg dis-45 charge as well as rerouting of surface runoff (Tarasov and Peltier, 2005). However, the climate model support for this connection between freshwater injection and climate transitions is problematic given at least three common experimental design problems that likely amplify climate system response compared to that which would ensue from more realistic freshwater injection experiments.
inhibit DWF through a persistent freshwater cap that results in near-immediate decreases in AMOC (Stouffer et al., 2006). This attempt to compensate for coarse model resolution via hosing is problematic, since it assumes that all of the freshwater reaches the near-surface DWF zone intact. It is unclear if a more realistic representation of runoff routing would yield a similar freshwater signal at the zones of DWF. The only eddy-permitting and boundary-current resolving modelling of freshwater 60 forcing from actual continental outlets to date under glacial boundary conditions suggests this is not the case (Condron and Winsor, 2012;Lohmann et al., 2020). However both of these studies have design limitations which limit the interpretability of their results. The unstructured mesh of FESOM in Lohmann et al. (2020) has refined (but not quite eddy-permitting) grid resolution largely only over the Arctic ocean and at coastal boundaries but is unable to resolve the impact of mesoscale eddies on freshwater transport over the central North Atlantic. In order to offset the short one-year interval of injection, Condron and 65 Winsor (2012) relied on fluxes of freshwater (50dSv) that were more than a factor of 20 larger than estimates derived from glaciological modelling over the Younger Dryas (Tarasov and Peltier, 2005) :::::::::::::::::::::::::: Peltier, 2005, 2006).
The third limitation involves the use of present-day rather than paleo-bathymetry, and especially its effect on ocean gateways.

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As such, we also conducted an additional experiment examining the impact of uncertainties in the state of the Bering Strait.
While it is clear that the Bering Strait was closed at the time of MWP1A, there is some evidence that it may have been open during the onset of the Younger Dryas (England and Furze, 2008) although the majority of available evidence indicates closure during this time (eg. Jakobsson et al., 2017) :::::::::::::::::::::: (e.g. Jakobsson et al., 2017). Hu et al. (2007Hu et al. ( , 2012Hu et al. ( , 2015 demonstrate that the transport of freshwater can be strongly affected by the state of the Bering Strait under various background climates, with the 90 effect that a closed Bering Strait leads to a stronger AMOC. Also, when the strait is closed, freshwater injected into the 50-70N band remains in the Arctic Ocean longer and results in a delayed recovery of the AMOC from freshwater forcing. We explore the ambiguity of the Bering Strait for the one key injection region that most likely be affected by its state, the Mackenzie River in the Canadian Arctic. The goal of this study is to directly address all of these limitations (ie. ::: i.e. unrealistically large volumes of freshwater injection, 95 injection directly onto sites of DWF, and misrepresentation of gateways) via a more realistic experimental design, and to elucidate how these limitations may bias inferences about the connection between glacial runoff and salinity anomalies at sites of deep water ::::::::: deep-water : formation. This study provides one of the first assessments to simultaneously address all of these issues, using freshwater injection amounts constrained by the output of a calibrated ensemble of glaciological models (Tarasov et al. (2012) ::::::::::::::::::::: Tarasov and Peltier (2006) and ongoing work) applied to a range of plausible source regions in a suite of 100 simulations that are eddy-permitting over all regions of freshwater transport except the Arctic, where mesoscale eddies tend to have spatial scales of O(10km) or less (Nurser and Bacon, 2014). We achieve this by assessing the amount of freshwater

Experimental Design
We start our discussion of the experimental design with a brief overview of the model configuration, followed by information regarding the simulations conducted, ending with a discussion of the limitations of our configuration. All of the simulations were performed using the Massachusetts Institute of Technology General Circulation Model (MITGCM, Marshall et al. (1997)) 110 :::::::::::::::::::::::::: (MITgcm, Marshall et al., 1997) coupled global sea-ice/ocean model in a Cubed-Sphere 6x510x510 (CS510) configuration, which provides ≈ 18km spatial resolution with 50 vertical levels. This grid geometry and resolution is eddy-resolving to eddy-permitting for all ocean regions equatorward ::::::::::: equator-ward of 60 • N (Chelton et al., 1998;Nurser and Bacon, 2014).
Our configuration is of comparable complexity and resolution to most members of the multi-model ensemble of present-day simulations presented in Hirschi et al. (2020). This resolution means the model is able to capture small-scale phenomena 115 like coastal boundary currents and mesoscale eddies that are among the primary mechanisms responsible for the transport of terrestrial meltwater discharged into coastal, near-shore, environments (Condron and Winsor, 2012;Hill and Condron, 2014).
Most of the coarser resolution models used in current and previous PMIP and CMIP working groups are unable to do this explicitly (Yang, 2003). A sample map of daily-mean salinity is shown in Fig. 2 in order to illustrate the turbulent characteristics of this model configuration. Generally, using eddy-resolving ocean model configurations results in a better representation 120 (primarily greater current velocities) of small-scale features and a better agreement between models and observations for present day (Hirschi et al., 2020). As well, some large-scale features, particularly the subpolar gyre, tend to be stronger at eddy-permitting resolutions (Treguier et al., 2005). An overall increase in the transport speed of tracers at higher resolutions is notable in Weijer et al. (2012). They find that a passive tracer released from the Greenland ice sheet covers the entirety of the subtropical gyre region within 2 years for a configuration at eddying resolution, whereas the non-eddying configuration 125 of the same ocean model takes up to 5 years to even reach the eastern seaboard of North America. These features show that conducting simulations at eddy-permitting resolutions results in an overall more vigorous transport of glacial runoff relative to coarser, non-eddy-permitting resolutions.
All simulations and relevant setups/forcings are listed in the supplemental table S1. The freshwater injection experiments were branched from one of two Younger Dryas control simulations, which were themselves initialized from a Last Glacial 130 Maximum (LGM) simulation. The LGM simulation was run for ≈ 20yr ::::::::: ≈ 20 years using MITGCM and the same boundary conditions as Hill and Condron (2014). This initial LGM simulation featured LGM bathymetry, sea level 120m lower than present, a glaciated Barents-Kara Sea and Canadian Archipelago, and a closed Bering Strait. The surface forcing used in the LGM simulation included winds, precipitation, 2m atmospheric temperatures, short and longwave radiation, surface runoff, and humidity from the CCSM3 working group's contribution to PMIP2 (Braconnot et al., 2007). We do not use surface restoration 135 in our experiments. Evaporation is handled internally by the model in the EXF (EXternal Forcing package) based on prescribed precipitation, relative humidity, and surface runoff fields. We used the 3D ocean salinity and temperature fields from the LGM simulation to initialise a control run with Younger Dryas bathymetry (including closed Bering Strait, CBS) and LGM surface forcing, which was integrated forward for an additional 10 years. The open Bering Strait (OBS) Younger Dryas control run was then branched from the CBS run, and both OBS and CBS control runs were integrated forward for an additional 10 years 140 before the freshwater forcing simulations (MAK, FEN, GSL, and GOM) were branched off.

Sea level was adjusted in all Younger Dryas runs to that provided by the sea-level solver component of the Glacial Systems
Model of Tarasov et al. (2012) at approx. 13ka. This sea level adjustment is not eustatic as was implemented in Hill and Condron (2014), but included major features which affect the geoid (Mitrovica and Milne, 2003) excepting the rotational component (Milne and Mitrovica, 1998), which has the weakest effect. The largest ensuing ocean gateway change at Younger 145 Dryas compared to LGM is the opening up of the Barents-Kara Seas. Opening both the Barents-Kara Seas and the Bering Strait increases the flow into and out of the glacial Arctic Ocean.

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Finally, we draw the reader's attention to three possibly significant experimental design limitations: the short duration of the integrations, issues with the surface forcing, and the uncoupled nature of the ocean simulations. These issues do not negate the value of our experiments for the question of freshwater routing during the deglacial interval for the following reasons.
Including the spin-up time, the injection runs are at longest ≈ 30yr ::::::::: ≈ 30 years : due to computational constraints. By using the same surface forcing in the Younger Dryas simulations as was used in the LGM simulation and initializing from the 180 temperature and salinity fields of the high-resolution LGM simulations, we were able to reduce the necessary spin-up time and thereby make efficient use of computational resources. As a result, these simulations are of sufficient duration to resolve surface ocean dynamical components (Le Corre et al., 2020), particularly the surface transports of freshwater by the glacial ocean, which is our primary focus here. However, they are of insufficient duration to spin up the deeper regions of the ocean, which require millennia. Cold-starting the YD simulations or initializing from present-day would have required substantially 185 longer spin-up before the surface conditions would have been considered "reasonable" approximations to YD.
We expect that the main effects of full equilibration of the deep ocean on the surface transports, relative to our state, would The Younger Dryas surface forcing fields we use are monthly values derived from a coupled climate model configured for LGM using ICE-5G boundary conditions. This ice sheet configuration has been shown to generate more zonal atmospheric 195 circulation patterns than more recent reconstructions of LGM ice sheets (Ullman et al., 2014), and LGM winds are expected to be stronger and more southward-shifted over the North Atlantic than winds during the Younger Dryas (Andres and Tarasov, 2019;Löfverström and Lora, 2017). These biases are expected to enhance zonal transport in the North Atlantic, as seen in comparison to a sensitivity experiment described in Supplemental Section S5. Thus, we would expect freshwater transported across the North Atlantic to be routed further south than under forcing which does not have this bias.

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Lastly, the configuration used is uncoupled and is lacking ocean-atmosphere interactions and feedback processes. At oceanic mesoscales, uncoupled configurations generally exhibit weaker AMOC relative to coupled configurations (Hirschi et al., 2020), and spatially variable sea surface temperature gradients can result in a wind stress curl which itself can modify sea surface temperatures (Chelton and Xie, 2010). However, the expected magnitude of this latter effect is small. For example, our injections can result in sea surface temperature differences of several degrees K (see Fig. S2), which may result in local changes in 10m 205 wind speeds of ≈ ±1m/s (Song et al., 2009).

Freshwater transport paths
We begin our examination of the injection experiments by tracing the pathways of freshwater transport from each injection location. We present in Fig. 3 salinity anomalies at the surface for each of the four injection locations. Figures S6, S7, S8, and S9 show the salinity anomalies at 50m, 100m, and 150m depth. These anomalies are calculated as the differences between averages over the last 5 years of the injection experiments and the corresponding 5 years of the relevant control simulation.

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From Figures 3a, b, and c, it can be seen that freshwater from MAK, FEN, and GSL tends to follow a single, continuous pathway around the Arctic, into the East and then West Greenland Currents, and following the Labrador Current to the northern margin of the Gulf Stream. There, the freshwater accumulates at the separation point of the Gulf Stream from the eastern coast of North America and is advected eastward. At the western coast of Europe, the freshwater is mixed into the northern North Atlantic via the collapse of eddies. The main difference between different outlets along this pathway is the magnitude of freshwater at 230 a given location, which is dependent on how far along this pathway the freshwater has traversed. The longer the pathway to that location, the greater opportunity for freshwater dilution through diffusion and eddy shedding and the greater time to get there. We note that if there is significant freshwater buildup ::::::: build-up along this pathway, it acts as a barrier, slowing down the transport of freshwater. This is exemplified in the case of the GSL in Fig. 3, which has much less freshwater in the eastern North Atlantic than the OBS MAK but much more entrainment of freshwater in the Gulf Stream at the location of its separation   Fig. S5. basin, passes through Fram Strait along the continental shelf of Greenland, and joins the East Greenland Current, the freshwater 240 remains primarily a surface signal. The concentration of freshwater in the surface current decreases dramatically, though, as it travels to the West Greenland Current and into the Labrador Sea and Baffin Bay. The large reduction in surface salinity anomaly along the east coast of Greenland coincides with the appearance of significant salinity anomalies at 100m depth and deeper. This is due to vertical mixing along the continental shelf of Greenland (with a local depth between 150-250m in this configuration) diluting the surface signature while introducing anomalies from the surface to 200m depth.

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While the freshwater pathway when the Bering Strait is open in Fig. 3A and Fig. S6 is broadly similar to that when it is closed, there are distinct features that provide insight into the mixing and transport processes occurring in a glacial ocean.
Firstly, the Arctic surface salinity anomaly does not spread into the Canada Basin to the same degree, because it is constrained to lie between the Transpolar Current (not noticeably present in the CBS case) and the coast of the Canadian Archipelago. As a result, the surface freshwater concentrations carried along the East Greenland Current and West Greenland Current and into the 250 Labrador Sea are much stronger than when the Bering Strait is closed. However, it is unclear that this contrast would persist if the simulation and injection were long enough to saturate accessible Arctic Ocean sectors. ::::: When ::::::::: comparing :::::: against ::::::::: OBS/CBS ::::: results ::::: from ::::::::::::::::::::: Karami et al. (2021) (with ::: the :::::: closed :::::::: Canadian ::::: Arctic ::::::::::: Archipelago) :: it : is :::::::: apparent ::: that :::: this :::::: contrast :: is ::::::: present :::: even Finally, freshwater released into the GOM initially fills that basin before leaking over the Florida shelf and into the Atlantic (see Fig. 3D and Fig. S9). Inflow from the Yucatán Channel acts as a barrier to the freshwater that has filled the GOM, preventing it from expanding southward. The lower sea level around the Younger Dryas results in a more isolated GOM relative to present and helps to sequester the GOM from the Atlantic. As in the other scenarios, the freshwater remains in the uppermost layers as it passes over the Florida shelf. Afterwards, it mixes downward as it travels north and eventually becomes 280 entrained in the Gulf Stream with freshwater present at least 200m deep. In neither the GSL nor the GOM injection is there evidence that the freshwater anomaly is able to cross the Gulf Stream as in Condron and Winsor (2012). The zonality of the Gulf Stream in this configuration does not affect this conclusion substantially. When the GOM experiment is repeated using modern wind forcing from ERA40 (Uppala et al., 2005) in section S5, the Gulf Stream is less zonal and closer to present-day observations. Yet, the majority of the freshwater remains primarily in a zonal band, while detectable pockets of freshwater now 285 enter the subpolar North Atlantic. Finally, none of these simulations account for the effect of sediment in the glacial runoff which can lead to bottom-riding (hyperpycnal) flow in (Parsons et al., 2001). Tarasov and Peltier (2005) suggested that outflow from the Mississippi (GOM) and the GSL at the magnitudes examined here would be heavily laden with sediment, rendering the outflow hyperpycnal with a resultant change in transport. By comparison, the MAK basin has limited surface sediments, and freshwater outflow would be much less affected by this process.

Injection site impact on DWF region salinity
Having traced the pathways of injected freshwater from each outlet, we now examine their respective contributions (Fig. 4) to three potential DWF regions: the Labrador Sea, the GIN Seas and the northern North Atlantic. Labrador Sea salinity is most strongly affected by freshwater injected into the MAK outlet. When the Bering strait is open, the peak freshening occurs within 7 years and appears to saturate after 10-15years ::::: 10-15 ::::: years. In contrast, closing the Bering Strait reduces the freshening 295 effect to half for the first decade of injection, after which its salinity anomaly gradually surpasses the OBS MAK. The FEN injection generates the next strongest anomaly in the Labrador Sea relative to the MAK outlets. None of the other tested outlets contribute noticeably to salinity anomalies in the Labrador Sea.
The GIN Seas region is most significantly affected by freshwater from the FEN injection, whose salinity anomaly is more than two times larger than that from the next largest contributor, the MAK. The reason for the importance of the FEN injection 300 to GIN Seas salinity is largely due to its being within the averaging domain combined with the local ocean circulation directing FEN freshwater across the region.
Finally, the primary location of deep mixing in these simulations, the northern North Atlantic, is affected by injection into all of the outlets examined here. The strongest contribution is from the OBS MAK injection, which generates approximately twice the freshening of the next strongest outlets, the FEN and GSL. Notably, the salinity anomaly from the FEN injection 305 location exhibits a much larger seasonal cycle compared to that of the other tested outlets.The GSL's freshening effect appears to increase in a step-wise fashion. None of the simulations appear to have reached equilibrium in the North Atlanticwith the possible : , :::: with ::: the : exception of FENwhose : . :::: The prominent seasonal cycle : of ::::: FEN, :::::: which : exhibits the largest amount of variability on inter-annual timescales : , :::::: reduces :::::::::: confidence :: in ::: this :::::::::: conclusion. The CBS Mackenzie sourced simulation has a more delayed response compared to that of the corresponding OBS simulation, as expected with the enhanced boundary 310 currents observed with an OBS, and it never reaches the rate of freshening achieved by the OBS over the duration of these simulations. Note that there is a detectable contribution to the salinity anomaly of the northern North Atlantic region from the GOM, although the salinity signal is not large enough in any single grid cell to be detectable in Fig. S9. Of all our explored injection scenarios, the GOM scenario has the least impact with regards to salinity change in key DWF regions. The Mississippi River (primary meltwater drainage route to the GOM) therefore offers a possible escape valve for minimizing the impact of 315 terrestrial meltwater injection on DWF, and therefore AMOC, at least on inter-annual to decadal timescales.
For comparison to conventional hosing studies, an order-of-magnitude calculation of the freshening effect of a 1-year 2dSv flux injected into each of the DWF regions (indicated in Fig. 2) is worth consideration. We assume that the freshwater displaces existing seawater from the regions, that the injection region is evenly inundated with freshwater, and the freshwater is evenly mixed over the top 50m of the water column. We do not account for the eventual flow of water in or out of the regions. ::: For 320 ::::: further :::::: details ::: see ::::::: Section ::: S6. Using the salinity field from the control run as our initial state, hosing directly onto the Labrador Sea region would result in a −4.2PSU change in salinity, which is more than 4x stronger a freshening effect than any of our equilibrated injection runs. Hosing the GIN Seas region results in a −0.65PSU salinity change, which is very similar to the top layer salinity shown in Fig. 4 after 1 year of injecting into the FEN injection location (located within the GIN Seas region).
Finally, hosing in the North Atlantic DWF region results in a −1.26PSU salinity change. As in the Labrador Sea region, this 325 represents an approximately 2-4x larger change than observed from any of the injection experiments presented herein.
Our results have significant differences compared to those of Condron and Winsor (2012) and Hill and Condron (2014), which both imposeda :::::: The lower but continual flux in the simulations shown here also does not allow freshwater to penetrate the Gulf Stream as in ::::::::: effectively :: by :::::::::: comparison :: to : Condron and Winsor (2012). Indeed, results from Condron and Hill (2021) indicate that our 335 freshwater flux is not of sufficient magnitude to allow it to penetrate the Gulf Stream, which would require at least a 10 fold increase in flux. As such, the GSL injection delivers, relatively, significantly more freshwater to the GIN Seas and North Atlantic DWF region than the GSL run in Condron and Winsor (2012) despite both a much lower flux and overall volume of freshwater.
Additionally, we can compare our results to Roche et al. (2009) andLohmann et al. (2020). The former performed a wide 340 suite of injection experiments using a much lower-resolution model with varying freshwater flux and injection location under LGM boundary conditions. The latter performed a set of 4 injection experiments using a model with enhanced grid resolution over large regions in the Arctic ocean and around the coasts while having the interior Atlantic grid resolution range upwards of 140km via their unstructured mesh approach. Since Roche et al. (2009) did not discuss the salinity signals at DWF sites directly, we interpret the freshening of the GIN Seas and northern North Atlantic DWF regions in this study to be analogous to changes 345 in NADW export from their two sites of DWF. Our results are in broad agreement with both Roche et al. (2009) andLohmann et al. (2020) except with regards to freshwater injected into the GOM. Roche et al. (2009) found their GOM injection to generate comparable or greater effects on NADW export than injection from the GSL. The freshwater signal at DWF sites in Lohmann et al. (2020) from GOM was also stronger than in this study. We attribute both differences to the lower resolutions of the Florida Strait and Gulf Stream in those studies (approximately 18 times coarser in Roche et al. (2009) and ≈ 2 − 3x coarser for 350 Lohmann et al. (2020)). :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: (approximately 18 times coarser in Roche et al. (2009) and ≈ 2 − 3x coarser in Lohmann et al., 2020).
This lower resolution combined with the much longer duration of simulations in these studies would increase export rates and allow freshwater built up in the GOM time to flow out of the region and freshen the Atlantic. Finally, the higher resolution of the Gulf Stream in our set of simulations appears to make it a more effective barrier to freshwater transport than in either of these studies.

Implications for last deglacial interval
We now present the implications of our results to the routing of runoff during the deglacial interval. The GSM freshwater flux time series in Fig. 1 :::::::::::::::::::: glaciologically-modelled ::::::::: discharge :::: time ::::: series :::: from :::::::::::::::::::::: Tarasov and Peltier (2006) indicates there is a steady background flux of freshwater ::::::: discharge : from NH ice sheets into the oceans from before Heinrich Event 1 to MWP1A, largely from the Gulf of Mexicoand Fennoscandia at a rate of ≈ 0.75dSv. During this time interval, we would expect extensive sea ice 360 over the GIN and Labrador Seas, and thus deep water ::::::::: deep-water : formation regions largely aligning with the NADW region in Fig. 2. As such, the runoff from Fennoscandia should have had a continual suppressing effect on deep water ::::::::: deep-water formation during this time interval relative to present-day conditions. Examining the RSL data, we see there is almost no change in sea level during this time interval indicating that the freshwater flux is largely in balance with NH ice sheet changes (1dSv over 1000yr ::::::::: 1000 years : contributes ≈ 8.8m of eustatic sea level rise).

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However, this conclusion has to be understood in the context of the assumptions that went into these results, particularly the treatment of freshwater as an external forcing to the system and not part of a coupled ice-ocean-atmosphere system. It is worth noting that there is no evidence B-A warming occurred in response to a cessation of freshwater forcing :::::::::::::::::::::: (Tarasov and Peltier, 2006), as it was reproduced by in Liu et al. (2009), for example. If the B-A warming occurred as a manifestation of internally driven, Dansgaard-Oeschger-like variability, then it may be that the mechanisms that led to this warming 395 could have also stabilized the AMOC against the freshwater resulting from the warming. It may be a similar mechanism also operated at the transition out of the Y-D and into the Holocene, when runoff is reconstructed to have derived from the GSL, which effectively reached ::::: North ::::::: Atlantic : deepwater formation sites in this study. Discerning whether this is indeed possible would require an analysis of the impact of freshwater on spontaneous Dansgaard-Oeschger-like variability, which we leave to future work.

Conclusions
This study provides the first assessment of freshwater transport to deepwater formation regions under Younger Dryas condi-420 tions using realistic freshwater injection amounts applied to a range of plausible source regions in a suite of eddy-permitting simulations. We have addressed three main shortcomings in common practice for freshwater injection experiments that inflate the salinity anomalies at locations of DWF. The first shortcoming we address is the injection of freshwater directly over the locations of DWF rather than at its source location to mitigate unresolved O(< 50km) oceanic processes known to be important in the transport of glacial runoff. Using our model configuration, we find the transport of freshwater from the coast to sites 425 of deepwater formation leads to a reduction in the effective freshwater forcing. We find in this study that one year of 2dSv injection at the mouth of the MAK (CBS) yields a freshening equivalent to direct regional hosing by amounts of ≈ 0.31dSv in the Labrador Sea, ≈ 0.33dSv in the northern North Atlantic, and ≈ 1.85dSv in the GIN Seas (using the same method and simplifications as in section :::::: Section : 3). Thus, while these practices may mitigate the inability of coarse resolution models to adequately resolve the small-scale features that are key to freshwater transport, like boundary currents and mesoscale eddies, 430 applying 2dSv directly into these regions is an inaccurate representation of the transport processes involved. Since non-eddypermitting models are currently and will likely continue to be used for paleoclimate studies, we are presently exploring better ways to mitigate this problem, the results of which are the subject of an upcoming study and outside the scope of this work.
The second shortcoming is the use of unrealistically large freshwater amounts. We find that limiting freshwater amounts to glaciologically-constrained values results in less diffusive spreading of the freshwater across the North Atlantic. In addition, 435 the lower amounts are unable to traverse the Gulf Stream, isolating the salinity anomalies introduced north and south of the Gulf Stream.
The final shortcoming involves the use of present-day rather than paleo-bathymetry, and especially its effect on the Bering Strait. For the most proximal site to the Bering Strait, the Mackenzie River, we find that the opening of this gateway leads to a faster increase of freshwater export from the Arctic ocean and a larger downstream effect on the salinity of the northern North 440 Atlantic.

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Finally, our results raise several ::: two questions which we leave to future work. Could a buildup ::::::: build-up and subsequent flushing (via changing oceanic gateways or changes in perennial sea ice) of freshwater in a partially isolated region, such as Baffin Bay, lead to a delayed onset of cooling after changing : a :::::: change :: in : routing or increase in glacial runoff? Additionally, can a transition from a stadial to an interstadial climate provide some means of stabilizing AMOC to the effects of freshwater and thus allow for both increased glacial runoff and increased warming such as seen at the onset of the Bølling-Allerød?

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Data availability. Model output data is available upon reasonable request.
Author contributions. All authors assisted with experimental design and analysis. RL prepared the manuscript with contributions from all authors.
Competing interests. The authors declare that they have no conflict of interest.