The model used in this study is the GRISLI-UCM ice-sheet model, an extension of the original GRISLI model developed by . GRISLI-UCM is a hybrid three-dimensional thermomechanical ice-sheet model. Inland ice flows through deformation under the shallow-ice approximation SIA,. The underlying assumption is that the flow is dominated by bed-parallel vertical shear for grounded ice (i.e., shear or deformational flow).

A nonlinear viscous flow law (the Glen flow law) is used with an exponent n=3. Viscosity depends on temperature through an Arrhenius law. A traditional enhancement factor, Ef, that decreases viscosity and accelerates inland flow is used in most ice-sheet models as a tuning parameter, in order to improve the agreement between modeled and measured ice thicknesses; here Ef=3. Further details can be found in . Thermomechanical coupling is extended to the ice shelves and ice streams. Ice viscosity, dependent on the temperature field, is integrated over the thickness, as in . Ice shelves and ice streams are described following the shallow-shelf approximation SSA,. In such fast flow areas bed-parallel shear is no longer dominant; instead, longitudinal and lateral stresses become important in such a way that the horizontal velocity is independent of depth (plug flow). Both approximations are valid when the spatial scale is much smaller in the vertical direction than in the horizontal direction, as is the case in large-scale ice-sheet modeling. Ice streams (areas of fast flow, typically faster than 102 m a-1) are considered to be dragging ice shelves, allowing for basal movement of the ice . Basal stress under ice streams (τb) is proportional to the ice velocity ub and to the effective pressure of ice Neff representing the balance between ice and water pressure: 1τb=-fub, where 2f=cfNeff. Here cf is an adjustable basal friction coefficient related to the bedrock topography that accounts for the basal type of material. The effects of varying this proportionality factor on the simulated ice streams are discussed in . In this study, cf values of 20 and 2×10-5 a m-1 were used for ice streams over bedrock and sediments, respectively, accounting for the lower basal friction in the latter case. For comparison, absolute values up to 7×10-4 a m-1 were inferred by in Antarctica, with a very heterogeneous distribution; low coefficient values were inferred in areas of fast motion dominated by sliding. Neff is calculated as 3Neff=ρgH-ρwg(h-b), where ρ and ρw are the densities of ice and water, H is the ice-sheet thickness, and h is the hydraulic head; h corresponds to the height that would be attained by water if it were not subject to confining pressure, calculated within the basal hydrology scheme implemented by . Thus, the first term on the right hand side represents the pressure due to the ice load, and the second term represents the subglacial water pressure. At the base of the ice shelves, friction (and thus basal drag) is set to zero. The locations of the ice streams are determined by the presence of basal water within areas where the sediment layer is saturated. The criterion to activate SSA inland relies on the presence of water above 1 m in regions of soft sediments and above 400 m in the absence of such sediments. Setting these thresholds ensures that ice streams are activated in regions that are robustly temperate. The presence of water at the base of the ice sheet implies that it is not frozen to the bedrock, i.e., sliding is physically possible. More water at the base further facilitates sliding by reducing the effective pressure, and sediments also facilitate sliding because they are deformable. The criteria of 1 m water thickness over sediments reduces noise in the SSA activation. The 400 m criterion over hard bedrock is a tunable parameter, which also allows for a more numerically robust calculation of velocities within the SSA. The grounding-line position dynamically evolves following the flotation criterion after the mass conservation equation is solved.

Calving takes place at the ice-shelf front when two conditions are met. First, the ice-shelf thickness must fall below a threshold Hcalv. This is a semiempirical parameter reflecting the fact that this is the typical thickness of ice-shelf fronts currently observed in Antarctica . Second, the upstream advection must fail to maintain the ice thickness above this threshold following a semi-Lagrangian approach to account for the fact that ice-flux divergence fosters the formation of crevasses . This method is standard in the GRISLI model. It was introduced after recognizing that a systematic cutoff of ice shelves below a given threshold led to a realistic simulation of the present-day ice shelves in Antarctica, as is the case in many models, but prevents any development of new ice shelves . When focusing on past climates, ice sheets should be able to evolve in response to climate changes, and in particular to allow the advance of ice shelves in cold climates. To this end, before calving ice in a certain point, we test whether advection allows for the growth of ice at the front, and therefore the ice-shelf advance. Hcalv was set to 150 m, in the standard setup. To assess the sensitivity of the ice dynamics to the value of the thickness threshold Hcalv (below which the ice is calved) we performed a new ensemble exploring a wide value range of this parameter's values, from 10 to 800 m (Fig. S4 in the Supplement). Values of this threshold above 400 m produce a drastic disintegration of the Barents–Kara complex due to its relative shallow bed. The overall effect of this sensitivity test around the preferred value is to modulate the amplitude of the response to the oceanic perturbations. Thus, GRISLI-UCM explicitly calculates grounding-line migration in addition to ice-stream and ice-shelf velocities. This allows the model to properly represent both grounded and floating ice. Note that there is no ambiguity in the model between calving and basal melt, which are two distinct processes in the model. Calving is the result of the threshold criterion described above; thus, the calving rate at a given time is given by the amount of ice lost to the ocean through this process by unit of time, converted to mass-water equivalent. Basal melt is dependent on the applied ocean temperature anomaly. GRISLI-UCM uses finite differences on a staggered Cartesian grid at a 40 km resolution, corresponding to 224×208 grid points for the Northern Hemisphere domain, including the EIS, with 21 vertical levels. By default, initial topographic conditions are provided by surface and bedrock elevations built from the ETOPO1 dataset and ice thickness . Note there are more recent datasets for Greenland topographic features e.g.,. However, as Greenland is not the focus of our study, this does not affect our results. The glacial isostatic adjustment (GIA) is described by the elastic lithosphere–relaxed asthenosphere method , for which the viscous asthenosphere responds to the ice load with a characteristic relaxation time for the lithosphere of 3000 years. For the sake of simplicity, in this study the isostatic adjustment is assumed to be only due to local ice mass variations, as other such research has assumed in the past e.g.,. The surface mass balance (SMB) is given by the sum of accumulation and ablation, both of which are calculated from monthly surface air temperatures (SATs) and monthly total precipitation. Accumulation is calculated by assuming that the fraction of solid precipitation is proportional to the fraction of the year with mean daily temperature below 2 ∘C. The daily temperature is computed from monthly SATs assuming that the annual temperature cycle follows a cosine function. Ablation is calculated using the positive-degree-day (PDD) method . Its main parameters are the standard deviation of daily temperature, σ, and the conversion factors from PDDs to melt for snow and ice, fPDDsnow and fPDDice. Here, σ=5 K, fPDDsnow=0.003 m.w.e. PDD-1 and fPDDsnow=0.008 m.w.e. PDD-1. fPDDice=0.008 m.w.e. PDD-1. Refreezing is considered, with a value of Csi=60 % (see Sect. 2 in the Supplement). This melting scheme is admittedly too simple for fully transient paleo-simulations, as it omits the contribution of insolation-induced effects on surface melting . Nevertheless, insolation changes are most relevant in long-term simulations including variations at orbital timescales, especially in past warmer periods such as the Eemian. As this study focuses on abrupt climate changes within a fixed glacial background climate, insolation changes are not important and the PDD melt model should be sufficient to give a good approximation of surface melt in response to interstadials in a reasonable manner. GRISLI-UCM accounts for changes in elevation at each time step considering a linear atmospheric vertical profile for temperature with different lapse rates in summer and in the annual mean (0.0065 and 0.0080 K m-1, respectively) to account for the smaller summer atmospheric vertical stability.

Basal melting for grounded ice depends on pressure and water content at the base of the ice sheet as well as on the geothermal heat flux, which is prescribed from the reconstruction by . Basal melting for floating ice is computed using a linear temperature anomaly with respect to the freezing point. The details of the implementation of the boundary conditions (SMB and oceanic basal melting) in this particular study are given below (Sect. ). Finally, ice flow was calculated with a 1-year time step, whereas thermodynamics and boundary conditions (including PDD) were updated every 5 years. The model parameters and the range of their values explored here are shown in Table 1.

SMB and oceanic basal melting are obtained through a time-varying synthetic climatology built with a novel method that is found to provide a more realistic off-line forcing for ice-sheet models than classical off-line methods . The method follows a perturbative approach in the sense that the forcing combines the present-day climatology, obtained from observational data, and simulated anomalies. However, in contrast to usual off-line forcing methods, orbital- and millennial-scale variabilities are not lumped in a sole anomaly pattern but differentiated. Thus, the method combines present-day observations, simulated LGM anomalies relative to present, scaled by an orbital-timescale index, and simulated stadial–interstadial anomalies, scaled by a millennial-timescale index: 4Tatm(t)=T0atm+1-α⋆(t)ΔTorbatm+β⋆(t)ΔTmilatmP(t)=P0α⋆(t)+1-α⋆(t)δPorb1-β⋆(t)5+β⋆(t)δPmil. Here, Tatm(t) and P(t) are the SAT and precipitation fields at time t. T0atm and P0 are the ERA-Interim present-day SAT and precipitation climatologies . ΔTorbatm=Tlgmatm-Tpdatm and δPorb=Plgm/Ppd are the orbital temperature anomaly and precipitation ratio relative to the present day (not shown, see ), respectively, obtained from previous equilibrium simulations for the preindustrial and LGM climates performed with the CLIMBER-3α model . ΔTmilatm=Tisatm-Tstatm and δPmil=Pis/Pst are the millennial temperature anomaly and precipitation ratio, respectively, for the interstadial relative to the stadial state (Sect. ). The key differences between these climate modes as simulated by with the CLIMBER-3α model are that in the stadial, North Atlantic Deep Water (NADW) formation is relatively weak and takes place south of Iceland. Accordingly the sea-ice front in the North Atlantic reaches 40∘ N. In the interstadial state there is a northward shift and intensification of NADW formation. Northward oceanic heat transport increases, and the North Atlantic and surrounding areas warm relative to the stadial state, in particular the Nordic seas. Thus, the simulated interstadial state is characterized by a more vigorous NADW formation and Atlantic meridional overturning circulation (AMOC) along with reduced sea ice in the Nordic seas, and a temperature increase of up to 10 K in the North Atlantic relative to the stadial state, with a maximum anomaly in the Nordic seas. Note that bold symbols indicate two-dimensional spatial fields. The stadial mode in our study is represented by a climate simulation of the LGM with CLIMBER-3α . The interstadial mode is taken from a recent glacial transient simulation performed with the same model under glacial climatic conditions, but with intensified NADW formation . α⋆ and β⋆ are two indices that separately modulate the contribution of the orbital and millennial anomalies. Both were built based on two recent complementary temperature reconstructions over Greenland, one from the NGRIP ice-core record for the LGP , and the other from several ice-core records for the Holocene . Their combination (hereafter, the KV reconstruction) results in a continuous temperature reconstruction for Greenland for the past 120 kyr . α⋆ is obtained after applying a low-pass frequency filter (fc=1/18 ka-1) to the original KV reconstruction based on a spectral decomposition; β⋆ is obtained following a similar procedure but retaining the high-frequency signal. Both indices are tuned in such a way that the resulting synthetic temperature time series at the NGRIP site exactly matches the KV reconstruction (this distinguishes α⋆ and β⋆ from the raw α and β indices previous to this tuning; ).

The net basal melting rate for floating ice, B, is assumed to follow a linear relation: 6B=κ(Tocn-Tf), where Tocn is the oceanic temperature close to the grounding line, Tf is the temperature at the ice base, which is assumed to be at the freezing point, and κ is the heat flux exchange coefficient between ocean water and ice at the ice–ocean interface; its standard value in the present study is κ=5 m a-1 K-1. Several marine-shelf basal melting parameterizations can be found in the literature, as recently reviewed by . The submarine melt rate is thought to be directly influenced by the oceanic temperature variations below the ice shelves. Accordingly, most basal melting parameterizations are built as a function of the difference between the oceanic temperature at the ice-–ocean boundary layer and the temperature at the ice-shelf base, generally assumed to be at the freezing point. The dependence on this temperature difference can be linear or quadratic (; ; ; ). The linear marine-shelf basal melting parameterization used in this study is the simplest case that allows for testing of the ice-sheet sensitivity to past oceanic temperature changes. Nevertheless, it accounts separately for basal melting below the ice shelves (away from the grounding line) and at the grounding line. The basal melting rate of the ice shelves (Bsh) is given by the grounding-line basal melt (Bgl) scaled by a constant factor (γ): 7Bsh=γBgl(t). In this study, γ is set to 0.1. Thus, we consider that the submarine melting rate for ice shelves is 10 times lower than that close to the grounding zone, which is in qualitative agreement with observations in some Greenland glaciers with floating tongues as well as in Antarctic ice shelves . Note that this value is subject to uncertainty. Although we did not explore any other values different from γ=0.1, we did consider a range of κ values between 1 and 10 m a-1 K-1, which accounts for a wide range of oceanic sensitivities (see Sect. ).

As in , in regions with ocean depths above 750 m, an artificially large melting rate (20 m a-1 is prescribed to avoid unrealistic growth of ice shelves beyond the continental-shelf break, where they would likely be subject to high melt rates in reality because of high heat exchanges with the ocean.

Following the approach described above, Tocn(t) is assumed to be given by an expression analogous to Eq. (). Thus Eq. () can be rewritten as follows: 8B=B0+κ1-α⋆(t)ΔTorbocn+β⋆(t)ΔTmilocn, where B0=κ(T0ocn-Tf) represents the present-day oceanic basal melting rate.

Finally, millennial-scale sea-level variations are prescribed according to the reconstruction by (2012, Sect. ). The specific details of the experimental setup used are described below.

In this study, we investigate the response of the EIS to millennial-scale climate variability during MIS 3. The starting point of our experiments is a control-run ice-sheet simulation with constant boundary conditions for MIS 3 that provides a representative configuration of the EIS for that time period (Fig. ). To this end, α⋆ was set to its value at 40 ka BP, that is, α⋆=α40K⋆=-0.1, and β⋆=0 to preclude millennial-scale variations. Note, however, that these values are to a certain extent arbitrary; they are intended to provide a stable mean background state similar but not necessarily identical to background MIS 3 conditions. Thus, 9T40Katm=T0atm+1-α40K⋆ΔTorbatm10P40K=P0α40K⋆+1-α40K⋆δPorb11B40K=B0+κ1-α40K⋆ΔTorbocn. Note that although Eq. () is formally correct and consistent with the scheme used, in contrast to the present-day SAT or precipitation the present-day rate of oceanic basal melting cannot be determined. Thus, in practice we replace this equation by directly tuning the value of B40K to obtain a reasonable ice-sheet configuration at 40 kyr BP (Fig. ) given the atmospheric forcing fields expressed by Eqs. ()–(). To this end, a constant basal melting rate of 0.1 m a-1 is assumed. The ice sheet was forced with the resulting climatologies for 100 kyr previous to the start of the perturbations described below. This allows the vertical temperature profile within the ice sheet to be equilibrated with the climate. This procedure was found to facilitate the growth of European ice sheets within the reconstructed limits for 60 and 20 kyr BP (Fig. ).

Our forcing method allows for the response of the EIS solely to millennial-scale climate variability at MIS 3 to be investigated by keeping the orbital component of the forcing (α⋆=α40K⋆) constant and letting β⋆ vary throughout the LGP (Eqs. , , ). In order to assess the relative roles of the atmosphere and the ocean, three independent experiments are carried out. First, an atmospheric-only forced simulation (ATM) in which the time evolution of SAT and precipitation on millennial timescales is considered, while the oceanic forcing is kept constant with MIS 3 (i.e., 40 kyr BP) background climatic conditions. Thus, 12Tatm(t)=T40Katm+β⋆(t)ΔTmilatm13P(t)=P40K1-β⋆(t)+β⋆(t)δPmil14B(t)=B40K. Second, an oceanic-only forced simulation (OCN) in which the atmospheric forcing is kept constant, while the oceanic basal melting is allowed to vary at millennial timescales around its background MIS 3 value: 15Tatm(t)=T40Katm16P(t)=P40K17B(t)=B40K+κβ⋆(t)ΔTmilocn. The magnitude and sign of oceanic temperature anomalies ΔTocn depends on the depth at which Tocn is considered. In our simulations, a large part of the northeastern sector of the EIS is marine based with shallow bedrock depths between 500 m and less than 100 m in several locations further south. Therefore, it is unclear whether this marine ice sheet should be more susceptible to changes in the surface or the subsurface of the ocean.

To investigate the effect of this uncertainty, we decided to perform two different simulations considering different depths: one corresponding to the surface (OCNsrf) and the other considering deeper (subsurface) oceanic waters by averaging temperatures within the depth range of 400–600 m (OCNsub). Therefore we hereafter distinguish between ΔTmilocn for surface or subsurface millennial-scale temperature anomalies, respectively (Fig. ). The realism and convenience of applying one or the other is addressed in Sect. .

Finally, a simulation “ALL” was carried out combining both the atmospheric and the oceanic forcings: 18Tatm(t)=T40Katm+β⋆(t)ΔTmilatm19P(t)=P40K1-β⋆(t)+β⋆(t)δPmil20B(t)=B40K+κβ⋆(t)ΔTmilocn. In all experiments β⋆(t) dictates the millennial-scale variability of the forcings (Fig. a). Because our simulated stadial–interstadial transition results from an intensification of the AMOC, positive β⋆ values imply an increase in Tatm relative to its background MIS 3 value (e.g., Eq. ; Figs. , ). As a consequence, the atmosphere warms at interstadials relative to stadial periods, as reflected by the ΔTmilatm millennial-scale anomaly field (Fig. a, b). Note that refreezing is not allowed to occur in our current model setup. If κβ⋆ΔTmilocn<-B40K (which would imply B(t)<0), we simply impose the value B(t)=0.

An ensemble of simulations for different values of κ have been considered to evaluate the sensitivity of the EIS to the forcing. Finally, varying sea-level forcing is considered (Fig. b), both alone (SL) and in combination with the previous forcings (ALL).

Substantial differences are found in the response of the EIS to the forcing scenarios. Under constant forcing, the CTRL run shows negligible millennial-scale sea-level equivalent (SLE) variations, although a lower frequency SLE fluctuation is found as a result of internal ice-sheet variability (Fig. ) through a thermomechanical feedback. This slow variability appears only in the southernmost parts of the Eurasian ice sheet where ablation exists. It is due to an interplay between the available basal water favoring sliding and the EIS associated thinning due to an increase in velocities. As this phenomenon concerns only the ablative borders of the ice sheet and its frequency corresponds to more than 20 kyr, its governing dynamics is not detailed here. When the model is forced only by changes in sea level (SL run), a small response of approximately 0.5 m SLE is observed on millennial scales. These changes appear not to be sufficient to cause a substantial migration of the grounding line, and thus do not affect ice velocities (not shown). In ATM, the atmospheric forcing alone causes a sequence of enhanced ablation episodes resulting in modest ice volume variations (up to 1.5 m SLE) during the most prominent stadial–interstadial transitions; this represents a change of approximately 7 % with respect to the initial ice-sheet volume. In contrast, the oceanic forcing in OCNsrf induces pronounced changes in the dynamics of the EIS on millennial timescales (see below), with episodes of large volume reduction occurring during interstadials. The combination of sea level, atmospheric and oceanic forcings (ALLsrf) results in a very similar response of the EIS to that obtained in OCNsrf (Fig. ) as a consequence of the larger effect of the oceanic forcing in OCNsrf with respect to ATM. OCNsub shows an antiphase relationship with respect to OCNsrf, with the largest reductions in ice volume occurring during prolonged stadial periods and regrowth during interstadials. This behavior can be explained by the fact that ocean waters at the subsurface warm (cool) during episodes of reduced (enhanced) convection in the Nordic seas as a result of variations in the AMOC strength (Fig. d, e). Note that the antiphase relationship is, however, not perfect. At the surface, the largest anomalies are found off the North Atlantic, the British Isles and the Norwegian coast, and result from the intensification of Atlantic northward heat transport associated to the enhanced AMOC during interstadials; at the subsurface the concomitant cooling is largest in the Nordic seas as a result of enhanced heat loss to the atmosphere associated with enhanced convection.

Thus, the out-of-phase relationship found in the dynamic response of the EIS between these two oceanic experiments results from the opposed sign of their spatial forcing patterns (Fig. ). When considering the forcing at the subsurface of the ocean along with the atmosphere (ALLsub), slight reductions of the EIS volume (less than 1 m of SLE) during interstadials are superimposed onto the previous behavior (Fig. ).

As a consequence of the millennial-scale forcing, a trend in ice volume from its initial value of 8.3×1015 km3 (about 21 m SLE) leading to a loss of 8–12 m SLE is found. This is a consequence of the fact that no refreezing is allowed and that a positive constant (and spatially uniform) basal melting of 0.1 m a-1 was imposed. As a consequence, accumulation is not able to compensate for ice loss through basal melt and calving after each ice-mass loss event. Note, however, that background conditions are fixed at 40 kyr BP; in a more realistic setup, as time proceeds forward, orbital forcing leading to gradually colder conditions would be expected to aid in the ice regrowth, thereby helping with its growth throughout the LGP. Spatially nonuniform background melting is also conceivable. However, we have no information on what this background value would have been. Because our focus was the response of the EIS to millennial-scale climatic variability, we opted for the simplest experimental setup possible, meaning a spatially uniform and fixed-in-time background value perturbed by a millennial-scale index.

The magnitude of these changes in terms of sea-level rise rate and discharge, specifically for the MIS 3 period, is illustrated in Fig. . The simulations forced with the surface of the ocean (OCNsrf and ALLsrf) show the largest amplitudes, with peaks of sea-level rise above 4 mm a-1 during DO-events and sustained contributions well above 1 mm a-1 during entire interstadial periods. In ATM, a decline of the EIS during stadial–interstadial transitions is still observed but presents a smaller amplitude of 1–2 mm a-1. The simulations in which the ice sheet is forced with the subsurface of the ocean (OCNsub and ALLsub) present a decline of their volume during stadial periods and regrowth during interstadials as a consequence of the inverted spatial pattern of temperature anomalies with respect to the surface. In OCNsub (and ALLsub) the amplitude of these changes is smaller than in OCNsrf (and ALLsrf), in the order of 0.5–1 mm a-1, reaching more than 1 mm a-1 during pronounced stadials (as ca. at 44 kyr BP). The ALLsrf and ALLsub simulations show a similar or slightly larger volume loss during interstadials, as a consequence of the additional atmospheric forcing, which is superimposed onto the OCNsrf and OCNsub behavior.

The response of the EIS has been analyzed in terms of its mass balance decomposition for the all-forcing runs (Fig. ). In ALLsrf the surface ocean temperature varies in phase with the atmosphere (Fig. ). Thus, during stadial–interstadial transitions, the high negative values of dV/dt can be explained by the conjunction of an initial sharp increase in ablation and pronounced increases in basal melting and calving, which allow for a large grounding-line retreat in the Bjørnøyrenna Basin (Fig. b). The rate of ice loss by basal melting is similar to that resulting from the increase in ablation (as reflected in the SMB) during the peak of a stadial–interstadial period. However, basal melting is much more efficient than surface mass balance at decreasing volume along the whole duration of an interstadial. This is due to the fact that ablation is restricted to the southern borders of the EIS. Thus, when the ice sheet has retreated to areas of no ablation, in spite of a slight further loss provided by the elevation feedback, it rapidly equilibrates and a negative surface mass balance cannot propagate further inland. In contrast, when enhanced basal melting from higher oceanic temperatures is applied, the associated retreat can propagate further inland occupying a large proportion of the Bjørnøyrenna Basin and facilitating high rates of volume loss (although similar in amplitude with respect to SMB) during the whole interstadial period (see the animation corresponding to ALLsrf and Fig. S5 in the Supplement). Note that basal melting, together with calving, is a very efficient method to remove ice; basal melting leads to thinning of the ice shelf which can subsequently undergo calving. During stadial periods, both the enhanced positive mass balance and the absence of basal melting (favored by the negative oceanic anomalies) favor the regrowth of the EIS. Subsurface ocean temperatures also evolve in phase with the atmosphere in the southwestern part of the EIS but in antiphase in its northeastern part. In other words, when forcing with the subsurface of the ocean, a slight warming (cooling) is observed around the Britain–Ireland ice sheet while cooling (warming) of the Bjørnøyrenna Basin is simulated during interstadial (stadial) periods (see Fig. ). Therefore, the ALLsub simulation presents volume declines during stadial–interstadial transitions due to an increase in ablation and basal melting in the southwestern part. The corresponding mass fluxes reach up to about 0.05 Sv; of these, approximately 0.025, 0.02 and 0.005 Sv originate in the Barents–Kara, Scandinavia and the British Islands, respectively. Subsequently, reduced basal melting in the northeastern part of the EIS favors regrowth of the Bjørnøyrenna Basin during interstadial periods. Finally, shifting to pronounced stadial periods (as in ca. 44 kyr BP) favors the penetration of warm subsurface waters that increase basal melting enough to produce an ice-sheet retreat in the northeastern part in spite of the enhanced positive surface mass balance (Figs. , ). When considering the atmosphere and the subsurface ocean forcing together in ALLsub, these competing processes translate into a smaller amplitude of millennial-scale EIS changes compared with the case with surface ocean forcing (ALLsrf). Furthermore, declines of the EIS can be observed both during the beginning of interstadial periods and during pronounced stadial periods in ALLsub (Figs. , ).

Focusing on the OCN and ATM simulations separately facilitates isolating the effects of the ocean on this complex pattern. To this end, the simulated ice-sheet distribution and velocities of OCNsrf, OCNsub and ATM are shown in Fig.  for the period around DO-event 12, at ca. 47 kyr BP. As expected, OCNsrf shows a widespread retreat both in the northeast and the southwest of the EIS from the stadial to the interstadial period (Fig. d). This is accompanied by an acceleration of the Bjørnøyrenna Basin due to its grounding-line thinning and retreat (Fig. a, d). OCNsub presents a collapsed Bjørnøyrenna Basin during the stadial period previous to DO-event 12 due to enhanced basal melting from warmer subsurface waters. The transition to the interstadial period favors a slight regrowth of this northeastern part of the EIS due to decreased basal melting, while its southwestern section slightly retreats (Fig. b, c)

Concerning ATM, only in the southwestern part of the EIS is the atmospheric forcing capable of generating an important reduction in the EIS volume in response to the stadial–interstadial transition (Figs. c, f, S5). This is a result of the spatial pattern of the forcing, with the largest SAT anomalies located around the Nordic seas (Fig. ). Therefore, the ice volume reduction of the EIS in ATM during interstadials is due to the positive SAT anomaly, which leads to enhanced ablation in the southwestern part of the EIS (Fig. S5). In turn, reduced SATs during stadials allow the regrowth of the ice sheet up to the continental margin of the Nordic seas. The more active dynamic response of the EIS in the OCN simulations can be attributed to the increase in oceanic temperatures by 2–4 ∘C (Fig. ) within the margins of the ice sheet during interstadial (in the case of OCNsrf) and stadial (OCNsub case) periods, which translates into enhanced basal melting at the margins of the EIS. The southwestern sector of the EIS also responds to the warmer SSTs, even displaying a larger reduction of ice volume than in ATM (Fig. ).

The spatial patterns shown in Fig.  are representative of the ice-sheet response during all other stadial–interstadial transitions. In OCNsrf, the EIS reacts to every abrupt surface warming with a substantial ice-flow acceleration, especially in the Bjørnøyrenna Basin (Figs. , , ). Ice shelves that are present during stadial periods suddenly retreat during DO-events and in combination with enhanced basal melting favor thinning and retreat of the grounding line that translate into large iceberg discharges of up to ca. 0.06 Sv. In OCNsub, ice velocities in the Bjørnøyrenna Basin increase during stadials, when enhanced basal melting erodes the grounding line and favors its retreat. Peaks in calving are recorded accordingly during pronounced stadial periods (Fig. ). However, these peaks are of smaller amplitude than in OCNsrf. This can be explained by the fact that, along the coast of Eurasia, the amplitude of the simulated SST anomalies used to compute basal melting in OCNsrf is larger than the subsurface temperature anomalies in OCNsub, as the basal melt was calculated by using ocean temperature at a fixed depth, either at the surface or at the subsurface. Also, transitions to stadials are usually more gradual than transitions to interstadials; thus, in this case, the incursion of warmer (subsurface) waters occurs in a smoother manner. High velocities reach their maxima at the end of the stadial and beginning of the interstadials. However, the latter are not accompanied by an increase in calving due to the fact that ice shelves are expanding and thickening during this period thanks to reduced basal melting (Fig. ). In general, the extension of ice shelves is greatly reduced during periods of enhanced basal melting (Figs. , ), with no large unconfined ice shelves surviving during these episodes. Some thinner ice shelves remain, in spite of the enhanced basal melting, thanks to an increase in advection from the Bjørnøyrenna ice stream triggered by a grounding-line retreat (Fig. ).

Changes in the position of the calving front are usually accompanied by a grounding-line displacement (not shown). For some minor ice-shelf breakups this close relationship can be broken, but with almost no effects upstream inland. Thus, we consider that the grounding-line position is the best indicator for characterizing the dynamic behavior of the marine part of the EIS. Inspection of the temporal evolution of the grounding-line position in OCN simulations confirms that ice dynamics control the majority of ice-volume variations in the EIS as opposed to the SMB processes involved in ATM (Fig. ). The migration of the grounding line through time has been characterized by means of an index (μ) that weighs the proportion of non-grounded points in the region of the Bjørnøyrenna Basin: 21μt=1-Ng(t)N⋅100, where Ng(t) represents the evolution of the number of points of grounded ice within a fixed area of N points in the Barents Sea region defined over the black square highlighting the Bjørnøyrenna Basin shown in Fig. . Note that other metrics are also possible; the same metric has been used in other studies in different domains such as Antarctica .

Thus, an increase (decrease) in μ indicates a retreat (advance) of the grounding line. While in ATM μ barely changes Fig. ), OCN runs show a large dynamic behavior of the basin. In OCNsrf, μ reflects a synchronous evolution of the grounding-line position and the oceanic forcing, with major retreats coinciding with interstadial states (Fig. ). Conversely, the Bjørnøyrenna Basin is generally much closer to a full retreat in OCNsub during stadials due to a larger penetration of warm subsurface waters (Fig. ; OCNsub) compared to the surface waters (Fig. ; OCNsrf). However, the grounding line is able to advance and reach Svalbard during episodes of reduced basal melting at the interstadials.

The direct coupling between the oceanic forcing and the response of the Bjørnøyrenna ice stream is also evident from the relatively high negative correlation (r≃-0.9) found between μ and ice thickness in this area (Fig. ). A local thinning of the grounding line produced by a warmer ocean triggers its retreat and starts the propagation of the dynamic imbalance of the ice stream. The propagation of a change in the surface slope occurs almost instantaneously at these timescales (with a typical propagation speed of about 10 km a-1). This chain of processes explains the tightened linear relationship between the Bjørnøyrenna Basin thickness and the grounding-line position, μ. Although a grounding-line retreat (advance) of the grounding line in this region produces an acceleration (deceleration) of the ice streams, its linear relationship is less obvious than that for ice thickness (Fig. c). This is explained by the fact that ice-stream velocities lag the grounding-line imbalance due to the characteristic time for the kinematic wave to propagate along the ice streams of the whole basin (typically of ∼1 km a-1).

As a consequence of the destabilization of the ice sheet, important ice-volume variations observed in the northeastern part of the EIS during millennial-scale climatic transitions, which added to the minor contribution of the southwestern retreat (Fig. ), result in fluctuations of more than 4 m SLE in OCNsrf, up to 2.5 m in OCNsub and ca. 1 m in ATM (Fig. ).

In order to investigate the sensitivity of the results to the model parameters, eight additional OCN simulations, both for the surface and the subsurface, have been carried out with different κ parameters between 1 and 10 m a-1 K-1, i.e., bracketing our standard case of κ=5 m a-1 K-1. This choice reflects the inferences based on measurements made on Antarctic ice shelves that a variation of 1 K in the effective oceanic temperature changes the melt rate by ca. 10 m a-1 . A robust response of the EIS is found, with a more reactive EIS response for increasing κ values (see Sect. S1 in the Supplement). The sensitivity of our results to the values of the atmospheric mass balance model has also been explored. In spite of largely exploring the values of the parameters that determine the sensitivity to surface mass balance, the EIS variability induced by the ocean is always found to be of greater amplitude than the one induced by the atmosphere provided that κ>2 m a-1 K-1 (see Fig. S3 of the Supplement).