The marine ice extent data provide critical constraints for evaluating model performance across Iceland's continental shelf sectors. Here we focus on the data-model comparison for the two NROY subsets NROY_tier1 and NROY_tier1-1A. Each of the NROY members are compared against the tier 1 and tier 1A past ice extent data which can infer proximal-to-GL (PGL) conditions, sub-ice shelf (SIS) conditions, or open marine conditions (OMC). Overall, while the tier 1 observations are bracketed by the NROY sub-ensembles (site 2003, 2006), tier-1A data fitting presents a greater challenge (2002, 2004, Fig. a).

In the Reykjafjarđaráll-Húnaflóadjúp trough located on the Northern shelf (∼20.2° W, 66.9° N), the NROY sub-ensembles perform well with the tier-1 observation (2003) but most of the NROY members struggle to bracket the oldest datum (2002). The latter PGL constraint (2002) suggests ice free conditions at 28.6 ka, whereas most NROY simulations indicate sustained glaciation around 30 ka or earlier.

In the Northwest Djúpáll trough (∼24.0° W, 66.6° N), none of the NROY members bracket the data point (2004), suggesting that the trough was ice free at ∼22.3 ka. However, the Djúpáll data are subject to methodological limitations including core depth, the number and location of cores, datable material, reservoir corrections, and interpretations of different stratigraphic units, all of which introduce ambiguity. claim that the exact location of the LGM margin is uncertain due to insufficient data, but that the Djúpáll trough was ice-free from 36 ka based on dated foraminifera in diamict and ice-rafted debris (IRD) in overlying sediment. Subsequent studies propose revising this chronology, indicating that Djúpáll trough was most likely ice-filled during the LGM. The older dates of ∼36 ka may reflect reworking of older sediments rather than indicating a restricted LGM extent in Djúpáll. Consequently, more recent studies depict the ice sheet margin at the continental shelf edge at the LGM e.g..

Moreover, this conflicts with multiple nearby observations (e.g., SITID 2003, 2006, and 2007), which indicate persistent grounded ice across the continental shelf from ∼25–15 ka. The scenario implied by this data (2004), with the Djúpáll trough ice-free by ∼22.3 ka while grounded ice persisting further south in the Jökuldjúp trough [24.21° W, 64.29° N] until ∼15.3±0.9 ka [SITID = 2006], is glaciologically dubious.

On the western shelf, in the Jökuldjúp trough (2006), the NROY models, particularly the NROY_tier1-1A subset, perform relatively well. The larger model-data mismatch for some NROY_tier1 simulations reflects the large spread in modelled grounding-line retreat within the Jökuldjúp trough (see details in Sect. ). This spread is a direct result of parameter variations within the NROY_tier1 ensemble. In particular, the highly non-linear grounding-line dynamics in this deep marine embayment are very sensitive to parameters controlling basal sliding and calving rates. Consequently, while the NROY_tier1-1A sub-ensemble captures the overall deglacial pattern, individual simulations can diverge from the timing of the constraint.

Cosmogenic exposure ages, and to a lesser extent radiocarbon ages, constrain past ice thickness enabling robust comparison between modelled and empirical ice sheet thinning (Fig. b). We evaluate NROY_tier1 and NROY_tier1-1A ensembles against each tier-1 past ice thickness observation using two complementary scoring components. First, “presence of ice” scoring gives zero misfit if modelled grid-cell ice thickness exceeds the empirical value prior to the data age. Second, ”absence of ice” scoring gives zero misfit if modelled ice thickness is below the inferred ice thickness at the data age (Fig. S3). Both misfit scores increase proportionally with temporal offset between modelled and empirical values.

While the NROY subsets successfully bracket all paleo ice thickness observations, certain NROY simulations yield higher misfit scores for specific data points. For example, at Herđubreiđ (SITID = 1005), the empirical age of deglaciation ranges between 11.4 and 9.4 ka, but in one of the NROY simulations (run identification number nn555), deglaciation occurs earlier at 15 ka, resulting in a high misfit score for the “presence of ice” (score = 19). However, given the early deglaciation, the “absence of ice” condition after 9.4 ka is satisfied and the associated score is zero. Conversely, further north at Bláfjall (SITID =1009), the empirical deglaciation window is 15.1–13.5 ka, whereas in one of the NROY simulations (nn599), deglaciation occurs later, at 10 ka. This leads to a low misfit score for the “presence of ice” but a high misfit (score = 36) for the “absence of ice”, as the model grid cell should not have ice after 13.5 ka. Persistent data-model mismatches are likely in good part attributable to inadequate grid resolution for resolving the complex topography of Iceland.

For the Last Interglacial spin-up state, we initialize the model with the present-day ice thickness field . At the onset of the last glacial cycle, ice in our NROY_tier1 ensemble expands from two main centers: the eastern part of the central highlands from the existing ice caps, particularly Vatnajokull and, a smaller glaciation over the Northwest peninsula (Fig. b). By ∼90 ka the two glaciated ice bodies merge into an ice sheet covering the entire terrestrial landmass. The ice sheet is characterized by a double dome configuration, established on the foundations of the initial two ice bodies. Subsequently, at ∼83 ka, a rapid retreat separates the two domes.

Between MIS 5a and the end of MIS 3 (80–30 ka), the grounding line advances further and fluctuates across the continental shelf, constrained at its maximum by the shelf edge. Within the NROY_tier1 sub-ensemble, the main variations of extent occur over the Northern and Southeastern continental shelf. For similar ice volumes, the direction of ice expansion can vary significantly, contingent on the parameter choice. For some parameter vectors, the absence of ice over the northern shelf (70 ka in Fig. b), can be attributed to the depth of bathymetric troughs (Fig. ). Conversely, simulations show that grounded ice can extend across this area when anchored on shallow parts of the continental shelf such as the Kolbeinsey Ridge (∼ 19° W, 67° N), part of the Mid-Atlantic Ridge. Furthermore, the Kolbeinsey Ridge can also act as a pinning point that buttresses and stabilizes the ice shelf, thereby affecting grounding line dynamics.

Owing to the underlying soft till, numerous troughs, and high geothermal heat flux, the ice sheet develops multiple ice streams across the continental shelf. Most of these ice streams activate and deactivate independently (Fig. S7), with basal velocities periodically dropping to zero, indicating complete shutdowns (Fig. S6a, d–f). Given this independence and the relatively stable, cold glacial climate (with insufficient oceanic or atmospheric warmth to induce substantial surface or sub-shelf melt (Fig. S8e), and thus little change in ice shelf buttressing) we infer that ice-stream activation is primarily driven by internal thermodynamic “binge-purge” cycling rather than external forcing. Preferential drainage pathways from the ice-sheet interior to the margin vary between simulations and through time within individual simulations, often favouring one trough over adjacent ones. In contrast, some ice streams remain continuously active in the Southwestern and northern shelf sectors (Fig. S6b, c).

The main limitation predating the LGM is lack of constraints. Consequently, no scenarios of ice expansion pathway can be ruled out and the ice margin position remains highly uncertain.

At MIS 2, the IIS advances further onto the shelf, specifically along the western margin. The ice sheet maintains its double-dome structure, with the primary dome centred over the present-day Vatnajokull region and a secondary dome over the Northwest peninsula (Fig. ). The simulated NROY_tier1 ice volume spans from 0.76 to 0.41 m eustatic sea level equivalent (m e.s.l.), with a median of 0.6 m e.s.l. at the local LGM (23.6 to 20.9 ka). The large variance in LGM volume is primarily due to differences in the extent of the grounding line across the Southwestern shelf, the potential link with Greenland as well as variations in the overall ice thickness.

During the global LGM, summer air temperatures vary within our NROY_tier1 sub-ensemble, but remain below freezing point, with little to no surface melt (Fig. S8e). The IIS expansion is therefore mainly constrained by the continental shelf edge and reaches it in most sectors. This is supported by the presence of numerous moraines all along the shelf edge (Fig. ). The exception is in the southwest where the grounding line position is more variable across NROY models (Fig. b). Our NROY_tier1 simulations at 25 ka bracket the empirical ice-margin reconstructions for 25.5±2.5 ka .

The ice sheet is bounded by ice shelves, particularly along the northern margin. Some NROY_tier1 simulations exhibit an ice bridge over Denmark Strait connecting the Northeastern Iceland ice shelf to the Greenland Ice Sheet (Fig. ). The latter reached the shelf edge over its Southeastern margin during the LGM . Even though not located within our model domain, core MD99-2323 at a depth of 1062 m, situated over the southern Denmark Strait, shows evidence of bioturbation during the LGM , which has been interpreted as indicating open water conditions at that location. However, documented benthic life under the Amery Ice Shelf, demonstrating that bioturbation does not preclude ice shelf cover. further infer that the Denmark Strait served as the primary gateway for iceberg passage, as the IRD sediments in core MD99-2323 are sourced from northern and northeastern Greenland, the Arctic Basin, and the European Arctic, though a contribution from the clockwise Irminger Current cannot be ruled out. Moreover, paleoceanographic data of the northern North Atlantic at the LGM reflect relatively warm conditions with perennial sea-ice cover confined to the northeast Greenland margin area . Conversely, there is evidence for a reduction in the strength of the Western Boundary Undercurrent (WBUC) around Southern Greenland during glacial stages . This is likely due to reduced Denmark Strait Overflow , potentially attributed to the presence of an ice shelf. In some simulations, grounded ice extends fully across Denmark Strait (Fig. b).

The presence of a thick, soft basal sediment layer in marine sectors and valley bottoms as well as high geothermal heat flux facilitate fast basal sliding. This partly explains why all simulations, regardless of the parameter choice, depict a highly dynamic ice sheet with numerous fast-flowing ice streams that effectively drain the ice from the interior to the margin (Fig. a). Another factor is the presence of numerous topographic troughs that over time guide ice stream drainage of the ice sheet (Fig.  and b). Most if not all of these troughs are likely the result of the two-way feedback between topographic excavation by subglacial erosion and topographic steering and confinement of ice streaming. Over time and location there are varying degrees of topographic steering and confinement with some ice streams clearly topographically confined, and others crossing over topographic ridges (Fig. b).

Given the temporal variation in ice stream configuration for a given simulation as well as the variation between ensemble members (Fig. S7), no single simulation at a given time is likely to be fully consistent with relevant geological data such as streamline ridges (Fig. a). A further challenge in such comparison is the poor age control on such features, with only indirect inferences that they were formed during the local LGM .

Such effective drainage results in an extensive ice sheet with a small mean ice thickness on the order of 811±71 m as per the NROY sub-ensemble. This is lower than crude estimates based on volume-area scaling (using a scaling exponent of 1.23 from , and an area of 250 000 km2 giving a mean ice thickness =1026 m), and even lower than past models for Iceland (939 m for , and 1172 m for ).

The IIS loses ∼95 % of its mass during the last glacial-interglacial transition (∼20.9 to ∼9 ka). The deglacial mass loss is dominated by calving until ∼11.5 ka. The IIS deglaciation history is characterized by a two-step evolution with five distinct phases: three of moderate ice retreat or even re-advance (I, III, and V in Fig. ), and two of intervals of rapid ice loss (II and IV in Fig. ).

First, between the end of the local LGM and 14.6 ka (Phase I), the grounding line retreats moderately across the South-western shelf (Fig. b). The mass loss is tied to a slight offset between ice discharge and surface mass balance (Fig. d). This is driven by sea level rise alone (Fig. a) as the climate is still relatively cold (Fig. b, c), consistent with TraCE-21000 simulations showing negative surface temperature anomalies relative to 22 ka until 15 ka over the North Atlantic region . However, we cannot rule out that the lack of an apparent submarine melt role in initiating deglaciation may be due to limitations of the relatively coarse resolution GCM used to generate the TRACE ocean temperature field. Between the end of the local LGM and ∼14.6 ka, the atmospheric temperatures surrounding Iceland for the NROY_tier1 simulations remain below the threshold necessary for substantial surface melt (Fig. c, e).

Between 14.6 and 14 ka (II), ice discharge significantly exceeds the surface mass balance (Fig. d) and the marine-based ice sheet collapses. The ice sheet transitions from a marine to a terrestrial setting (Fig. b). The mass loss is primarily driven by atmospheric warming during the Bølling–Allerød. We hypothesize that atmospheric warming drives increased ice discharge through hydrofracturing. Accordingly, we conducted a sensitivity experiment without hydrofracturing (see Sect. below). An increase in surface melting, particularly at lower altitudes (i.e., on the ice shelves over the northern margin and tidewater glaciers over the southern margin; Fig. S9), intensifies surface crevasse growth through hydrofracturing, thereby increasing calving flux (Fig. e). The resulting ice shelf disintegration (Fig. S10) together with the tidewater front retreat reduces back stress, which would enhance ice flux across the grounding line and thereby at the calving front. The disintegration of the ice shelves leads to less total sub-shelf melt (Fig. e) in spite of an increase in ocean temperature forcing. The marine ice sheet instability (MISI) potentially further accelerates the grounding-line retreat . Based on several NROY runs, it appears that the Kolbeinsey ridge (∼19° W, 67° N in Fig. ) may act as a pinning point that buttresses the ice, maintaining continuous and sustained drainage of the ice streams until ∼14.6 ka. Once this anchoring stops, the ice sheet retreats rapidly across the mid-outer shelf. Such a combination of feedbacks results in the steepest rate of mass loss throughout the deglaciation (Fig. e). This aligns with previous geological inferences of marine ice sheet collapse during the Bolling-Allerød .

Following the phase of rapid mass loss, most of the NROY_tier1 runs have ice regrowth from 14 to 11.8 ka (III). This is driven by both an increase in accumulation and a substantial reduction in surface melt, which simultaneously increases the surface mass balance (Fig. d) and reduces calving by inhibiting hydrofracturing (Fig. e). Simulations from the whole ensemble exhibit a range of behaviours over this time interval: there is either a strong decrease in deglaciation rate, stabilization, or a re-advance of the IIS (Fig. S4). Simulations with smaller ice volumes generally exhibit proper re-advance, while those with larger ice volumes experience a decreased deglaciation. At 12 ka, our minimum NROY_tier1 extent closely matches the empirical ice-margin reconstructions for 12.5±3.0 ka (Fig. b, ).

By 11.8 ka (IV), the ice sheet shrinks rapidly. The ice loss is primarily driven by atmospheric warming at the end of the Younger Dryas. This results in a large increase in surface runoff which gives rise to a sharp decrease in surface mass balance as well as a brief increase in calving (Fig. d, e). The increased surface melt increases hydrofracturing and therefore calving until it is offset by decreasing the marine fraction of the ice margin.

At 11.5 ka, the IIS margin generally coincides with the present-day coastline, aligning with past empirical inferences based on shorelines and moraines . From 11.5 to 9 ka (V), the mass change becomes progressively dominated by the surface mass balance. By 10.7 ka, the magnitude of surface ablation offsets the snow accumulation, resulting in a negative total surface mass balance. The thinning accelerates as surface melt extends to higher elevations (Fig. S11), strengthening the melt-elevation feedback. Once the main ice dome is gone, the residual ice margin retreats gradually to the higher elevations until reaching a configuration comparable to present-day conditions at ∼9 ka. This is consistent with empirical evidence indicating that ice extent was similar to present prior to 9 ka .

Our above analysis demonstrates that the IIS deglaciation is dominated by ice discharge during the Phase II rapid retreat episode. Large volumes of ice discharge are associated with the acceleration and expansion of ice streams which drain interior ice to the margin (Fig. ). This acceleration is initiated by atmospheric warming, which triggers both ice shelf disintegration and tidewater glacier retreat via hydrofracturing (see Sect.  on hydrofracturing below). With the elimination of ice shelf buttressing and reduced backstress at tidewater margins, ice streams accelerate. Here, ice stream acceleration is therefore triggered by ice shelf removal and tidewater glacier retreat (see Sect.  on hydrofracturing sensitivity), in correspondence with recent observations of ice stream and outlet glacier acceleration in Antarctica and Greenland , rather than internal processes as simulated for the Laurentide Ice Sheet during last glacial cycle or IIS throughout MIS 2 (this study). Therefore, contrary to inferences for the Laurentide ice sheet , we conclude that ice streams can play a critical role in changing ice sheet mass balance. However, once the IIS fully retreats to non-marine margins (phase V), ice streams largely shut down (Fig. S7), consistent with geomorphological signatures .

On the basis of this data-model comparison, we conclude that the IIS deglaciation is most likely caused by a non-linear series of mechanisms. That is, once a temperature threshold is crossed, surface runoff on the ice shelf increases calving via hydrofracturing, leading to both ice shelf disintegration and tidewater glacier front retreat. The resulting elimination of ice shelf buttressing and reduced backstress at tidewater margins trigger ice stream acceleration and thereby increased ice discharge into the ocean. Hydrofracturing thereby provides a coupling between atmospheric forcing, specifically surface warming and rain, and enhanced grounding line discharge of ice.

Hydrofracturing is a key component of both ice shelf and tidewater calving in the GSM c.f. Eqs. 31 and 32 in. To decipher the relative role of hydrofracturing in the IIS deglaciation, we conducted three deglacial sensitivity experiments on the full NROY set of ensemble parameter vectors. In turn, these experiments were: without hydrofracturing, with hydrofracturing only for tidewater margins, and with hydrofracturing only for ice shelves.

The NROY ensemble without hydrofracturing has a much reduced rate of net mass loss during the 14.6 to 14.0 ka phase II interval over which the NROY ensemble with hydro-fracturing loses more than 60 % of its mass (Fig. ). The experiment therefore shows that hydrofracturing plays a key role in the non-linear response of simulated ice sheet retreat to atmospheric warming for at least our NROY set of parameter vectors. With hydrofracturing, the NROY ensemble has an approximate doubling in ice discharge across the grounding line at ∼14.5 ka, which is also the start of the interval of strongest mass loss from ice calving (Fig. S8). Without hydrofracturing, there is no increase in ice discharge across the grounding line during the whole phase II interval (Fig. S12). From 15 to 11.6 ka, the no hydrofracturing ensemble has moderate grounding line retreat. Subsequently, at ∼11.6 ka, once a certain threshold of temperature is crossed, the rate of mass loss increases significantly. Here, contrary to the reference set-up, surface mass balance completely dominates the mass loss, with subshelf melt and, to an even lesser extent, calving playing secondary roles (Fig. S12). The limited calving and sub-shelf melt are not enough to trigger major ice shelf disintegration or tidewater calving (Figs. S12, S13b). Therefore, ice stream acceleration is substantially reduced compared to the reference experiment with hydrofracturing (Fig. S14d).

The experiments with hydrofracturing only for tidewater margins, and with hydrofracturing only for ice shelves indicate that both mechanisms contribute comparably to total hydrofracturing (Fig. ). Thus, regardless of whether margins terminate in ice shelves or grounded tidewater glaciers, hydrofracturing remains critical in deglaciation. The normalized ice stream discharge in the no tidewater hydrofracturing experiment is slightly higher than in the experiment without any hydrofracturing (Fig. S14f), while the no ice shelf hydrofracturing experiment is comparable to the experiment without any hydrofracturing (Fig. S14h).

Given the model's high sensitivity to hydrofracturing and its potential reliance on this process to capture critical tier-1 marine constraints, there is the possibility that our analysis is skewed by this reliance. To address this, we reran the whole 2000 member initial ensemble with hydrofracturing turned off over the whole glacial cycle. We then sieved it against the tier-1 data using the same 3σ implausibility threshold applied to NROY_tier1. Only 2 members meet the NROY criterion, and neither are nominally consistent with the data. In these instances, the model fails to reproduce the last deglaciation dynamics of the IIS, in particular the collapse of the marine ice sheet suggested by the data. As such, for at least the GSM, hydrofracturing is required in order for the IIS simulation to be consistent with our tier I constraints. However, other potential IIS deglaciation drivers not considered here, such as episodic volcanic intervals , cannot be ruled out.

These results highlight the potentially critical role that hydrofracturing can play in marine ice sheet deglaciation. draw similar conclusions in their reconstruction of the Antarctic penultimate deglaciation. We therefore suggest that recent projections e.g. may underestimate the relative contribution of atmosphere in driving future marine ice sheet mass loss unless they incorporate hydro-fracturing . This is particularly likely as 60±10 % of Antarctic ice shelves that buttress upstream ice has been inferred to be prone to hydrofracturing if surface crevasses are filled with water .

To partly address structural uncertainties in the representation of hydrofracturing (i.e. uncertainties not covered by ensemble parameters), the NROY_tier1 parameter vector set was re-run with linear (as opposed to quadratic) dependence of hydro-fracturing on surface runoff for the whole glacial cycle. The linear coefficient was scale matched to that of the default quadratic dependence for a 0.5 myr-1 surface runoff. This scale choice approximately matches mean ensemble deglacial runoff over the ice shelves during the 15 to 14 ka interval. The impact of this structural change is nearly unbiased on the ensemble (Fig. S17), with less than 5 % impact on 15 ka grounded ice area for most simulations. The impact for three other metrics (20 ka ice volume, ice thickness misfit score, and marine ice extent misfit score) is larger over the ensemble, but in each case it is still less than 5 % for the majority of simulations.

Another potential driver of marine ice sheet collapse is sea level rise due to increasing ocean volume during deglaciation as well as associated changes in the gravitational field. To isolate the relative impact of this, we carried out a sensitivity experiment repeating the 15 to 0 ka deglacial interval of the simulations with the geoid held constant at its 15 ka value (≈-100 m around Iceland relative to the Earth's center of mass). This was applied to the whole NROY_tier1 set of simulations. This change in forcing had minimal impact on the ensemble. A few simulations had slightly reduced mass loss rates (maximum difference at any time of ∼0.02 m e.s.l.), while the rest had almost no visually discernible response (Fig. S15).

The GSM visco-elastic GIA solver is restricted to a spherically symmetric earth rheology. However, there are likely significant lateral variations in the visco-elastic earth structure under Iceland. To bound potential uncertainties due to such variations, we reran the NROY_tier1 set with nominal stiff and soft bound earth rheology values. These rheologies were respectively assigned upper mantle viscosities of 5×1019 and 5×1018 Pa s along with respective lithospheric thicknesses of 96 and 46 km in accord with the previously inferred range of values for a deglacial timescale . Simulations with the stiffer earth rheology tended to have a bit more 20 ka ice volume (ranging to 14 % larger, Fig. S16). In contrast, the stiff bound earth rheology gave less 15 ka grounded ice area (ranging to 10 % smaller) as well as larger “iceTot” ice thickness misfits against cosmogenic age constraints. The latter is also indicative of insufficient regional ice. The difference in half-space timescale for this rheology range (approximately 1050 years) is not much larger than the nominal ice sheet dynamical timescale during early to mid deglaciation (average grounded ice thickness/average accumulation ≈850 years). As such, a non-negligible impact is not unexpected.

Finally, to partly address uncertainties due to the impact of a simplified “leaky bucket” local sub-glacial hydrology model, the NROY_tier1 set was rerun with a 10 m (as opposed to the default 2 m) limit on subglacial water thickness. In comparison to the reference ensemble, differences in 15 ka grounded ice area, 20 ka ice volume, and IceTot score were all less than 5 % for all but a handful of ensemble members (Fig. S18). The paleoExt marine misfit score again showed the largest impact, but differences in individual scores were still less than 10 % for all but two of the NROY_tier1 parameter vectors. A much more detailed assessment of the impact of basal hydrology model complexity in the context of Hudson Strait scale ice stream surge cycling found that most of the differences were within the range of what was already covered by parametric uncertainties for the simplistic basal hydrology model employed herein.