The model domain, shown in Fig. , spans 6.7 × 10⁶ km2, from the continental shelf in the east to the Canadian Arctic Archipelago in the west. A north polar stereographic projection with a standard parallel at 70° N and central longitude of -45° W (ESPG 3413) is used. The projection introduces distortions of up to +5 % in the north and -11 % in the southwest relative to the central latitude and longitude. PISM uses a flat-Earth approximation, so volume is not conserved when transforming thickness between projections. Volumes and mass-loss rates are reported using the actual grid area.

To partition mass between Greenland and Canada, we introduce an extended continental shelf (ECS) mask, corresponding to Greenland's exclusive economic zone . This divides the two regions at the Nares Strait and Baffin Bay, extending to the continental shelf in the north, east, and south. For mass-loss partitioning when the grounding line advances, we extend the basins from to the ECS using nearest-neighbor extrapolation.

The present-day bedrock topography over Greenland is from BedMachine v5 and extended using data from IBCAO v4.2 and the to cover the larger domain, in that order of preference, to get the best bedrock available.

At the lateral boundary, a Dirichlet boundary condition of zero ice thickness is used; the influence of the majority of the Laurentide Ice Sheet is thereby neglected. The north and south are bounded by open ocean, while Iceland and Svalbard are just visible toward the east. At the base of a 2 km deep bedrock thermal layer, the thermal heat flux from is applied constantly in time.

To model the surface mass balance (SMB), we apply a positive degree day (PDD) scheme to calculate the surface melting. This approach bases the SMB solely on temperature, T, and precipitation, P. In the PDD scheme, the surface melt rate is proportional to the extent to which the temperature exceeds the freezing point e.g.,, 1m˙s∝max⁡(0°C,T), where we use two constants of proportionality: one for snow, fs, and another for ice, fi.

To force the PDD model, we use a 12-month reference climatology based on the multi-year monthly averages of temperature and precipitation for the period 1960–1989 from RACMO . Since our model domain is not covered by a single RACMO simulation, we combine different simulations (see Fig. ). We merged three areas with precipitation data: Greenland, the northern Canadian Arctic Archipelago, and the southern Canadian Arctic Archipelago , treating areas outside these regions as having no precipitation. For temperature, we used RACMO2.3p2 at 5.5 km for Greenland , combined with a broader 11 km simulation for the rest of the area. The mean precipitation and summer temperatures for the resulting climatology are shown in Fig. .

Following , we account for paleo temperature changes by applying a spatially uniform time-varying temperature anomaly, ΔT, along with a lapse rate adjustment, Γ, which modifies the surface temperature based on deviations from the RACMO surface topography. The temperature reconstructions are shown in Fig. . Insolation changes are not included in this approach.

Reconstructions 1 and 2 use the GRIP ice core with linear and quadratic transfer functions from and , respectively. Reconstruction 3 uses the NGRIP core with the same transfer function from , while Reconstruction 4 is the GrIS-wide reconstruction from  – the only one that accounts for elevation change. Reconstruction 5 is based on the NGRIP core with an isotope diffusion inversion scheme .

The Holocene Thermal Maximum is only captured by Reconstructions 3, 4, and 5, while Reconstructions 1 and 2 suggest a more constant Holocene climate. Reconstruction 1 was used by the SeaRISE project .

Since the vapor pressure scales approximately exponentially with temperature in the Clausius–Clapeyron relation, we account for paleo precipitation changes by scaling the reference precipitation field with a time-dependent scaling factor, exp⁡(ω(ϕ)ΔT(t)). Here, ω has the latitude dependence 2ω(ϕ(x,y))=ω↓ϕ≤ϕ↓pω↓+ϕ-ϕ↓pϕ↑p-ϕ↓pω↑-ω↓ϕ↓p≤ϕ≤ϕ↑pω↑ϕ↑p≤ϕ, where ϕ is the latitude and ϕ↓p = 60° N and ϕ↑p = 75°N are chosen to cover most of Greenland; ω↓ and ω↑ are the southern and northern precipitation scaling parameters, respectively, which are varied in our ensemble. This approach allows for different precipitation histories in northern and southern Greenland, in contrast to the uniform scaling used in many previous modeling attempts e.g.,.

Following , we take the sub-shelf ocean melt to be separable in space and time: 3m˙o(x,y,t)=m˙xo(ϕ(x,y))m˙to(t), with the spatial dependence controlling the present-day melt rate given by 4m˙xo(ϕ(x,y))=m˙↓oϕ≤ϕ↓om˙↓o+ϕ-ϕ↓oϕ↑o-ϕ↓om˙↑o-m˙↓oϕ↓o≤ϕ≤ϕ↑om˙↑oϕ↑o≤ϕ, where ϕ↓o = 71° N and ϕ↑o = 80° N, following , while m˙↓o and m˙↑o are the upper and lower melt values, which we vary. To allow the formation of an ice bridge to Canada, the sub-shelf melt rate is scaled by 5m˙to(t)=0t≤τt-τΔττ≤t≤τ+Δτ1τ+Δτ≤t, such that there is no ocean melt for times earlier than τ, while it increases to present-day values in the time Δτ, inspired by the rapid change in ocean temperatures found by . In addition to sub-surface melt, ice is calved off at the ocean front at a rate that is proportional to the tensile von Mises stress and inversely proportional to a characteristic parameter, σmax⁡ . Additionally, all ice thinner than Hcr is calved off, and a eustatic sea-level forcing from is applied, changing the ocean level by 130 m in the last 19 ka.

The constitutive relation that relates the strain rate, ϵ˙ij, to the stress, τij, in the ice sheet is 6ϵ˙ij=EAτen-1τij, where E is the enhancement factor, τe is the effective deviatoric stress, n is the creep exponent, and A is the ice softness, which depends on temperature, pressure, and water content of the ice. The enhancement factor and the creep exponents are taken to be different for the SIA and the SSA. We use ESSA=1.3, nSIA=3 while varying ESIA and nSSA following . The numerical value of A in Eq. () is not changed; only the units are adjusted.

The basal sliding velocity ub in the SSA is related to the basal shear stress τb through the pseudo-plastic power law: 7τb=-tan⁡(φ)Ntillubuthq|ub|1-q, where q is the sliding exponent and uth = 100 ma-1 is a characteristic speed. The till friction angle, φ, is parameterized as a continuous function of bedrock topography that increases linearly from φmin⁡ to φmax⁡ between zmin⁡ and zmax⁡. The effective pressure on the till, Ntill, decreases exponentially with the water level in the till, Wtill : 8Ntill=min⁡P0,Ñ0δP0Ñ0Wtill/Wtillmax⁡. It decreases to a fraction δ of the overburden pressure, P0, when the water level reaches its maximum value, Wtillmax⁡ = 2 m. The parameter Ñ0 = 5.6 × 10⁸ Pa represents the effective pressure that the till would have at zero water content if it were not capped by the overburden pressure.

The bedrock response to changes in ice load is given by the visco-elastic bed deformation model of and , with flexural rigidity D = 5 × 10²⁴ Nm and upper mantle viscosity η = 1 × 10²¹ Pas.

We initialize the GrIS by running the model from -100 to -20 ka (all times are relative to 2 ka CE) at 20 km grid resolution using the parameters listed in Table  and with the initial bedrock topography taken to be the same as at the present day .

Since the modeled ice extent, and consequently the surface elevation, is sensitive to ocean melt and sea-level forcing, we apply an artificial correction to the bed topography to ensure that the present-day ocean mask closely aligns with observations.

To achieve this, we iteratively adjust the bedrock at -20 ka (as illustrated in Fig. ) so that the modeled bedrock topography at the end of the simulation better matches the observed present-day topography. A simulation with 20 km resolution is run from -20 ka to the present, and the deviation between the modeled and observed bedrock topography is used to update the initial bedrock according to 9bi+10=bi0+Kbobs-bi1, where bobs is the observed present-day topography , bi0 is the modeled bedrock topography at -20 ka, and bi1 is the modeled bedrock topography at the present day. This iterative correction method is similar to the approach used by , who employed a comparable scheme to improve present-day topography. The relaxation parameter K=0.7 is introduced to prevent overcompensation from any potential positive feedback associated with the updated bedrock, although such feedback may not be significant, given that the bedrock–mass balance feedback is likely to be negative. After 20 iterations, the root mean square error (RMSE) of the bedrock decreased from 77.4 to 3.3 m, as shown in Fig. . The impact of these iterations on the surface elevation is illustrated in Fig. .

At -20 ka, the simulation is branched using the adjusted bedrock (b0) from the last step (shown in Fig. ), and an ensemble of simulations is run at a 10 km grid resolution until the present day, varying the 20 parameters listed in Table .

Figure  shows the modeled and ice-core-derived surface elevations during the Holocene at the four ice-core sites. The site-specific modeled elevations closely match the ice-core-derived reconstructions, reproducing the substantial thinning observed at CC and Dye 3, as well as the more moderate thinning at the interior sites GRIP and NGRIP, with RMSEs ranging from 12 to 53.6 m. The combined elevation estimate is lower than the site-specific estimates at CC and Dye 3 at the onset of the Holocene, while it is too high at GRIP. The corresponding histories of bedrock elevation and ice thickness associated with these surface changes are shown in Fig. .

To illustrate the effect of allowing the ice sheet to advance beyond its present-day boundaries, we ran two additional simulations: one restricted from advancing beyond the present-day GrIS coast and another restricted from advancing beyond the ECS mask. Both simulations started from the unrestricted branch-off point at -20 ka and used the same parameters as the ensemble member with the highest combined likelihood, although these parameters may not necessarily be optimal for either of the restricted runs. The simulation restricted to the present-day GrIS coast could not reproduce the observed surface-elevation history at CC, NGRIP, and Dye 3, showing the importance of a dynamic grounding line. The simulation restricted to not advancing beyond the ECS performed better but also failed to reproduce the thinning at CC, showing the effect of including the Canadian Arctic Archipelago when modeling the GrIS Holocene history. The RMSEs associated with the four ice-core-derived elevation histories are listed in Table  for the five estimates.

The ice-core-derived surface-elevation histories provide constraints on the model parameters, with the marginal PDFs for each of the five posteriors shown in Fig. . The degree to which individual parameters are constrained varies, and the estimated values are summarized in Table .

Notably, the site-specific and combined estimates of the SIA enhancement factor, ESIA, differ substantially. The site-specific estimate based on CC is 2.7 ± 0.2, while that based on GRIP is 3.1 ± 0.2. Similarly, the site-specific estimates of the SSA creep exponent, nSSA, differ, with higher values for CC and NGRIP than for GRIP and Dye 3.

Among the five temperature reconstructions, Reconstruction 1, being the coldest throughout the Holocene, has the highest combined probability (61 %) and the highest site-specific probability for CC (40 %), where the largest surface thinning is observed. In contrast, Reconstruction 2 is more than 1 °C warmer during the early Holocene and performs worse than Reconstruction 1. Reconstructions 4 and 5, the warmest of the set, have near-zero probability at CC but perform better at other sites; notably, Reconstruction 4 has the highest site-specific probability for both NGRIP and Dye 3.

The northern precipitation parameter, ω↑, is more constrained by the northern sites CC and NGRIP, where it has the most influence. Likewise, the southern precipitation parameter, ω↓, is most constrained by Dye 3. Both parameters are estimated to be 2 ± 1 %K-1, which is substantially lower than the default of 7.3 %K-1 introduced by , resulting in less accumulation in the warm periods of the Holocene and more accumulation in the cold glacial periods, where the ice sheet builds up.

The onset of sub-shelf ocean melt is well constrained by CC, occurring at 5.6 ± 0.6 ka before the present.

From the branch-off point at -20 ka until the onset of the Holocene (11.7 ka ago), the modeled ice sheet bridges the gap between Canada and Greenland across the Baffin Bay and the Nares Strait. Figure  shows the ice sheet configuration at -12, -9 ka, and the present day, while Fig.  presents the volume and area evolution from the branch-off point to the present. The model clearly responds to the change in resolution at the branch-off point, showing a positive drift in volume, though this shock appears to have stabilized before the start of the Holocene. By -12 ka, the ice sheet reaches its glacial maximum extent, grounding on the continental shelf and through the Nares Strait.

At -12 ka, the GrIS has a modeled grounded area of 2.96 ± 0.03 × 10⁶ km2 within the ECS. This is 49 % or 0.98 ± 0.05 × 10⁶ km2 larger than the present-day modeled area and it is 0.9 % larger than the minimum LGM extent and 5.6 % smaller than the maximum LGM extent from . Compared with the modeled present-day GrIS, the modeled grounded volume is 6.6 ± 0.4 mSLE larger at -12 ka. Additionally, the grounded volume above flotation at -12 ka was 5.3 ± 0.3 mSLE greater than at present. The modeled times of the last glaciation are shown in Fig. .

Outside the ECS, the IIS and Laurentide Ice Sheet are cut off at the domain boundary with a Dirichlet boundary condition of zero thickness. This moves the ice divide at Baffin Island farther to the east than if it had been connected to a complete Laurentide Ice Sheet. Together, they have a grounded area of 1.20 ± 0.03 × 10⁶ km2 and a grounded volume of 5.0 ± 0.2 mSLE.

During the Holocene collapse of the IIS, the ice divide at the GrIS moves toward the west and the ice streams reorganize in northern Greenland, as shown in Fig. . This divide migration could explain the onset of NEGIS, as found by , and the shutdown of the older, more northern ice stream, as observed by .

Figure  shows the rate of change of grounded ice for the ensemble member with the highest combined likelihood for the seven basins of the GrIS. The GrIS rate of change becomes negative at -10.7 ka and exhibits two distinct peaks: one at -7.8 ka, with a mass-loss rate of 548 Gta-1, and another at -4.95 ka, following the onset of sub-shelf melting, with a mass-loss rate of 511 Gta-1. It continues to be negative for the rest of the Holocene, except for a few times during the last 2 ka, where the average mass-loss rate is 23.7 Gta-1. The mass-loss rates stated here are averaged over 50 years.

The modeled present-day extent of grounded ice deviates from the observed extent, as shown in Fig. a. Most notably, the modeled extent is larger in the Canadian Archipelago, while it fails to cover an area of 0.08 ± 0.01 × 10⁶ km2 and inaccurately covers an area of 0.19 ± 0.01 × 10⁶ km2 compared with the observed GrIS extent. This comparison includes peripheral glaciers and excludes ice thinner than 10 m, which is considered to be seasonal.

The modeled GrIS grounded volume at the present day is 9.1 ± 0.1 mSLE, which is 1.5 mSLE larger than the observed grounded volume, including peripheral glaciers . This discrepancy can be attributed to the ice thickness deviations at the GrIS margin, as shown in Fig. b.

In the northwest, the modeled ice sheet is thinner than that observed at the Humboldt Glacier, resulting in an overestimation of surface speed. In the northeast, the model fails to reproduce the flow pattern of NEGIS and instead simulates a faster-flowing ice stream located farther north. These discrepancies are illustrated by the deviations in modeled surface speeds shown in Fig. c, compared with observations by .

The modeled present-day uplift rates deviate from the GPS-derived glacial isostatic adjustment (GIA) uplift rates reported by , as shown in Fig. a. The largest deviations occur in the area formerly covered by the IIS, where the modeled present-day bedrock topography differs by up to 93 m from observations (Fig. b), with a RMSE of 27 m. The total modeled uplift from -12 ka to the present reaches a maximum of 509 m in the IIS region (Fig. c). At Agassiz and Renland, the modeled bedrock uplifts are 345 ± 9 and 168 ± 9 m, respectively. These values are slightly higher than the 275 and 110 m uplifts, respectively, used by in their surface-elevation reconstructions.

The focus of this study is to reproduce surface-elevation histories at four ice-core locations in the interior of Greenland. To accurately model the early Holocene thinning in northwest Greenland, we include the Canadian Arctic Archipelago in our domain and allow the ice sheet to advance beyond its present-day boundaries. With these model choices, the ice bridge across the Nares Strait that connected the Greenland Ice Sheet (GrIS) and the Innuitian Ice Sheet (IIS) during the Last Glacial Maximum is formed in the model, as well as the ice shelf that covered Baffin Bay. This, in turn, enables the ice sheet to grow thicker in Greenland's interior during the Last Glacial Maximum at the four ice-core sites, due to the development of the ice bridge. This is demonstrated by comparing two simulations: one constrained to the present-day land margin and the other to the ECS (Fig. ).

In our model, the IIS is connected to the GrIS across the Nares Strait during the glacial maximum. From the saddle point between the ice sheets, the ice flow diverges into two oppositely flowing ice streams in the Nares Strait: one flowing southwestward, which is similar to the Smith Sound Ice Stream suggested by , and another flowing northeastward. The southwestward ice stream discharges into Baffin Bay, which is covered by an extensive ice shelf, as proposed by , that provides buttressing for the western GrIS.

In our simulations, deglaciation occurs in two stages (Fig. ). The ice sheet begins to thin and retreat in response to the abrupt temperature rise at the transition at -11.7 ka. Increased surface melting drives the first stage of mass loss in the early Holocene, prior to the onset of ocean forcing. This enhanced melting leads to the collapse of the ice shelf in Baffin Bay around -9 ka, reducing the buttressing effect and causing further thinning and retreat of the ice sheet. Just before -9 ka, a large paleo ice stream develops inland from Baffin Bay, accelerating ice flow along the northwest coast into the bay and driving additional inland thinning in this region. Mass loss slows after -8 ka, before ocean forcing begins at -5.6 ka, initiating the second stage of accelerated mass loss (Fig. ). This culminates in the collapse of the ice bridge across the Nares Strait at -4.9 ± 0.5 ka.

The timing of the modeled collapse of the ice bridge in the Nares Strait occurs more recently than suggested by geological evidence. In our simulation, the collapse takes place at -4.9 ± 0.5 ka, approximately 0.7 ka after the onset of sub-shelf melting and about 3 ka later than the estimate by . Additionally, the lateral retreat of the ice margin also occurs several thousand years later than found by , as shown in Figs.  and .

Our simulation is, however, in good agreement with the surface-elevation lowering at the CC ice-core site in northern Greenland, where the Holocene thinning rate peaks around -9 ka (Fig. ). The surface lowering at the CC site at -9 ka coincides with the emergence and acceleration of the paleo ice stream along the Baffin Bay coast (Fig.  and the Supplementary Material), and occurs several thousand years prior to the collapse of the ice bridge.

At present, many marine-terminating ice streams in the northwest sector of the Greenland Ice Sheet flow into Baffin Bay, bounded by high bedrock topography near Upernavik to the south and Pituffik to the north. Our simulation indicates that paleo ice streams formed in this sector during the glacial period (Fig. a). Around -9 ka, these evolved into a transient, 50 km-wide ice stream terminating in Melville Bay, with a fast-flowing central trunk reaching velocities of several kilometers per year, comparable in size to the present-day NEGIS outlets. This ice stream developed over a bedrock valley system that links the northwestern interior to Melville Bay, rapidly draining the northwest sector of the GrIS and driving a retreat of the ice margin to near its present-day position within approximately 1 ka.

Thus, the primary cause of the surface-elevation lowering at the CC ice-core site is the formation of the paleo ice stream inland from Baffin Bay, rather than the collapse of the ice bridge. This is a novel finding of our study, which links to the work by , who associated Holocene elevation changes in interior Greenland with an acceleration of the paleo NEGIS.

Further work, beyond the scope of this study, may be able to reconcile the modeled ice sheet evolution with both the ice-core-derived interior surface-elevation histories and the lateral retreat and timing of the ice bridge collapse inferred from geological evidence. It should be noted, however, that ensemble members with earlier onsets of sub-shelf ocean melting, while leading to earlier retreat, result in the ice sheet becoming too thin at the CC site during the mid-Holocene, whereas those with later onsets remain too thick at present (Fig. ). This issue might be resolved if the precipitation in early Holocene were higher than assumed here.

Overall, our simulations show that the deglaciation in Greenland occurred between around 10 and 3.5 ka ago, where the total area and volume of the GrIS dramatically decreased from its glacial maximum values to approximately the present-day volume and extent (Fig. ). The minimum ice-covered area occurred approximately at -2 ka and slightly increased toward the present, while the ice volume has remained relatively constant over the last millennia. Our simulation shows no clear evidence of a minimum ice volume during the Holocene Thermal Maximum. It ends at the present day with a simulated area and volume that exceed the observed values by 5.9 % and 20.5 %, respectively (Fig. ).

A previous study by showed that the evolution of the GrIS depends on the assumed climate history through the Holocene. found that the GrIS retreated to a smaller than present-day volume at around 8 ka ago when forced by temperature anomalies containing the Holocene Thermal Maximum, but their simulations did not include Canada in the domain, and thus were initiated with a GrIS of similar size as at the present day. In our simulations, we used the same climate forcing histories as in the study by but we do not find a similar minimum in our simulations for the ensemble members that include the Holocene Thermal Maximum, most probably because the GrIS is too far from equilibrium during the Holocene Thermal Maximum, due to the large initial ice sheet. In fact, the simulations that best fit all surface-elevation histories are those forced with climate reconstruction history number 1 (see Fig. ), which did not show any Holocene Thermal Maximum. For this climate reconstruction, our simulated Holocene ice volume follows a similar pattern to that found by .

The spatial pattern of mass-loss rates from the GrIS has shifted significantly during the Holocene (Fig. ). In the earliest part of the Holocene, the rate of mass change was slightly positive in all basins, due to an increase in snow accumulation over the GrIS. During the first deglaciation phase, between 10 and 5.5 ka ago, the mass-loss rate was large in all basins, with the largest mass-loss rate in the northwest basin, being about the same rate as all the other basins combined. The central west basin also had significant mass-loss rates, followed by the north and southwest basins. Toward 5.5 ka ago, the mass-loss rates decreased toward zero; this is also seen in the volume record as a temporary stabilization. Between 5.5 and 3.5 ka ago, after the onset of the sub-shelf melt, a second phase in the deglaciation occurred, with a total higher mass-loss rate than the first phase, and this time dominated by high mass-loss rates from the northeast basin and to a lesser extent from the north and central west basins. These two deglaciation phases are also seen in the total volume (Fig. b), with a kink around 5.5 ka ago separating the two phases.

Our simulated Holocene mass-loss rates exceed those estimated by , who modeled the evolution of the CW and SW basins and assumed that these regions were representative of the entire GrIS. They found the maximal value of mass loss during the Holocene to be 60 Gta-1 and that it would most likely be exceeded within this century, with rates of mass loss of 8.8 to 359 Gta-1, depending on the climate scenario, which is less than our maximal Holocene rate of mass loss of 548 Gta-1 for the ensemble member with the highest likelihood. Our results show that the spatial pattern of retreat has shifted geographically during the Holocene and that the mass-loss rates from the GrIS basins have peaked thousands of years earlier in the northwest and west than in the northeast. We conclude that one basin cannot be representative of the entire GrIS; thus, our results are not directly comparable to the results of .

The importance of calibrating the GrIS evolution with paleo constraints is underscored when examining the mass change rates of the GrIS over the last 500 years. These rates range from a decrease of 487 mmka-1 to an increase of 105 mmka-1 across the ensemble of simulations. Excluding the simulations that utilize the temperature reconstruction from , where the temperature anomaly peaks at 4.5 K during this period, we find that the remaining mass-loss rates primarily depend on the timing of the onset of ocean forcing, τ (Fig. ). This relationship exhibits a strong Pearson correlation coefficient of 0.8. Consequently, the estimated mass-loss rate shifts from a prior of -12 ± 40 mmka-1 to a posterior of -23 ± 26 mmka-1. This adjustment highlights the critical role of paleo calibration in accurately modeling ice sheet dynamics.

The atmospheric conditions and spatial patterns of temperature and precipitation during the glacial period and early Holocene were probably quite different from those of the present day. The Laurentide Ice Sheet is thought to have both shielded Ellesmere Island from precipitation and deflected the jet stream, directing more moisture north of the Laurentide from the north Pacific Ocean into the polar regions. This makes the amount of precipitation over Greenland during that time uncertain .

Furthermore, the presence of an ice shelf in Baffin Bay probably influenced temperature and precipitation in a spatially non-uniform manner. Additionally, changes in insolation, which were not accounted for here, would have unevenly increased melt, particularly at higher latitudes e.g.,.

Non-uniform temperature anomaly products do exist, such as the TraCE-21K climate simulations and the derived product of , which was assimilated to match ice-core-derived temperatures. However, we chose not to use these products because they were simulated using the surface topography from ICE-5G . Avoiding these inputs ensures that our ice sheet reconstruction remains independent of previous reconstructions and avoids circular reasoning.

In our setup, we apply uniform temperature anomalies to be consistent with the assumption of , namely that local temperature offsets result from a Greenland-wide anomaly combined with local elevation feedback. However, by varying the applied temperature anomalies, lapse rate, and northern and southern precipitation scaling parameters, we explore a range of plausible spatial and temporal variability in SMB. Shortcomings of this model assumption would then be likely to manifest as differences in the site-specific inferred PDFs of the atmospheric parameters.

Our model setup also adopts a simplified approach to ocean forcing, reflecting both the limited understanding of its temporal evolution and the desire to maintain interpretability. Once the issue of excessive thinning at CC during the mid-Holocene – caused by earlier ocean-forcing onsets – is addressed, it may become feasible to further constrain the model using the lateral retreat reconstruction of . This could be done by introducing regionally distinct onset timings for ocean forcing in western and eastern Greenland, potentially yielding deeper insights into its spatial and temporal variability.

The modeled evolution of the ice sheet during the Holocene is influenced by multiple model parameters, which may compensate for each other, due to the complexity of the dynamic processes and climate forcings involved. As a result, interactions between these parameters can obscure their individual effects, making it difficult to draw definitive conclusions from the inferred parameter PDFs.

Nonetheless, differences in the site-specific PDFs suggest spatial variations in SMB that our model does not capture. For instance, the surface-elevation history at Dye 3 in the south favors reconstructions with a warm Holocene Thermal Maximum, while CC in the north favors a colder Holocene climate. This could indicate regional temperature differences that challenge the assumption by that local temperature offsets were solely due to a uniform, Greenland-wide anomaly and elevation feedback. However, these differences might also reflect compensations for other spatial factors, such as variations in ice rheology or basal friction.

The differences in the estimated ice-flow parameters may also stem from poorly resolved outlet glaciers, which lead to an underestimation of ice flux. This is often compensated for by increasing the enhancement factors. Notably, both Kangerlussuaq Gletscher in eastern Greenland and Sermeq Kujalleq in western Greenland require a resolution finer than 3.6 km to be properly resolved, as suggested by , which is not feasible for this study. Additionally, it is possible that the ice-core-derived surface-elevation records do not provide sufficient constraints for all model parameters.

The orthogonal Latin Hypercube Sampling technique was chosen for its ability to cover the high-dimensional parameter space more uniformly than simple random sampling, thereby reducing estimation errors. The effective sample size of the combined estimate is 9.28 (Table ), indicating that the weight is concentrated among a few samples, with the two most likely members contributing 42 % to the estimates. To improve this, an adaptive sampling technique could be implemented to increase sampling density in the regions of parameter space that most influence the estimates.

The present-day bedrock RMSE for the ensemble members ranges from 11.9 to 70.9 m. This is an improvement from the initial RMSE of 77.4 m before any bedrock adjustment, but it is still higher than the RMSE of 1.47 m achieved after the 12th iteration of the bedrock adjustment scheme. The discrepancy may partly arise from the bedrock adjustment being performed at a 20 km resolution, while the ensemble uses a 10 km resolution. The variation in bedrock RMSE suggests that the modeled bedrock topography is highly sensitive to the ice load history. To improve agreement between the modeled and observed present-day bedrock, additional bedrock adjustment iterations could be performed for each ensemble member, though this would significantly increase computational demands. However, the reported error in is up to 1000 m in the interior, where data coverage is sparse, and the RMSE is 145 m over land. Given these uncertainties, further refining the bedrock topography may provide limited improvements.

The modeled uplift rates are generally larger than the GPS-derived GIA uplift rates from . This discrepancy may be due to the modeled collapse occurring too late, not allowing enough time for the bed to fully relax, or it could be because the assumed viscosity of the upper mantle is too low. A higher viscosity would result in smaller past elevation changes, leading to an earlier collapse.

The viscosity of the upper mantle was not varied in our ensemble; instead, we used the default value of 10²¹ Pas from . Estimates of viscosity vary across several orders of magnitude , with suggesting a plausible range of 10²⁰ to 10²² Pas for Antarctica. Varying the viscosity would further alter the bedrock topography history of the ensemble members, providing additional justification for adjusting the bedrock for each member individually.

Our work, along with the elevation histories of , relies on the assumption that changes in moisture sources did not significantly affect the 18O fractionation across the ice sheet. It does not consider the potential influence of a paleo ice shelf in Baffin Bay or the presence of the Innuitian Ice Sheet (IIS) on the fractionation process along the moisture transport pathway from ocean source to ice-core site. Ideally, the ice sheet model should be coupled to an atmospheric model that simulates the transport and isotopic evolution of moisture from ocean evaporation to ice sheet precipitation. The resulting modeled 18O values could then be compared directly with the ice-core measurements. Nevertheless, the derived elevation histories used in our study are supported by measurements of total gas content, which provide an independent proxy for pressure – and thus elevation – at the close-off depth.

proposed revised elevation histories, arguing that the bedrock history along the eastern coastline of Ellesmere Island should be used instead of the Agassiz site itself, due to the complicating influence of the Innuitian Ice Sheet (IIS) prior to 8 ka ago. Building on this, assumed that the elevation correction to the δ18O signal at the Agassiz ice cores should be based on coastal sites. This led to revised temperature anomalies for Agassiz, which, in turn, increased the ice-core-derived surface elevation at Camp Century (CC) by 400 m at the onset of the Holocene. This suggests that our model may underestimate the surface elevation at that time; this could potentially be resolved by increasing the SMB during the last glacial period to allow for greater ice sheet thickening. We attempted to use the temperature anomalies from ; while this did result in increased thinning, the modeled present-day elevation became far too low, with the ice sheet retreating excessively far inland in the northwest.

The assumption that the thickness of the Renland ice cap remains constant throughout the Holocene contradicts our model results. We find that the Renland ice cap thins by 399 ± 56 m from the Holocene onset to the present day. This discrepancy may be due to the low resolution of our model, as the Renland ice cap covers only 1200 km2 and the model cannot capture the steep descents in topography that limit its lateral extent.