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### Calving entrance positions

We map the positions of the calving fronts of ZI and NG utilizing aerial and Landsat 5–8 optical satellite tv for pc imagery^{51,52} from 2000 to 2021 (Prolonged Knowledge Fig. 1). For ZI, essentially the most notable modifications occurred between 2011 and 2013, when a big portion of its floating extension collapsed, leading to a retreat of 10 km (ref. ^{53}). This collapse has been adopted by a gentle retreat of about 700 m yr^{−1}. NG misplaced massive sections of its floating tongue from 2002 to 2004; after this, calving occasions of the primary floating tongue have been much less frequent. Nevertheless, in 2020, the northern part of NG fully collapsed, releasing greater than 120 km^{2} of floating shelf ice into the ocean (Prolonged Knowledge Fig. 1).

### GNSS knowledge processing

We course of the GNSS knowledge utilizing the GIPSY-OASIS software program package deal with high-precision kinematic knowledge processing strategies^{27} and with ambiguity decision utilizing the orbit and clock merchandise of the Jet Propulsion Laboratory (JPL). We use GIPSY-OASIS model 6.4, which was developed on the JPL^{30}. We use JPL ultimate orbit merchandise, which embrace satellite tv for pc orbits, satellite tv for pc clock parameters and Earth orientation parameters. The orbit merchandise take the satellite tv for pc antenna section centre offsets into consideration. The atmospheric delay parameters are modelled utilizing the Vienna Mapping Perform 1 (VMF1) with VMF1 grid nominals^{54}. Corrections are utilized to take away the strong Earth tide and ocean tidal loading. The amplitudes and phases of the primary ocean tidal loading phrases are calculated utilizing the Computerized Loading Supplier (http://holt.oso.chalmers.se/loading/), which is utilized to the FES2014b ocean tide mannequin together with correction for the centre of mass movement of the Earth owing to the ocean tides. The positioning coordinates are computed within the IGS14 body^{55}. We convert the Cartesian coordinates at 15-s intervals into native up, north and east coordinates for every GNSS website monitored on the NEGIS floor. An instance of a 15-s resolution is proven in Prolonged Knowledge Fig. 2a–c.

### GNSS-derived floor speeds and their uncertainties

We use the 15-s resolution to estimate every day options of the ice floor pace (blue dots, Prolonged Knowledge Fig. second–f). The time collection have been screened for outliers. To take away outliers, we match and take away a development to every time collection of pace, latitude and longitude. We estimate the imply of detrended pace, latitude and longitude and outline outliers as values higher than three normal deviations from the imply. For NEG1, we eliminated in complete eight knowledge factors or (8/387 = 0.02) 2% of knowledge. For NEG2, we eliminated in complete 4 knowledge factors or (4/195 = 0.02) 2% of knowledge and 0% for NEG3. We use every day options of the ice floor pace (screened for outliers) to estimate the month-to-month imply ice pace (pink error bars). We estimate the root-mean-square of every month-to-month imply to assign uncertainties. The black strains denote the tendencies (utilizing least sq. adjustment) that greatest match the noticed ice speeds and signify imply move accelerations from 2016 to 2019 of two.7 ± 0.2 m yr^{−2} at NEG1, 4.5 ± 0.3 m yr^{−2} at NEG2 and 4.9 ± 0.3 m yr^{−2} at NEG3 (corrected for downhill acceleration).

### Floor pace and acceleration from mosaics primarily based on ESA Sentinel-1 SAR offset monitoring

We derive ice speeds from mosaics primarily based on ESA Sentinel-1 SAR offset monitoring obtained from https://dataverse01.geus.dk/dataverse/Ice_velocity. The ice velocity maps of the NEGIS are derived from the depth monitoring of the ESA Sentinel-1 knowledge with a 12-day repeat; the operational interferometric post-processing chain is utilized for the evaluation^{29}. We use all out there pace mosaics (offered on a grid with a spatial decision of 500 m) and related normal deviation of the underlying shift maps generated by the offset monitoring to create a time collection of pace for every grid level (Prolonged Knowledge Fig. 3b–d). We then take away outliers. To take away outliers, we match and take away a development to every time collection of pace and estimate the imply. We outline outliers as values higher than three normal deviations from the imply. For every grid level, we take away from 0 to 1.5% of knowledge equivalent to 0 to three knowledge factors. Subsequent, we use the screened time collection at every grid level and match a development that represents the move acceleration (the black line in Prolonged Knowledge Fig. 3b,c). For every grid level, we use the least-squares match to estimate the acceleration and related uncertainty. Prolonged Knowledge Fig. 3a reveals the imply acceleration from 2016 to 2022 in m yr^{−2} at every grid level. The uncertainty is ± 0.7 m yr^{−2}.

### Downhill correction for GNSS

We use mosaics primarily based on ESA Sentinel-1 to estimate the downhill correction of the move acceleration at GNSS stations. We estimate the time collection of the ice pace at two pixels on a velocity map on a 0.5 × 0.5-km grid. Pixel 1 is situated on the GNSS beginning place (when the station was deployed) and pixel 2 is situated on the GNSS end-point place. The distinction between the 2 time collection is used to estimate the downhill correction for the move acceleration. The uncertainty stage in Prolonged Knowledge Fig. 3a is ±0.7 m yr^{−2}. Nevertheless, two pixels shut to one another (similar to 1,000 m aside) expertise nearly the identical noise. Thus, when estimating the distinction between two neighbouring time collection, the noise is lowered to ±0.3 m yr^{−2}. To estimate the downhill correction of the move acceleration, we match a development to the time collection of the variations between two pixels.

Our corrections of the move acceleration, which compensate for the downhill motion of the GNSS stations, are as follows: 0.06 ± 0.18 m yr^{−2} at NEG1, 0.14 ± 0.29 m yr^{−2} at NEG2 and 0.12 ± 0.30 m yr^{−2} at NEG3.

### Elevation modifications from CryoSat-2

To estimate elevation modifications over the ice floor, we use an everyday grid with a decision of 500 × 500 m that covers the NEGIS. We denote the centre of every grid level as **C**(*x*_{0}, *y*_{0}). For every grid level, we choose CryoSat-2 knowledge with coordinates **P**(*x*_{i}, *y*_{i}), with a most distance of 1,000 m from **C**. The CryoSat-2 knowledge factors with coordinates **P**(*x*_{i}, *y*_{i}) have an elevation *h*_{i} measured at time *t*_{i}. The index *i* denotes the *i*th knowledge level. We use all out there CryoSat-2 knowledge measured between July 2010 and July 2021 to create floor elevation time collection at every grid level **C**. Earlier research have used a third-order polynomial equation to explain modifications within the elevation and a third-order polynomial equation to explain the form of the floor^{2,56,57}. Nevertheless, to explain floor modifications over 10 years, we match a polynomial with a level of seven to explain modifications within the elevation and we use a third-order polynomial equation to explain the form of the floor. As well as, we match a seasonal time period to account for the annual floor modifications. For every grid level with a centre **C**(*x*_{0}, *y*_{0}), we discover the closest knowledge level inside 1,000 m and match a seventh-order polynomial *H*(*t*_{i})_{poly}, a third-order floor topography polynomial *H*_{topo} and an annual time period *H*(*t*_{i})_{Annual}:

$$H({t}_{i})={H({t}_{i})}_{{rm{poly}}}+{H}_{{rm{topo}}}+{H({t}_{i})}_{{rm{Annual}}}$$

Prolonged Knowledge Fig. 4a reveals all of the grid factors on the NEGIS the place we now have efficiently estimated the time collection of *H*(*t*).

Prolonged Knowledge Fig. 4b,c reveals two examples of elevation time collection *H*(*t*). P1 is some extent closest to the ice margin and is situated at about 590 m elevation. Prolonged Knowledge Fig. 4b reveals CryoSat-2 elevations corrected for the topography *H*_{topo} (black error bars) and a mixture of our best-fitting seventh-order polynomial *H*(*t*)_{poly} and the annual time period *H*(*t*)_{Annual} (pink curve). The annual time period at this elevation has an amplitude of 1.41 ± 0.10 m. Prolonged Knowledge Fig. 4d reveals CryoSat-2 elevations corrected for topography and the annual time period (black error bars), and our best-fitting seventh-order polynomial (pink curve) for level P1.

Prolonged Knowledge Fig. 4c reveals the identical info as Prolonged Knowledge Fig. 4b however for the purpose P2, which is situated at about 1,078 m elevation. Right here the amplitude of the annual sign is 0.16 ± 0.08 m.

We use the best-fitting seventh-order polynomial (such because the pink curve in Prolonged Knowledge Fig. 4d,e) for every location proven in Prolonged Knowledge Fig. 4a to estimate the annual charges of elevation modifications from April to April, for instance, from April 2011 to April 2012, from April 2012 to April 2013 and so on.

### Elevation modifications from ICESat-2

We use ICESat-2 knowledge from October 2018 to June 2021 and estimate elevation modifications over the ice floor^{33}. We use the ICESat-2 Algorithm Theoretical Foundation Doc for Land Ice Alongside-Observe Peak (ATL06) Launch 004, which was retrieved from https://nsidc.org/knowledge/atl06 (ref. ^{58}).

We estimate elevation modifications utilizing the identical methodology described within the earlier part. Nevertheless, to explain floor modifications over about 2.5 years, we match a third-order polynomial (versus the seventh-order polynomial used for CryoSat-2 knowledge) and we additionally use a third-order polynomial equation to explain the form of the floor and a seasonal time period to account for the annual floor modifications. Prolonged Knowledge Fig. 5a reveals the grid factors on the NEGIS the place we now have efficiently estimated the ICESat-2 elevation time collection.

Prolonged Knowledge Fig. 5 reveals two examples of ICESat-2 elevation time collection *H*(*t*). P3 is some extent near the ice margin and is situated at about 267 m elevation (Prolonged Knowledge Fig. 5b). Prolonged Knowledge Fig. 5b reveals ICESat-2 elevations corrected for topography (black error bars) and a mixture of our best-fitting third-order polynomial and the annual time period (pink curve). Prolonged Knowledge Fig. 5d reveals ICESat-2 elevations corrected for topography and the annual time period (black error bars), and our best-fitting third-order polynomial (pink curve) at P3.

Prolonged Knowledge Fig. 5c reveals the identical info as Prolonged Knowledge Fig. 5b however for the purpose P4, which is situated at about 1,071 m elevation.

We use the best-fitting third-order polynomial (pink curves in Prolonged Knowledge Fig. 5d,e) for every location proven in Prolonged Knowledge Fig. 5a to estimate the annual charges of elevation modifications from April 2019 to April 2020 and from April 2020 to April 2021.

### Elevation modifications from NASA’s Operation IceBridge ATM flights

We estimate elevation modifications utilizing NASA’s ATM surveys in Greenland from spring 2011 to spring 2019 (ref. ^{32}). The ATM flights are primarily concentrated alongside the margin of the GrIS. To estimate elevation modifications, we take the peak distinction between overlapping factors from two completely different campaigns, that’s, we take the peak variations between the 2011 survey and the 2012 survey, between the 2012 survey and the 2013 survey and so on. Nevertheless, it ought to be famous that no survey was carried out in spring 2020. Prolonged Knowledge Fig. 6 reveals ATM flight strains over the NEGIS.

Prolonged Knowledge Fig. 6 (lower-right panel) reveals an instance of elevation modifications on the overlapping factors from 2016 to 2017. The most important elevation change is noticed close to the glacier margin.

### Gridded elevation modifications and their uncertainties

You will need to notice that we don’t merge CryoSat-2, ICESat-2 and NASA’s ATM surveys once we create elevation time collection. As a substitute, we estimate the annual elevation change charges from April to April for every dataset independently after which merge the charges.

The noticed annual elevation change charges from CryoSat-2, ICESat-2 and NASA’s ATM surveys are used to interpolate elevation change charges onto an everyday grid of 1 × 1 km. The interpolation is carried out utilizing the abnormal kriging methodology^{59,60}. We use the noticed annual elevation change charges to estimate an empirical semi-variogram. We match a mannequin variogram to the empirical semi-variogram to take the spatial correlation of elevation change charges into consideration. For every grid level, we estimate the elevation change charge d*h*_{i,krig} and the related error *σ*_{i,krig}.

We right the noticed ice floor elevations for bedrock motion brought on by elastic uplift owing to present-day mass modifications and long-term previous ice modifications (glacial isostatic adjustment (GIA)). We right for GIA utilizing the GNET-GIA empirical mannequin^{61}. For every grid level, we estimate the GIA uplift charge d*h*_{GIA} and the related uncertainty *σ*_{GIA}. We right for the elastic uplift of the bedrock by convolving ice loss estimates (from CryoSat-2, ATM and ICESat-2) with the Inexperienced’s capabilities derived by Wang et al.^{62} for the elastic Earth mannequin iasp91 with a refined crustal construction taken from CRUST 2.0. For every grid level, we estimate the elastic uplift charge d*h*_{elas} and the related uncertainty *σ*_{elas}. The elevation change charge for every grid level is

$${{rm{d}}h}_{i}={{rm{d}}h}_{i,{rm{krig}}}-{{rm{d}}h}_{i,{rm{elas}}}-{{rm{d}}h}_{i,{rm{GIA}}}$$

and the related uncertainty is

$${sigma }_{i}=sqrt{{sigma }_{i,{rm{krig}}}^{2}+{sigma }_{i,{rm{elas}}}^{2}+{sigma }_{,i,{rm{GIA}}}^{2}}$$

Prolonged Knowledge Fig. 7 reveals annual elevation change charges from April to April for the interval from April 2011 to April 2021 which might be corrected for GIA and elastic uplift. Prolonged Knowledge Fig. 7 (decrease panels) reveals the uncertainties related to the annual elevation change charges from April to April.

### Ice move modelling

We use the Ice-sheet and Sea-level System Mannequin (ISSM)^{63}, a finite-element ice move mannequin, to mannequin the NEGIS. The horizontal mesh decision varies from 200 m close to the ice entrance to twenty km inland, and it’s vertically extruded into 4 layers. The mannequin relies on a 3D higher-order approximation of the total Stokes mannequin to incorporate vertical shear for the stress steadiness; it is a good approximation for each fast-moving and slow-moving areas^{64,65}. We use the floor and mattress geometry from BedMachine Greenland^{50} (model 3). We infer the ice viscosity parameter over floating ice and basal situations below grounded ice utilizing inversions. To deduce the preliminary basal situations, we use the Budd friction regulation and invert for the friction coefficient utilizing floor velocities from 2007 to 2008 (ref. ^{66}). We then analytically calculate the friction coefficient for a regularized Coulomb friction regulation that produces the identical basal stress. The friction coefficient is saved fixed in time in the course of the simulations. Earlier research have proven that the selection of friction regulation can have a substantial influence on simulations^{67,68,69,70}. Nevertheless, right here we choose the friction regulation primarily based on observations.

The mannequin makes use of the level-set-based shifting boundaries to trace ice entrance positions. We use the von Mises tensile stress calving regulation to calculate the calving charge^{71,72}. We calibrate the stress threshold of the calving regulation to match the noticed ice entrance retreat from 2007 to 2017. We use the identical stress threshold values, 1 MPa for grounded ice and 150 kPa for floating ice, utilized by Choi et al.^{24}. The calibrated stress thresholds for 2 glaciers (NG and ZI) are assumed to be fixed for all simulations.

Utilizing these practically plastic friction legal guidelines, and the identical atmospheric and oceanic forcing as Choi et al.^{24}, we calibrate the calving regulation to qualitatively match the noticed entrance modifications from 2007 to 2017 (ref. ^{72}). For hindcast simulation, the mannequin is compelled by month-to-month SMB knowledge from the Regional Atmospheric Local weather Mannequin (RACMO) model 2.3 (ref. ^{73}). We apply ocean forcing that considers melting below floating ice for ZI and NG^{74}, together with the undercutting on the ice entrance of the terminus of ZI as soon as it turns into grounded^{75,76}. The main points of the ocean forcing parameterizations will be present in Choi et al.^{8}. We preserve the ice temperature fixed, as it isn’t affected by the floor temperature on the timescales thought-about on this examine^{77}. We discover that the mannequin with a regularized Coulomb regulation yields significantly better settlement with noticed accelerations (Fig. second,e) and the noticed mass loss from 2011 to 2021 (Fig. 4).

### Friction regulation choice

Prolonged Knowledge Fig. 8 reveals maps of the noticed and modelled ice move acceleration from 2016 to 2022. The noticed accelerations are an identical to these proven in Prolonged Knowledge Fig. 3a. Right here we present the Budd friction regulation^{35} with completely different exponents, the regularized Coulomb friction regulation^{36,69}, the Schoof friction regulation^{37} and the Weertman friction regulation^{38} with completely different exponents. We examined a variety of fashions with completely different exponents; nevertheless, our mannequin outcomes point out that solely the regularized Coulomb friction regulation or the Budd friction regulation with exponents of 1/5 or 1/6 can produce the deep inland acceleration noticed within the satellite tv for pc knowledge. For all fashions in Prolonged Knowledge Fig. 8, we used NorESM1 and RCP4.5. The selection of the GCM and RCP has a a lot smaller influence than the selection of the friction regulation.

In Prolonged Knowledge Fig. 9, we take into account fashions which might be capable of reproduce deep inland acceleration. Due to this fact, the selection of friction legal guidelines is lowered to the regularized Coulomb friction regulation and the Budd friction regulation with exponents of 1/5 and 1/6, as all the opposite fashions have been unable to generate deep inland acceleration.

Prolonged Knowledge Fig. 9 reveals the modelled cumulative modifications within the ice mass from 2007 to 2100 for the regularized Coulomb friction regulation and the Budd friction regulation with exponents of 1/5 and 1/6. For every friction regulation, we mannequin the mass change utilizing RCP4.5 and RCP8.5, respectively. For all fashions, NorESM1 was used. For comparability, we embrace outcomes from ref. ^{8} that have been calculated utilizing the Budd friction regulation (linear viscous). Prolonged Knowledge Fig. 9 means that solely the mass change from the regularized Coulomb friction regulation is throughout the uncertainty stage of the noticed mass change from 2007 to 2021. The Budd friction regulation with exponents of 1/5 or 1/6 barely overestimates the mass change from 2007 to 2021. Nevertheless, we notice that, by 2100, the mass loss from the Budd friction regulation with exponents of 1/5 or 1/6 is sort of the identical as that from the regularized Coulomb friction regulation. The retreat of the terminus from 2007 to 2100 utilizing NorESM1, RCP4.5 and regularized Coulomb friction regulation is proven in Supplementary Video 1.

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