# Rapid expansion of Greenland’s low-permeability ice slabs

## Abstract

In recent decades, meltwater runoff has accelerated to become the dominant mechanism for mass loss in the Greenland ice sheet1,2,3. In Greenland’s high-elevation interior, porous snow and firn accumulate; these can absorb surface meltwater and inhibit runoff4, but this buffering effect is limited if enough water refreezes near the surface to restrict percolation5,6. However, the influence of refreezing on runoff from Greenland remains largely unquantified. Here we use firn cores, radar observations and regional climate models to show that recent increases in meltwater have resulted in the formation of metres-thick, low-permeability ‘ice slabs’ that have expanded the Greenland ice sheet’s total runoff area by 26 ± 3 per cent since 2001. Although runoff from the top of ice slabs has added less than one millimetre to global sea-level rise so far, this contribution will grow substantially as ice slabs expand inland in a warming climate. Runoff over ice slabs is set to contribute 7 to 33 millimetres and 17 to 74 millimetres to global sea-level rise by 2100 under moderate- and high-emissions scenarios, respectively—approximately double the estimated runoff from Greenland’s high-elevation interior, as predicted by surface mass balance models without ice slabs. Ice slabs will have an important role in enhancing surface meltwater feedback processes, fundamentally altering the ice sheet’s present and future hydrology.

## Main

A field campaign carried out in spring 2012 at the KAN_U field site at 1,840 m above sea level (a.s.l.) in southwest Greenland’s accumulation area found 3–5-m-thick layers of refrozen meltwater in firn cores just below the seasonal snow layer5,6. The record-breaking 2012 Greenland summer melt7,8 caused meltwater to visibly run off from KAN_U over the top of these layers for the first time on record instead of refreezing locally in porous firn. Thick ice layers resulted in approximately 11 ± 3% more runoff in that region than would have occurred without the blocking effect of subsurface ice5.

The Spring 2013 Arctic Circle Traverse (ACT-13) campaign in southwest Greenland mapped a continuous 40-km-long, multimetre-thick ice slab along an uphill transect in southwest Greenland (Fig. 1). Runoff was routed over the top of this slab instead of being fully absorbed into the firn column. During the 2012 summer, the equilibrium line altitude, where annual melt equals accumulation, was estimated to be approximately 1,900 m a.s.l.

In this work we distinguish between ice lenses and ice slabs in firn. Ice lenses are thin (0–10 cm) refrozen ice layers that form in a single melt season in the percolation area of the ice sheet9,10. Meltwater can percolate through and around lenses11 along preferential flow paths, sometimes reaching depths of 10 m or more before refreezing12. Layers of refrozen ice between 10 cm and 1 m thick—primarily multi-annual refreezing features—were documented in 201611 in cores and deep pits in southwest Greenland’s percolation area up to an altitude of 2,100 m a.s.l., but their horizontal extent appeared limited and not able to cause runoff over wide areas. Low-permeability ice slabs are thicker refrozen layers (≥1 m thick) that form when water refreezes between preexisting ice layers, annealing them together. Slabs form over multiple years, can span horizontally for tens of kilometres and cause the permeability of the near-surface firn layer to approach zero13 despite pore space availability at greater depth. Ice slabs are spatially continuous enough to be mapped over great distances by ground-penetrating radar surveys. Here we focus solely on ice slabs in Greenland’s firn that block deep percolation and enhance runoff.

We present an observational map of ice slabs across the Greenland ice sheet, created from surveys performed by ground-penetrating radar (GPR) and NASA’s IceBridge airborne Accumulation Radar (IceBridge AR), and validated against firn cores drilled along the GPR surveys. We use an empirical model to quantify the present-day formation of ice slabs from the outputs of regional climate models (RCMs). Using RCMs forced on their boundaries by forward-looking general circulation models (GCMs), we forecast the growth of ice slabs and their contributions to runoff under the Representative Concentration Pathway (RCP) 4.5 and 8.5 (moderate- and high-emissions, respectively) scenarios through the end of the 21st century.

Shallow firn cores retrieved along the ACT-13 transect contain ≥1-m-thick ice slabs at sites below 2,000 m a.s.l. (Extended Data Fig. 1a, cores 1–3, and Extended Data Fig. 2)5. Ice slabs at KAN_U have grown progressively thicker; in five years, the ice volume content of the top 10 m grew from 54% in 2012 to 73% in 2017 (Extended Data Fig. 1b), with nearby locations experiencing similar growth (Extended Data Fig. 1c).

In situ GPR measurements show ice slabs beginning at approximately 1,700 m a.s.l. along the ACT-13 transect (Fig. 1b), indicating that in 2012 the long-term runoff limit had migrated up to the KAN_U site at 1,840 m a.s.l., consistent with satellite observations5. Ice slabs detected from a spatially coincident transect of IceBridge AR, flown three weeks before the ACT-13 transect, closely match results in the top 20 m of firn with a vertical error of −21% to +6% compared to adjacent cores, partially underestimating the ice volume but accurately measuring the overall extent of ice slabs within the top 20 m of firn. A survey of IceBridge AR flight lines from 2010–2014 (Fig. 2) show that ice slabs covered 64,800–69,400 km2 of the Greenland ice sheet in 2014, or approximately 4% of the ice sheet’s total area. We identify ice slabs as continuous layers of near-surface ice above porous layers of firn; they have a thickness of 1–16 m in the top 20 m of firn and extend continuously for ≥1 km along an IceBridge flight line. We adjust the thickness observations of IceBridge AR according to the range of thickness uncertainties, map spatially continuous slabs of 1–16 m thickness and interpolate polygons around continuous areas of ice slabs to estimate their area. Potential gaps in airborne data coverage make this range a conservative estimate of the total extent of ice slabs in Greenland.

RCMs forced at their boundaries by atmospheric reanalysis data (see Methods) at the locations where IceBridge AR has observed ice slabs suggest that ice slabs occur where annual snow accumulation is below 572 ± 32 mm water equivalent (w.e.). Ice slabs appear to be absent in regions of high accumulation in which surface meltwater is trapped in perennial firn aquifers instead of refreezing14,15; this is consistent with firn models showing aquifers that form in regions with annual accumulation rates exceeding about 600 mm w.e.16. RCMs forced at their boundaries by atmospheric reanalysis data show that ice slabs have formed in regions receiving 266–573 mm w.e. yr−1 excess melt for a decade or more (Supplementary Information Fig. 16). Here, ‘excess melt’ refers to the amount of meltwater beyond the capacity of annual accumulation to absorb and refreeze it, resulting in excess water, which fills surrounding firn layers or runs off to lower elevations (see Methods). In ten years, the upper value of that range (573 mm w.e. yr−1) would transform a shallow porous firn layer (density of 450–550 kg m−3) into refrozen ice with bubbles (density of 873 kg m−3) to a thickness of 13.6–17.7 m, in agreement with the maximum-thickness threshold of 16 m used when detecting ice slabs with IceBridge AR. RCMs show that in data pixels containing ice slabs detected by IceBridge AR, excess melt increased slowly since the 1990s (Extended Data Fig. 3) and then rapidly after 2001, causing the inferred annual rates of ice slab formation to increase ten times or more (Table 1, Fig. 3a). At the end of 2013, RCMs estimate that ice slabs in Greenland covered an area 62,100–78,900 km2 larger than Greenland’s pre-1990 runoff area. Maps of simulated ice slabs at the end of 2013 (Fig. 3b–e) are consistent with one another, as well as with the extent observed by IceBridge AR (Fig. 2). Within individual ice-sheet drainage basins, simulated ice slab elevations match within uncertainties in nearly every case (Extended Data Fig. 4). Inconsistencies between observed and simulated ice slabs exist primarily in east and southeast Greenland, where ice slabs are limited to relatively small and isolated areas that are difficult to cover fully by airborne IceBridge AR campaigns.

RCMs forced by GCMs until 2100 show that the area of ice slabs across Greenland is likely to expand moderately through 2050 under both RCP 4.5 (Fig. 3f) and RCP 8.5 (Fig. 3l) forcing, approximately doubling in area compared to its present extent. Models forced by RCP 4.5 show a relative slowdown of growth in ice-slab extent after 2050 through 2100 (Fig. 3f). Most ice-slab simulations forced by GCMs underestimate the current extent of ice slabs when compared to reanalysis-forced RCMs (Fig. 3a), in part because present-day GCMs do not capture atmospheric circulation changes over Greenland that have contributed to recent summer melt increases17. Under the RCP 8.5 scenario, the formation of new ice slabs accelerates from their 1990–2050 growth (1,240–4,160 km2 yr−1) to approximately double that rate (2,890–7,130 km2 yr−1) in the latter half of the century (Fig. 3l, Table 1). In all cases, trends before and after 2050 are statistically significant (P < 0.02).

In 1990–2100, ice slabs are expected to cover 2.3 times larger area and cause 2.4 times more surface runoff, on average, under the RCP 8.5 pathway than under RCP 4.5. Once ice slabs have formed, runoff is calculated as the amount of melt that exceeds the near-surface pore space and the cold content that have accumulated since the ice slabs initially formed (see Methods). Without explicitly handling the effects of ice slabs, by 2100 RCMs underestimate the cumulative runoff from areas that are above the pre-1990 runoff area by an average of 56% under RCP 4.5 and 42% under RCP 8.5, compared to equivalent estimates including ice slabs. In both scenarios, this implies a near-doubling of runoff from the interior of the ice sheet due to rapidly decreased surface porosity.

Polar firn is sensitive to relatively small changes in annual meltwater production18,19, and the addition of large areas of new ice slabs in Greenland is indicative of a departure from steady-state climate that amplifies several types of positive-mass-loss feedback. For instance, meltwater saturation of the ice-sheet surface at KAN_U in 2012 resulted in 9% lower summer albedo and the absorption of 28% additional solar radiation, of which 71% was translated into melt20. This melt–albedo feedback is not fully captured in the RCMs presented here, so future meltwater estimates may be underestimated. Under linear warming conditions, linear changes in runoff elevation cover increasingly larger areas of the ice sheet’s flat interior6, resulting in parabolic increases in runoff area (parabolic fit with a power of ~2.5 with respect to elevation) and runoff volume (power of ~3.5)21.

Surface features such as firn cracks, supraglacial streams, lakes and moulins are important components of the ice sheet’s hydrological network22. The amount of recent meltwater in Greenland has been unprecedented over the past several centuries23 and is expected to keep rising in a warming climate, forming supraglacial lakes and other features progressively higher on the ice sheet24. It is uncertain whether such features at high elevations could facilitate water reaching the englacial or subglacial system25, which is a necessary condition for dynamic feedback processes such as cryo-hydrologic warming26 or meltwater reaching previously frozen regions of the ice-sheet bed27. However, recent observations of ice motion at KAN_U show accelerated flow in 2009–2013 and seasonal accelerations that were previously unseen at that elevation28. Although the exact mechanisms of such dynamic feedback processes are beyond the scope of this paper, they are consistent with meltwater saturation at the same locations and suggest that one or more meltwater-dynamic feedback processes may already influence dynamic flow at the current locations of ice slabs. Further research is needed to explore the feedback between the hydrologic and dynamic systems of the Greenland ice sheet at high elevations.

Once ice slabs have formed, they need relatively small amounts of meltwater to sustain themselves. Following the extraordinary melt years of 2010 and 2012 in southwest Greenland, melt was more moderate in 2013–2017 (ref. 29), although still greater than the 1949–2017 average30. Ice slabs continued to grow in thickness in 2013–2017, with new ice freezing atop them, and little to no pore space added to the firn column (Extended Data Fig. 1b). Once low-permeability ice slabs have formed, the only known effective mechanism to eliminate their impact on saturation and runoff is a prolonged period of cooler climate or higher snow accumulation that would allow pore space to reaccumulate at the surface19. The fact that ice slabs have continued to thicken and remain close to the surface once they have formed leaves these areas highly vulnerable to enhanced runoff in subsequent warm summers. In a progressively warming Arctic, ice slabs in Greenland’s interior are poised to become increasingly widespread persistent features, with far-reaching consequences for ice-sheet hydrology, runoff and sea level rise.

## Methods

### Firn core and in situ GPR measurements

Firn cores were drilled at 100-m elevation intervals between 1,840 m and 2,350 m along the ACT-13 ground-penetrating radar transect (Extended Data Fig. 2, Extended Data Table 1), with two cores drilled at KAN_U approximately 3 km north of the main transect and two more cores at Dye-2, 40 km south of the main transect. Cores were logged for stratigraphy at 1 cm resolution and cut into 10-cm intervals to record density. Using core sections with clean cuts consisting of purely refrozen ice, we measured the density of refrozen ‘bubbly’ ice in firn to be 873 ± 25 kg m−3 (ref. 5). Core data presented here are publicly available in the latest release of the NASA SumUp dataset32.

A Malå 800-MHz shielded GPR was used in situ to collect data in a 1 km × 1 km grid at KAN_U adjacent to cores 1 and 2, in select tracks at Dye-2 near cores 5 and 6, and along the main transect line adjacent to the remaining coring sites. The GPR data were resampled at a constant trace spacing of 1.5 m. We applied a dewow filter to remove low-frequency artefacts and an exponential-gain filter to compensate for depth-dependent signal attenuation. We then processed the traces with a moving window to compute local variance in the GPR signal, which is considerably lower in thick refrozen ice than in porous firn5. We applied an adaptive linear-gain filter to eliminate residual depth attenuation that remained after data post-processing. We converted the radar’s two-way travel time to depth using a correlation function that maximized the negative correlation between the core density and the local signal variance at core locations. We chose a cutoff for local signal variance to identify refrozen ice layers within the firn, in order to minimize both type-1 (commission) and type-2 (omission) errors compared to adjacent cores. The chosen cutoff of 5.0 dB in local relative variance of the GPR signal was sufficient to identify ice slabs ≥1 m thick with an average error of −13.4% to +3.2% compared to adjacent cores. Ice thickness estimates derived from this GPR technique should be considered as ‘lower bound’ estimates, only suitable for reliably identifying ice layers that are both thick and spatially continuous, consistent with the purpose of this study. Further details of GPR processing are available in Supplementary Information.

### IceBridge AR

Data obtained with IceBridge AR33 during 2010–2014 were acquired from the public FTP website (https://data.cresis.ku.edu/) of the Center for Remote Sensing of Ice Sheets. We filtered flight lines to cover the extent of Greenland’s ice using the Greenland Ice Mapping Project34 land classification dataset. Because we are only interested in firn processes, we additionally subset the data to include only IceBridge AR data above the long-term equilibrium line altitude where past long-term average melt does not exceed long-term accumulation, and within the percolation area where melt exceeds 10% of accumulation in an average year as determined by the RCMs.

Raw IceBridge AR data were processed to improve surface selections and minimize surface selection artefacts caused by signal echoes and mismatches. To correct for the weakening of the IceBridge AR signal due to roll of the aircraft, a depth-dependent roll correction factor was applied to each flight line. In 2012, flight path curvature substituted aircraft roll because roll data were not provided (Supplementary Information, section S2.3).

Liquid water in or on the firn causes a bright reflection at the water’s surface and a rapid attenuation of the signal to depth, making IceBridge AR samples unsuitable for detecting ice slabs beneath the water table. Radar lines were manually filtered to eliminate 113 surface lakes35 and regions containing visible subsurface aquifers.

The IceBridge AR data were exponentially depth-corrected in the top 50 m to provide a homogeneous signal strength by dividing with a best-fit exponential decay curve on each file and correcting for signal decay. Because flight lines from different years and instrument configurations provide different radar behaviours, exponential de-trending was performed independently on each flight line. We then normalized returns from each IceBridge AR flight line to have a mean value of 0 and a standard deviation of 1, providing consistent return strengths throughout the dataset and minimizing inter-campaign variability of the returns.

We identified a signal threshold cutoff to differentiate weaker signals from relatively homogeneous ice from surrounding firn with stronger backscatter. We applied a simple noise filter to eliminate small-scale (1–2 pixels) noise from the images and then used a continuity filter to remove small disconnected groups of pixels from the image and leave only spatially continuous regions of pixels identified as ice slabs. We used a two-dimensional minimization search to validate the reference track ‘20130409_01_010_012’ against the 800-MHz GPR line and chose a signal threshold and continuity cutoff that minimize type-1 and -2 errors. A sensitivity threshold of −0.45 (in normalized decibels) and a continuity threshold of 350 pixels minimized the sum of type-1 and type-2 errors compared to ice identified in the GPR data (Supplementary Information Fig. 13). IceBridge AR traces with more than 16 m of ice in the top 20 m of firn were discarded to eliminate regions of bare ice to depth. The IceBridge AR data give estimates of ice content in the firn with an error rate of −16% to +5% compared to the GPR data. Combined with a GPR accuracy of −13% to +3% compared to the core data (previous section), we estimated the root-sum-squared error of the IceBridge AR data to be −21% to +6% accurate when identifying ice slabs >1 m in the top 20 m of firn, compared to the ‘truth’ in firn cores drilled along the GPR surveys. Generally, IceBridge AR underestimates the total ice content compared with firn cores retrieved at the same location, primarily owing to its limited data resolution and quality. The IceBridge AR reference track was a straight flight line (<1° aircraft roll) with relatively high data quality, but data from some IceBridge AR flight lines had low quality owing to aircraft roll, pitch or other factors, resulting in the data gaps shown in Fig. 2, where ice slabs may exist in the firn but are not identified (type-2 omission errors).

### Excess melt calculations

We modified a previously defined relationship for the threshold between annual melt and snow accumulation18 to include rainwater, which affects firn in a similar manner to meltwater and is projected to increase across Greenland’s accumulation area in a warming climate36. We calculate the amount of excess melt Me (in kg m−2) as

$${M}_{{\rm{e}}}=\left\{\frac{M+R}{C}-\left[\left(\frac{h}{L}{T}_{{\rm{f}}}+\frac{{\rho }_{{\rm{r}}}-{\rho }_{{\rm{c}}}}{{\rho }_{{\rm{c}}}}\right){\left(1+\frac{{\rho }_{{\rm{r}}}-{\rho }_{{\rm{c}}}}{{\rho }_{{\rm{c}}}}\right)}^{-1}\right]\right\}C$$
(1)

where M, melt (in kg m−2); C, accumulation (kg m-2); R, rainwater (kg m−2); h, heat capacity of ice (J K−1 kg−1); L, latent heat refreezing capacity of ice (J kg−1); Tf, temperature of underlying firn (°C, positive below freezing; that is, Tf = 20 denotes a temperature of −20 °C), derived from mean annual air temperature; ρr, density of refrozen ice (kg m−3); and ρc, density of fresh snow accumulation (kg m−3). We calculated ρc using a geographically based parameterization used in surface mass balance models37, and obtained accumulation density values of 300–380 kg m−3, a range consistent with independent observations32. We used ρr = 873 kg m−3 for the density of refrozen ice, as found in firn cores5. Excess melt calculations are generally insensitive to reasonable variations in ρr and ρc, consistent with previous reports18. In this work, excess melt is calculated on a 10-year running mean (that is, mean values in 2001 were calculated from 1992–2001, inclusive) to compute decadal averages and to smooth inter-annual variability when considered for the formation of ice slabs. In the main text excess melt values are given in millimetres water equivalent, which is functionally equivalent to the unit of kilograms per square metre in equation (1).

### Ice-slab model simulations

We used three regional climate models1,2,38 forced by the ERA-Interim39 and NCEPv140 reanalysis datasets (Table 1) to determine the range of decadal excess melt volumes that have caused ice slabs to form within the firn, as identified by IceBridge AR data from 2010–2014. We used a subset of IceBridge flight lines that transect ice-slab areas in straight ‘downhill to uphill’ (from the ice edge to the interior) orientations, where both the thick ‘bottom’ and the thin ‘top’ extents of ice slabs are identified (Supplementary Table 2). The range of 266–573 mm w.e. of mean annual excess melt during the full decade before the observations fits the observations of current ice slabs with good agreement between the models (Supplementary Information Fig. 16). Areas that averaged this amount of excess melt or more during the prior ‘baseline’ period before 1990 were masked out as being in the long-term ablation area, where porous firn would not exist in appreciable volume. Regions with enough annual accumulation to form perennial firn aquifers were masked out and not included in ice-slab calculations.

We applied identical thresholds to RCMs forced at their boundaries by five GCMs41,42,43,44,45 under the RCP 4.5 and RCP 8.5 climate scenarios46 (Table 1). For the HIRHAM 5 RCM, no data were available to compute a pre-1990 baseline period, and 1990–1999 was used instead with ice slabs growing after the year 2000, which may bias the results to lower values for that particular RCM. GCM time periods using GCM historical forcing were combined with each respective 21st-century forcing to form continuous datasets.

### Runoff calculations

Inter-annual variability in melt and accumulation are high in Greenland, with some years demonstrating exceptional melt and others showing relatively low levels of melt and runoff. When excess melt is negative, it represents the amount of pore volume (absence of melt) added at a given location. When the model estimates that an ice slab has formed on/near the ice-sheet surface, pore volume added atop the slab in subsequent years is tallied on an annual basis from RCM accumulation and melt results. Surface melt in future years is expected to saturate accumulated pore volume and overwhelm near-surface firn pore space and cold content before further runoff occurs. Melt that filled near-surface pore space but did not melt out further adds to the ice slabs and grows them thicker, consistent with Extended Data Fig. 1b. Runoff from the top of ice slabs is tallied on an annual basis and is presented in Fig. 3 as a running sum total. Means and trends are outlined in Table 1. Runoff estimates from the RCMs without the effects of ice slabs were estimated by measuring the runoff zone (maximum area in which runoff has occurred at least once) before the formation of ice slabs and totalling the future runoff from regions higher on the ice sheet where runoff did not previously occur.

## Data and code availability

Firn cores presented in Extended Data Fig. 1 are available in the 2018 release of Greenland’s SumUp dataset32. Post-processed GPR and IceBridge AR transects, shapefiles and CSV-summaries are publicly available in Figshare project ‘Greenland Ice Slabs Data’ at https://doi.org/10.6084/m9.figshare.8309777. Codes for post-processing core, GPR, IceBridge AR and RCM data are available at https://github.com/mmacferrin/Greenland_Ice_Slabs. RCM outputs are available from the respective online data repositories for each model and/or upon request from the authors. Greenland boundary outlines used in all maps are available from the Natural Earth open-access GIS repository at https://www.naturalearthdata.com/downloads/.

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## Acknowledgements

We acknowledge National Aeronautics and Space Administration (NASA) awards NNX10AR76G and NNX15AC62G for funding most of the work, including field campaigns. This work was also supported by the Retain project, funded by the Danish Council for Independent Research (grant number 4002-00234). Research leading to these results received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement 610055 as part of the ice2ice project. We thank the field team members for their contributions to field data collection in 2012–2017.

## Author information

M.MF. conceived the study question, processed the core, GPR and IceBridge AR data, post-processed the RCM output data and is the primary author of the manuscript and supplement. All authors contributed to the manuscript text, analyses, figures and revisions. M.MF., H.M., and D.v.A. planned, organized and undertook field campaigns dedicated to the data presented in this paper. C.C., C.M.S., B.V. and A.H. collected, interpreted and/or plotted field data. P.L.L., R.M., X.F. and M.R.V.d.B. provided regional climate model outputs and assisted with their results and interpretations. W.T.P. helped formulate and interpret the excess melt model. M.S.M. performed remote-sensing validation of runoff over ice slabs. W.A. supervised and oversaw the direction and formulation of the manuscript and project.

Correspondence to M. MacFerrin.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Firn core density profiles.

Firn density is plotted in black with ice layers indicated in blue. a, Firn cores drilled during the ACT-13 campaign5. b, A time series of firn core measurements at the KAN_U field site; data obtained in 2009–2017. c, Firn cores from the BAB_U field site, 40 km southeast of KAN_U, measured in 2015 and 2017.

### Extended Data Fig. 2 Map of core locations.

IceBridge flight lines are shown in light blue and 50-m-elevation contours in grey, derived from ArcticDEM dataset31. KAN_U, at an elevation of 1,840 m, is identified on the left. IceBridge flight lines that overlap core locations are highlighted in orange.

### Extended Data Fig. 3

RCM calculations of excess melt in pixels in which ice slabs are detected by IceBridge AR data.

### Extended Data Fig. 4 Simulated ice slabs in Greenland drainage basins.

a, Area (×103 km2; top) and mean elevation (in metres, ±1 s.d.; bottom) of ice slabs, as detected by IceBridge AR and simulated by RCMs, around 2014. b, Ice slabs simulated using RACMO ERA-Int 2014 model results in each drainage basin.

## Supplementary information

### Supplementary Information

Text and figures describing the GPR and IceBridge AR processing steps used in the main manuscript (Fig. 2).

### Supplementary Table 3

List of derived empirical formula variables for the roll-correction parameters of every IceBridge AR track (Supplementary section S.2.3.2).

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• #### DOI

https://doi.org/10.1038/s41586-019-1550-3