The surface program includes a repeated in situ survey using the Global Positioning System (GPS) with a strain net consisting of 63 stakes. Observations cover the years 2015–2019. The stake network was established in 2015 with 16 stakes, including a central reference stake (75∘38′ N, 35∘58′ W) located 300 m from the EastGRIP deep-drilling site, and gradually expanded in 2016, 2017, and 2018 to include 63 stakes (Fig. 2). The growing network of stakes was measured by GPS every year from 2015 to 2019 and supplemented with additional temporary stakes that were measured only once. The layout of the stakes was designed to provide (1) transects of flow velocities along and transverse to the flow and (2) longitudinal and transverse strain rates in the center of the fast flow and at both shear margins. To fulfill these requirements, the stake network contains sets of stakes placed in a diamond shape centered around the midpoint of NEGIS and at both shear margins. The stake network extends 35 km along NEGIS and 40 km across NEGIS, thereby covering the entire 25 km width of NEGIS and extending across both shear margins into the slower-moving regions outside the ice stream. The purpose of the additional stakes added in 2018 was to obtain detailed information of strain rates across a topographic surface undulation northwest of NEGIS (a 20–30 km dark–bright pattern perpendicular to NEGIS, Fig. 2a). All stake observations are included in this analysis.

The GPS observations were carried out with a Leica GX1230 GPS receiver with data acquisition lasting a minimum of 1 h and typically 2–4 h. The GPS antenna was mounted on the top of each stake, and the height above the surface was measured manually. The stakes were 3.5 m long aluminum stakes, which were drilled approximately 2 m below the surface and extended when needed due to continuous snow accumulation in the area (approximately 0.3 m of snow equivalent per year; Vallelonga et al., 2014). All stakes established in 2015, 2016, and 2017 were extended during the observational period when the antenna heights decreased below 1 m above the surface. A few stakes were moved and/or replaced due to camp activities.

The GPS observations were postfield processed using the open-source software package ESA/UPC GNSS-Lab Tool (gLAB; Sanz Subirana et al., 2013; Ibáñez et al., 2018). We use the Center for Orbit Determination in Europe (CODE) final orbit and clock product, which includes Earth rotation parameters. We took the antenna phase center offset and variation into account. Receiver clock parameters are modeled, and the atmosphere delay parameters are modeled using the CODE maps for the ionosphere and ESA's Niell mapping function with simple nominal values for the troposphere. We applied solid Earth tidal corrections using the IERS Convention's degree 2 tides displacement model (Sanz Subirana et al., 2013). Ocean tidal correction is not implemented in the gLAB processing tool, and for our interior site the associated error is estimated to be within 1 cm. The coordinates are computed in the IGS14 frame. We use the software in static mode and developed an automated protocol in order to perform a systematic precise point positioning (PPP) processing of the stake observations. The PPP approach can introduce systematic errors if the stake is moving (King, 2004). To optimize our processing protocol and evaluate timing estimates and position uncertainties, we observed the central reference stake at the EastGRIP site (red dot in Fig. 2) over extended periods each season and compared separate 1 h static, 24 h static, and kinematic solutions. We found that the 24 h static solution performed better than the average position of a 24 h kinematic solution. With a maximum observed surface speed of approximately 60 m a-1, the uncertainty related to the static solution is estimated to be <2 cm. We estimate the combined uncertainty in our GPS positions to be within 3 cm. We process the stake observations from each year, including multiple observations of some of the stakes within the annual field seasons.

The gLAB processing protocol was assessed by comparing processing results from two 1 h observations with PPP processing results from the GIPSY-OASIS version 6.4 software developed at the Jet Propulsion Laboratory (JPL). We use JPL final orbit products, which include satellite orbits, satellite clock parameters, and Earth orientation parameters. The orbit products take the satellite antenna phase center offsets into account. Receiver clock parameters are modeled, and the atmospheric delay parameters are modeled using the Vienna Mapping Function 1 with VMF1 grid nominal values (http://vmf.geo.tuwien.ac.at/, last access: 13 September 2019; Kouba, 2008; Boehm et al., 2006). Corrections are applied to remove the solid Earth tide and ocean tidal loading. The amplitudes and phases of the main ocean tidal loading terms are calculated using the automatic loading provider (http://www.oso.chalmers.se/, last access: 13 September 2019; Scherneck and Bos, 2002) applied to the FES2014 ocean tide model including correction for center of mass motion of the Earth due to the ocean tides. The site coordinates are computed in the IGS14 frame (Altamimi et al., 2016). All GIPSY-OASIS processing results were within <1.7 cm of the gLAB processing results (Table 1) and within our estimated uncertainty of 3 cm.

To derive the horizontal surface velocity, a linear fit was performed to the observed northing and easting positions, respectively (projected to the National Snow and Ice Data Center – NSIDC – Sea Ice Polar Stereographic North and referenced to the WGS84 horizontal datum – EPSG:3413), assuming a constant displacement rate. A small tilt of the stake can lead to uncertainties in the horizontal velocity. We take this into account by including an unknown horizontal shift in the position of stakes that were vertically extended, and we neglect any other changes in the tilt. For each stake, the shift was determined independently from the other stakes and the linear fit and the shift were determined simultaneously. The estimated shifts are in the range of 0.05 to 0.2 m and often exceed 0.10 m. The surface velocity was calculated by assuming that the flow is along the surface, thereby neglecting vertical movement. We estimate the uncertainty in the derived velocities due to the combined uncertainty in the GPS observations and the method to be on the order of 10-2 m a-1. As a horizontal reference position of the stakes, we use the estimated horizontal position of the stakes on 1 January 2017, assuming a constant horizontal displacement of each stake over the observational period. We select a common reference for the network in order to consistently derive horizontal strain rates and assess surface elevations, but the reference date is not an accurate timestamp due to the different initial dates of the stakes.

We also estimate a mean GPS-derived surface elevation of the stakes to be used below for the assessment of satellite-based observations. In the interior areas of the Greenland Ice Sheet, climate-driven variations in snow accumulation and firn compaction lead to seasonal and interannual variations in the surface elevation that are not resolved by our annual GPS observations. We estimate the mean GPS-derived surface elevation as the mean of the individual observations at each stake, neglecting trends over the observational period due to changes in snow accumulation, firn processes, or ice dynamical changes.

The resulting horizontal stake velocities are shown in Fig. 2, and the reference positions and horizontal velocities are listed in the Supplement, Table S1. The GPS-derived surface elevations and the magnitudes of the horizontal stake velocities are shown along three transects across NEGIS in Fig. 3 and one transect along NEGIS in Fig. 4. The stake velocities show that the surface speed is relatively constant at approximately 56.6 m a-1 along the centerline of NEGIS and is above 55 m a-1 in the central flow band wider than 10 km. The GPS-derived surface elevations reveal 20 m deep topographic troughs at the shear margins. The direction of the fast flow at the center line is 33.5∘ from the north.

After having derived horizontal surface velocities, we calculate horizontal strain rates, which are essential in understanding the ice flow pattern and internal stratigraphy of the ice stream and its surroundings. We calculate the horizontal principal strain rates in 32 different triangular sections within the GPS strain net. Each triangle is defined by a combination of three GPS stakes and assumes a linear velocity field within the triangle, i.e., constant strain rates within the triangles (Fig. 5). The principal strain rates are generally on the order of 10-4 a-1 in a wider-than-10 km central flow band along NEGIS, as well as in the slow-moving areas outside NEGIS. In the two shear margins, horizontal principal strain rates increase by an order of magnitude and reach a maximum in the northern shear margin of 3.8×10-3 a-1 (horizontal extension) and -3.6×10-3 a-1 (horizontal compression) and in the southern shear margin of 3.6×10-3 a-1 (extension) and -4.3×10-3 a-1 (compression). In both shear margins, the principal strain rates are oriented at an angle of approximately ±35∘ relative to the direction of the flow, due to a combination of longitudinal extension, transverse compression, and a high shear strain rate along the shear margins. The principal strain rates are slightly higher in the triangles north of the central flow line of NEGIS than in those south of the central flow line, probably because the northern shear margin is wider than the southern shear margin and not captured as precisely by the GPS strain net as the southern shear margin. We estimate the uncertainty in the strain rates averaged over the triangles (>2 km) to be on the order of 10-5 a-1.

Along a transect across NEGIS, we calculate the horizontal strain rate tensor along the direction of the flow at three stakes. The three stakes are located in the northern shear margin, in the center (EastGRIP site), and in the southern shear margin, respectively (Fig. 5). The strain rates along the direction of the flow are calculated as the mean of the rotated strain rate tensors in the four adjacent triangles, and they are ±2 km horizontal averages, corresponding to the dimensions of the adjacent triangles. The normal strain rate components along the direction of the flow at these three stakes are plotted in Fig. 3b. At the central flow line at the EastGRIP site, the normal strain rates are (0.9±0.2)×10-4 a-1 in the longitudinal (along-flow) direction and (-0.9±0.5)×10-4 a-1 in the transverse direction. The ±2 km average longitudinal and transverse strain rates relative to the local flow direction in the northern shear margin are (0.8±1.9)×10-3 a-1 and (-0.8±0.4)×10-3 a-1, respectively. The horizontal shear strain rate is (-2.1±0.9)×10-3 a-1. The ±2 km average longitudinal and transverse strain rates relative to the local flow direction in the southern shear margin are (0.8±1.6)×10-3 a-1 and (-1.3±0.5)×10-3 a-1, respectively, and the horizontal shear strain rate is (2.6±0.8)×10-3 a-1. The resolution of the GPS strain net is limited by the position of the stakes and may not capture the peak strain rates at the shear margins, but the sharp transition in the southern shear margin stands out in the relative velocity pattern in the Supplement, Fig. S1, and in the strain rates along the transect across NEGIS (Fig. 3b).

The GPS-derived surface elevations are used to validate the accuracy of ArcticDEM release 7. ArcticDEM is a digital elevation model (DEM) based on stereo auto-correlation techniques on optical imagery from WorldView satellites (Porter et al., 2018). The resolution of ArcticDEM is 2 m with a bias of less than 5 m (Noh and Howat, 2015). The timestamp of ArcticDEM in the EastGRIP area is 2017 (estimated), thus overlapped by the GPS observation period, and the vertical accuracy has not been verified (Porter et al., 2018).

The GPS-derived surface velocities are used to validate and assess the accuracy of several available ice velocity products derived from satellite data from the interior of the Greenland Ice Sheet. The ice velocity can be derived from space using data from synthetic aperture radar (SAR) or optical sensors. Optical feature tracking can provide velocities in very high resolution from coherent pairs of visual images. In the interior of the Greenland Ice Sheet, the surface is mostly featureless and SAR processing methods between pairs of SAR images are useful for deriving surface velocities, based either on speckle tracking or on phase displacements from interferometric synthetic aperture radar (InSAR).

We include several experimental ice velocity products in our assessment, as well as several 1-year and multiyear products constructed from various remote sensing sources and methods. For each type of velocity product, we have also calculated a long-term average of all the velocity maps and included this in our assessment. In total, we include 165 velocity products from the following sources:

NASA MEaSUREs Multi-year Greenland Ice Sheet Velocity map v1, 1995–2015 (MEaSUREs Multi-year v1; Joughin et al., 2018a). This map was derived from InSAR, SAR, and Landsat 8 optical imagery data using a combination of speckle-tracking, InSAR, and optical feature-tracking methods, supplemented with balance velocities near the ice divides where the flow speeds are <5 m a-1. The data are provided with a resolution of 250 m. In the interior of the ice sheet, the estimated errors in this product are up to ∼2 m a-1 and reported to be <1 m a-1 in areas where InSAR is used.

We compare GPS-derived surface elevations with the surface elevation sampled from ArcticDEM release 7 at the stake positions (WGS84 ellipsoidal heights) and find an agreement within ±1 m, except for one stake with a deviation of >1.5 m (Supplement Figs. S2 and S3). Minor differences between the two datasets could be due to variable snow accumulation through the years, leading to seasonal and interannual variability in surface elevation, which is captured differently by the two datasets due to their different timestamps. The outlier is located in the exceptionally deep and narrow trough in the southern shear margin (Fig. 3a). Local topography effects at these stakes could possibly be due to interpolation or shadow effects in the Arctic DEM (Porter et al., 2018). The difference between the 63 GPS-derived surface elevations and ArcticDEM at the location of the GPS stakes is 0.48 m (mean) and 0.47 m (median) with a standard deviation of 0.53 m, confirming the low uncertainty in ArcticDEM (Noh and Howat, 2015; Porter et al., 2018).

The assessment consists of an intercomparison between the GPS-derived velocities of the stakes from the period 2015–2019 and the interpolated surface velocity at the location of the stakes from the satellite-derived velocity products. For each velocity product, we determine the accuracy (the bias) and precision (the standard deviation, i.e., the root mean square difference – RMS – after removing the bias) between the GPS-derived velocities and the satellite-derived velocities at the location of the stakes. In addition to the direct intercomparison between the GPS-derived velocities and the satellite-derived velocities, we also investigate the variability in the satellite-derived velocity products. In order to do so, we perform a spatial smoothing of the satellite-derived velocity product with a running-mean filter with a smoothing length, and we then vary the smoothing length in order to determine the optimum smoothing length (σ) that minimizes the standard deviation (RMS) between the GPS observations and the velocity product. The results of the intercomparison for the top 10 products (sorted according to the standard deviation) are listed in Table 2 (with a complete overview of the results from all products in the Supplement, Table S2), and they are illustrated in Fig. 6.

It is important to note that the different timestamps and temporal coverage Δt of the observations are not taken into account in the intercomparison. In satellite-derived velocity products with longer temporal coverage, possible temporal variability and/or noise are smoothed, and there is a clear relationship between increasing temporal coverage and decreasing bias, standard deviation, and optimum smoothing length. Similarly, spatial smoothing can remove noise. The improvement of the products with the temporal coverage Δt is significant, with the bias decreasing approximately linearly with 1/Δt, as illustrated in Fig. 6. Some long-term products were calculated as averages of short-term products, i.e., based on more observations, which would also help reduce the temporal variability in and noise of these products compared to short-term products. The bias in all the 165 products is in the range of ∼0.3–40 m a-1, with a standard deviation in the range of ∼0.4–22 m a-1. The velocity products already include some smoothing as part of their production, but additional smoothing both temporally and spatially, for most products, reduced the standard deviation. After applying optimum spatial smoothing, the standard deviation is reduced to a range of ∼0.4–10 m a-1. The optimum smoothing length σ is typically on the order of 500–3000 m.

As part of the assessment, we use the whole set of satellite-derived surface velocity products to trace flow lines along NEGIS. We use a starting point at the central reference stake near the EastGRIP site, which is located in the center of our observed area in a relatively narrow section of the NEGIS ice stream. We trace the flow lines upstream into the slower-moving areas where flow converges into NEGIS and downstream into faster flow where the ice stream widens (Fig. 7). The flow lines are gradually displaced depending on their bias and fluctuate depending on their standard deviation.

In the interior regions of the Greenland Ice Sheet, validation of satellite-derived ice velocity and surface elevation products is generally limited due to lack of in situ data. Our GPS stake network provides a unique dataset for validation in the interior accumulation area of the ice stream, and it represents a range of velocities and velocity gradients over 1 order of magnitude in the NEGIS ice stream, the shear margins, and the surrounding slow-moving areas. However, the assessment is restricted due to the limited spatial extent of the GPS data, and our conclusions may not apply to margin areas with very fast flow, seasonal variability, or high surface slopes.

In our comparison, the DTU-Space-S1 experimental product stands out among all the investigated products with its short temporal coverage (∼10–20 d); low bias of 0.35 m a-1; and the low standard deviation of 0.55 m a-1, which can be reduced to 0.53 m a-1 after optimum smoothing of 354 m. The AWI-TSX experimental product stands out because of its minimum standard deviation of 0.39 m a-1 of all the investigated products and its high spatial resolution, which results in a very low optimum smoothing length of 10 m, i.e., no further smoothing is needed to reduce the noise, and the bias in the AWI-TSX product is 0.51 m a-1, also among the lowest of the investigated products. Both these products are based entirely on InSAR processing methods.

The widely used MEaSUREs multiyear velocity product, the MEaSUREs Multi-year v1 product (Joughin et al., 2018a), has a bias of 0.77 m a-1 and a standard deviation of 0.50 m a-1. Since this product is already a 20-year average, the optimum smoothing length is only 200 m and only slightly reduces the standard deviation to 0.48 m a-1. It is notable that the bias in this product is similar to several other MEaSUREs products with shorter temporal coverage, while the standard deviation of this product is smaller than the other MEaSUREs products. If the interior of the ice sheet changes slowly over time, the differences between the temporal stamp of the GPS observations and of the multiyear velocity product covering 1995–2015 may become important. However, the MEaSUREs winter velocity map from 2008 to 2009, the MEaSUREs InSAR v2 product, performed very similarly to the MEaSUREs Multi-year v1 product, with a bias of 0.89 m a-1, standard deviation of 0.46 m a-1, and an optimum smoothing length of 51 m. The winter velocity product from 2008 to 2009 is based on InSAR and stands out with its low standard deviation and a relatively short temporal coverage of 9 months. The similar agreement between these products and the GPS-derived velocities suggests that the velocity in the interior part of NEGIS has not changed significantly in the last decade.

The five products with a minimum bias are the MEaSUREs ITS_LIVE 6-year average product with a bias of 0.31 m a-1, the MEaSUREs combined SAR&Landsat v1 1-year product for 2015 with a bias of 0.33 m a-1, the DTU-Space-S1 18 d product from 2019 with a bias of 0.35 m a-1, the ESA CCI annual velocity product from 2015 to 2016 with a bias of 0.43 m a-1, and the 24 d PROMICE product from February 2018 with a bias of 0.46 m a-1. Of these, the DTU-Space-S1 product stands out as mentioned above. MEaSUREs ITS_LIVE product stands out with its long temporal coverage, low standard deviation, and very low optimal smoothing length and because it is the only product in our study entirely based on optical feature tracking. The four other products with a minimum bias have a timestamp that overlaps with the first 1 to 2 years of the GPS observation period, but their standard deviations are much higher due to the SAR speckle-tracking processing techniques. The MEaSUREs combined SAR&Landsat v1 product has a standard deviation of 1.85 m a-1, which reduces to 1.65 m a-1 after optimum smoothing over 1224 m. The ESA CCI product performs very similarly with a standard deviation of 1.94 m a-1, which reduces to 1.11 m a-1 after an optimum smoothing length over 1185 m. The PROMICE product with its very high temporal resolution of 24 d has a standard deviation of 5.39 m a-1, which reduces to 2.6 m a-1 after an optimum smoothing length over 2264 m.

Among the top five products with the lowest standard deviation, three are entirely based on InSAR (DTU-Space-S1, 2019; AWI-TSX, 2016–2017; MEaSUREs InSAR v2, 2008–2009) and two are combined products averaged over a multiyear period (MEaSUREs Multi-year product v1, 1995–2015; MEaSUREs Multi-year SAR&Landsat v1, 2014–2018). Overall, the assessments show that for interior velocity estimates, the InSAR-based products stand out with higher resolution in time and space and with lower errors. SAR speckle-tracking products (ESA CCI, PROMICE, and MEaSUREs) can obtain comparable accuracy and low standard deviation if they are averaged over time (multiyear averages) and smoothed spatially. The optical product (MEaSUREs ITS_LIVE) can obtain a comparably high accuracy when averaged over long time intervals (several years), but the standard deviation is slightly higher than the radar-based products. Mouginot et al. (2017) also derived optical ice velocities from Landsat 8 and concluded similarly that the quality of the products derived from optical satellite sensors is comparable to data obtained with SAR speckle tracking.

Knowing the accurate flow lines of an ice sheet is useful for many applications, such as defining the outlines of drainage basins or identifying the source area for ice flowing through a specific survey site. For studies related to the internal stratigraphy and ice properties, e.g., in ice cores or radar profiles, it is essential to know the upstream flow path in order to infer the deformation history of the internal layers. However, minor uncertainties and bias in satellite-derived velocity products can severely affect flow lines traced along the velocity field, as these uncertainties can displace the flow line and propagate along the flow line (Fig. 7). The flow lines for the products with minimum bias are marked (Fig. 7), showing that flow lines can only be reliably traced if the bias is small. These products have a low bias of 0.31 to 0.43 m a-1 or approximately 1 % of the surface speed. This is particularly critical when the flow is strongly convergent or divergent. We notice that the back trajectories diverge more than the forward trajectories, and we attribute this to the higher uncertainty in the upstream lower velocities compared to downstream. As a result, it may be better to use surface slopes instead of surface velocity products to trace flow trajectories in slow-moving areas.

Strain rates are derived from the satellite-derived products as derivatives of the velocity fields and have therefore higher errors. Our assessment provides an estimate of the strain rate error depending on the resolution from the standard deviation of the velocity product. For velocity products with a standard deviation on the order of 0.5 m a-1, the strain rate uncertainty is on the order of 10-3 a-1 on a 500 m grid, but it could be improved by smoothing the velocity product using the optimum smoothing length from the assessment. We compare the GPS-derived strain rates with strain rates from the MEaSUREs Multi-year Velocity v1 product in transects across NEGIS (Fig. 3) and along NEGIS (Fig. 4). We calculate the satellite-derived strain rate tensor directly from the gridded 250 m resolution velocity product without further smoothing according to the optimum smoothing length (included in Table 2) and rotate according to the local flow direction in order to determine the strain rates along the flow. While the GPS-derived strain rates are limited in resolution and do not exactly capture the maximum strain rate at the southern shear margin, they do capture the enhanced strain rates in the shear margins. The fluctuations in the satellite-derived strain rates are less than 10-3 a-1, thus confirming our estimated uncertainty above. The satellite-derived strain rates capture the high-resolution strain rate peaks of approximately 3–4×10-3 a-1 in the shear margins (Fig. 3) and approximately 2×10-4 a-1 along NEGIS (Fig. 4).

The assessment of satellite-derived velocity and height products inform us of the accuracy and limitations of the satellite-derived products in the interior regions of the Greenland Ice Sheet. In our study area the best products have a bias and precision of less than approximately 0.5 m a-1, i.e., about 5 % of the smallest observed GPS-derived velocities of around 10 m a-1 in the slow-moving areas north of NEGIS. Knowing the limitations of the satellite-derived products, we are now able to combine the GPS-derived velocities and strain rates with satellite-derived data to characterize spatial patterns in surface structure and ice flow in the interior part of the NEGIS ice stream. We discuss here the observed patterns.

The flow and surface topography across the NEGIS ice stream reveal a distinct 25 km wide fast-flowing ice stream near the EastGRIP site, which is sharply marked at both sides in speed, strain rates, and surface geometry (Fig. 3). The cross sections show a central 10 km wide section with an almost uniform speed of 55 m a-1 and well-defined shear margins at both sides with a width of about 5 km separating the ice stream from the surrounding slow-moving ice (Fig. 3). The velocities are above 20 m a-1 on the southern side where a broad flow field is merging with NEGIS and approximately 10 m a-1 on the northern side (Figs. 2 and 3). The strain rates are at a level of approximately 10-4 a-1 within the ice stream and in the surrounding slow-moving areas outside the ice stream. In the shear margins, they increase by an order of magnitude to a maximum value of approximately 10-3 a-1. The remarkably uniform velocities and low strain rates in the fast-flowing central band of NEGIS with narrow shear zones at the margins with enhanced strain rates are characteristic of ice stream flow (e.g., Minchew et al., 2018). In our study area in NEGIS, Holschuh et al. (2019) proposed that thermal softening of ice is present in the shear margins, despite the relatively low strain rates. The surface topography reveals a 30–40 m deep lowering coinciding with the fast flow within NEGIS with well-defined deep troughs marking the shear margins. These deep shear margin troughs form due to a combination of enhanced longitudinal stretching and shear as the ice flow enters the fast-flowing ice stream from both sides at an angle of ∼15∘, accelerates, and turns and an enhanced firn densification in the shear margins due to the enhanced horizontal deformation (Riverman et al., 2019a).

The location of the shear margins cannot be clearly linked to the bedrock topography in the area (Christianson et al., 2014; Franke et al., 2020). Christianson et al. (2014) proposed that the shear margins of NEGIS are controlled by a self-stabilizing mechanism related to gradients in the subglacial hydropotential due to the surface troughs that restrict widening of the ice stream, and the internal stratigraphy suggests that the shear margins have been relatively stable during the Holocene (Keisling et al., 2014). Detailed maps of bedrock topography in the area reveal subglacial landforms proposed to be related to basal erosion due to the fast flow (Franke et al., 2020) and elongated bedforms aligned with the flow (Franke et al., 2020; Riverman et al., 2019b). These elongated bedforms are seen in the transects across NEGIS as 100–300 m undulations in bedrock topography (Fig. 3), and they appear here to be related to the location of the shear margins. The southern very well-defined shear margin trough is consistently located above a local bedrock low in the three cross-sectional profiles spanning a 5 km distance along NEGIS (Fig. 3). The northern broad shear margin trough is located over a wide bedrock valley, and the shear margin trough narrows from a wide double trough to a single trough in the three cross-sectional profiles over a 5 km distance along NEGIS, as the bedrock valley over the same distance narrows (Fig. 3). Thus, our observations support that these bedforms are related to the shear margins (Franke et al., 2020; Riverman et al., 2019b), but further studies are needed to fully understand the conditions at the shear margins.

The ArcticDEM surface topography of the NEGIS ice stream shows that an organized spatial pattern of wavy undulations develops perpendicularly to the NEGIS flow in the area around EastGRIP (Fig. 8). The undulations develop within the fast-flowing central flow band of NEGIS in a 25 km section along NEGIS where the surface velocity remains at a level of approximately 55 m a-1. Upstream from this section, the flow accelerates over tens of kilometers with an acceleration of approximately 10 m a-1 over 10 km, i.e. longitudinal strain rates of ∼10-3 a-1. The undulating patterns start forming as ice velocity exceeds a threshold velocity of approximately 55 m a-1 and as the ice flows over a 200–300 m bedrock transition to a bedrock plateau of an approximately 200 m elevation and widens (Franke et al., 2020), suggesting that the undulations are related to the bedrock topography (Fig. 4). The undulations in surface slope are connected to undulations in the longitudinal and transverse surface strain rates and to some degree related to undulations in bedrock topography (Fig. 4). Similar organized undulating patterns in driving stress were previously reported in Antarctic and Greenland ice sheets in fast-flowing areas (Sergienko and Hindmarsh, 2013; Sergienko et al., 2014) and related to patterns in basal stress located in areas with significant sliding. These previous studies attributed the patterns to instabilities related to subglacial water beneath a sliding glacier, and our results support that bedrock topography plays a role in relation to these undulations.