To study ungrounding, glacier thinning was derived from ArticDEM strips of 2013–2017 . The digital elevation models (DEMs) were coregistered using the method outlined in and implemented in the GeoUtils library (http://github.com/GeoUtils, last access: January 2020). Additionally, a 2D linear function is estimated from the elevation difference over stable areas and removed from the map of elevation change.

In 2019, two rows of five Emlid Reach M+ single-frequency, low-cost (about USD 300), differential GPS receivers were installed on stakes drilled into the ice, in close vicinity to the calving front (Fig. c), and powered by solar panels. Most of the stations were running from 8 to 25 July 2019, and data were downloaded on a regular basis using Wi-Fi, without touching the devices. Pairs of stations were numbered 1–5, starting from the centre towards the south-eastern margin, with “f” (forward) for the station closest to the front and “b” (backward) further back (Fig. c). The spacing between receivers was ≈ 215 m in the across-flow direction and ≈ 115 m in the along-flow direction. A base station was installed on the bedrock next to the glacier to provide a stationary reference point (Fig. a). GPS data were processed with RTKLIB using a kinematic mode to obtain the position every second . To assess the positioning accuracy, we performed a static test. In addition to the base station, we left another receiver immobile on a stable off-glacier area for ≈ 12 d and monitored the variability in its position over time. After differential processing, 95 % of the recorded positions were within 10 mm horizontally and 29 mm vertically from the mean values. When taking the 1 h moving average of the vertical position, the maximum deviation of 95 % of the recorded positions to the mean position is 6 mm, which we interpret as the vertical positioning accuracy of our processed GPS data.

One GPS station (3f) calved off during the 20 July event. Data from 3f were downloaded the last time on 15 July. Two of the remaining stations (2f and 4f) were retrieved on 22 July due to the risk of a subsequent calving event. All remaining stations were retrieved by the end of the field campaign on 25 July, 4 d prior to the second-observed major calving event.

To monitor the time evolution of flotation conditions, another GPS station was also installed in between 1b and 2b, at approximately the same coordinate during each field campaign (positions shown in Fig. ). The installation positions in 2015, 2016, and 2019 were located within 20 m, but in 2017 the GPS station was installed approximately 30 m further upstream. The distance to the front varied from 240 m (2015) to 140 m (2019) due to variations in the front position. For more information on this different GPS set-up and processing, we refer to .

The fixed-wing uncrewed aerial vehicle (UAV) “WingtraOne” with vertical take-off and landing was used to conduct photogrammetrical surveys on 17, 19, 21, and 28 July 2019. The missions consisted of one to four flights of four lines each, parallel to the calving front ≈ 400 m above the glacier surface, covering 800–3000 m of the terminus of Bowdoin Glacier. The UAV was programmed to take aerial photographs overlapping 90 % in the flight direction and 75 % in the across-flight direction, with a ground sampling distance of ≈ 0.12 m. Ortho-images with 0.5 m resolution were derived by structure-from-motion photogrammetry using Agisoft PhotoScan software. All 10 GPS stations were marked with tarps and served as ground control points (GCPs) for georeferencing. UAV surveys in 2015 and 2017 are described in and .

We constructed an inventory of calving events from 2015–2019, containing all calving events which were large enough to be detected on satellite images. A combination of Landsat 8 Operational Land Imager panchromatic imagery, Sentinel-2 imagery, and Sentinel-1 synthetic aperture radar (SAR) imagery is used (Table ). The visual satellite imagery (Landsat 8 and Sentinel-2) is complemented by Sentinel-1 SAR imagery in case of clouds, such that the image pairs used to outline calving events are maximum 6 d apart. Spatial resolution of the images varies from 30 m (Landsat 8) to 10 m (Sentinel). Sentinel-1 data were downloaded using the Google Earth Engine , which provides backscatter coefficients orthorectified using the ASTER DEM to the same coordinate system as Sentinel-2 imagery (UTM 19N). To minimize incidence-angle-dependent effects and also artefacts due to inaccuracies in the DEM, we processed data from a single orbit (026, descending). To correct for sub-pixel shifts between the orthorectified images, we coregistered them to a common reference (intensity average of all scenes) using intensity cross-correlation .

In order to put the scale of detected events into perspective, their area is expressed relative to the annual areal ice discharge. To allow direct comparison of calving event sizes between years, we used the annual discharge averaged for 2015–2019 estimated from Sentinel-2 imagery in combination with the estimate for 2015 derived in. From these images, we derive 50 m resolution monthly velocity fields from 2016–2019 by the orientation correlation method with a window size of 40×40 pixels using the software package ImGRAFT . We estimated an annual ice discharge of approximately 0.9±0.2 km2yr-1 by integrating monthly velocities from 2015–2019 over the flux gate shown in Fig. c. The velocities are not integrated over the ice thickness.

An automated camera was installed next to the calving front (Fig. a), taking daily pictures from July 2014 to July 2017 and hourly pictures during field campaigns in July 2015, 2016, 2017, and 2019. The images were used to further constrain the timing of calving events in the inventory.

To investigate tidal forcings, observations of tidal height at Thule Air Base were used, 125 km south of Bowdoin Glacier, provided as a part of the Global Sea Level Observing System network (https://www.gloss-sealevel.org/, last access: 1 September 2020). These records show the same phase and amplitude as in Bowdoin Fjord . We obtained hourly air temperatures at Qaanaaq Airport (16 m a.s.l.), located 30 km south-west of Bowdoin Glacier, from the National Oceanic and Atmospheric Administration (http://www.ncdc.noaa.gov/cdo-web/datasets, last access: 20 March 2020). The temperature dataset was used to constrain the melt season duration as an indicator for the possibility of hydro-fracturing as a potential driver of calving. The first and last occurrence of at least 2 consecutive days with positive hourly air temperature are used as proxy for surface melt.

ArcticDEMs show that most of the glacier front lowered from 2013–2017 (Fig. ). A particularly strong local lowering is observed after 2015 in the area close to the medial moraine where GPS stations 4b–f are located. There, the lowering rate reached up to 12 myr-1 between 2015 and 2017. On the bedrock, elevation differences are within ±1 m, which we interpret as the accuracy of the detected elevation change.

To investigate the influence of thinning on flotation conditions at the calving front, we analyse the vertical response to semi-diurnal tidal modulation. We calculate the tidal admittance as the range in vertical surface displacement relative to the tidal range . We define the range of tidally modulated vertical motion as the elevation difference during low and subsequent high tide. GPS data show that the vertical tidal modulation increased since 2017 (Fig. ), with a stronger correlation between detrended elevation and tidal height in 2017 and 2019 (r=0.64) than in 2015 and 2016 (r=0.28). In both 2017 and 2019, the mean tidal admittance was 0.9 %. Also the maximum tidal admittance was equal: 2.6 %, observed on 10 July 2017 and 15 July 2019.

Two major calving events were detected from UAV and time lapse imagery, on 20 and 29 July 2019 (Figs. c, d and S3). UAV imagery shows that the size of the 20 July event was approximately 700 m by 50 m and was centred close to the moraine (Fig. c). Because the field campaign ended on 29 July (Table ), we have no UAV imagery after the calving event on 29 July. However, by combining UAV and satellite imagery, we find that the 29 July calving event was almost 3 times as large in area as the 20 July event. It was approximately 1 km by 100 m and widest in the central part of the glacier (Fig. d).

In contrast to large-scale calving events observed in July 2015 and 2017, no major surface crevasses were observed prior to calving, neither in the field nor from aerial imagery. Figure a shows an image taken by the UAV 17 h before calving occurred on 20 July without a crevasse visible at the calving location. Also during the last UAV survey on 28 July, no crevasse was seen on the surface where calving occurred 14 h later (Fig. b). The lack of a precursor crevasse was also evident from the meltwater stream on the moraine, which was at all times observed to discharge into the sea through a waterfall at the calving front (Fig. a). A surface crevasse draining the stream was not observed, contrary to 2015 and 2017 .

Both GPS and satellite-derived horizontal velocity are shown in Fig. . The velocity in July 2019 is similar in magnitude and tidal modulation as observed in previous years . Stations 1–4 show very similar velocities in general (Fig. a). As expected, velocity is much lower at stations 5b and 5f, which are located in the slow-moving area in the south-east (Fig. c; see Fig. c for positions). The horizontal velocity at stations 1–4 usually reaches a minimum at high tide. A temporary flow acceleration occurred on 14 July, which was most likely induced by surface meltwater input into the subglacial drainage system, resulting in enhanced sliding as the accelerated flow coincided with the only 2 consecutive days of temperatures above 15 ∘C in Qaanaaq in July 2019. Similar speed-up events were observed after a few days of high air temperatures or rainfall . The stations' horizontal velocities are not visibly affected by the 20 July calving event (red line, Fig. a), neither when velocities are calculated over a shorter time range nor in the 1 s interval positioning data (not shown).

As a measure of cumulative strain, we calculate the relative distance increase over time t according to d(t)/d(t0)-1, where d is the distance between two stations aligned along flow (Fig. c) and t0 the initial time. Stations 2b–f and 4b–f show increased extension after the 20 July calving event (Fig. b and d), which is likely due to their position closer to the new calving front. A similar increase in extension seems present at the other stations as well, although less clearly. Stations 1b–f show strong horizontal surface compression after 23 July (Fig. e), prior to the second major calving event on 29 July.

Figure  shows the time series of elevation for the GPS stations. Three periods of distinct vertical motion are visible (separated by vertical lines in Fig. ): (1) prior to the speed-up on 14 July, (2) between the speed-up and calving event on 20 July, and (3) between the calving events on 20 and 29 July. The spatial distribution of the time-averaged vertical motion is displayed in Fig. . Prior to the speed-up, almost all stations west of the moraine move downward (except 1b, which shows limited vertical motion), whereas the stations east of the moraine move upward (Fig. a).

After the speed-up, only station 1f still moves downward, stations 4f–b move upward quickly, and the other stations are initially almost stagnant (Fig. b). An abrupt change in vertical motion in response to the speed-up is observed at stations 5f–b, located in the slow-moving area (Fig. a), whereas the change is rather smooth at the other stations (Figs. b–d). A total upward vertical displacement of ≈ 0.2 m occurred at stations 4f–b between the 14 July speed-up and 20 July calving event (Fig. b).

After calving on 20 July, stations 2f, 3b, 4b, and 4f show changes in vertical motion (Fig. c). The uplift observed prior to calving stops (station 4b; Fig. d in red) or turns into downward motion (4f; Fig. d in blue), or downward motion increases (3b; Fig. c red; and 2f; Fig. b blue). The highest rates of downward displacement are observed at 2f and 4f, which are situated closest to the calving event (Fig. c). No changes are observed at stations 1b–f, 2b, and 5b–f.

Stations 1–4 show tidal modulation of the vertical position (Fig. ), whereas this modulation is not visible at stations 5f and 5b, located in the slow-moving area. When subtracting a linear trend, the tidal modulation becomes more clearly visible (Fig. S1). Besides the semi-diurnal tidal modulation, a modulation with a 2-week period similar to the spring–neap tidal cycle also seems present, most clearly for stations 3b and 4f–4b. However, as the observational period only spans slightly more than one spring–neap cycle, it is not possible to conclude whether this cycle also modulates vertical motion.

For most stations, the largest admittance occurred on the evening low tide of 17 July, which is shown in Fig. b. The largest range on 17 July is measured at stations 2f and 4f, which lifted 0.07 m, 3.0 % of the tidal range. The range quickly diminishes upglacier and is only about half as large at 2b and two-thirds at 4b. The range is also smaller towards the glacier centre (left side of Fig. ). At station 1f, only 0.04 m uplift is measured, which is slightly more than half the uplift measured at station 2f, 180 m closer to the moraine. These numbers agree well with the additional GPS (Sect. ). On 17 July 2019, a tidal admittance of 1.8 % was measured, which is very close to the admittance linearly interpolated from the four nearest stations (1f–b and 2f–b, where interpolation by triangulation yields 1.9 %). At station 3f, for which we have no data on 17 July, the largest admittance is 3.2 %, which is obtained on 8 July, as shown in Fig. a.

We manually outlined large calving events visible from satellite imagery from 2015–2019 and calculated the area per event relative to the averaged annual ice discharge. We detected 73 events, which form 40 %–80 % of the annual ice discharge. Detected area loss between an image pair can reach up to 25 % of the annual ice discharge. However, it is impossible to determine from satellite imagery whether these losses are single calving events, even for a minimum time span of 1 d between image acquisitions. Therefore we have used time lapse imagery (when available) to confirm that these area losses are due to single calving events (Figs. S2, S3). Major loss (≥ 15 % of annual ice discharge) in one image pair is detected 6 times, at least once every year. Together the six largest events form 22 % of the estimated ice discharge in the entire period. Figure  shows that large calving events (≥5 % of annual ice discharge) are rare outside of the melt season (orange lines), except for four events on 4 May 2015, 1 May 2018, 19 March 2019, and one event between 28 December 2019 and 3 January 2020. The relative contribution of calving events outside the melt season to the yearly total is larger in 2018 and 2019 than in the 3 years before, in terms of both area and number.

Our GPS measurements indicate in three ways that Bowdoin Glacier's terminus was (at least partially) ungrounded in July 2019:

Vertical motion at Bowdoin's terminus is modulated by tide at stations 1–4 but not at 5f–b (Fig. ). The magnitude of vertical tidal modulation strongly varies spatially (Fig. ), which suggests that flotation conditions vary across the front. The absence of tidal modulation in the slow-flowing area, where 5f–b are located, indicates that this area is still grounded. The largest tidal modulation is observed close to the moraine; thus this area is presumably subject to largest buoyant forces.

Our GPS observations are consistent with buoyant calving as observed at Helheim Glacier by . They observed uplift and rotation of the front, creating basal crevasses and forming a surface depression above the basal crevasses, which they call a “flexion zone”. The basal crevasses induced buoyant calving of the entire area downglacier of the flexion zone. Such behaviour is particularly clearly visible at our stations 1b–f (Fig. a). Station 1f lies on the outline of the 29 July calving event and thus in the flexion zone. Downward motion is observed at 1f in the entire measurement period, whereas no downward motion is observed at station 1b, which is located only 115 m upstream (Fig. a). The horizontal compression at stations 1b–f could be related to buoyant calving on 29 July as well. During the afternoon high tide at 24 and 25 July, sudden longitudinal compression is observed between stations 1b–f (Fig. a). On such short timescales, ice is expected to behave as a brittle-elastic material . Therefore, we interpret basal crevasse formation as the most likely cause of the longitudinal compression at the surface. The highest observed compression at high tide is also favourable for this interpretation as buoyant forces which trigger basal crevasse formation increase at high tide.

On the other hand, the uplift at 4b–f prior to calving on 20 July (Fig. d) is not entirely consistent with since they observed that the entire zone which lifted up subsequently calved off. However, observed similar behaviour on Helheim Glacier, using daily DEMs derived from terrestrial photographs, showing that the uplifting part of the terminus did not calve at once but broke off in multiple stages. Stations 2f, 3b, and 4b–f, which were all close to the area which calved on 20 July, showed downward motion after calving (Fig. c). If the part of the terminus that broke off on 20 July was indeed afloat before calving, the buoyant forces on the terminus became smaller after calving, which could explain the downward motion.

Another sign of buoyant calving is visible in Fig. a. The pile of white, clean ice fragments, located close to the moraine, was already present when the field campaign started on 1 July 2019. We speculate that this feature formed during a previous calving event. During detachment of an iceberg by buoyant calving, buoyant forces can push the iceberg above the calving front. A portion of the iceberg could then have fragmented and fallen on the glacier surface immediately behind the calving front. In the field campaigns prior to 2019, a similar feature was never observed.

Bowdoin Glacier has experienced further thinning since the front stabilized to its new position in 2013. The region of strongest thinning (dark red in Fig. ) coincides with the region of largest observed vertical tidal response in 2019 (yellow in Fig. ). A surface depression in this region is clearly visible in the field, with the lowest ice cliff located at the moraine. Because the strongest thinned area also coincides with the shear zone, the large velocity gradients likely caused this surface depression by dynamic thinning. A similar case was reported by , who used satellite data to show that high shear resulted in surface depressions. Their observations suggest that the locally thinned ice was subsequently pushed upward by buoyant forces, and basal troughs formed beneath the depressions. Plumes were observed to focus into these basal troughs, which amplified melt locally and thinned these areas further. This proposed shear thinning mechanism agrees with our observations at Bowdoin Glacier, where a plume has been clearly visible on the sea surface close to the moraine during field campaigns in 2015–2017 and in early July during the field campaign in 2019 (picture not shown).

Significant vertical tidal modulation was first observed by GPS in July 2017 (Fig. ). The mean and maximum tidal admittance were similar in July 2017 and 2019, although the GPS was located ≈ 55 m further away from the front in 2017 (Sect. ). Because there was only one GPS installed close to the front in previous years, outside of the area which showed largest tidal response in 2019, it is difficult to conclude whether vertical tidal modulation changed since 2017.

Numerical modelling showed that an undercut is necessary in order to reproduce the initiation of the crevasse which led to the major calving event observed in 2017 . Furthermore, high-resolution terrestrial radar interferometry data revealed that crevasse opening prior to that calving event was fastest at low tide, which suggests a non-buoyant calving style . Additional modelling work identified the crevasse water level, and thus hydro-fracturing, as a key driver of opening rates . Unlike the deep and most likely water-filled surface crevasses which formed prior to the observed calving events in 2015 and 2017 (Fig. ), no precursor crevasse was visible in the field prior to the calving events in July 2019. This suggests that the events in July 2019 were not triggered by extensional stress at the glacier surface but resulted from basal crevasse propagation due to buoyant flexure instead.

Our large-scale calving event inventory is consistent with a changing calving mechanism from hydro-fracturing-induced and undercutting-induced calving towards buoyant calving. Since the precursor surface crevasse in 2017 was not visible in satellite imagery, we cannot use satellite imagery to directly conclude whether precursor-free calving events happened in previous years as well. However, the timing of observed large-scale calving events may help to distinguish plausible calving mechanisms. Initiation and propagation of surface crevasses are promoted by undercutting and hydro-fracturing, which depend on external forcings such as surface and submarine melt. Therefore, they are expected to follow a seasonal pattern e.g. . Contrarily, buoyant calving does not depend as directly on seasonal variations.

There is a large variation in the cumulative area loss by calving detected in each year in our satellite-derived calving inventory (Fig. ), which has two possible explanations. Firstly, the low cumulative percentage of calved area reported for 2017 (44 %) is likely due to the front advance which occurred in 2017 (Fig. ), which suggests that the calving rate was smaller in 2017, such that the averaged annual ice discharge for 2015–2019 overestimates the frontal ablation in 2017. Similarly, the front retreat in 2016 and 2019 can explain the high reported cumulative area loss relative to annual discharge in those years (≈ 80 %). Secondly, our inventory aims to study large-scale calving events. Small calving events cannot be detected from low-resolution satellite imagery. analysed calving-generated tsunami waves and detected 11 calving events per day from 11 to 21 July 2015 and 15 per day from 15 to 30 July 2016, whereas we did not detect any calving events in these periods. As such, variations in area loss by small-scale calving events could also explain part of the variation in undetected area loss in each year.

Major calving events (≈ 25 % of the estimated yearly ice discharge) occurred on 1 May 2018 and 19 March 2019 (Fig. ). These calving events are unlikely induced by hydro-fracturing of surface crevasses as it is improbable that surface melt occurred. Furthermore, warm Atlantic water is not available in winter since the glacier flows into a fjord shallower than 200 m, which means that substantially large submarine melting capable of destabilizing the front by undercutting is expected to start once fjord circulation is increased by subglacial meltwater discharge .

A major calving event (≈ 20 %) was also observed on 4 May 2015, prior to surface melt, without a surface crevasse visible in time lapse imagery (Fig. S2a–b). New sonar data collected close to the front (; not included in Fig. b) show that the fjord bed topography is seaward-sloping at the current front position before sloping upward towards the bed bump where the front was located in 2007. The winter advance therefore relocated the front to a deeper part of the fjord in 2015, which could have induced temporary flotation of the front and buoyant calving. A similar mechanism of buoyant calving triggered by winter advance can also have caused the 12 % calving event which occurred around 31 December 2019 (Fig. ).

The relative contribution of calving outside of the melt season has increased since 2018 (Fig. ). These calving events were most likely not melt-driven but mechanically driven in response to buoyant flexure . Although buoyant calving may have occurred in 2015 already, a change seems to have occurred towards buoyant calving as the dominant calving style since 2018. However, a longer time span of high-resolution ice motion data is necessary to confirm a switch towards buoyant calving. On Columbia Glacier (Alaska), found that calving behaviour changed from rather steady discharge of small icebergs to episodic release of large icebergs when the glacier's tongue became afloat. We do not see a similar trend in the calving inventory at Bowdoin Glacier, which could be due to the different flotation conditions. Whereas the entire last 2 km of Columbia Glacier became afloat, the eastern marginal area at Bowdoin Glacier is still grounded.