Large spatial variations in the frontal mass budget of a Greenland tidewater glacier

We investigate the frontal mass budget of a medium-sized tidewater glacier in western Greenland. This is done by comparing the seasonal retreat of the glacier to ice advection and ablation along the front. Frontal ablation is partitioned into calving and submarine melting, both of which are estimated from in situ observations. We observe large spatial variability in all mass budget terms along the glacier front. In particular, we find that the ablation of the glacier front is characterized by two main regimes: melting dominated versus calving dominated. While melting-dominated segments appear to be associated 5 with subglacial discharge plumes, calving-dominated regions occur outside such plumes. The melting-dominated segments are rather localized, and the majority of ablation is estimated to occur in the form of calving. However, we stress the large uncertainty in melt rate estimates and consider the possibility that current parameterizations substantially underestimate melting. Finally, we argue that localized melt incisions into the glacier front can be significant drivers of calving. Our results suggest a complex interplay of melting and calving marked by high spatial variability along the glacier front. Understanding the impact 10 of such local variability on larger scale ice dynamics may help guide future mass balance projections for tidewater glaciers.


Introduction
The retreat of Greenland's tidewater glaciers may be among the most noticeable manifestations of a changing global climate (Carr et al., 2017).Tidewater glaciers present an important boundary between the ocean and the Greenland ice sheet; they act as thermodynamic buffers as well as mechanical buttresses (Rignot and Thomas, 2002;Howat et al., 2007;Nick et al., 2009).The speed-up of the Greenland ice sheet observed since the year 2000 (Howat et al., 2008;Moon et al., 2012) has likely been caused (at least to some degree) by the thinning of the glaciers' termini (Vieli and Nick, 2011) and, in some cases, the disappearance of their floating tongues (Holland et al., 2008;Wilson et al., 2017).The processes that determine the flux balance at the glacier front therefore impact the ice sheet as a whole, yet a comprehensive understanding of these processes remains elusive.
Increased ocean and air temperatures are expected to further increase the rates of glacier retreat in the coming decades (Joughin et al., 2012;Nick et al., 2013), lending additional weight and urgency to the study of calving front dynamics.For a retreating Oftentimes calving and melt fluxes are not considered separately, but rather as a single ablation term, in particular when derived from satellite imagery (Luckman et al., 2015).Previous studies of explicit calving activities of Greenland's tidewater glaciers have typically been limited to visible daylight hours (see, for example, the calving event catalogue of Åström et al., 2014), or somewhat indirect detection methods such as teleseismicity (Veitch and Nettles, 2012).
Finally, the calving and melt fluxes of glaciers are oftentimes described by single mean values (Rignot et al., 2016).However, both melting and calving can vary substantially along the front of a glacier, with largely unknown implications for the overall stability of a glacier front.For example, submarine melt is enhanced by an order of magnitude in the vicinity of subglacial discharge plumes (Slater et al., submitted), leading to pronounced undercutting and incision into the ice front (Fried et al., 2015).Spatially resolving these differences is challenging, and in particular spatial calving distributions are difficult to obtain.
Here we use a multifaceted dataset to quantify the relative contribution of calving and melting and their spatial variability along a glacier front.The dataset consists of both in-situ and remotely-sensed observations of the front of Saqqarliup Sermia, a mid-sized Greenland tidewater glacier.The data is unique in its detail, close proximity to the glacier front, and in that it contains observations of all of the main physical quantities of interest.The dataset consists of (i) detailed bathymetry at the glacier front, (ii) high-resolution ice-surface elevations, (iii) InSAR-derived ice-velocities at and upstream from the glacier front, (iv) a continuous 3-week calving event catalogue, (v) local hydrographic measurements that allow for estimates of melt rates, and (vi) multibeam sonar imagery of the underwater shape of the glacier front.The spatial and temporal concurrence of these observations allows us to compare and contrast the individual components that make up the frontal mass budget of the glacier.
2 Field campaigns and physical setting Saqqarliup Glacier and the adjacent Sarqardleq Fjord were visited during two field seasons in the summers of 2012 and 2013.
The fjord is a tributary to the Ilulissat Icefjord, with the north-west facing front of the glacier (Fig 1) located 30 km south-east of Ilulissat Icefjord.At the glacier front, the fjord is about 5 km wide and the terminus is mostly, if not completely, grounded.2016).We refer to this as the "main" plume.While this plume appears to be a yearly recurring feature, it is likely amplified in some years by the cyclical drainage of the large ice-dammed lake Tininnilik located to the south-west of the promontory (Kjeldsen et al., 2017).We note that the dramatic retreat of the glacier front in 2015 coincided with a major drainage event of lake Tininnilik (Kjeldsen et al., 2017).The second recurring plume is located closer to the north-eastern margin of the glacier (Fig 1), which we'll refer to as the "secondary" plume.
In what follows, we use bathymetry data from both years, while the other in-situ observations were mostly collected during the 2013 season (see Stevens et al., 2016;Mankoff et al., 2016, for further details on the field campaigns).

Bathymetry
The bathymetry of Sarqardleq Fjord was first mapped in detail during these two field seasons and the immediate bay in front of the terminus was found to feature depths of 40 -150 m (Stevens et al., 2016).These initial results were limited to data from REMUS and shipboard ADCP, which did not get closer than ∼ 200m to the glacier front.Here, we supplement this data with several additional near-terminus datasets from the 2013 field campaign (Fig S1 ), which allows for a detailed bathymetry map along the grounding line.The new data consists of circa 39,000 depth readings taken with Jetyak-mounted (Kimball et al., 2014) and ship-mounted ADCPs.In addition, there are approximately 6000 readings from the ship-mounted NMEA bottomrange profiler and 6 readings from XCTDs deployed in the otherwise undersampled region of the main plume.Most of these readings are between 10-100 m from the glacier front.
Fig 1c shows the new bathymetry at the glacier front as a function of x, the distance along the glacier front.The bathymetry can be split into two main regimes: For x < 1800 m (the promontory) the glacier is grounded in shallow waters and its surface heights are elevated substantially above flotation.From here on, we refer to the eastern part of the glacier (x > 1800 m) as the 'main' glacier.In 2013, the front of the promontory was grounded on a sill that runs parallel to the glacier front.This sill coincides approximately with the furthest advance of the glacier in 1992 (Stevens et al., 2016).By 2013 the main glacier had retreated ∼ 500 m from the sill, but the promontory was still perched on it in bathymetry of 60 m depth or less (

Glacier surface topography
We obtained a digital elevation map (DEM) from an ArcticDEM overflight on 22 March 2013, which covers the full span of the Saqqarliup glacier front and some of the upstream region (Fig 1).The DEM has a horizontal resolution of 2 m and is capable of resolving individual crevasses on the glacier surface.
The DEM shows that the front of the glacier is heavily crevassed and has several pronounced dips in the surface elevation at the terminus.The ice cliff is highest (up to 50 m) and most uniform in the region of the promontory, while the main part of the glacier is much more variable with four distinct depressions that reach below 10 m surface elevation (indicated by symbols in The coincident high-resolution surface elevation and bathymetry data near the terminus enables us to compute the total ice thickness along the glacier front, H(x), which allows for an estimation of the total ice flux (discussed in Section 3).
The data suggests that the terminus might be floating at several locations: the four highlighted surface depressions at the  in Section 4.2).The ice would be grounded everywhere else.In particular, the ice surface is elevated substantially beyond its isostatic height in the region of the promontory.the spatial distribution of velocities was remarkably consistent during summer months from 2012-2014 (Fig 2b), followed by a substantial overall slowdown in 2015 (not shown).This slowdown has been linked to a major drainage event of lake Tininnilik (Kjeldsen et al., 2017).In what follows, we will consider the 2012-2014 mean July velocity profile along the glacier front.
Using the mean summer (May-September) velocities instead does not change the results appreciably.
The magnitude of the summer ice velocity along the glacier front,

Ablation
In order for the mass budget along the glacier front to be balanced, the sum of advective ice flux and frontal retreat must be balanced by total ablation (i.e., by the sum of melting and calving fluxes).Here we consider a steady state, vertically averaged balance.At a given point x along the glacier front this can be written as The terms on the left hand side (retreat rate and advective ice flux) have been discussed in Section 3. The first term on the right represents the ice loss due to submarine melting, where D is the draft of the glacier and M is the depth-averaged melt rate.M is derived from in-situ hydrographic observations, in concert with a high-resolution numerical model (see Section 4.2).
The final term on the right hand side of equation ( 1) is the volume loss due to calving.This is estimated from in-situ pressure sensors (see Section 4.1), and presents the least well constrained term of equation ( 1).
In what follows we consider the volume flux across the glacier front during the summer of 2013.We make the assumption that this flux was steady during the study period and ignore time-dependencies of the individual terms in equation (1).

Calving frequency and distribution
Calving events were detected over a 19-day period from 12 July to 31 July 2013, using two pressure sensor moorings located on the western and eastern banks of the fjord, each at a distance roughly 2 km from the nearest point along the glacier front (Fig 5a).The dispersion of waves that are created by individual calving events can be inverted to estimate the distance between the mooring and the origin of the wave.Wave packets that are detected by both moorings can be used to triangulate the time and position of the corresponding calving event (Minowa et al., 2018).The method has been validated against a photographyderived calving record by and good correspondence was observed (not shown).The study by Minowa et al. (2018) provides a detailed description of the method.
In total, 336 calving events were identified using this method over the period that both sensors were recording.A pronounced peak in frequency is found at the promontory, where shallow bathymetry causes the glacier to be elevated substantially beyond its isostatic height of flotation.With its high ice cliffs the promontory can be regarded as a region that is subject to a rather different calving regime than the rest of the glacier.
For the main part of the glacier, we observe a peak in calving activity at a distance x ≈ 2400 m along the glacier front, near the concave bend in the glacier front (Fig 5b ).A second peak in calving activity is found around x ≈ 4300m.Both peaks appear slightly offset from the location of the two plumes.The calving activity is lowest at the northeast edge of the glacier.
Even though this dataset presents a rather accurate record of calving frequencies, it remains challenging to infer a total volume of calved ice (Minowa et al., 2018).This is due to the different modes of calving (e.g., ice cliff calving versus submarine calving), as well as the different shapes of calved ice blocks and the differing heights from which they fall (or depths from which they rise).Distinguishing between these events from the pressure sensor data is a difficult task and beyond the scope of this study.The pressure sensors do record an amplitude of the incoming wave packet associated with a given calving event, and assuming that this amplitude is correlated with the size of the calved ice we can estimate a relative calving volume (black curve in Fig 5b).However, since a small cone-shaped ice block can act as a more efficient wave generator than a large flat piece of ice (N.Pizzo, personal communication, Bühler, 2007), it is difficult to ascertain a direct relation between wave amplitudes and calving volume.In what follows we therefore only consider the calving frequency record and will scale this record such that the resulting mean calving flux approximately closes the mass budget at the glacier front.

Submarine melting
The submarine melting regime at Saqqarliup has been studied in detail by Slater et al. (submitted) and is briefly described here.
Submarine melt rates are thought to respond primarily to fjord water velocities and temperatures adjacent to the calving front (Holland and Jenkins, 1999).Given the great difficulties of directly measuring submarine melt rates, it is common to instead estimate water velocities and temperatures and then employ a parameterization to estimate melt rates.Slater et al. (submitted) used both data collected close to the calving front and a numerical model to estimate water properties, and thus, submarine melt rates at Sarqardleq Sermia.There is good agreement between the melt rates estimated with the numerical model and with the observations.Here, we only consider the modeled melt rates, which have the advantage of covering the whole extent of the glacier front (unlike rates inferred from observations, which have data gaps in and around the plumes).
The most relevant term for the frontal mass budget is the depth-averaged melt rate (Fig 6b).However, we also consider the possibility for melting to have a dynamic impact on calving, in which case the vertical profile of the melt rates becomes of interest.
There is large spatial variability in submarine melt rates along the glacier front.Submarine melt rates are highest (both in a depth-averaged and maximum sense) within the two plumes where the discharge of buoyant surface meltwater from beneath the glacier gives high water velocities.Outside of the two plumes melt rates are much smaller in a depth-averaged sense, however the lateral circulation excited by the plumes combines with warm surface waters to give high melt rates near the surface outside of the plumes (Slater et al., submitted).While these melt-rate estimates represent the state-of-the-art in terms of melt-rate modeling, we stress that they are based on a melt-rate parameterization that has not been confirmed by observations, especially for the case of a mostly vertical front of a tidewater glacier.The uncertainty associated with these melt-rate estimates is further discussed in Section 6. retreat rate and the spring-fall retreat rate.This gives as a best estimate for the total rate of ice loss ∼ 0.5 Gt yr −1 .
Using the aforementioned melt-rate parameterizations we find a total melting flux of 0.03 Gt yr −1 .This would suggest that 94% (0.47 Gt yr −1 ) of ablation occurs in the form of calving.Thus, the glacier would lose mass almost exclusively due to calving in most places, apart from in localized areas near the subglacial discharge plumes.However, there are large uncertainties associated with the total melt-rate estimate.And even for a small total melt flux, melting may be important for the overall flux balance due to its dynamic impact on calving.These findings are discussed further in Section 6.

High spatial variability along the glacier front
A striking feature of almost all components of this multipartite dataset is their high spatial variability along the glacier front.
The ice thickness at the front ranges from thin (<40 m) sections near the northeast edge to ∼100 m along the promontory and up to 192 m near the main plume, with substantial variations throughout.Overall, we observe a mean thickness of 128 m with a variability of ±38 m (one standard deviation).
We find that the advective flux is suppressed at the promontory and highest near the outflow location of the main plume, with a second smaller peak near the secondary plume (Fig 3).
The retreat rates are overall of comparable magnitude to the advective flux.However, the retreat rates are spatially extremely variable, in particular the observed July 2013 rates, which exhibit three regions of enhanced retreat, two of which are close to the two discharge plumes, with peaks at x = 2400 and 4400 m (Fig 4c).Averaged over longer time periods, the retreat rates also become more uniform (as discussed above), which suggests that observations over shorter time periods are more strongly influenced by individual calving events.
Calving frequencies are strongly enhanced at the promontory, which -given the reduced advection and retreat in this area -suggests that calved pieces are in general smaller here.Since we are unable to adequately distinguish between the different calving sizes, the heightened calving activity at the promontory results in a large discrepancy between the estimated total The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-143Manuscript under review for journal The Cryosphere Discussion started: 24 July 2018 c Author(s) 2018.CC BY 4.0 License.6 Discussion -the role of melting in the frontal mass budget

Uncertainty in melt rate estimates
The finding that calving appears to make up almost the entire loss of ice is somewhat unexpected, in particular since during the study period the glacier's calving activity was limited to relatively small events, and the fjord was by-and-large devoid of icebergs.These observations, along with the large uncertainty of the melt-rate parameterization used to convert near-ice ocean properties to melt rates, warrants the consideration of an end-member scenario: suppose that submarine melting accounted for all of the frontal ablation beneath the fjord surface, with calving only removing ice above the water.How would the melt rate parameterization need to be modified in order to achieve this?Scaling the turbulent transfer coefficients in the melt rate parameterization upward by an order of magnitude would increase melt rates by approximately an order of magnitude, allowing the melting outside of the plumes to roughly balance the total loss (Figs 6b and c).We do not think this is realistic however as the melt rates inside the plumes would also increase by an order of magnitude, and this would presumably drive retreat at a much faster rate than observed.
We next consider how water velocity enters the melt rate parameterization.Since plumes drive an entrainment velocity which is ∼10% that of the plume velocity (Morton et al., 1956), mean flow velocities outside of plumes will always be approximately an order of magnitude smaller than inside the plumes.One could argue that the mean modeled velocities, particularly outside the plumes, are too small for a number of reasons including coarse model resolution and the lack of tides, surface waves, and calving events which may excite water motion.These factors might crudely be taken into account by placing an additional velocity in the melt-rate parameterization.Such an approach has some precedent with the inclusion of tides beneath ice shelves (Jenkins and Physical, 2010).In order for melting to account for all of the ice loss an additional velocity with magnitude 1 m s −1 would have to be added to the parameterization.This appears physically improbable, and perhaps 0.2 m s −1 (accounting for ∼20% of the ice loss) is more reasonable.Clearly this is an observationally underconstrained discussion.However, it appears worth highlighting that through a reasonable modification of the melt rate parameterization, melting can account for a larger fraction of the ice loss than reported here.

Dynamic impact of melting on overall ablation
Even if the volume of ice lost through submarine melting is small, melting may still play an important role in the glacier's frontal flux balance: since it is highly focused on discrete regions of the glacier front, melting can lead to sharp incisions in the front profile that may be significant drivers of calving.Slater et al. (submitted) found that fjord recirculation driven by subglacial discharge plumes can cause substantial nearsurface horizontal melting along the glacier front (away from the discharge locations of the plumes).This near-surface melting has in turn been suggested as a potential driver for large calving events at glacier fronts that are floating or close to floating (Wagner et al., 2016): Preferential near-surface melting at the glacier front leads to a horizontal melt incision near the water surface which in turn causes erosion of the above-water ice cliff.As a result, the front of the glacier is left with an underwater protrusion (or "ice foot") as in the profiles C and D of Fig 7.This frontal profile is statically unstable, since the ice foot is net buoyant and exerts bending stresses on the glacier.Calving events occur when such stresses surpass the yield strength of the terminus.This process has also been observed on icebergs in temperate waters (Scambos et al., 2005;Wagner et al., 2014).It is likely that profiles C and D represent sizable ice feet which exert bending stresses that enhance the calving flux in this region.
Furthermore, it is possible that the regions adjacent to the meltwater plumes are more prone to calving since the high melt rates at the plumes cause vertical incisions in the glacier front (Fried et al., 2015).These in turn would reduce the transverse

Conclusions
We have presented a multi-faceted dataset of a Greenland tidewater glacier and its surroundings.The unique dataset enables us to investigate the individual terms that determine the flux balance along the glacier front.
We find that the individual terms that comprise the glacier's frontal mass budget are marked by high spatial variability.
Ice velocities feature maxima that coincide with troughs in the bathymetry and locations of subglacial discharge plumes.The retreat rates are spatially particularly variable when calculated over shorter periods of time (days to weeks).Spikes and troughs The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-143Manuscript under review for journal The Cryosphere Discussion started: 24 July 2018 c Author(s) 2018.CC BY 4.0 License. in glacier retreat rates over such short timescales are likely dominated by somewhat stochastic calving events.Melting, on the other hand, is more consistent throughout the summer and can be expected to only feature gradual changes.Overall, ice loss due to melting, as calculated from commonly used melt-rate parameterizations and observed ocean properties, is an order of magnitude smaller than ice loss due to calving.We note, however, the large uncertainty in the melt rate estimates and stress the possibility that melting could account for a larger proportion of mass loss with modest modifications of the submarine melt rate parameterization.
The spatial variability of the observed processes suggests the presence of two distinct ablation regimes: a melting-dominated one near the discharge plumes and a calving-dominated regime away from the plumes.We suggest that melting, through its horizontal and vertical variability, may play an important role in driving calving, thus having a dynamic effect out of proportion to the fraction of mass lost by melting.If calving is indeed dependent on the localized melt rates, this may have far-reaching implications for the overall stability of the glacier.Understanding the impact of these spatially highly variable processes on ice sheet dynamics should thus be a priority in the study of ice-ocean interactions.

Figure 1 .5
Figure 1.(a) Landsat-8 image of the lower part of Saqqarliup Sermia, and Sarqardleq Fjord.The inset of Greenland shows the location of the glacier.(b) Gridded bathymetry from in-situ observations (readings indicated by gray dots).Also shown is the surface height from ArcticDEM (Digital Elevation Map created by the Polar Geospatial Center from DigitalGlobe, Inc. imagery).Red line shows the front position on 9 July 2013.(c) Surface height (blue) and bathymetry (black) along glacier front (following the red line in panel b).Also shown is the isostatic bottom of the ice (blue dashed).Locations of two main plumes are highlighted in panels (b) and (c) by and ▽; two additional surface dips are indicated by ▲ and •.The green horizontal line above panel (c) and the letters A-D indicate the locations of the front profiles shown in Fig 7.
Fig 1c).Since 2013, this part of the glacier front has also retreated by several hundred meters (Fig S2).In 2013, the main part of the glacier front was in waters of depth 40-150 m.A pronounced dip in bathymetry -suggestive of a subglacial channel -is found near the location of the main plume (x = 2000 − 2400 m).A number of smaller dips are observed between x = 3400 − 4700 m.Beyond 4700 m the water depth decreases as one approaches the northeastern shoreline.

Figure 2 .
Figure 2. (a) InSAR Ice velocity data near the glacier front.Shown are mean summer (June-September) values averaged over 28 velocity fields, collected during 2012-2014.Note that there is a consistent data gap near the promontory.The shading represents the horizontal velocity magnitude.(b) Velocity profiles along the glacier front.Here, as in all figures, the perspective is with the direction of ice flux into the page.The faint gray lines show the 28 individual velocity fields.Also indicated are the approximate locations of the two plumes ( , ▽).

5
glacier front are all low enough to raise the isostatic bottom of the ice above the local sea floor.The locally-isostatic bottom of the ice is indicated in Fig 1c (blue dashed line).Here we assume an average ice density of 883 kg m −3 , obtained as a mean of low and high values commonly used for glacier and ice shelf front densities, namely 850 kg m −3(Silva et al., 2006) and 917 kg m −3 (pure ice).It should be noted that the surrounding ice and the associated stiffness of the glacier will likely prevent the ice from assuming local isostasy everywhere along the glacier front.However, the isostatic bottom can be used to compute a lower 10 bound on the ice thickness in regions where the ice may be floating.It may be speculated that the ice appears to be floating in these regions due to undercutting by submarine melt (which in turn is associated with rising discharge plumes, as discussed The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-143Manuscript under review for journal The Cryosphere Discussion started: 24 July 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 3 .
Figure 3. (a) Mean July ice velocity along the glacier front in blue (right vertical axis).Here we used cubic interpolation to fill the data gap shown in Fig 2. In blue (right vertical axis) is shown the estimated ice thickness along the glacier front, obtained by computing the difference of the surface and bathymetry profiles of Fig 1(c).The dotted red line shows the ice thickness at the glacier front assuming the ice is locally in isostatic equilibrium everywhere.(b) Ice flux along the glacier front (in black), computed from the product of velocity and thickness (shown in panel a).The shaded gray areas under the curve show the ice-flux range due to potential flotation.This is a result of the thickness ranges indicated as red shaded areas in panel a.Also indicated are the approximate locations of the two known plumes ( , ▽), which coincide with two areas of possible flotation.

3
Ice flux and retreat 3.1 Ice velocity and advective ice flux Several dozen ice-velocity reconstructions of the lower part of the glacier are available for the years 2009 -2015 from InSAR 5 data (Joughin et al., 2011).The mean flow velocity at the glacier front (averaged over all available fields) is ∼ 350 m yr −1 with minima at the edges of the glacier.There is a notable peak in ice velocity (up to 750 m yr −1 ) near the location of the main plume (Fig 2).A second region of elevated velocities is found near x = 4500 m and is more pronounced further upstream from the glacier front.The drainage location of this second stream coincides with that of the secondary plume.It is worth noting that 6 The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-143Manuscript under review for journal The Cryosphere Discussion started: 24 July 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 4 .
Figure 4. Seasonal advance and retreat of glacier front.(a) 15 front profiles acquired from February to September 2013; the legend highlights every 2nd profile.The thick red and blue profiles represent the May-June and Sept averages, respectively.Also indicated are the location of the two plumes ( , ▽).(b) Mean front position, shown as an anomaly from the yearly mean position.2012 values are shown in gray, 2013 in black.The spring profiles used in panel (a) are highlighted in red, fall profiles in blue.The vertical dotted lines demarcate the period from 12 to 31 July during which calving was observed.(c) Retreat rates, R(x), along the glacier front.The dashed line represents the spring-fall mean retreat rates; the solid line that of 9 to 31 July, computed from the profiles marked green in panel (b).

7
v i (x), shown in Fig 2b, together with the ice thickness5profile H(x), allows for an estimate of total advective ice flux(Fig 3).This assumes plug flow, i.e., that the ice velocity is approximately constant from the surface to the ice-bedrock interface, which is considered a good approximation for fastflowing tidewater glaciers(Meier and Post, 1987).The uncertainty in ice thickness associated with the glacier potentially floating at several points along the front is illustrated by the shaded areas in Fig 3.In the figure, the upper bound of the ice thickness assumes a fully grounded glacier front, while the lower (dashed) bound assumes local isostasy everywhere.The ice 10 The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-143Manuscript under review for journal The Cryosphere Discussion started: 24 July 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 5 .8
Figure 5. (a) Close-up of glacier front and adjacent fjord, with the red rectangle outlining the region of interest (panel b) and red stars indicating the location of the wave moorings; (b) spatial calving distribution as estimated from pressure sensor data; the shaded rectangle indicates the promontory; (c) calving count along glacier front, obtained as total number of calving events detected within a 300 m running window along the glacier front (red bars, left axis).Also shown is an estimate for the relative calving volume, computed from the product of the frequency of calving events and the corresponding magnitudes of the detected waves (black line, right axes).Plume and surface dip locations are indicated as in previous figures.
Fig 5b shows the location and an estimated magnitude of the individual events.The calving frequency distribution along the glacier front is illustrated in Fig 5c.The Cryosphere Discuss., https://doi.org/10.5194/tc-2018-143Manuscript under review for journal The Cryosphere Discussion started: 24 July 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 6 .
Figure 6.Flux balance along the glacier front.(a) The green line represents the July 2013 retreat rate and the blue line the advective ice flux.The sum of these two terms (black) must be equal to total ablation.(b) Melt flux (red) and calving flux (dark red).The total ablation, i.e., the sum of melting and calving, is shown by the gray line.Note that the calving flux has been scaled to approximately close the budget.(c) Approximate closure of the volume flux budget along the glacier front.The black line shows the sum of ice advection and retreat as in panel (a), while the gray line shows the total ablation as in panel (b).

Figure 7 .
Figure 7. Multibeam sonar data of glacier front from 26 July 2013.(a) Map illustrating the location of the shown multibeam cross-sections A-D and the two plumes ( , ▽).(b) 3D point-cloud transect showing a part of the eastern side of the glacier (distance along glacier front, ∼ 4000 − 4800 m).Data is color-coded by depth below sea level.Indicated are the locations of the four cross-sections A-D shown in panels c and d.(c) Cross-sections A and B near subglacial plume, exhibiting characteristic undercutting.(d) Cross-sections C and D away from plume, showing submarine protrusions without undercutting.

The
Cryosphere Discuss., https://doi.org/10.5194/tc-2018-143Manuscript under review for journal The Cryosphere Discussion started: 24 July 2018 c Author(s) 2018.CC BY 4.0 License.(i.e., along-front) stability of the terminus, and trigger further calving.A surface expression of such a vertical incision in the glacier front can be found near the main plume in the profile of August 2012 (Fig S2).Considering the particular geometry of Saqqarliup, as the two main plumes drive rapid melt near the two edges of the main part of the glacier, this may cause the entire front between the plumes to be more prone to calving, in particular since we have found this region to be close to (or at) flotation.In summary, from the observations presented in the previous sections, we propose that there are two distinct regimes driving ablation at Saqqarliup: (a) melting-dominated ablation in spatially confined regions near the discharge plumes, and (b) calvingdominated ablation in the regions away from the plumes (which may nevertheless be enhanced by near-surface horizontal melt incisions).This is further supported by the local minima in calving activity at the location of the two discharge plumes (Fig 6b).The two ablation regimes are summarized in the schematic of Fig 8.

Figure 8 .
Figure 8. Schematics of two distinct ablation regimes.(a) Melt-dominated regime: the vertical structure of melting due to a rising subglacial discharge plume which entrains warm ambient water results in substantial undercutting of the glacier front (as in profiles A and B in Fig 7).These front profiles likely do not cause large calving events with calving mostly confined to the smaller above-water cliff.Profiles are drawn for an earlier time t1 and a later time t2 by which the glacier has retreated mostly due to melting.(b) Calving-dominated regime: here the growth of sizable and buoyant underwater feet (as in profiles C and D in Fig7) can accelerate calving, with the melt contribution confined to a small region near the water surface.Again, profiles are shown at t1 and t2 (pre and post-calving), as part of the "footloose" calving cycle(Wagner et al., 2014).