The geometry of the sea floor immediately beyond
Antarctica's marine-terminating glaciers is a fundamental control on
warm-water routing, but it also describes former topographic pinning points
that have been important for ice-shelf buttressing. Unfortunately, this
information is often lacking due to the inaccessibility of these areas for
survey, leading to modelled or interpolated bathymetries being used as
boundary conditions in numerical modelling simulations. At Thwaites Glacier
(TG) this critical data gap was addressed in 2019 during the first cruise of
the International Thwaites Glacier Collaboration (ITGC) project. We present more than 2000 km2 of new multibeam
echo-sounder (MBES) data acquired in exceptional sea-ice conditions
immediately offshore TG, and we update existing bathymetric compilations.
The cross-sectional areas of sea-floor troughs are under-predicted by up to
40 % or are not resolved at all where MBES data are missing, suggesting that
calculations of trough capacity, and thus oceanic heat flux, may be
significantly underestimated. Spatial variations in the morphology of
topographic highs, known to be former pinning points for the floating ice
shelf of TG, indicate differences in bed composition that are supported by
landform evidence. We discuss links to ice dynamics for an overriding ice
mass including a potential positive feedback mechanism where erosion of
soft erodible highs may lead to ice-shelf ungrounding even with little
or no ice thinning. Analyses of bed roughnesses and basal drag contributions
show that the sea-floor bathymetry in front of TG is an analogue for extant
bed areas. Ice flow over the sea-floor troughs and ridges would have been
affected by similarly high basal drag to that acting at the grounding zone
today. We conclude that more can certainly be gleaned from these 3D
bathymetric datasets regarding the likely spatial variability of bed
roughness and bed composition types underneath TG. This work also addresses
the requirements of recent numerical ice-sheet and ocean modelling studies
that have recognised the need for accurate and high-resolution bathymetry to
determine warm-water routing to the grounding zone and, ultimately, for
predicting glacier retreat behaviour.
Introduction
Knowledge of Antarctica's coastal bathymetry is essential when considering
ocean circulation and recent dynamic changes at the ice-sheet margin.
Sea-floor bathymetry influences ice–ocean interactions in two ways. First,
deep (>500 m water depth) bathymetric troughs and channels
provide access routes for warm, salty Circumpolar Deep Water (CDW:
∼0.5–1.5 ∘C, located below ∼300–500 m water depth; Jacobs et al., 1996, 2013) to present-day grounding zones.
The inflow of CDW increases basal melting and ice-shelf thinning (Jacobs et
al., 1996; Rignot et al., 2013), leading to ice-shelf disintegration, reduced
buttressing, the acceleration of the ice shelves and grounded ice upstream,
and ultimately grounding-zone retreat (Schoof, 2007; Joughin et al., 2010;
Favier et al., 2014; De Rydt and Gudmundsson, 2016). This effect is
particularly significant for ice resting on reverse-slope beds (i.e.
retrograde, when the bed slopes down towards the interior of the continent)
where grounding-zone retreat may initiate marine ice-sheet instability, a
positive feedback that could lead to runaway retreat (Weertman, 1974;
Schoof, 2007). Secondly, bathymetric highs can slow ice retreat by acting
either as pinning points for floating ice or as “sticky spots” at the
grounding zone itself, as well as by partially blocking warm-water access to modern
grounding zones (e.g. De Rydt et al., 2014). An ice shelf pinned on a
bathymetric high is subject to increased buttressing, and a topographic high
at the grounding zone similarly contributes to basal drag that restricts ice
flow. Both have the potential to act as stabilising influences (Alley et
al., 2007; Parizek and Walker, 2010).
Geophysical mapping at marine-terminating ice-sheet margins is often
difficult due to more or less persistent floating ice cover in the form of
icebergs, ice tongues, ice shelves and sea ice. This is certainly the case
at Thwaites Glacier (TG), West Antarctica, which is one of the two dominant
fast-flowing glaciers draining into the eastern Amundsen Sea Embayment (ASE);
the other being Pine Island Glacier (PIG; Fig. 1). Together, Thwaites and
Pine Island glaciers were responsible for >30 % of the annual
ice discharge from the West Antarctic Ice Sheet (WAIS) between 2009 and 2017
(compared with 25 % for 1979–1989; Rignot et al., 2019), and TG and
adjacent smaller glaciers accounted for ca. 50 %–55 % of the annual net mass
loss from the WAIS since 1992 (Shepherd et al., 2019; Smith et al., 2020).
Recent observations and mass balance calculations show that TG is
experiencing some of the highest rates of flow acceleration (Mouginot et
al., 2014), discharge (Rignot et al., 2019), thinning (McMillan et al.,
2014; Milillo et al., 2019; Shepherd et al., 2019) and grounding-zone
retreat (Rignot et al., 2014; Milillo et al., 2019) across the entire ice
sheet. For example, over the past four decades net mass loss from TG is
calculated to have increased from 4.6 Gt yr-1 during the period
1979–1989 to 34.9 Gt yr-1 from 2009 to 2017 (Rignot et al., 2019).
Its configuration, on a reverse-bed slope with direct connectivity to the
deep WAIS interior (Holt et al., 2006), and its wide marine-terminating ice
front (>120 km), with only small, unconfined frontal ice shelves,
implies that TG is particularly susceptible to retreat via marine ice-sheet
instability (Weertman, 1974; Hughes, 1981; Schoof, 2007; Vaughan and
Arthern, 2007). Furthermore, a significant retreat in this system could lead
to a much wider WAIS retreat, and the future behaviour of this glacier system
is now in the spotlight (e.g. Joughin et al., 2014; Scambos et al., 2017).
Regional bathymetry for the Amundsen Sea Embayment and location of
Thwaites Glacier (TG), West Antarctica. Bathymetry is from IBCSO (Arndt et
al., 2013); arrows show observed (solid) and inferred (dashed) pathways for
CDW across the continental shelf towards the grounding zones of Pine Island,
Thwaites and Smith glaciers (following Nakayama et al., 2013; Dutrieux et al.,
2014) and along the Dotson–Getz trough (Ha et al., 2014). PIT is Pine Island Trough;
PITE is Pine Island Trough East; PITW is Pine Island Trough West; TGT is
Thwaites Glacier Tongue; EIS is Eastern Ice Shelf; other ice shelves (I.S.)
are also labelled. White outlines north of TG are mapped positions of the
B-22A iceberg from 2002, 2010 and 2018, from south to north. Note the more
blurry look of the bathymetry in front of TG (in IBCSO this bathymetry
is based on the Tinto and Bell, 2011, gravity inversion and interpolation),
where ship access has been hampered before austral summer 2018/2019 by
persistent fast ice and the presence of the B-22A iceberg.
At present, the eastern and central parts of TG are fronted by two
protruding floating ice masses, the Eastern Ice Shelf (EIS) and the Thwaites
Glacier Tongue (TGT), which extend for 40–50 km beyond the grounding zone,
to the west of which a 20 km wide mélange of icebergs and sea-ice exists
(Fig. 2). For simplicity, we shall refer to these floating ice masses
collectively as the Thwaites Ice Shelf (Fig. 2a; see Heywood et al., 2016).
The TGT extends from the fastest-flowing region of TG (Fig. 2a) and has, on
multi-decadal timescales, advanced up to 130 km from the grounding zone
before the majority of the floating tongue has calved (MacGregor et al.,
2012). As a result, marine areas beyond this have been rendered
inaccessible by remnants of the TGT as they have drifted north-northwest,
including the very large B-10 and B-22A icebergs that remained grounded on
the continental shelf for decades after they had calved before 1965 and in 2002,
respectively (Fig. 1) (Ferrigno et al., 1993; Rabus et al., 2003; MacGregor
et al., 2012). In contrast, the EIS remains pinned on a sea-floor high that
restricts its flow (Rignot et al., 2001; Tinto and Bell, 2011; Jordan et
al., 2020) and induces shear between the EIS and TGT. Satellite imagery
confirms that since 2006 increased crevassing and fracturing has weakened
the shear zone between the EIS and TGT (Kim et al., 2015), with the two ice
shelves remaining connected until 2010 (MacGregor et al., 2012). Due to its
inaccessibility, few marine observations have been made on the inner continental shelf
in front of TG (Jacobs et al., 2012). The existing oceanographic data, along
with more comprehensive results from Pine Island Bay, confirm the presence
of CDW in the deep troughs east and north of the EIS (Dutrieux et al., 2014;
Jenkins et al., 2016) and identify these troughs as potential pathways for
warm water to the TG grounding zone (Fig. 2a; Milillo et al., 2019).
(a) New MBES grid for the inner Amundsen Sea Embayment.
Ice-velocity data from the MEaSUREs V2 dataset (Mouginot et al., 2019);
grounding lines for 1992 and 2011 are from Rignot et al. (2011) and that
for 2017 is from Milillo et al. (2019); red arrows delineate CDW pathways following
Dutrieux et al. (2014) and Milillo et al. (2019). The black dashed line
marks the boundaries of the drainage basin of Thwaites Glacier (Vaughan et
al., 2001). (b) NBP19-02 data coverage versus other MBES datasets (Table 1).
The dark blue coastline illustrates the ice-shelf and ice mélange extent
during survey on NBP19-02 and was digitised from Landsat 8 imagery.
(a) High-resolution bathymetry map of the inner Amundsen Sea shelf
in front of TG and the adjacent part of Pine Island Bay showing the
large-scale sea-floor morphology including bathymetric troughs (Thwaites Trough, T2–T4; main
axes highlighted by black dashed lines) and highs (H1–H3) that form a broad
NNE–SSW ridge continuing into a ridge further offshore in Pine Island Bay,
northeast of the Eastern Ice Shelf (white dashed line). (b) Mapped sea-floor
landforms; streamlined features show the former flow direction of an
expanded TG (white arrows). (c) Cross-sectional profiles of the bathymetric
troughs; locations of profiles in (a).
Regional bathymetric compilations for the ASE shelf use multibeam
echo-sounder (MBES) data where available in offshore regions (Nitsche et
al., 2007, 2013; Arndt et al., 2013), with gravity inversions and a limited
amount of echo-sounding data from autonomous underwater vehicles (AUVs) for sub-ice-shelf cavities (Jenkins et al., 2010; Tinto and Bell, 2011; Millan et al.,
2017; Jordan et al., 2020). These datasets have identified
glacially modified depressions on the continental shelf that act as conduits
for CDW transport towards present-day ocean-terminating glacier margins in
the ASE (Fig. 1) (e.g. Nitsche et al., 2007; Walker et al., 2007; Jacobs et
al., 2012; Nakayama et al., 2013). Landward of the MBES data coverage that
existed prior to this study, gravity inversions had indicated the presence
of a NE–SW-trending ridge on which the EIS is pinned (Rignot, 2001; Tinto
and Bell, 2011; Millan et al., 2017). Millan et al. (2017) reported that
the ridge is interrupted by at least three channels with water depths
between 600 and 1000 m, interpreted to be potential CDW pathways towards the
grounding zone.
Considering the use of sea-floor bathymetry at higher spatial scales (than
regional compilations), the analysis and interpretation of submarine glacial
landforms revealed by MBES datasets provides important information on the
dynamics and configuration of former glaciers and ice sheets. On the inner
ASE shelf, for example, the bed of an expanded PIG has revealed the past
flow direction of a large ice stream that extended more than 400 km to the
continental shelf break (Evans et al., 2006; Graham et al., 2010; Jakobsson
et al., 2012), as well as evidence for extensive erosion by subglacial water
during past glaciations (Nitsche et al., 2013; Kirkham et al., 2019). These
offshore areas also contain well-preserved information on the form and
composition of the former ice-sheet bed that may, by analogy, shed light on
basal conditions under the modern ice sheet (e.g. Clark et al., 2003; Ó
Cofaigh et al., 2005). The roughness of an ice-sheet bed, or its variation
in the vertical over a certain horizontal distance, is a primary control on
basal drag, and therefore ice-flow velocity, and can be analysed for past
ice-sheet beds from MBES datasets (offshore) or from satellite-derived digital elevation models (onshore) (e.g. Falcini et al., 2018). Even small (metre-scale) obstacles on
the bed have been shown, theoretically, to exert critical basal drag on an
overlying ice mass (e.g. Nye, 1970; Schoof, 2002). The great value in
analysing MBES datasets for this purpose lies in their higher-resolution and
even two-dimensional spatial coverage when compared with radar or
seismic-reflection data acquired in over-ice studies (Spagnolo et al.,
2017). Previous roughness analyses (from contemporary ice-sheet beds) have
associated fast-flowing ice with smoother beds (e.g. Siegert et al., 2004;
Rippin et al., 2011); however, recent papers acknowledge that the picture is
likely to be much more complex than this with observations of fast flow
occurring over even hard, rough beds, including at TG (Schroeder et al.,
2014), and acknowledging that processes acting at a variety of spatial
scales (including erosion and deposition) will affect spatially varying bed
conditions and roughnesses (Jordan et al., 2017; Falcini et al., 2018).
Here, we present the first direct observations of sea-floor bathymetry
adjacent to Thwaites Ice Shelf acquired as part of the first International Thwaites Glacier Collaboration (ITGC) cruise on
RV/IB Nathaniel B. Palmer in January–March 2019 (cruise NBP19-02). In the first part of the
paper, we use these data to investigate the character (bed geometry and
substrate composition) of topographic highs that were former grounding zones and
ice-shelf pinning points as well as to better resolve sea-floor troughs as
potential modified CDW pathways to the modern Thwaites grounding zone. In
the second part of the paper, we investigate the roughness characteristics
of this palaeo-glacier bed as a potential analogue for the current bed of TG,
and we relate flow-line roughness to the drag contribution of an overriding
ice mass. We compare bed roughnesses and basal drag contributions from
bathymetric profiles from the inner ASE shelf to bed profiles from upstream
areas of PIG and TG, as well as to a smooth palaeo-ice-stream bed
offshore the nearby Getz A Ice Shelf. To reflect these two components of the
paper we describe (1) the observational (geophysical) datasets used and
interpret the new bathymetric dataset, which is also provided as a
publicly available stand-alone grid; and (2) the spectral approach and how
we use it to quantitatively examine the roughness and basal drag
contributions from former and modern TG beds. We use sea-floor landform
evidence to describe both the flow of an expanded TG over the area as well
as the spatial variability in bed composition over a series of topographic
highs that once acted as both the grounding zone for TG and as pinning
points for its ice shelf. We demonstrate that the offshore area just seaward
of Thwaites Ice Shelf is an appropriate analogue for the modern grounding
zone of TG, both in terms of its bed characteristics and in the effect of
its rugged bed topography on ice flow, by calculating drag contribution for
different scales of roughness. Finally, we highlight the importance of
high-resolution MBES observational data for constraining gravity inversions
and regional bathymetry compilations, which are essential boundary
conditions for predictive numerical modelling experiments and for
accurately calculating the flux of warm water to the grounding zone.
Methods I: multibeam echo-sounder (MBES) datasets
During ITGC cruise NBP19-02, the marine areas in front of TG were unusually
clear of sea ice and icebergs, providing a unique opportunity for bathymetric
data acquisition at the margin of Thwaites Ice Shelf (Larter et al., 2020).
MBES data were acquired using a hull-mounted 1∘×1∘
Kongsberg EM122 echo sounder with 288 across-track beams and an operational
frequency in the range 11.25–12.75 kHz. Navigation information and vessel motion
information, used to correctly locate depth measurements in real time, were
taken from the ship's Seapath 330, a combined GPS and motion reference unit.
The MBES was configured with “high-density equidistant” beam spacing,
meaning that more than one sounding can be produced per beam (up to 432),
effectively increasing across-track resolution, and in “dual-ping” mode,
which ensures equal across- and along-track sounding spacing. As an example,
in 600 m water depth with maximum port and starboard beam angles set at 60∘ from nadir (typical conditions and
settings on NBP19-02), this results in a sounding spacing on the sea floor
of ∼5–7 m; in 1200 m water depth (near maximum survey depths
during NBP19-02) this sounding spacing would effectively double to 10–14 m.
Here, in addition to this new dataset, we have compiled all available MBES
data in the area from UK, US, German, Swedish and Korean expeditions (Table 1; Fig. 2) to produce gridded bathymetric data products. Note that the
sounding spacing achievable by each MBES system varies considerably
depending on the system setup, with older systems generally attaining lower
spatial resolution. For example, at 1200 m water depth and maximum beam angles 60∘
each side of nadir, the Kongsberg EM120 MBES would achieve an across-track sounding
spacing of only 22 m and the SeaBeam 2112 MBES only 35 m. Together, these
two systems were responsible for acquiring data from five cruises in the
area (Table 1).
Research cruises that acquired MBES data used in this compilation.
IEDA MGDS is the Interdisciplinary Earth Data Alliance Marine Geoscience
Data System (USA; http://www.marine-geo.org/index.php, last access: 21 January 2020); UK PDC
is the United Kingdom Polar Data Centre (UK; https://www.bas.ac.uk/data/uk-pdc/, last access: 21 January 2020); BAS is the British Antarctic Survey; AWI
is the Alfred Wegener Institute (Germany); LDEO is the Lamont-Doherty Earth
Observatory of Columbia University; KOPRI is the Korea Polar Research
Institute.
For NBP19-02, data processing was performed on board using MB-System (Caress
and Chayes, 1996; Caress et al., 2020) in order to apply optimal sound
velocity profiles (SVPs) to each data file and to remove erroneous
soundings. Ray tracing and sea-floor depths were calculated using SVPs
generated from conductivity–temperature–depth (CTD) and expendable
bathythermograph (XBT) casts made during NBP19-02 (Larter et al., 2020).
Most of the other bathymetry datasets were also initially ping edited during
each respective cruise; however, minor additional cleaning was performed in
MB-System and QPS Fledermaus (Mayer et al., 2000) after the datasets were
collated when clear outliers could be easily identified. Ultimately, and to
accommodate the different resolutions of the original datasets, the
bathymetric sounding data were gridded in MB-System using a Gaussian
weighted mean filter algorithm to produce an isometric 50 m digital
elevation model (DEM) for the sea floor on the southern ASE shelf. A degree
of interpolation was applied to the final grids in data gaps only, filling
areas six cell widths away from cells with real soundings, i.e. for a 50 m
grid interpolation will fill cells up to 300 m away from a cell with real
soundings. A lower-resolution DEM (500 m grid cells) was produced for
studies that typically use coarser bathymetric information. Together, the
50 and 500 m DEMs are presented as a stand-alone regional mid-resolution
bathymetric dataset (Hogan et al., 2020) In addition, in order to examine the nature of specific
sea-floor features (e.g. ice-shelf pinning points), higher-resolution grids
(30 m grid cells) were produced where sounding densities allowed (e.g. Fig. 4). Final grids were visualised and analysed in QPS Fledermaus 7.8.6 and
ArcGIS 10.6. Sea-floor trough and channel metrics (including widths, depths,
symmetry, form ratio, u-/v-shape characterisation) were derived using the
methods described in Kirkham et al. (2019); the reader is referred to Fig. 2 of Kirkham et al. (2019) for a graphical depiction of the channel metrics
measured.
Detailed maps of the MBES data and their first derivative and slope
over the sea-floor highs in front of Thwaites Glacier. Panels (a) and (c) show the H3
high. Panels (b) and (d) show the H2 high and western flank of H1. Red arrows in (a) and
(b) point to gullies incised into the seaward flanks of the highs; the white
lines in (c) and (d) mark glacial lineations; bl shows the isolated blocks of
H3, and black arrows in (a) and (c) denote their possible transport paths,
with the black dotted lines in (a) illustrating semicircular indentations;
white arrows in (c) point to a channel at the base of one of the blocks;
blue arrows in (a) indicate the downslope transport direction of material
into sediment fans at the front of H3 highlighted by bulges in the contours
(contour levels 1100, 1125 and 1150 m). Black dashed lines in (c) and (d)
locate the profiles in Fig. 5a. GZW is grounding-zone wedge.
Results I: a new bathymetric compilation for the inner Amundsen Sea
Embayment shelf
Our bathymetric compilation includes more than 2000 km2 of new MBES
data between the EIS and the TGT and west of the TGT that provides
near-continuous bathymetric coverage for ∼40 km north of the
present-day ice-shelf margin (Figs. 2, 3). Data gaps remain in the western
part of the area in front of the ice mélange, east of Crosson Ice Shelf,
as icebergs and bergy bits released from the ice mélange persistently
covered this region during NBP19-02. In addition, perennial fast ice and
huge icebergs, such as the 80 km long and 45 km wide iceberg B-22A, that
calved periodically from the TGT and then moved slowly north- and northwest,
thereby episodically running aground, have generally prevented survey
between TGT and Crosson Ice Shelf (see area with B-22A outlines in Fig. 1).
The sea-floor bathymetry offshore Thwaites Ice Shelf is dominated by an
elongate depression oriented NNE–SSW (Thwaites Trough) and a series of
topographic highs (H1-H3) along its southern margin (Fig. 3a). The
depression is characterised by water depths of 1100–1250 m, which is 200 to
400 m deeper than the sea floor on its flanks; it typically has a relatively
flat or gently inclined floor (Fig. 3a, c). Although the depression appears
to be continuous for at least 75 km, and connects with areas of deep
(>1300 m) sea floor directly north of the EIS and in Pine Island
Trough further east (Fig. 2a), its width varies significantly along its
length and the flanks are discontinuous in form. As a result, we do not
define this feature as a channel, which implies incision by water flow,
but rather as a small trough. The topographic highs that make up the
southern flank of the trough (H1-H3) decrease in height (above the
surrounding sea floor) from NNE to SSW and appear to form a broad
(>15 km) but discontinuous ridge, also oriented NNE–SSW. The
large, discontinuous ridge is the extension of a bedrock ridge in Pine
Island Trough to the east that has the same orientation (Figs. 2, 3a;
Nitsche et al., 2013). The most prominent high (H1) occurs immediately north
of the EIS with a shallowest recorded water depth of just 82 m and extends
at least 40 km in a north–south direction. The northern part of the EIS is
pinned, about 45 km downstream of the grounding zone (Rignot et al., 2001;
Tinto and Bell, 2011; MacGregor et al., 2012), on the southern part of this
high, forming an ice rumple in the EIS (Matsuoka et al., 2015). The
shallowest water depths on the two highs H2 and H3 (from NNE to SSW) are 362
and 611 m, respectively. Indeed, a pinning point for TGT on H2 has been
identified from remote-sensing data (Rignot et al., 2011), but the TGT must
have fully retreated from that point prior to NBP19-02. North of the trough
and ridge (north of 74∘30′ S) is an area of rugged morphology
characterised by shallow sea-floor ridges and deep basins (>1400 m); this area merges with similar terrain in Pine Island Trough described by
Nitsche et al. (2013) as their “area 2” (Fig. 2). East of the EIS, the
eastern flank of H1 is just exposed but the bathymetry is dominated by a
deep (1000–1200 m), rugged area of sea floor, bounded on its eastern edge by
a bedrock high in Pine Island Bay that continues southeastwards towards the
grounding zone (Fig. 2a). The deepest part of this area appears to form a
poorly defined bathymetric trough oriented NNE–SSW (T4; Fig. 3a);
oceanographic measurements and models confirm that this deep acts as a
pathway for CDW towards grounding lines in western Pine Island Bay (Fig. 2a)
(Dutrieux et al., 2014; Nakayama et al., 2019).
Glacial landforms
The large-scale morphology of the sea-floor offshore Thwaites Ice Shelf is
overprinted by linear features oriented subparallel to the trough and
ridge. Streamlined subglacial landforms occur in areas where bedrock crops
out at the sea floor, either on topographic highs or interrupting the smooth
trough floor or rugged basin floors (Fig. 3a, b). These features are
identified as crag and tails by their tapering form and are 750–4000 m long,
200–2000 m wide and 25–250 m high (Figs. 3, 4, S1a in the Supplement), as well as their morphological
similarity to crag and tails from other deglaciated terrains (e.g.
Dowdeswell et al., 2016; Maclean et al., 2016; Nitsche et al., 2016). The
wider southern ends of the crag and tails are rugged and have significant
relief, suggesting bedrock composition, whereas the northern ends are smooth
and elongate, indicative of a sedimentary composition. These landforms are
produced subglacially as glacier ice flows across bedrock obstacles
producing the characteristic morphology through erosion and deposition (Benn
and Evans, 2010; Nitsche et al., 2016). The tapering of these features
north-northeastwards indicates palaeo-ice flow of TG in this direction
towards Pine Island Trough (Fig. 3b); east of the EIS the orientation of
these landforms varies from N–S to NW–SE, depicting flow around the H1 high
(Fig. 3b). Curved or semicircular moats – crescentic scours (Lowe and
Anderson, 2003; Graham et al., 2009; Graham and Hogan, 2016) – occur around
the southern (upstream) sides of some crag and tails (Figs. 3b, 4a, S1d) and
are suggestive of erosion by meltwater or, alternatively, a till slurry or
mobile basal ice, upstream of bedrock obstacles (see Graham and Hogan,
2016). On the H2 and H3 highs, subtle elongate ridges separated by linear
grooves also occur (Fig. 3a). These glacial lineations have parallel sides;
lack a pronounced and wider end; and are 1000–2500 m long, 100–200 m wide
and 2–10 m high; their crest-to-crest spacing is typically 200–500 m (e.g.
Fig. S1b). These features, which were produced subglacially, have relatively
short elongation ratios (<10:1) and are oriented parallel to
crag and tails also on the tops of the highs but are slightly oblique to
crag and tails in the trough (Fig. 3). A distinct but discontinuous scarp is
mapped on the top of the H2 high, upstream from its frontal edge (Figs. 3,
4b, d). The scarp has a curved planform and a steep (3–4∘)
northern and gentle (0.5∘) southern slope; glacial lineations
occur on the gentle back-slope of this feature which extends for about 15 km
in a SW–NE direction. The asymmetric geometry and lineated back-slope of
this landform identify it as a grounding-zone wedge (GZW; Fig. S1c) (Alley
et al., 1989; Larter and Vanneste, 1995; Dowdeswell and Fugelli 2012;
Jakobsson et al., 2012), i.e. a wedge of sedimentary material that built up
at the grounding zone when it was stable for a time on the H2 high. This
feature is interrupted, however, by a ∼40 m deep groove or
small channel with bedrock ridges visible on either side, suggesting that the
sedimentary wedge is not thick enough to fully bury the underlying
topography; i.e. it is only tens of metres thick. Discrete 6–10 m deep
linear to curvilinear furrows with small berms (4–6 m) were mapped on H3 and
north of the GZW front scarp (Fig. 4a, b); these are interpreted as iceberg
plough marks.
Sea-floor highs in the area are also variously gouged and streamlined,
resulting in a pattern of grooves and bedrock ridges (Fig. S1e). Grooves on
the H1–H3 ridges occur on their southern (upstream) parts and exhibit a
range of orientations that probably relate to the structure of the
underlying bedrock exploited by glacial erosion. The grooves are typically
<20 m deep, <200 m wide and <6000 m long. The
surfaces of sea-floor highs north of the H1–H3 ridge have a more streamlined
appearance resulting from shallow, semi-parallel shallow grooves that are
preferentially aligned with the crag and tails (Figs. 2, 3). Streamlined
bedrock highs of this type are typical of inner-shelf morphologies around
Antarctica (e.g. Wellner et al., 2006; Livingstone et al., 2013) including
in the adjacent eastern part of Pine Island Bay (Nitsche et al., 2013).
Taken together, the orientations of the streamlined subglacial landforms
(crag and tails, glacial lineations, bedrock grooves/ridges) define the
former ice-flow directions of an expanded TG (depicted by white arrows in
Fig. 3b), confirming that this area is the former bed for grounded glacier
ice.
Trough and channel metrics
Multiple bathymetric troughs and bedrock channels were mapped and analysed
in the area beyond Thwaites Ice Shelf as part of this study (Fig. 3a).
Troughs and channels in the adjacent part of Pine Island Bay have been
described comprehensively by Nitsche et al. (2013) and Kirkham et al. (2019). The larger troughs in our study area, which have also been
identified on gravity-derived regional bathymetry maps (Millan et al., 2017;
Jordan et al., 2020), are considered important as potential pathways for the
transport of CDW towards the grounding zone of TG and warrant full
description here. We distinguish these comparatively larger troughs, based
on their size, connectivity and variable flank form (as described above),
from the channels which are notably smaller in scale (Fig. S2). The latter have continuous, parallel-sided flanks and undulating thalwegs and incise into rugged sea-floor areas interpreted as bedrock (e.g. Fig. S1e). It is widely
accepted that channels of the latter type were eroded by pressurised
subglacial water flow (Lowe and Anderson, 2003; Nitsche et al., 2013;
Kirkham et al., 2019), whereas the troughs likely relate, at least in part,
to underlying geological structures such as dykes and tectonic deformations
(see Gohl et al., 2013) that have been variously modified by ice, as well as
possibly by subglacial water flow.
Cross-sectional analyses of the troughs (n=166) reveal their large
scale, with average widths, depths and cross-sectional areas being 2090 m,
90 m and 144 000 m2, respectively (Fig. S2). The troughs are typically
10–30 times as wide as they are deep, although we note that there is a
significant size difference between the main NE–SW trough (Thwaites Trough)
and the remaining troughs (Figs. 3a, S2). By comparison, the bedrock
channels (n=822) are on average 520 m wide, 50 m deep with a
cross-sectional area of 18 000 m2. The channels are generally 5–10
times wider than they are deep. The derived b values, which characterise
cross-sectional shape (Pattyn and Van Huele, 1998), suggest that the bedrock
channels are between v and u shaped, whereas the larger troughs have no
dominant cross-section shape (Fig. S2). In general, the trough floors are
flat or inclined in cross profiles (Fig. 3c) and are gently undulating in
along-trough profiles.
The main Thwaites Trough is oriented NNE–SSW, which is oblique to the northerly
palaeo-ice-flow directions immediately in front of Thwaites Ice Shelf (Fig. 3b). This indicates that, at the time that the subglacial landforms were
produced, ice was thick enough not to be fully steered by even major
elements of the bed topography. The two southernmost troughs that we have
analysed (T2 and T3 in Fig. 3a) are oriented perpendicular to Thwaites
Trough (i.e. NNW–SSE), and the troughs north and east of the EIS are
generally aligned with palaeo-ice-flow directions (Figs. 2, 3a). Note that
the T1 trough is not well covered by our MBES dataset and is not discussed
in detail here. The T2 and T3 troughs, whose floors have water depths of
800–900 m, separate the H1–H3 bathymetric highs and are of interest as
potential pathways for CDW to the TG grounding zone. Long profiles from the
T2–T4 troughs (Fig. S3) identify sill depths along the pathways of the
troughs that may act as important pinch points for ocean circulation, in
particular if they impede CDW inflow towards the Thwaites grounding zone
(cf. De Rydt et al., 2014). T2 has a smooth long profile with a prominent
sill at 710 m depth at about 107∘3′ W, 75∘3.6′ S, whereas
T3 has a rugged profile with three bathymetric sills in its northern (ice
distal) part with depths of 750–760 m, as well as several other sills further south
(ice proximal) around 780 m water depth (Fig. S3a). The bathymetry around
T4, east of the EIS, is generally deeper (>1000 m) than most of
T2 and T3, so the main constriction on this trough seems to be where it crosses the
NE–SW-trending sea-floor ridge in Pine Island Bay (Fig. 2a). At this
location, around 105∘24.4′ W, 74∘35.4′ S, there is a
sill at 880 m depth (Fig. S3d). Channel widths at these locations are 5000 m
for the T3 sills and 2500 m for the T4 sill (although this is not the only
interruption in the ridge in Pine Island Bay). Widths were measured at 500 m
depth as this is taken to be a reasonable top-CDW depth for the area (based
on oceanographic measurements; Bastien Queste, personal communication, 2020). The bathymetry of the highs
west of T2 is >500 m depth, meaning that CDW could effectively
flood over this topography rather than be constrained to the trough;
however, if it was topographically routed (see Nakayama et al., 2019)
through T2, then the channel width at the sill is 4700 m (at 640 m water
depth).
Bathymetric highs and ridges
Owing to the importance of sea-floor highs in front of the Thwaites Ice
Shelf as barriers to CDW inflow, and as former ice shelf/sheet pinning
points, we examine the morphology of the discontinuous NNE–SSW-trending
ridge in detail (Fig. 4). The ridge comprises the H1–H3 highs separated by
the two troughs described above (T2 and T3; Fig. 3a). The width of the ridge
varies significantly, from 6 km in the SW of the study area to at least 40 km over H1, although we acknowledge that data coverage is limited. In some
places, the bathymetric highs are strikingly flat topped. These planar
features are accentuated in maps of the first derivative of bathymetry,
slope, which reveals both low slopes (<2∘) (Fig. 4c,
d) and low roughness over H2, H3 and the western part of H1. The
continuation of the ridge further north into Pine Island Trough has a
similar surface expression but is generally narrower (Fig. 3a). These areas
with low surface slopes are atypical when compared with other bathymetric
highs in the area, which have rugged surface morphologies characterised by
bedrock grooves and channels (Figs. 2, 4d) (Nitsche et al., 2013; Arndt et
al., 2018; Kirkham et al., 2019). Instead, the low slope values are similar
to those derived for the base of the troughs in front of Thwaites Ice Shelf
(Fig. 4a) and the sediment-filled basins just seaward of the Pine Island Ice
Shelf front (Nitsche et al., 2013; Kuhn et al., 2017). At least two distinct
levels of flat-topped surfaces occur at 400 and 640 m water depth (Fig. 5). We suggest that this morphology was generated as the highs were
overridden and eroded by a formerly expanded TG and Thwaites Ice Shelf (with
the necessary ice thickness to reach the depth of the flat-topped surfaces).
A value of ∼400–500 m is similar to ice-shelf thicknesses for
Thwaites Ice Shelf today (Griggs and Bamber, 2011; Jordan et al., 2020), and
a prevalence of flat-topped highs at this depth may, therefore, support
recent modification of the sea-floor highs at TG. In contrast, the deeper
flat top of H3 (640 m depth) was probably formed at an earlier stage, as was
the flat top of the high in Pine Island Trough, as that area is known to
have been ice-free (sheet and shelf) for at least the last 10 kyr (e.g.
Kirshner et al., 2012; Hillenbrand et al., 2013). The interpretation of
erosion or planing off by an ice shelf is supported by the occurrence of
glacial lineations on the tops of the highs (Fig. 3b), which are in line
with modern ice-velocity vectors (Mouginot et al., 2019) but oblique to the
orientation of crag and tails in the troughs, thus indicating a change in
flow direction from grounded ice flow to ice-shelf flow over the high. A
similar interpretation was made for the lineated surface of a former pinning
point of the Pine Island Ice Shelf (PIIS) that has been recently exposed by
ice-shelf calving events (Arndt et al., 2018), although that feature was not
planed off to form a flat-topped high but rather has a stepped and rugged
surface morphology albeit with some gently sloping parts (see their Fig. S3). We note, however, that alternative explanations are possible for this
morphology, namely that the flat tops are an inherited feature produced by
erosion down to horizontal bedrock strata or that rugged bedrock highs,
which are typical of the inner Amundsen Sea shelf (see Nitsche et al.,
2013), were mantled by some thickness of glacigenic material that levelled
the topography below. The former is relatively easy to discount accepting
that the inner shelf of the ASE is composed of crystallite basement with
seismic-reflection profiles showing that northward-dipping sedimentary
strata only occur on the middle and outer shelf (see Graham et al., 2009;
Gohl et al., 2013). In this setting close to the current TG grounding zone,
it is perhaps easier to conceive of the latter explanation that rugged
bedrock features were mantled by glacigenic material delivered to the area
when the grounding zone was located on or near the highs and then flattened
by some degree of glacial compaction and/or erosion as it was overtopped by
TG and the subsequent Thwaites Ice Shelf. This is consistent with our
suggestion for the formation of these flat tops as we cannot tell from our
data either what sediment thickness occurs on the highs or how much erosion
took place, and we acknowledge that the amount of ice-shelf erosion may have
been small, only skimming unconsolidated material from the surface of
the highs. The presence of GZWs and glacial lineations on the highs, and
sub-bottom profiler data (Fig. S4), confirms that at least some thickness of
unconsolidated material occurs on the highs, but seismic-reflection profiles
would be required to fully capture the internal structure of these features.
Flat-topped highs in the Amundsen Sea. (a) Cross-sectional
profiles over H1–H3 highs at Thwaites Glacier (for location of profiles, see
Fig. 4c, d), further offshore in Pine Island Bay (PIB; location of high in
Fig. 2a, location of profile in Fig. 5b) and offshore from the Getz A Ice
Shelf (location of high in Fig. 1; location of profile in Fig. 5c), showing
sea-floor highs planed off at different depth levels. The flat portions of
the profiles are marked with grey bars and the depth elevation for that
flat top given above, so “H1:400 m” means the flat part of the profile
over H1 high is at 400 m water depth. (b) MBES of flat-topped highs part of
the discontinuous sea-floor ridge in PIB. (c) MBES of a flat-topped high
with glacial lineations (white lines) just in front of the Getz A Ice Shelf
(following Nitsche et al., 2016). White arrows show direction of past ice flow
based on streamlined subglacial landforms.
No matter the exact formation mechanism, the flat-topped morphology of the
highs in our study area is striking and notably rare for sea-floor highs
around Antarctica. We note a similar but less pronounced terrain over some
highs along the same structural ridge in Pine Island Bay, i.e. east of the
EIS (Fig. 5b), and a solitary very flat topped high, with comparable
dimensions to those offshore TG, is visible <5 km north of the
Getz A Ice Shelf (Fig. 5c). Beyond these rare examples, the best analogy
for this morphology probably comes from a set of “iceberg terraces” on
terminal moraines at the mouth of a Svalbard fjord, which display remarkably
flat topped surfaces at several bathymetric levels. These are interpreted to
have formed as tabular, flat-based icebergs overtopped and eroded morainal
sediments (Noormets et al., 2016). It should be noted, however, that
sediments of this morainal bank complex probably consist of unconsolidated
material that has not been overridden (or compacted) by grounded ice,
meaning that they are likely more erodible than basement highs in front of
Thwaites Ice Shelf. Nevertheless, the flat-topped morphology is suggestive
of a sedimentary cap on the pinning points at TG, and the fact that similar
features exist in Pine Island Bay and beyond the Getz A Ice Shelf may
indicate that pinning points with such sedimentary caps are
widespread on the inner shelf in the Amundsen Sea.
New geomorphic information is also revealed by the flanks of the highs
(Fig. 4a, b). The northern (ice distal) flanks of the H2 and H3 highs are
characterised by subtle downslope-trending gullies that transition into a
smooth but inclined sea floor in the troughs at a distinct break of slope.
There are also a few, discrete semicircular indentations in the scarp
between the surface of the highs and their flanks (Fig. 4a). The gullies
have simple non-branching geometries, have small dimensions (widths 150–700 m,
depths 5–50 m, lengths <2 km), and typically define broad u shapes
in cross section, although some v-shaped forms are present. In addition,
their form is consistent with other Antarctic submarine gully systems (e.g.
Fig. S1f; Gales et al., 2013; Post et al., 2020). Thus, we interpret the
gullies as the result of the downslope mass movement of material from the
tops and sides of the H2 and H3 highs via gravitational processes into the
small sediment fans at the base of the slope (Fig. 4a). The semicircular
indentations may be the headwalls of small slide scars (cf. Noormets et al.,
2009; Gales et al., 2013). One 6 km by 2.6 km segment of the H3 high is
somewhat detached from other parts of the ridge and appears particularly
fragmented on its flanks (Fig. 4a). About 1500 m south of this, on the main
H3 high, is a distinct break in slope with the same planform shape as the
back of the detached segment that we refer to as a “block” (bl in Fig. 4a, c). Similarly, 2 km west of this block is another somewhat isolated 3 km
by 1.8 km block of H3 that is incised by gullies on its northern front and
lacks lineations on its surface (Fig. 4a). We consider several
interpretations for these features. First, it is possible that they are
detached blocks of the H3 high that had been displaced downslope over a
short distance (black arrows in Fig. 4a, c), remaining largely intact, but
subsequently affected by some gravitational collapse of their flanks. Slide megablocks with similar dimensions (or larger), non-crystalline
compositions and degraded flanks are known from, for example, the Hinlopen
Slide scar on the northern Barents Sea margin (Vanneste et al., 2006; Hogan
et al., 2013). The second possibility is that the blocks are small bedrock
highs that have been variously mantled by and surrounded by glacigenic
sediment, either deposited subglacially on their surfaces or as it was
transported downslope by gravity-driven processes (towards the sediment
fans) from the H3 high (see blue arrows in Fig. 4a). If the latter case is
true, then the pronounced semicircular indentation on the eastern block
(labelled in Fig. 4a) may be an erosional scour mark formed by the
recurrent flow of water, as is evidenced by the small channel on the
eastern side of the block (white arrows in Fig. 4c).
Methods II: bed roughness and basal dragSpectral analysis of bed roughness
The idea that the drag experienced by a glacier can be analysed by treating
the basal roughness as a superposition of sine waves of different
wavelengths (λ) has a long history in glaciology (e.g. Nye, 1970;
Kamb, 1970; Hubbard et al., 2000). In these approaches, Fourier methods are
used to find the drag contributed by roughness that falls within some range
of wavelengths (or band of spatial frequencies). More recently, a similar
approach has treated the longer wavelength undulations that can affect flow
near the upper surface of the ice (Schoof, 2002). Knowledge about the power
spectrum of the basal roughness is an essential input to all of these
studies.
The high-resolution bathymetric grid that we have produced (Fig. 2)
represents the former beds of expanded TG and PIG. As such, it contains
information about bed geometry and roughness that can be used to investigate
the behaviour of glacier ice over this terrain, specifically how roughness
due to bedrock topography and subglacial landforms at various wavelengths,
λ, might generate form drag within the ice (Schoof, 2002). As
an example, Fig. 6a shows a bed elevation profile from Pine Island Bay
(profile 6 in Fig. S5a) sampled at 25 m intervals along a flow line. To
analyse the variance of roughness at each wavelength scale we computed the
power spectrum of the bathymetric topography (e.g. Fig. 6b). It is
conventional to plot the power spectrum as a function of spatial frequency,
defined as f=λ-1, rather than wavelength. This function,
Pf, referred to as the periodogram, shows how the variance
of roughness is distributed among different frequency intervals. Thus, the
variance attributable to roughness within any frequency interval is the
integral of the periodogram over that interval. Figure 6b shows the
one-sided periodogram Pfn, evaluated at equally spaced
frequencies fn=n/a, where a is the length of a moving window. The
periodogram was obtained in MATLAB R2017a using Welch's method (Welch,
1967), with a window of length a=6.4 km and 50 % overlap between
consecutive windows along the bed profile. Within each 6.4 km window we
removed a linear trend from the bed profile and applied a Hamming window
before computing the one-sided power spectrum using the absolute square of
the fast Fourier transform, appropriately scaled. We then averaged spectra
from the multiple windows along the bed profile to provide results for the
flow line as a whole.
(a) Bed elevation (equal to water depth for sea-floor data) versus
distance along flow line. (b) Roughness power spectra
Pn versus spatial frequency
fn. (c) Scaled basal drag contributions βn/β∗ versus
fn for along-flow profile (6) offshore from Pine
Island and Thwaites glaciers (for location see Fig. S5a). The red lines in
(b) and (c) are based on an assumption of Brown-noise power spectrum that
falls off as the inverse square of spatial frequency. At low spatial
frequencies, drag contributions depend on the function F (see
Sect. 4.2) with the two limiting cases shown:
F1 (blue), F2
(black).
Periodograms were computed for a total of 14 palaeo- and modern flow
lines for TG and the Dotson–Getz palaeo-ice stream (locations in Figs. S5,
S6). For TG and PIG, six palaeo-flow lines were picked manually across the
bathymetric grid by tracing lines parallel to subglacial landforms that
indicate palaeo-ice-flow directions (e.g. Fig. 3b, profiles 1–6, Fig. S5a).
We performed calculations for bed profiles from four additional areas for
comparison: (i) modern along-flow bed profiles for TG (profiles 8–9, Fig. S6a), (ii) modern bed profiles for PIG (profiles 10–11, Fig. S6b), (iii) an
area of smooth bed topography on the middle continental shelf in the
Dotson–Getz palaeo-ice-stream trough (profile 7, Fig. S5b), and (iv) six
across-flow profiles from the bathymetric datasets (profiles a–f, Fig. S5a, b). Onshore bed profiles were extracted from the AGASEA (Holt et al.,
2006) and Operation IceBridge (OIB; Tinto et al., 2010, updated 2019)
airborne radar datasets for TG and PIG beds, respectively. Profiles were
selected based on their location, along the central glacier trunk, and their
quality in terms of continuity and fewer outliers. The profiles from the
Dotson–Getz Trough, offshore from the Getz A Ice Shelf (Fig. S5b), were
selected as representative of a sedimentary palaeo-ice-stream bed
characterised by mega-scale glacial lineations (MSGL) (Graham et al., 2009;
Spagnolo et al., 2014). These were extracted from a MBES dataset fully
described by Larter et al. (2009) and Graham et al. (2009).
The power spectrum of natural terrain is often approximated as a power law
in frequency (e.g. Jordan et al., 2017). The results of our spectral analysis
(Figs. 6 and 7) show that a good approximation can be obtained using an
inverse-square power law,
P=Af-2,
where the constant A has units of length. This is the periodogram expected
for a Brown-noise or random-walk elevation profile, as produced by
taking an uncorrelated random step in the vertical direction for each unit
step in the horizontal.
Selection of bed profiles (top), derived power spectra (middle)
and basal drag contributions (bottom) for (a, b) along-flow profiles (1)
and (3) offshore Thwaites Glacier, (c) onshore along-flow bed profile (8)
for Thwaites Glacier, (d)
along-flow profile (7) for Dotson–Getz Trough, and (e) across-flow profile “c” offshore Thwaites Glacier. Profile locations are shown
in Figs. S5 and S6. The red line in power spectra and drag contribution plots
are based on an assumption of Brownian motion (i.e. power decays as inverse
square of spatial frequency). At low spatial frequency, drag contributions
depend on the function F. Two limiting cases are shown:
F1 (blue) and F2
(black).
For Brown noise, the parameter A represents the roughness variance per
unit length of profile. If we consider a section of profile having length
l and restrict our definition of roughness to all wavelengths λ<l, we expect this roughness to have variance obtained by
integrating the periodogram P over frequencies f>l-1. For the
Brown-noise periodogram (Eq. 1), this integration provides
σ2=Al.
Thus, for Brown noise, the variance grows in proportion to the section
length considered, and the rms roughness σ=Al
grows with the square root of the section length (e.g. Jordan et al. 2017).
If we take a longer section of profile, we expect to see larger rms
roughness within it. This makes it clear that, at least for Brown noise, the
roughness can only be characterised by its rms value if reference is also
made to the length scale under consideration. Next, we examine the
consequences of roughness for the drag that resists the sliding of a
glacier. We pay particular attention to the case when the periodogram
follows an inverse-square law (Eq. 1) that is appropriate for a Brown-noise
power spectrum.
Relating bed topography to basal drag
In this section, we will use the power spectra of the high-resolution
bathymetry, together with a theoretical expression for form drag (Schoof,
2002, Eq. 67), to assess how roughness at different scales affects the
drag that opposes glacier sliding. This allows us to consider the
contribution that the observed sea-floor bathymetric roughness at short
wavelengths would make to form drag when covered by flowing ice.
The theory of ice flow over an undulating bed (Schoof, 2002) provides an
approximate expression for the form drag τ, expressed as a basal
shear stress that acts to resist sliding. Here, we use dimensional
quantities rather than the non-dimensional quantities (as used by Schoof, 2002). In our notation, Schoof's (2002, Eq. 67) expression for form
drag becomes
τβ=U.
In this expression, β is the drag coefficient and U is the speed of
ice flow averaged over some horizontal length scale significantly larger
than the ice thickness. Here, we choose this length as a=6.4 km, the
window length used in our spectral analysis. According to Schoof (2002), the
drag coefficient β=∑n=1∞βn is the sum of
contributions, βn. Each contribution βnis caused by
roughness that falls within a frequency band of width 1/a centred at
frequency, fn=n/a. The spatial wavenumbers corresponding to these
frequencies are defined as kn=2πfn.
Schoof (2002) provides an expression for the drag contributed by roughness
within each frequency band. In our notation, this translates to
βn=4β∗kn/k∗3Fkn/k∗h^n2/H2.
In this expression, h^n is the Fourier component of the bed
roughness at spatial frequency, fn. We estimate h^n2=12Pna-1 as appropriate for the Fourier series
defined by Schoof (2002). The one-sided periodogram Pn can be
obtained either directly from the bathymetric observations as described above
(Sect. 4.1) or by fitting the inverse-square power law described by
Eq. (1) to those periodograms (see Figs. 6 and 7 for examples). The
scaling constants are β∗=η/H and k∗=1/H, where
viscosity η and thickness H are representative values averaged over
the length scale a (Schoof, 2002).
We consider two limiting cases for the function F:
5F1kn/k∗=sinh2kn/k∗-kn/k∗2kn/k∗+coshkn/k∗sinhkn/k∗,6F2kn/k∗=kn/k∗+sinhkn/k∗coshkn/k∗sinh2kn/k∗.
These are derived by Schoof (2002) as his Eqs. (65) and (66) for small and
large bed roughness, respectively. We use dimensional quantities, so
kn/k∗h^n/H and Fkn/k∗ in our notation equate respectively to non-dimensional quantities
kn, νh^n and fkn in Schoof (2002).
For sufficiently small wavelengths kn≫k∗, the functions
F1kn/k∗ and F2kn/k∗ both tend to unity. In this case, the contribution to form drag
becomes insensitive to ice thickness and to the choice of function used
(Schoof, 2002).
If the bed follows a Brown-noise power spectrum, we can use the
inverse-square law Pn=Afn-2. Under those circumstances, the drag
contribution βn will grow approximately linearly with frequency at
sufficiently high wavenumbers kn≫k∗:
βn=16ηπ3Aa-1fn.
For the Brown-noise power spectrum, the amplitude of roughness decreases at
shorter wavelengths. Nevertheless, Eq. (7) shows that those
short-wavelength scales will still be more effective at causing form drag
than the longer wavelengths, despite their smaller amplitude. This is
because the factor kn/k∗3 increases faster
than the inverse-square law decreases.
As a consequence of the linear increase in the drag contribution with
frequency, the total drag would become unbounded, and the sliding would
stop, unless the bed of the glacier departs from the Brown-noise assumption
and becomes smooth at scales smaller than some wavelength (Nye, 1970). This
wavelength, λN, provides an upper bound to the spatial
frequencies that cause drag, fN=λN-1=N/a. Under this
assumption, the total drag can be approximated by truncating the sum:
β=∑n=1Nβn=16ηπ3Aa-2∑n=1Nn=8ηπ3Aa-2NN+1.
When λN≪a, so that N≫1, this gives the approximation
β=8ηπ3AλN-2.
Therefore, if the Brown-noise inverse-square law power spectra applies down
to the finest wavelength, λN, the drag will be determined by
that scale, along with the viscosity η, and the coefficient of the
power law A that can be recovered from the periodogram.
It is common in sliding theories to define the slip length, L=η/β. The slip length L is an important quantity that allows us to
make a distinction between two regimes of ice flow. When the slip length is
much larger than the ice thickness H, the drag is too small to induce
significant shearing within the ice column, and the ice can be considered to
slide over the base as a plug flow having uniform velocity with depth.
This is the situation modelled for slippery-based ice streams by MacAyeal
(1989). By contrast, when the slip length is much smaller than the ice
thickness, the drag is able to induce a substantial amount of shearing
through the ice column, so the flow velocity varies significantly with
depth.
Using Eq. (9), we obtain the following expression for the slip length
under the assumption of a Brown-noise power spectrum, truncated at some
frequency, fN=λN-1:
L=λN2/(8π3A).
One consequence of this is that if we wish to infer the amount of form drag
using Eq. (9), or the slip length using Eq. (10), it is not enough to
evaluate the roughness parameter A alone. We must also establish λN, the smallest wavelength that is effective at causing drag.
Results II: assessing roughness and drag contributions for palaeo- and
modern glacier bedsBed roughnesses
The power spectra of selected bathymetric profiles are shown in Figs. 6
and 7. Figure 6b shows that the one-sided periodogram Pfn, computed using the bathymetric profile shown in Fig. 6a
(location in Fig. S5a), has no strong peaks at any particular preferred
scales of roughness. Instead, the periodogram decreases continuously as
spatial frequency increases. This decrease approximately follows the
inverse-square power law appropriate for Brown noise, so that the
periodogram can be approximated as Pn=P(fn)=Afn-2. The
red line in Fig. 6b shows this power law, with a value A=0.1 m. The
spectra are remarkably consistent across many of the profiles considered
(Figs. 7, S7), with the exception of the smoother MSGL area (Figs. 7d, S5b).
There, the Brown-noise inverse-square law can still provide a good
approximation to the periodogram, but the value of A=0.001 m that is
required to provide a good match to the observations is much smaller (Figs. 7, S7p, q).
The power-law approximation to the power spectrum also agrees closely with
power spectra of profiles of bed elevation from airborne radar flown over TG
(Fig. 7c), so the MBES data provide a good analogue to the subglacial
undulations that control the sliding of TG today. Despite improvements in
the methodology of high-resolution radar surveys of the active subglacial
bed (King et al., 2016; Bingham et al., 2017), the MBES data provide a more
detailed view of the shorter spatial scales than airborne or ground-based
radar. Comparisons with previous studies of subglacial roughness are not
straightforward because individual studies have used different window
lengths to investigate roughness (e.g. Jordan et al., 2017; Falcini et al.,
2018). However, for the Brown-noise power spectra in Eq. (1), we expect
the rms roughness for a section of length l to be σ=Al. Most of our spectra are close to the Brown-noise
spectra with A=0.1 m (Figs. 6, 7), and for this value, we would
expect window lengths from 80 to 1000 m to produce rms roughness
estimates in the range 2.8 to 10 m. These values are similar to those
reported previously for glaciated terrains (Jordan et al., 2017; Falcini et
al., 2018).
Basal drag contributions
For the example bed profile in Fig. 6a, values of βn/β∗ obtained using the periodogram shown in Fig. 6b and
Eq. (4) are plotted against spatial frequency fn in Fig. 6c.
The linear dependence predicted by Eq. (7) for the Brown-noise
approximation is shown as a red line in Fig. 6c. In these plots we used a
value A=0.1 m and a representative ice thickness H=1 km.
The expression for the basal slip length (Eq. 10) lets us use the
bathymetry to make a dynamical distinction between regions of fast sliding
with little internal deformation L>H and regions of slow sliding and
shearing flow L<H. Using Eq. (10), the ratio of slip length to ice
thickness is L/H=λN2/(8π3AH). For a value of A=0.1 m and a typical ice thickness scale of H=1 km, this suggests
that features on scales smaller than λN=150 m would provide
sufficient drag to induce significant vertical shearing within the ice.
Since features on this scale are well resolved by the bathymetric profiles
(e.g. Figs. 3, 4) and fall within the range of frequencies where the inverse-square power law applies, we conclude that the form drag produced by the
observed subglacial roughness would have produced significant shearing
within the flow of the grounded ice as it retreated over the highs and
ridges surveyed by the MBES. This suggests that it is important to include
the effects of form drag caused by basal roughness over such terrain, and by
extension over the extant parts of TG today.
A distinction must be made for the region of MSGLs on the Dotson–Getz
palaeo-ice-stream bed (Fig. S5b). Here, the elevation profile is
exceptionally smooth. The spectral analysis confirms this (Figs. 7d, S7p, q),
and the coefficient A that best fits the observations is some 2 orders
of magnitude below the more generally applicable value of A=0.1 m.
Repeating the above analysis with A=0.001 m shows that the power law
would have to apply down to horizontal scales smaller than λN=15 m. Features on this scale are not well resolved in our bed profiles (e.g.
the MBES grids have cell sizes of 50 m). This means that, in contrast to the
more general case, it remains possible that the MSGL terrain is so smooth
that the resulting form drag produced little vertical shearing within ice
that flowed over it, making the ice dynamics of this area more akin to the
flow described for slippery-based ice streams by MacAyeal (1989). This
result is consistent with our understanding of how MSGLs form, i.e. via the
self-organisation of deforming sediment at the bed under fast-flowing ice
(e.g. Spagnolo et al., 2014). We also repeated the analysis in the direction
perpendicular to elongated features (Figs. 7d, S7k–o, q). There is no
evidence that ice flowed in this direction, but the theory can nevertheless
compute the contributions to form drag that would arise in that hypothetical
situation. For most of the across-flow lines (Fig. S7), the power spectra
are similar to the along-flow direction, and the drag contributions at each
frequency are similar. This suggests that the drag coefficient over much of
the surveyed terrain is not especially sensitive to the flow direction. For
the MSGL terrain there does appear to be some indication that drag would be
higher for ice flow in the direction perpendicular to elongated features.
DiscussionImplications from the new bathymetric data
Our results provide the first observation-based, high-resolution geomorphic
characterisation of the coastal bathymetry at TG, a former bed for the
glacier. These data allow us to investigate bathymetric controls on ocean
circulation towards the modern grounding zone, as well as to identify the
locations, water depths and substrate compositions of ice-shelf pinning
points and former grounding zones. The dominant bathymetric features, a
NNE–SSW-trending trough and landward-flanking discontinuous ridge (Fig. 2a),
represent a subtly different morphologic terrain from highly rugged,
basin-dominated areas north and east of the EIS (Fig. 3a) or the
moderate-relief areas of lineated terrain with fewer bathymetric highs in
eastern Pine Island Bay (Fig. 2a) (Nitsche et al., 2013; Arndt et al., 2018;
Kirkham et al., 2019). The continuity and orientation of the trough and
ridge relate to the structure of basement rocks on the inner shelf. NNE–SSW
to ENE–WSW structural lineaments have been identified by previous
aeromagnetic surveys (Gohl, 2012; Gohl et al., 2013), and gravity-derived
bathymetries all resolve a broad NNE–SSW ridge coincident with H1–H3, as
well as deeper troughs on either side of the ridge (Tinto and Bell, 2011;
Millan et al., 2017; Jordan et al., 2020). Thermochronological analyses of
onshore rock samples also infer a NNE–SSW-trending tectonic rift structure
(Spiegel et al., 2016).
We highlight several key differences between our new dataset and the
available regional bathymetric compilations (Fig. 8). Note that we do not
compare our MBES grid with the newly published gravity inversion of Jordan
et al. (2020) as that study utilised the MBES dataset to constrain the
inversion. Beyond that study, for the area of new MBES data in front of TG,
gravity-derived bathymetry generally underestimates sea-floor depths
(average of 119 m; Fig. 8a, b), whereas the IBCSO bathymetry, which is
based on real sea-floor soundings but relies on gravity-inversion elevations
and interpolation in this area (Arndt et al., 2013), generally overestimates
sea-floor depths (average of 65 m; Fig. 8c). All of the regional datasets we
examined fail to capture the higher-frequency topographic variability
revealed by the new MBES data (e.g. Fig. 8d). Although sea-floor highs are
sometimes >100 m shallower than the regional products predict,
this effect is most notable for the troughs, which are in reality 100 to 550 m deeper than gravity-derived bathymetries and 50 to 250 m deeper than in
the IBCSO dataset (Fig. 8d). When we consider cross sections of three
troughs that are potential pathways for CDW to the grounding zone (T2, T3,
T4; locations marked by asterisks in Fig. 8a), the depth errors are up to
250, 500 and 400 m from west to east. Using a conservative top-CDW depth
of 500 m for the TG area (based on hydrographic data acquired during
NBP19-02; Bastien Queste, personal communication, 2020; see Nakayama et al., 2013), we calculate the
cross-sectional area that CDW occupies in these troughs from our MBES data
and from the grid of Millan et al. (2017). We find that the gravity-derived
bathymetry underestimates the cross-sectional areas by 7 %–38 % for two
of the three troughs and that trough T3 between H1 and H2 (Fig. 3a) is not
resolved at all on the Millan et al. (2017) grid (Table S1; Fig. S8).
Taking this one step further, we perform a simple calculation of the oceanic
heat flux through T2 for the two cross-sectional areas (Millan et al., 2017; MBES) and utilise oceanographic observations from the ASE for
ocean temperatures and flow velocities (see Supplement for
methods). The total heat flux through the trough cross section defined by
the gravity inversion is ∼0.5 TW, and for the MBES cross
section it is 1.1–1.3 TW (Table S2). This equates to an underestimation of
the heat flux through T2 based on the gravity-derived bathymetry of
55 %–65 %, or more than a doubling in the heat flux through the trough using
the deeper bathymetry provided by the MBES grid. To fully quantify the
significance of this for the inflow of CDW to the Thwaites ice-shelf cavity
and grounding zone requires the use of an ocean circulation model with the
MBES as its bathymetry and that is, ideally, calibrated by CTD data within
the troughs. Conversely, the identification (and implementation in models)
of critical sill depths along the trough pathways could limit CDW inflow
along certain routes. These findings have implications for the numerical
modelling of warm-water access to the grounding zone, oceanic heat fluxes,
the resultant ice-shelf melting rates, and, ultimately, projected mass losses
from TG and the WAIS. However, our first-pass calculations underline the
importance of high-resolution observational datasets like MBES for capturing
high-amplitude bathymetric variations at short to medium wavelengths (i.e.
λ<103 m), particularly in areas close to ice-shelf
cavities and the grounding zone.
Difference maps between regional bathymetric datasets and the MBES
grid. (a) Millan et al. (2017) minus MBES grid. Yellow asterisks mark the
locations of channels discussed in Sect. 6.1. (b) BedMachine Antarctica
(Morlighem et al., 2019) minus MBES grid. (c) IBCSO (Arndt et al., 2013)
minus MBES grid. (d) Profile data for two profiles for each of the regional
datasets compared with profiles from the MBES grid; profiles are located in
(b). Note that the Millan et al. (2017) and the BedMachine Antarctica
bathymetries are very similar and thus return near-identical bed profiles in
(d); the BedMachine Antarctica grid is included for completeness as the most
recent regional dataset to cover the area, and its authors highlight the need
for more coastal bathymetric datasets (Morlighem et al., 2019).
A new gravity-derived bathymetry model for the Thwaites, Crosson and
Dotson–Getz area, constrained by the NBP19-02 MBES data, produced recently
by Jordan et al. (2020) has improved resolution compared to previous
gravity-derived models as a result of using a strapdown instrument with
closer flight line spacing. Despite the improved resolution of their new
model, Jordan et al. (2020) concluded that still higher-resolution
observations are necessary in areas where knowledge of the bed at scales of
less than a few kilometres is required. The need for high-resolution
bathymetry has been underscored by recent predictive modelling studies of
Antarctic outlet glaciers, which conclude that the shape of the ice-shelf
cavity and knowledge of small, kilometre-scale pinning points are both key
to improving predictions of ice-sheet retreat and sea-level change (Berger
et al., 2016; Favier et al., 2016). Similarly, the latest high-resolution
ocean models demonstrate that warm deep water reaches the grounding zone of
TG through topographically constrained pathways, again highlighting the
critical need for high-resolution bathymetry in making accurate predictions
(Nakayama et al., 2019).
Implications from sea-floor morphology
The geometry and detailed morphology of the H1–H3 ridge also provide insight
on ice-shelf pinning points. Historical grounding-zone positions, as mapped
from remotely sensed ice-shelf tidal response, confirm that the Thwaites Ice
Shelf is still pinned on high H1 and was pinned on high H2 as recently as
1992 and 2011 (Rignot et al., 2011). By 2011, the area of grounding on H2
had reduced to <0.5 km2 (Fig. 3a), but the recent configuration
and persistence of the TGT suggests that at least some parts of it remain in
(ephemeral) contact with the sea floor. Thus, the exposed H1 and H2
sea-floor highs, and by analogy H3, can be studied as current or recent
pinning points for the Thwaites Ice Shelf. Glacial lineations and (or)
grounding-zone wedges (GZWs) on the surface of H2 and H3, as well as rare
iceberg plough marks (Fig. 4b), confirm that these pinning points are mantled
by some amount of unconsolidated sediment that can be ploughed or moulded by
ice. Sub-bottom profiles over the H2 and H3 highs support this as they show
either an incredibly smooth sea-floor response, strongly indicative of
unconsolidated sediment cover, or up to 10–15 m of unconsolidated
sedimentary units (Fig. S4); furthermore, coring of the top of H3 recovered
several metres of sediment (Larter et al., 2020). Although the upper section
of the sediment on H3 is glacimarine, deposited after grounded ice had
retreated or lifted-off from the high, the presence of a GZW there and on H2
(Fig. 4b, d) suggests that at least the uppermost part of this high may
have been constructed via sedimentation at the grounding zone (see Alley et
al., 1989, 2007). The potential effects of this grounding-zone sedimentation
are twofold: when the TG grounding zone had retreated onto these highs
during the Holocene (i.e. sometime before 10.3 ka cal BP; Hillenbrand et
al., 2013), GZW formation could have temporarily slowed further retreat
(Alley et al., 2007). Second, continued pinning of an ice shelf on the high
and GZW, when most of the grounding line had eventually retreated further
landward, would have buttressed the grounded upstream section of TG. The new
MBES dataset we present here and the sea-floor landforms it reveals,
supported by core recovery and sub-bottom profiles, indicate that more
sediment is present in this area than is typical of other Amundsen Sea inner
shelf environments that experienced rapid ice-sheet retreat, including the
adjacent Pine Island Bay and the Dotson–Getz palaeo-ice-stream trough (e.g.
Larter et al., 2007, 2009; Graham et al., 2009; Nitsche et al., 2013, 2016).
This is likely because the grounding zone was positioned for a relatively
long period of time in this area immediately offshore TG and probably
because areas so close to the grounding zones of most other large glacier
systems have not yet become accessible for shipborne survey. Furthermore, TG
has a much larger drainage basin than the Dotson–Getz palaeo-ice-stream
trough and therefore the potential to erode and deliver a greater flux of
basal sediment to its grounding zone. Our only constraints on grounding-zone
retreat through this area (during the Holocene) are from the core on the H1
high, which shows grounded ice withdrawal from the northern part of that high
by 10.3 ka cal BP (Hillenbrand et al., 2013) and grounding zones mapped
from satellite-era datasets (Rignot et al., 2011). Thus, the TG grounding
zone was most probably located between H1 and the current grounding zone,
potentially on the sea-floor ridges identified here, for thousands of years
delivering a significant volume of sediment to the area. This retreat
history is in line with what we know about deglaciation more generally in
the Amundsen Sea, where rapid grounding-zone retreat occurred from 15 to 10 ka to reach near modern limits (Hillenbrand et al., 2013; Larter et al.,
2014; Smith et al., 2014); however, more marine dates and terrestrial
thinning histories will certainly provide additional clarity and
chronological constraints for TG.
The submarine landforms observed on and around the sea-floor highs raise the
question of the composition of these features. Landforms on the flanks of
the pinning points (gullies, slide scars, isolated blocks; Fig. 4) may
indicate that these highs consist, at least in part, of an erodible (soft)
material with a probable (hard) bedrock core. In marine settings, slide
scars and gullies incise large, pronounced sedimentary scarps like the shelf
edge (e.g. Noormets et al., 2009; Gales et al., 2013) or the headwalls of
major submarine slides (e.g. Laberg and Vorren, 2000; Vanneste et al., 2006)
but do not characterise hard bedrock (crystalline) settings. Further
evidence comes from the new observation of flat-topped (compacted or
planed-off) morphology of the H2 and H3 highs confirming that the upper part
of these (down to the level of flattening) consists of a lithology that is
apparently erodible by the motion of an ice shelf (based on the orientation
of lineations on the highs). Other examples of flat glacial erosion surfaces
planed off by ice shelves or flat-based tabular icebergs from the Arctic all
document erosion into sedimentary substrates (e.g. Vogt et al., 1994;
Jakobsson et al., 2010; Noormets et al., 2016). Small (<100 m high,
<5 km wide), flat-topped mounds in the Ross Sea are also thought to
consist of unconsolidated volcanogenic deposits rather than crystalline
bedrock, and, interestingly, GZWs have built up on them, indicating that
these features slowed grounding-zone retreat in that area (Lawver et al.,
2012; Greenwood et al., 2018). Although we suggest flattening of the highs
by the action of Thwaites Ice Shelf, we cannot say, from our data, how much
erosion may have occurred. It may be that surface sediments were simply
skimmed from the tops of the highs and transported towards their seaward
flanks, which, in conjunction with instabilities relating to ice-shelf
grounding (or ungrounding) on the highs, could have promoted slope failures
on the fronts and sides of these features (cf. Bellwald et al., 2019).
Despite this caveat, all of the landform evidence presented here, supported
by cores and acoustic sub-bottom profiles, suggests that the tops, fronts and
sides of the H2 and H3 highs are mantled by some thickness of sediment,
probably over a bedrock core. Seismic-reflection profiles would be needed to
determine the internal structure of these features and sediment thicknesses.
In contrast, the morphology of H1 is consistent with it having a crystalline
composition. This very shallow, rugged feature is cross-cut by bedrock
grooves and channels typical of hard rock exposures on the inner Antarctic
shelf (Lowe and Anderson, 2002; Livingstone et al., 2013), and, although
bathymetric coverage over this high is incomplete, it has few planed-off
sections and no glacial lineations have been identified on its surface yet
(Figs. 3b; S4b). Therefore, it is clear that there is a spatial variability
in pinning point morphology and composition at TG, as well as across the
wider Amundsen Sea area (Figs. 2, 5). More broadly, we also note the
relative scarcity of bedrock channels or other landforms related to
subglacial meltwater flow in the TG MBES dataset, with the crescentic scours
(H3 only; Fig. 4a) being the exception. As an example, Kirkham et al. (2019)
mapped more than 1000 subglacial channels in Pine Island Bay, whereas we map
only 175 forms here, albeit over a smaller area. It is not clear whether
evidence of previous meltwater routing is buried by sediment in the deep
troughs or has been destroyed by ice flow over the highs. Physical-property
and geochemical analyses on cores from the area, acquired as part of ITGC,
should shed light on the frequency and magnitude of meltwater release during
the retreat of grounded ice over the sea-floor highs. Schroeder et al. (2013) identified a transition from a distributed channel network with
ponded water behind ridges at the modern grounding zone to a system of
concentrated channels downstream. It is possible that a similar
configuration for the basal hydrological system occurred in this area as ice
retreated over the offshore highs and that evidence is preserved in the
marine sedimentary record.
The apparent shaping and fragmentation of the H2 and H3 highs (Fig. 4a, b)
highlights a potential feedback mechanism between bed properties
(composition and topography) and glacier retreat dynamics. If the substrate
of a pinning point is soft enough to be moulded by the flow of an ice shelf
and to be susceptible to slope failures, it might be eroded over time.
Erosion of material from the surface of a pinning point, as it is planed
off, in conjunction with retrogressive failures at its seaward flank and
possibly larger slide or slump events may act to reduce its surface height,
as well as its surface area, by “eating away” at the frontal/side flanks
until it cannot serve as a pinning point for the ice shelf (and glacier ice
upstream) any longer. As long as the ice shelf continues to move over the
high, this process of unpinning would be exacerbated by any increase in flow
velocities (leading to increased erosion) and/or by ice-shelf thinning
(leading to ungrounding), due to either flow acceleration or sub-ice-shelf
melting. The result, in a setting with soft erodible pinning points, is
the potential for increased ice-flow velocities to accelerate pinning point
destruction which, in conjunction with simultaneous ice-shelf thinning in
response to sub-ice-shelf melting, could promote ungrounding earlier than
would occur on a corresponding hard, less erodible pinning point.
Needless to say, in order for this feedback to occur, an ice shelf would
have to continue to flow quickly over the sea-floor high(s) and not form an
ice rise, under which erosion rates are considered to be low (e.g. Matsuoka
et al., 2015). At TG we note that, at least for the duration of the
observational record (∼55 years), the fast-flowing part of
the glacier, which feeds the TGT (Fig. 2), has continued to move over the H2
and H3 highs, periodically extending several tens of kilometres before
calving (Ferrigno et al., 1993; Rabus et al., 2003; MacGregor et al., 2012),
whereas the ice rumple at the end of the EIS restricts flow over H1, with
most ice flow being diverted around the rumple (Rignot et al., 2001). It is
perhaps interesting to also consider that upwards of 50 m of relative
sea-level fall due to glacio-isostatic uplift is thought to have occurred on
the inner Amundsen Sea shelf during the Holocene (Whitehouse et al., 2012)
and that the uplift of any pinning points would naturally counter
ungrounding. Therefore, although we can only speculate on the exact
mechanisms affecting rates of unpinning, we suggest that the composition of
sea-floor pinning points may be an important factor in their ongoing ability
to buttress large Antarctic ice shelves.
Implications from the new bed roughness data
One major objective of our research is to assess the deglaciated submarine
terrain offshore from TG as an analogue for the modern bed to gain new
insights on TG bed characteristics. The consistency of derived power spectra
and drag contributions for bed profiles from the inner ASE shelf and for
upstream areas of Pine Island and Thwaites glaciers (Figs. 7, S7) indicates
that the roughness properties of the offshore and onshore areas are
comparable across all resolvable frequencies. Furthermore, observations
confirm that recent grounding-zone retreat affecting TG has occurred over a
series of bedrock ridges with the loss of pinning points and formation of
new cavities (Tinto and Bell, 2011; Milillo et al., 2019; Jordan et al.,
2020). Further upstream, about 100 km from the recent grounding zone,
analyses of radar specularity suggest that the modern TG bed is
characterised by high roughness attributed to bedrock cropping out at the
glacier base (Schroeder et al., 2014). Our data reveal that the bedrock
ridges and intervening troughs underlying the modern grounding zone (Holt et
al., 2006; Morlighem et al., 2019), with length scales of up to tens of
kilometres and amplitudes of up to several hundreds of metres, constitute a
morphological terrain similar to the coastal bathymetry (Figs. 2, 3).
Further, we demonstrate that this rugged terrain would exert the same strong
influence on basal drag for an overriding ice mass (assuming no cavitation)
(Figs. 7, S7). This is consistent with results from inverse methods that
determine basal drag for the modern TG bed (Joughin et al., 2009; Arthern et
al., 2015). We also note that crag-and-tail landforms (which form
subglacially) extend down to the floors of the deep troughs (e.g. Figs. 3,
4b). This confirms that, at least at the time when these features formed,
ice of an expanded TG was grounded in the troughs as well as on the highs
and probably experienced high basal shear similar to ice at the present-day
grounding zone. The orientation of the crag and tails also confirms that ice
flow was not directed along troughs but rather overrode the existing
topography; this finding is consistent with cosmogenic exposure data from
Bear Peninsula (Fig. 1) showing that the ice-sheet surface rose above the
top of this terrain during the last glacial period (Johnson et al., 2017).
For shorter wavelengths of bed topography, we can consider the form of the
individual sea-floor highs over length scales of several kilometres. We
interpret the morphological characteristics of these features as being
consistent with the correlation of morphology with bed type known from
onshore glacial–geological studies of crag-and-tail type features (e.g. Benn
and Evans, 2010), which more recently has been described from on-ice seismic-reflection profiles both for TG (Muto et al., 2019a, b; Holschuh et al.,
2020) and beneath the Rutford Ice Stream (Fig. 4 in King et al., 2016).
Still, we recognise that high-resolution seismic-reflection data over our
bathymetric highs would be required to confirm this. Specifically, the
correlation is between hard beds on the stoss sides of topographic
highs, associated with crag-and-tail landforms, and soft or sedimentary
beds on the lee sides of these features. This pattern is clearly replicated
over the H2 and H3 highs, which have rugged upstream ends with crag-and-tail
landforms, glacial lineations over their tops and sedimentary tails on
their downstream ends (Fig. 4). The correlation of bed types with sea-floor
highs (and ridges) holds true for several other areas of the inner shelf
around West Antarctica, where streamlining of bedrock highs has often
produced landforms with sedimentary tails on the lee sides of bedrock
obstacles (e.g. Larter et al., 2009, Graham et al., 2009; Livingstone et
al., 2013; Nitsche et al., 2013, 2016), although this is not always the
case. Thus, the variability in bed types on topographic highs in offshore
regions may provide useful constraints on bed type variability beneath the
modern glacier.
Regarding the spectral analysis of roughness and basal drag contributions
presented here (Figs. 6, 7, S7), we acknowledge that these only provide an
order of magnitude assessment of the contribution to basal drag from the
different wavelength scales resolved by the bathymetric DEM (Fig. 2).
Analysis beyond the simple 2D-flow-line theory used here (see Sect. 4.2)
would be needed to account for 3D-flow effects, as well as for the non-linear
dependence of ice viscosity on stress (Glen, 1955). Here, we have not
specified the physical mechanism controlling λN, the shortest
roughness wavelength that influences basal drag. Candidate mechanisms that
might limit the influence of roughness at small spatial scales include
cavitation (Fowler, 1986), fracture and plucking of crystalline or
sedimentary rocks, the formation of a weak internal shear zone (Liu et al.,
2020), bulldozing of unconsolidated sediment, or regelation flow around
small obstacles (Weertman, 1957). More sophisticated theories accounting for
the potential of ice to form cavities in the lee of obstacles could be
deployed similarly, but the drag contribution would then depend also on
water pressure (Fowler, 1986; Schoof, 2005). Process models of subglacial
hydrology, phase change, fracture and sediment transport could all be
incorporated in to a more elaborate analysis using MBES datasets as input.
It is clear from our results that the increased spatial resolution of the
MBES data is critical for capturing the high-frequency bathymetric
variability on the inner continental shelf seaward of TG, which is necessary
to understand warm-water incursions into sub-ice-shelf cavities (Figs. 8,
S8; Nakayama et al., 2019). The strong correlation of our observations with
interpretations of the present bed conditions of TG and, therefore, the
robustness of this deglaciated terrain as an analogue for the modern bed
further demonstrates that more information can be gleaned from this type of
marine dataset (i.e. near-continuous bathymetry with spatial resolution
better than 0.05 km). For example, the 3D nature of MBES (with approximately
equal resolution in all directions) means that bathymetric variability could
be examined in any direction, not only along survey lines, as has been the
case until recently with all onshore radar or seismic-reflection profiles of
extant bed topography, and over a variety of spatial scales. These analyses
add to our understanding of across-flow contributions to basal drag or
hydraulic potential (e.g. Muto et al., 2019a) and allow us to consider the
spatial variability of bed types (e.g. sedimentary vs. hard beds),
particularly where sea-floor sediments are also imaged by seismic profiles
and/or cored for ground truthing. Similarly, the application of theories of
subglacial processes as discussed above to high-resolution bathymetric
datasets will increase our understanding of ice flow over high-frequency bed
roughness, particularly if combined with ultra-high-resolution (sub-metre-resolution) bathymetries from AUV surveys (e.g. Davies et al., 2017;
Dowdeswell et al., 2020). Indeed, AUV surveys and (or) a dense grid of
seismic soundings (only obtainable from non-crevassed ice shelves) are the
only way to determine bed geometry in ice-shelf cavities. New techniques
such as swath radar that can image the present glacier bed in 3D (Paden et
al., 2010; Jezek et al., 2011), albeit in narrow swaths, have already been
employed on TG (Holschuh et al., 2020) and could be used in conjunction
with offshore bathymetric data to build a better-informed, more complete and
more uniform resolution picture of basal conditions under TG and at its
grounding zone.
Conclusions
New 3D bathymetric data from just offshore Thwaites Glacier reveal that the
coastal bathymetry is dominated by a ∼65 km long,
∼1200 m deep trough and a discontinuous ridge with water depths
of 650 to <100 m. Spatial variations in the morphology of the
ridge segments/highs and available acoustic sub-bottom profiler data suggest
differences in substrate composition along the ridge, with the two
southernmost highs having a significant erodible component at least in
their upper parts, which are sedimentary in composition. The geometry (flat
tops) and landform evidence (glacial lineations, gullies, sediment fans)
indicate that the bathymetric highs were planed off and variously eroded by
the action of Thwaites Ice Shelf as it flowed over them, presumably reducing
the height of these former pinning points over time. A feedback mechanism
during unpinning may have occurred, whereby as the ice shelf started to lose
contact with the high and frontal buttressing weakened, the resultant
increase in flow velocities exacerbated erosion of the high and facilitated
further unpinning of Thwaites Glacier.
We present three lines of evidence that this coastal bathymetry provides a
good analogue for the modern grounding zone of Thwaites Glacier. First, on
length scales of several tens of
kilometres, the ridge and trough morphology is
consistent with the bed topography of the grounding-zone area based on
available DEMs and over-ice geophysical data. Second, our spectral
decomposition of roughness and basal drag over this rugged, deglaciated
terrain is consistent with similar spectral decompositions, and inversions
of basal drag, for profiles from the modern grounding zone area and for
areas of the Thwaites bed, where bedrock crops out subglacially (e.g.
Schroeder et al., 2014). In contrast, smooth beds, characterised by thick
sedimentary substrates and linear glacial landforms, produce distinctly
different power spectra and drag contributions. Third, the distribution of
landforms and substrate types (unconsolidated sediment vs. bedrock) over the
ridge indicates that it displays the same correlation of bed type with
topography that has been described for upstream bed areas and inferred for
the grounding zone (Muto et al., 2019a, b; Holschuh et al., 2020). As such,
further analyses of this deglaciated terrain may provide realistic
constraints on across-flow roughness and bed type distribution and should inform geophysical observations of the modern TG bed that will be acquired
as part of ITGC.
As discussed above, observational datasets like MBES are required seaward of
Antarctic ice shelves in order to capture the high-frequency variability
that characterises the bathymetry of nearshore areas. Bathymetry derived from gravity inversions
cannot adequately reproduce the kilometre- to sub-kilometre-scale features that are
important for accurately calculating inflows of warm ocean water in troughs and for defining the topographic highs that may act as pinning points for
ice shelves and as barriers to warm-water incursions.
Data availability
Processed MBES data grids with grid spacings of 50 and 500 m are available from the UK Polar Data Centre 10.5285/F2DFEDA9-BF44-4EF5-89A3-EE5E434A385C (Hogan et al., 2020). Raw data sources are indicated in Table 1.
The supplement related to this article is available online at: https://doi.org/10.5194/tc-14-2883-2020-supplement.
Author contributions
KAH, RDL, RA, TAJ and AGCG developed the concept of the paper. KAH, RDL,
AGCG, RLT, JDK, RC and VF acquired and performed initial processing on the
bathymetry data during NBP19-02; JDK performed all channel metric analyses.
KG, JEA and JH provided bathymetric data from German and Korean cruises,
respectively. KAH compiled, part-processed, and gridded all bathymetric
datasets and wrote the first draft of the paper with substantial
contributions from RA and RDL. RA developed the methodology, performed
spectral analyses and basal drag estimations, and wrote the text for these
sections; KAH and TAJ provided the profile data. AW performed the ocean heat
flux calculations. All authors contributed to the development of the final
paper and data visualisation.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This work is an output of the Thwaites Offshore Research (THOR) project and
Glacial Habitat of Subglacial Thwaites (GHOST) projects, components of the
International Thwaites Glacier Collaboration (ITGC). Logistics were
provided by the NSF United States Antarctic Program and the NERC British Antarctic Survey.
ITGC contribution no. ITGC-011. We thank the NBP19-02 science party, the Edison
Chouset Offshore Inc. captain and crew, and the Antarctic Support Contract
technical staff aboard the RV/IB Nathaniel B. Palmer. In addition to the editor and reviewers, we are also grateful to Nick Holschuh for constructive comments on the submitted manuscript. This study is part of the Polar Science
for Planet Earth programme of the British Antarctic Survey.
Financial support
This research has been supported by the National Science Foundation, Office of Polar Programs (grant no. 1738942), the Natural Environment Research Council (grant nos. NE/S006664/1 and NE/S006672/1).
Review statement
This paper was edited by Chris R. Stokes and reviewed by Martin Jakobsson and Matteo Spagnolo.
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