Calving rates at tidewater glaciers vary strongly with ocean temperature

Abstract

Rates of ice mass loss at the calving margins of tidewater glaciers (frontal ablation rates) are a key uncertainty in sea level rise projections. Measurements are difficult because mass lost is replaced by ice flow at variable rates, and frontal ablation incorporates sub-aerial calving, and submarine melt and calving. Here we derive frontal ablation rates for three dynamically contrasting glaciers in Svalbard from an unusually dense series of satellite images. We combine ocean data, ice-front position and terminus velocity to investigate controls on frontal ablation. We find that frontal ablation is not dependent on ice dynamics, nor reduced by glacier surface freeze-up, but varies strongly with sub-surface water temperature. We conclude that calving proceeds by melt undercutting and ice-front collapse, a process that may dominate frontal ablation where submarine melt can outpace ice flow. Our findings illustrate the potential for deriving simple models of tidewater glacier response to oceanographic forcing.

Full text

ARTICLE
Received 27 Jan 2015 |Accepted 4 Sep 2015 |Published 9 Oct 2015
Calving rates at tidewater glaciers vary strongly
with ocean temperature
Adrian Luckman1,2, Douglas I. Benn3,4, Finlo Cottier5,6, Suzanne Bevan1, Frank Nilsen2,7 & Mark Inall5
Rates of ice mass loss at the calving margins of tidewater glaciers (frontal ablation rates) are
a key uncertainty in sea level rise projections. Measurements are difficult because mass lost
is replaced by ice flow at variable rates, and frontal ablation incorporates sub-aerial calving,
and submarine melt and calving. Here we derive frontal ablation rates for three dynamically
contrasting glaciers in Svalbard from an unusually dense series of satellite images. We
combine ocean data, ice-front position and terminus velocity to investigate controls on frontal
ablation. We find that frontal ablation is not dependent on ice dynamics, nor reduced
by glacier surface freeze-up, but varies strongly with sub-surface water temperature. We
conclude that calving proceeds by melt undercutting and ice-front collapse, a process that
may dominate frontal ablation where submarine melt can outpace ice flow. Our findings
illustrate the potential for deriving simple models of tidewater glacier response to
oceanographic forcing.
Q5
DOI: 10.1038/ncomms9566 OPEN
1Department of Geography, College of Science, Swansea University, SA2 8PP, UK. 2Department of Arctic Geophysics, University Centre in Svalbard, Po Box
156, 9171 Longyearbyen, Norway. 3Department of Arctic Geology, University Centre in Svalbard, Po Box 156, 9171 Longyearbyen, Norway. 4Department of
Geography, University of St Andrews, St Andrews, Fife, KY16 9AJ, UK. 5Scottish Association for Marine Science, Oban PA37 1QA, UK. 6Faculty of
Biosciences, Fisheries and Economics, UiT The Arctic University of Norway, Po Box 6050 Langnes 9037 Tromsø, Norway. 7The Geophysical Institute,
University of Postboks 7803 5020 Bergen, Norway. Correspondence and requests for materials should be addressed to A.L.
(email: A.Luckman@Swansea.ac.uk).
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Loss of mass at the termini of tidewater glaciers, or frontal
ablation, occurs by a combination of calving and submarine
melting1,2. In addition to its direct contribution, submarine
melting can amplify calving by undercutting and destabilizing the
glacier front3. Several recent studies have concluded that
submarine melting can dominate mass loss at tidewater termini,
particularly where glaciers are impacted by incursions of warm
water from the continental shelf or beyond2,4,5. However, there
remains a distinct lack of direct measurements of either calving or
subaqueous melt rates. Almost all estimates of the latter are based
on calculations of the frontal heat budget using oceanographic
data, for example, refs 1,6,7, and because these estimates rely on
extrapolations from spatially and temporally limited CTD and
current measurements, they tend to be subject to large
uncertainties. Some attempt has been made to directly measure
frontal ablation rates at tidewater glaciers8,9 but temporal and
spatial resolution is often poor, and winter months are
inadequately sampled. This scarcity of direct measurements of
frontal ablation rates and their relationship to conditions both
above and below the waterline places severe limits on our ability
to predict the response of tidewater glaciers to oceanographic
forcing10.
We address this problem by combining high temporal and
spatial resolution satellite radar data with oceanographic and
meteorological time series to investigate controls on frontal
ablation rates. We derive time series of frontal velocities, terminus
positions and frontal ablation rates for three Svalbard tidewater
glaciers using 11-day repeat, 2 m resolution, TerraSAR-X images
spanning more than a year. Analysis of these data allows us to
quantify evolution of frontal ablation rates in unprecedented
detail through a complete seasonal cycle, and to identify the key
environmental controls on calving behaviour. We find that rates
of frontal ablation are not dependent on glacier dynamics, nor
reduced by the onset of glacier surface freeze-up, but closely
follow the temperature of the fjord waters at depth. Our findings
imply that submarine melt undercut and collapse is the dominant
calving mechanism at these glaciers, and that frontal ablation is
therefore controlled primarily by ocean temperatures.
Results
Glaciers studied. We choose three glaciers for their contrasting
dynamic characteristics (Fig. 1): Kronebreen, a glacier with one of
the highest flux rates in Svalbard; Tunabreen, a quiescent-phase
surge-type glacier; and Aavatsmarkbreen, an active-phase surge-
type glacier that began a surge during our observation period. In
addition to their contrasting dynamical characteristics, these
glaciers also vary in their fjord settings (Fig. 1): Kronebreen
terminates in Kongsfjorden which has a deep, unrestricted
connection to the warm West-Spitsbergen Current (WSC), but
has a relatively shallow connection between the outer and inner
parts of the fjord at B60 m depth. Tunabreen terminates in
Tempelfjorden which is shallower and further removed from the
WSC than Kongsfjorden (Fig. 1). Aavatsmarkbreen terminates in
Forlandsundet, which is as close to the WSC as Kronebreen, but
lacks a direct, deep connection.
Calving rate measurement and potential controls. The rate of
ice loss from a tidewater glacier terminus is the sum of that due to
calving, and that due to submarine melting, and is commonly
referred to as the frontal ablation rate _
a(ref. 2). A change in
ice-front position over time must equal the rate at which ice is
delivered to the terminus minus _
a. Thus satellite data of sufficient
spatial resolution may be used to calculate this quantity through
regular measurements of ice-front position, from which dl/dtmay
be derived, and of terminus ice speed U
T
:
_
a¼UTdl=dtð1Þ
We use equation (1) to calculate the frontal ablation rate
between pairs of TerraSAR-X images from surface velocities
derived by feature tracking, and ice-front position change derived
by manual digitization and geographical information systems
(GIS) (Methods section). The images, in ‘Stripmap’ mode
(B2 m ground range pixel size), were acquired every orbital
cycle for 19 months during 2013 and early 2014, providing an
image pair every 11 days barring a few acquisition failures. In the
cases of Kronebreen and Aavatsmarkbreen, we incorporate
images from more than one satellite track, giving a greater
frequency of observations during some time periods.
To investigate the controls on measured frontal ablation rates
we explore a variety of environmental variables that have
previously been associated with calving behaviour. These include
local weather data (air temperature and precipitation), sea-surface
temperature (SST), fjord ice presence and water temperatures at
depth in the glacier fjords (henceforth ‘sub-surface temperatures’;
Methods section).
Glacier dynamic behaviour. Glacier terminus speeds (Fig. 2)
show significantly different behaviours between the three glaciers
during our observation period. Kronebreen has a winter speed of
1.5–2m per day, with summer peaks of 3–4 m per day associated
with positive air temperatures and periods of high rainfall. The
winter speed of Tunabreen is only 0.2 m per day, rising to a peak of
B1 m per day in October. Aavatsmarkbreen flowed at B1 m per
day before its surge but by November 2013 had attained B3 m per
day, a speed maintained without major fluctuations until May
2014 when a further summer speed-up occurred. These different
West
Spitsbergen
current
Billefjorden
A
K
T
Ny Ålesund
Kongsfjorden
Longyearbyen
km
0
–500 –400 –300 –200
Depth (m)
–100 0
100
Figure 1 | Svalbard location map. Arrows show positions of glaciers
(K ¼Kronebreen, T ¼Tunabreen, A ¼Aavatsmarkbreen), weather stations,
and moorings. Background bathymetry from IBCAO Version 3.0 (ref. 35)
illustrates the possible routes for warm water from the WSC via troughs
to fjords.
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–500
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Kronebreen
Mean ice front position
Mean retreat rate
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or concentration (0–1)
2013 2014 2013 2014
Ocean surface temperature
20–60m ocean temperature
Sea ice concentration
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Mean ice front position
Mean retreat rate
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Fast ice presence
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Mean ice front position
Mean retreat rate
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rate (m per day)
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Temperature (°C)Temperature (°C)
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rate (m per day)
Precipitation (mm)Sea ice presence
or concentration (0–1)
Retreat rate (m per day)Frontal ablation
rate (m per day)
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Figure 2 | Glacier time series. Data derived from a series of 11-day repeat TerraSAR-X images from 2013 to 2014 for three contrasting Svalbard glaciers to
illustrate the frontal ablation rate and its two key components: the rate of change of ice-front position and the terminus speed. Also shown are: temperature
and precipitation from the nearest weather station (Ny Ålesund for (a) Kronebreen and (c) Aavatsmarkbreen; Longyearbyen for (b) Tunabreen);
OSTIA SST and sea ice concentration32 from close to the ice front; fast ice presence in each fjord immediately in front of the ice front; and mean weekly
water temperature between 20 and 60 m from the nearest ocean mooring. For (a,c) these data are from Kongsfjorden (Fig. 1); for (b) these data are from
Billefjorden. Dashed vertical lines indicate year transitions.
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behaviours reflect contrasting controls on the terminus dynamics
of the three glaciers. The summer acceleration of
Kronebreen is consistent with enhanced basal lubrication from
surface melt water and precipitation11, and is in accord with
reports of seasonal dynamic variation at tidewater glaciers
elsewhere8,9,12,13. Detectable motion of the quiescent Tunabreen
is confined to the frontal zone, where high longitudinal stress
gradients induce outward stretching of the ice. Stretching rates are
proportional to ice cliff height, which exhibits systematic seasonal
variations in response to calving losses14. The sustained high
velocities of Aavatsmarkbreen between summer 2013 and the end
of our time series are characteristic of a surge, possibly modulated
by the influx of surface melt water during the summer months.
Mean ice-front positions at Kronebreen and Tunabreen reveal
comparable seasonal patterns, although of different magnitudes
(Fig. 2). Both glaciers advance modestly during winter and retreat
strongly during summer and autumn, a period associated with
greater seismic activity13, with net annual retreats of B350 and
B150 m, respectively. Similar patterns of seasonality in ice-front
position are seen in Alaska15 and Greenland16. Aavatsmarkbreen
followed the same pattern in spring 2013, but then advanced by
B500 m between the start of the surge in summer 2013 and May
2014, after which it began to retreat.
By combining ice-front positions with terminus velocities
(equation (1)) we quantify frontal ablation rates and their
seasonal variation at an unprecedented temporal resolution
(Fig. 2). Maximum frontal ablation rates for Kronebreen,
Tunabreen and Aavatsmarkbreen are B8, B3 and B5 m per
day, respectively. Despite their diverse dynamic behaviours and
fjord settings, the magnitudes of these frontal ablation rates are
notably comparable, and their seasonal patterns very similar.
Rates for all three glaciers peak in September and October and
continue at a high level well after air temperature has fallen
consistently below 0 °C. Frontal ablation lags air and SSTs by
1–2 months but is in synchrony with the peak in sub-surface
ocean temperature. We note that frontal ablation rates at a
sample of Alaskan Glaciers appear to peak earlier in the summer9,
but that a strongly similar seasonal pattern of calving rate to our
glaciers is seen at Columbia Glacier (also in Alaska)8. Of the three
glaciers studied, only Tunabreen experienced sea ice during our
study period. The loss of sea ice in spring heralds an increase in
calving, but frontal ablation drops to a minimum long before the
return of sea ice in January.
Controls on calving. To explore these interactions in more detail,
we further examine relationships between frontal ablation rate
and potential controls on calving at Kronebreen and Tunabreen,
the glaciers for which we have proximal oceanographic data.
Previous studies have investigated calving relationships with
water depth, ice thickness and ice speed8,17, or modelled calving
as a process driven by surface melt18. Since we need to explain the
seasonal variation in frontal ablation, we present relationships
with seasonally varying parameters: air temperature, ice speed
and sub-surface ocean temperature (Fig. 3). Simple linear
regressions between frontal ablation rate and each of the three
possible determinants are all statistically significant at the 99%
confidence level but demonstrate that sub-surface ocean
temperature is by far the strongest predictor of frontal ablation
rate at both Kronebreen (R2¼0.84) and Tunabreen (R2¼0.80).
Multiple linear regression reveals that including air temperature
as a second predictor accounts for only an additional 1.4%
of the variance for Kronebreen, and is not significant for
Tunabreen. Of the three variables, only sub-surface ocean
temperature can adequately explain the seasonal variation in
calving behaviour.
Discussion
Calving events at Kronebreen, Tunabreen and Aavatsmarkbreen,
in common with valley-confined tidewater glaciers elsewhere in
Svalbard and beyond, typically involve relatively small sections of
ice (o50 m across) detaching from the terminus19,20. Calving
events at these glaciers are therefore unlike the massive block
rotation events seen in the largest Greenland glaciers, for
example, refs 21,22 or tabular events occurring at ice shelf
margins, for example, ref. 23. Nevertheless, these Svalbard glaciers
may be typical of medium-sized glaciers terminating in fjords that
experience a seasonal incursion of warm water. The submarine
melt and calving processes investigated here may therefore be
representative of many high-latitude glaciers.
The persistence of frontal ablation at all three glaciers well after
winter freeze-up of the glacier surface implies that melt water in
crevasses is not a primary control on calving, in contrast to some
model findings, for example, ref. 18, and this is further supported
by the lack of substantial correlation between local air
temperature and frontal ablation. Despite significant contrasts
in dynamical behaviour, our studied glaciers have very similar
seasonal frontal ablation cycles, implying that dynamic regime
also has little influence on the calving process. This is further
confirmed by the weak correlation between terminus speed and
frontal ablation rate. Surprisingly perhaps, even the initiation of a
surge at Aavatsmarkbreen did not seem to influence its frontal
ablation rate. These observations imply that frontal ablation rate
controls terminus position and is not sensitive to terminus speed
(Equation (1)). Whilst a basic consideration of mass balance
implies that mean annual calving rates would be expected to
correlate well with mean annual ice speed, the weakness of
association between ice speed and calving rate on seasonal
timescales seen in our data is significant. At Columbia Glacier the
seasonal relation between calving rate and ice speed is also much
weaker than the annual one8. On the other hand, where
Kronebreen terminus speeds exceed 2.5 m per day, there is
some evidence that frontal ablation rate also varies with glacier
speed (Fig. 3b).
The strong correlation between frontal ablation rate and ocean
temperature at Kronebreen and Tunabreen is indicative of
melt-driven convection at the ice–ocean interface, which is highly
sensitive to ambient ocean temperature24,25. The less strong
relationship for Tunabreen may be because our oceanographic
data have weaker spatial and temporal relevance. The water
temperatures around the depths of the calving fronts of these
glaciers are comparable to those elsewhere that give rise to
submarine melt on the order of metres per day1,5,7. With the
possible exception of the fastest phases of summer flow, this rate
of melt appears sufficient to seasonally outpace the delivery of ice
to the terminus of our glaciers. Our findings are consistent
with melt undercut and collapse being the dominant calving
mechanism at these glaciers.
The seasonal cycles of observed ocean temperature in
Kongsfjorden and Billefjorden are similar, but the proximity of
Kongsfjorden to the WSC and the deep channel that supports a
greater exchange of Atlantic-origin waters during summer and
autumn26 compared with Billefjorden27 explain the difference in
magnitude of sub-surface temperature between Kongsfjorden and
Billefjorden in late September (Fig. 2). The greater frontal
ablation rate at Kronebreen, compared with Tunabreen and
Aavatsmarkbreen, may therefore be due to the more direct and
open connection between this glacier terminus and the source of
warm water. In addition, Kronebreen has a much larger ablation
area than Tunabreen, and will therefore experience higher
summer melt-water discharges. These factors will encourage
more efficient subaqueous melting and may help to explain the
higher calving rates at Kronebreen25,28.
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On shorter timescales, frontal ablation may be influenced by
other factors. For instance, spikes in frontal ablation rates at
Kronebreen occasionally coincide with terminus velocity peaks
(Fig. 2). It is possible that on these occasions delivery of ice to the
glacier terminus outstrips the melt undercut process allowing
other calving mechanisms to contribute, and causing the frontal
ablation rate to respond more strongly to ice dynamics (Fig. 3b).
Alternatively, surface melt-water pulses, as well as promoting
faster glacier flow by lubrication, may lead to higher summer
melt-water discharge, enhancing convective circulation and melt
at the ice front28.
Since the relationships between frontal ablation and sub-
surface ocean temperature are strong and linear, the data from
Kronebreen and Tunabreen (Fig. 3) are in keeping with a simple
linear calving law:
_
a¼kTð2Þ
Where _
ais the frontal ablation rate (m per day), Tis the
temperature at a depth appropriate for each glacier (here
20–60 m) and the coefficient kcaptures the nature of the heat
transfer in this setting (1.015 for Kronebreen; 0.35 for
Tunabreen). General calving laws of this type, perhaps incorpor-
ating other variables such as melt-water discharge, might be
developed using data from further glaciers.
We propose that submarine melt is an integral part of a
mechanism that promotes calving by undercut and collapse,
rather than a process which renders calving potentially unim-
portant2. Where terminus ice velocity is matched or outpaced by
submarine melt and undercut calving, a glacier will be stable or
will retreat at a rate dependent on the availability of warm water
at depth and the circulation of that water through estuarine and
glacial discharge processes. Where the ice velocity is greater than
the rate at which ice can be removed by melting, the front may be
able to advance to a position where other calving processes come
–20
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Kronebreen
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Mean ice-front speed (m per day) 20-60m ocean temperature (°C)
Frontal ablation rate (m per day)
Kronebreen
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R2 = 0.31 R2 = 0.36 R2 = 0.80
R2 = 0.84R2 = 0.30R2 = 0.43
Tunabreen
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Tunabreen
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Mean air temperature (°C)
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Mean ice-front speed (m per day)
Mean air temperature (°C)
3.0
1.0
0.4
Figure 3 | Glacier scatterplots. Correlation data and coefficients of determination for Kronebreen and Tunabreen between frontal ablation rate and:
(a,d) mean air temperature (at Ny Ålesund for Kronebreen and at Longyearbyen for Tunabreen); (b,e) mean ice-front speed at the glacier terminus;
and (c,f) nearby sub-surface ocean temperature (Kongsfjorden for Kronebreen and Billefjorden for Tunabreen). Note that for Kronebreen in (b) frontal
ablation rate varies more strongly with ice-front speed when the ice is flowing faster than B2.5m per day.
30−12−2012
01−02−2013
06−03−2013
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09−05−2014
Date
04−06−2014
0.0 0.5 1.0 1.5 2.0 2.5 3.0
km
01
Speed (m per day)
Figure 4 | Kronebreen velocity map. Example TerraSAR-X speed map of
Kronebreen from January 2013 illustrating glacier surface texture exploited
by feature tracking, typical quality of speed data acquired right up to the ice
front, and variation in ice-front position over the observation period (green
to magenta lines). The ice-front measurement flow-lines along which ice
velocity and retreat rate are measured are shown in white.
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into play29. This view is consistent with the theoretical framework
proposed by Benn et al.30, in which ‘‘first-order’’ calving processes
(determined by the large-scale velocity structure of the glacier)
provide the ultimate limit on glacier extent, while ‘‘second-order’’
processes (including melt undercutting) may cause more rapid
calving and glacier retreat. The present study, and work
elsewhere, for example, ref. 2, indicates that second-order
processes currently dominate in some regions. First-order
calving may be the rate-limiting process at only the fastest
outlet glaciers, for example, ref. 22 or in the coldest ocean
settings, for example, ref. 23, these representing only a part of the
global ice–ocean interface. Knowledge of submarine melt rates, or
much better availability of high-resolution satellite data such as
those used in this study, are therefore required to properly
understand tidewater calving mechanisms and rates in full.
We have investigated in unprecedented detail the seasonal
variation in calving rates at three dynamically contrasting glaciers
in Svalbard and their relationships to environmental controls. We
find that rates of frontal ablation are not dependent on glacier
dynamics, nor reduced by the onset of glacier surface freeze-up,
but closely follow the temperature of the fjord waters at depth.
Our findings imply that submarine melt undercut and collapse is
the dominant calving mechanism at these glaciers, and that
frontal ablation is therefore controlled primarily by ocean
temperatures. The calving process of melt undercut and collapse
may dominate frontal ablation at any glacier where it can match
or outpace the delivery of ice to the glacier terminus. This opens
up the possibility of being able to predict the response of many
tidewater glaciers to oceanographic forcing. We have identified a
growing need to assess sub-surface temperatures at tidewater
glacier margins and to evaluate the relative prevalence of melt
undercut versus other calving processes.
Methods
Satellite image data.Feature tracking was applied to TerraSAR-X image pairs in
slant range using correlation windows of 200 200 pixels spaced every 20 pixels,
for example, ref. 31, and subsequently ortho-rectified to a pixel size of 40 m using a
Digital Elevation Model. Ice fronts were manually digitized from dB-scaled images
ortho-rectified to a pixel size of 2 m using the same Digital Elevation Model.
Ice-front position change was derived by locating the intersections between each
ice front and a set of flow-lines equally spaced at 100 m intervals across the active
glacier terminus width (Fig. 4), and finding the distance between these intersections
for each image pair. Surface velocities were extracted at the locations of these
ice-front intersections, and the frontal ablation rate at each intersection was
calculated using equation (1). These ‘‘specific frontal ablation rates’’ were averaged
to produce a mean frontal ablation rate for the entire glacier width for each image
pair. This is the first report of frontal ablation calculated using surface velocity
measured at the evolving ice front.
Uncertainties in surface velocity U
T
are estimated to be o0.4 m per day, and
comprise co-registration error (±0.2 pixels) and error arising from unavoidable
smoothing of the velocity field over the feature-tracking window size
(400 400 m). Uncertainties in the rate of ice-front position change dl/dtare
estimated to be o2.0 m per day and are dominated by digitization error (±4 pixels
for each of 2 images over 11 days). The combined estimated specific frontal
ablation rate error of up to 2.4 m per day is too large to confidently assess the
variation in specific frontal ablation rate between individual measurements across
the terminus. The RMS frontal ablation rate error for B30 flow-line crossing
points of B0.4 m per day, however, is sufficiently small to allow mean frontal
ablation rates to be meaningfully compared between glaciers.
Weather and sea-surface data.We used daily mean air temperatures and
precipitation totals from the Norwegian Meteorological Institute (www.yr.no),
measured at the closest available weather station. For Kronebreen and
Aavatsmarkbreen this was Ny Ålesund and for Tunabreen, Longyearbyen.
To characterize the fjord surface conditions, we used daily Operational
Sea-Surface Temperature and Sea Ice Analysis (OSTIA) data supplied by the Met
Office (Crown Copyright 2014). OSTIA SSTs are produced at B5 km resolution
using an optimal interpolation method to incorporate in situ and satellite
observations, and sea ice fractional coverages are based on data from the
EUMETSAT Ocean & Sea Ice Satellite Application Facility32.
We also present data on the presence of fast ice (sea ice frozen to the shoreline)
from the Norwegian Ice Service (wms.met.no/icechart). Ice charts are derived by
manual classification of satellite images33.
Ocean sub-surface temperature data.Sub-surface fjord water temperatures
were measured using moored instrumentation as described by Cottier et al.26
Temperature sensors, with a precision of better than 0.1 °C after calibration, were
positioned from B20 m below the surface to within 15 m of the seabed. The
moorings typically include 10 sensors over the full 200 m depth with 4–5 sensors at
10 m intervals over the 20–60 m depth range used in this study. To characterize
sub-surface ocean temperatures at Kronebreen and Aavatsmarkbreen, we used
mooring data from Kongsfjorden (78°580N11°480E; Fig. 1) available for the
entire 2013–2014 study period with the exception of September 2013. For
Tunabreen in Tempelfjorden, we used the closest available data from neighbouring
Billefjorden (78°390N16°410E; Fig. 1). These data may be considered a reliable
indicator of near-surface oceanographic conditions at Tunabreen because the two
fjords are similar in shape and connect adjacently to the same Isfjorden system.
The Billefjorden data were available only until September 2013 so our best
oceanographic comparison is to the mean value over the period 2008 and 2013.
The mean temperature in the 20–60 m depth range for the two moorings was
calculated at weekly intervals to provide an appropriate comparison with the
calving time series derived every 11 days or better. The choice of a 60 m maximum
for Kongsfjorden was dictated by the depth at which water in the inner fjord is
connected to the outer fjord34, and for Billefjorden by the presence of a sill at
B50 m (ref. 22). In add ition, both Kronebreen and Tunabreen are grounded in
B70 m of water.
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Acknowledgements
TerraSAR-X data were provided by DLR (project OCE1503), and funded by the Conoco
Phillips-Lundin Northern Area Program through the CRIOS project (Calving Rates and
Impact on Sea level). A.L. and S.B. are affiliated to the Climate Change Consortium of
Wales (C3W). Mooring work is supported by the UK Natural Environment Research
Council (Oceans 2025 and Northern Sea Program) and the Research Council of Norway
(projects Cleopatra: 178766, Cleopatra II: 216537, and Circa: 214271/F20). Contribution
by F.C. was undertaken through the Scottish Alliance for Geoscience Environment and
Society (SAGES).
Author contributions
A.L. designed the study, analysed the satellite data and led the writing of the manuscript.
D.I.B. led the project that funded the satellite data acquisition and contributed
significantly to the writing of the manuscript. S.B. analysed the sea-surface data and
performed the statistical analyses. F.C. and M.I. provided ocean temperature data and
F.N. provided information on fjord bathymetry. All authors contributed to the writing of
the manuscript.
Additional information
Competing financial interests: The authors declare no competing financial interests.
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How to cite this article: Luckman, A. et al. Calving rates at tidewater glaciers vary
strongly with ocean temperature. Nat. Commun. 6:8566 doi: 10.1038/ncomms9566
(2015).
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