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Article https://doi.org/10.1038/s41467-022-32036-2
Three-dimensional imaging of waves and
floes in the marginal ice zone during
acyclone
Alberto Alberello
1,2,14
,LukeG.Bennetts
1
, Miguel Onorato
3,4
,
Marcello Vichi
5,6
, Keith MacHutchon
7
,ClareEayrs
8
,
Butteur Ntamba Ntamba
9
, Alvise Benetazzo
10
, Filippo Bergamasco
11
,
Filippo Nelli
12
, Rohinee Pattani
13
,HansClarke
2
,IppolitaTersigni
2
&
Alessandro Toffoli
2
The marginal ice zone is the dynamic interface between the open ocean and
consolidated inner pack ice. Surface gravity waves regulate marginal ice zone
extent and properties, and, hence, atmosphere-ocean fluxes and ice advance/
retreat. Over the past decade, seminalexperimentalcampaigns have gener-
ated much needed measurements of wave evolution in the marginal ice zone,
which, notwithstanding the prominent knowledge gaps that remain, are
underpinning major advances in understanding the region’s role in the climate
system. Here, we report three-dimensional imaging of waves from a moving
vessel and simultaneous imaging of floe sizes, with the potential to enhance
the marginal ice zone database substantially. The images give the
direction–frequency wave spectrum, which we combine with concurrent
measurements of wind speeds and reanalysis products to reveal the complex
multi-component wind-plus-swell nature of a cyclone-driven wave field, and
quantify evolution of large-amplitude waves in sea ice.
Improved observational capabilities are needed to understand the
often paradoxical and baffling regional and inter-annual variabilities of
Antarctic sea ice1,2. Autonomous platforms that operate in harsh polar
environments, such as autonomous underwater vehicles3and drones4,
are pushing the boundaries for in-situ observations, generating data
for essential calibration and validation of satellite remote sensing, and
measuring properties beyond the capabilities of contemporary satel-
lites. The marginal ice zone (MIZ), which is characterised by dynamic
interactions between large-amplitude surface waves and relatively
small and thin ice floes, is difficult for satellites to capture5,6and a
major target for improved observations7,8. Wave evolution and ice
properties in the MIZ are intimately coupled9–11,and,hence,thereis
demand for a technology capable of simultaneously monitoring both
wave activity and ice cover properties, which can capture data during
storms when wave–ice interactions are most intense.
Historical in-situ measurements of waves in the MIZ show the ice
cover attenuates wave energy exponentially over distance12 at a
frequency-dependent rate that induces a downshift of the peak
frequency13, as well as modifying the directional wave spectrum14.
The attenuation rate has become a research focus, as it informs
Received: 28 September 2021
Accepted: 12 July 2022
Check for updates
1
University of Adelaide, 5005 Adelaide, SA, Australia.
2
The University of Melbourne, 3010 Parkville, VIC, Australia.
3
Università di Torino, 10125 Torino, Italy.
4
INFN, 10125 Torino, Italy.
5
Department of Oceanography, Universityof Cape Town, 7701Rondebosch,South Africa.
6
Marine and Antarctic Research centre for
Innovation and Sustainability (MARIS), University of Cape Town, 7701 Rondebosch, South Africa.
7
Department of Civil Engineering, University of Cape Town,
7701 Rondebosch, South Africa.
8
New York University Abu Dhabi, Abu Dhabi, United Arab Emirates.
9
Cape Peninsula University of Technology, 7535 Cape
Town, South Africa.
10
Istituto di Scienze Marine, Consiglio Nazionale delle Ricerche, 30122 Venice, Italy.
11
Università Ca’Foscari, 30123 Venice, Italy.
12
Swinburne University of Technology, 3022 Hawthorn, Australia.
13
Atkins, SW1E 5BY London, United Kingdom.
14
Present address: University of East Anglia,
NR4 7TJ Norwich, UK. e-mail: alberto.alberello@outlook.com
Nature Communications | (2022) 13:4590 1
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predictions of the width of the ice-covered region impacted by waves
and, hence, the MIZ extent15,16. Major advances in measuring wave
attenuation in the MIZ have been made over the past decade,
including dedicated campaigns in the Arctic17 and Antarctic11,18.State-
of-the-art in-situ measurements mostly come from arrays of wave
buoys, where the buoys can be traditional open water buoys19,20
deployed between floes in regions of low ice concentration (usually
close to the ice edge) or bespoke buoys deployed on ice floes11,18,20
large enough to support the buoys (usually away from the ice edge)
but small enough that the floes followthe waves. Attenuation rates are
generally calculated by applying an exponential decay ansatz to
measurements provided by neighbouring buoys, in terms of the sig-
nificant wave height11,18,20 or a more detailed analysis in which
the ansatz is applied to each component of the one-dimensional
(frequency) wave spectrum, under the assumption of a stationary
wave field20–23.
The recent surge in measurements (including remote sensing24,25)
has generated a new understanding of wave attenuation in the
MIZ, particularly on how the wave attenuation rate depends on
frequency21,26. Certain theoretical models reproduce the observed
frequency dependence, but the dominant sources of attenuation are
still hotly debated27 and empirical models often rely upon15,28.Further,
the measurements have revealed a large range of attenuation rates23,25,
even at comparable frequencies, which is attributed to dependence on
ice cover properties, such as ice thickness, areal ice concentration
and floe sizes, as well as momentum transfer from winds over the ice
cover. Satellite and model-hindcast data have been used to derive
empirical relationships between measured attenuation rates and ice
concentration18,22,23, ice thickness29 and winds22,23.Incontrast,floe sizes
in the MIZ are below satellite resolutions and have only recently been
integrated into large-scale models16,30, so that coincident floe size data
have been limited to visual observations during deployment. Overall,
data on ice properties are too sparse or unreliable to validate theore-
tical models.
Stereo-imaging techniques are emerging as a tool for in-situ
monitoring of waves and ice properties in the MIZ. In principle, the
images can be used from a moving vessel, as in open waters, to
reconstructthe sea surface elevation in timeand space, thus enabling
analysis of wave dynamics in two-dimensional physical space, the
frequency–direction spectral domain, and wave statistics31.Airborne
synthetic aperture radar (SAR) is an alternative method to measure
frequency–direction wave spectra and has been applied over
60–80km long transects of the MIZ32,33. However, stereo-imaging,
being an in-situ technique, can be used to measure sea-ice geome-
trical properties simultaneously34 and can be combined with co-
located meteorological measurements, e.g., wind velocities. Further,
in contrast to SAR35,stereo-imaging resolves wind sea components of
the wave spectrum (short wavelength systems under the influence of
local winds), as well as swell (long wavelength systems no longer
under the effect of winds).
To date, the use of stereo-imaging techniques in the MIZ has been
limited in scope. Campbell et al.36 use a camera system on a fixed
platform on the edge of a lake to quantify incoming and reflected
energy fluxes of relatively small waves (<0.3m) in pancake and brash
ice. Smith & Thomson37 use camera images froma moored vesselin the
Arctic MIZ during calm conditions (significant wave heights typically
around 1m) to calculate bulk wave properties and pancake floe velo-
cities. Alberello et al.34 use an autonomous stereo-camera system on a
vessel moving through the winter Antarctic MIZ during a cyclone to
measure pancake floe shapes and sizes.
In this article, we demonstrate the potential to monitor the evo-
lution of the frequency–direction wave spectrum from the images
captured by Alberello et al.34 combined with automated image recon-
struction software. We report the extreme sea state created by the
cyclone over a >40km transect into the Antarctic MIZ, and validate a
subset of the results with co-located buoy measurements. The sea state
deep into the MIZ during the cyclone is shown to be more complex
than previously thought, and partitioning of the two-dimensional
spectra is required to analyse wave evolution of the cyclone-driven
wind sea.Further, evidence is given of momentum transfer from winds
through 100% ice concentration, based on comparing attenuation of
the significant wave height over distance with an empirical model18,
which is considered to be a benchmark due to the large size of the
underlying data set and that the measurements were made in the
Antarctic MIZ during the sea-ice growth period.
Results
Experimental conditions
On the 4th July 2017, the South African icebreaker S.A. Agulhas II
entered the Antarctic MIZ at 62∘South and 30∘East during an explosive
polar cyclone. It encountered the ice edge (the northernmost location
where ice concentration exceeds 10% in a 1km radius around the
vessel38) at 08:00 UTC, and reached 100% ice concentration at 09:00
UTC, approximately 10km from the iceedge. It continued South, whilst
remaining in 100% ice concentration34. Over this time, strong winds
(18–19ms−1from North-East according to ERA5 reanalysis, which
underestimates in-situ measurements39; Fig. 1a) generated extreme sea
states in the surrounding area, with significant wave heights (H
S
=4σ
η
,
where σ
η
is the surface elevation standard deviation) up to 10m North-
East of the icebreaker and >6m at the ice edge (i.e., in the 90th
Fig. 1 | Daily averaged environmental conditions on the 4th July 2017 from
ERA5. a Wind speed; btotal wave height and cswellwave height. Vectorsshow the
direction, where in b,cthe length is proportional to the wave period. The hor-
izontal and vertical axis denotes Easting (longitude) and Northing (latitude) in
degrees. b,cThe white area indicates sea-ice concentration ≥15% (ERA5 wave data
are only provided for ice concentrationup to 15%). The shipposition at the iceedge
is denoted by the red dot.
Article https://doi.org/10.1038/s41467-022-32036-2
Nature Communications | (2022) 13:4590 2
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percentile40) when the icebreaker entered the MIZ (Fig. 1b). The mean
wave direction at the ice edge was aligned with the wind throughout
the day41 (from North-East). The mean directional spread, a measure of
the breadth of the wave spectrum in direction42,was≈60∘and, like the
mean wave direction, was steady during the day41.Waveheightand
period at the ice edge increased throughout the day, due to the
intensification of the cyclone, thus creating a non-stationary incident
wave field. A detailed analysisof the sea state indicates that ≈70% of the
total significant wave height is due to waves generated locally (wind
sea). Swell contributes the remaining 30%, which also comes from a
north-easterly direction but with a slight offset of less than 20∘from the
wind sea.
As the icebreaker travelled South into the MIZ, six sequences of
three-dimensional images of the ocean surface were captured by a pair
of synchronised cameras installed on the icebreaker. The measure-
ment locations are defined by average distances from the ice edge,
d=5–44km, where the distanceis taken along themean wave direction
(Fig. 2a). Each sequence was taken over a 20-minute interval, during
which the ship heading and forward speed was almost constant, with
the first sequence starting at 08:05 UTC and the last at 11:50 UTC. The
20-minute time interval is a World Meteorological Organisation stan-
dard for analysis of wave measurements43, which balances stationarity
of wave conditions with collecting a large enough number of waves for
a statistically robust analysis.
An automatic algorithm for floe size reconstruction was applied to
the digital images collected along the transect (see Methods)34,and
used to calculate floe size distributions, mean floe diameters and the
areal concentration of floes. At the first measurement loc ation, close to
the ice edge (d= 5km), the ice concentration was i
c
≈50%44 and con-
sisted of pancake ice floes (small, approximately circular floes that
form in wavy conditions45,46) and the remaining 50% was water between
the floes (Fig. 2b). At all five subsequent locations, which were deeper
into the MIZ (d≥15km; Fig. 2c, d), ice covered 100% of the ocean
surface, in the form of ≈60% pancake floes and ≈40% interstitial frazil
ice34, which increased in density with distance from the ice edge.
Pancake floe diameters generally increased with distance from the ice
edge, with the median diameter increasing from ≈3.0m at the ice edge
to ≈3.5m at the deepest measurement locations (Fig. 2e), and the floe
size distribution skewing towards larger diameters (Fig. 2f). At all
measurement locations, over 50% of the pancake-covered area was
comprised of floes with diameters in the interval 2–4m (vertical error
bars in Fig. 2e). Therefore, the ice conditions during the experiment
are considered relatively insensitive to distance from the ice edge, in
comparison to the changes in the incident wave field.
Fig. 2 | Sea-ice properties on the4th July 2017. a Overview of study area with sea-
ice concentration from AMSR2 on the 4th July 2017 (longitude and latitude are
horizontal and vertical axes, respectively), with bullets indicating six mean mea-
surement locations during 20min acquisitions. b–dExample of image acquisitions
(axes in pixels) at d= 5km, 24km and 43km from the ice edge, respectively.
eMedian pancake floe diameter (D, vertical axis) versus distancefrom the edge (d,
horizontal axis) shown as bullets, plus 25th and 75th diameter percentiles (vertical
error bars) and uncertainty in distance from ice edge (horizontal error bars). Sha-
ded background denote the measurement location in intermediate ice con-
centration. fArea weighted floe size distribution (a, vertical axis) as a function of
floe diameter (D, horizontal axis) at each measurement location. Colour coding is
used in all panels to denote the distance from ice edge.
Article https://doi.org/10.1038/s41467-022-32036-2
Nature Communications | (2022) 13:4590 3
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Three-dimensional imaging of ocean surface and comparison
with buoy data
The three-dimensional images (Fig. 3a) are used to extract ocean sur-
face elevation timeseries, η(t), at each measurement location, from
which the one-dimensional frequency spectra, E(f), and two-
dimensional frequency–direction spectra, E(f,θ), are derived (see
Methods). At the two deepest measurement locations (d=43–44km),
wave buoys (waves-in-ice observation systems47 ofthetypeusedinthe
previous studies11,18,20,21), were deployed on ice floes48 and the fre-
quency spectra they provide are used to validate the analysis of the
stereo-camera images (Fig. 3b, c). The overall shape of the corre-
sponding spectra is consistent, noting that the buoys do not show the
multiple peaks clearly due to a low resolution. Discrepancies occur for
the lower (f< 0.05Hz) and upper tails (f> 0.10Hz), which show over
and under estimation of energy, respectively, relative to the buoys.
These modes carry a small amount of energy and make only minor
contributions to integrated parameters, such as the significant wave
height and mean period, for which values derived from the images and
buoys differ by ≈5% and ≈2.5%, respectively.
The uncertainty associated with spectra derived from the stereo-
cameraimages is primarily white noise (i.e., equal across any frequency
band; see Methods). The noise level is negligibl efor the most energetic
modes (0.04 Hz < f<0.16Hz, or −1.4 < log
10
(f)<−0.8, corresponding
to periods of ≈7–25s; see error bands in Fig. 3b, c insets) and produces
an integrated error of ≈0.02m, which corresponds to ~0.5% of the
measured significant wave heights. The spectral density estimated
from buoys is subjected to red noise (i.e., it decreases with increasing
frequency), which also produces a negligible effect on the significant
wave height49.
Surface elevation and wave spectra as a function of distance
from the ice edge
Surface elevation timeseries around the largest individual waves
recorded (Hmax; maximum crest to trough distance) at the six mea-
surement locations are shown in Fig. 4a. The significant wave height is
also reported for each timeseries (Fig. 4a; horizontal dashed lines). The
significant wave height decreases along the transect, from 6.6m close
to the ice edge (d=5km; toppanel)to H
S
=4.6mat d= 44km (bottom
panel), and, hence, wave energy attenuates over distance. Statistical
analysis of the individual waves indicates consistency with Gaussian
(linear) theory. For instance,the kurtosis (fourth order moment of the
probability density function of the surface elevation and a measure of
wave nonlinearity50) is close to three, similar to Gaussian sea states50,51.
The maximum individual wave heights at each location, which are part
Fig. 3 | Three-dimensional surface elevation retrieval and validation against
buoys. a Reconstructed surface elevation, η(axes in pixels). b,cFrequency spectra
were obtained from the surface elevations measured at the two deepest mea-
surement locations (d=43–44km; solid curves) and co-located buoy
measurements (broken curves). Insets show thespectra in logarithmicscale and the
shaded area denotes noise level associated to wave spectra derived from stereo
images. b,cThe horizontal axes denote frequency (f) and the vertical ones
energy (E).
Article https://doi.org/10.1038/s41467-022-32036-2
Nature Communications | (2022) 13:4590 4
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of energetic wave groups,tend to diminish with distance into the MIZ.
Nevertheless, large waves are recorded tens of kilometres into 100%
ice concentration, e.g., H
max
≈8m at d= 43km (second to bottom
panel), which corresponds to H
max
/H
S
≈1.6, close to the maximum
height expected in a linear sea state43. The steepness associated with
the largest individual waves, ε
max
=πH
max
/(2λ), where λis the wave-
length, is a measure of the strength of the wave42. It decreases from
ε
max
≈0.19 at the ice edge (d=5km) to ≈0.10 at the deepest mea-
surements locations (d=43–44km). Despite the attenuation of the
steepness over distance, these maximum values are expected to be
large enough to have an impact on the ice cover, for example, by
keeping the ice cover unconsolidated46,52.
Attenuation of wave energy with distance into the MIZ is also
evident in the one-dimensional spectra (Fig. 4b). As expected, higher
frequencies (shorter periods) experience greater attenuation than
lower frequencies (longer periods), causing narrowing of the spectral
bandwidth (the breadth of the spectrum in frequency42), with the
bandwidth at the two deepest measurement locations ≈80% of the
bandwidth close to the ice edge. The frequency spectrum is unimodal
at the first four measurement locations (d≤36km) but becomes
bimodal at the deepest two measurement locations (d=43–44km)
where a low-frequency peak appears (peak period ≈15s). The low-
frequency peak indicates the swell initially north of the ice edge
(Fig. 1c) catches up with the higher frequency wind sea generated
close to the ice edge (peak period ≈12.7s at d= 36km). The swell
overlaps the wind sea system in frequency space, but the two systems
are clearly separated in two-dimensional frequency–direction
space (Fig. 4c) as they are travelling in different directions. The offset
is ≈20∘, which is consistent with the difference in direction between
wind sea and swell reported at the ice edge. For further analysis, the
frequency–direction spectra are used to partition the total sea into
swell and wind sea (see Methods). Note that the buoys do not return
the directional spectrum18 and, hence, their measurements cannot
be used to separate wind sea and swell systems, as they overlap in
frequency space.
Wave evolution
The wave age c
p
/u
10
42,wherec
p
is the phase velocity (ratio of wave-
length to wave period) and u
10
is the wind speed, is computed at each
measurement location using wind speeds from the onboard met-
station (Fig. 5a). The values obtained indicate waves are young
(growing in size and length under the action of wind) at the first four
measurement locations (c
p
/u
10
< 1.2553). The waves switch sharply to
old (c
p
/u
10
> 1.25) at the deepest two measurement locations. The
sharp transition is partially due to the arrival of the swell system, but, as
implied by the similar sharp transition in wave age for the wind
sea (denoted total sea without swell), a sudden drop in wind speed
from ≈25ms−1to ≈17ms−1is the primary cause.
Lengthening of the peak period with distance is evident in the
frequency spectra (Fig. 4b). The peak period of the incident field also
increases over the duration of the experiment, from 12.4s to 13.5s, and
the measured peak period normalised by the corresponding ERA5
peak period at the ice edge to account for the changing conditions in
the open ocean (based on the mean wave direction and group velocity
of the mean period; see Methods), is relatively insensitive to distance
until the swell system is detected at the deepest two measurement
locations (Fig. 5b), indicating the peak period elongation due to pre-
ferential attenuationof shorter periodcomponents of thespectrum21,54
is negligible. The normalised peak period sharply increases when the
swell system appears at the deepest two measurement locations
(d=43–44km), but the increase is relatively small for the wind sea. The
normalised peak period values for the wind sea are consistent with
the MBK spectral attenuation model15,21, where the ERA5 spectrum at
the ice edge is used as the incident field for the model.
The frequency averaged directional spread (σ
0
) is calculated from
the two-dimensional spectra20 and normalised using the ERA5 spectra
Fig. 4 | Reconstructed surface elevation timeseries and wave spectra. a Surface
elevation timeseries at progressive distances from the ice edge (top–to–bottom;
time on horizontal axes and surface elevation on vertical axes; colour-coding cor-
responds to locations shown in Fig. 3a) around the largest wave in each record.
Dashed lines indicate significant wave heights, H
S
.bFrequency and
cfrequency–direction wave spectra at progressive distances from the ice edge.
b,cThe horizontal axis denotes frequency, in bthe vertical axiswave energy and in
cdirection. Two-dimensional spectra are shown in Cartesian coordinates as the
spectracover only a narrow directional range, −60∘<θ<60
∘, and normalised by the
peak energy to highlight directional properties (colorbar shown next to the title).
a–cShaded backgrounds denote the measurement location in intermediate ice
concentration.
Article https://doi.org/10.1038/s41467-022-32036-2
Nature Communications | (2022) 13:4590 5
Content courtesy of Springer Nature, terms of use apply. Rights reserved
at the ice edge (Fig. 5c). For the total sea, the normalised directional
spread is relatively insensitive to distance over the first three mea-
surement locations (0.60 < σ
0
/σ
0,ERA5
< 0.77) but increases sharply at
the final three locations (σ
0
/σ
0,ERA5
> 1), with the maximum spread (σ
0
/
σ
0,ERA5
≈1.27) at d= 36km. The wind sea shows little variation in nor-
malised directional spread over all locations (0.44 < σ
0
/σ
0,ERA5
<0.88).
Thus, the peak in directional spread of the total sea at d= 36km is likely
due to a combination of attenuation of the wind sea peak and emer-
genceoftheswellsystem.Thedirectionalspreadofthetotalsea
decreases at the deepest two locations as the swell dominates. The
MBK attenuation model applied to the ERA5 two-dimensional incident
spectra, with propagation distances of the spectral components
dependent on their direction, predicts the normalised directional
spread slightly decreases over distance from 50∘(σ
0
/σ
0,ERA5
=0.82)at
5km to 43∘(σ
0
/σ
0,ERA5
=0.52)at43–44km, as the components travelling
at oblique directions travel farther and, hence, experience greater
attenuation leading to collimation14. This trend contrasts with the weak
increasing trend in the observed directional spread of the wind sea
by ≈1.22% per kilometre.
The significant wave height of the total sea normalised by the
ERA5 ice edge counterpart (to account for the non-stationary wave
conditions at the ice edge, where the significant wave height
grows from 6.7m to 7.4m during the measurements; see Methods)
attenuates with distance (Fig. 5d). The best-fitexponentialcurvetothe
normalised measurements, expðαdÞ, gives the attenuation rate
α=8.3×10
−6m−1. The wind sea attenuates at a greater rate, with the
best-fit exponential curve giving the attenuation rate α= 23.5 × 10−6m−1.
Subtracting the contribution of wind input to the wind sea (based on
theory for open water and using winds recorded by the onboard met-
station; see Methods) further increases the attenuation rate to
α=29.4×10
−6m−1. For comparison, the benchmark empirical model18
gives the rate 32.7 × 10−6m−1(for ice concentrations greater than 80%,
peak periods less than 14s and significant wave heights up to 6m).
The uncertainty in the calculation of the distance from the ice edge
(see error bars in Fig. 5), which is due to ambiguity introduced by the
coexistence of multiple wave systems, does not affect the reported
trends of wave parameters.
Discussion
The benchmark significant wave height attenuation rate is greater than
that derived for the total sea from the stereo-camera images by
approximately a factor four. The benchmark rate is based primarily on
measurements of low-energy sea states (H
s
< 1m), where wind speeds
were generally < 10ms−1(from ERA5 reanalysis; see Fig. 9 by Montiel
et al.23) and the wave spectra were most likely unimodal (as indicated in
Fig.10cbyKohoutetal.
18). Therefore, we argue that the fairest com-
parison is with the wind sea without wind input (i.e., attenuation of the
large waves generated by the cyclone in the open ocean), although
noting the subtracted wind input represents an upper bound as it does
not consider ice cover. With these modifications to the wave field,
which rely on analysis of the frequency–direction spectrum, the
attenuation rate is less than the benchmark by ≈10% only. The agree-
ment is remarkable considering the potential differences in conditions
that may affect attenuation rates, such as the extreme wave heights
and strong winds associated with the cyclone, and the ice properties.
Therefore, the results provide support for the benchmark attenuation
rate and evidence it holds for considerably larger waves than pre-
viously recorded in similar ice conditions. However, the results show
the benchmark attenuation rate only applies to single-component
seas, and does not describe the evolution of the complex sea observed
deep into the MIZ during the cyclone.
Theresultsprovideevidencethatstrongwindsfeedwavegrowth
in 100% ice concentration for tens of kilometres over pancake/frazil ice
cover. This contradicts the assumption made in most contemporary
models that wind input scales according to the open water fraction55,56,
i.e., no wind input in 100% ice concentration. The assumption is
already being debated, particularly for frazil, brash and/or pancake
ice conditions22, and theories for wind-to-wave momentum transfer
through ice covers are being proposed57.
The benchmark attenuation rate is greater than the attenuation
rate of the wind sea without wind input possibly due to the properties
of the ice cover. Based on observations during deployment of the
buoys for the benchmark measurements, the ice cover consisted of
unconsolidated pancake/frazil ice, similar to the stereo-camera mea-
surements, and also consolidated, larger, thicker floes and continuous
Fig. 5 | Wave properties at progressive distances from the ice edge. a Wave age;
bpeak period;cdirectional spreading; and dsignificant wave height (vertical axes)
versus distance (horizontal axes). Dots are used to denote total sea, and triangles
the wind sea (total sea without swell). The horizontal error bars denote uncer-
tainties in distancefrom the ice edge due to variability in wind and wave directions.
The shaded area denotes intermediate ice concentration. b,cThedashedlineis
derived by applying the MBK model21 to corresponding ERA5 spectra at the ice
edge. dThe solid grey line denotes the best (exponential) fit for the total sea, the
dashed line for the wind sea (total sea without swell) and the dash-dotted line the
wind sea without wind input over ice. The thin dashed line is the benchmark
attenuation derived for i
c
> 0.8 and T
P
<14s
18.
Article https://doi.org/10.1038/s41467-022-32036-2
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ice18, which is likely to cause stronger attenuation58,59.Buildingalarger
database of stereo-camera images in the MIZ will drive improved
understanding of how ice type influences the attenuation rate. More-
over, collecting stereo-camera images during conditions when the
incoming wave field is steady will allow the spectral attenuation rate to
be calculated and compared with benchmarks21,23, thus giving more
detailed understanding of the attenuation process.
In conclusion, measurements have been reported of extreme
wave conditions in the winter Antarctic MIZ during an explosive
polar cyclone, which were captured by a stereo-camera system on
a moving vessel over a 44km transect and validated by co-located
buoy measurements. The images empowered analysis of the
frequency–direction wave spectrum evolution, and revealed the
complex multi-component nature of the sea state in the MIZ where
wind sea and swell co-exist and attenuate at different rates. Con-
comitant measurements of winds gave evidence of wind input through
100% ice cover. The success of stereo-imaging system shown in this
study is likely to influence the design of future field campaigns in the
MIZ. Moreover, it has the potential to be installed on vessels that
routinely traverse the Antarctic MIZ and autonomously monitor the
sea state, vastly increasing the data available as well as providing
concomitant information on the ice cover. In turn, this will open new
frontiers to advance current knowledge of MIZ dynamics and underpin
the development of the next generation of climate models.
Methods
Image acquisition
The acquisition device consists of two GigE monochrome industrial
CMOS cameras with a 2/3 inch sensor, placed side-by-side at a distance
(i.e., baseline) of 4m. The stereo rig was installed on the monkey bridge
of the icebreaker, ≈34m from the waterline and tilted 20∘below the
horizon. The cameras were equipped with 5mm lenses to provide a
field of view of the ocean surface ≈90∘around the port side of the ship
(Fig. 3a). Additionally, an inertial measurement unit (IMU) was firmly
attached close to the two cameras (between the cameras at the same
height and ≈1m behind them) to capture the stereo-rig movement with
respect to the sea surface during the acquisition. Images were recor-
ded with a resolution of 2448× 2048 pixels and a sampling rate of 2Hz
during daylight on the 4 July 2017 (from 07:00 to 14:00 UTC).
Floe size
An automatic algorithm, developed using the MatLab Image Proces-
sing Toolbox, was applied to extract sea-ice metrics from the recorded
images. To avoid sampling the same floe twice, images every 10s were
analysed. Images were ortho-rectified and projected on a horizontal
plane. A camera-dependent calibration was applied to convert pixel to
metres. The images were processed to eliminate the vessel from the
field of view, adjust the image contrast andconvertthe grey scales into
a binary map, which isolates the solid ice shapes from background
water or frazil ice. A morphological image processing was applied to
improve the fidelity of the shape of identified pancakes. Floe area (S)
was calculated based on pixels and approximated by a disk, from
which a characteristic diameter D=ffiffiffiffiffiffiffiffiffiffiffi
4S=π
pwas defined. Further
details on the algorithm and floe size distribution can be found in
Alberello et al.34.
Estimation of the surface elevation
The Wave Acquisition Stereo System (WASS60)wasusedtoestimatea
set of data points in space (a dense 3D point cloud) representing the 3D
ocean surface. WASS analyses left and right stereo images to find
photometrically distinctive corresponding points (i.e., projections of
the same 3D point in space) that can be triangulated to recover their
original 3D position in space.The operation is performed for each pixel
of the stereo frames to produce a temporal sequence of 3D point
clouds composed of millions of samples each. The data is also
automatically filtered to remove possible outliers and the mean sea-
plane is estimated independently for each frame.
To be effective, the technique requires the geometrical config-
uration of the two cameras to be known a priori. WASS can estimate
that property as part of the process, with the added advantage of
correcting slight variations in the camera’s reciprocal orientation due
to vibrations. The motion of the vessel under the effect of waves,
however, is more significant than vibrations induced, for example, by
wind. It follows that points clouds from different pair of images lie in a
different reference frame. Measurements of ship motion from the IMU
are therefore used to align and geo-localise each cloud to a common
horizontal plane defining the mean sea level. As the IMU does not
estimate the absolute elevation accurately, an approach combining
surface orientations estimated from the stereo data with the altitude
computed by the IMU was developed to recover the camera motion
throughout the sequence. An unscented Kalman filter is applied to
model the six degrees of freedom position and orientation of the
cameras (i.e., the system state) as a discrete-time random variable. At
each frame, the system state is updated with both the absolute IMU
data (yaw-pitch-roll) and the mean sea-plane distance vector estimated
from the point clouds. Both are modelled as Gaussian distributions in
which the measurement covariance is given by the sensor manu-
facturer specifications, in the case of the IMU, or the empirical stereo
estimation error for the cameras31. With the estimated camera motion,
each scattered point cloud is transformed on a common reference
frame with the x–yaxes aligned with the mean sea-plane, and inter-
polated on a regular grid to reconstruct a timeseries of 3D surface
elevations. The final dimension of the reconstructed surfaces is about
150m × 200m, which is ≈5 times larger than Smith & Thompson37.
A systematic source of uncertainty is the resolution error61, also
referred to as quantisation noise, which depends on the object dis-
tance, the focal length and the cameras’resolution, mutual position
and declination. An estimate of this error was calculated as the dif-
ference between a known synthetic surface and its “back and forth”
transformation, which consists of projecting the known surface onto
the camera coordinate system and re-projecting it onto the original
coordinate system by using the specific geometry of the stereo-camera
setup61. This difference provides the spatial distribution of the error,
the amplitude of which is uniformly distributed across wavenumbers/
frequencies (i.e., white noise).
Estimation of the attenuation rate
The sea state conditions were non-stationary during the observation
period, with wave height increasing ≈10%from6.7mto7.4m.There-
fore, the attenuation rate αis estimated with respect to the ice edge
and the dimensionless significant wave height according to the fol-
lowing equation:
log HS
HS,ERA5
=αd,ð1Þ
where dis the distance of each measurement location from the ice
edge calculated along the mean wave direction in the open ocean as
provided by the ERA5 reanalysis, and H
S
/H
S,ERA5
is the significant wave
height normalised by the incident (open ocean) counterpart from the
ERA5 reanalysis. To estimate the incident wave conditions (H
S,ERA5
), the
delay between the time at which waves enter into the MIZ and the time
at which waves are measured at a specific location was estimated
through the wave group velocity. A standard least square fitting is
applied to extrapolate an overall attenuation rate. Owing to the non-
stationarity of the sea state conditions, each frequency components of
the wave field is subjected to different forcing, besides ice-induced
attenuation. Thereby, the estimate of a frequency-dependent attenua-
tion rate18 is impractical herein as it would be subjected to significant
uncertainty.
Article https://doi.org/10.1038/s41467-022-32036-2
Nature Communications | (2022) 13:4590 7
Content courtesy of Springer Nature, terms of use apply. Rights reserved
Note thatthe coexistence of wind sea and swell systems generated
an ambiguity for the selection of the relevant wave direction, which
translates into uncertainties in the distance from the ice edge. By
assuming an overall mean wave direction, the error associated to d
is ≈± 5% (this is reported as an horizontal error bar in Fig. 5).
Frequency–direction spectrum
The directionalwave spectrum can be computed from three measured
quantities of the ocean surface (for example, a buoy uses either heave,
pitch and roll or three accelerations) with a Fourier expansion
method62. This approach produces accurate mean wave direction, but
the directional spreading is typically too broad and with spurious
bimodal properties. An improvement in the directional resolving
power can be achieved by increasing the number of measured ele-
ments with a spatial array of sensors, which are cross-correlated using
the maximum likelihood method or a wavelet directional method62,63.
With the stereo images, the strategy is to apply an array approach
to extract timeseries ofthe surface elevation and a wavelet directional
method to approximate the directional spectrum, noting that the
estimate of the spectrum from timeseries allows resolving compo-
nents with periods > 11.5s and, hence, wavelength > 200m (i.e., longer
than the field of view). A virtual array with geometry comprising of a
triangle inscribed in a circle of radius ≈1m inside a pentagon inscribed
in a circle of radius ≈3m and with an additional probe in the central
position (a co-array configuration) was used to allow a sufficient
number of non-redundant spatial lags between elements and asym-
metry, which ensure an accurate estimation of the directional
spreading function62. The wavelet directional method resolve modes
around the spectral peak (0.5 < f/f
p
<3,wheref
p
is the peak frequency)
more accuratelythan the maximum likelihood method63. Thereby, it is
the preferred approach to identify the complex multiple peak feature
of the spectrum.
Correction of Doppler shift and true wave spectrum
The sea surface elevation extracted from the images is in a frame of
reference that moves with the forward speed and heading of the ship.
The directional spectrum is ther efore distorted due to a Doppler shift64
and it is typically referred to as the encountered spectrum E
S
(f
S
,θ),
where f
S
is the frequency detected by a moving object. To restore the
original spectral shape, the encounter frequency is converted into the
true frequency fthrough the linear wave dispersion relation as
follows64:
fS=f+4π2f2
gUScos β,ð2Þ
where βis the angle between the ship heading and the (open water)
mean wave direction from the ERA5 reanalysis. The true wave spec-
trum, E(f,θ), is computed by performing a change of variable:
Eðf,θÞ=ESðfS,θÞdfS
df =ESðfS,θÞ1+8π2f
gUScos β
:ð3Þ
where df
S
/df is the Jacobian of the transformation.
Partitioning of spectrum
The partitioning of the wave spectrum is performed using the path of
steepest ascent technique65, which is a specific implementation of the
inverse catchment scheme introduced by Hasselmann et al.66.The
spectral peak that satisfies the condition
1:2u10
cp
cosðθψÞ>1, ð4Þ
where u
10
is the wind speed, c
p
is the phase velocity, θis the wave
direction and ψis the wind direction, is assumed to be associated with
the wind sea. All other systems are swell and are ranked based on their
energy contents as primary, secondary and tertiary swell. Only primary
swell was considered.
ERA5 incident sea state
The incident sea state at the ice edge is obtained from ERA5 reanalysis,
which provides hourly wave data at a resolution of ≈40km. The model
performs well in the Southern Ocean but can miss the swell arrival
time67 and the shape of the spectrum is limited by directional resolu-
tion (15∘), which makes it difficult to discriminate wind seas and swell
that propagate in approximately the same direction.
TheERA5wavemodelusesasimplisticwaveattenuationschemes
in sea ice, which acts only at the outskirts of the MIZ (up to 15% ice
concentration), and assumes waves are completely dissipated for ice
concentration > 15%. To overcome uncertainties related to the model
assumptions, we adopt, as a reference, the wave data in open ocean
(0% ice concentration), in the proximity of the ice edge along the mean
wave direction (the distances from the ice edge specified in Fig. 2aare
the one projected in the direction of the mean wave direction). We also
account for the time delay due to wave energy advection (based on the
wave group velocity from the incident ERA5 mean period) to associate
sea states in the MIZ with the open ocean counterpart.
Comparison against ERA5 reanalysis
To provides evidence of consistency between the ERA5 reanalysis and
the observations presented herein, and thus to allow using the former
to produce incident sea states, a comparison against open ocean
conditions recorded on July 2nd (between 12:00 and 14:00 UTC at 52∘
South and 26∘East) and July 3rd (between 12:00 and 13:00 UTC at 56∘
South and 28∘East) is shown in Table 1. For this comparison, the ERA5
reanalysis data refers to the value at the closest grid point, while
observations are an average over the time period. Overall the agree-
mentisgood,withdifferenceinwaveheight<0.2m(<4%),waveper-
iod < 0.2s (< 2%) and directional spread <0. 3∘.A more thorough
evidence of the accuracy of the ERA5 reanalysis in the Southern Ocean
through comparison against a large data set acquired during the
Antarctic Circumnavigation Expedition is detailed by Derkani68.
MBK attenuation model
Based on field measurements in the Antarctic MIZ, MBK (Meylan
et al.21) proposed an(exponential) attenuation rate for each frequency
component in the spectrum as
βðfÞ=af2+bf4where a=2:12 × 103and b=4:59 × 102:ð5Þ
The MBK attenuation rate is used to propagate the incident
directional wave spectrum into sea ice up to the measurements loca-
tions using the expression
Eðf,θÞ=EERA5ðf,θÞexpðicβðfÞdðθÞÞ:ð6Þ
Table 1 | Integrated spectral wave parameters from our measurements and ERA5
–H
S,WASS
[m] H
S,ERA5
[m] T
P,WASS
[s] T
P,ERA5
[s] σ
0,WASS
[∘]σ
0,ERA5
[∘]
2nd July 2017 4.93 4.94 10.18 10.37 35.6 35.9
3rd July 2017 4.16 4.35 8.01 7.84 36.3 36.2
Article https://doi.org/10.1038/s41467-022-32036-2
Nature Communications | (2022) 13:4590 8
Content courtesy of Springer Nature, terms of use apply. Rights reserved
The attenuation rate depends on the ice concentration (i
c
), the fre-
quency of the wave component and the distance from the ice edge on
the direction of each component.
Wind input
In the open ocean, wind transfers momentum to the sea surface, for-
cing ocean waves to grow over distance (fetch). Wave growth is esti-
mated with empirical models, which are expressed as42
~
HS=a1
~
Fb1ð7Þ
where
~
F=gF=u2
10 and
~
HS=gHS=u2
10 are the dimensionless fetch and
wave height, respectively, and a
1
=2.88×10
−3and b
1
= 0.4569.Eqn.(7)is
used to estimate the fetch at the ice edge (F
ERA5
) from the known ERA5
wave height (H
S,ERA5
). The distance from the edge (d) is added to the
fetch
F=FERA5+d:ð8Þ
Eqn. (7) is then applied again to give an updated estimate of the wave
height (H
S,wind
) over theentire distance (F). The difference between the
updatedwaveheightandtheoneattheedgeprovidesanestimateof
the wave height attributed to wind input, i.e.
ΔHS=HS,wind HS,ERA5:ð9Þ
Data availability
Data sets for this research (reconstructed surface elevations) are
available through the Australian Antarctic Data Centre (AADC):
Alberello et al. (2021) Wave acquisition stereo-camera system mea-
surements (WASS) from a voyage of the S.A. Agulhas II, July2017, Ver. 1,
Australian Antarctic Data Centre—https://doi.org/10.26179/q9bd-5f74.
Code availability
MATLAB was used for the analysis. Data processing is described within
the manuscript and code is available from the first author upon
request.
References
1. Turner,J.&Comiso,J.SolveAntarctica’s sea-ice puzzle. Nature 547,
275–277 (2017).
2. Eayrs,C.,Li,X.,Raphael,M.N.&Holland,D.M.Rapiddeclinein
Antarctic sea ice in recent years hints at future change. Nat. Geosci.
14,460–464 (2021).
3. Williams, G. et al. Thick and deformed Antarctic sea ice
mapped with autonomous underwater vehicles. Nat. Geosci. 8,
61–67 (2015).
4. Li,T.etal.Resolvingfine-scale surface features on polar sea ice: a
first assessment of UAS photogrammetry without ground control.
Remote Sens. 11, 784 (2019).
5. Hobbs, W. R. et al. A review of recent changes in Southern Ocean
sea ice, their drivers and forcings. Glob. Planet. Change 143,
228–250 (2016).
6. Brouwer, J. et al. Altimetric observation of wave attenuation
through the antarctic marginal ice zone using icesat-2. Cryosphere
16,2325–2353 (2022).
7. Pope, A. et al. Community review of Southern Ocean satellite data
needs. Antarct. Sci. 29,97–138 (2017).
8. Newman,L.etal.Delivering sustained, coordinated, and integrated
observations of the Southern Ocean for global impact. Front. Mar.
Sci. 6, 433 (2019).
9. Williams,T.D.,Bennetts,L.G.,Squire,V.A.,Dumont,D.&Bertino,L.
Wave-ice interactions in the marginal ice zone. Part 1: theoretical
foundations. Ocean Model. 71,81–91 (2013).
10. Williams,T.D.,Bennetts,L.G.,Squire,V.A.,Dumont,D.&Bertino,L.
Wave-ice interactions in the marginal ice zone. Part 2: Numerical
implementation and sensitivity studies along 1D transects of the
ocean surface. Ocean Model. 71,92–101 (2013).
11. Kohout, A., Williams, M., Dean, S. & Meylan, M. Storm-induced sea-
ice breakup and the implications for ice extent. Nature 509,
604 (2014).
12. Robin, G. D. Q. Wave propagation through fields of pack ice. Philos.
Trans. Roy. Soc. A 255,313–339 (1963).
13. Squire, V. A. & Moore, S. M. Direct measurement of the attenuation
of ocean waves by pack ice. Nature 283,365–368 (1980).
14. Wadhams, P., Squire, V. A., Ewing, J. A. & Pascal, R. W. The effect of
the marginal ice zone on the directional wave spectrum of the
ocean. J. Phys. Oceanogr. 16,358–376 (1986).
15. Bennetts, L. G., O’Farrell, S. & Uotila, P. Impacts of ocean-wave-
induced breakup of Antarctic sea ice via thermodynamics in a
stand-alone version of the CICE sea-ice model. Cryosphere 11,
1035–1040 (2017).
16. Roach,L.A.,Horvat,C.,Dean,S.M.&Bitz,C.M.Anemergentseaice
floe size distribution in a global coupled ocean-sea ice model. JGR
Oceans 123,4322–4337 (2018).
17. Thomson, J. et al. Overview of the Arctic sea state and boundary
layer physics program. J. Geophys. Res. Oceans 123,
8674–8687 (2018).
18. Kohout, A. et al. Observations of exponential wave attenuation in
Antarctic sea ice during the pipers campaign. Ann. Glaciol. 61,
1–14 (2020).
19. Doble, M. J. & Bidlot, J. R. Wave buoy measurements at the Antarctic
sea ice edge compared with an enhanced ECMWF WAM: Progress
towards global waves-in-ice modelling. Ocean Model. 70,
166–173 (2013).
20. Montiel, F., Squire, V. A., Doble, M., Thomson, J. & Wadhams, P.
Attenuation and directional spreading of ocean waves during a
storm event in the autumn Beaufort Sea marginal ice zone. J.
Geophys. Res. Oceans 123,5912–5932 (2018).
21. Meylan, M. H., Bennetts, L. G. & Kohout, A. L. In situ measurements
and analysis of ocean waves in the Antarctic marginal ice zone.
Geophys. Res. Lett. 41,5046–5051 (2014).
22. Rogers, W. E., Meylan, M. H. & Kohout, A. L. Estimates of spectral
wave attenuation in Antarctic sea ice, using model/data inversion.
Cold Reg. Sci. Technol. 182, 103198 (2020).
23. Montiel, F., Kohout, A. L. & Roach, L. A. Physical drivers of ocean
wave attenuation in the marginal ice zone. J. Phys. Oceanog.
https://doi.org/10.1175/JPO-D-21-0240.1 (2022).
24. Ardhuin, F. et al. Estimates of ocean wave heights and attenuation in
sea ice using the sar wave mode on sentinel-1a. Geophys. Res. Lett.
42,2317–2325 (2015).
25. Stopa, J. E., Sutherland, P. & Ardhuin, F. Strong and highly variable
push of ocean waves on Southern Ocean sea ice. Proc. Natl. Acad.
Sci. 115, 5861–5865 (2018).
26. Meylan, M. H. et al. Dispersion relations, power laws, and energy
loss for waves in the marginal ice zone. J. Geophys. Res. Oceans
123, 3322–3335 (2018).
27. Squire, V. A. Ocean wave interactions with sea ice: a reappraisal.
Annu.Rev.FluidMech.52,37–60 (2020).
28. Meylan, M. H., Horvat, C., Bitz, C. M. & Bennetts, L. G. A floe size
dependent scattering model in two- and three-dimensions for wave
attenuation by ice floes. Ocean Model. 161, 101779 (2021).
29. Doble, M. J., De Carolis, G., Meylan, M. H., Bidlot, J.-R. & Wadhams,
P. Relating wave attenuation to pancake ice thickness, using field
measurements and model results. Geophys. Res. Lett. 42,
4473–4481 (2015).
30. Boutin, G. et al. Towards a coupled model to investigate wave-sea
ice interactions in the Arctic marginal ice zone. Cryosphere 14,
709–735 (2020).
Article https://doi.org/10.1038/s41467-022-32036-2
Nature Communications | (2022) 13:4590 9
Content courtesy of Springer Nature, terms of use apply. Rights reserved
31. Benetazzo, A. et al. Stereo wave imaging from moving vessels:
practical use and applications. Coast. Eng. 109,114–127 (2016).
32. Sutherland, P. & Gascard, J.-C. Airborne remote sensing of ocean
wave directional wavenumber spectra in the marginal ice zone.
Geophys. Res. Lett. 43,5151–5159 (2016).
33. Sutherland, P., Brozena, J., Rogers, W. E., Doble, M. & Wadhams, P.
Airborne remote sensing of wave propagation in the marginal ice
zone. J. Geophys. Res. Oceans 123,4132–4152 (2018).
34. Alberello, A. et al. Pancake ice floe size distribution during the
winter expansion of the Antarctic marginal ice zone. Cryosphere 13,
41–48 (2019).
35. Collard, F., Ardhuin, F. & Chapron, B. Monitoring and analysis of
ocean swell fields from space: new methods for routine observa-
tions. J. Geophys. Res.114, C07023 (2009).
36. Campbell, A. J., Bechle, A. J. & Wu, C. H. Observations of surface
waves interacting with ice using stereo imaging. J. Geophys. Res.
Oceans 119,3266–3284 (2014).
37. Smith, M. & Thomson, J. Pancake sea ice kinematics and dynamics
using shipboard stereo video. Ann. Glaciol. 1–11, https://doi.org/10.
1017/aog.2019.35 (2019).
38. Worby, A. P. A technique for making ship-based observations of
Antarctic sea ice thickness and characteristics. 14 (Antarctic
CRC, 1999).
39. Vichi, M. et al. Effects of an explosive polar cyclone crossing the
Antarctic marginal ice zone. Geophys. Res. Lett. https://doi.org/10.
1029/2019GL082457 (2019).
40. Young, I. R., Fontaine, E., Liu, Q. & Babanin, A. V. The wave climate of
the southern ocean. J. Phys. Oceanogr. 50,1417–1433 (2020).
41. Copernicus Climate Change Service. ERA5: Fifth generation of
ECMWF atmospheric reanalyses of the global climate (Copernicus
Climate Change Service Climate Data Store (CDS), 2017).
42. Holthuijsen, L. H. Waves in Oceanic and Coastal Waters (Cambridge
University Press, 2007).
43. World Meteorological Organization. Guidetowaveanalysisand
forecasting, WMO-No 702 (World Meteorological Organization
Geneva, Switzerland, 1998).
44. de Jong, E. et al. Sea iceconditions within theAntarctic marginal ice
zone in winter 2017, onboard the SA Agulhas II, https://doi.org/10.
1594/PANGAEA.885211 (2018).
45. Wadhams, P., Aulicino, G., Parmiggiani, F., Persson, P. O. G. & Holt,
B. Pancake ice thickness mapping in the Beaufort sea from wave
dispersion observed in SAR imagery. J. Geophys. Res. Oceans
https://doi.org/10.1002/2017JC013003 (2018).
46. Shen, H. H., Ackley, S. F. & Hopkins, M. A. A conceptual model for
pancake-ice formation in a wave field. Ann. Glaciol. 33,
361–367 (2001).
47. Kohout, A. L., Penrose, B., Penrose, S. & Williams, M. J. A device for
measuring wave-induced motion of ice floes in the Antarctic mar-
ginal ice zone. Ann. Glaciol. 56,415–424 (2015).
48. Alberello, A. et al. Drift of pancake ice floes in the winter Antarctic
marginal ice zone during polar cyclones. J. Geophys. Res. Oceans
125, e2019JC015418 (2020).
49. Thomson, J., Hošeková, L., Meylan, M. H., Kohout, A. L. & Kumar, N.
Spurious rollover of wave attenuation rates in sea ice caused by
noise in field measurements. J. Geophys. Res. Oceans 126,
e2020JC016606 (2021).
50. Onorato, M. et al. Statistical properties of directional ocean waves:
the role of the modulational instability in the formation of extreme
events. Phys. Rev. Lett. 102,114502(2009).
51. Toffoli, A. et al. Wind generated rogue waves in an annular wave
flume. Phys.Rev.Lett.118,144503(2017).
52. Womack, A., Vichi, M., Alberello, A.&Toffoli,A.Atmosphericdrivers
of a winter-to-spring lagrangian sea-ice drift in the eastern antarctic
marginal ice zone. J. Glaciol. 1–15, https://doi.org/10.1017/jog.2022.
14 (2022).
53. Aouf, L. et al. New directional wave satellite observations: Towards
improved wave forecasts and climate description in southern
ocean. Geophys. Res. Lett. 48, e2020GL091187 (2021).
54. Bennetts, L. G. & Squire, V. A. On the calculation of an attenuation
coefficient for transects of ice-covered ocean. Proc.R.Soc.Math.
Phys.Eng.Sci.468,136–162 (2012).
55. Li,J.,Kohout,A.L.&Shen,H.H.Comparisonofwavepropagation
through ice covers in calm and storm conditions. Geophys. Res.
Lett. 42,5935–5941 (2015).
56. Liu, Q., Rogers, W. E., Babanin, A., Li, J. & Guan, C. Spectral mod-
eling of ice-induced wave decay. J. Phys. Oceanogr. 50,
1583–1604 (2020).
57. Zhao, X. & Zhang, C. A theoretical model of wind-wave
growth over an ice-covered sea. Bound.-Layer Meteorol. 178,
1–19 (2020).
58. Dolatshah,A.etal.Hydroelasticinteractions between water waves
and floating freshwater ice. Phys. Fluids 30,091702(2018).
59. Ardhuin, F., Otero, M., Merrifield, S., Grouazel, A. & Terrill, E. Ice
breakup controls dissipation of wind waves across
southern ocean sea ice. Geophys. Res. Lett. 47,
e2020GL087699 (2020).
60. Bergamasco, F., Torsello, A., Sclavo, M., Barbariol, F. & Benetazzo,
A. WASS: an open-source pipeline for 3D stereo reconstruction of
ocean waves. Comput. Geosci. 107,28–36 (2017).
61. Benetazzo, A. Measurements of short water waves using
stereo matched image sequences. Coast. Eng. 53,
1013–1032 (2006).
62. Young, I. R. On the measurement of directional wave spectra. Appl.
Ocean Res. 16,283–294 (1994).
63. Donelan, M. A., Drennan, W. M. & Magnusson, A. K. Nonstationary
analysis of the directional properties of propagating waves. J. Phys.
Oceanogr. 26,1901–1914 (1996).
64. Faltinsen, O. Sea loads on ships and offshore structures, vol. 1
(Cambridge university press, 1993).
65. Hanson, J. L. & Phillips, O. M. Automated analysis of ocean surface
directional wave spectra. J. Atmos. Ocean. Technol. 18,
277–293 (2001).
66. Hasselmann, S., Brüning, C., Hasselmann, K. & Heimbach, P. An
improved algorithm for the retrieval of ocean wave spectra from
synthetic aperture radar image spectra. J. Geophys. Res. 101,
16615–16629 (1996).
67. Jiang, H., Babanin, A. V. & Chen, G. Event-based validation of swell
arrival time. J. Phys. Oceanogr. 46,3563–3569 (2016).
68. Derkani,M.H.Waves in the Southern Ocean and Antarctic Marginal
Ice Zone: Observations and modelling. Ph.D. thesis (2021).
69. Kahma, K. K. & Calkoen, C. J. Reconciling discrepancies in the
observed growth of wind-generated waves. J. Phys. Oceanogr. 22,
1389–1405 (1992).
Acknowledgements
The expedition was funded by the South African National Antarctic
Programme through the National Research Foundation. This work was
motivated by the Antarctic Circumnavigation Expedition (ACE) and
partially funded by the ACE Foundation and Ferring Pharmaceuticals.
A.A., L.B. and A.T. were supported by the Australian Antarctic Science
Programme (project 4434). A.A. acknowledges support from the Japa-
nese Society for the Promotion of Science (PE19055). L.G.B. is supported
by the Australian Research Council (FT190100404). L.G.B. and A.T. are
supported by the Australian Research Council (DP200102828). M.O. was
supported by the Simons Collaboration on Wave Turbulence, Award No.
617006, and from the “Departments of Excellence 2018-2022”Grant
awarded by the Italian Ministry of Education, University and Research
(MIUR, L.232/2016). M.O. acknowledges the EU H2020 FET Open
BOHEME, Grant No. 863179. M.V. and K.M. were supported by the NRF
SANAP contract UID118745. C.E. was supported under NYUAD Center for
Article https://doi.org/10.1038/s41467-022-32036-2
Nature Communications | (2022) 13:4590 10
Content courtesy of Springer Nature, terms of use apply. Rights reserved
Global Sea Level Change project G1204. We are indebted to Captain
Knowledge Bengu and the crew of the S.A. Agulhas II for their invaluable
contribution to data collection. ERA5 reanalysis was obtained using
Copernicus Climate Change Service Information. M.O. acknowledges
B. GiuliNico for interesting discussions. A.A., A.T. and M.O. thank
L. Fascette for technical support during the cruise.
Author contributions
Conceptualisation: A.A., L.G.B., M.O., A.T. Methodology: A.A., L.G.B.,
M.O., M.V., K.M.H., C.E., B.N.N., A.B., F.B., F.N., R.P., H.C., A.T. Investi-
gation: A.A., L.G.B., M.O., M.V., A.T. Visualisation: A.A., L.G.B., I.T., A.T.
Supervision: A.A., L.G.B., A.T. Writing-original draft: A.A., L.G.B., M.O.,
M.V., A.B., F.B., A.T. Writing-review & editing: A.A., L.G.B., M.O., M.V.,
K.M.H., C.E., B.N.N., A.B., F.B., F.N., R.P., H.C., I.T., A.T.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version contains
supplementary material available at
https://doi.org/10.1038/s41467-022-32036-2.
Correspondence and requests for materials should be addressed to
Alberto Alberello.
Peer review information Nature Communications thanks Clarence
Collins and Dany Dumont for their contribution to the peer review of this
work. Peer reviewer reports are available.
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