# Analysis of Arctic Buoy Dynamics using the Discrete Fourier Transform and
Principal Component Analysis

James H. Hepworth  Department of Mechanical Engineering
University of Cape Town
Cape Town, South Africa
<EMAIL_ADDRESS>Amit Kumar Mishra  Department of Electrical
Engineering
University of Cape Town
Cape Town, South Africa
<EMAIL_ADDRESS>
###### Abstract

Sea-Ice drift affects various global processes including the air-sea-ice
energy system, numerical ocean modelling, and maritime activity in the polar
regions. Drift has been investigated via various technologies ranging from
satellite based systems to ship or ice-borne processes. This paper analyses
the dynamics of sea-drift in the Arctic over 2019-2021 by Fourier Analysis and
Principal Component Analysis of displacement data generated from the drift
tracks of Ice-Tethered Profilers. We show that the frequency characteristics
of drift support the notion that it is a function of both slowly varying
processes, and higher frequency, random, forcing. In addition, we show that
displacement data features high correlation between deployment locations and,
consequently, suggest that there is scope for the optimisation of profiler
deployment locations and for the reduction in number of instruments required
to capture the displacement characteristics of drift.

###### Index Terms:

Ice-Tethered Profilers, Sea-Ice Drift, Fourier Analysis, Principal Component
Analysis

##  I Introduction

Sea-ice drift is a phenomenon of interest as a scientific parameter due to its
role in the air-sea-ice energy systems at the poles, its role in high
resolution regional ocean models, and as it relates to the operation of marine
vessels in ice-covered waters [1]. Since the 1980s sea-ice drift has been
understood to be a combination of seasonal (or longer time scale) effects
which are responsible for slowing changing, mean motion, and rapidly changing,
higher frequency, random components [2, 3]. Low-frequency effects are the
response to the mean effect of phenomena such as ocean currents [3], wind [4],
and tidal forcing [5], however the high-frequency artifacts present in sea-ice
drift velocities in the Arctic have been shown to be multi-fractal and more
complex than can be explained purely be forcing due to the ocean and
atmosphere [3, 6, 7].

Several remote sensing technologies have been employed to assess sea-ice
drift: These include various satellite-based approaches such visual and Infra-
Red spectrum imaging [8]; Synthetic Aperture Radar [9, 10, 11] and Passive
Microwave imaging [12, 13]; whilst ship borne marine radar [1] has recently
been used for the analysis of sub-mesoscale drift at high resolutions. In
addition to these, the use of in-situ data sets generated by ice-tethered
instruments which drift with the ice and act as Lagrangian trackers, provide
useful data from which drift can be directly investigated.

Ice-Tethered Profilers (ITPs) are in-situ, ocean monitoring instruments
designed to sample temperature and salinity of the ocean at a range of depths
up to 800 m below the surface of the ocean via a sensor unit able to travel a
tether suspended from an ice-floe mounted surface unit [14, 15]. The surface
unit collects the Global Positioning System (GPS) locations of top of the
tether and thus, in addition to temperature and salinity depth profiles, sea-
ice drift can be tracked against time from the Eulerian viewpoint of the GPS.
Several of these instruments have been successfully deployed in the Arctic
each year since the mid-2000s resulting in over 100 unique data sets being
generated: Several are ongoing whilst numerous missions are complete. In this
paper, the terms, “buoys” and “ITPs” are used synonymously.

In this paper we investigate the latest available data sets from completed ITP
missions in the Arctic Ocean for instrument deployments spanning the period
from October 2019 to August 2020 and again from late October 2021 until the
end of that year. The motion characteristics of ice drift over this period are
determined using two methods: Fourier analysis of discrete buoy displacement
data sets and Principal Component Analysis (PCA) of the same data.

Here we show, first, that the drift of buoys deployed across the Arctic show
similar primary frequency components which do not depend on the actual
location of the instrument and the corresponding geometry of the drift track.
Second, our results confirm the notion of sea-ice drift being a function of
two parts: slow, low frequency drivers governing mean motion, and high
frequency additions responsible for the random motion of ice at short time
scales. Finally, we show a high degree of correlation within data from
concurrently deployed buoys and, hence, make the argument that the number of
deployed buoys can be reduced if specific experimental goals can be met using
analysis of displacement derived from the drift profiles, such as experiments
which investigate the rates of surface drift for various regions.

The remainder of this paper is organised as follows. First, in in Section II,
the methodological approach used to perform the investigation is presented,
including the source of data and its pre-processing. The particular drift
profiles in this analysis are then shown in Section III before the results of
Fourier Analysis and PCA are shown in Sections IV and V, respectively.
Finally, the contributions made by this paper are discussed and concluded in
Section VI.

##  II Methodology

###  II-A Source of data sets

In this paper, drift tracks and sequential displacement data sets of ITPs were
developed from the raw GPS position data of ITPs deployed in the Arctic Ocean
between 2019 and 2021. The Ice-Tethered Profiler data were collected and made
available by the Ice-Tethered Profiler Program based at the Woods Hole
Oceanographic Institution (https://www2.whoi.edu/site/itp/) [14, 16]. The full
data sets for the years of analysis in this paper as well as those for all
other completed missions are available on request.

###  II-B Pre-processing of data

For the purpose of this analysis, only completed ITP mission data sets from
the 2019-2021 period are used. GPS locations are sampled from the buoys at
varying frequencies with different buoys using a variety of nominal sample
frequencies ranging from every 30 minutes to every 6 hours. Additionally, all
raw data sets show gaps where GPS locations were unable to be determined for
several sample periods. Both Fourier analysis and time-domain PCA require
constant sampling rates, whilst PCA also requires parallel samples to be taken
at the same instant in time. Thus, the data required pre-processing to ensure
that position measurements were rounded to a equatable time instances and to
ensure that each data set contained entries at equal sample rates.
Accordingly, the raw data sets were pre-processed as shown by the flowchart in
Figure 1 below.

Figure 1:  Pre-processing algorithm applied to the raw locations data set from
each completed ITP mission.

As Figure 1 indicates, data sets were abandoned after a time gap of more than
24 hours was detected. From the collection of new data sets produced, each
containing data points separated by 30 minutes on the daily half-hour marks
(UTC) the analyses described in Sections IV and V below were conducted.

###  II-C Fourier Analysis

The Fourier transform is used, in general, to decompose, continuous, cyclic
signals in the time-domain into a sum of sinusoids whose amplitudes and can be
represented in the frequency domain. This allows investigation into the
effects of processes occurring at particular frequencies on the motion as a
whole to be evaluated. However, the data used in this investigation are
discrete and finite rather than continuous and cyclic, with buoy locations
starting in one position and ending at another in the data set. Therefore, to
account for the discontinuity in the data sets between these start and end
locations, a Hanning window, as shown in Equation 1, below, was used in
conjunction with the Discrete Fourier Transform (DFT).

$w(i)=0.5-0.5\cos\left(\frac{2\pi i}{N-1}\right),\quad 0\leq i\leq N-1$ (1)

Here, $w(i)$ is the magnitude of the window output, i is the instantaneous
sample number of the window, and N is the length of the window output data
set, necessarily of the same length as the displacement data set under
evaluation. The DFT was applied to the data according to Equation 2, below
[17]:

$|X_{k}|=\frac{1}{N}\sum_{n=0}^{N-1}x_{n}e^{-i2\pi knw(i)/N},\quad
k=0,\ldots,N-1.$ (2)

Here, N is, again, the number of entries in the data set, n is the
instantaneous sample, k is the instantaneous frequency, xn is the sinusoidal
value of the instantaneous sample, and $|X_{k}|$ is the amplitude of the
signal.

###  II-D Principal Component Analysis

PCA is a data transformation technique used to determine the optimal bases of
data sets such that maximal variance in the data is captured using the fewest
basis vectors. Individual ITP data sets (time series) were first collected
into a matrix, $\bm{X}$, with each column representing each sensor/data set,
and then centred about their mean values, $\bm{\mu}$, and standardised by
their standard deviations, $\bm{\sigma}$, to eliminate the effect of possible
wide variation of magnitude in the original data. This produces the matrix,
$\bm{Z}$. The covariance matrix of $\bm{Z}$, the correlation matrix, was then
calculated, before the matrix of eigenvectors, $\bm{P}$, were determined
according to Equation 3, below:

$\bm{corr}=\bm{Z^{T}Z}=\bm{PDP^{-1}}$ (3)

Here, $\bm{D}$ is a diagonal matrix of the eigenvalues corresponding to the
eigenvectors $\bm{P}$. Once the vectors of $\bm{P}$ are sorted according to
the descending order of the eigenvalues in $\bm{D}$ to form $\bm{P^{\prime}}$,
the centred representation of $\bm{X}$ according to the new basis vectors
given by the eigenvectors of the correlation matrix of $\bm{Z}$ is determined,
$\bm{Z^{\prime}}$, according to Equation 4, below:

$\bm{Z^{\prime}}=\bm{PZP^{\prime}}$ (4)

The reconstruction of data, $\bm{X^{\prime}}$, according to the original bases
can be accomplished according to Equation 5, below:

$\bm{X^{\prime}}=\bm{Z^{\prime}P^{\prime T}}\bm{\sigma}+\bm{\mu}$ (5)

##  III Drift of ITPs in the Arctic

The drift tracks shown in Figure 2, below, are those of concurrently deployed
ITPs in the Arctic in 2019-2020, and 2021. From these figures it is evident,
that, broadly speaking, drift behaviour is dependent on location with buoys
deployed in the Eurasian Basin showing more linear translation southward (e.g.
ITPs 102 and 116 in 2020), and buoys deployed in the Amerasian Basin showing a
less linear drift (e.g. top2 and top4 in 2021). From these drift tracks, the
half-hourly displacement (geodesic distance) was calculated between
consecutive locations to produce a displacement data set.

Due to the significant differences in apparent motion for buoys in the
Amerasian Basin from those in the Eurasian Basin, the displacement data sets
were then split into two data sets: The first, termed the Amerasian section in
this paper, consisting of buoys deployed in the window bounded by 180-120 ºW
and 65-85 ºN, and the second, termed the Eurasian section, for those not
deployed in that window. These location specific data sets of ITP
displacements every half-hour were then used in the analyses of Section IV and
Section V.

Figure 2:  Drift tracks of concurrently deployed ITPs in the Arctic in years
2019-2020 (top) and 2021 (bottom). The end locations of the instruments are
shown with a square marker.

##  IV Fourier Analysis

The DFT described in Section II-C, above, was applied to the zonal and
meridional displacement data sets, via a Hanning window, and normalised by the
number of samples to produce the frequency responses shown in Figure 3, above.
These plots, whilst only showing the responses for buoys in the Eurasian
section in 2019-2020 and the Amerasian section in 2021, are representative of
those from the corresponding sections in the years not shown as well.

Figure 3:  Normalised DFTs of the ITP displacements for the Amerasian section
in 2021 (top), and the Eurasian section in 2019-2020 (bottom).

The description of sea-ice drift in the Arctic as the sum of slow, seasonal
(or longer), processes and high frequency fluctuations is supported by the
results of Figure 3. Here, it is clear from the low frequency peaks,
predominantly between 10-1 and 100 km2/$\mu$Hz, that displacement is primarily
driven by slow, DC, processes. However it can also be seen that a secondary
dominant component of the order of 10-2 km2/$\mu$Hz is evident at $\sim$22.6
$\mu$Hz (or every 12.3 hours) which corresponds well with the tidal frequency
[18]. In addition to these primary features in the data, of interest are the
peaks in almost all ITP data sets of $\sim$10-3 km2/$\mu$Hz which begin at
$\sim$81 $\mu$Hz (or 3.4 hours) and repeat with increasing frequency with
every $\sim$11.6 $\mu$Hz above this threshold until the Nyquist frequency for
the data is reached at $\sim$277 $\mu$Hz (or every 1 hour).

##  V Principal Component Analysis

PCA was then applied to the same displacement drift data sets as used in the
Fourier analysis above, and applied separately to the Eurasian and Amerasian
sections for each year as before. Presented in Table I, overleaf, are the
percentages of the cumulative variance captured by the first two principal
components (PCs) for the data assessed.

TABLE I:  Cumulative variance of ITP displacement captured by the first two PCs  Year |  Eurasian Section |  Amerasian Section
---|---|---
2019-2020 |  95.3% |  74.5%
2021 |  100% |  83.9%

Reconstruction of the displacement data sets using only the first two PCs was
then performed. Figure 4, overleaf, shows the similarity of the reconstructed
displacement signals with the original data. Here it can be seen that the plot
of ITP 103 has been reconstructed more effectively than that of ITP 104.
Quantitatively, the RMS error in reconstruction of ITP 103 is 0.030 km
compared to 0.078 km for ITP 104. This is due to the magnitudes of ITP 103’s
motion being greater than 104’s and thus contributing more to the total
variance of the original data set. Therefore, its motion is more likely to be
captured by the first two PCs which capture the dominant sources of variation.

Figure 4:  Comparison between selected original data plots of two ITPs in
2019-2020 (top) with the reconstructed plots formed using two PCs.

The DFT was also applied to these reconstructed data sets in the same manner
shown in Section IV. The results of these transforms are shown in Figure 5,
opposite. It’s similarity with Figure 3 suggests that the frequency
characteristics of the displacement data sets consisting of (in these cases)
up to 10 ITPs can be approximated with far fewer, optimal, drifters. I.e.
those that would have drifted according to a pattern sufficient to generate
the displacements given by the first two PCs.

Figure 5:  DFT results from the displacement data reconstructed from the first
two PCs for the 2019-2020 Eurasian ITPs (bottom) and 2021 Amerasian ITPs
(top).

Further, during the PCA analysis, the coefficients of correlation, r, between
distinct ITPs were resultant. ITPs in close vicinity of each other show high
degrees of correlation in their drift motion whilst those separated by great
distances are not correlated. Table II, opposite, shows the r values between
the displacements of selected ITPs. ITPs 102 and 94 (the blue and orange
tracks at the top of Figure 2) which overlap and follow very similar
trajectories in 2019-2020 are highly correlated. Conversely, ITPs 102 and 94
are highly uncorrelated with ITP 112 (purple in Figure 2). Similar results are
evident for 2021 as well.

TABLE II:  Correlation coefficients for selected ITPs in 2019-2020  ITP |  102 |  94 |  112
---|---|---|---
102 |  1 |  0.841 |  0.039
94 |  0.841 |  1 |  0.052
112 |  0.039 |  0.052 |  1

##  VI Discussion and Conclusion

In this paper we have described the process followed to investigate the drift
of ITPs deployed in the Arctic over the years 2019-2021 via Fourier analysis
and PCA of the displacement data sets derived from the time series of GPS
locations available for each completed ITP mission in that period. The drift
plots shown in Section III highlight the fact that drift of sea-ice in the
Arctic is highly variable between significantly separated buoys but can show
high similarity in profile if the points of observation are close together.

Section IV analysed the frequency components of the displacement data using
the DFT. Here, it was shown that, despite the vastly different different drift
profiles evident across the Arctic sections, similar processes drive the
displacement of sea-ice: The low-frequency primary component of the signals at
$\sim$0 Hz can be attributed to the average of long-term features in the
environment such as ocean currents and prevailing winds [2, 19], whilst the
second dominant peak at $\sim$22.6 $\mu$Hz aligns with the tidal frequency.
Together these support the notion that sea-ice drift is primarily driven by
slow processes. Of interest are the repeating peaks in the DFT outputs of all
displacement data every 11.6 $\mu$Hz increasing from $\sim$81 $\mu$Hz.
Physical drivers of these features have not been determined and are the
ongoing subject of further investigation. The nature of the DFT results here
have implications for ice-tethered sensor design and their sampling strategy
when drift analysis is the primary experimental goal; most notably that they
should be optimised for low frequencies due to the fact that the low frequency
features in the DFT response are 1-3 orders of magnitude greater in amplitude
than those which repeat with increasing frequency. Sensors can, therefore, be
sampled at low frequencies with low-power states being entered between
sampling to reduce their power demands and increase their battery run time
whilst still capturing the dominant drivers of drift. In addition, the use of
low-pass filtering can be employed to reduce the influence of noise on the
data obtained. Further, due to the similarities in the DFT results across all
regions of the Arctic, one can have confidence that a drift sensor design and
sampling strategy developed for deployment in one region will also be suitable
for any other region.

Section V applied PCA to the data sets and showed, empirically, that high
correlation in drift dynamics are evident between sensors deployed in near
vicinity to each other. This was shown by the correlation coefficients of
example buoys approaching 1 in these cases. This section also showed that the
displacement data from concurrently deployed buoys can be reconstructed with
high accuracy from only two principal components. This implies that fewer
buoys can be deployed for experiments which aim to analyse the displacement of
sea-ice drift from in-situ sensors (for example [19]). This has potential
implications to both reduce the cost of experiments through the use of fewer
buoys if their deployment locations are optimally chosen, and to and increase
the efficiency of experimental deployments from time and resource constraint
perspectives. These results help to present the case for the development of a
methodology to optimise the choice of deployment locations for ice-tethered
sensors measuring sea-ice drift. This subject is the immediate focus of the
authors attention.

Further, for a given experimental monetary budget, the fewer the number of
buoys that are required to achieve a particular experimental goal, the greater
the proportion of the budget that can be allocated to the engineering
requirements of the project. I.e higher quality sensors or materials could be
used to increase the confidence or accuracy of data generated, or the lifespan
of the system. Several studies highlight that despite the wealth of existing
historical data from the Arctic, both from remote sensing and in-situ methods,
there is a need for increased measurements to provide the required data to
better understand the rapidly changing environment of the Arctic [20, 21, 22].
Consequently, optimising the deployment of buoys such that high quality data
may be timeously obtained across a wide area, is a pressing need in order to
provide these data to the physical and numerical oceanography scientific
communities.

These factors, discussed above, also apply to the study of the Southern Ocean
(SO), where they are, arguably, of even greater concern. The SO has a
significant effect on the major ecological, climate and environmental systems
of the Earth, however, the SO is simultaneously one of the most under-sampled
and least observed environments on Earth, leading to large uncertainties with
and wide variations between the outputs of various climate related products
[23]. This under-sampling is primarily due to the extreme remoteness and
harshness of the environment making it difficult and expensive to access and
to deploy in-situ sensors [24, 25, 26]. Our own experience has shown that ice-
tethered sensors which are routinely deployed in the Arctic do not survive the
conditions of the Antarctic well. Thus, ourselves and other researchers in
this field have resorted to the development of specifically designed buoys to
measure drift and other features in the Southern Ocean [27, 28]. In these
cases where deployment is difficult and costly, and turnkey sensor solutions
are not suitable, optimisation of sensor deployment and project budgets is of
great potential benefit. Accordingly, further analysis is underway to
determine the applicability of the results shown in this paper, and any
resultant deployment optimisation methodology developed, to regions of the
Antarctic ocean where the characterisation of the free-drift of sea-ice is
primitive and a subject of active research [29, 30].

##  VII Acknowledgement

This work has been supported with funding from Sentech Soc Ltd, South Africa.

## References

  * [1] B. Lund, H. C. Graber, P. O. G. Persson, M. Smith, M. Doble, J. Thomson, and P. Wadhams, “Arctic sea ice drift measured by shipboard marine radar,” _J. Geophys. Res. C: Oceans_ , vol. 123, no. 6, pp. 4298–4321, Jun. 2018.
  * [2] A. S. Thorndike, “Diffusion of sea ice,” _J. Geophys. Res._ , vol. 91, no. C6, p. 7691, 1986\.
  * [3] P. Rampal, J. Weiss, D. Marsan, and M. Bourgoin, “Arctic sea ice velocity field: General circulation and turbulent-like fluctuations,” _J. Geophys. Res._ , vol. 114, no. C10, Oct. 2009.
  * [4] N. F. Tandon, P. J. Kushner, D. Docquier, J. J. Wettstein, and C. Li, “Reassessing sea ice drift and its relationship to long‐term arctic sea ice loss in coupled climate models,” _J. Geophys. Res. C: Oceans_ , vol. 123, no. 6, pp. 4338–4359, Jun. 2018.
  * [5] P. Heil, J. K. Hutchings, A. P. Worby, M. Johansson, J. Launiainen, C. Haas, and W. D. Hibler, “Tidal forcing on sea-ice drift and deformation in the western weddell sea in early austral summer, 2004,” _Deep Sea Res. Part 2 Top. Stud. Oceanogr._ , vol. 55, no. 8-9, pp. 943–962, Apr. 2008.
  * [6] P. Rampal, V. Dansereau, E. Olason, S. Bouillon, T. Williams, A. Korosov, and A. Samaké, “On the multi-fractal scaling properties of sea ice deformation,” _cryosphere_ , vol. 13, no. 9, pp. 2457–2474, Sep. 2019.
  * [7] J. Weiss, D. Marsan, and P. Rampal, “Space and time scaling laws induced by the multiscale fracturing of the arctic sea ice cover,” in _IUTAM Symposium on Scaling in Solid Mechanics_. Springer Netherlands, 2009, pp. 101–109.
  * [8] W. J. Emery, A. C. Thomas, M. J. Collins, W. R. Crawford, and D. L. Mackas, “An objective method for computing advective surface velocities from sequential infrared satellite images,” _J. Geophys. Res._ , vol. 91, no. C11, p. 12865, 1986\.
  * [9] J. Curlander, B. Holt, and K. Hussey, “Determination of sea ice motion using digital SAR imagery,” _IEEE J. Oceanic Eng._ , vol. 10, no. 4, pp. 358–367, Oct. 1985.
  * [10] B. Holt, D. A. Rothrock, and R. Kwok, “Determination of sea ice motion from satellite images,” in _Microwave Remote Sensing of Sea Ice_ , ser. Geophysical monograph. Washington, D. C.: American Geophysical Union, 1992, pp. 343–354.
  * [11] S. Bouillon and P. Rampal, “On producing sea ice deformation data sets from SAR-derived sea ice motion,” _The Cryosphere_ , vol. 9, no. 2, pp. 663–673, 2015.
  * [12] R. Kwok, “Satellite remote sensing of sea-ice thickness and kinematics: a review,” _J. Glaciol._ , vol. 56, no. 200, pp. 1129–1140, 2010.
  * [13] H. Sumata, T. Lavergne, F. Girard-Ardhuin, N. Kimura, M. A. Tschudi, F. Kauker, M. Karcher, and R. Gerdes, “An intercomparison of arctic ice drift products to deduce uncertainty estimates,” _J. Geophys. Res. C: Oceans_ , vol. 119, no. 8, pp. 4887–4921, Aug. 2014.
  * [14] J. Toole, R. Krishfield, M.-L. Timmermans, and A. Proshutinsky, “The Ice-Tethered Profiler: Argo of the Arctic,” _Oceanography_ , vol. 24, no. 3, pp. 126–135, sep 1 2011. [Online]. Available: http://dx.doi.org/10.5670/oceanog.2011.64
  * [15] W. H. O. Institution, “Technology - ice tethered profilers,” https://www2.whoi.edu/site/itp/background/technology/, accessed: 2022-10-25.
  * [16] R. Krishfield, J. Toole, A. Proshutinsky, and M.-L. Timmermans, “Automated Ice-Tethered Profilers for Seawater Observations under Pack Ice in All Seasons,” _Journal of Atmospheric and Oceanic Technology_ , vol. 25, no. 11, pp. 2091–2105, nov 1 2008. [Online]. Available: http://dx.doi.org/10.1175/2008JTECHO587.1
  * [17] Q. Kong, T. Siauw, and A. Bayen, “Discrete fourier transform (dft) — python numerical methods,” https://pythonnumericalmethods.berkeley.edu/notebooks/chapter24.02-Discrete-Fourier-Transform.html/, accessed: 2022-10-21.
  * [18] NOAA, “Frequency of tides - the lunar day - tides and water levels: Noaa’s national ocean service education,” https://oceanservice.noaa.gov/education/tutorial_tides/tides05_lunarday.html/, accessed: 2022-10-21.
  * [19] M.-L. Timmermans, J. Toole, A. Proshutinsky, R. Krishfield, and A. Plueddemann, “Eddies in the canada basin, arctic ocean, observed from Ice-Tethered profilers,” _J. Phys. Oceanogr._ , vol. 38, no. 1, pp. 133–145, Jan. 2008.
  * [20] M.-L. Timmermans and J. Marshall, “Understanding arctic ocean circulation: A review of ocean dynamics in a changing climate,” _J. Geophys. Res. C: Oceans_ , vol. 125, no. 4, Apr. 2020.
  * [21] M.-L. Timmermans, R. Krishfield, C. Lee, and J. Toole, “ALPS II autonomous lagrangian platforms and sensors. a report of the ALPS II workshop,” in _ALPS in the Arctic Ocean_ , D. Rudnick, D. Costa, K. Johnson, C. Lee, and M.-L. Timmermans, Eds. National Science Foundation, 2018, pp. 37–39.
  * [22] A. T. Nguyen, C. Lee, L. Rainville, and P. Heimbach, “Arctic argo-type floats: The needs, potentials and challenges,” Tech. Rep., 2017.
  * [23] G. C. Smith, R. Allard, M. Babin, L. Bertino, M. Chevallier, G. K. Corlett, J. Crout, F. Davidson, B. Delille, S. T. Gille, D. Hebert, P. Hyder, J. Intrieri, J. Lagunas, G. Larnicol, T. Kaminski, B. J. Kater, F. Kauker, C. Marec, M. Mazloff, E. J. Metzger, C. Mordy, A. G. O’Carroll, S. M. Olsen, M. Phelps, P. Posey, P. Prandi, E. Rehm, P. Reid, I. Rigor, S. Sandven, S. Swart, O. M. Smedstad, A. Solomon, A. Storto, P. Thibaut, J. Toole, K. Wood, J. Xie, and Q. Yang, “Polar ocean observations: A critical gap in the observing system and its effect on environmental predictions from hours to a season,” _Frontiers in Marine Science_ , vol. 6, no. JUL, p. 429, Aug. 2019.
  * [24] L. Newman, P. Heil, R. Trebilco, K. Katsumata, A. J. Constable, E. van Wijk, K. Assmann, J. Beja, P. Bricher, R. Coleman, D. Costa, S. Diggs, R. Farneti, S. Fawcett, S. T. Gille, K. R. Hendry, S. F. Henley, E. Hofmann, T. Maksym, M. Mazloff, A. J. Meijers, M. P. Meredith, S. Moreau, B. Ozsoy, R. Robertson, I. R. Schloss, O. Schofield, J. Shi, E. L. Sikes, I. J. Smith, S. Swart, A. Wahlin, G. Williams, M. J. Williams, L. Herraiz-Borreguero, S. Kern, J. Lieser, R. Massom, J. Melbourne-Thomas, P. Miloslavich, and G. Spreen, “Delivering sustained, coordinated and integrated observations of the southern ocean for global impact,” _Frontiers in Marine Science_ , vol. 6, no. JUL, p. 433, Aug. 2019.
  * [25] L. Newman, O. Schofield, A. Wåhlin, A. Constable, S. Swaart, M. Williams, M. Mazloff, Y. Firing, and P. Bricher, “Understanding the southern ocean through sustained observations,” _Bull. Aust. Meteorol. Oceanogr. Soc._ , vol. 28, no. January, p. 170, 2016.
  * [26] F. Barbariol, A. Benetazzo, L. Bertotti, L. Cavaleri, T. Durrant, P. McComb, and M. Sclavo, “Large waves and drifting buoys in the southern ocean,” _Ocean Eng._ , 2019.
  * [27] J. N. Jacobson, “SHARC buoy: Robust firmware design for a novel, low-cost autonomous platform for the antarctic marginal ice zone in the southern ocean,” Master’s thesis, 2021.
  * [28] A. L. Kohout, B. Penrose, S. Penrose, and M. J. M. Williams, “A device for measuring wave-induced motion of ice floes in the antarctic marginal ice zone,” _Ann. Glaciol._ , vol. 56, no. 69, pp. 415–424, 2015.
  * [29] M. de Vos, M. Barnes, L. C. Biddle, S. Swart, C.-L. Ramjukadh, and M. Vichi, “Evaluating numerical and free-drift forecasts of sea ice drift during a southern ocean research expedition: An operational perspective,” _Journal of Operational Oceanography_ , vol. 15, no. 3, pp. 187–203, Sep. 2022.
  * [30] A. Womack, M. Vichi, A. Alberello, and A. Toffoli, “Atmospheric drivers of a winter-to-spring Lagrangian sea-ice drift in the Eastern Antarctic marginal ice zone,” _J. Glaciol._ , vol. 68, no. 271, pp. 999–1013, 2022.