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  <front>
    <journal-meta><journal-id journal-id-type="publisher">TC</journal-id><journal-title-group>
    <journal-title>The Cryosphere</journal-title>
    <abbrev-journal-title abbrev-type="publisher">TC</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">The Cryosphere</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1994-0424</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/tc-16-3005-2022</article-id><title-group><article-title>Reversal of ocean gyres near ice shelves in the Amundsen Sea caused by the
interaction of sea ice and wind</article-title><alt-title>Reversal of ocean gyres near ice shelves</alt-title>
      </title-group><?xmltex \runningtitle{Reversal of ocean gyres near ice shelves}?><?xmltex \runningauthor{Y. Zheng et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Zheng</surname><given-names>Yixi</given-names></name>
          <email>yixi.zheng@uea.ac.uk</email>
        <ext-link>https://orcid.org/0000-0003-3136-1311</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Stevens</surname><given-names>David P.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-7283-4405</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Heywood</surname><given-names>Karen J.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-9859-0026</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Webber</surname><given-names>Benjamin G. M.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-8812-5929</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Queste</surname><given-names>Bastien Y.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3786-2275</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Centre for Ocean and Atmospheric Sciences, School of Environmental
Sciences, University of East Anglia,<?xmltex \hack{\break}?> Norwich NR4 7TJ, UK</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Centre for Ocean and Atmospheric Sciences, School of Mathematics,
University of East Anglia, Norwich NR4 7TJ, UK</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Department of Marine Sciences, University of Gothenburg, Box 461, 405
30 Gothenburg, Sweden</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Yixi Zheng (yixi.zheng@uea.ac.uk)</corresp></author-notes><pub-date><day>28</day><month>July</month><year>2022</year></pub-date>
      
      <volume>16</volume>
      <issue>7</issue>
      <fpage>3005</fpage><lpage>3019</lpage>
      <history>
        <date date-type="received"><day>20</day><month>December</month><year>2021</year></date>
           <date date-type="rev-request"><day>18</day><month>January</month><year>2022</year></date>
           <date date-type="rev-recd"><day>13</day><month>May</month><year>2022</year></date>
           <date date-type="accepted"><day>5</day><month>June</month><year>2022</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2022 </copyright-statement>
        <copyright-year>2022</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://tc.copernicus.org/articles/.html">This article is available from https://tc.copernicus.org/articles/.html</self-uri><self-uri xlink:href="https://tc.copernicus.org/articles/.pdf">The full text article is available as a PDF file from https://tc.copernicus.org/articles/.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d1e133">Floating ice shelves buttress the Antarctic Ice Sheet,
which is losing mass rapidly mainly due to ocean-driven melting and the
associated disruption to glacial dynamics. The local ocean circulation near
ice shelves is therefore important for the prediction of future ice mass
loss and related sea-level rise as it determines the water mass exchange,
heat transport under the ice shelf and resultant melting. However, the
dynamics controlling the near-coastal circulation are not fully understood.
A cyclonic (i.e. clockwise) gyre circulation (27 km radius) in front of the
Pine Island Ice Shelf has previously been identified in both numerical
models and velocity observations. Mooring data further revealed a potential
reversal of this gyre during an abnormally cold period. Here we present
ship-based observations from 2019 to the west of Thwaites Ice Shelf,
revealing another gyre (13 km radius) for the first time in this habitually
ice-covered region, rotating in the opposite (anticyclonic, anticlockwise)
direction to the gyre near Pine Island Ice Shelf, despite similar wind
forcing. We use an idealised configuration of MITgcm, with idealised forcing
based on ERA5 climatological wind fields and a range of idealised sea ice
conditions typical for the region, to reproduce key features of the observed
gyres near Pine Island Ice Shelf and Thwaites Ice Shelf. The model driven
solely by wind forcing in the presence of ice can reproduce the horizontal
structure and direction of both gyres. We show that the modelled gyre
direction depends upon the spatial difference in the ocean surface stress,
which can be affected by the applied wind stress curl filed, the percentage
of wind stress transferred through the ice, and the angle between the wind
direction and the sea ice edge. The presence of ice, either it is fast
ice/ice shelves blocking the effect of wind or mobile sea ice enhancing the
effect of wind, has the potential to reverse the gyre direction relative to
ice-free conditions.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e145">Antarctic ice shelves are thinning rapidly due primarily to basal melting,
allowing the ice sheets to accelerate and lose mass (e.g. Pritchard et al.,
2012) to significantly contribute to the future sea-level rise (e.g. Bamber
et al., 2019; Golledge et al., 2019; DeConto et al., 2021). The highest
thinning rate has been observed among those ice shelves draining towards the
Amundsen Sea (e.g. Rignot et al., 2019; Paolo et al., 2015),
where relatively warm modified Circumpolar Deep Water (mCDW) intrudes onto
the Amundsen Sea continental shelf via bathymetric troughs, allowing it to
come into direct contact with the base of ice shelves (e.g. Rignot et al.,
2019; Heywood et al., 2016). The flux of the mCDW entering the ice shelf cavity determines the rate of ice shelf
melting (e.g. Jacobs et al., 2011; Dutrieux et al., 2014). Therefore,
understanding the local circulation that determines the flow of mCDW and its
associated heat transport toward the ice shelves is crucial for a better
prediction of ice shelf melting, future sea level and climate.</p>
      <p id="d1e148">Models and observations have revealed the presence of a cyclonic gyre in the
centre of Pine Island Bay (PIB; hereafter PIB gyre for this gyre). The gyre
is well defined between the sea surface and about 700 m depth, in front of
Pine Island Ice Shelf (Thurnherr et al., 2014; Heywood et al., 2016). Gyres
play an important role in local ocean circulation, distributing heat and
enhancing water mass exchange in the Amundsen Sea (Zheng et al., 2021;
Schodlok et al., 2012). Schodlok et al. (2012) use a high-resolution model to infer
that the strength of this small PIB gyre can be the main determinant of heat
transport toward the ice shelf and the associated glacial melt rate
(Schodlok et al., 2012). Zheng et al. (2021), Mankoff et al. (2012) and
Tortell et al. (2012) also suggest that the PIB gyre entrains water as it
exits the ice cavity, contributing to the spreading of glacial meltwater and
its associated heat, nutrients and freshwater. Yoon et al. (2022) further
mention that the PIB gyre can modulate heat delivery to the Pine Island Ice
Shelf.</p>
      <p id="d1e151">Despite the importance of gyres near ice shelves, they are poorly observed
and modelled as polar oceans are often ice-covered and their bathymetry
largely unknown, which limits the regular observations and high-resolution
models that resolve small gyres. The formation of the PIB gyre has been
attributed to the wind forcing and the meltwater outflow in the
southeastern Amundsen Sea (e.g. Thurnherr et al., 2014). Model results from
Heimbach and Losch (2012) show that the PIB gyre would be weaker by more
than two-thirds if wind forcing were absent. From October 2011 to May 2013,
moored current meters in PIB revealed a reversal of the ocean current
velocity (Webber et al., 2017), potentially indicating a change of PIB gyre
direction from cyclonic to anticyclonic. However, the driver of any reversal
is still uncertain as the limited available observations do not show a
change in the sign of the wind stress curl field or in meltwater outflow
locations.</p>
      <p id="d1e154">Sea ice may play a role in circulation in polar oceans by regulating the
heat and momentum exchange between the ocean and the atmosphere (e.g.
Meneghello et al., 2018). Meneghello et al. (2018) suggest that the
interplay among sea ice, wind and ocean can affect the wind-driven Beaufort
Gyre dynamics through the influence of sea ice on dampening ocean surface
currents, the so-called ice–ocean stress governor. This mechanism focuses
mainly on mobile ice and the processes occurring under ice cover (e.g.
Meneghello et al., 2018; Elvidge et al., 2016). Mobile ice may drag the
ocean and increase the wind stress field felt by the ocean through sea ice
(i.e. ocean surface stress, hereafter OSS), while fixed ice, including fast
ice and ice shelves, will reduce or entirely block OSS below ice.
Nevertheless, relatively little attention has been paid to fixed ice and
processes near the boundary of ice coverage in the context of wind-driven
polar gyres.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e160">Map of the southeastern Amundsen Sea. Schematics of Pine Island
Bay and Thwaites gyres are shown by thick blue arrows in front of Pine
Island Ice Shelf and to the west of Thwaites Ice Tongue, respectively. The
ice imagery is from Worldview Aqua/MODIS corrected reflectance (true colour)
on 3 March 2019. The climatological 10 m wind velocity from 2009–2019 ERA5
reanalysis (Hersbach et al., 2018) data (<inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">0.25</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">0.25</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>
resolution; wind velocity data are interpolated to 0.25 <inline-formula><mml:math id="M2" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> <inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">0.125</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> resolution. Only every other arrow in the zonal
direction is plotted for clarity) is denoted by orange arrows (see orange
scale vectors). The blue box covers the region of Thwaites gyres that is
used for Figs. 2 and 4. The inset map shows our study region.</p></caption>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f01.png"/>

      </fig>

      <p id="d1e209">The sparse spatial coverage of observations in these often-ice-covered
regions limits our understanding of the mechanisms regulating these gyres,
which motivates this study. In Sect. 2, we present a set of new observations
of another gyre near Thwaites Ice Shelf (hereafter Thwaites gyre;
Fig. 1). Similar to the PIB gyre, Thwaites gyre is influenced by a
climatologically cyclonic wind field (which favours cyclonic gyres);
however, it is anticyclonic, raising the intriguing question of what
mechanism(s) controls the direction of these gyres. We note the different
sea ice coverage over the Thwaites and PIB gyres and hence hypothesise that
sea ice can influence the OSS to alter the gyre direction. Considering the
sparse observations in the Amundsen Sea, we adopt a new approach to this
complex question. In Sect. 3, we introduce an idealised model designed to
explore the roles of wind and sea ice in determining the gyre features.
Section 4 presents the results of the idealised model when different ice
conditions and wind stress fields are applied. We discuss the limitations
and applications of the results and summarise the results in Sect. 5.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Observations of gyres in the west of Thwaites Ice Tongue</title>
      <p id="d1e220">From 25 February to 4 March 2019, the RV <italic>Nathaniel B. Palmer</italic> collected the
first hydrographic dataset to the west of Thwaites Ice Tongue as part of the
International Thwaites Glacier Collaboration: Thwaites-Amundsen Regional
Survey and Network (ITGC: TARSAN) project. Temperature and salinity profiles
were obtained using a Sea-Bird SBE 911<inline-formula><mml:math id="M4" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> CTD (conductivity, temperature,
depth) profiler with two pairs of conductivity and temperature sensors and
then vertically averaged into 1 dbar bins. Ocean current velocities over the
upper 980 m of the water column were obtained using a 75 kHz ocean surveyor
(OS75) and a 38 kHz ocean surveyor (OS38) shipboard acoustic Doppler current
profiler (sADCP). The amount of good-quality data reduced significantly, if
not completely, below a depth depending on the sADCP frequency, rolling of
the ship, water turbidity and bubbles passing below the sADCP. During
this campaign in the Thwaites gyre region, these depths are 400 m for OS75
and 760 m for OS38. Velocity measurements taken below these depths are
removed. All velocity measurements are then horizontally averaged into
<inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow><mml:mo>×</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> bins. No de-tiding has been applied to the
velocity measurements presented in this study because the moored current
meters and models in the region suggest that tidal currents are less than 2 cm s<inline-formula><mml:math id="M6" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> (Jourdain et al., 2019), and
bathymetry is so poorly known in this region that uncertainties in predicted
tidal model currents are of a similar magnitude.</p>
      <p id="d1e265">This region is habitually covered by sea ice year-round and has only opened
twice since 2000 (Worldview Aqua/MODIS corrected reflectance). The
newly obtained velocity dataset reveals the previously unreported Thwaites
gyre (blue arrows in Fig. 2). Based on the observations, we identify the
centre of Thwaites gyre at <inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">75</mml:mn></mml:mrow></mml:math></inline-formula><inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> S, <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">107.55</mml:mn></mml:mrow></mml:math></inline-formula><inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> W. We then calculate the tangential components of ocean
current around concentric circles centred on Thwaites gyre and average them
into 1 km radius bins (Fig. 3a). Thwaites gyre has an approximate radius of
13 km and can be well identified in the 30 to 430 m depth range covered by
the sADCP (Fig. 3a), recirculating about 0.2 Sv (i.e. <inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> m<inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:math></inline-formula> s<inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) of water. The ship
CTD survey reveals a detectable density gradient across the gyre (Fig. 3b, c, d). The tangential velocity increases with depth from the near surface
to about 130 m, where it reaches its highest speed (about 10 cm s<inline-formula><mml:math id="M14" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, Fig. 3a) and then decreases with depth to zero
at about 620 m. We calculate the average vertical shear of the tangential
velocities between 3–7 km from the gyre centre to quantify the baroclinicity
of the gyre, defined as the vertical gradient of the tangential velocity
between the velocity maximum (130 m) and minimum (620 m). The gyre velocity
decreases with depth at a relatively constant rate between these depths. The
calculated averaged vertical shear is <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> s<inline-formula><mml:math id="M16" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, i.e. a
change of 0.1 m s<inline-formula><mml:math id="M17" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> over 490 m. Note that Thwaites gyre is
anticyclonic, despite the local cyclonic wind stress curl, evident in both
the climatology (Fig. 1) and contemporaneous observations (Fig. 4),
favouring cyclonic gyres.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e393">Map of the Thwaites gyre region. The blue arrows indicate the
depth-averaged (30–430 m) current velocity from sADCP measurements
(observations are averaged to <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow><mml:mo>×</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> bins; see blue scale
vectors). The red star indicates the gyre centre. The orange arrows indicate
the 2009–2019 climatological wind from the ERA5 reanalysis (Hersbach et al., 2018)
(<inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">0.25</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">0.25</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> resolution; for
clarity, velocity data are interpolated to <inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">0.25</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">0.125</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> resolution; see orange scale vectors). The
pink shaded dots show the full-depth-averaged meltwater content calculated
from ship-based CTD data (see colour bar).</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f02.png"/>

      </fig>

      <p id="d1e459">To identify the role of the gyre in transporting meltwater, and test if
meltwater outflow can help to explain the gyre rotation, we calculate
meltwater content from temperature and salinity profiles in the gyre region
using the composite-tracer method (Jenkins, 1999; Pink dots in Fig. 2). In
this calculation, we use three water masses including mCDW, Winter Water and
glacial meltwater, and the two tracers conservative temperature (<inline-formula><mml:math id="M21" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>)
and absolute salinity (<inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), defined following the
Thermodynamic Equations of Seawater-10 standard (McDougall and Barker,
2011). Both tracers are assumed to be conservative for all observations. We
chose the endpoints following previously published research. The endpoints
of mCDW (<inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:mi mathvariant="normal">Θ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.044</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">34.8795</mml:mn></mml:mrow></mml:math></inline-formula>) are
consistent with Wåhlin et al. (2021), and the endpoints of Winter Water
(<inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:mi mathvariant="normal">Θ</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.86</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">34.32</mml:mn></mml:mrow></mml:math></inline-formula>) and glacial meltwater
(<inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:mi mathvariant="normal">Θ</mml:mi><mml:mo>=</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>-</mml:mo><mml:mn mathvariant="normal">90.8</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>) are the same as used by
Zheng et al. (2021) and Biddle et al. (2019). The fraction of
meltwater can be derived from observations with the equation below:
          <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M29" display="block"><mml:mrow><?xmltex \hack{\hbox\bgroup\fontsize{7.5}{7.5}\selectfont$\displaystyle}?><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi mathvariant="normal">meltwater</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi mathvariant="normal">observed</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi mathvariant="normal">mCDW</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">observed</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">mCDW</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>×</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi mathvariant="normal">WW</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi mathvariant="normal">mCDW</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">WW</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">A</mml:mi><mml:mrow><mml:mi>m</mml:mi><mml:mi mathvariant="normal">CDW</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi mathvariant="normal">meltwater</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi mathvariant="normal">mCDW</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">meltwater</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">mCDW</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfenced><mml:mo>×</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi mathvariant="normal">WW</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi mathvariant="normal">mCDW</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">WW</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="normal">A</mml:mi><mml:mi mathvariant="normal">mCDW</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:mfrac></mml:mstyle><?xmltex \hack{$\egroup}?><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
        where <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mi mathvariant="normal">meltwater</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the meltwater fraction, and <inline-formula><mml:math id="M31" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi mathvariant="normal">A</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> with subscripts define the conservative temperature
and absolute salinity endpoints of each water mass.</p>
      <p id="d1e789">The highest meltwater content is detected in the southeast of the Thwaites
gyre (Fig. 2). This is consistent with observations collected by an autonomous
underwater vehicle presented in Wåhlin et al. (2021) that suggest a
north-westward meltwater-rich outflow emanating from the cavity beneath
Thwaites Ice Tongue. The Thwaites gyre may entrain this meltwater plume and
thus play a role in circulating meltwater near Thwaites Ice Shelf and boost
water-mass mixing.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e794">Vertical structure of the Thwaites gyre. <bold>(a)</bold> Tangential velocity of
the Thwaites gyre with distance to the gyre centre (colours). All velocity
profiles are horizontally averaged into 1 km radius bins (pale dots and
lines) and then vertically averaged into 30 m bins (thick lines). <bold>(b–d)</bold> Section
plots of CTD measurements collected in the Thwaites gyre region, with distance
to the gyre centre. Potential-density isopycnals (in kg m<inline-formula><mml:math id="M33" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>) are
denoted by grey contours. Positions of profiles are marked as triangles at
the top of the panel. Below 650 m, the water column is occupied by modified
Circumpolar Deep Water and is very stable so is not presented here.
Conservative temperature above freezing is presented in <bold>(b)</bold>. Absolute salinity
is presented in <bold>(c)</bold>. Meltwater content is presented in <bold>(d)</bold>.</p></caption>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f03.png"/>

      </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e833">The ice conditions in the Thwaites gyre region. The orange arrows
denote daily-averaged wind speed from the ERA5 reanalysis (Hersbach et al., 2018)
(<inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">0.25</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">0.25</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> resolution; for
clarity, velocity data are meridionally interpolated to <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">0.25</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">0.125</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> resolution). Dots are coloured by the wind stress
curl calculated from the interpolated <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">0.25</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">0.125</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> resolution daily-averaged wind speed from the ERA5 reanalysis (Hersbach et al., 2018). Thick blue
arrows indicate the Thwaites gyre. Ice imagery is from <bold>(a)</bold> 25 January, <bold>(b)</bold> 1 February, <bold>(c)</bold> 13 February and <bold>(d)</bold> 23 February 2019, respectively,
as stated above each panel.</p></caption>
        <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f04.png"/>

      </fig>

      <p id="d1e909">Although a previous study suggests that the buoyancy of glacial meltwater at
depth may facilitate gyres (Mathiot et al., 2017), Thwaites gyre is not
likely to be meltwater-driven. As glacial meltwater plumes coming out from
the base of glacier are more buoyant than the ambient water, they rise and
turn left due to Coriolis force, as seen in Pine Island Bay (e.g. Thurnherr
et al., 2014; Zheng et al., 2021). Glacial meltwater coming out from Thwaites
Ice Tongue to the southwest of the Thwaites gyre will therefore impede the
anticyclonic gyre, rather than accelerate it. Hence, neither the cyclonic
wind stress curl shown in Fig. 2 nor the meltwater discharge can directly
generate an anticyclonic gyre. Therefore, we explore other factors that
might explain this apparent contradiction.</p>
      <p id="d1e913">Sea ice coverage is often remarkably different between the PIB and Thwaites
gyre regions (Fig. 1). Satellite imagery shows that the PIB gyre region was
generally open during the whole summer of 2009 (Worldview Aqua/MODIS
corrected reflectance), when the PIB gyre was firstly observed (Thurnherr et
al., 2014). At the same time, fast ice covered most of the Thwaites gyre
region, and the sea ice did not open until late January 2019 (Fig. 4a), about
a month before the sADCP survey revealed the gyre (in late February to early
March 2019). During February, ice coverage in the Thwaites gyre region
changed from covering the western part of the Thwaites gyre (1 February 2019,
Fig. 4b) to completely open (12 February 2019, Fig. 4c). Sea ice covered the
western part of the Thwaites gyre again (23 February 2019, Fig. 4d) 2 d
before the start of the sADCP data collection.</p>
      <p id="d1e916">The presence of sea ice alters OSS (e.g. Elvidge et al., 2016; Meneghello et
al., 2018). Thus, we hypothesise that the sea ice coverage may mediate the
OSS and the resulting surface stress curl felt by the ocean (i.e. ocean
surface stress curl, hereafter OSSC) sufficiently to reverse a gyre, leading
to the different PIB and Thwaites gyre directions. To test this hypothesis,
we use an idealised model to reproduce wind-driven gyres and run a set of
conceptual experiments to simulate the response of wind-driven gyres to
different sea ice coverages.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e921">Model schematic. Sea ice is indicated by the pale grey patch
covering the northwestern half of the gyre domain. The orange arrow
indicates the wind direction, perpendicular to the ice shelf front.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f05.png"/>

      </fig>

</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Model experimental design</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Model set-up</title>
      <p id="d1e945">We employ the MIT general circulation model (MITgcm; Marshall et al., 1997)
with an idealised barotropic set-up. The model has an ocean domain with a
size of 60 km <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:mo>×</mml:mo><mml:mn mathvariant="normal">60</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> and a horizontal grid spacing of 1 km
(Fig. 5; for comparison, the baroclinic Rossby radius in this region is
about 5 km, following the calculation described by Chelton et al., 1998). It
has one 1 km thick vertical layer with a free surface. The size of the model
domain is comparable to the PIB gyre region. The bottom boundary is
free-slip with no drag, and the lateral boundaries are no-slip. We set the
Coriolis parameter <inline-formula><mml:math id="M38" display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula> to be <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.4083</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, appropriate for <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:mn mathvariant="normal">75</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">S</mml:mi></mml:mrow></mml:math></inline-formula>, with a
meridional gradient <inline-formula><mml:math id="M41" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula>  of <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">11</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> s<inline-formula><mml:math id="M43" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> m<inline-formula><mml:math id="M44" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>. The
time step is 120 s. The southern boundary is envisaged to be the ice shelf
(Fig. 5).</p>
      <p id="d1e1062">We run all simulations for 6 model months, which allows all of them to
spin up to be sufficiently close to a steady state. The spin-up time of the
simulations varies from 51  to 91 d, assessed as the time at which
the daily change of the total kinetic energy of the ocean is less than
0.1 % of the total kinetic energy of the ocean at the final model day of
the 6 model months.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Wind forcing</title>
      <p id="d1e1073">The wind field is the only external forcing applied to the model ocean. We
generate a simplified wind forcing field (Fig. 6a) based on the key features
of the climatological wind in the southeastern Amundsen Sea to include the
ice conditions for both Pine Island Bay and around the Thwaites Ice Tongue
(Fig. 1). The ERA5 climatological 10 m wind (Hersbach et al., 2018) above the PIB and Thwaites gyres
blows from the ice shelves to the ocean, with a speed decreasing from the
southeast to the northwest. As mentioned in Sect. 3.1, we rotate the domain
relative to true north such that these offshore winds are purely meridional
in the model, with zero zonal wind (Fig. 5). The maximum wind speed (<inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:mn mathvariant="normal">10</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) occurs in the southwestern corner
of the model domain (Fig. 6a). The meridional gradient of wind speed
(<inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.667</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) is one-fifth of the
zonal gradient of wind speed (<inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">8.333</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). The meridional wind stress is given by
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M48" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub><mml:mfenced open="|" close="|"><mml:mi>v</mml:mi></mml:mfenced><mml:mi>v</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is the drag coefficient, <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">air</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.275</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is the air
density and <inline-formula><mml:math id="M51" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula> is the wind speed. The wind forcing field applied in our
study can be downloaded from the link in the Data availability section.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e1246">Wind fields applied in this study. <bold>(a)</bold> The wind field representing
simplified climatological conditions in the southeastern Amundsen Sea. <bold>(b)</bold> Same as <bold>(a)</bold>, but with wind stress curl reduced by 50 %. <bold>(c)</bold> Same as <bold>(a)</bold>, but
anticyclonic. <bold>(d)</bold> Same as <bold>(c)</bold>, but with wind stress curl reduced by 50 %. The
arrows show wind stress (only every 13th arrow is plotted for clarity),
with the scale on the southwestern corner of <bold>(c)</bold>. Shading shows wind stress
curl, red for cyclonic and blue for anticyclonic.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f06.png"/>

        </fig>

      <p id="d1e1280">We vary the strength and sign of the wind stress curl to generate four wind
forcing fields: strong or weak and cyclonic or anticyclonic wind stress curl
(Fig. 6a–d). The simplified wind field representing the climatological
conditions in the southeastern Amundsen Sea is shown in Fig. 6a. The same
strength of wind stress curl, but anticyclonic, is shown in Fig. 6c. The two
remaining wind fields have wind stress curls weaker by 50 % (Fig 6b, d).
The average wind speed over the whole ocean model domain is kept the same
for all four wind fields.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Sea ice coverage</title>
      <p id="d1e1291">We do not include a sea ice model in our study, but we change the strength of
OSS to simulate the influence of sea ice in the ice-covered area. Fast ice
and ice shelves are unable to move significantly and so are expected to
completely block the wind stress, but other types of ice coverage may have
different impacts on the OSS. Previous research has found a generally higher
momentum transfer over ice-covered regions than open water due to ice drift
dragging the ocean (e.g. Martin et al., 2014; Meneghello et al.,
2018). The magnitude of this additional stress on the ocean surface from ice
drift may change due to the different types and concentrations of ice
coverage. We vary the magnitude of OSS in the ice-covered half of the model
domain from 0 % to 200 % of wind stress to sample a range of possible
OSS modification by ice in steps of 20 %. For all simulations, OSS remains
unaltered in the ice-free half.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e1296">Ice coverages applied in this study. <bold>(a)</bold> Comparison of all ice
coverages. Angles are between the ice edges (thick coloured lines) and wind
direction (thick orange line). The thick black line denotes the ice shelf front.
<bold>(b–f)</bold> Schematics of sea ice coverage (shaded patches) and sea ice edge (thick
coloured lines), with the same colour scheme as shown in <bold>(a)</bold>. Ice-free
regions are shaded in pale blue.</p></caption>
          <?xmltex \igopts{width=199.169291pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f07.png"/>

        </fig>

      <p id="d1e1314">In addition, we vary the angle between the sea ice edge and wind direction
from <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:mi mathvariant="italic">π</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">π</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula> (Fig. 7a) to generate five different ice
coverages as shown in Fig. 7b–f. For all ice coverages applied in this
study, the ice covers exactly half the model domain, with the sea ice edges
always intersecting the centre of the domain.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Model results</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Effect of wind stress on simulated gyres</title>
      <p id="d1e1359">We first
consider results from simulations with no sea ice coverage. Here the
strength and direction of gyres solely depend on the wind field. Cyclonic
wind stress curl fields (Fig. 6a, b) generate cyclonic gyres (Fig. 8a, b),
stronger wind stress curl fields (Fig. 6a, c) generate stronger gyres (Fig. 8a, c), and vice versa, as expected.</p>
      <p id="d1e1362">For both the StrongCyclonic and StrongAnticyclonic wind fields, the simulated gyres have a maximum
streamfunction of <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.58</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">Sv</mml:mi></mml:mrow></mml:math></inline-formula> and a maximum current speed of
<inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:mn mathvariant="normal">3.2</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Compared with the PIB gyre
surveyed in 2009 (1.5 Sv, <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:mn mathvariant="normal">30</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>,
Thurnherr et al., 2014), which is also located in an ice-free area, the
simulated gyres are weaker with a slower current speed. The different
strength between simulated gyres and PIB gyre might be due to the lack of
surface intensification of the currents and the lack of meltwater injection
in our barotropic model. Nevertheless, our idealised model captures the
characteristics of the gyre sufficiently to be a useful tool to explore the
effects of different forcing fields and sea ice coverage on gyre strength,
shape and direction.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e1418">Simulated steady-state gyre streamfunction (<inline-formula><mml:math id="M57" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula>) and
current velocity, when sea ice is absent. Shading indicates streamfunction
while arrows indicate current velocity (only every eighth arrow is plotted
for clarity). The wind forcing for each of panels <bold>(a)</bold>–<bold>(d)</bold> is shown in Fig. 6a–d.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f08.png"/>

        </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><?xmltex \def\figurename{Figure}?><label>Figure 9</label><caption><p id="d1e1443">Ocean surface stress curl (OSSC) and simulated gyre streamfunction
(<inline-formula><mml:math id="M58" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula>) for simulation with the WeakCyclonic wind field and the
SeaIce<inline-formula><mml:math id="M59" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> and <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> ice coverage. <bold>(a)</bold> Shading indicates
OSSC, and arrows indicate wind stress (only every 13th arrow is plotted
for clarity). <bold>(b)</bold> Shading indicates simulated gyre <inline-formula><mml:math id="M61" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula>, and
arrows indicate current velocity (only every eighth arrow is plotted for
clarity).</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f09.png"/>

        </fig>

<?xmltex \hack{\newpage}?>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Effect of sea ice on simulated gyres</title>
<sec id="Ch1.S4.SS2.SSS1">
  <label>4.2.1</label><title>An example of a simulated gyre similar to the Thwaites gyre</title>
      <p id="d1e1514">As an example of the sea ice influencing OSSC, we first discuss the
simulation that generates an anticyclonic gyre similar to the observations
of the Thwaites gyre discussed in Sect. 2. As mentioned in Sect. 2, in early
March 2019, sea ice covered the western part of the Thwaites gyre (Fig. 2),
at an angle to the wind stress similar to the SeaIce<inline-formula><mml:math id="M62" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> ice
coverage (Fig. 7f). The ERA5 wind (Hersbach et al., 2018) stress curl was about <inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">7.5</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">7</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> N m<inline-formula><mml:math id="M65" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, similar to the WeakCyclonic wind field (Fig. 6d). We
therefore consider the WeakCyclonic wind field and the SeaIce<inline-formula><mml:math id="M66" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> and <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> ice coverage to mimic (in an idealised way) the response of the
ocean to the wind and ice conditions in the Thwaites gyre region in March 2019 (Fig. 9).</p>
      <p id="d1e1597">The OSSC is zero over the ice-covered domain (northwestern half of Fig. 9a)
and negative (i.e. cyclonic in the Southern Hemisphere) over the ice-free
domain (southeastern half of Fig. 9a). Due to the different OSS between
ice-covered and ice-free domains, positive OSSC (i.e. anticyclonic in
the Southern Hemisphere) occurs along the sea ice edge, with a magnitude about
10 times larger than the negative values occurring in the ice-free domain
(Fig. 9a). The magnitude of the OSSC along the sea ice edge decreases from
the southwest to the northeast, due to the negative meridional and zonal
gradients in wind stress (Fig. 9a).</p>
      <p id="d1e1600">This asymmetric positive OSSC along the sea ice edge then results in an
asymmetric anticyclonic gyre with its centre located slightly left of the
centre of the model domain (Fig. 9b). The anticyclonic gyre has a maximum
<inline-formula><mml:math id="M68" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula> of <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.56</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">Sv</mml:mi></mml:mrow></mml:math></inline-formula> and a maximum current speed of
<inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:mn mathvariant="normal">3.0</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at steady state. Thwaites
gyre in reality has a higher maximum speed (10<inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, Fig. 3a) but circulates less water (0.2 Sv) than
the simulated gyre. This is partly because the thickness of the water column
influenced by the Thwaites gyre is only about 400 m, while it is 1000 m in
our simulation presented here. We tested the same model set-up with a 400 m
depth and compare the results with the 1000 m depth model results. The
simulated gyre from the 400 m deep model set-up has a faster speed, but the
streamfunction and gyre features remain very similar to the gyre from
the 1000 m depth simulation, e.g. 7.6 cm s<inline-formula><mml:math id="M72" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula> and 0.58 Sv when sea ice is
not present (similar to conditions for the PIB gyre) and 7.1 cm s<inline-formula><mml:math id="M73" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>
and <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.55</mml:mn></mml:mrow></mml:math></inline-formula> Sv when SeaIce<inline-formula><mml:math id="M75" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula>, <inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> and WeakCyclonic are applied (similar
to conditions for the Thwaites gyre). Overall, this experiment demonstrates
that, even with an idealised barotropic model, the presence of sea ice can
enable a cyclonic wind field to generate an anticyclonic gyre, similar to
that observed in 2019.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F10" specific-use="star"><?xmltex \currentcnt{10}?><?xmltex \def\figurename{Figure}?><label>Figure 10</label><caption><p id="d1e1724">Simulated maximum gyre streamfunction (<inline-formula><mml:math id="M77" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula>) for
cyclonic wind stress curl experiments. Positive streamfunction values are
cyclonic and negative values are anticyclonic. The line colours indicate the
angle between the wind direction and the sea ice edge, as shown in Fig. 7.
Thick lines denote the simulations with strong wind stress curl (i.e.
StrongCyclonic; Fig. 6a) while thin lines denote the simulations with weak wind stress
curl (i.e. WeakCyclonic; Fig. 6b). Blue dots mark the turning points where the lines of
simulated <inline-formula><mml:math id="M78" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula> have a discontinuity in gradient caused by the
occurrence of dipoles or tripoles. Orange circles with texts mark the
simulations shown in Figs. 8, 9, 12, 13.</p></caption>
            <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f10.png"/>

          </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F11" specific-use="star"><?xmltex \currentcnt{11}?><?xmltex \def\figurename{Figure}?><label>Figure 11</label><caption><p id="d1e1749">Simulated maximum streamfunction (<inline-formula><mml:math id="M79" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula>) changes with
area-integrated OSSC over model domain. There are 11 filled or open circles
for each combination of different sizes and colours, indicating simulations
with 11 percentages of wind stress transferred to the ocean. Positive
streamfunctions are cyclonic (in the Southern Hemisphere) and negative
streamfunctions are anticyclonic (in the Southern Hemisphere), while the
opposite is true for OSSC. The colours of circles indicate the angle between
sea ice edge and ice shelf front, as shown in Fig. 7. Filled circles denote
the simulations with cyclonic wind stress curl forcings while open circles
denote the simulations with anticyclonic wind stress curl forcings. Large
circles denote the simulations with strong wind stress curl forcings while
small circles denote the simulations with weak wind stress curl forcings.
Orange circles with texts mark the simulations shown in Figs. 8, 9, 12 and 13.</p></caption>
            <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f11.png"/>

          </fig>

</sec>
<sec id="Ch1.S4.SS2.SSS2">
  <label>4.2.2</label><title>Overview of the effect of sea ice coverage on simulated gyres</title>
      <p id="d1e1773">The example discussed above illustrates the influence of a single
configuration of ice coverage (SeaIce<inline-formula><mml:math id="M80" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> and <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula>) on
the simulated gyre. To make our results more generally applicable, we run
our model while varying the ice edge angle and the percentage of wind stress
transferred through the sea ice. Figures 10 and 11 illustrate that
wind-driven gyres can reverse despite an unchanged wind field for a range of
parameters. Here we use Figs. 10 and 11 to present an overview of the
simulated gyre features being affected by both the angle between the wind
and sea ice edge, and the amount of stress transferred to the ocean. In the
following Sect. 4.2.3 and 4.2.4, we discuss the mechanisms underlying these
processes in more detail.</p>
      <p id="d1e1800">We use the ocean model streamfunction to diagnose the strength and direction
of the simulated gyre – the maximum magnitude of streamfunction reflects
the gyre strength, and its sign reflects gyre direction. Some of our
simulations generate two or three connected gyres with different strengths
and directions (i.e. dipoles or tripoles). In the analysis we discuss only
the gyre with the greatest magnitude of streamfunction (i.e. dominant gyre)
in such simulations, unless otherwise stated.</p>
      <p id="d1e1803">Figure 10 shows that strong wind stress curl fields (i.e. StrongCyclonic, thick lines)
lead to stronger gyre strength (i.e. higher magnitude of streamfunction)
than those from weak wind stress curl fields (i.e. WeakCyclonic, thin lines). Note that
Fig. 10 only contains the simulations with cyclonic wind fields (i.e.
StrongCyclonic and WeakCyclonic). Results from simulations with anticyclonic wind fields (i.e.
StrongAnticyclonic and WeakAnticyclonic) are mirror images of those from simulations with cyclonic wind fields
about the 0 Sv line.</p>
      <p id="d1e1806">For all simulations, the simulated gyre transport is always quasi-linearly
related to the percentage of stress transferred through the ice to the ocean
(Fig. 10). For cyclonic forcing with the increase in the percentage of wind
stress felt by the ocean, if the angle between the sea ice edge and wind
direction is less than <inline-formula><mml:math id="M82" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> (i.e. sea ice in the top left,
denoted by dark and pale pink lines in Fig. 10), the simulated <inline-formula><mml:math id="M83" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula> increases monotonically, i.e. enhances the cyclonic gyre and opposes the
anticyclonic gyre. In contrast, if the angle between the sea ice edge and
wind direction is greater than <inline-formula><mml:math id="M84" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> (i.e. sea ice in the
top right, denoted by dark and pale green lines in Fig. 10), the simulated
<inline-formula><mml:math id="M85" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula> decreases monotonically, i.e. enhances the anticyclonic
gyre and opposes the cyclonic gyre.</p>
      <p id="d1e1846">The lines of the simulated streamfunction sometimes have a discontinuity in
gradient (blue dots in Fig. 10). Those turning points occur when the model
simulates a dipole of two gyres, or a tripole of three gyres, as mentioned
in the end of Sect. 3.1. We discuss examples of this in more detail in the
following Sect. 4.2.3 and Fig. 12e, f. At the turning points indicated in
Fig. 10, the weaker gyre(s) of the dipole or tripole do follow the quasi-linear
relationship, but the dominant gyre (which is captured as blue dots in Fig. 10) does not.</p>
      <p id="d1e1849">We use Fig. 11 to illustrate how the change in area-integrated OSSC depends
on the angle between the wind direction and the ice edge. It is
well-established that the strength of gyres is closely related to the OSSC
integrated over the wind-influenced area (Stommel, 1948). In agreement with
this, we find that negative area-integrated OSSCs tend to generate cyclonic
gyres while positive area-integrated OSSCs tend to generate anticyclonic
gyres (Fig. 11). The simulated maximum streamfunction and the
area-integrated OSSC are approximately linearly correlated (Fig. 11), such
that stronger OSSC leads to stronger gyres. Although this relationship is
very strong, demonstrating the dominant influence of the magnitude of the
area-integrated OSSC, the location and distribution of the OSSC do have a
secondary influence that accounts for deviations from a perfect correlation.</p>
      <p id="d1e1852">Because the imposed zonal gradient of wind stress is greater than the
meridional gradient in our experiments, the difference between the OSS of
ice-covered and ice-free domains is greater when the ice edges are more
meridional. Hence, the integrated OSSC along ice edges that are more
meridional is higher than along those that are more zonal. Therefore,
SeaIce<inline-formula><mml:math id="M86" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> and SeaIce<inline-formula><mml:math id="M87" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> (Fig. 7f, d) can lead to a
higher area-integrated OSSC along the ice edge than SeaIce<inline-formula><mml:math id="M88" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">5</mml:mn><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mn mathvariant="normal">8</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula>
and SeaIce<inline-formula><mml:math id="M89" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mn mathvariant="normal">8</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> (Fig. 7c, e). Accordingly, the streamfunction
responds more sensitively to the percentage of wind stress transferred to
the ocean when orientation of the ice edge is more meridional (i.e. diagonal
ice edge, denoted by dark pink and dark green lines in Fig. 10).</p>
</sec>
<sec id="Ch1.S4.SS2.SSS3">
  <label>4.2.3</label><?xmltex \opttitle{Effect of the percentage of $\tau$
transferred to the ocean}?><title>Effect of the percentage of <inline-formula><mml:math id="M90" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula>
transferred to the ocean</title>
      <p id="d1e1924">Applying the StrongCyclonic wind field and SeaIce<inline-formula><mml:math id="M91" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> ice coverage, we
gradually change the percentage of wind stress transferred to the ocean (<inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula>) to isolate its influence on the gyre features. The spatial
distribution of the OSSC and the circulation pattern are shown in Fig. 12.</p>
      <p id="d1e1948">As in the 0 <inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> simulation discussed in Sect. 4.2.1 and 4.2.2, the
<inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:mn mathvariant="normal">20</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> simulation has negative OSSC over the entire model domain
except along the sea ice edge where it has positive OSSC (Fig. 12a).
However, the OSS over the ice-covered domain is higher in the <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:mn mathvariant="normal">20</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula>
simulation (Fig. 12a) than in the <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> simulation (Fig. 10), which
reduces the difference in OSS between ice-covered and ice-free regions,
resulting in a decrease in the positive OSSC along the sea ice edge.
Therefore, the <inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:mn mathvariant="normal">20</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> simulation generates an anticyclonic gyre
centred in the model domain (Fig. 12e), in the same location as the <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> simulation (Fig. 10b) but slightly weaker. In addition, a second very
weak cyclonic gyre is generated in the ice-free domain (southeastern corner
in Fig. 12e).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F12"><?xmltex \currentcnt{12}?><?xmltex \def\figurename{Figure}?><label>Figure 12</label><caption><p id="d1e2029"><bold>(a–d)</bold> Ocean surface stress (arrows; only every 13th arrow is
plotted for clarity) and ocean surface stress curl (shading) for <bold>(a)</bold> <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:mn mathvariant="normal">20</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> <bold>(b)</bold> <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:mn mathvariant="normal">40</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> <bold>(c)</bold> <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:mn mathvariant="normal">80</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> and <bold>(d)</bold> <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:mn mathvariant="normal">200</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> transferred to
the ocean. Sea ice covers the northwestern half of the gyre domain (i.e.
SeaIce<inline-formula><mml:math id="M103" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula>) and the StrongCyclonic wind field is applied. <bold>(e–h)</bold> Simulated
streamfunction (<inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:mi mathvariant="normal">Ψ</mml:mi><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">shading</mml:mi></mml:mrow></mml:math></inline-formula>) and ocean current velocity
(arrows; only every eighth arrow is plotted for clarity) resulting from
the forcing in panels <bold>(a–d)</bold> respectively.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f12.png"/>

          </fig>

      <p id="d1e2141">Likewise, for the <inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:mn mathvariant="normal">40</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> simulation, the decreased OSS over the
ice-covered domain leads to a decreased magnitude of positive OSSC along the
sea ice edge (Fig. 12b). The anticyclonic gyre found in the <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:mn mathvariant="normal">20</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula>
simulation almost vanishes in the <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:mn mathvariant="normal">40</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> simulation, and only a very
weak and small anticyclonic gyre is identified in the southwest corner of
Fig. 12f. In the ice-free domain, the very weak cyclonic gyre previously
found in <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:mn mathvariant="normal">20</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> becomes stronger (southeastern corner in Fig. 12f). A
weaker cyclonic gyre is also formed in the ice-covered domain (northwestern
corner in Fig. 12f), generating a tripole. As mentioned above in Sect. 4.2.2,
this simulation shows an example of one of the turning points in Fig. 10.</p>
      <p id="d1e2196">In the <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:mn mathvariant="normal">80</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> simulation, the OSS in the ice-covered domain is only
20 % smaller than that felt in the ice-free domain, making the OSSC along
the sea ice edge very weak (Fig. 12c). The anticyclonic gyre found in the
previous simulations near the ice edge has now completely vanished, so the
other two weak cyclonic gyres identified in Fig. 12g have merged into a
single, stronger cyclonic gyre dominating the whole gyre domain (Fig. 12g),
similar to the equivalent ice-free simulation (Fig. 8b).</p>
      <p id="d1e2212">Finally, the <inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:mn mathvariant="normal">200</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> simulation has negative OSSC all over the domain
(Fig. 12d), forming a very strong cyclonic gyre (Fig. 12h). Despite the
asymmetry of the forcing, with the strongest OSSC in the northwest sector
and along the diagonal, the gyre is nearly symmetric and centred on the
middle of the domain. As discussed previously (Figs. 10 and 11), between
80 %<inline-formula><mml:math id="M111" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula> and  200 %<inline-formula><mml:math id="M112" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula> there is a steady increase in the cyclonic
gyre strength.</p>
      <p id="d1e2242">Overall, changing the percentage of the wind stress transferred through ice
to the ocean in this configuration has a dramatic impact on the gyre. With
increasing transfer of wind stress through the ice, the simulated gyre
starts from anticyclonic rotation when there is no transfer, develops to
dipole and tripole, and finally reverses to cyclonic. This demonstrates that
the percentage of wind stress transferred through sea ice to the ocean alone
can regulate the gyre strength, and even change the gyre direction.</p>
</sec>
<sec id="Ch1.S4.SS2.SSS4">
  <label>4.2.4</label><title>Effect of the angle between the wind and sea ice edge</title>
      <p id="d1e2253">Now we consider how the gyre responds to changing the angle of the sea ice
edge when the wind field is StrongCyclonic and sea ice completely blocks the wind (i.e.
<inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula>). In these experiments, the OSSC over the ice-covered domain is
zero, and the OSSC over the ice-free domain is always negative. The OSSC
along the sea ice edge is the same sign as over the ice-free domain
(cyclonic) when the angle between wind and sea ice edge is greater than
<inline-formula><mml:math id="M114" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> but the opposite sign (anticyclonic) when the direction
between wind and sea ice edge is less than <inline-formula><mml:math id="M115" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula>. When the angle
is exactly <inline-formula><mml:math id="M116" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> there is zero OSSC along the sea ice edge,
resulting in a cyclonic gyre forced by cyclonic OSSC in the ice-free domain
(Fig. 13b). Both SeaIce<inline-formula><mml:math id="M117" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">5</mml:mn><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mn mathvariant="normal">8</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> and SeaIce<inline-formula><mml:math id="M118" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula>
generate cyclonic gyres (Fig. 13c, d), as the OSSC is cyclonic over the whole
model domain. For both SeaIce<inline-formula><mml:math id="M119" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mn mathvariant="normal">8</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> and SeaIce<inline-formula><mml:math id="M120" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula>,
the area-integrated OSSC is anticyclonic (Fig. 11), demonstrating that the
anticyclonic OSSC along the ice edge dominates relative to the cyclonic OSSC
over the ice-covered domain in these simulations. Anticyclonic gyres are
thus generated in both SeaIce<inline-formula><mml:math id="M121" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mn mathvariant="normal">8</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> and SeaIce<inline-formula><mml:math id="M122" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula>
(Fig. 13e, f). As discussed in Sect. 4.2.2, simulations with more
“meridional” ice edges (i.e. SeaIce<inline-formula><mml:math id="M123" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> and SeaIce<inline-formula><mml:math id="M124" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula>) have greater impacts on the OSSC and so generate stronger gyres (Fig. 13d, f). Overall, these experiments demonstrate how the ice edge orientation
relative to the wind forcing can determine the gyre strength and direction.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F13"><?xmltex \currentcnt{13}?><?xmltex \def\figurename{Figure}?><label>Figure 13</label><caption><p id="d1e2409">Simulated gyre streamfunction (<inline-formula><mml:math id="M125" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula>) when wind field
is StrongCyclonic and sea ice completely blocks the wind (i.e. <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula>). Arrows indicate the current speed (only every eighth arrow is plotted
for clarity). Sea ice coverage information for panels <bold>(b–f)</bold> is shown in Fig. 7b–f.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f13.png"/>

          </fig>

      <?xmltex \floatpos{t}?><fig id="Ch1.F14" specific-use="star"><?xmltex \currentcnt{14}?><?xmltex \def\figurename{Figure}?><label>Figure 14</label><caption><p id="d1e2443">Ocean surface stress curl (OSSC) and simulated gyre
streamfunction (<inline-formula><mml:math id="M127" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula>) for the simulation with the WeakCyclonic wind field. Sea ice
covers the whole model domain. Sea ice in the northeast has 200 % of <inline-formula><mml:math id="M128" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula> transferred to the ocean (representing mobile ice) while sea ice in the
southwest has 0 % of <inline-formula><mml:math id="M129" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula> transferred to the ocean (representing fast
ice). <bold>(a)</bold> The shading indicates the OSSC and the arrows indicate the wind
stress. <bold>(b)</bold> The shading indicates the simulated gyre <inline-formula><mml:math id="M130" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula> and the
arrows indicate the current velocity.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/3005/2022/tc-16-3005-2022-f14.png"/>

          </fig>

</sec>
<sec id="Ch1.S4.SS2.SSS5">
  <label>4.2.5</label><title>Fast ice combined with mobile ice</title>
      <p id="d1e2496">As described in Sect. 4.2.1, the simulation with wind field and ice
conditions similar to those experienced in the Thwaites gyre region in March 2019 (WeakCyclonic  wind field, SeaIce<inline-formula><mml:math id="M131" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> and <inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi><mml:mi mathvariant="italic">τ</mml:mi></mml:mrow></mml:math></inline-formula> ice condition, Fig. 9a) generates an anticyclonic gyre (Fig. 9b) similar to the ADCP
observations (Fig. 2). Here we explore a very different ice configuration
that may also generate an anticyclonic gyre and is similar to sea ice
conditions observed in the Thwaites gyre region in previous seasons
(negative streamfunction; lines falling below the 0 Sv horizontal black line
in Fig. 10).</p>
      <p id="d1e2523">Suppose that the southwestern half of the domain is covered in fast ice
transferring 0 % of <inline-formula><mml:math id="M133" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula> to the ocean, and the northeastern half of the
domain is covered in mobile sea ice transferring 200 % of <inline-formula><mml:math id="M134" display="inline"><mml:mi mathvariant="italic">τ</mml:mi></mml:math></inline-formula> to the
ocean, as shown in Fig. 14a. The steady-state solution for this scenario is
an anticyclonic gyre centred near the middle of the model domain (Fig. 14b).
Due to the strong OSSC along the sea ice edge (Fig. 14a), this anticyclonic
gyre is stronger (<inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.11</mml:mn></mml:mrow></mml:math></inline-formula> Sv) than all gyres simulated from the original model
set-up (Fig. 10).</p>
      <p id="d1e2550">This scenario is reminiscent of the sea ice conditions in late January 2019
(Fig. 4a), when fast ice covered the southern part of the Thwaites gyre
region while loose sea ice covered the northern part of the Thwaites gyre
region. Hence, the sea ice coverage that occurred in January 2019 might
generate or facilitate the Thwaites gyre observed in March. To generate
gyres, all that is required is a spatial difference in the amount of wind
stress transferred to the ocean, whether that is through fast ice blocking
the effect of the wind or mobile ice enhancing the effect of the wind.</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Discussion</title>
      <p id="d1e2564">Regional circulation models have often been used to study ocean gyres (e.g.
Meneghello et al., 2021; Regan et al., 2020). However, to comprehensively
explore the impact of the ice coverage on the gyre formation through its
modification of the stress imparted to the ocean, we need to isolate the
individual forcings and conduct a very large number of experiments to
examine how they interact. We therefore invoke an idealised model that
represents the surface forcing in a simple manner, excluding other features
of the real ocean such as baroclinicity, ice-shelf processes and topography.
Some biases may occur due to the lack of those mechanisms. For example, the
meltwater injection that is thought to facilitate gyres (Mathiot et al.,
2017) is not included, which may explain the differences in the magnitude of
<inline-formula><mml:math id="M136" display="inline"><mml:mi mathvariant="normal">Ψ</mml:mi></mml:math></inline-formula> between the simulated gyres (<inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.58</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">Sv</mml:mi></mml:mrow></mml:math></inline-formula> for PIB
and <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.42</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">Sv</mml:mi></mml:mrow></mml:math></inline-formula> for Thwaites) and gyre observations (about
<inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.5</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">Sv</mml:mi></mml:mrow></mml:math></inline-formula> for PIB, Thurnherr et al., 2014, and <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.27</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">Sv</mml:mi></mml:mrow></mml:math></inline-formula> for Thwaites). Our argument is not to dispute the effect of meltwater,
but rather to highlight the role of wind forcing and the sea ice conditions.</p>
      <p id="d1e2622">Since our model has much lower computational costs than other regional
models, we can run our model hundreds of times to test the gyre response in
different wind–ice combinations and apply the results in different polar
oceans under varying conditions. All of our simulated gyres reached
steady state within 2 months and respond to changed surface conditions on
a similar timescale. We also tested a 1.5-layer reduced-gravity model as a
comparison for the barotropic case presented here, with all forcings and
model design remaining the same. Although the baroclinic model produced
gyres with more intensified surface currents and a slightly longer spin-up
time, the gyres in baroclinic and barotropic model cases have the same
direction and similar sizes and transports. To explore the sensitivity of
the model results to the width of this marginal ice zone, we created two new
ice conditions with the smaller gradients (not shown) in surface stress and
weaker OSSC over three grid points (3 km) and four grid points (4 km). The
simulated gyres have almost the same strengths (both about <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.41</mml:mn></mml:mrow></mml:math></inline-formula> Sv) and
same shapes as the simulated gyre from simulations without a wider marginal
ice zone. This indicates that the width of the marginal ice zone is not
important for gyre generation. Hence, our model reproduces the observed gyre
direction and response to ice coverage well.</p>
      <p id="d1e2635">The influence of mobile ice on changing OSS has been well studied (e.g.
Meneghello et al., 2018) while little progress has been made towards fixed
ice. We have considered both the increase and decrease in OSS, which
included scenarios caused by both mobile ice and fixed ice altering OSS. We
further discussed the significant effects of the associated OSSC along the
ice boundary on gyre formation and gyre features. Our results are especially
useful in Antarctic continental shelf seas where climatological winds often
blow offshore from the ice shelves/fast ice to the ocean, which allows the
gyres near fixed ice to fully develop.</p>
      <p id="d1e2638">In Antarctic continental shelf seas, gyres near ice shelves contribute
significantly to the spreading of glacial meltwater and its associated heat
and nutrients (Zheng et al., 2021; Mankoff et al., 2012). Meltwater can
impede sea ice formation, causing polynyas, or alter the locations and
timing of hotspots of marine productivity (Zheng et al., 2021; Mathis et
al., 2007; Mankoff et al., 2012). Gyres may transport heat, which is carried
by warm water entrained into the gyre, towards ice shelf cavities (Schodlok
et al., 2012). The existence of gyres can cause isopycnal displacement. For
cyclonic gyres, isopycnals shoal in the gyre centre, as regularly observed
in Pine Island Bay (e.g. Thurnherr et al., 2014; Zheng et al., 2021;
Dutrieux et al., 2014; Heywood et al., 2016); for anticyclonic gyres,
isopycnals deepen in the gyre centre. Below warm-cavity ice shelves, the
water is stratified with a fresh meltwater-rich upper layer and a warm yet
salty mCDW lower layer. This isopycnal displacement may allow warmer mCDW to
enter the ice cavity and melt ice shelves (Yoon et al., 2022). The intrusion of warm water into the base of warm-cavity ice
shelves is via the dense lower layer, the so-called “salt wedge” (Robel et al.,
2022). The water mass exchanges due to gyres may impact the
stratification in front of the ice shelve and hence affect this salt wedge and
the related intrusions of warm water to ice shelves. Similarly, gyres formed
near the sea ice edge can circulate ambient water masses. The redistribution
of water masses and the heat and freshwater might feed back onto sea ice
formation to affect the ice formation and regeneration of ice cover in the
next winter. By changing both the ocean stratification and the sea ice
cover, gyres will affect heat fluxes in the vicinity of ice shelves, which
may in turn influence the heat available for basal melting (e.g.
St-Laurent et al., 2015; Webber et al., 2017). Therefore, it
is important to understand the conditions that can generate or modify such
gyres.</p>
      <p id="d1e2642">Due to the importance of gyres for the regional ocean environment, more
observations and simulations are required to better understand the
relationship between surface conditions and gyre strength and direction. We
highlight the importance of wind–ice–ocean interactions, especially the wind
stress curl at the ice edge, to polar ocean gyres. These interactions occur
at small scales (of the order of tens of kilometres) that will be poorly resolved by
global coupled models. Simulating these processes is also dependent on
accurate sea ice conditions including the representation of fast ice and
polynyas. Gyres in typically ice-covered regions (such as Thwaites gyre)
present extreme challenges for repeat ship-based surveys. We show that the
sea ice coverage can change rapidly (Fig. 4) and has a large influence on
the ocean surface stress (Figs. 10–13); however, it is yet difficult to
monitor. The PIB gyre changes its location interannually and seasonally
(Heywood et al., 2016; Zheng et al., 2021), further demonstrating the need
for long-term continuous monitoring. Such continuous gyre observations would
also be useful for model evaluation and could be obtained with
high-resolution sea ice motion from satellites, which can clearly show the
surface current through sea ice movement. We urge that further effort is
needed for improving the quality of sea ice satellite products, especially
the data coverage, operating frequency and spatial resolution. Future work
should also include quantifying the effect of different types of sea ice on
enhancing or reducing the ocean surface stress, which may be made by the
combination of ice-tethered profilers providing under-ice current velocity
and autonomous surface vehicles providing the near-surface wind speed and
heat fluxes.</p>
      <p id="d1e2645">Despite the important role that gyres play, small wind-driven gyres have
received limited attention in the Antarctic continental shelf seas. There
are a few other gyres documented in the Antarctic continental shelf seas,
such as the Prydz Bay Gyre (Smith et al., 1984), and the cyclonic gyre in
front of Filchner Ice Shelf (Foldvik et al., 1985), but none of them are
primarily driven by local wind, so they are not discussed here. Model
representations of ocean currents show the existence of some small gyres
with a radius of about 15–30 km, including PIB gyre, in Antarctic continental
shelf seas (e.g. Fig. 4c, d in Nakayama et al., 2019). However, except for
the PIB gyre, which has been observed in several different years, little
attention has been paid to such gyres and their formation mechanisms. This
is partly because polar observations often cover either too short a time
period or too small an area to provide in situ verification for the gyres
found in models. Our study provides a possible mechanism to explain the
formation of the gyres formed near the ice–ocean boundary that might be explored
for other small gyres shown in high-resolution ocean model results in
Antarctic continental shelf seas.</p>
</sec>
<sec id="Ch1.S6" sec-type="conclusions">
  <label>6</label><title>Conclusions</title>
      <p id="d1e2656">This study uses new observations to identify the Thwaites gyre for the first
time, located in a habitually ice-covered region of the southeastern
Amundsen Sea. This gyre rotates anticyclonically, despite the climatological
cyclonic wind forcing that implies the gyre should rotate cyclonically, as
is the case for the only other gyre reported in the eastern Amundsen Sea,
PIB gyre (e.g. Thurnherr et al., 2014; Heywood et al., 2016). To investigate
this apparent discrepancy, we use a barotropic model with idealised sea ice
and wind forcing only to simulate gyres similar to those observed in the
vicinity of ice shelves. Our model suggests that sea ice plays a key role in
mediating the wind stress transferred to the ocean and hence determines the
direction and strength of the gyre rotation. The percentage of wind stress
transferred to the ocean, and the angle between the wind direction and sea
ice edge, can alter the OSSC over ice-covered regions and along sea ice
edges sufficiently to reverse gyres. Although the simulated gyres are slower
than those observed, we demonstrate the potential of sea ice to control gyre
direction and intensity. We suggest that these processes may explain gyre
formation and reversal in polar oceans, for example, the PIB gyre reversal
hypothesised by Webber et al. (2017). We further suggest that this
wind–ice–ocean interaction may contribute to the development of gyre
features throughout the polar oceans.</p>
</sec>

      
      </body>
    <back><notes notes-type="codeavailability"><title>Code availability</title>

      <p id="d1e2663">Model code and code for generating wind forcings used in this study are
freely available at <ext-link xlink:href="https://doi.org/10.5281/zenodo.6757626" ext-link-type="DOI">10.5281/zenodo.6757626</ext-link> (Zheng et al., 2022a).</p>
  </notes><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e2672">Processed SADCP data are freely available at <ext-link xlink:href="https://doi.org/10.5281/zenodo.6757570" ext-link-type="DOI">10.5281/zenodo.6757570</ext-link> (Zheng et al., 2022b) and CTD data are freely available at <ext-link xlink:href="https://doi.org/10.5285/e338af5d-8622-05de-e053-6c86abc0648" ext-link-type="DOI">10.5285/e338af5d-8622-05de-e053-6c86abc0648</ext-link> (Queste and Wåhlin, 2022).</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e2684">YZ, DPS, KJH and BGMW initiated the concept of this paper and designed the
model experiments. BYQ led the NBP-1902 cruise SADCP measurement collection
and identified the Thwaites gyre. YZ ran the model experiments and
visualised the results with help from DPS, KJH and BGMW. YZ analysed the CTD
date and calculated the meltwater content. YZ wrote the manuscript with help
from DPS, KJH, BGMW and BYQ. All authors discussed the results and
contributed to the final manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e2690">The contact author has declared that neither they nor their co-authors have any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e2696">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e2702">We thank the scientists, technicians and crew working on the NBP-1902
cruise for everyone's hard work during the cruise to make the data
collection possible. We are grateful to Robert D. Larter (British Antarctic
Survey), the chief scientist of NBP-1902, for his patience and support
on board. We thank Shenjie Zhou (British Antarctic Survey) for helping Yixi Zheng
with debugging the MITgcm codes.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e2707">This work is from the Thwaites-Amundsen Regional Survey and Network (TARSAN) project, a component of the International Thwaites Glacier Collaboration (ITGC), with ITGC contribution no. ITGC-059. Support was received from the National Science Foundation and Natural Environment Research Council (NERC grant NE/S006419/1). Logistics were provided by the NSF-US Antarctic Program and NERC British Antarctic Survey. This work is also funded by the European Research Council (H2020-EU.1.1.) under research grant Climate-relevant Ocean Measurements and Processes on the Antarctic continental Shelf and Slope (COMPASS, grant agreement ID 741120). Yixi Zheng is supported by the China Scholarship Council and the University of East Anglia.</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e2714">This paper was edited by Nicolas Jourdain and reviewed by two anonymous referees.</p>
  </notes><ref-list>
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