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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-16-1181-2022</article-id><title-group><article-title>Modelling the effect of submarine iceberg melting on
glacier-adjacent water properties</article-title><alt-title>Modelling the effect of submarine iceberg melting on
glacier-adjacent water properties</alt-title>
      </title-group><?xmltex \runningtitle{Modelling the effect of submarine iceberg melting on
glacier-adjacent water properties}?><?xmltex \runningauthor{B.~J.~Davison et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff2">
          <name><surname>Davison</surname><given-names>Benjamin Joseph</given-names></name>
          <email>b.davison@leeds.ac.uk</email>
        <ext-link>https://orcid.org/0000-0001-9483-2956</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Cowton</surname><given-names>Tom</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1668-7372</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Sole</surname><given-names>Andrew</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-5290-8967</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4 aff5">
          <name><surname>Cottier</surname><given-names>Finlo</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>Nienow</surname><given-names>Pete</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Department of Geography and Sustainable Development, University of St
Andrews, St Andrews, UK</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>School of Earth and Environment, University of Leeds, Leeds, UK</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Department of Geography, University of Sheffield, Sheffield, UK</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Scottish Association for Marine Science, Scottish Marine Institute,
Oban, UK</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Department of Arctic and Marine Biology, UiT The Arctic University of
Norway, Tromsø, Norway</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>School of Geosciences, University of Edinburgh, Edinburgh, UK</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Benjamin Joseph Davison (b.davison@leeds.ac.uk)</corresp></author-notes><pub-date><day>7</day><month>April</month><year>2022</year></pub-date>
      
      <volume>16</volume>
      <issue>4</issue>
      <fpage>1181</fpage><lpage>1196</lpage>
      <history>
        <date date-type="received"><day>8</day><month>October</month><year>2021</year></date>
           <date date-type="rev-request"><day>1</day><month>November</month><year>2021</year></date>
           <date date-type="rev-recd"><day>8</day><month>February</month><year>2022</year></date>
           <date date-type="accepted"><day>25</day><month>February</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="d1e152">The rate of ocean-driven retreat of Greenland's tidewater glaciers remains
highly uncertain in predictions of future sea level rise, in part due to
poorly constrained glacier-adjacent water properties. Icebergs and their
meltwater contributions are likely important modifiers of fjord water
properties, yet their effect is poorly understood. Here, we use a 3-D ocean
circulation model, coupled to a submarine iceberg melt module, to
investigate the effect of submarine iceberg melting on glacier-adjacent
water properties in a range of idealised settings. Submarine iceberg melting
can modify glacier-adjacent water properties in three principal ways: (1) substantial cooling and modest freshening in the upper <inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> m
of the water column; (2) warming of Polar Water at intermediate depths due
to iceberg melt-induced upwelling of warm Atlantic Water and; (3) warming
of the deeper Atlantic Water layer when vertical temperature gradients
through this layer are steep (due to vertical mixing of warm water at
depth) but cooling of the Atlantic Water layer when vertical temperature
gradients are shallow. The overall effect of iceberg melt is to make
glacier-adjacent water properties more uniform with depth. When icebergs
extend to, or below, the depth of a sill at the fjord mouth, they can cause
cooling throughout the entire water column. All of these effects are more
pronounced in fjords with higher iceberg concentrations and deeper iceberg
keel depths. These iceberg melt-induced changes to glacier-adjacent water
properties will reduce rates of glacier submarine melting near the surface, increase them in the Polar Water layer, and cause typically modest
impacts in the Atlantic Water layer. These results characterise the
important role of submarine iceberg melting in modifying ice sheet-ocean
interaction and highlight the need to improve representations of fjord
processes in ice sheet scale models.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e174">Predicting the rates of ocean-driven retreat of Greenland's tidewater
glaciers remains one of the largest uncertainties in estimating future sea
level rise
(Edwards
et al., 2021; Meredith et al., 2019). This uncertainty is partly due to
limited constraints on the ocean-driven thermal forcing of tidewater glacier
calving fronts, which reflects in part the difficulty in obtaining
hydrographic observations in the proximity of tidewater glacier termini
(Jackson
et al., 2017, 2020; Sutherland et al., 2019). The few observations of water
properties in the inner part of glacial fjords demonstrate that there are
typically substantial differences between glacier-adjacent water properties
and those near the fjord mouth
(e.g. Inall et al., 2014;
Jakobsson et al., 2020; Straneo et al., 2011), indicating that substantial
modification of water temperature and salinity can occur within glacial
fjords. Due to the relatively small number of observations and insufficient
model constraints on glacier-adjacent water properties, ice sheet models
used to simulate glacier retreat must be forced with far-field (i.e. acquired on and beyond the continental shelf) ocean boundary conditions that
do not include fjord-scale influences
(Goelzer et al.,
2020; Slater et al., 2019), thereby introducing uncertainty into the
resulting projections of ice sheet mass loss.</p>
      <p id="d1e177">Glacier-adjacent water properties can differ from those near the fjord mouth
for several reasons. Meltwater runoff enters the fjord at depth where
tidewater glaciers meet the ocean (“subglacial discharge”). In Greenland's
fjords, warm water of Atlantic origin (Atlantic Water, AW) is generally
found at depth, whilst colder, fresher water of polar origin (Polar Water,
PW) is found at intermediate depths
(Straneo and Heimbach, 2013;
Sutherland and Pickart, 2008). The cold, fresh subglacial discharge is
buoyant when it enters the fjord and rises as a turbulent plume
(Jenkins, 2011). As it rises it entrains fjord water, which
mixes with the subglacial discharge as it ascends towards the fjord surface
(e.g. Beaird et al., 2018). In this way,
subglacial discharge-driven plumes act as mixing engines at the head of
glacial fjords. Due to the temperature stratification in Greenland's fjords,
plumes at deeply grounded glaciers (i.e. deeper than the PW-AW interface)
often draw the relatively warm AW towards the fjord surface, thereby warming
surface and near-surface waters
(e.g. Carroll et al.,
2016; Straneo et al., 2010, 2011). In contrast, plumes at shallowly grounded
glaciers can cause cooling at and near the fjord surface as cold subglacial
discharge and entrained PW is upwelled into surface layers that are
seasonally warmed by solar radiation (Carroll et al.,
2016). Models that include glacial plumes are able to reproduce these
effects convincingly
(Carroll et al.,
2016; Cowton et al., 2015; Jackson et al., 2017). However, there remain
substantial differences between modelled water properties and those that are
observed adjacent to tidewater glaciers
(Cowton et al.,
2016; Davison et al., 2020; Fraser and Inall, 2018).</p>
      <p id="d1e180">Several recent studies have identified icebergs as a substantial freshwater
source in some of Greenland's fjords, with iceberg freshwater volumes
comparable to or greater than ice sheet runoff
(Enderlin
et al., 2016, 2018; Jackson and Straneo, 2016; Moon et al., 2017; Moyer et
al., 2019; Rezvanbehbahani et al., 2020). Furthermore, modelling of one of
these fjords suggests that including the heat and salt fluxes associated
with submarine iceberg melting greatly increases the model's ability to
reproduce observed glacier-adjacent water properties
(Davison et al., 2020). However, iceberg
concentration, keel depth, and the size-frequency distribution likely vary
hugely between fjords as well as over time, although observations of icebergs
at the fjord scale are sparse
(Enderlin
et al., 2016; Moyer et al., 2019; Rezvanbehbahani et al., 2020; Sulak et
al., 2017). As such, it is likely that the effect of icebergs on
glacier-adjacent water properties will also vary both spatially (i.e. between fjords) and temporally. This variability likely results in different
thermal forcing of tidewater glaciers for a given set of far-field ocean
conditions. Constraining the effect of icebergs on glacier-adjacent water
properties and thus glacier submarine melt rates, is therefore a necessary
step in order to improve projections of ice sheet mass loss.</p>
      <p id="d1e183">Here, we use an ocean circulation model in a series of idealised fjord-scale
simulations to examine how icebergs affect glacier-adjacent water properties
across a range of Greenland-relevant scenarios. We first consider how
iceberg concentration, keel depth and size-frequency distribution
individually affect glacier-adjacent water properties. We then consider a
range of representative iceberg and ocean scenarios, to examine how these
parameters interact to determine water properties in the critical region
adjacent to tidewater glacier termini. Greenland's fjords are complex and
varied in their geometry, ranging from short, narrow inlets to those that
are long and wide, each with varying sinuosity and bathymetry, and often
with several tributaries and sills of varying depth along their length. It
would be impractical to attempt to characterise all of these systems.
Therefore, we focus here on two simple fjord geometries: one with no sills
and another with a single entrance sill, which we expect to be of particular
importance for iceberg-ocean interaction given the capacity of sills to
concentrate fjord-shelf water exchange near the surface where icebergs are
concentrated (Schaffer et al., 2020).</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="d1e189">Model domain and boundary conditions. <bold>(a)</bold> Plan view of model
bathymetry with sill, with the ice wall at the left end of the domain (0 km)
and the open boundary on the right. Hatching indicates model resolution
(note that grid cells are <inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:mn mathvariant="normal">500</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mo>×</mml:mo><mml:mn mathvariant="normal">500</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> in the horizontal). The red dot
marks the location of subglacial discharge injection and the red box
indicates the region from which steady-state glacier-adjacent water
properties were extracted. In simulations without a sill, the domain is
uniformly 500 m deep. Vertical profiles of <bold>(b)</bold> temperature, <bold>(c)</bold> salinity and
<bold>(d)</bold> density with <italic>BCstandard</italic>. <bold>(e)</bold> Temperature profiles with varying PW temperature. <bold>(f)</bold> Temperature profiles with varying AW temperature. <bold>(g)</bold> Example of plume vertical
velocity from the simulation with iceberg scenario 5, 500 m<inline-formula><mml:math id="M3" 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="M4" 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> subglacial discharge and <italic>BCstandard</italic> boundary conditions.</p></caption>
        <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/1181/2022/tc-16-1181-2022-f01.png"/>

      </fig>

</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Model domain</title>
      <p id="d1e283">We used the Massachusetts Institute of Technology general circulation model
(MITgcm) in its non-hydrostatic configuration (Marshall
et al., 1997a, b) to model submarine ice melting and circulation in an
idealised fjord 50 km in length and 5 km in width. In most simulations, the
domain is uniformly 500 m deep. However, in some simulations, we include a
sill which limits the overlying water depth to 100 m (uniform across the
entire width of the fjord, and approximately 5 km wide in the along-fjord
direction, with a Gaussian profile), centred 10 km from the open boundary
(Fig. 1a). Model resolution is uniformly 500 m horizontally and 10 m
vertically. The fjord sides are closed boundaries, while at the open ocean
boundary we impose a 5 km sponge layer, in which conditions are relaxed
towards those imposed at the boundary
(e.g. Cowton et al.,
2016; Sciascia et al., 2013; Slater et al., 2015).</p>
      <p id="d1e286">The glacier-end of the domain is closed and consists of a virtual ice wall 5 km wide and 500 m high. In simulations
incorporating subglacial discharge, this is input at a rate of 500 m<inline-formula><mml:math id="M5" 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="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>, a value typical of many of Greenland's tidewater glaciers
(Mankoff et al., 2020a), at the
centre of the base of the ice wall (Fig. 1a). The velocity of the subglacial
discharge-driven plume (e.g. Fig. 1g) and the melting of the ice wall were
calculated using the IcePlume package (Cowton et al., 2015).
In common with several previous studies
(Kimura et
al., 2014; Slater et al., 2015; Xu et al., 2013), we implement a free slip
condition on the fjord walls and ice front and do not simulate the effects
of sea ice, atmospheric forcing or tides.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Initial and open boundary conditions</title>
      <p id="d1e318">We use idealised representations of temperature and salinity profiles
commonly observed at the mouth of Greenland's southeastern fjords during
late summer as initial and open boundary conditions
(Sutherland et al., 2014). In our standard set-up, this
idealised profile is a cubic interpolation between 6 <inline-formula><mml:math id="M7" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C and 31 psu
at the fjord surface, 0 <inline-formula><mml:math id="M8" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C and 34 psu at 100 m depth, 2 <inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C at 200 m and 3.5 <inline-formula><mml:math id="M10" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C at 500 m depth, where salinity is greatest
at 35 psu (Fig. 1b–d). In this way, the upper several tens of metres represent waters that are seasonally warmed by solar insolation, whilst the
relatively cold intermediate layer, centred 100 m below the fjord surface,
represents the PW layer, which is underlain by warmer, more saline water
representing the AW layer. Henceforth, we refer to this set of boundary
conditions as <italic>BCstandard</italic>. In separate simulations, we use temperature minima at 100 m
of <inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (<italic>PWcool</italic>) and 1 <inline-formula><mml:math id="M13" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (<italic>PWwarm</italic>) and temperature maxima at 500 m
of 2.5 <inline-formula><mml:math id="M14" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (<italic>AWcool</italic>) and 4.5 <inline-formula><mml:math id="M15" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C (<italic>AWwarm</italic>) (Fig. 1e and f). Changing the
temperature of the AW and PW layers causes corresponding changes in the
vertical temperature gradient (Fig. 1e and f), the effects of which are
discussed in Sect. 3.2. Initial and open boundary salinity are kept constant
between simulations, but density changes between simulations are negligible.
Boundary conditions were kept constant throughout each simulation. We focus
on late-summer ocean conditions because of the greater availability of
observations at that time to both force the model and with which to make
comparisons.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Iceberg-ocean interaction</title>
      <p id="d1e428">Submarine iceberg melting is simulated using the IceBerg package within
MITgcm (Davison et al., 2020), with an ice
temperature of <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M17" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C
(Inall et al., 2014; Luthi et
al., 2002; Sciascia et al., 2013; Sutherland and Straneo, 2012). This
package uses the velocity-dependent 3-equation melt rate
parameterisation (Hellmer and Olbers, 1989;
Holland and Jenkins, 1999; Xu et al., 2012). We chose to use this melt rate
parameterisation rather than existing iceberg melt parameterisations (e.g. Bigg et al., 1997), because it enables us to resolve the vertical pattern of
submarine melting of individual icebergs. The temperature and salinity
fluxes associated with melting of individual iceberg faces within a grid
cell are calculated based on local temperature, salinity and face-normal
velocity. Face-normal current speed is calculated assuming that icebergs
drift with the average current velocity along their draught (although we note
that the iceberg locations are kept constant through each simulation).
Melt-driven plumes are not simulated directly; instead, their effect on melt
rates is parameterised by applying a minimum face-normal current speed of
0.06 m s<inline-formula><mml:math id="M18" 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> to each iceberg face. This minimum current speed is based on
line plume modelling (Davison et al., 2020). The package does not include
the effect of waves or mechanical iceberg break-up; therefore, melt rates
calculated here are conservative. We use standard parameter values
(Cowton
et al., 2015; Davison et al., 2020; Jackson et al., 2020) for the drag
coefficient (0.0025), and thermal and salt turbulent transfer coefficients
(0.022 and 0.00062, respectively). The icebergs are rectangular in plan-view
and have flat, vertical sides. All icebergs have length (<inline-formula><mml:math id="M19" display="inline"><mml:mi>l</mml:mi></mml:math></inline-formula>) to width ratios
of <inline-formula><mml:math id="M20" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.62</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> (Dowdeswell et
al., 1992), and iceberg keel depth (<inline-formula><mml:math id="M21" display="inline"><mml:mi>d</mml:mi></mml:math></inline-formula>) is related to iceberg length through
<inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2.91</mml:mn><mml:msup><mml:mi>l</mml:mi><mml:mn mathvariant="normal">071</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (Barker et al., 2004).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e508">Iceberg concentration <bold>(a, c, e, g, i)</bold> and maximum iceberg keel depth <bold>(b, d, f, h, j)</bold> for iceberg scenarios 1–5 (top to bottom). All panels
show the domain in plan-view and are 50 km long and 5 km across.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/1181/2022/tc-16-1181-2022-f02.png"/>

        </fig>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e526">Details of each iceberg scenario. Concentration is the percentage
of the fjord in plan-view occupied by icebergs. Iceberg concentration was
linearly interpolated from the maximum value (adjacent to the glacier wall)
to the minimum value 40 km down the fjord.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1">Iceberg</oasis:entry>
         <oasis:entry colname="col2">Max. draught</oasis:entry>
         <oasis:entry colname="col3">Exponent</oasis:entry>
         <oasis:entry colname="col4">Concentration</oasis:entry>
         <oasis:entry colname="col5">Surface area</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">scenario</oasis:entry>
         <oasis:entry colname="col2">(m)</oasis:entry>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4">[max,min] (%)</oasis:entry>
         <oasis:entry colname="col5">(km<inline-formula><mml:math id="M23" display="inline"><mml:msup><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:math></inline-formula>)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Scenario 1</oasis:entry>
         <oasis:entry colname="col2">50</oasis:entry>
         <oasis:entry colname="col3">1.6</oasis:entry>
         <oasis:entry colname="col4">[10,1]</oasis:entry>
         <oasis:entry colname="col5">44.5</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Scenario 2</oasis:entry>
         <oasis:entry colname="col2">100</oasis:entry>
         <oasis:entry colname="col3">1.7</oasis:entry>
         <oasis:entry colname="col4">[20,1]</oasis:entry>
         <oasis:entry colname="col5">76.5</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Scenario 3</oasis:entry>
         <oasis:entry colname="col2">200</oasis:entry>
         <oasis:entry colname="col3">1.8</oasis:entry>
         <oasis:entry colname="col4">[40,1]</oasis:entry>
         <oasis:entry colname="col5">141</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Scenario 4</oasis:entry>
         <oasis:entry colname="col2">300</oasis:entry>
         <oasis:entry colname="col3">1.9</oasis:entry>
         <oasis:entry colname="col4">[60,5]</oasis:entry>
         <oasis:entry colname="col5">235</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Scenario 5</oasis:entry>
         <oasis:entry colname="col2">400</oasis:entry>
         <oasis:entry colname="col3">2.1</oasis:entry>
         <oasis:entry colname="col4">[80,5]</oasis:entry>
         <oasis:entry colname="col5">316</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d1e686">In Sect. 3.1, we consider a range of iceberg concentrations, maximum keel
depths and size-frequency distributions, whilst using only the <italic>BCstandard</italic> boundary
conditions. In all set-ups, iceberg
concentration is uniform across the fjord and decreases linearly from a
maximum adjacent to the virtual ice wall to a minimum 10 km from the open
boundary. In Sect. 3.1, iceberg concentration (defined as the percentage of
the fjord surface in plan-view occupied by icebergs), is 80 % adjacent to
the ice wall and decreases to 5 % in our <italic>c1</italic> experiment, and is reduced to
75 %, 50 % and 25 % of these values in our <italic>c0.75</italic>, <italic>c0.5</italic>, and <italic>c0.25</italic> experiments, respectively.
Regardless of concentration, we used a maximum iceberg keel depth of 300 m
and the size-frequency distribution of the icebergs is described using a
power law with an exponent of <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula>, which is similar to that observed in
Sermilik Fjord (Sulak et al.,
2017). In separate simulations, we assign maximum iceberg keel depths of 50, 150, 250, 350
and 450 m, whilst maintaining the <italic>c1</italic> concentration and the <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> power law
exponent. We then vary the size-frequency distribution power law exponent
from <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.6</mml:mn></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.1</mml:mn></mml:mrow></mml:math></inline-formula> in increments of 0.1 (covering the range observed to date
in Greenland's fjords
(Rezvanbehbahani
et al., 2020; Sulak et al., 2017)), whilst retaining the <italic>c1</italic> concentration and
the 300 m maximum keel depth. In Sect. 3.1 we show the results
from simulations both with and without subglacial discharge, to demonstrate
the effect of icebergs in isolation and in combination with subglacial
discharge.</p>
      <p id="d1e751">In Sect. 3.2 onwards we consider five realistic combinations of iceberg
concentration, maximum iceberg keel depth and power law exponent, in order
to approximate the range of iceberg geometries and distributions found in
Greenland's fjords in summer (Fig. 2). In these set-ups, iceberg
concentration decreases linearly in the along-fjord direction away from the
glacier between specified maximum and minimum values (Table 1) and icebergs
are distributed randomly in the across-fjord direction (Fig. 2). These
iceberg set-ups range from those representing a fjord hosting few and small
icebergs, such as Kangerlussuup Sermia Fjord
(Sulak et al., 2017) (scenario
1), to those representing an iceberg-congested fjord, such as Sermilik
Fjord (scenario 5) (Fig. 2; Table 1). In all simulations shown in this
section (Sect. 3.2) 500 m<inline-formula><mml:math id="M28" 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="M29" 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> subglacial discharge is injected
into the fjord as described in Sect. 2.1.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>The effect of iceberg concentration, keel depth and size-frequency distribution on glacier-adjacent water properties</title>
      <p id="d1e791">The effect of iceberg melt on glacier-adjacent water properties depends on
iceberg geometry, iceberg concentration and iceberg size-frequency
distribution (Fig. 3) as well as on the presence or absence of subglacial
discharge. In the absence of subglacial discharge, icebergs modify
glacier-adjacent water properties (here defined as the average properties of
the water within 2 km of the ice wall; Fig. 1a) in two main ways.</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="d1e796">Glacier-adjacent water temperature vs. iceberg geometry and
distribution. Effect of iceberg concentration <bold>(a, d)</bold>, maximum iceberg
draught <bold>(b, e)</bold> and exponent describing the size-frequency distribution <bold>(c, f)</bold>. Panels <bold>(a)</bold>–<bold>(c)</bold> are for simulations without subglacial discharge,
whilst panels <bold>(d)</bold>–<bold>(f)</bold> are for simulations with 500 m<inline-formula><mml:math id="M30" 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="M31" 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> subglacial
discharge.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/1181/2022/tc-16-1181-2022-f03.png"/>

        </fig>

      <p id="d1e848">Firstly, they cause substantial (6–7.5 <inline-formula><mml:math id="M32" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) cooling in the upper
<inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> m of the water column, relative to the initial conditions
(Fig. 3a–c). The amount of cooling in this near-surface layer depends
somewhat on iceberg concentration, with steady-state water temperature
varying between <inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M36" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C over the range of iceberg concentrations considered but is
otherwise relatively insensitive to changing iceberg geometry and
distribution (Fig. 3a–c). Secondly, warming of up to <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M38" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C occurs below <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">80</mml:mn></mml:mrow></mml:math></inline-formula> m because iceberg melting
causes localised freshening at depth. The resulting iceberg melt-modified
water (i.e. the mixture of iceberg freshwater and ambient water at depth) is
less dense than the surrounding water and rises buoyantly towards the fjord
surface. The vertical extent and magnitude of the resulting warming
generally increase with maximum iceberg keel depth (Fig. 3b), because
icebergs with deeper keels cause upwelling of deeper AW (which in this case
is also warmer (Fig. 1b)). This warming effect does not extend to the fjord
surface, because the stronger stratification near the surface limits
upwelling and because iceberg-ocean contact areas are much greater near the
surface, so that cooling due to localised iceberg melting dominates. When
subglacial discharge is included, the effect of iceberg melt on
glacier-adjacent water properties at depth (below 60 m) is similar to that
in simulations without subglacial discharge but glacier-adjacent water
temperatures in the upper <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> m of the water column display a
greater range and the cooling of the near-surface waters is considerably
reduced (Fig. 3d–f). This is because the subglacial discharge causes strong
upwelling of AW towards the fjord surface and increases rates of fjord-shelf
exchange, which counters some of the iceberg-induced cooling of near-surface
waters.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Combining iceberg scenarios and ocean conditions</title>
      <p id="d1e949">In reality, changes in iceberg concentration, keel depth and size-frequency
distribution do not occur in isolation and there are characteristic
relationships between those iceberg descriptors
(Sulak et al., 2017). Fjords
hosting large glaciers, such as Sermilik Fjord and Helheim Glacier in east
Greenland, tend to contain both high iceberg concentrations and large,
deeply draughted icebergs, whilst those with lower iceberg concentrations,
such as Kangerlussuup Sermia Fjord, also tend to contain smaller icebergs.
To better represent the range of iceberg conditions found in Greenland's
fjords, we consider five iceberg scenarios (Fig. 2; Table 1), ranging from
a fjord with low iceberg concentration, shallow iceberg keels and fairly
uniform iceberg sizes (iceberg scenario 1), to a fjord with high iceberg
concentration, deep iceberg keels and a large range of iceberg sizes
(iceberg scenario 5). For each of these scenarios, we examine
steady-state glacier-adjacent water temperatures for a range of ocean
boundary conditions, with and without a shallow (100 m) sill. We
therefore consider three different PW and AW temperatures in turn (Fig. 1e and f), and examine the resulting glacier-adjacent water properties for each
of the five iceberg scenarios. To isolate the effect of iceberg melting from
other processes, we compare each of the above simulations to identical
simulations without icebergs.</p>
<sec id="Ch1.S3.SS2.SSS1">
  <label>3.2.1</label><title>Changing Polar Water temperature</title>
      <p id="d1e959">Figure 4 shows steady-state glacier-adjacent water properties for the range of
iceberg scenarios and PW temperatures considered. In all iceberg scenarios,
there is substantial (<inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M42" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C or more) cooling in the
upper <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> m, with greater cooling in scenarios with higher
iceberg concentrations. Other than this near-surface cooling,
glacier-adjacent water properties are very similar to open ocean conditions
in iceberg scenarios 1 and 2 (which have the lowest iceberg
concentrations; Fig. 2; Table 1). However, in iceberg scenarios 3–5 the PW layer is increasingly modified (Fig. 4c–e). With <italic>PWcool</italic>, icebergs in
these scenarios cause on average a net warming of 1.02 <inline-formula><mml:math id="M44" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in the 80–200 m
depth range, compared to simulations without icebergs. Conversely, with
<italic>PWwarm</italic>, the icebergs cause a net cooling of 0.30 <inline-formula><mml:math id="M45" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C over the same depth
range, such that the steady-state temperature profiles for both sets of
initial conditions (<italic>PWcool</italic> and <italic>PWwarm</italic>) are similar.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e1024">Steady-state glacier-adjacent water temperature for a range of
initial Polar Water conditions. In all plots, solid and dashed lines
indicate simulations with and without icebergs, respectively. Panels <bold>(a)</bold>–<bold>(e)</bold> show
configurations with a flat-bottomed domain, whilst <bold>(f)</bold>–<bold>(j)</bold> show those with a 100 m deep sill. Grey, blue and red lines show scenarios using the <italic>BCstandard</italic>, <italic>PWcool</italic> and
<italic>PWwarm</italic> boundary conditions, respectively (shown in Fig. 1e). The horizontal grey
lines indicate the maximum iceberg keel depth in each scenario, and the
horizontal orange lines in panels <bold>(f)</bold>–<bold>(j)</bold> indicate the sill depth.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/1181/2022/tc-16-1181-2022-f04.png"/>

          </fig>

      <p id="d1e1061">With <italic>BCstandard</italic>, the influence of icebergs on glacier-adjacent water properties falls
between the two, with the net effect being a slight (0.43 <inline-formula><mml:math id="M46" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C)
warming (Fig. 4c–e). These changes arise due to differing balances between
cooling due to iceberg melting, and warming due to buoyancy-induced
upwelling of relatively warm AW. With <italic>PWcool</italic> there is relatively little
iceberg melting in the PW layer (because the PW is close to the <italic>in-situ</italic> freezing
point), and so warming due to upwelling of AW dominates (driven by iceberg
melting at greater depth in the warmer AW layer). In contrast, with
<italic>PWwarm</italic>, iceberg melt rates in the PW layer are comparatively high, and the
temperature difference between the PW and AW layers is reduced, so localised
cooling offsets warming due to turbulent upwelling. In short, under the
conditions represented by these simulations, submarine iceberg melting acts
to make glacier-adjacent water temperature more uniform with depth (Fig. 4c–e).</p>
      <p id="d1e1086">The addition of a 100 m deep sill near the fjord mouth serves to amplify the
cooling effect of icebergs (Fig. 4f–j). Sills typically block external shelf
waters below the sill depth from entering the fjord (unless external forcing
causes a shallowing of isopycnals seaward of the sill), causing the fjord
basin bounded by the sill to be replenished by waters sourced only from
above the sill depth (e.g. Jakobsson et al., 2020). When icebergs reach down
to the sill depth, all water entering the fjord may thus be subject to
melt-driven cooling. The result is that icebergs cause cooling throughout
the water column, even below the deepest iceberg keels and below the sill
depth (Fig. 4f–j). This cooling is increasingly pronounced as the PW
temperature increases and with more concentrated and deeper icebergs (Fig. 4f–j). For example, over the 100–500 m depth range with <italic>PWcool</italic>, icebergs cause
0.21 <inline-formula><mml:math id="M47" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C cooling on average in iceberg scenarios 3–5
(0.06 <inline-formula><mml:math id="M48" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in scenario 3 and 0.35 <inline-formula><mml:math id="M49" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in scenario
5); whilst with <italic>PWwarm</italic>, icebergs cause 0.67 <inline-formula><mml:math id="M50" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C cooling on average
(0.33 <inline-formula><mml:math id="M51" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in scenario 3 and 0.91 <inline-formula><mml:math id="M52" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in scenario
5).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e1152">Glacier-adjacent temperature and salinity with (solid circles) and
without icebergs (open circles) for various iceberg and sill scenarios and
with <italic>BCstandard</italic> boundary conditions. Panels <bold>(a)</bold> and <bold>(b)</bold> show iceberg scenario 1
without a 100 m sill <bold>(a)</bold> and with a sill <bold>(b)</bold>. Panels <bold>(c)</bold> and <bold>(d)</bold> show
iceberg scenario 5 without a sill <bold>(c)</bold> and with a 100 m sill <bold>(d)</bold>. Solid
lines joining open and closed circles indicate connected data points
extracted from the same model depth.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/1181/2022/tc-16-1181-2022-f05.png"/>

          </fig>

      <p id="d1e1189">The varied effects of icebergs on glacier-adjacent water properties are
apparent in temperature-salinity space (Fig. 5). Initial glacier-adjacent
water properties are inherited from those prescribed at the fjord mouth;
however, icebergs modify fjord waters through ice melt and meltwater-driven
vertical mixing. Comparing temperature-salinity profiles of simulations with
and without icebergs illustrates these effects (Fig. 5). In the upper
<inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> m of all simulations with icebergs, iceberg melting
causes substantial cooling and slight freshening (e.g. compare solid and
open circles in Fig. 5 – solid circles are drawn down and slightly left in
temperature-salinity space). Deeper in the water column (below 100 m), the
influence of iceberg melting on water properties depends on the iceberg
scenario and the presence or absence of a sill. In iceberg scenario 1
(Fig. 5a and b), iceberg melting causes very little modification of waters
below 100 m, even in the presence of a sill (Fig. 5b). This is because the
icebergs do not extend to the sill water depth and so there is some
unmodified exchange between the fjord and the shelf. In iceberg scenario 5
icebergs cause on average 0.19 <inline-formula><mml:math id="M54" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C warming of waters below 100 m
when there is no sill, and cooling of 0.61 <inline-formula><mml:math id="M55" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C below 100 m when
there is a sill (Fig. 5b). This cooling below the maximum iceberg draught
occurs in all iceberg scenarios in which icebergs extend to sill depth but
is most apparent in the higher iceberg concentration scenarios (e.g. Fig. 5d). The simulated changes in water properties arise due the combined
effects of local iceberg melting and fjord circulation. Submarine iceberg
melting reduces the density of surrounding waters causing upwelling until
those waters equilibrate at a new neutral buoyancy depth with respect to the
fjord stratification. Within the temperature-salinity space of Greenland's
fjords, density is predominantly controlled by salinity. Therefore, the
salinity stratification is little changed by iceberg melting, whilst the
temperature changes are much more pronounced. This means that the iceberg
melt-induced migrations through temperature-salinity space that are often
steeper than predicted by the submarine melt mixing line (Gade, 1979).</p>
</sec>
<sec id="Ch1.S3.SS2.SSS2">
  <label>3.2.2</label><title>Changing Atlantic Water temperature</title>
      <p id="d1e1228">We also examine the interactions between iceberg scenarios and changes to AW
temperature (Fig. 6). As in the PW scenarios, there is always marked cooling
in the upper <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> m of the water column and water modification
below this is minimal for iceberg scenarios 1 and 2. In iceberg
scenarios 3–5, icebergs penetrate to a greater depth and thus into
the AW layer, releasing freshwater which causes upwelling of AW. In these
cases, the net effect of icebergs on water properties between
<inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">80</mml:mn></mml:mrow></mml:math></inline-formula> m and the maximum iceberg keel depth depends on the
balance between cooling due to localised iceberg melting, and warming due to
upwelling of AW. With <italic>AWwarm</italic>, there is a steep temperature gradient between the
cold PW and warmer AW layers. Consequently, upwelling of AW causes notable
warming in the PW layer that offsets localised iceberg-induced cooling. In
the scenarios with greater iceberg concentration (e.g. iceberg scenario
5; Fig. 6e), the icebergs penetrate deeper into the AW layer and so can
induce upwelling of the deeper, warmer water, resulting in more warming and
over a greater depth range than in the lower iceberg concentration
scenarios. However, with <italic>AWcool</italic>, the vertical temperature gradient is reduced, therefore
cooling due to localised iceberg melting dominates the signal between the
maximum iceberg draught and <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">80</mml:mn></mml:mrow></mml:math></inline-formula> m.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e1269">Steady-state glacier-adjacent water temperature for a range of
initial Atlantic Water conditions and with a flat-bottomed domain. In all
plots, solid and dashed lines indicate simulations with and without
icebergs, respectively. Grey, blue and red lines show scenarios using the
<italic>BCstandard</italic>, <italic>AWcool</italic> and <italic>AWwarm </italic>boundary conditions, respectively (shown in Fig. 1f). The
horizontal grey lines indicate the maximum iceberg keel depth in each
scenario.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/1181/2022/tc-16-1181-2022-f06.png"/>

          </fig>

      <p id="d1e1287">This dependence of iceberg modification of glacier-adjacent water properties
on the temperature gradient through the AW layer is further illustrated by
sensitivity tests in which the temperature of the
AW layer was modified in two ways relative to <italic>BCstandard</italic>. First, to examine whether
the absolute temperature of the water column affected the balance between
upwelling and melting, the entire water column was uniformly warmed by
1 <inline-formula><mml:math id="M59" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. With this uniform shift in temperature, the pattern of
temperature with depth is similar to that of <italic>BCstandard</italic> (compare dashed grey and red
lines in Fig. 7b), illustrating that the additional upwelling-driven warming
with <italic>AWwarm</italic> is due to the steeper temperature gradient between the PW and AW
layers, rather than the absolute temperature of the AW. Secondly, to
illustrate the importance of the temperature gradient within the AW layer,
we made the AW layer uniformly 3.5 <inline-formula><mml:math id="M60" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C. With this set of boundary
conditions, upwelling-driven warming dominates in the PW layer, because of
upwelling of warm AW, whilst melt-driven cooling dominates in the AW layer
because upwelling-driven warming is muted (Fig. 7c). Thus, the average
warming below <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">80</mml:mn></mml:mrow></mml:math></inline-formula> m that we simulate with <italic>AWwarm</italic> is strongly
sensitive to the vertical temperature gradient and not only the average or
maximum temperature of the AW.</p>
      <p id="d1e1332">With the addition of a 100 m sill, AW does not propagate into the fjord
under the conditions simulated here. Thus in steady-state, glacier-adjacent
water properties are unaffected by AW and adopt the properties of the PW
layer (modified by iceberg melting and subglacial discharge). The resulting
profiles therefore resemble the dashed pale blue lines in Fig. 4f–j and are
not shown here.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7" specific-use="star"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e1337">AW temperature gradient sensitivity tests. Panels show simulations
using <bold>(a)</bold> <italic>BCstandard</italic>, <bold>(b)</bold> temperature profile shifted by 1 <inline-formula><mml:math id="M62" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C throughout the
water column, and <bold>(c)</bold> uniform initial AW temperature of 3.5 <inline-formula><mml:math id="M63" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C.
Steady-state conditions without icebergs using <italic>BCstandard</italic> (grey line) are also shown
in <bold>(b)</bold> and <bold>(c)</bold> for reference.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/1181/2022/tc-16-1181-2022-f07.png"/>

          </fig>

</sec>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Comparison with observations and applicability to real fjords</title>
      <p id="d1e1403">Our simulations suggest that several changes to glacier-adjacent water
properties can occur due to submarine iceberg melting. In almost all
simulations, we simulate pronounced (<inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M65" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) cooling in
the
upper several tens of metres of the water column. Deeper in the water column
(between <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">80</mml:mn></mml:mrow></mml:math></inline-formula> m and the maximum iceberg keel depth), both
iceberg-induced cooling and warming can occur (e.g. Figs. 4 and 6), depending
on the balance between cooling due local iceberg melting and warming due to
melt-driven upwelling.</p>
      <p id="d1e1435">The balance between these processes depends on the iceberg contact area at
depth available for local melting (and therefore cooling) and on the
temperature of the upwelling water. When vertical temperature gradients are
steep (e.g. with <italic>AWwarm</italic>; Fig. 6), icebergs can cause warming between their maximum
keel depth and the surface layer. This is particularly apparent in the PW
layer, where the temperature difference between an upwelled parcel of water
and that at the parcel's new neutral buoyancy depth in the PW layer is
greatest, and where iceberg melt rates (and therefore melt-driven cooling)
are generally smaller because of the low water temperatures. In contrast,
when vertical temperature gradients are shallower (e.g. with <italic>AWcool</italic>), cooling due
to localised melting dominates (blue lines in Figs. 6d and e and 7c). These
effects tend to reduce vertical temperature variations of glacier-adjacent
waters compared both to simulations without icebergs and compared to
conditions at the fjord mouth.</p>
      <p id="d1e1444">Detailed near-glacier hydrographic observations against which to make
comparisons are sparse, but those that do exist provide some useful insight
into the applicability of our model results to Greenland's fjords. The
pronounced surface and near-surface cooling (relative to conditions at the
mouth) that we simulate is a common feature in Greenland's fjords. For
example, a transect of conductivity, temperature, depth (CTD) casts along
Sermilik Fjord revealed cooling of approximately 4 <inline-formula><mml:math id="M67" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C in the upper
<inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> m (Straneo et al., 2011, 2012),
which was also reproduced in a detailed modelling study of Sermilik Fjord
that included icebergs (Davison et al., 2020).
Similar along-fjord near-surface cooling has also been observed in other
iceberg-congested fjords, such as Illulissat Isfjord
(Beaird et al., 2017; Gladish et
al., 2015) and Upernavik Isfjord (Fenty et al., 2016), both
in West Greenland. In Illulissat Isfjord, the cold surface layer usually
extends along-fjord to a shallow sill at the fjord mouth, where icebergs
frequently become grounded (Gladish et al., 2015).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e1469">Fjord temperature profiles from the Oceans Melting Greenland
project (<uri>https://omg.jpl.nasa.gov/</uri>, last access: 14 April 2020). The blue lines are
profiles acquired within the fjord, close to tidewater glacier termini, and
the grey lines are acquired at or beyond the fjord mouth. Fjords (or nearest
glacier) shown are <bold>(a)</bold> Sermilik Fjord, <bold>(b)</bold> Daugaard-Jensen, <bold>(c)</bold> Upernavik
Isstrom, <bold>(d)</bold> Nunatakassaap Sermia Fjord, <bold>(e)</bold> Ilulissat Isfjord, and <bold>(f)</bold> Timmiarmiut Fjord. Data are available from: <uri>https://omg.jpl.nasa.gov/portal/data/OMGEV-AXCTD</uri>, last access: 14 April 2020).</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/1181/2022/tc-16-1181-2022-f08.png"/>

        </fig>

      <p id="d1e1503">Iceberg-induced changes to water properties below <inline-formula><mml:math id="M69" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 80 m are
harder to identify in hydrographic observations, most likely because they
also contain the signature of glacial plumes resulting from subglacial
discharge, or other external forcings. Our modelling suggests that if
vertical temperature gradients are shallow, then icebergs can cause cooling
over large depth ranges (e.g. Fig. 7c). As one example, hydrographic
observations in Kangerdlugssuaq Fjord showed relatively uniform near-glacier
temperatures with substantial cooling in both the upper 100 m and between depths of 300 and 400 m, relative to a transect acquired at the fjord mouth
(Straneo et al., 2012), consistent with the modelling
results presented here. Iceberg melt-induced warming of parts of the water
column is even harder to
identify in published hydrographic observations because of the difficulty in
distinguishing it from relatively warm subglacial discharge-driven plume
outflow.</p>
      <p id="d1e1513">To further compare our modelling results to observations, we examined CTD
casts acquired as part of the Oceans Melting Greenland (OMG) project
(<uri>https://omg.jpl.nasa.gov/</uri>, last access: 14 April 2020; data available at: <uri>https://omg.jpl.nasa.gov/portal/data/OMGEV-AXCTD</uri>, last access: 14 April 2020). In keeping with our
simulation design, we selected pairs of CTD casts acquired less than a week
apart, one near or outside the fjord mouth and the other as close as
possible to the tidewater glacier at the head of the fjord. These profiles
(Fig. 8) show many of the characteristics that we have simulated here.
Specifically, the profiles show that near-surface water temperatures are
substantially colder adjacent to tidewater glaciers compared to those
observed outside each fjord, and the observed temperature differences
between the mouth and near-glacier region are comparable to those simulated
here. In all but two of the surveyed fjords (Illulissat Isfjord and
Timmiarmiut Fjord, shown in Fig. 8e and f), the profiles also show warming
at intermediate depths (<inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula>–200 m) relative to the waters
outside the fjord, consistent with our simulations using icebergs scenarios
3–5, particularly using our <italic>AWwarm</italic> boundary conditions (Fig. 6c–e).
These observations do not allow us to quantify the relative contributions to
intermediate depth warming between plume outflow and iceberg melt-induced
upwelling. However, we note that the vertical pattern and magnitudes of
intermediate depth warming are similar to those simulated here. In addition,
the intermediate depth warming occurs over a large depth range, which is not
easily explained by plume outflow and is consistent with our simulations.
Some of the profiles also show notable cooling at depth (e.g. Illulissat
Isfjord, Fig. 8e), which we are only able to reproduce in simulations
including a shallow sill (e.g. the red line in Fig. 4j). Our simulations may
underestimate cooling at depth because power law size-frequency
distributions underestimate the number of very large icebergs
(Sulak et al., 2017) and because
the parameter values used in our melt calculation may underestimate
submarine melt rates (Jackson et
al., 2020).</p>
      <p id="d1e1535">In our simulations, we have generally considered a glacier-fjord system in
which the glacier face and subglacial discharge interact with the entire
water column, and with icebergs affecting a range of depths between the
surface and their keels, which is a coarse representation of many fjords in
Greenland. In many other fjords in Greenland, glacier grounding lines are
shallower, such that the calving front and subglacial discharge interact
predominately with the surface and PW layers. Although our simulations do
not encompass this geometry, they still provide some insights into the
potential effect of icebergs on near-glacier conditions in these fjords.
With this geometry, subglacial discharge is injected directly into the PW
layer. Therefore, plume outflow is relatively cool and we would expect,
based the simulations presented here, that iceberg-driven cooling of the
surface layer to be significant (resembling Fig. 3a–c). In addition,
icebergs calved from such shallow glaciers would not be able to cause
upwelling of warm AW (as in our scenarios 1 and 2), and so we would not
expect any iceberg melt-driven warming of the PW layer. Overall, based on the insights gained from our simulations we expect that the effect of
iceberg melt on near-glacier water properties in shallow fjords therefore
largely manifests as a cooling in the upper several tens of metres of the
water column, thereby reducing vertical variations in water column
temperature. Such patterns have been observed in fjords hosting glaciers
with relatively shallow (<inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">250</mml:mn></mml:mrow></mml:math></inline-formula> m) grounding lines resting in
the PW layer (e.g. Mortensen et al., 2020).</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Implications for glacier-ocean interaction</title>
      <p id="d1e1556">If iceberg-induced changes to glacier-adjacent water properties
significantly affect the magnitude and/or the vertical pattern of glacier
submarine melting, then icebergs may play an important role in modifying
glacier response to ocean forcing. To assess the effect of icebergs on
glacier submarine melting, we first consider how iceberg melt impacts
subglacial discharge-driven plume dynamics and then assess how the simulated
temperature changes could affect melt rates across the parts of glacier
fronts that are not directly affected by subglacial discharge-driven plumes.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F9" specific-use="star"><?xmltex \currentcnt{9}?><?xmltex \def\figurename{Figure}?><label>Figure 9</label><caption><p id="d1e1561">Plume dynamics for iceberg scenarios 1–5. <bold>(a)</bold> Plume
vertical velocity. <bold>(b)</bold> Plume temperature. <bold>(c)</bold> Glacier submarine melt rate in
the plume. All simulations are based on <italic>BCstandard</italic> boundary conditions and 500 m 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> subglacial discharge.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://tc.copernicus.org/articles/16/1181/2022/tc-16-1181-2022-f09.png"/>

        </fig>

      <p id="d1e1594">To examine the effect of icebergs on subglacial discharge plume-driven
glacier submarine melting, we evaluated plume properties for a single set of
ocean boundary conditions (<italic>BCstandard</italic>; Fig. 1b–d) using
each of the five iceberg scenarios. We find that submarine iceberg melting
has negligible influence on plume vertical velocity and only a modest
influence on plume temperature, meaning that plume-induced glacier submarine melt
rates appear relatively insensitive to the changes in temperature and
salinity induced by changes in iceberg geometry, concentration and
size-frequency distribution (Fig. 9).</p>
      <p id="d1e1601">Although subglacial discharge-driven plume dynamics appear to be relatively
insensitive to iceberg-induced modification of glacier-adjacent water
properties, submarine melting distal to glacial plumes (“background melting”
(e.g. Slater et al., 2018)) may be more
directly affected. Qualitatively, the iceberg melt-induced changes to
glacier-adjacent water properties presented above suggest that iceberg melt
will affect background glacier melt rates in three key ways: (1) at and near
the fjord surface cooling will reduce background melt rates, (2) in the PW
layer background melting will usually increase due to upwelling of warmer
AW, and (3) in the AW layer iceberg melt-induced changes in background
melt rates are expected to be modest with slight increases in fjords with
steep vertical temperature gradients and slight decreases in other fjords
(assuming icebergs penetrate into the AW layer). These effects will be more
pronounced in fjords with higher concentrations of larger (and thus deeper
keeled) icebergs. In fjords where icebergs cause cooling near
the surface and warming at depth, we expect icebergs will increase glacier
undercutting through impacting submarine melt rates, which may in turn
influence the rate and mechanism of calving
(Benn et al.,
2017; James et al., 2014; O'Leary and Christoffersen, 2013).</p>
      <p id="d1e1604">To explore these effects quantitatively, we calculate the percentage change
in background melt rate of the glacier terminus due to iceberg-induced
modification of glacier-adjacent water temperature (relative to simulations
without icebergs). Modelling studies indicate that background melt rates
scale linearly with ocean temperature
(Sciascia et
al., 2013; Slater et al., 2016; Xu et al., 2013); thus, changes in
temperature, <inline-formula><mml:math id="M73" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>, should cause proportional changes in background melting
(Jackson et al., 2014). We choose to focus on
relative changes in melt rate rather than absolute changes, because of poor
constraints on important melt rate parameter values
(Jackson et al., 2020). We calculate
the relative change in submarine melt rate, SMR, following Jackson et al. (2014), as
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M74" display="block"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mtext>SMR</mml:mtext><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">ib</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">nib</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">nib</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:mfenced></mml:mrow></mml:mfrac></mml:mstyle><mml:mn mathvariant="normal">100</mml:mn><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where the subscripts “ib” and “nib” indicate simulations with “icebergs” and “no
icebergs”, respectively, and <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the <italic>in-situ</italic> freezing point, given by
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M76" display="block"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mi>S</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub><mml:mi>z</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">λ</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> are constants representing the freezing point slope
(<inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0573</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M79" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C psu<inline-formula><mml:math id="M80" 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>), offset (0.0832 <inline-formula><mml:math id="M81" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C) and depth
(0.000761 <inline-formula><mml:math id="M82" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>C m<inline-formula><mml:math id="M83" 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>), respectively (Cowton et al., 2015). <inline-formula><mml:math id="M84" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> is
the local salinity (horizontally averaged within 2 km of the terminus) and
<inline-formula><mml:math id="M85" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula> is depth in the water column. It is worth noting that changes in melt rate
calculated using this method assume that all changes in heat supply are
accommodated by changes in submarine melt rates, and so this method provides
an indication of the maximum relative changes in submarine melt rates
expected due to changes in ambient ocean temperature.</p>
      <p id="d1e1823">Using this approach, we find that the impact on water properties resulting
from iceberg melt substantially modifies background glacier submarine melt
rates. Firstly, in the upper 50 m and using <italic>BCstandard</italic>, iceberg melt causes a 34.9 %
reduction in melt rate on average. Even in iceberg scenario 1, iceberg
melt causes a 29.5 % reduction in melt rate over this depth range.
Secondly, between 100 and 200 m depth, iceberg melt causes a 13.5 %
increase in melt rate on average when using <italic>BCstandard</italic>, but this increases to 59.2 %
when using <italic>PWcool</italic> (for which warming of the PW layer due to upwelling is most
pronounced). Changes in iceberg melt rates in the AW layer are minimal, with
the most pronounced effect being a 5.4 % increase in the 200–400 m depth
range using iceberg scenario 5 and <italic>PWwarm</italic>. When averaged through the entire
water column, these effects largely compensate for each other, resulting in
a net 3.1 % decrease in melt rates with <italic>BCstandard</italic>. Overall therefore, this analysis
suggests that iceberg melt can influence the vertical pattern of glacier
terminus background melting by decreasing melt rates at the surface and
increasing them in the PW layer, with minimal changes in the AW layer.</p>
      <p id="d1e1841">As well as affecting glacier-adjacent water temperatures, iceberg melt
likely affects submarine melt rates in other ways not examined here. For
example, the cooling and freshening of the surface and near-surface layers
induced by iceberg melting may prevent or hinder plume surfacing
(De Andrés et al., 2020), and may expedite sea ice
formation after the melt season, promoting the development of an ice
mélange. In addition, mechanical iceberg break-up, iceberg calving and
iceberg rotation can cause vigorous mixing of fjord waters, which can
temporarily increase glacier and iceberg submarine melt rates
(Enderlin et al., 2018), and increase the iceberg-ocean
contact area available for melting. Iceberg melt-induced invigoration of
fjord circulation can increase oceanic heat flux towards tidewater glaciers
(Davison et al., 2020), likely resulting in
faster terminus submarine melting. Icebergs likely also exert a mechanical
influence on the circulation and plume dynamics at the ice-ocean interface
(Amundson et al., 2020) and may prevent
plume surfacing (Xie et al., 2019).</p>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Implications for oceanic forcing of ice sheet scale models</title>
      <p id="d1e1852">Current state of the art projections of dynamic mass loss from the Greenland
Ice Sheet (Goelzer et al., 2020) are
forced by far-field ocean temperature profiles, provided by ocean modelling
output that does not include fjord-scale processes (except for the
obstruction of shelf-water intrusion by shallow sills)
(Slater et al., 2019, 2020).
The results presented here suggest that such an approach is broadly
appropriate for fjords with maximum iceberg keel depths of less than 200 m
and iceberg concentrations less than <inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> % on average,
where iceberg modification of glacier-adjacent water properties appears to
be limited other than in the upper several tens of metres (Figs. 4 and 6).
The majority of Greenland's fjords likely fall into this category
(Mankoff
et al., 2020b; Sulak et al., 2017). Even in such fjords, however, this
approach would not capture the surface and near-surface cooling caused by
iceberg melting. In order to capture this near surface cooling, one
relatively simple modification to such an approach could be to reduce
surface water temperature to close to the <italic>in-situ</italic> melting point during winter
periods, and proportionally to the iceberg surface area at the fjord surface
during summer periods.</p>
      <p id="d1e1868">In fjords hosting icebergs with keel depth greater than or equal to
200 m and with average concentrations of more than <inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> %
(i.e. our iceberg scenario 3 or higher), iceberg modification of
glacier-adjacent water properties becomes increasingly more important. In such
fjords that also exhibit relatively shallow sills, icebergs act to cool
glacier-adjacent water throughout the water column, with the amount of
cooling proportional to the draught and concentration of the icebergs, as
well as to the temperature of the ambient water at the fjord mouth (Fig. 4).
In such fjords that do not have shallow sills, the effect is more
complicated with both iceberg melt-induced warming and cooling, depending
on the vertical temperature gradient of the water column and iceberg
concentration at depth. Overall, these changes to the water column
temperature can cause non-negligible (up to several tens of percent) changes
in terminus submarine melt rates across the large areas of the calving front
that are not directly affected by plume-inducing subglacial discharge. The
vertical pattern of changes to terminus submarine melt rates (reduced near
the surface and increased at intermediate depths) induced by iceberg melting
is expected to exacerbate undercutting of glacier termini, with potentially
important impacts on calving rates
(Benn et
al., 2017; Ma and Bassis, 2019; O'Leary and Christoffersen, 2013; Todd and
Christoffersen, 2014). Although fjords hosting icebergs this large and
numerous are relatively few in number, it is these fjords (and the glaciers
hosted by them) that contribute the most to dynamic mass loss from the
Greenland Ice Sheet
(Enderlin et al.,
2014; Khan et al., 2020).</p>
</sec>
<sec id="Ch1.S4.SS4">
  <label>4.4</label><?xmltex \opttitle{Transience vs.\ steady state}?><title>Transience vs. steady state</title>
      <p id="d1e1890">All of the results presented here were extracted from the final 10 d of
simulations that were run to a quasi-steady state (i.e. the variable of
interest had stabilised). In our domains without sills, steady state of
temperature and salinity was generally reached after just 10–30 d. However, our simulations with sills could take as many as 1000 d to reach such a steady state because fjord-shelf exchange is reduced.
For an equivalent steady state to be reached in reality, open ocean
conditions, subglacial discharge and iceberg size and distribution would
also have to remain quasi-stable for an equivalent time period. In reality,
this is unlikely to occur (particularly in fjords with shallow sills)
because subglacial discharge and coastal and open ocean conditions change on
subseasonal to seasonal time scales
(Moon
et al., 2017; Mortensen et al., 2014; Noël et al., 2016; Sutherland et
al., 2014; Sutherland and Pickart, 2008). In reality therefore,
glacier-adjacent water properties in fjords with shallow sills are likely a
complex amalgamation of temporally evolving source waters, modified by
processes operating within the fjord. In addition, some variations in
coastal conditions can be transmitted towards glaciers very rapidly. During
winter, strong wind events on the east coast of Greenland drive fast
shelf-forced flows (or intermediary currents) in glacial fjords, delivering
coastal waters to tidewater glaciers over just a period of a few days, and
potentially reducing the magnitude of iceberg-driven modification
(Jackson et al., 2014,
2018). Such currents are strongest in winter, when hydrographic observations
are sparse, so this remains speculative.</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d1e1903">We have used a general circulation model (MITgcm) to quantify the effect of
submarine iceberg melting on glacier-adjacent water properties in an
idealised fjord domain. A large range of iceberg concentrations, keel depths
and size-frequency distributions were examined to represent the range of
iceberg conditions found in Greenland's marine terminating glacier fjords.
We focused primarily on iceberg melt-induced changes to glacier-adjacent
water temperatures throughout the water column, because of their principal
importance to glacier submarine melting.</p>
      <p id="d1e1906">Our results suggest that icebergs can substantially modify glacier-adjacent
water properties and that the precise impact depends on iceberg size and on
the temperature profile and stratification of water within and beyond the
fjord. In particular, we find that (1) temperature in the upper
<inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> m of the water column is reduced by several degrees Celsius over a wide range of iceberg scenarios, (2) fjords with more and
deeper icebergs are subject to greater iceberg melt-induced modification,
which can result in either cooling or warming at different depths depending
on the balance between melt-driven cooling and upwelling-driven warming,
which in turn depends on fjord temperature stratification and (3) when
icebergs extend to or below the fjord mouth sill depth, they can cause
significant cooling throughout the water column. Particularly with respect to
point (2), our results highlight that oceanic forcing of large fast-flowing
glaciers, which contribute the most to ice sheet dynamic mass loss, in
existing projections of tidewater glacier dynamics is strongly affected by
ignoring the impact of icebergs on fjord water properties. The
iceberg-induced changes to the vertical temperature profile of
glacier-adjacent waters identified here are likely to reduce submarine melt
rates at and near the fjord surface while increasing them in the PW layer,
which may influence the rate and mechanism of calving by exacerbating
glacier terminus undercutting. Our results therefore identify a critical
need to develop simple parameterisations of iceberg-induced modification of
fjord waters, and other fjord-scale processes, to better constrain oceanic
forcing of tidewater glaciers.</p>
</sec>

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

      <p id="d1e1923">MITgcm is freely available at <uri>https://github.com/MITgcm/MITgcm/archive/master.zip</uri> and <ext-link xlink:href="https://doi.org/10.5281/zenodo.4968496" ext-link-type="DOI">10.5281/zenodo.4968496</ext-link> (Campin et al., 2021; Marshall et al., 1997a). The IcePlume
module is available from Tom Cowton on request. The IceBerg module is
available at <ext-link xlink:href="https://doi.org/10.5281/zenodo.3979647" ext-link-type="DOI">10.5281/zenodo.3979647</ext-link> (Davison, 2020)
or from Benjamin Davison on request.</p>
  </notes><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e1938">The model domains, boundary conditions and output are available from the corresponding author on request.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e1944">BJD and TC conceived the study. BJD developed the model code with support from
TC and AS. BJD designed and conducted the simulations and analysis, and led
the manuscript write up. TC, FC, AS and PN supported the interpretation of
the model results and contributed to the preparation of the manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e1950">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="d1e1956">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="d1e1962">The simulations were conducted on the Sheffield Advanced Research Computer (ShARC). The authors thank the editor, Nicolas Jourdain, for considering our paper for publication, and Thomas Rackow and one anonymous reviewer for providing thorough reviews of the paper.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e1967">This research has been supported by the Scottish Alliance for Geoscience, Environment and Society and the University of St Andrews (PhD studentship).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e1973">This paper was edited by Nicolas Jourdain and reviewed by Thomas Rackow and one anonymous referee.</p>
  </notes><ref-list>
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