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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-17-4549-2023</article-id><title-group><article-title>Assessing the potential for ice flow piracy between the Totten and Vanderford glaciers, East Antarctica</article-title><alt-title>Flow piracy of the Totten and Vanderford glaciers</alt-title>
      </title-group><?xmltex \runningtitle{Flow piracy of the Totten and Vanderford glaciers}?><?xmltex \runningauthor{F.~S.~McCormack~et~al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>McCormack</surname><given-names>Felicity S.</given-names></name>
          <email>felicity.mccormack@monash.edu</email>
        <ext-link>https://orcid.org/0000-0002-2324-2120</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Roberts</surname><given-names>Jason L.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-3477-4069</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3 aff4 aff5">
          <name><surname>Kulessa</surname><given-names>Bernd</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-4830-4949</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6 aff7">
          <name><surname>Aitken</surname><given-names>Alan</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-6375-2504</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff8 aff9">
          <name><surname>Dow</surname><given-names>Christine F.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1346-2258</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Bird</surname><given-names>Lawrence</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-6541-2768</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2 aff5 aff10">
          <name><surname>Galton-Fenzi</surname><given-names>Benjamin K.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1404-4103</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Hochmuth</surname><given-names>Katharina</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-2789-2179</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Jones</surname><given-names>Richard S.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-2988-0999</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Mackintosh</surname><given-names>Andrew N.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff8">
          <name><surname>McArthur</surname><given-names>Koi</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Securing Antarctica's Environmental Future, School of Earth, Atmosphere and Environment, Monash University,<?xmltex \hack{\break}?> Clayton, Kulin Nations, Victoria, Australia</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Australian Antarctic Division, Kingston, nipaluna / Hobart, Tasmania, Australia</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>School of Biosciences, Geography and Physics, Swansea University, Swansea, UK</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>School of Technology, Environments and Design, University of Tasmania, nipaluna / Hobart, Tasmania, Australia</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>The Australian Centre for Excellence in Antarctic Science, University of Tasmania, nipaluna / Hobart, Tasmania, Australia</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>School of Earth Sciences, The University of Western Australia, Perth, Western Australia, Australia</institution>
        </aff>
        <aff id="aff7"><label>7</label><institution>The Australian Centre for Excellence in Antarctic Science, The University of Western Australia, Perth,<?xmltex \hack{\break}?> Western Australia, Australia</institution>
        </aff>
        <aff id="aff8"><label>8</label><institution>Department of Applied Mathematics, University of Waterloo, Waterloo, Canada</institution>
        </aff>
        <aff id="aff9"><label>9</label><institution>Department of Geography and Environmental Management, University of Waterloo, Waterloo, Canada</institution>
        </aff>
        <aff id="aff10"><label>10</label><institution>The Australian Antarctic Program Partnership, Institute for Marine and Antarctic Studies, University of Tasmania, nipaluna / Hobart, Tasmania, Australia</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Felicity S. McCormack (felicity.mccormack@monash.edu)</corresp></author-notes><pub-date><day>1</day><month>November</month><year>2023</year></pub-date>
      
      <volume>17</volume>
      <issue>11</issue>
      <fpage>4549</fpage><lpage>4569</lpage>
      <history>
        <date date-type="received"><day>2</day><month>May</month><year>2023</year></date>
           <date date-type="accepted"><day>7</day><month>September</month><year>2023</year></date>
           <date date-type="rev-recd"><day>1</day><month>September</month><year>2023</year></date>
           <date date-type="rev-request"><day>8</day><month>June</month><year>2023</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2023 </copyright-statement>
        <copyright-year>2023</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="d1e238">The largest regional drivers of current surface elevation increases in the Antarctic Ice Sheet are associated with ice flow reconfiguration in previously active ice streams, highlighting the important role of ice dynamics in mass balance calculations. Here, we investigate controls on the evolution of the flow configuration of the Vanderford and Totten glaciers – key outlet glaciers of the Aurora Subglacial Basin (ASB) – the most rapidly thinning region of the East Antarctic Ice Sheet (EAIS). We synthesise factors that influence the ice flow in this region and use an ice sheet model to investigate the sensitivity of the catchment divide location to changes in surface elevation due to thinning at the Vanderford Glacier (VG) associated with ongoing retreat and thickening at the Totten Glacier (TG) associated with an intensification of the east–west snowfall gradient. The present-day catchment divide between the Totten and Vanderford glaciers is not constrained by the geology or topography but is determined by the large-scale ice sheet geometry and its long-term evolution in response to climate forcing. Furthermore, the catchment divide migrates under relatively small changes in surface elevation, leading to ice flow and basal water piracy from the Totten to the Vanderford Glacier. Our findings show that ice flow reconfigurations occur not only in regions of West Antarctica like the Siple Coast but also in the east, motivating further investigations of past, and the potential for future, ice flow reconfigurations around the whole Antarctic coastline. Modelling of ice flow and basal water piracy may require coupled ice sheet thermomechanical and subglacial hydrology models constrained by field observations of subglacial conditions. Our results have implications for ice sheet mass budget studies that integrate over catchments and the validity of the zero flow assumption when selecting sites for ice core records of past climate.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Australian Research Council</funding-source>
<award-id>DE210101433</award-id>
<award-id>DE210101923</award-id>
<award-id>SR200100005</award-id>
<award-id>SR200100008</award-id>
</award-group>
<award-group id="gs2">
<funding-source>Natural Sciences and Engineering Research Council of Canada</funding-source>
<award-id>NSERC RGPIN- 03761-2017</award-id>
</award-group>
<award-group id="gs3">
<funding-source>Canada Research Chairs</funding-source>
<award-id>CRC 950-231237</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

      <?xmltex \hack{\newpage}?>
<?pagebreak page4550?><sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d1e252">The Vanderford Glacier (VG) is the fastest-retreating glacier in the East Antarctic Ice Sheet (EAIS), with approximately 18.6 <inline-formula><mml:math id="M1" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> of grounding line retreat observed over the period 1996 to 2020 <xref ref-type="bibr" rid="bib1.bibx64" id="paren.1"/>. The Vanderford Glacier drains part of the ice contained in the Aurora Subglacial Basin (ASB; Fig. <xref ref-type="fig" rid="Ch1.F1"/>a), which contains approximately 7 <inline-formula><mml:math id="M2" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> of global sea level equivalent <xref ref-type="bibr" rid="bib1.bibx56" id="paren.2"/>. However, half of that water-equivalent ice volume lies on topography that is grounded below sea level, and hence the ASB is highly vulnerable to significant deglaciation as the climate warms. The ASB is the most rapidly thinning basin in East Antarctica <xref ref-type="bibr" rid="bib1.bibx86" id="paren.3"/>, and modelling studies indicate that it will continue to be the dominant East Antarctic contributor to global sea level rise over the coming decades to centuries <xref ref-type="bibr" rid="bib1.bibx62 bib1.bibx63 bib1.bibx79" id="paren.4"/>. Geological data proximal to the East Antarctic coastline from Princess Elizabeth Land to Adélie Land <xref ref-type="bibr" rid="bib1.bibx18 bib1.bibx97 bib1.bibx98" id="paren.5"/> suggest markedly reduced ice volumes could have been present in the ASB and Wilkes Subglacial Basin during the mid-Pliocene warm period (MPWP; 3.3 to 3 <inline-formula><mml:math id="M3" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Ma</mml:mi></mml:mrow></mml:math></inline-formula>), when global temperatures were <inline-formula><mml:math id="M4" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2.5 to 4 <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> warmer than the 1850 to 1900 mean. Ice sheet model simulations of the MPWP show preferential ice loss from the ASB and Wilkes subglacial basins <xref ref-type="bibr" rid="bib1.bibx8 bib1.bibx19" id="paren.6"/>, highlighting the potential of the ASB to reach a tipping point as the climate warms <xref ref-type="bibr" rid="bib1.bibx52 bib1.bibx60" id="paren.7"/>.</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="d1e325">Aurora Subglacial Basin bed elevation and uncertainty derived from the BedMachine Antarctica v3 dataset <xref ref-type="bibr" rid="bib1.bibx56" id="paren.8"/>. <bold>(a)</bold> Bed topography (<inline-formula><mml:math id="M6" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>), with red enlarged inset shown in panel <bold>(b)</bold>, and <bold>(c)</bold> uncertainty (<inline-formula><mml:math id="M7" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>). The ASB catchment outline is from <xref ref-type="bibr" rid="bib1.bibx102" id="text.9"/>, and the coastline and grounding line (black) are from MEaSUREs2. All data are referenced to the WGS84 ellipsoid and displayed in eastings (<inline-formula><mml:math id="M8" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> axis) and northings (<inline-formula><mml:math id="M9" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> axis) using polar stereographic coordinates (<inline-formula><mml:math id="M10" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>). Locations of regions in panel <bold>(a)</bold> are the following: Vostok Highland, ASB main basin, Highland A, Highland B, Highland C, Sabrina Subglacial Basin (SSB), Totten Glacier (TG), Vanderford Glacier (VG), Sabrina Coast (SC), Knox Coast (KC), the Elcheikh saddle point (X), and Law Dome (LD). The Vanderford Trench (VT) is highlighted in panel <bold>(b)</bold>.</p></caption>
        <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://tc.copernicus.org/articles/17/4549/2023/tc-17-4549-2023-f01.png"/>

      </fig>

      <p id="d1e395">Currently, ice flow, ice discharge, and sediment discharge from the Totten Glacier (TG) is larger than at the Vanderford Glacier <xref ref-type="bibr" rid="bib1.bibx38 bib1.bibx45 bib1.bibx69" id="paren.10"/>. However, paleo-sediment records indicate that the Vanderford Glacier has likely been the dominant contributor to offshore sedimentation along the Sabrina and Knox coast sectors on geologic (million-year) timescales, rather than the Totten Glacier <xref ref-type="bibr" rid="bib1.bibx38" id="paren.11"/>. In particular, sedimentation rates at the Vanderford Glacier were twice those at the Totten Glacier during the mid–late Oligocene (27 to 24 <inline-formula><mml:math id="M11" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Ma</mml:mi></mml:mrow></mml:math></inline-formula>), when global temperatures were approximately 3 to 4 <inline-formula><mml:math id="M12" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> higher than the present day <xref ref-type="bibr" rid="bib1.bibx96" id="paren.12"/>. Furthermore, modelling indicates similar levels of erosion potential for the bed under both the Totten and Vanderford glaciers – and indeed, that these glaciers have the highest erosive potential in East Antarctica – such that similar magnitudes of sediment discharge from each of these two glaciers are possible under present-day ice sheet geometries <xref ref-type="bibr" rid="bib1.bibx2" id="paren.13"/>.</p>
      <p id="d1e432">Changes in basal water accumulation and routing have been hypothesised to play a role in flow diversion (piracy) – and even ice flow stagnation – between neighbouring ice streams of the Siple Coast in the past. For example, <xref ref-type="bibr" rid="bib1.bibx5" id="text.14"/> propose that a diversion of basal meltwater from Kamb Ice Stream into Whillans Ice Stream, associated with an inland extension of the ice streams due to increased basal melt over the Holocene, led to a reduction in basal lubrication and meltwater production beneath Kamb Ice Stream and its consequent stagnation. These changes may have also impacted the slowdown of the adjacent Whillans Ice Stream and may impact the likelihood of future stagnation here <xref ref-type="bibr" rid="bib1.bibx10 bib1.bibx40" id="paren.15"/>. More recent modelling of the Siple Coast system indicates that basal hydromechanical processes, including thermal switching between basal melting and freezing states, are a dominant control on the ice flow configuration and that further large-scale flow reconfiguration could be possible in the next tens to hundreds of years <xref ref-type="bibr" rid="bib1.bibx12" id="paren.16"/>, consistent with century-scale changes in the routing of ice streams in this region <xref ref-type="bibr" rid="bib1.bibx16 bib1.bibx39" id="paren.17"/>.</p>
      <p id="d1e447">Basal water accumulation and routing has also been suggested to play a role in the stagnation of Carlson Inlet – a proposed relict ice stream – and reconfiguration of ice flow from Carlson Inlet to Rutford Ice Stream over 240 years ago <xref ref-type="bibr" rid="bib1.bibx94" id="paren.18"/>. Changes in basal water routing are strongly linked to ice sheet geometry changes, and modelling by <xref ref-type="bibr" rid="bib1.bibx94" id="text.19"/> suggests that thickening of Rutford Ice Stream by only 4 % would be sufficient enough to reroute subglacial water to Carlson Inlet, potentially reactivating its flow. Similar mechanisms may have been involved in the reconfiguration of ice streams in the Weddell Sea sector in the past few thousand years <xref ref-type="bibr" rid="bib1.bibx81 bib1.bibx83" id="paren.20"/>. The precise drivers of ice flow and basal water routing changes are uncertain and likely to vary between ice stream pairs due to variations in the basal hydromechanics and topography and ice sheet geometry, geology, and climate. Importantly, ice flow reconfiguration could be an important process for multiple regions around the Antarctic margin, occurring even under minor changes in ice sheet geometry.</p>
      <p id="d1e459">Given the significant potential of the ASB to raise global sea levels, it is essential to understand controls on the present-day flow configuration between the Totten and Vanderford glaciers and its potential evolution as the climate warms. In this study, we first conduct a synthesis of the geology, topography, subglacial hydrology, and geomorphology of the ASB to ascertain how these factors may influence the past and present flow configuration of the Totten and Vanderford glaciers and of climate drivers in the ASB and how they might change in the future. We then use an ice sheet model to generate ice surface elevation change fields to investigate the sensitivity of ice flow and basal water piracy between the Totten and Vanderford glaciers.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e464"><bold>(a, b)</bold> Ice surface speeds (<inline-formula><mml:math id="M13" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</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>) from MEaSUREs2 and <bold>(c)</bold> driving stress <inline-formula><mml:math id="M14" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M15" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kPa</mml:mi></mml:mrow></mml:math></inline-formula>). Black contours are as for Fig. <xref ref-type="fig" rid="Ch1.F1"/>. Light-grey contours in panel <bold>(a)</bold> are velocity streamlines. Locations of the Totten Glacier (TG) and the Vanderford Glacier (VG) are indicated.</p></caption>
        <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://tc.copernicus.org/articles/17/4549/2023/tc-17-4549-2023-f02.png"/>

      </fig>

</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Controls on the ASB flow configuration</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Current flow and trends</title>
      <?pagebreak page4551?><p id="d1e531">The Totten Glacier is one of the fastest-flowing glaciers in East Antarctica <xref ref-type="bibr" rid="bib1.bibx67 bib1.bibx69" id="paren.21"/>, with ice surface speeds of over 750 <inline-formula><mml:math id="M16" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</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 the main tributary grounding line (southernmost region) – more than 100 <inline-formula><mml:math id="M17" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</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> greater than the corresponding ice surface speed at the Vanderford grounding line (Fig. <xref ref-type="fig" rid="Ch1.F2"/>a). Average ice discharge from 2009 to 2017 at the Totten Glacier (71.4 <inline-formula><mml:math id="M18" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2.6 <inline-formula><mml:math id="M19" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Gt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</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 almost twice that at the Vanderford Glacier (36.2 <inline-formula><mml:math id="M20" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.5 <inline-formula><mml:math id="M21" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Gt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</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>), naturally reflecting thicker ice, a steeper surface slope, and hence greater driving stresses (Fig. <xref ref-type="fig" rid="Ch1.F2"/>c) near the Totten Glacier grounding line. Both glaciers have accelerated in recent decades: the Vanderford Glacier surface speeds increased by 31 % over the period 2000 to 2013, with little subsequent change <xref ref-type="bibr" rid="bib1.bibx64" id="paren.22"/>; the Totten Glacier experienced insignificant increases in surface speed from 2007 to 2022 <xref ref-type="bibr" rid="bib1.bibx70" id="paren.23"/>, but with quasi-decadal cyclicity <xref ref-type="bibr" rid="bib1.bibx73" id="paren.24"/>. Furthermore, the Vanderford Glacier grounding line retreated by <inline-formula><mml:math id="M22" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 18.6 <inline-formula><mml:math id="M23" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> over the period 1996 to 2020 <xref ref-type="bibr" rid="bib1.bibx64" id="paren.25"/>, making it the fastest-retreating glacier in East Antarctica <xref ref-type="bibr" rid="bib1.bibx89" id="paren.26"/>. Changes at both glaciers are consistent with ocean-driven ice shelf thinning and calving (Sect. <xref ref-type="sec" rid="Ch1.S3.SS2"/>) and consequent reductions in buttressing <xref ref-type="bibr" rid="bib1.bibx25 bib1.bibx34" id="paren.27"/>.</p>
      <p id="d1e661">Discharge rates from each glacier are related to the broad-scale flow configuration of the ASB (Fig. <xref ref-type="fig" rid="Ch1.F2"/>). The Totten Glacier is currently fed by a catchment of 267 904 <inline-formula><mml:math id="M24" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>. The majority of discharge through Totten is channelled from the west through its main tributary, with a smaller portion channelled through the eastern flank of the glacier (Fig. <xref ref-type="fig" rid="Ch1.F2"/>b). Ice sheet models suggest ongoing grounding line retreat along the eastern flank and into the Sabrina Subglacial Basin (SSB) will occur in coming decades <xref ref-type="bibr" rid="bib1.bibx50 bib1.bibx62 bib1.bibx90" id="paren.28"/>. Despite the fact that the undulating bed topography in the SSB lies largely below sea level (Fig. <xref ref-type="fig" rid="Ch1.F1"/>), this portion of the Totten catchment is generally thinner, having a sea level potential that is much smaller than that of the ASB main basin <xref ref-type="bibr" rid="bib1.bibx56" id="paren.29"/>.</p>
      <p id="d1e688">The current Vincennes Bay catchment that feeds the Vanderford Glacier is approximately 71 329 <inline-formula><mml:math id="M25" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> – just over a quarter of the size of the adjacent Totten catchment. Similarly to Totten, discharge from the Vanderford Glacier is channelled through a western and an eastern trunk (Fig. <xref ref-type="fig" rid="Ch1.F2"/>b). The western trunk largely originates from, and is to the west of, Highland A (compare Figs. <xref ref-type="fig" rid="Ch1.F1"/> and <xref ref-type="fig" rid="Ch1.F2"/>). The eastern trunk originates in the same region as the main Totten tributary, east and south of Highland A; the Elcheikh saddle point (cross in Fig. <xref ref-type="fig" rid="Ch1.F1"/>a) marks the divergence of flow to either the main Totten tributary or the eastern trunk of the Vanderford Glacier.</p>
</sec>
<?pagebreak page4552?><sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Geology</title>
      <p id="d1e718">The geology of the ASB – in particular, the extents and types of sedimentary basins in the Totten and Vincennes Bay catchments – shows correspondence with patterns in ice sheet flow and subglacial hydrology (Sect. <xref ref-type="sec" rid="Ch1.S2.SS4"/>). The ASB region is dominated by sedimentary basins, interpreted to represent deposition during rifting events that occurred well before the EAIS developed <xref ref-type="bibr" rid="bib1.bibx4" id="paren.30"/>. Sequences of these sedimentary rocks are stacked vertically, ranging from an older Neoproterozoic to lower Paleozoic sequence <xref ref-type="bibr" rid="bib1.bibx48" id="paren.31"/> and a younger sedimentary sequence dating from the Permian–Triassic to the Cenozoic <xref ref-type="bibr" rid="bib1.bibx4" id="paren.32"/>. The topographic barriers of Highlands A, B, and C and the Knox Highlands typically comprise erosional remnants of the older sequence, while the topographic basins typically comprise rocks of the younger sequence (Fig. <xref ref-type="fig" rid="Ch1.F3"/>).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e736">Interpreted bedrock geology of the ASB region showing the distribution of sedimentary rocks <xref ref-type="bibr" rid="bib1.bibx4" id="paren.33"/>. Variations in basement geology are not shown here.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://tc.copernicus.org/articles/17/4549/2023/tc-17-4549-2023-f03.png"/>

        </fig>

      <p id="d1e748">The sedimentary cover in the main topographic lows reaches thicknesses of several kilometres, while the cover on the highlands is thinner. In regions of enhanced glacial erosion, the geology has been eroded to basement or possesses a mixture of basement with remnants of the younger sedimentary sequence <xref ref-type="bibr" rid="bib1.bibx3" id="paren.34"/>. Areas with sedimentary basins are in general floored by more easily erodible rocks than in basement-dominated regions, and upstream basins – particularly upstream of the main Totten tributary – are likely to provide an abundance of sediment to the downstream glacier bed, facilitating till continuity and basal sliding <xref ref-type="bibr" rid="bib1.bibx11 bib1.bibx44" id="paren.35"><named-content content-type="pre">see Sect. <xref ref-type="sec" rid="Ch1.S2.SS4"/>;</named-content></xref>.</p>
      <p id="d1e762">Sedimentary basins also permit the occurrence of a viable hydrogeology system, where the permeable bed allows fluid exchange between the subglacial hydrological system and groundwater storage <xref ref-type="bibr" rid="bib1.bibx82" id="paren.36"/>. Groundwater discharge into the glacier bed varies with ice sheet retreat rate and also with the thickness and permeability of the sedimentary basins, with major potential impacts on the basal sliding of contemporary glaciers in East and West Antarctica <xref ref-type="bibr" rid="bib1.bibx44" id="paren.37"/>. In the case of the Vincennes Bay catchment, the bed is dominated by the older sedimentary sequence and crystalline basement (Fig. <xref ref-type="fig" rid="Ch1.F3"/>), which are more likely to have low permeability; here, capacity for active hydrogeology may be restricted (although these regions of hard bed are characterised by channelised subglacial hydrology and faster flow; see Sect. <xref ref-type="sec" rid="Ch1.S2.SS1"/> and <xref ref-type="sec" rid="Ch1.S2.SS4"/>). In contrast, the ASB main basin – which both is thick and contains relatively young sedimentary rocks – has higher potential to support active hydrogeology, with potential impacts on basal sliding processes and hence ice streaming <xref ref-type="bibr" rid="bib1.bibx82 bib1.bibx44" id="paren.38"/>. Although estimates for the contributions of groundwater to the subglacial hydrology system exist broadly across Antarctica <xref ref-type="bibr" rid="bib1.bibx44" id="paren.39"/>, they are currently not available for the ASB specifically.</p>
</sec>
<?pagebreak page4553?><sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Bed topography</title>
      <p id="d1e792">Approximately 75 % of the bed topography in the Totten and Vincennes Bay catchments is below sea level, and over 10 % is more than 1 <inline-formula><mml:math id="M26" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> below sea level, particularly in the ASB main basin (Fig. <xref ref-type="fig" rid="Ch1.F1"/>). Regions of topographic highs play a role in determining the overall ASB catchment boundary as well as the orientation of flow within the Totten and Vincennes Bay catchments. This is notably the case with the topographic barriers of Highlands A and B, the western edge of the Vanderford Glacier, Law Dome, and the coastal ridge adjacent to the Totten Glacier and the Moscow University ice shelf (Figs. <xref ref-type="fig" rid="Ch1.F1"/>, <xref ref-type="fig" rid="Ch1.F3"/>). Ice flowing into the main Totten tributary has a similar flow trajectory to ice that flows into the eastern trunk of the Vanderford; ice from both glaciers originates in a region of generally high topography north of Lake Vostok (Vostok Highland; Fig. <xref ref-type="fig" rid="Ch1.F1"/>a). Downstream, both the Totten and Vanderford glaciers flow into the Vanderford Trench – a deeply incised subglacial channel that borders Law Dome and records the lowest known topography of the ASB (<inline-formula><mml:math id="M27" display="inline"><mml:mo lspace="0mm">-</mml:mo></mml:math></inline-formula>2782 <inline-formula><mml:math id="M28" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> below sea level; Fig. <xref ref-type="fig" rid="Ch1.F1"/>b). While topography provides a clear control on the overall ASB catchment boundary, there are no distinguishing features of the bed topography that clearly control the location of the drainage divide between the Totten and Vincennes Bay catchments. However, possible local controls in the Vanderford Trench are difficult to observe where very steep topography and thick ice hinder imaging of the ice base by ice-penetrating radar.</p>
      <p id="d1e829">In terms of the susceptibility of each glacier to ongoing retreat, bathymetric pinning points on the Totten ice shelf, in the <inline-formula><mml:math id="M29" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 20 <inline-formula><mml:math id="M30" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> downstream of the main Totten tributary grounding line, provide significant buttressing of the upstream glacier <xref ref-type="bibr" rid="bib1.bibx50 bib1.bibx73" id="paren.40"/>. A prograde bed slope in the <inline-formula><mml:math id="M31" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 20 <inline-formula><mml:math id="M32" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> upstream of the present-day grounding line decreases the likelihood of substantial retreat occurring under climate change projections to 2100 <xref ref-type="bibr" rid="bib1.bibx62 bib1.bibx90" id="paren.41"/>. For the Vanderford Glacier, there is a high degree of uncertainty in the underlying bed topography within the Vanderford Trench; notably, uncertainties of 600 <inline-formula><mml:math id="M33" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> and greater exist within the 10 <inline-formula><mml:math id="M34" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> upstream of the present-day Vanderford grounding line <xref ref-type="bibr" rid="bib1.bibx56" id="paren.42"><named-content content-type="pre">see discussion in Sect. <xref ref-type="sec" rid="Ch1.S5"/> and Fig. <xref ref-type="fig" rid="Ch1.F1"/>c;</named-content></xref>. Given the controlling influence of the bed elevation and slope on grounding line retreat, this has significant implications for the observed and simulated timing and rate of retreat. These lines of evidence, coupled with the current rates of retreat from each glacier, suggest that the Vanderford Glacier could retreat more rapidly, and further into the Vanderford Trench, than the Totten Glacier over the coming decades.</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="d1e896"><bold>(a)</bold> Water depth (<inline-formula><mml:math id="M35" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>) in the distributed and channelised subglacial hydrology system generated using GlaDS <xref ref-type="bibr" rid="bib1.bibx21" id="paren.43"/> and <bold>(b)</bold> basal shear stress (<inline-formula><mml:math id="M36" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kPa</mml:mi></mml:mrow></mml:math></inline-formula>) from the ice sheet model simulation, as described in Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>) in Sect. <xref ref-type="sec" rid="Ch1.S4.SS1"/>. Black contours are the same as in Fig. <xref ref-type="fig" rid="Ch1.F1"/>.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://tc.copernicus.org/articles/17/4549/2023/tc-17-4549-2023-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Subglacial hydrology and geomorphology</title>
      <p id="d1e944">Observations and modelling confirm the presence of a widespread, persistent subglacial hydrological network in the ASB <xref ref-type="bibr" rid="bib1.bibx21" id="paren.44"/>, consisting of a distributed “sheet-like” system in the ASB main basin and a channelised system in the few hundred kilometres upstream of the Totten and Vanderford Glacier grounding lines (Fig. <xref ref-type="fig" rid="Ch1.F4"/>a). The proximal ice–bed interface of the distributed system is well lubricated and supports little to no basal shear stress (<inline-formula><mml:math id="M37" display="inline"><mml:mo lspace="0mm">&lt;</mml:mo></mml:math></inline-formula> 20 <inline-formula><mml:math id="M38" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kPa</mml:mi></mml:mrow></mml:math></inline-formula>; Fig. <xref ref-type="fig" rid="Ch1.F4"/>b). Basal specularity content derived from radar is reduced within the channelised system <xref ref-type="bibr" rid="bib1.bibx21" id="paren.45"/>, consistent with a rougher ice–bed interface where channels are present <xref ref-type="bibr" rid="bib1.bibx75 bib1.bibx101" id="paren.46"/>, and a strong bed here supports most of the basal shear stresses for each glacier (Fig. <xref ref-type="fig" rid="Ch1.F4"/>b). The calculation of the basal shear stresses in Fig. <xref ref-type="fig" rid="Ch1.F4"/>b is described in Sect. <xref ref-type="sec" rid="Ch1.S4.SS1"/>, and the striped pattern in the approach to the grounding line is consistent with previous studies <xref ref-type="bibr" rid="bib1.bibx77" id="paren.47"><named-content content-type="pre">e.g.</named-content></xref>.</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F5" specific-use="star"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e989">Geomorphology of the continental shelf in front of the Vanderford Glacier. <bold>(a)</bold> High-resolution multibeam bathymetry <xref ref-type="bibr" rid="bib1.bibx17" id="paren.48"/> highlighting a submarine canyon overlaid on previous bathymetric estimates <xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx56" id="paren.49"/> with contours at 250 <inline-formula><mml:math id="M39" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> intervals. <bold>(b)</bold> Bedrock channels (black lines) and black square show the location of <bold>(c)</bold>. <bold>(c)</bold> Bedrock channels of the inner continental shelf, interpreted as relict subglacial meltwater channels, and flat-bottom parts of these channels (slope <inline-formula><mml:math id="M40" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> 2<inline-formula><mml:math id="M41" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>), interpreted as relict lakes. <bold>(d)</bold> Geometry of the meltwater landforms highlighted in cross-section profiles. Channels follow lines of geological weakness in shallow and deep areas (from 450 to 2280 <inline-formula><mml:math id="M42" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> water depth). A large bedrock high has major channels (150 to 280 <inline-formula><mml:math id="M43" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> deep, 1 <inline-formula><mml:math id="M44" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> wide and 9 to 16 <inline-formula><mml:math id="M45" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> long) connected by shorter, less-incised channels. Within the two troughs, bedrock channels have an anastomosing pattern, with meandering central channels linked in multiple places to neighbouring channels. Flat surfaces are found in deeper parts of the main channels, reflecting localised sedimentation.</p></caption>
          <?xmltex \igopts{width=284.527559pt}?><graphic xlink:href="https://tc.copernicus.org/articles/17/4549/2023/tc-17-4549-2023-f05.jpg"/>

        </fig>

      <p id="d1e1077">The majority of basal water in the ASB is routed towards the Totten Glacier <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx99 bib1.bibx101" id="paren.50"/>; output from the Glacier Drainage System (GlaDS) subglacial hydrology model estimates approximately 42 <inline-formula><mml:math id="M46" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></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> discharge from the Totten catchment into the ocean, compared with only 3 <inline-formula><mml:math id="M47" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></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> from the Vanderford Glacier <xref ref-type="bibr" rid="bib1.bibx21" id="paren.51"/>. This is partly due to fewer channels developing in the approach to the Vanderford grounding line in the steady-state GlaDS simulations compared to the Totten grounding line. Nevertheless, the subglacial<?pagebreak page4554?> hydrological networks of the Totten and Vincennes Bay catchments are strongly connected. For example, ICESat surveys identified at least two “active” lakes located within the 200 <inline-formula><mml:math id="M48" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> upstream of the Totten grounding line, with lake drainage and filling evidenced in surface elevation changes between 2003 and 2006 <xref ref-type="bibr" rid="bib1.bibx87" id="paren.52"/>. Hydraulic potential analysis of one of these lakes shows that basal water drainage may be routed from the Totten to the Vanderford Glacier with only small changes in the ice surface elevation <xref ref-type="bibr" rid="bib1.bibx101" id="paren.53"/>.</p>
      <p id="d1e1142">The geomorphology of the continental shelf proximal to the Vanderford Glacier – revealed in high-resolution multibeam bathymetry <xref ref-type="bibr" rid="bib1.bibx17" id="paren.54"/> – provides evidence for an active subglacial hydrology network in the Vincennes Bay region in the past. Of particular note is the presence of deeply incised bedrock channels, which are the most abundant landform on the inner continental shelf and which span depths of 450 to 2280 <inline-formula><mml:math id="M49" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> below sea level. Similar bedrock channels and flat-bottomed basins are also observed in front of the Thwaites and Pine Island glaciers in West Antarctica <xref ref-type="bibr" rid="bib1.bibx46 bib1.bibx59" id="paren.55"/>, where hydrological modelling suggests that these are relict subglacial meltwater channels and lakes <xref ref-type="bibr" rid="bib1.bibx9 bib1.bibx41" id="paren.56"/>. The presence of these landforms on the inner shelf of Vincennes Bay supports the existence of an active, dominant subglacial hydrological system beneath a more extensive Vanderford Glacier, which formed over multiple glacial periods. A previous study <xref ref-type="bibr" rid="bib1.bibx41" id="paren.57"/> has also documented a series of relict subglacial lakes akin to those mapped in front of Vanderford (indicated in grey in Fig. <xref ref-type="fig" rid="Ch1.F5"/>). The network of subglacial meltwater channels and lakes would have formed during the last glacial period, or possibly over multiple glacial periods <xref ref-type="bibr" rid="bib1.bibx41 bib1.bibx9" id="paren.58"/>. Based on lake geometry and contemporary subglacial water transfer, these lakes likely drained episodically through the subglacial meltwater channels on decadal timescales <xref ref-type="bibr" rid="bib1.bibx41" id="paren.59"/>, facilitating ice basal sliding over the rugged topography of the inner continental shelf.</p>
      <p id="d1e1174">In summary, the large-scale geometry of the ASB controls the current divergence of flow between the Totten and Vanderford glaciers. However, it is likely that the characteristics of, and variability in, the subglacial environment, particularly those elements that influence basal motion (e.g. the bed substrate and deformability, subglacial hydrological network, groundwater system) in the ASB, play a key role in the flow configuration. As basal water pressure and water accumulation vary into the future – e.g. associated with drawdown of the Vanderford Glacier due to grounding line retreat and subsequent thinning – basal water and ice flow piracy towards the Vanderford may also occur.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Climate drivers of the ASB</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Atmospheric drivers</title>
      <?pagebreak page4556?><p id="d1e1193">Surface mass balance (SMB) is the primary atmospheric driver of variability between the Totten and Vanderford glaciers. The atmospheric circulation over Law Dome is predominately polar easterlies <xref ref-type="bibr" rid="bib1.bibx13" id="paren.60"/>, and the orography of the Dome causes relatively large snow accumulation, with a strong east–west gradient <xref ref-type="bibr" rid="bib1.bibx53 bib1.bibx92" id="paren.61"/>. The temporal distribution of the snow accumulation is related to the passage of synoptic-scale features and is therefore episodic, typical of coastal Antarctica <xref ref-type="bibr" rid="bib1.bibx13" id="paren.62"/>.</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="d1e1207">Surface mass balance over Law Dome (LD) and surrounding area. <bold>(a)</bold> RACMO2.3p2 reanalysis <xref ref-type="bibr" rid="bib1.bibx93" id="paren.63"/> averaged over the period 1979 to 2021, showing a strong east–west snow accumulation gradient over Law Dome. Totten (larger) and Vanderford (smaller) bounding boxes for the SMB analysis in panel <bold>(b)</bold> are shown (blue). <bold>(b)</bold> Vanderford annual snow accumulation as a function of Totten annual snowfall. Least-squares linear regression line shows slopes less than unity, indicating that for increasing local snow accumulation the mismatch between the Totten and Vanderford SMB is expected to increase.</p></caption>
          <?xmltex \igopts{width=455.244094pt}?><graphic xlink:href="https://tc.copernicus.org/articles/17/4549/2023/tc-17-4549-2023-f06.png"/>

        </fig>

      <p id="d1e1228">Antarctic snow accumulation is expected to increase as water vapour increases with a warming atmosphere <xref ref-type="bibr" rid="bib1.bibx42" id="paren.64"/>. While there is no clear trend in Law Dome accumulation rates over the past 2000 years <xref ref-type="bibr" rid="bib1.bibx72" id="paren.65"/>, a trend of increasing total Antarctic annual snow accumulation has been observed since 1800 <xref ref-type="bibr" rid="bib1.bibx91" id="paren.66"/>. While high-spatial-resolution snow accumulation observations are broadly lacking, the RACMO2.3p2 reanalysis model <xref ref-type="bibr" rid="bib1.bibx93" id="paren.67"/> captures the strong east–west gradient in snow accumulation over Law Dome on annual timescales. Results averaged over the Totten and Vanderford glaciers (Fig. <xref ref-type="fig" rid="Ch1.F6"/>) suggest that without major changes in atmospheric circulation patterns, a local increase in snow accumulation over Law Dome will amplify the east–west gradient.</p>
      <p id="d1e1246">In addition to the direct snow accumulation implications, there is a secondary effect on glacier flow related to the enhanced vertical advection of cool surface temperature into the interior at increased snow accumulation rates. For pseudo-steady-state surface elevations and approximately equal surface temperatures, the higher snow accumulation over the Totten will result in higher vertical velocities compared to the Vanderford. Without compensating differences in geothermal heat flow, deformational heating, or heat transport from basal hydrology processes, this increased vertical advection of cold will result in the bulk ice properties of the Totten being colder and stiffer than those of the Vanderford.</p>
      <p id="d1e1249">Without considering the effects of ocean-driven ice shelf melting (and associated surface lowering), the projected SMB changes in the ASB under a warming climate could lead to enhanced surface elevation and thickness increases at the Totten Glacier compared with the Vanderford Glacier. These effects could be further enhanced if they were to occur in concert with a dynamics-driven deceleration of the Totten Glacier due to cooling and stiffening ice over timescales of centuries to millennia.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Oceanic drivers</title>
      <p id="d1e1260">Similarly to glaciers in the Amundsen Sea sector of West Antarctica, ice shelf thinning, grounding line retreat, and increased discharge at the Totten Glacier are linked to the incursion of warm modified circumpolar deep water (mCDW) through deeply incised bathymetric channels <xref ref-type="bibr" rid="bib1.bibx73 bib1.bibx84 bib1.bibx85" id="paren.68"/>, evidenced from both airborne and shipborne measurements <xref ref-type="bibr" rid="bib1.bibx30 bib1.bibx71" id="paren.69"/>. Ice shelf melt rates at the Totten Glacier have been estimated to exceed 50 <inline-formula><mml:math id="M50" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</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> near the grounding line <xref ref-type="bibr" rid="bib1.bibx1" id="paren.70"/> and are among the largest observed melt rates in East Antarctica. Modelling indicates increased melt in recent decades, attributed primarily to freshening shelf water <xref ref-type="bibr" rid="bib1.bibx57" id="paren.71"/>. This is despite a consistent trend of poleward migration and warming of mCDW off the shelf <xref ref-type="bibr" rid="bib1.bibx37 bib1.bibx100" id="paren.72"/>, which is projected to increase as the climate warms. However, observational evidence and modelling outputs are consistent with significant variability in melt rates as a result of variable mCDW supply in this region <xref ref-type="bibr" rid="bib1.bibx35 bib1.bibx36 bib1.bibx57 bib1.bibx61 bib1.bibx85" id="paren.73"/>.</p>
      <p id="d1e1299">Links between ocean forcing and recent trends at the Vanderford Glacier are less well established than at the Totten Glacier. Data from seal dives suggest that the mCDW in Vincennes Bay is up to 0.5 <inline-formula><mml:math id="M51" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> and the warmest sampled to date in East Antarctica; however, temperatures at the Vanderford Glacier ice shelf of <inline-formula><mml:math id="M52" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.5 <inline-formula><mml:math id="M53" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> are comparable to those at the Totten Glacier ice front of <inline-formula><mml:math id="M54" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.4 <inline-formula><mml:math id="M55" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>
<xref ref-type="bibr" rid="bib1.bibx66" id="paren.74"/>. The presence of a deep bathymetric trough at the Vanderford ice front <xref ref-type="bibr" rid="bib1.bibx17" id="paren.75"/> provides a clear pathway for mCDW incursion to the ice shelf cavity, although the bathymetric connection from this trough to the continental shelf slope has not been mapped. It is hypothesised that the ocean is driving the observed retreat and thinning of the Vanderford Glacier 2003 to 2020 <xref ref-type="bibr" rid="bib1.bibx64" id="paren.76"/>, but observations and modelling are needed to establish causal relationships.</p>
      <p id="d1e1362">Modelling has been used to evaluate the potential for enhanced melting on the Sabrina and Knox coasts over the coming centuries <xref ref-type="bibr" rid="bib1.bibx90" id="paren.77"/>. Upwelling of mCDW is positively correlated with the Southern Annular Mode (SAM), and positive SAM trends are projected to continue through the 21st century, which could lead to enhanced mCDW-driven ice shelf melt <xref ref-type="bibr" rid="bib1.bibx37 bib1.bibx65" id="paren.78"/>. Surface winds near the East Antarctic coastal margin are projected to intensify under climate warming <xref ref-type="bibr" rid="bib1.bibx26 bib1.bibx88 bib1.bibx95" id="paren.79"/>, which could also increase wind-driven upwelling of mCDW to the continental shelf, and the supply of warm water to ice shelf cavities <xref ref-type="bibr" rid="bib1.bibx32" id="paren.80"/>. <xref ref-type="bibr" rid="bib1.bibx58" id="text.81"/> suggested that warming surface waters linked to a decline in summer sea ice cover could dominate freshening associated with ice sheet mass loss trends in this sector. A key caveat on modelling results is the generally low spatial resolution (hence coarsely resolved bathymetry) used and the fact that previous bathymetry products do not incorporate the deep bathymetric trough in Vincennes Bay <xref ref-type="bibr" rid="bib1.bibx17" id="paren.82"/> important for warm water supply to the ice shelf cavity. Nevertheless, evidence consistently points to the possibility of increasing ocean-driven ice shelf melt in this sector.</p>
      <p id="d1e1384">The cumulation of these factors – the warmer mCDW in Vincennes Bay, the pathway for its incursion into the Vanderford ice shelf cavity, and the greater potential for<?pagebreak page4557?> grounding line retreat of the Vanderford Glacier into the Vanderford Trench compared to the buttressed Totten Glacier – suggests a potential heightened vulnerability of the Vanderford Glacier to continued thinning in the coming decades to centuries.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Sensitivity of driving stress and hydraulic potential to changes in surface elevation</title>
      <p id="d1e1397">Here, we use the Ice-sheet and Sea-level System Model <xref ref-type="bibr" rid="bib1.bibx43" id="paren.83"><named-content content-type="pre">ISSM;</named-content></xref> to quantify the impact on ice and basal water routing due to ice surface elevation changes at the Totten and Vanderford glaciers that are consistent with present-day flow dynamics and address the potential climate scenarios discussed in Sect. <xref ref-type="sec" rid="Ch1.S3"/>. That is, we generate three ice surface elevation perturbations, based on (1) an increase in SMB in the Totten catchment (defined as expSMB), (2) a decrease in basal friction in the Vincennes Bay catchment (defined as expFriction), and (3) a combination of (1) and (2) (defined as expCombined). The model setup and experiments are discussed in more detail below.</p>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Model setup and experiments</title>
      <p id="d1e1414">The model domain covers the ASB (Fig. <xref ref-type="fig" rid="Ch1.F1"/>a) and comprises 58 938 anisotropic mesh elements. The initial bed topography, thickness, surface elevation, and ice masks are from BedMachine Antarctica v3 <xref ref-type="bibr" rid="bib1.bibx56 bib1.bibx54" id="paren.84"/>, and surface velocities are from MEaSUREs version 2 <xref ref-type="bibr" rid="bib1.bibx67 bib1.bibx68" id="paren.85"><named-content content-type="pre">MEaSUREs2;</named-content></xref>. Using the shallow shelf approximation <xref ref-type="bibr" rid="bib1.bibx47" id="paren.86"><named-content content-type="pre">SSA;</named-content></xref> and inverse methods, we calculate the basal friction coefficient across the grounded ASB using the Budd friction law <xref ref-type="bibr" rid="bib1.bibx14" id="paren.87"/>, given by
            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M56" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mi>C</mml:mi><mml:mi mathvariant="normal">f</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mi>N</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M58" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Pa</mml:mi></mml:mrow></mml:math></inline-formula>) is the basal shear stress, <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M60" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) is the friction coefficient, and <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi>u</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M62" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</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 the basal sliding velocity. The effective pressure <inline-formula><mml:math id="M63" display="inline"><mml:mi>N</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M64" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Pa</mml:mi></mml:mrow></mml:math></inline-formula>) is given by <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ice</mml:mtext></mml:msub><mml:mi>g</mml:mi><mml:mi>h</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>water</mml:mtext></mml:msub><mml:mi>g</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ice</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the ice density (<inline-formula><mml:math id="M67" display="inline"><mml:mrow class="unit"><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>), <inline-formula><mml:math id="M68" display="inline"><mml:mi>g</mml:mi></mml:math></inline-formula> is the gravitational acceleration (<inline-formula><mml:math id="M69" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</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">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), <inline-formula><mml:math id="M70" display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula> is the ice thickness (<inline-formula><mml:math id="M71" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>), <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>water</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the density of freshwater (<inline-formula><mml:math id="M73" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><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>), and <inline-formula><mml:math id="M74" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> is the bed elevation (<inline-formula><mml:math id="M75" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>). We assume a Glen-type flow relation <xref ref-type="bibr" rid="bib1.bibx28" id="paren.88"/>, where the viscosity <inline-formula><mml:math id="M76" display="inline"><mml:mi mathvariant="italic">μ</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M77" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Pa</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:math></inline-formula>) is given by
            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M78" display="block"><mml:mrow><mml:mi mathvariant="italic">μ</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>B</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:msubsup><mml:mover accent="true"><mml:mi mathvariant="italic">ε</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mi mathvariant="normal">e</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi>n</mml:mi><mml:mo>/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          and inverse methods over the entire domain to calculate the ice rigidity <inline-formula><mml:math id="M79" display="inline"><mml:mi>B</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M80" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Pa</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:math></inline-formula><inline-formula><mml:math id="M81" display="inline"><mml:msup><mml:mi/><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math></inline-formula>), for effective strain rate <inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi mathvariant="italic">ε</mml:mi><mml:mo mathvariant="normal">˙</mml:mo></mml:mover><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M83" display="inline"><mml:mrow class="unit"><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>) and <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>. The inverse method relies on minimising a cost function that includes terms for the linear and logarithmic misfit between the simulated and observed surface velocities, as well as regularisation parameters that smooth strong gradients in the rigidity and basal friction coefficient <xref ref-type="bibr" rid="bib1.bibx55" id="paren.89"/>. MEaSUREs2 velocities are used at the inflow boundaries, and a free-flux boundary condition is applied at the calving front.</p>
      <?pagebreak page4558?><p id="d1e1845">Holding the grounding line positions fixed, we run a 200-year spin-up simulation with monthly time stepping, at the end of which the ice surface speed and geometry are in a pseudo steady state. For this simulation we use annual average surface mass balance from RACMO2.3p2 and basal melt rates are calculated using a parameterisation that linearly decreases the basal melt from 30 <inline-formula><mml:math id="M85" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</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 ice shelf drafts of 400 <inline-formula><mml:math id="M86" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> below sea level or deeper to 5 <inline-formula><mml:math id="M87" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</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 ice shelf drafts of 200 <inline-formula><mml:math id="M88" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> below sea level or shallower <xref ref-type="bibr" rid="bib1.bibx78" id="paren.90"/>. The final ice velocities, surface elevation, and thicknesses from this simulation are used as the initial conditions for our perturbation experiments described below.</p>
      <p id="d1e1901">To generate ice surface elevation increases at the Totten Glacier (expSMB), we increase the annual average SMB as follows:
            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M89" display="block"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SMB</mml:mi><mml:mi mathvariant="normal">new</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SMB</mml:mi><mml:mi mathvariant="normal">RACMO</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SMB</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M90" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SMB</mml:mi><mml:mi mathvariant="normal">new</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the perturbation field, <inline-formula><mml:math id="M91" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SMB</mml:mi><mml:mi mathvariant="normal">RACMO</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the observed annual average SMB from RACMO2.3p2 over the period 1979 to 2021 <xref ref-type="bibr" rid="bib1.bibx93" id="paren.91"/>, and <inline-formula><mml:math id="M92" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SMB</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the observed annual average SMB within the Totten catchment with zero SMB elsewhere in the ASB. Values for the constant <inline-formula><mml:math id="M93" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> increase from 0.06 to 0.42, in increments of 0.06, and are chosen to represent the percentage increases in SMB that correspond to 1 <inline-formula><mml:math id="M94" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> increases in air surface temperature from 1 to 7 <inline-formula><mml:math id="M95" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx24" id="paren.92"/>. Although we note that other surface processes influence the SMB, we assume that increases in accumulation will dominate at basin scale.</p>
      <p id="d1e2007">To generate ice surface elevation decreases at the Vanderford Glacier (expFriction), we decrease the basal friction coefficient within the Vincennes Bay catchment as follows:
            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M96" display="block"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mtext>new</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi mathvariant="italic">σ</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub><mml:msup><mml:mi>M</mml:mi><mml:mi mathvariant="italic">α</mml:mi></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mtext>new</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the perturbation field, <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the basal friction coefficient calculated using inversion (Fig. A1a), and <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">v</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the basal friction coefficient within the Vincennes Bay catchment which is zero elsewhere in the ASB (Fig. A1b). Values for the constant <inline-formula><mml:math id="M100" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula> increase from 0.1 to 0.7 in increments of 0.1. These values are chosen to yield the same area-weighted percentage changes between the simulated surface elevation compared with the control, when averaged over the Vincennes Bay catchment, as the corresponding surface elevation change generated from expSMB. <inline-formula><mml:math id="M101" display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula> is a mask that is generated by calculating the distance from the grounding line within the Vincennes Bay catchment and then normalising the field to vary linearly from 1 at the grounding line to 0 at the furthest point (on the southern inflow catchment boundary). We choose <inline-formula><mml:math id="M102" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> as the exponent to <inline-formula><mml:math id="M103" display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula>, which concentrates the change in the basal friction coefficient within the <inline-formula><mml:math id="M104" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 100 <inline-formula><mml:math id="M105" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> upstream of the Vanderford Glacier grounding line (see Appendix <xref ref-type="sec" rid="App1.Ch1.S1"/>). We reduce the basal friction coefficient in the Vincennes Bay catchment rather than modify the basal melt rate because, although not directly observable, we expect a reduction in basal traction as a consequence of increased ocean melting, retreat, and acceleration. In this way, we avoid increasing the basal melt rates at the Vanderford Glacier relative to the Totten Glacier (given the lack of evidence for such a relative increase in ocean forcing), while still capturing the effects of continued retreat at the Vanderford Glacier, which is more likely than at the Totten Glacier over the coming decades to century (Sect. <xref ref-type="sec" rid="Ch1.S3"/>). We also emphasise that the aim here is not to model the expected evolution of this system but to generate surface change fields that are dynamically consistent with increasing SMB at the Totten Glacier and continued retreat at the Vanderford Glacier, to ascertain the impact of perturbations in the surface elevation on ice and basal water flow piracy.</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="d1e2134">Surface elevation changes (<inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dS</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) in the perturbation experiments compared with the control (<inline-formula><mml:math id="M107" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>) for the 1 <inline-formula><mml:math id="M108" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> increase. <bold>(a)</bold> <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dS</mml:mi></mml:mrow><mml:mtext>SMB</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M110" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), <bold>(b)</bold> <inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dS</mml:mi></mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M112" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expFriction</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), and <bold>(c)</bold> <inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dS</mml:mi></mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M114" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>).</p></caption>
          <?xmltex \igopts{width=426.791339pt}?><graphic xlink:href="https://tc.copernicus.org/articles/17/4549/2023/tc-17-4549-2023-f07.png"/>

        </fig>

      <p id="d1e2255">In addition to the expSMB and expFriction experiments, a third experiment (expCombined) combines the SMB and basal friction coefficient fields in Eqs. (<xref ref-type="disp-formula" rid="Ch1.E3"/>) and (<xref ref-type="disp-formula" rid="Ch1.E4"/>). Using the output geometries (thickness and surface elevation) and velocities from the pseudo-steady-state simulation, we run each of the perturbation experiments expSMB, expFriction, and expCombined for 1000 years with monthly time stepping. A 1000-year control run that uses the original <inline-formula><mml:math id="M115" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">SMB</mml:mi><mml:mi mathvariant="normal">RACMO</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fields is also simulated. Figure <xref ref-type="fig" rid="Ch1.F7"/> shows the differences between the perturbed surface elevations and the control (<inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dS</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, where the subscript <inline-formula><mml:math id="M118" display="inline"><mml:mi>i</mml:mi></mml:math></inline-formula> refers to SMB, <inline-formula><mml:math id="M119" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula>, or <inline-formula><mml:math id="M120" display="inline"><mml:mi>C</mml:mi></mml:math></inline-formula>) for an air surface temperature increase of 1 <inline-formula><mml:math id="M121" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> (i.e. for <inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.06</mml:mn></mml:mrow></mml:math></inline-formula> in Eq. <xref ref-type="disp-formula" rid="Ch1.E3"/> and <inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> in Eq. <xref ref-type="disp-formula" rid="Ch1.E4"/>), hereafter denoted <inline-formula><mml:math id="M124" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M125" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expFriction</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M126" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Driving stresses and ice flow routing</title>
      <p id="d1e2402">We investigate the impact of the changed surface elevations on the driving stresses and ice flow routing within the ASB. The driving stress <inline-formula><mml:math id="M127" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M128" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Pa</mml:mi></mml:mrow></mml:math></inline-formula>) is given by
            <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M129" display="block"><mml:mrow><mml:mi>p</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ice</mml:mtext></mml:msub><mml:mi>g</mml:mi><mml:mi>h</mml:mi><mml:mi mathvariant="normal">∇</mml:mi><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:mi mathvariant="normal">∇</mml:mi><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the gradient in the perturbed surface elevation and the sum of the BedMachine surface elevation and each <inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dS</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> field.</p>
      <p id="d1e2473">For <inline-formula><mml:math id="M132" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, the driving stress decreases through much of the interior of the ASB but increases within <inline-formula><mml:math id="M133" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 10 <inline-formula><mml:math id="M134" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> of the Totten Glacier grounding line. This is consistent with decreasing velocities upstream of the Totten Glacier grounding line but increasing velocities on the Totten Glacier ice shelf and the Vanderford Glacier ice shelf. The divide between the Totten and Vincennes Bay catchments migrates eastwards for <inline-formula><mml:math id="M135" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> compared with the catchments defined using the MEaSUREs2 velocities, increasing the Vincennes Bay catchment area by <inline-formula><mml:math id="M136" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1208 <inline-formula><mml:math id="M137" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (1.7 %; Table <xref ref-type="table" rid="Ch1.T1"/>). This leads to a rerouting of ice flow from the Totten Glacier towards the Vanderford Glacier, with an increase in discharge from the Vanderford Glacier of <inline-formula><mml:math id="M138" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 0.02 <inline-formula><mml:math id="M139" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Gt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</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> (i.e. 1.6 % increase; Table <xref ref-type="table" rid="Ch1.T2"/>). Both trends increase with increasing air surface temperature change; for <inline-formula><mml:math id="M140" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, the Vincennes Bay catchment area increases by 17 % and the ice discharge increases by 11 %.</p>

<?xmltex \floatpos{p}?><table-wrap id="Ch1.T1"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e2574">Absolute (abs) and percentage changes in the Vincennes Bay catchment areas at the end of the 1000-year perturbation experiments. The catchment area defined by the MEaSUREs2 velocities is 71 329 <inline-formula><mml:math id="M141" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (compared with 68 902 <inline-formula><mml:math id="M142" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> defined by the Ice Sheet Mass Balance Intercomparison Exercise (IMBIE; <xref ref-type="bibr" rid="bib1.bibx80" id="altparen.93"/>).</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.98}[.98]?><oasis:tgroup cols="7">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right" colsep="1"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right" colsep="1"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry rowsep="1" namest="col2" nameend="col3" align="center" colsep="1">expSMB </oasis:entry>
         <oasis:entry rowsep="1" namest="col4" nameend="col5" align="center" colsep="1">expFriction </oasis:entry>
         <oasis:entry rowsep="1" namest="col6" nameend="col7" align="center">expCombined </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">abs (<inline-formula><mml:math id="M143" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col3">%</oasis:entry>
         <oasis:entry colname="col4">abs (<inline-formula><mml:math id="M144" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5">%</oasis:entry>
         <oasis:entry colname="col6">abs (<inline-formula><mml:math id="M145" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col7">%</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">1 <inline-formula><mml:math id="M146" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">1208</oasis:entry>
         <oasis:entry colname="col3">1.7</oasis:entry>
         <oasis:entry colname="col4">958</oasis:entry>
         <oasis:entry colname="col5">1.3</oasis:entry>
         <oasis:entry colname="col6">2122</oasis:entry>
         <oasis:entry colname="col7">3.0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2 <inline-formula><mml:math id="M147" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">2737</oasis:entry>
         <oasis:entry colname="col3">3.8</oasis:entry>
         <oasis:entry colname="col4">1226</oasis:entry>
         <oasis:entry colname="col5">1.7</oasis:entry>
         <oasis:entry colname="col6">2961</oasis:entry>
         <oasis:entry colname="col7">4.2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">3 <inline-formula><mml:math id="M148" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">4692</oasis:entry>
         <oasis:entry colname="col3">6.6</oasis:entry>
         <oasis:entry colname="col4">1181</oasis:entry>
         <oasis:entry colname="col5">1.7</oasis:entry>
         <oasis:entry colname="col6">6493</oasis:entry>
         <oasis:entry colname="col7">9.1</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4 <inline-formula><mml:math id="M149" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">6695</oasis:entry>
         <oasis:entry colname="col3">9.4</oasis:entry>
         <oasis:entry colname="col4">1152</oasis:entry>
         <oasis:entry colname="col5">1.6</oasis:entry>
         <oasis:entry colname="col6">8633</oasis:entry>
         <oasis:entry colname="col7">12</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">5 <inline-formula><mml:math id="M150" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">8073</oasis:entry>
         <oasis:entry colname="col3">11</oasis:entry>
         <oasis:entry colname="col4">1865</oasis:entry>
         <oasis:entry colname="col5">2.6</oasis:entry>
         <oasis:entry colname="col6">12 324</oasis:entry>
         <oasis:entry colname="col7">17</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">6 <inline-formula><mml:math id="M151" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">11 657</oasis:entry>
         <oasis:entry colname="col3">16</oasis:entry>
         <oasis:entry colname="col4">2259</oasis:entry>
         <oasis:entry colname="col5">3.2</oasis:entry>
         <oasis:entry colname="col6">14 779</oasis:entry>
         <oasis:entry colname="col7">21</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">7 <inline-formula><mml:math id="M152" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">12 104</oasis:entry>
         <oasis:entry colname="col3">17</oasis:entry>
         <oasis:entry colname="col4">2885</oasis:entry>
         <oasis:entry colname="col5">4.0</oasis:entry>
         <oasis:entry colname="col6">15 890</oasis:entry>
         <oasis:entry colname="col7">22</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table><?xmltex \gdef\@currentlabel{1}?></table-wrap>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8" specific-use="star"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e2955">Driving stress changes (<inline-formula><mml:math id="M153" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kPa</mml:mi></mml:mrow></mml:math></inline-formula>) in the perturbation experiments for a 1 <inline-formula><mml:math id="M154" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> increase compared with the control (<inline-formula><mml:math id="M155" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>). <bold>(a)</bold> <inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dS</mml:mi></mml:mrow><mml:mtext>SMB</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M157" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), <bold>(b)</bold> <inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dS</mml:mi></mml:mrow><mml:mi mathvariant="normal">F</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M159" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expFriction</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), and <bold>(c)</bold> <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">dS</mml:mi></mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M161" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>). The contours are the changes in the catchment divides for each of the perturbation experiments for 1 to 7 <inline-formula><mml:math id="M162" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>, coloured brightest to dullest (yellow to purple), respectively.</p></caption>
          <?xmltex \igopts{width=398.338583pt}?><graphic xlink:href="https://tc.copernicus.org/articles/17/4549/2023/tc-17-4549-2023-f08.png"/>

        </fig>

      <p id="d1e3084">Decreasing the friction coefficient in the Vincennes Bay catchment (<inline-formula><mml:math id="M163" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expFriction</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) leads to immediate acceleration of the Vanderford Glacier and surface elevation lowering upstream of the grounding line (Fig. <xref ref-type="fig" rid="Ch1.F7"/>). The driving stress also decreases close to the grounding line and on the Vanderford Glacier ice shelf, although it increases upstream of the grounding line to the Elcheikh saddle point (Fig. <xref ref-type="fig" rid="Ch1.F8"/>). This also results in an eastwards migration of the divide (i.e. into the<?pagebreak page4559?> Totten catchment) between the Totten and Vincennes Bay catchments, increasing the Vincennes Bay catchment area by 958 <inline-formula><mml:math id="M164" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (1.3 %), which is less of a migration than observed in <inline-formula><mml:math id="M165" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. By contrast, the flux across the Vanderford Glacier grounding line increases by 5.1 %, which is over 3 times that of <inline-formula><mml:math id="M166" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, reflecting the greater increase in velocities in the Vincennes Bay catchment. For <inline-formula><mml:math id="M167" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expFriction</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, the discharge increases by 42 %, reflecting the greater sensitivity to relative increases in ice surface speed.</p>
      <p id="d1e3147">The driving stress changes for <inline-formula><mml:math id="M168" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, along with the changes in the Vincennes catchment areas and discharges, are close to a linear combination of <inline-formula><mml:math id="M169" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M170" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expFriction</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="Ch1.F8"/>). The magnitude of the differences increases for increasing air surface temperature, such that in <inline-formula><mml:math id="M171" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, the increase in the Vincennes Bay catchment area is <inline-formula><mml:math id="M172" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5 % larger than <inline-formula><mml:math id="M173" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and the discharge 15 % larger than in <inline-formula><mml:math id="M174" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expFriction</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T2"><?xmltex \currentcnt{2}?><label>Table 2</label><caption><p id="d1e3229">Absolute and percentage changes in the Vanderford Glacier discharge (<inline-formula><mml:math id="M175" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Gt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</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 the end of the 1000-year perturbation experiments. Differences are with respect to the values calculated using MEaSUREs2 velocities.</p></caption><oasis:table frame="topbot"><?xmltex \begin{scaleboxenv}{.85}[.85]?><oasis:tgroup cols="7">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right" colsep="1"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right" colsep="1"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry rowsep="1" namest="col2" nameend="col3" align="center" colsep="1">expSMB </oasis:entry>
         <oasis:entry rowsep="1" namest="col4" nameend="col5" align="center" colsep="1">expFriction </oasis:entry>
         <oasis:entry rowsep="1" namest="col6" nameend="col7" align="center">expCombined </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">abs (<inline-formula><mml:math id="M176" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Gt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</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>)</oasis:entry>
         <oasis:entry colname="col3">%</oasis:entry>
         <oasis:entry colname="col4">abs (<inline-formula><mml:math id="M177" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Gt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</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>)</oasis:entry>
         <oasis:entry colname="col5">%</oasis:entry>
         <oasis:entry colname="col6">abs (<inline-formula><mml:math id="M178" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Gt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</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>)</oasis:entry>
         <oasis:entry colname="col7">%</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">1 <inline-formula><mml:math id="M179" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.02</oasis:entry>
         <oasis:entry colname="col3">1.6</oasis:entry>
         <oasis:entry colname="col4">0.05</oasis:entry>
         <oasis:entry colname="col5">5.1</oasis:entry>
         <oasis:entry colname="col6">0.07</oasis:entry>
         <oasis:entry colname="col7">6.8</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">2 <inline-formula><mml:math id="M180" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.03</oasis:entry>
         <oasis:entry colname="col3">3.2</oasis:entry>
         <oasis:entry colname="col4">0.10</oasis:entry>
         <oasis:entry colname="col5">11</oasis:entry>
         <oasis:entry colname="col6">0.14</oasis:entry>
         <oasis:entry colname="col7">14</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">3 <inline-formula><mml:math id="M181" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.05</oasis:entry>
         <oasis:entry colname="col3">4.8</oasis:entry>
         <oasis:entry colname="col4">0.16</oasis:entry>
         <oasis:entry colname="col5">16</oasis:entry>
         <oasis:entry colname="col6">0.21</oasis:entry>
         <oasis:entry colname="col7">22</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">4 <inline-formula><mml:math id="M182" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.06</oasis:entry>
         <oasis:entry colname="col3">6.3</oasis:entry>
         <oasis:entry colname="col4">0.22</oasis:entry>
         <oasis:entry colname="col5">22</oasis:entry>
         <oasis:entry colname="col6">0.29</oasis:entry>
         <oasis:entry colname="col7">30</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">5 <inline-formula><mml:math id="M183" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.08</oasis:entry>
         <oasis:entry colname="col3">7.9</oasis:entry>
         <oasis:entry colname="col4">0.28</oasis:entry>
         <oasis:entry colname="col5">28</oasis:entry>
         <oasis:entry colname="col6">0.37</oasis:entry>
         <oasis:entry colname="col7">38</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">6 <inline-formula><mml:math id="M184" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.09</oasis:entry>
         <oasis:entry colname="col3">9.5</oasis:entry>
         <oasis:entry colname="col4">0.34</oasis:entry>
         <oasis:entry colname="col5">35</oasis:entry>
         <oasis:entry colname="col6">0.46</oasis:entry>
         <oasis:entry colname="col7">47</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">7 <inline-formula><mml:math id="M185" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.11</oasis:entry>
         <oasis:entry colname="col3">11</oasis:entry>
         <oasis:entry colname="col4">0.41</oasis:entry>
         <oasis:entry colname="col5">42</oasis:entry>
         <oasis:entry colname="col6">0.56</oasis:entry>
         <oasis:entry colname="col7">57</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup><?xmltex \end{scaleboxenv}?></oasis:table><?xmltex \gdef\@currentlabel{2}?></table-wrap>

</sec>
<?pagebreak page4560?><sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Basal water routing</title>
      <p id="d1e3625">We next examine the sensitivity of basal water routing between the Totten and Vanderford glaciers due to changes in the surface elevation. We use the MATLAB TopoToolbox <xref ref-type="bibr" rid="bib1.bibx76" id="paren.94"/> to calculate the basal water accumulation across the ASB (the total upstream area in <inline-formula><mml:math id="M186" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> that contributes to water accumulation within each individual grid cell). The upstream area is defined based on the basal water flow direction vector, which is calculated using the local slope in the effective pressure at the base of the ice sheet <xref ref-type="bibr" rid="bib1.bibx31" id="paren.95"/>, and an upstream cell can provide water to only one neighbouring outlet cell. Here, rather than assuming overburden hydraulic potential, we use the parameterisation for the effective pressure <inline-formula><mml:math id="M187" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> given by <xref ref-type="bibr" rid="bib1.bibx49" id="text.96"/>, defined as
            <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M188" display="block"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ice</mml:mtext></mml:msub><mml:mi>g</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal" stretchy="false">̃</mml:mo></mml:mover><mml:mi>m</mml:mi></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal" stretchy="false">̃</mml:mo></mml:mover><mml:mi>m</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>h</mml:mi><mml:mi>i</mml:mi><mml:mi>m</mml:mi></mml:msubsup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M190" display="inline"><mml:mover accent="true"><mml:mi>h</mml:mi><mml:mo stretchy="false" mathvariant="normal">̃</mml:mo></mml:mover></mml:math></inline-formula>, and <inline-formula><mml:math id="M191" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula> are constants, and the fields <inline-formula><mml:math id="M192" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are calculated by summing the BedMachine thickness and the perturbed thickness from each simulation. A summary of the derivation of this parameterisation is provided in Appendix <xref ref-type="sec" rid="App1.Ch1.S2"/>.</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="d1e3781">Basal water accumulation (<inline-formula><mml:math id="M193" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) using <bold>(a)</bold> BedMachine geometries (<inline-formula><mml:math id="M194" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mtext>obs</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>), <bold>(b)</bold> geometry fields from <inline-formula><mml:math id="M195" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M196" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mtext>SMB</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>), <bold>(c)</bold> geometry fields from <inline-formula><mml:math id="M197" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expFriction</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M198" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">F</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), and <bold>(d)</bold> geometry fields from <inline-formula><mml:math id="M199" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M200" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). The black square represents the switch point of changes in water routing between the different experiments. The black contours demarcate the IMBIE Totten and Vincennes Bay ice catchments. The red contours show the subglacial hydrological catchment divides, demarcating catchments that drain into the Knox and Sabrina coasts, respectively.</p></caption>
          <?xmltex \igopts{width=384.112205pt}?><graphic xlink:href="https://tc.copernicus.org/articles/17/4549/2023/tc-17-4549-2023-f09.png"/>

        </fig>

      <p id="d1e3892">The basal water accumulation calculated using the BedMachine bed topography, thickness, and surface elevation is shown in Fig. <xref ref-type="fig" rid="Ch1.F9"/>a. Currently, basal water is preferentially routed towards Totten over any other glacier in the ASB. This pattern of basal water accumulation is very similar for each of the surface change experiments under 1 to 4 <inline-formula><mml:math id="M201" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> warming. However, for the <inline-formula><mml:math id="M202" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M203" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> experiments, basal water piracy to Vincennes Bay occurs, with the glaciers in this sector draining almost the entire region in the interior of the ASB (Fig. <xref ref-type="fig" rid="Ch1.F9"/>b, d). Under these scenarios, the only water routing towards the Totten Glacier originates north of Highland B. The pattern is consistent, with little subsequent change, for air surface temperature increases above 5 <inline-formula><mml:math id="M204" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>. By contrast, basal water accumulation is relatively insensitive to changes in surface elevation associated with the basal traction reduction over the Vanderford catchment imposed in our experiments, over the entire investigated range (i.e. <inline-formula><mml:math id="M205" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expFriction</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M206" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expFriction</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>; Fig. <xref ref-type="fig" rid="Ch1.F9"/>c).</p>
</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Discussion and summary</title>
      <p id="d1e3979">This study examined the potential for ice flow and basal water piracy between the Totten and Vincennes Bay catchments due to changes in the ice surface elevation induced by thinning at the Vanderford Glacier (e.g. due to ongoing grounding line retreat) and increased SMB at the Totten Glacier. For each scenario of ice surface elevation change, irrespective of the corresponding degree of warming, a rerouting of ice flow from the Totten Glacier towards the Vanderford Glacier occurred, with subsequent increases in the ice discharge at Vanderford. Increasing the SMB led to a greater eastward migration of the boundary between the two catchments than decreasing the basal traction, although the discharge towards Vanderford increased more substantially with increases in the basal friction coefficient. There was no amplification in the response when the two effects were combined, with increases in the discharge and Vincennes Bay catchment area towards the Vanderford that were essentially a linear superposition of the two separate effects.</p>
      <p id="d1e3982">Very little change was observed in the basal water routing for surface elevation changes corresponding to air surface temperature increases up to 4 <inline-formula><mml:math id="M207" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>. However, surface elevation increases in the <inline-formula><mml:math id="M208" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expSMB</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M209" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> scenarios led to a re-routing of basal water from the Totten Glacier to the Vincennes Bay glaciers. This effect persisted under increasing air surface temperatures, with no subsequent change in routing. Interestingly, this effect was not observed in the cases of thinning at the Vanderford Glacier, even in the most extreme case (<inline-formula><mml:math id="M210" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expFriction</mml:mi><mml:mn mathvariant="normal">7</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>). The switch in basal water routing from the Totten to the Vanderford Glacier was sudden, with otherwise relatively small variations in the overall basal water routing calculations. In all scenarios, the switch occurred within a region where the basal water routing from the ASB main basin converged, before diverging again to the Totten and Vincennes Bay catchments (as indicated in the black box, Fig. <xref ref-type="fig" rid="Ch1.F9"/>). The median ice surface increase from the <inline-formula><mml:math id="M211" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M212" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> experiments compared with the control was 3.1 <inline-formula><mml:math id="M213" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> in this region (i.e. from 12.4 <inline-formula><mml:math id="M214" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> in <inline-formula><mml:math id="M215" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to 15.5 <inline-formula><mml:math id="M216" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> in <inline-formula><mml:math id="M217" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">expCombined</mml:mi><mml:mn mathvariant="normal">5</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>). Although this particular “switch” region may differ in our calculations using the hydraulic potential from those using a subglacial hydrology model, this result may indicate the importance of considering regions of flow convergence in the identification of tipping points in basal water routing.</p>
      <p id="d1e4102">The surface elevation changes generated in expFriction, and consequent impacts on ice and basal water routing, were strongly impacted by both how far inland the effect of reduced friction penetrated and the magnitude of the perturbation itself. Due to the limited region over which the<?pagebreak page4561?> perturbation in basal friction was concentrated, changes in the surface elevation far upstream were relatively minor compared with those resulting from thickening simulated at the Totten Glacier, limiting the corresponding magnitude of changes in the ice and basal water piracy. Hence, a greater response might occur if the thinning were to penetrate deeper into the ASB.</p>
      <?pagebreak page4562?><p id="d1e4105">Our analysis relied on parameterised hydraulic potential to infer changes in basal water routing, which is not as robust as using a subglacial hydrology model that incorporates the full physics <xref ref-type="bibr" rid="bib1.bibx20" id="paren.97"/>. For example, the growth of channels will impact the local hydraulic potential gradients – an effect which is neglected in this study. <xref ref-type="bibr" rid="bib1.bibx20" id="text.98"/> also showed that the basal water routing between the Totten and Vanderford glaciers is highly sensitive to details in the bed topography elevations, such that uncertainties in the bed topography may influence calculations based on hydraulic potential. Furthermore, ice sheet–hydrology interactions could influence the sensitivity of ice and basal water routing, even under more minor changes in the overlying ice sheet geometry than those found here. If basal water piracy were to occur as the Vanderford Glacier retreats, enhanced basal lubrication at Vanderford could cause acceleration beyond what is currently predicted by many stand-alone ice sheet models <xref ref-type="bibr" rid="bib1.bibx79" id="paren.99"/>. On the other hand, steeper surface elevation slopes in the Vanderford Glacier could result in larger and more efficient subglacial hydrology channel formation, which could cause a reduction in ice speed near the grounding line due to lower basal water pressures <xref ref-type="bibr" rid="bib1.bibx5 bib1.bibx22" id="paren.100"/>. Our analysis excluded the influence of variable melt rates <xref ref-type="bibr" rid="bib1.bibx51" id="paren.101"><named-content content-type="pre">due to frictional or geothermal heat flow, e.g.</named-content></xref> and changes in the groundwater flux due to loading and unloading <xref ref-type="bibr" rid="bib1.bibx44 bib1.bibx82" id="paren.102"/>, both of which impact the supply of water, as well as the flow routing. We also neglected basal hydro-thermomechanical processes, which impact overall ice flow dynamics <xref ref-type="bibr" rid="bib1.bibx7 bib1.bibx77" id="paren.103"/> and which have been shown to play a role in redistributing meltwater and impacting the strength of the bed in the Siple Coast ice streams <xref ref-type="bibr" rid="bib1.bibx12" id="paren.104"/>. Uncertainty associated with these competing processes and the exact thresholds under which we might expect basal water piracy to occur motivates further investigation into coupled hydro-thermomechanical interactions and dynamics in the ASB.</p>
      <p id="d1e4136">Our numerical experiments were designed to simulate only the effects of increased surface elevation at the Totten Glacier and decreased surface elevation at the Vanderford Glacier and did not include the competing influence of thinning at the Totten Glacier nor ongoing grounding line retreat at the Vanderford Glacier. Satellite observations from 2012 have shown a lowering of the Totten Glacier surface elevation <xref ref-type="bibr" rid="bib1.bibx64 bib1.bibx86" id="paren.105"/>, with estimates of 1.2 <inline-formula><mml:math id="M218" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.6 <inline-formula><mml:math id="M219" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</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> <xref ref-type="bibr" rid="bib1.bibx23" id="paren.106"/>, linked to ocean-driven thinning of the ice shelf and consequent dynamic thinning of the upstream glacier <xref ref-type="bibr" rid="bib1.bibx45 bib1.bibx69 bib1.bibx73" id="paren.107"/>. Various ice sheet models predict continued thinning at the Totten Glacier under climate change scenarios into the future <xref ref-type="bibr" rid="bib1.bibx79" id="paren.108"/>, which could outweigh gains in surface elevation from increased SMB. Nevertheless, the main Totten tributary is topographically constrained <xref ref-type="bibr" rid="bib1.bibx62" id="paren.109"/>, currently limiting its retreat beyond the Vanderford Trench ridge and into the upstream ASB main basin. By contrast, the Vanderford Glacier is currently the fastest-retreating glacier in EAIS and is retreating into a deepening subglacial bed <xref ref-type="bibr" rid="bib1.bibx56" id="paren.110"/>. We did not include the effect of grounding line retreat at the Vanderford Glacier on the surface elevation changes generated here, although grounding line retreat is likely to compound the thinning simulated by our model. It is unclear how the rates of thinning at the Totten and Vanderford glaciers will evolve in the future, and it is possible that proportionally higher thinning at Vanderford than Totten could be sufficient to divert flow to the Vanderford Glacier.</p>
      <p id="d1e4182">There are a number of key uncertainties in how rapidly these glaciers will retreat in the future – including the impact of retreat into the marine basin of the ASB, as has been evidenced during past warm periods <xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx19 bib1.bibx29" id="paren.111"/>. First, detailed knowledge of the subglacial topography is essential in accurately predicting retreat rates, both in the ASB <xref ref-type="bibr" rid="bib1.bibx50" id="paren.112"/> and elsewhere in Antarctica <xref ref-type="bibr" rid="bib1.bibx15 bib1.bibx74 bib1.bibx79" id="paren.113"/>, and the sensitivity of basal water routing to relatively small changes in the topography <xref ref-type="bibr" rid="bib1.bibx20" id="paren.114"/>. There are relatively high uncertainties in ASB topography, particularly where there is (1) a paucity of radar transects, e.g. in the ASB main basin and basal water switch region (black box; Fig. <xref ref-type="fig" rid="Ch1.F9"/>); (2) relatively slow-flowing ice, e.g. in the interior of the ASB where mass conservation estimates of bed topography are less reliable; and (3) deep topography, where side reflections are strong and mask bed returns (Fig. <xref ref-type="fig" rid="Ch1.F1"/>d). For the latter, this is particularly the case in the Vanderford Glacier, upstream of the grounding line. Improved knowledge of the bed geometry and sediment characteristics in these regions is essential and should be a focus of future airborne surveys.</p>
      <p id="d1e4202">Second, SMB impacts the long-term evolution of the ice sheet geometry, yet projections in this region are highly uncertain. This is largely because coupled general circulation models used to project changes in accumulation are relatively coarse resolution (typically <inline-formula><mml:math id="M220" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 100 <inline-formula><mml:math id="M221" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>) – too coarse to accurately capture topographic or other effects that are essential in modelling Antarctic accumulation <xref ref-type="bibr" rid="bib1.bibx27" id="paren.115"><named-content content-type="pre">e.g.</named-content></xref>. This is likely to influence SMB projections, particularly in the region of high accumulation at the Totten Glacier, and hence predictions of whether, or to what degree, surface increases due to SMB could compensate for surface lowering due to ocean-driven thinning.</p>
      <p id="d1e4225">Finally, while links have been made between the presence of mCDW in the Vincennes Bay region <xref ref-type="bibr" rid="bib1.bibx66" id="paren.116"/> and rapid retreat of the Vanderford Glacier in the past few decades <xref ref-type="bibr" rid="bib1.bibx64" id="paren.117"/>, a causal relationship between ocean drivers and thinning and retreat has not been established. This is partly due to the relatively coarse spatial resolution of melt rates beneath the Vanderford Glacier ice shelf generated from satellite observations, which are also sparsely sampled in time <xref ref-type="bibr" rid="bib1.bibx33" id="paren.118"/>, and a lack of consistent ocean state measurements in Vincennes Bay. Given that accurate knowledge of ocean melt rates is critical for ice sheet model simulations of retreat and the evidence for a strong observed warming trend of mCDW in this region of East Antarctica <xref ref-type="bibr" rid="bib1.bibx37" id="paren.119"/>, this emphasises the need for long-term ocean state monitoring in this region.</p>
</sec>
<sec id="Ch1.S6" sec-type="conclusions">
  <label>6</label><title>Conclusions</title>
      <p id="d1e4248">Coupled ice sheet–hydrology interactions may be at the heart of substantial ice and basal water reconfigurations in the past. For the Siple Coast ice streams, such reconfigurations have had a lasting impact on ice sheet mass balance: although the Kamb Ice Stream shutdown occurred about 170 years ago, its surface elevation is still increasing, contributing to positive mass balance. In this study, we considered the potential of the Totten and Vanderford glaciers, East Antarctica, to undergo such a reconfiguration. We find that the drainage divide between the Totten and Vanderford glaciers is transient and that relatively minor changes in the ice sheet geometry<?pagebreak page4563?> could cause ice flow piracy from the Totten to the Vanderford Glacier. For example, increasing the SMB at the Totten Glacier for scenarios between 1 and 7 <inline-formula><mml:math id="M222" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> of warming (SMB experiments), for corresponding magnitudes of thinning at the Vanderford Glacier (friction experiments) and for combinations of the two effects (combined experiments), leads to an increase in the Vincennes Bay catchment area of between 3 % and 22 %. The catchment boundary shifts up to 275 449 <inline-formula><mml:math id="M223" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> for the SMB experiments, up to 30 019 <inline-formula><mml:math id="M224" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> for the friction experiments, and up to 284 165 <inline-formula><mml:math id="M225" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> for the combined experiments, where the maximum boundary migration occurs at the most inland point of the catchment and the minimum distance at the Elcheikh saddle point.</p>
      <p id="d1e4287">Our assessment of the basal water routing suggests that basal water piracy could also occur under larger ice sheet geometry changes, although this estimate is preliminary. The longer-term impacts of potential piracy from the Totten to the Vanderford Glacier on the flow dynamics, and hence overall mass balance, of this region are unknown. Given our finding that ice surface geometry changes can drive migration of the Totten–Vincennes Bay catchment boundary, determining how fast such changes might occur and their subsequent impacts on ice mass loss from the ASB and consequent global sea level rise deserves further investigation. If ice flow and basal water piracy is a result of coupled ice sheet–subglacial hydrology interactions, then without inclusion of these processes we may not be able to predict the occurrence of piracy here or elsewhere in Antarctica. The findings motivate further investigation into other regions of Antarctica that may be vulnerable to substantial flow reconfiguration, including the relevant processes that drive these changes and the timescales over which they could occur.</p>
</sec>

      
      </body>
    <back><app-group>

<app id="App1.Ch1.S1">
  <?xmltex \currentcnt{A}?><label>Appendix A</label><title>Friction coefficient reduction</title>
      <p id="d1e4301">In Eq. (<xref ref-type="disp-formula" rid="Ch1.E4"/>) for the perturbed friction coefficient field, we choose <inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> to concentrate the reduction in basal friction close to the Vanderford Glacier grounding line, as it corresponds well with the region of maximal, weighted friction <inline-formula><mml:math id="M227" display="inline"><mml:mrow><mml:mi>M</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (i.e. the region where <inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:mi>M</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M229" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><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">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). We note that this impacts the depth of penetration of changes in the surface elevation into the ASB, as discussed in Sect. <xref ref-type="sec" rid="Ch1.S5"/>.</p><?xmltex \hack{\clearpage}?><?xmltex \floatpos{h!}?><fig id="App1.Ch1.S1.F10"><?xmltex \currentcnt{A1}?><?xmltex \def\figurename{Figure}?><label>Figure A1</label><caption><p id="d1e4382"><bold>(a)</bold> Basal friction coefficient <inline-formula><mml:math id="M230" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M231" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) calculated using inversion for the spin-up and weighted by <inline-formula><mml:math id="M232" display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula> and <bold>(b)</bold> difference between <inline-formula><mml:math id="M233" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mi mathvariant="normal">f</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M234" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mtext>new</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> for <inline-formula><mml:math id="M235" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M236" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><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">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>).</p></caption>
        <?xmltex \hack{\hsize\textwidth}?>
        <?xmltex \igopts{width=483.69685pt}?><graphic xlink:href="https://tc.copernicus.org/articles/17/4549/2023/tc-17-4549-2023-f10.png"/>

      </fig>

</app>

<?pagebreak page4564?><app id="App1.Ch1.S2">
  <?xmltex \currentcnt{B}?><label>Appendix B</label><title>The effective pressure calculation</title>
      <p id="d1e4517">We use the parameterisation for the effective pressure (<inline-formula><mml:math id="M237" display="inline"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) defined in <xref ref-type="bibr" rid="bib1.bibx49" id="text.120"/>, which is given by

              <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M238" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="App1.Ch1.S2.E7"><mml:mtd><mml:mtext>B1</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>N</mml:mi><mml:mi mathvariant="normal">E</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ice</mml:mtext></mml:msub><mml:mi>g</mml:mi><mml:mi>h</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msup><mml:mover accent="true"><mml:mi>h</mml:mi><mml:mo mathvariant="normal" stretchy="false">̃</mml:mo></mml:mover><mml:mi>m</mml:mi></mml:msup></mml:mrow><mml:mrow><mml:msup><mml:mover accent="true"><mml:mi>h</mml:mi><mml:mo stretchy="false" mathvariant="normal">̃</mml:mo></mml:mover><mml:mi>m</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>h</mml:mi><mml:mi>m</mml:mi></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="App1.Ch1.S2.E8"><mml:mtd><mml:mtext>B2</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mover accent="true"><mml:mi>h</mml:mi><mml:mo stretchy="false" mathvariant="normal">̃</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">γ</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mi>m</mml:mi></mml:mrow></mml:msup><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="App1.Ch1.S2.E9"><mml:mtd><mml:mtext>B3</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mi>m</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:msub></mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi></mml:mfrac></mml:mstyle><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mi>ln⁡</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>ln⁡</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi>ln⁡</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>ln⁡</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e4749">Here, <inline-formula><mml:math id="M239" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ice</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the density of ice (<inline-formula><mml:math id="M240" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><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>), <inline-formula><mml:math id="M241" display="inline"><mml:mi>g</mml:mi></mml:math></inline-formula> is the gravitational acceleration (<inline-formula><mml:math id="M242" display="inline"><mml:mrow class="unit"><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">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), and <inline-formula><mml:math id="M243" display="inline"><mml:mi>h</mml:mi></mml:math></inline-formula> is ice thickness (<inline-formula><mml:math id="M244" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>). Both <inline-formula><mml:math id="M245" display="inline"><mml:mover accent="true"><mml:mi>h</mml:mi><mml:mo stretchy="false" mathvariant="normal">̃</mml:mo></mml:mover></mml:math></inline-formula> and <inline-formula><mml:math id="M246" display="inline"><mml:mi>m</mml:mi></mml:math></inline-formula> are constants, <inline-formula><mml:math id="M247" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula> is a constant representing the typical effective pressure as a fraction of the ice overburden pressure for regions of thick ice, <inline-formula><mml:math id="M248" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the basal water pressure as a fraction of the ice overburden pressure for ice thicknesses tending to zero, <inline-formula><mml:math id="M249" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is a typical thickness value for thick ice, <inline-formula><mml:math id="M250" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is a typical thickness value for thin ice, and <inline-formula><mml:math id="M251" display="inline"><mml:mi mathvariant="italic">ϵ</mml:mi></mml:math></inline-formula> is a small constant chosen so that the water pressure in regions of thin ice is low <inline-formula><mml:math id="M252" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mo>)</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ice</mml:mtext></mml:msub><mml:mi>g</mml:mi><mml:mi>h</mml:mi></mml:mrow></mml:math></inline-formula>. To find values for the constants <inline-formula><mml:math id="M253" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M254" display="inline"><mml:mi mathvariant="italic">γ</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M255" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M256" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and for <inline-formula><mml:math id="M257" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula>, we use output from the GlaDS model from <xref ref-type="bibr" rid="bib1.bibx21" id="text.121"/> for the Totten and Vincennes Bay catchments, and similarly to <xref ref-type="bibr" rid="bib1.bibx49" id="text.122"/>, this results in <inline-formula><mml:math id="M258" display="inline"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi mathvariant="normal">l</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.7</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M259" display="inline"><mml:mrow><mml:mi mathvariant="italic">γ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.96</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M260" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">500</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M261" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M262" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi mathvariant="normal">t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2800</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M263" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>.</p><?xmltex \hack{\newpage}?><?xmltex \hack{\vspace*{9.1cm}}?>
</app>
  </app-group><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e5052">All of the datasets used in this study are publicly available. We use version 4.20 of the open-source ISSM software, which is freely available for download from <uri>https://issm.jpl.nasa.gov/download/</uri> (see <xref ref-type="bibr" rid="bib1.bibx43" id="altparen.123"/>). The datasets used to initialise the model are available via the corresponding articles cited in this paper. Namely, ice sheet geometries from BedMachine Antarctica v3 (Morlighem et al., 2020; Morlighem, 2022, <ext-link xlink:href="https://doi.org/10.5067/FPSU0V1MWUB6" ext-link-type="DOI">10.5067/FPSU0V1MWUB6</ext-link>) and surface velocities from MEaSUREs version 2 (Rignot et al., 2011, 2017, <ext-link xlink:href="https://doi.org/10.5067/MEASURES/CRYOSPHERE/nsidc-0484.001" ext-link-type="DOI">10.5067/MEASURES/CRYOSPHERE/nsidc-0484.001</ext-link>).</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e5070">FSM conceived and led the study, conducted the ice sheet modelling and analysis, and prepared the paper. BK contributed to the paper planning. JLR assisted with the ice sheet modelling methodology. KM provided analysis on the new effective pressures. All authors contributed to the preparation and editing of the paper.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e5076">At least one of the (co-)authors is a member of the editorial board of <italic>The Cryosphere</italic>. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d1e5085">Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes<?pagebreak page4565?> every effort to include appropriate place names, the final responsibility lies with the authors.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e5092">We thank Poul Christoffersen for helpful discussions that improved the paper. This research was undertaken using resources from the National Computational Infrastructure Merit Allocation Scheme, supported by the Australian Government.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e5097">This research has been supported by the Australian Research Council (ARC) Special Research Initiative (SRI) Securing Antarctica's Environmental Future (SR200100005), ARC Discovery Early Career Awards (DE210101433, DE210101923), the ARC SRI Australian Centre for Excellence in Antarctic Science (SR200100008), the Natural Sciences and Engineering Research Council of Canada (grant no. NSERC RGPIN; 03761-2017), and the Canada Research Chairs (grant no. CRC 950-231237).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e5103">This paper was edited by Joseph MacGregor and reviewed by two anonymous referees.</p>
  </notes><ref-list>
    <title>References</title>

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