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<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0" article-type="research-article">
  <front>
    <journal-meta><journal-id journal-id-type="publisher">OS</journal-id><journal-title-group>
    <journal-title>Ocean Science</journal-title>
    <abbrev-journal-title abbrev-type="publisher">OS</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Ocean Sci.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1812-0792</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/os-22-1965-2026</article-id><title-group><article-title>Interaction of AMOC and intrinsic multidecadal  Southern Ocean variability</article-title><alt-title>Interaction of AMOC and intrinsic multidecadal Southern Ocean variability</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Smolders</surname><given-names>Emma J. V.</given-names></name>
          <email>e.j.v.smolders@uu.nl</email>
        <ext-link>https://orcid.org/0009-0000-3975-4668</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>van Westen</surname><given-names>René M.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-8807-7269</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Dijkstra</surname><given-names>Henk A.</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Utrecht, the Netherlands</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Emma J. V. Smolders (e.j.v.smolders@uu.nl)</corresp></author-notes><pub-date><day>23</day><month>June</month><year>2026</year></pub-date>
      
      <volume>22</volume>
      <issue>3</issue>
      <fpage>1965</fpage><lpage>1985</lpage>
      <history>
        <date date-type="received"><day>14</day><month>January</month><year>2026</year></date>
           <date date-type="rev-request"><day>23</day><month>January</month><year>2026</year></date>
           <date date-type="rev-recd"><day>27</day><month>May</month><year>2026</year></date>
           <date date-type="accepted"><day>3</day><month>June</month><year>2026</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2026 Emma J. V. Smolders et al.</copyright-statement>
        <copyright-year>2026</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://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026.html">This article is available from https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026.html</self-uri><self-uri xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026.pdf">The full text article is available as a PDF file from https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e97">A strongly-eddying version (0.1° horizontal resolution) of the Parallel Ocean Program (POP) shows pronounced intrinsic multidecadal variability in the Southern Ocean, the so-called Southern Ocean Mode (SOM).  This Southern Ocean multidecadal variability is induced by eddy-mean flow interaction and deep convection. The SOM variability propagates through the global ocean and influences the strength of the Atlantic Meridional Overturning Circulation (AMOC) by about 3 Sv. The opposite role on how the AMOC influences the SOM is unknown, as this requires long simulations and preferably with different AMOC background states. Here, using the results of a simulated AMOC collapse in the strongly-eddying ocean-only POP version, we find that the amplitude of the SOM is substantially reduced following an AMOC collapse. Associated changes in horizontal and vertical density variations lead to a weakening of the Antarctic Circumpolar Current transport and a shutdown of deep convection in the Weddell Sea. In contrast, these changes promote deep convection events and the emergence of multidecadal variability in the Pacific sector of the Southern Ocean. A mechanical energy budget analysis shows both a reduction in the wind input and a disruption of the phase difference between wind work and the potential to kinetic energy conversion. The results highlight the strong connection between the AMOC and intrinsic multidecadal variability in the Southern Ocean.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Universiteit Utrecht</funding-source>
<award-id>BN.000732.1.</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d2e109">Although observations are limited, there is now more and more evidence for the existence of multidecadal variability in the Southern Ocean. For example, signatures of such variability have been identified in sea surface temperatures (SSTs) <xref ref-type="bibr" rid="bib1.bibx19 bib1.bibx9 bib1.bibx4" id="paren.1"/>, and are connected to polynya formation in the Weddell Sea <xref ref-type="bibr" rid="bib1.bibx20 bib1.bibx44" id="paren.2"/>. Furthermore, paleoclimate data assimilation based reconstructions of Antarctic sea-ice anomalies over the period 1700–2000 <xref ref-type="bibr" rid="bib1.bibx2 bib1.bibx4" id="paren.3"/> indicate significant multidecadal variability with dominant periods of 40–50 and 80–100 years <xref ref-type="bibr" rid="bib1.bibx24" id="paren.4"/>.</p>
      <p id="d2e124">Models that participated in the most recent Climate Model Intercomparison Projects (CMIP5 and CMIP6) have simulated multidecadal variability in the Southern Ocean. In a 2000 years pre-industrial control simulation of the SPEAR (GFDL) model, multidecadal variability in the strength of the Antarctic Bottom Water cell is found <xref ref-type="bibr" rid="bib1.bibx43" id="paren.5"/>. The subsequent initialization phases of the model for the historical period, in particular related to convective activity, are shown to be important to explain recent trends in Antarctic sea ice. The 3000 years simulations of two versions of the SPEAR model (having different atmospheric resolutions) also display significant multidecadal variability with dominant time scales around 95 years <xref ref-type="bibr" rid="bib1.bibx24" id="paren.6"/>.  The multidecadal variability in these models is explained <xref ref-type="bibr" rid="bib1.bibx24" id="paren.7"/> by the interaction of the Southern Annular Mode (SAM) and ocean deep convection. Stronger westerlies enhance upwelling of relatively warm and saline (subsurface) water that weakens the upper ocean stratification, inducing convection.  This then mixes more saline and warm water in the upper layer, in a typical Welander salinity-convective feedback <xref ref-type="bibr" rid="bib1.bibx40" id="paren.8"/>.  Another mechanism which has been suggested is a teleconnection with El Niño variability, through the propagation of Rossby waves <xref ref-type="bibr" rid="bib1.bibx1 bib1.bibx37" id="paren.9"/>.</p>
      <p id="d2e142">While the effects of ocean eddies were parameterised in the models mentioned above, it was shown that when strongly-eddying ocean models are used, a new mode of multidecadal variability appears <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx31 bib1.bibx1 bib1.bibx6" id="paren.10"/>. In the ocean-only version of the Parallel Ocean Program (POP), this variability was named <xref ref-type="bibr" rid="bib1.bibx21" id="paren.11"/> the Southern Ocean Mode (SOM).  The effects of the SOM extend into the North Atlantic, where it induces a <inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">Sv</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">Sv</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">6</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><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:mrow></mml:math></inline-formula>) variability in the strength of the Atlantic Meridional Overturning Circulation (AMOC) at 26° N.  The mechanism of the SOM was analysed in <xref ref-type="bibr" rid="bib1.bibx16" id="text.12"/> by investigating its Lorenz Energy Cycle (LEC). Clear support was found for a mechanism suggested earlier by <xref ref-type="bibr" rid="bib1.bibx13" id="text.13"/>, where enhanced baroclinic instability in the Antarctic Circumpolar Current (ACC) region affects the mechanical energy input by the wind through a decrease of the zonality of the jet. This weakens the ACC and hence also eddy formation, leading to a more zonal jet, thereby closing the cycle.  This also explains the absence of the SOM in the non-eddying version of the POP <xref ref-type="bibr" rid="bib1.bibx34" id="paren.14"/>, as the explicit representation of ocean eddies is required for this mechanism <xref ref-type="bibr" rid="bib1.bibx16 bib1.bibx21" id="paren.15"/>.  Apart from this eddy-mean flow interaction mechanism, deep convection in the Weddel Gyre region is also modified along this cycle, and it turned out to be difficult to determine whether it plays an active or passive role in the SOM mechanism <xref ref-type="bibr" rid="bib1.bibx16 bib1.bibx10" id="paren.16"/>.</p>
      <p id="d2e216">While the SOM induces variability of the AMOC at 26° N, the role of the AMOC in the existence of the SOM has not been studied. Very recently, a quasi-equilibrium freshwater flux forcing simulation was performed using the same strongly-eddying POP model as in <xref ref-type="bibr" rid="bib1.bibx21" id="text.17"/>, showing that the AMOC collapses to a weak state of about 5 Sv <xref ref-type="bibr" rid="bib1.bibx34" id="paren.18"/>. This simulation provides an opportunity to study the AMOC-SOM connection in more detail, which is the aim of this paper. Our main focus is on how a large decrease in AMOC strength modifies the density field in the Southern Ocean, the ACC, deep convection and the properties of the SOM. Given the strong coupling between intrinsic Southern Ocean variability and key climate processes, such as Antarctic sea-ice variability <xref ref-type="bibr" rid="bib1.bibx11 bib1.bibx23 bib1.bibx12" id="paren.19"/>, oceanic heat and carbon uptake <xref ref-type="bibr" rid="bib1.bibx22 bib1.bibx41" id="paren.20"/>, and teleconnections to other modes of variability <xref ref-type="bibr" rid="bib1.bibx30" id="paren.21"/>, the results of this study are relevant for interpreting past, present and future Southern Ocean multidecadal climate variability.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Ocean model simulations</title>
      <p id="d2e249">We use output from the quasi-equilibrium freshwater forcing simulation performed by <xref ref-type="bibr" rid="bib1.bibx34" id="text.22"/> using a strongly-eddying configuration of the Parallel Ocean Program (POP, version 2) <xref ref-type="bibr" rid="bib1.bibx8" id="paren.23"/>, with a nominal horizontal resolution of 0.1° and 42 non-equidistant vertical levels. The model is forced using observed river run-off fields and a prescribed atmospheric state based on the repeat annual cycle (normal year) Coordinated Ocean Reference Experiment (CORE) forcing data set <xref ref-type="bibr" rid="bib1.bibx18" id="paren.24"/>, with 6 hourly forcing averaged to a monthly resolution. Precipitation is also taken from the CORE forcing dataset. Wind stress is computed offline using the Hurrell SST climatology <xref ref-type="bibr" rid="bib1.bibx15" id="paren.25"/> and standard bulk formulae, whereas evaporation and sensible heat flux are calculated online using the model prescribed SST and bulk formulae. A diagnosed freshwater flux, determined from an equilibrium spin-up, is also prescribed. Sea-ice cover is prescribed based on the <inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.8</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> isoline of the SST climatology, with both temperature and salinity restored on a timescale of 30 d under diagnosed climatological ice <xref ref-type="bibr" rid="bib1.bibx38" id="paren.26"/>. Apart from this, there is no salinity restoring in the model. Details on model configuration and simulation procedure can be found in the Supplementary Material of <xref ref-type="bibr" rid="bib1.bibx38" id="text.27"/>.</p>
      <p id="d2e287">The quasi-equilibrium freshwater flux forcing simulation in <xref ref-type="bibr" rid="bib1.bibx34" id="text.28"/> was initialised from model year 300 of the multi-century simulation performed by <xref ref-type="bibr" rid="bib1.bibx21" id="text.29"/>.  Model drift is still present <xref ref-type="bibr" rid="bib1.bibx35" id="paren.30"/>, but occurs on much longer timescales than the AMOC decline. From the start of the quasi-equilibrium simulation, a freshwater flux with strength <inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is applied over the North Atlantic sector (20–50° N) with a constant rate of <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">Sv</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:mrow></mml:math></inline-formula>, similar to the hosing simulation performed in the Community Earth System Model (CESM) <xref ref-type="bibr" rid="bib1.bibx32" id="paren.31"/>. The freshwater flux anomaly is globally compensated to conserve salinity.  The AMOC strength is weakening under increasing <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> values and collapses around <inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mi>H</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.125</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">Sv</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> (model year 415); more details on this simulation can be found in <xref ref-type="bibr" rid="bib1.bibx34" id="text.32"/>.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>The Southern Ocean Mode (SOM)</title>
      <p id="d2e386">In the simulations of <xref ref-type="bibr" rid="bib1.bibx21" id="text.33"/>, the temperature anomalies associated with the SOM (see their Fig. 2) propagate eastward along the ACC in the South Atlantic, where they are disrupted south of Africa around 30° E due to the interaction with the Agulhas Current Retroflection <xref ref-type="bibr" rid="bib1.bibx21" id="paren.34"/>. The anomalies then split into two pathways, where one continues along the ACC and slowly dissipates, while the other enters the Weddell Gyre, likely due to enhanced cross-stream eddy diffusivity compared to the South Atlantic <xref ref-type="bibr" rid="bib1.bibx25" id="paren.35"/>. The heat anomalies also propagate northward through the Atlantic basin, thereby inducing multidecadal variations in the AMOC strength up to 3 Sv. The SOM is associated with a peak-to-peak variability of approximately 60 ZJ (<inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">ZJ</mml:mi></mml:mrow><mml:mo>≡</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">21</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">J</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula>) in global ocean heat content (OHC), highlighting its potential significance for large-scale climate variability.</p>
      <p id="d2e421">Although the spatial pattern of the SST anomalies associated with the SOM extends across the entire Southern Ocean, the largest anomalies can be found in the South Atlantic sector <xref ref-type="bibr" rid="bib1.bibx21" id="paren.36"/>. To quantify this variability, it is measured using the SOM index, which is defined as the SST anomaly averaged over the region 50–35° S, 0–50° W (black outlined region in Fig. <xref ref-type="fig" rid="F2"/>a).</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Energetics of the SOM</title>
      <p id="d2e437">Previous studies have analysed the mechanical energy budget of the SOM in the POP control simulation <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx16" id="paren.37"/>.  It was shown that eddy-mean flow interactions are central to explain the SOM, similar to that of a mode of multidecadal variability identified in a three-layer, eddy-resolving, quasi-geostrophic model of a zonal channel flow <xref ref-type="bibr" rid="bib1.bibx13" id="paren.38"/>. The oscillatory behaviour arises from phase lags between mechanical energy input by the wind, generation of eddies by baroclinic instability, and the zonality of the mean flow.  Below, we also apply a similar mechanical energy budget analysis to the quasi-equilibrium POP simulation to investigate the effects of an AMOC weakening on the SOM.</p>
      <p id="d2e446">The Lorenz Energy Cycle (LEC) framework <xref ref-type="bibr" rid="bib1.bibx36" id="paren.39"/> has proven effective for analysing the multidecadal variability of the SOM <xref ref-type="bibr" rid="bib1.bibx16" id="paren.40"/>. Further simplifications of the full LEC framework have been proposed by <xref ref-type="bibr" rid="bib1.bibx26" id="text.41"/>, and these have been successfully applied to the POP model output to explain the oscillatory behaviour of the SOM <xref ref-type="bibr" rid="bib1.bibx17" id="paren.42"/>.  In the following, we denote <inline-formula><mml:math id="M9" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M11" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as the volume-integrated total kinetic energy, mean kinetic energy and eddy kinetic energy, respectively; and <inline-formula><mml:math id="M12" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as the volume-integrated available potential energy, mean available potential energy and eddy available potential energy, respectively.</p>
      <p id="d2e520">The total kinetic energy <inline-formula><mml:math id="M15" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula> is computed according to:

            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M16" display="block"><mml:mrow><mml:mi>K</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:munder><mml:mo movablelimits="false">∫</mml:mo><mml:mi>V</mml:mi></mml:munder><mml:mo>(</mml:mo><mml:mover accent="true"><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mi>v</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>)</mml:mo><mml:mi mathvariant="normal">d</mml:mi><mml:mi>V</mml:mi><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">u</mml:mi><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>v</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> denotes the horizontal velocity vector, <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> the global average density of sea water, and <inline-formula><mml:math id="M19" display="inline"><mml:mi>V</mml:mi></mml:math></inline-formula> the volume over which the energetics are evaluated. The overbar represents a 5 year time average used to perform the eddy-mean decomposition, consistent with previous studies on the energetics of the SOM <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx16" id="paren.43"/>. The results are not sensitive to small changes in the averaging window (tested for 3–10 year time averages). The mean kinetic energy is given by: 

            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M20" display="block"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:munder><mml:mo movablelimits="false">∫</mml:mo><mml:mi>V</mml:mi></mml:munder><mml:mo>(</mml:mo><mml:msup><mml:mover accent="true"><mml:mi>u</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:msup><mml:mover accent="true"><mml:mi>v</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>)</mml:mo><mml:mi mathvariant="normal">d</mml:mi><mml:mi>V</mml:mi><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          and the eddy kinetic energy is computed as the difference between <inline-formula><mml:math id="M21" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> per gridpoint. The available potential energy is expressed as:

            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M23" display="block"><mml:mrow><mml:mi>P</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mi>g</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:munder><mml:mo movablelimits="false">∫</mml:mo><mml:mi>V</mml:mi></mml:munder><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle><mml:mover accent="true"><mml:mrow><mml:msup><mml:mi mathvariant="italic">ρ</mml:mi><mml:mrow><mml:mo>*</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mi mathvariant="normal">d</mml:mi><mml:mi>V</mml:mi><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where the potential density anomalies are defined as <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ref</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></inline-formula> with <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ref</mml:mtext></mml:msub><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mo>〈</mml:mo><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>,</mml:mo><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:msub><mml:mo>〉</mml:mo><mml:mtext>av</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> representing the global reference state <xref ref-type="bibr" rid="bib1.bibx36" id="paren.44"/>. In the expression for <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, the angled brackets indicate a global area average, while the subscript denotes a time average over one SOM cycle. Furthermore, <inline-formula><mml:math id="M27" display="inline"><mml:mi>g</mml:mi></mml:math></inline-formula> denotes the gravitational acceleration and <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> the vertical gradient of the reference potential density. An eddy-mean decomposition can be performed to determine the mean and eddy potential energies (<inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, respectively). The analysis is conducted over the entire Southern Ocean south of 30° S (SO30 region), thereby capturing the complete SOM variability and avoiding problems of boundary terms <xref ref-type="bibr" rid="bib1.bibx16" id="paren.45"/>.</p>
      <p id="d2e935">Under the approximations outlined in detail by <xref ref-type="bibr" rid="bib1.bibx17" id="text.46"/>, the evolution equations for the volume integrated eddy kinetic energy <inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and available potential energy <inline-formula><mml:math id="M32" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> are given by:

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M33" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E4"><mml:mtd><mml:mtext>4</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>≈</mml:mo><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E5"><mml:mtd><mml:mtext>5</mml:mtext></mml:mtd><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>≈</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

          Here, the generation of mean kinetic energy by the wind forcing exerting a stress on the ocean surface <inline-formula><mml:math id="M34" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> is expressed as:

            <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M35" display="block"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:munder><mml:mo movablelimits="false">∫</mml:mo><mml:mi>S</mml:mi></mml:munder><mml:mo>(</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mover accent="true"><mml:mi>u</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>+</mml:mo><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mover accent="true"><mml:mi>v</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>)</mml:mo><mml:mi mathvariant="normal">d</mml:mi><mml:mi>S</mml:mi><mml:mspace width="0.33em" linebreak="nobreak"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          with <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">τ</mml:mi><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi mathvariant="italic">τ</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> the wind stress. The exchange of potential to eddy kinetic energy associated with baroclinic instability, <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, is determined by:

            <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M38" display="block"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:munder><mml:mo movablelimits="false">∫</mml:mo><mml:mi>V</mml:mi></mml:munder><mml:mover accent="true"><mml:mrow><mml:msup><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:msup><mml:mi>w</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mi mathvariant="normal">d</mml:mi><mml:mi>V</mml:mi><mml:mo>≈</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>P</mml:mi><mml:mo>,</mml:mo><mml:mi>K</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo><mml:mspace linebreak="nobreak" width="0.33em"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M39" display="inline"><mml:mi>w</mml:mi></mml:math></inline-formula> denotes the vertical velocity and the prime indicates anomalies with respect to the 5 year time average. The terms in the mechanical energy budget are calculated using 5 year moving averages, while eddy contributions are determined from monthly mean data.  The terms <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:mi>D</mml:mi><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> above are dissipation terms, but are not crucial to study the SOM cycle <xref ref-type="bibr" rid="bib1.bibx16" id="paren.47"/>.  The degree of non-zonality of the mean flow, which is a proxy for the baroclinic generation of eddies, is quantified by <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:mi mathvariant="italic">ζ</mml:mi><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mo>∫</mml:mo><mml:mover accent="true"><mml:mrow><mml:msup><mml:mi>v</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mi mathvariant="normal">d</mml:mi><mml:mi>V</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mo>(</mml:mo><mml:mo>∫</mml:mo><mml:mover accent="true"><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mi mathvariant="normal">d</mml:mi><mml:mi>V</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, where the squared meridional and zonal velocities are computed first and then volume integrated over the SO30 region and the top 300 m.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Changing SOM variability</title>
      <p id="d2e1402">In the quasi-equilibrium simulation of the POP, a gradual increase in surface freshwater forcing leads to a weakening of the AMOC (Fig. <xref ref-type="fig" rid="F1"/>a).  The AMOC strength at 26° N decreases from a mean of 19.4 Sv during the first 50 model years to a mean of 4.8 Sv during the last 50 model years. The onset of the collapse occurs around model year 415 <xref ref-type="bibr" rid="bib1.bibx34" id="paren.48"/>.  The SOM index (Fig. <xref ref-type="fig" rid="F1"/>b, black curve) exhibits distinct multidecadal variability over the first 200 model years, with a dominant period of approximately 45 years that is statistically significant at the 95 % confidence level based on a Morlet wavelet power spectrum (Fig. <xref ref-type="fig" rid="FA1"/>b). As the freshwater forcing increases, this period becomes longer, reaching approximately 50 years between model years 300–500.  After the AMOC collapse and over the last 100 model years, the variability in the SOM index disappears entirely (Fig. <xref ref-type="fig" rid="FA1"/>b).  The Drake Passage transport (Fig. <xref ref-type="fig" rid="F1"/>c) displays the same multidecadal variability as the SOM index over the first 300 years (Fig. <xref ref-type="fig" rid="FA1"/>a), with a peak-to-peak amplitude of about 17 Sv. Subsequently, the mean transport and the amplitude of multidecadal variability slightly decrease, the former by about 10 Sv and the latter being minimal just before the onset of the AMOC collapse. Interestingly, this amplitude increases again after the AMOC collapse, while the frequency of variability slightly decreases (Fig. <xref ref-type="fig" rid="FA1"/>a).</p>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e1425">Results for the quasi-equilibrium, high-resolution POP simulation. Time series of <bold>(a)</bold>: the AMOC strength at 1000 m depth and 26° N, <bold>(b)</bold>: the SOM (black) and SOM-P (blue) index, and <bold>(c)</bold>: the Drake Passage volume transport. The inset in panel <bold>c</bold> shows the black (blue) outlined region used to determine the SOM (SOM-P) index. The full-depth Drake Passage volume transport is determined over the red section (66–55° S, 66° W).</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f01.png"/>

        </fig>

      <p id="d2e1446">To understand the disappearing multidecadal variability in the AMOC strength time series, we conduct an empirical orthogonal function (EOF) analysis on annual mean SSTs south of 30° S for the first and last 100 model years of the simulation.  All time series are first linearly detrended and normalised by their standard deviations, and subsequently weighted to their surface area prior to conducting the EOF analysis.  The dominant EOF pattern and associated principle component (PC) are shown in Fig. <xref ref-type="fig" rid="F2"/>.  During the first 100 model years (Fig. <xref ref-type="fig" rid="F2"/>a), the EOF exhibits relatively strong (negative) amplitudes over the Atlantic sector in the Southern Ocean.  This motivates the choice of the region used for the SOM index <xref ref-type="bibr" rid="bib1.bibx21" id="paren.49"/>, as indicated by the black outlined region (50–35° S, 0–50° W).  The corresponding PC (Fig. <xref ref-type="fig" rid="F2"/>c) exhibits a similar period to that of the SOM index, highlighting the dominance of this multidecadal variability in the SO30 region.</p>
      <p id="d2e1459">After the AMOC collapse (last 100 model years), the pattern of the EOF changes significantly, with the largest amplitudes now located in the Pacific sector of the Southern Ocean (Fig. <xref ref-type="fig" rid="F2"/>b).  The period of the associated PC increases to approximately 75 years (Fig. <xref ref-type="fig" rid="F2"/>d), matching the period of the Drake Passage transport over the last 100 years (Fig. <xref ref-type="fig" rid="FA1"/>a).  This motivates us to also study the variability in the Pacific sector, where we define the SOM-P index as the spatially-averaged SSTs over the blue outlined region (60–45° S, 170° E–150° W), which coincides with the region of largest EOF amplitudes (Fig. <xref ref-type="fig" rid="F2"/>b). Interestingly, a pronounced mode of multi-decacal variability emerges in the SOM-P index only after the onset of the AMOC collapse around model year 415 (blue curve in Fig. <xref ref-type="fig" rid="F1"/>b).  The dominant period during the last 150 model years is approximately 75 years, and is statistically significant at the 95 % confidence level based on a Morlet wavelet power spectrum (Fig. <xref ref-type="fig" rid="FA1"/>c). The dominant period of the SOM-P index is consistent with that of the Drake Passage transport after the AMOC has collapsed (Fig. <xref ref-type="fig" rid="FA1"/>a). This suggests that Pacific variability is associated with the multidecadal behaviour of the Drake Passage transport after the AMOC has collapsed, as will be further explored below in Sect. <xref ref-type="sec" rid="Ch1.S3.SS4"/>.</p>

      <fig id="F2" specific-use="star"><label>Figure 2</label><caption><p id="d2e1481">First EOFs of annual mean SSTs south of 30° S for the first 100 model years <bold>(a)</bold> and the last 100 model years <bold>(b)</bold>, with the explained variance indicated. A moving average of 5 years has been applied to the data prior to the EOF analysis. The black (blue) outlined region shows the region used to determine the SOM (SOM-P) index. Panels <bold>(c, d)</bold> show the corresponding first PCs.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f02.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>AMOC–SOM coupling</title>
      <p id="d2e1507">Density anomalies associated with the SOM propagate northward and submerge around 40° S <xref ref-type="bibr" rid="bib1.bibx30" id="paren.50"/>, generating multidecadal variability in the subsurface temperature and salinity fields (Fig. <xref ref-type="fig" rid="FA2"/>). These subsurface anomalies continue to propagate northward within the Atlantic basin, thereby influencing the strength of the upper branch of the AMOC <xref ref-type="bibr" rid="bib1.bibx30" id="paren.51"/>. As a result, the AMOC strength at 26° N exhibits a similar 45 year oscillation period as the SOM index during the first 300 model years (Fig. <xref ref-type="fig" rid="FA3"/>a). As the AMOC weakens, the distinct temperature and salinity patterns associated with the positive and negative phases of the SOM disappear (Fig. <xref ref-type="fig" rid="FA2"/>), and the AMOC loses its multidecadal variability (Fig. <xref ref-type="fig" rid="FA3"/>b).</p>
      <p id="d2e1525">The substantially weakened AMOC leads to a pronounced reduction in meridional heat and salinity transport <xref ref-type="bibr" rid="bib1.bibx34" id="paren.52"/>, resulting in an accumulation of heat and convergence of salt in the Southern Hemisphere ocean interior, extending to depths up to 1000 m north of the Antarctic subpolar front (50° S). This causes both warming (Fig. <xref ref-type="fig" rid="F3"/>a) and salinification (Fig. <xref ref-type="fig" rid="F3"/>b) of the subsurface waters, consistent with previous studies on a weakened AMOC <xref ref-type="bibr" rid="bib1.bibx39 bib1.bibx33 bib1.bibx5" id="paren.53"/>.  In contrast, the deep waters experience a freshening and slight cooling related to the reduced formation of North Atlantic Deep Water (NADW), and a reorganization of the water masses in the Southern Ocean. The resulting density changes show an increase in the upper 1000 m between 50 and 20° S, and a decrease further north (Fig. <xref ref-type="fig" rid="F3"/>c). At greater depths, the waters become less dense, primarily driven by salinity changes (Fig. <xref ref-type="fig" rid="FA4"/>).</p>

      <fig id="F3" specific-use="star"><label>Figure 3</label><caption><p id="d2e1545">Temperature, salinity, density, meridional density gradient and buoyancy frequency (<italic>N</italic><sup>2</sup>) differences in the Atlantic sector. Zonally averaged (60° W–25° E) <bold>(a)</bold> temperature, <bold>(b)</bold> salinity, <bold>(c)</bold> density, <bold>(d)</bold> meridional density gradient, <bold>(e)</bold> <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, and <bold>(f)</bold> salinity-driven <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> differences in the upper 2500 m before and after the AMOC collapse (model year (500–600) minus model year (1–100)). In <bold>(c–f)</bold>, the solid (dashed) black lines denote isopycnals of model year 1–100 (500–600). Plotted isopycnals are (from top to bottom): 1027.0, 1027.5, and 1027.7 <inline-formula><mml:math id="M44" 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> for model year 1–100 (500–600). The markers in panel <bold>a, b</bold> indicate non-significant (<inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>≧</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula>, two-sided Welch's test) differences, which are not shown in panels <bold>c–f</bold> to enhance visibility.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f03.png"/>

        </fig>

      <p id="d2e1640">Between 50–40° S and over the upper 1000 m, the isopycnals slope downward and this is indicative of the Antarctic subpolar front (solid curves in Fig. <xref ref-type="fig" rid="F3"/>c–f).  This meridional density gradient becomes less negative after the AMOC collapse, resulting in a decrease of the isopycnal slope (shading and dashed curves in Fig. <xref ref-type="fig" rid="F3"/>c).  By contrast, a negative meridional density gradient difference is found at subsurface depths (1000–2000 m) and near 50° S, corresponding to a steepening of the isopycnals.  Changes in the isopycnal slopes modify the baroclinicity, thereby influencing the strength of the ACC through thermal wind balance (Fig. <xref ref-type="fig" rid="F1"/>c). The changes in the meridional density gradient are not uniform across the ACC latitude band (50° S - 40° S), and may therefore lead to spatially heterogeneous changes in the ACC. <xref ref-type="bibr" rid="bib1.bibx31" id="text.54"/> showed that an increased meridional slope of the isopycnals near 50° S corresponds to a reduction of the SOM period in the CESM model.  This is consistent with the results here, where an increase in the SOM period occurs simultaneously with the meridional isopycnal slopes becoming less negative (near 50° S and upper 1000 m).</p>
      <p id="d2e1652">The displacement of the isopycnals leads to changes in the stratification of the water masses (Fig. <xref ref-type="fig" rid="F3"/>e), with clear bands of increased and decreased stratification. Stratification decreases in the water mass north of 50° S between 1000 and 1500 m, but, in contrast, waters below 1500 m and those that upwell south of 50° S show an overall increase in stratification. The latter increases are primarily driven by salinity-controlled changes in <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="F3"/>f), while stratification changes north of 50° S and in the upper 1500 m result from a combination of temperature- and salinity-driven effects.</p>
      <p id="d2e1670">Similar to the Atlantic sector, the Indian and Pacific sectors of the Southern Ocean also exhibit warming and salinification over the upper 1000 m and north of 45° S (Figs. <xref ref-type="fig" rid="FA5"/> and <xref ref-type="fig" rid="FA6"/>). These changes are accompanied by a decrease of the meridional density gradient over the near-surface layer, and an increase of this gradient in the subsurface layers across the ACC latitude band (between 50 and 40° S). Stratification weakens north of 60° S in the upper 1500 m, while deeper waters show an overall increase in stratification.  The AMOC weakening therefore leads to a basin-wide reorganization of the Southern Ocean density structure, which appears to suppress SOM-related variability in the Atlantic sector while enabling the emergence of a new mode of multidecadal variability in the Pacific sector.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Mechanisms of SOM changes</title>
      <p id="d2e1685">To understand the reduced SOM variability after the AMOC collapse, we analysed the mechanical energy changes over the SO30 region. The dominant terms of the mechanical energy budget are evaluated over the full simulation period, and over three different SOM cycles: one early in the simulation (SOM cycle 1, model years 63–114), one during the AMOC collapse (SOM cycle 2, model years 410–480), and one during the weak AMOC state (SOM cycle 3, model years 500–600).  The difference in cycle length reflects the increasing SOM (SOM-P) period under increasing freshwater flux forcing.  The mechanical energy budget analysis is displayed in Fig. <xref ref-type="fig" rid="F4"/>.</p>

      <fig id="F4" specific-use="star"><label>Figure 4</label><caption><p id="d2e1692">Energetics in the SO30 region. Time series of <bold>(a)</bold> volume integrated (90–30° S) available potential energy (<inline-formula><mml:math id="M47" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula>), <bold>(b)</bold> total kinetic energy (<inline-formula><mml:math id="M48" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula>), <bold>(c)</bold> energy conversion of eddy potential energy to eddy kinetic energy (<inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>), <bold>(d)</bold> mean energy input by the wind (<inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>) and <bold>(e)</bold> a measure of the normalised, mean-centered non-zonality of the flow field <inline-formula><mml:math id="M51" display="inline"><mml:mi mathvariant="italic">ζ</mml:mi></mml:math></inline-formula>. All time series represent 5 year running averages. In panel <bold>(a)</bold>, the blue line represents the time series of <inline-formula><mml:math id="M52" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> calculated with a reference density <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> taken from the first 50 model years, whereas the cyan line uses a <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> averaged over the corresponding SOM cycle.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f04.png"/>

        </fig>

      <p id="d2e1812">The available potential energy, <inline-formula><mml:math id="M55" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula>, is dependent on the reference density <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> used (see Eq. <xref ref-type="disp-formula" rid="Ch1.E3"/>).  We compute <inline-formula><mml:math id="M57" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> over the full simulation using a fixed <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> derived from the first 50 model years (dark blue curve in Fig. <xref ref-type="fig" rid="F4"/>a), such that all changes in <inline-formula><mml:math id="M59" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> reflect variations in the density structure rather than changes in the reference state. In contrast, <inline-formula><mml:math id="M60" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> for the individual SOM cycles is computed using <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> averaged over the corresponding SOM cycle period (cyan curves in Fig. <xref ref-type="fig" rid="F4"/>a).  The different choices of <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mtext>ref</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> do influence the magnitude of <inline-formula><mml:math id="M63" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula>, but not their overall variability and tendency.</p>
      <p id="d2e1904">The available potential energy starts to increase in the SO30 region following the AMOC collapse, with the Atlantic, Indian, and Pacific sectors contributing approximately 29 %, 30 %, and 41 %, respectively, to the total <inline-formula><mml:math id="M64" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> in this region.  An increase in <inline-formula><mml:math id="M65" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> indicates that the water column is further displaced from its stable reference state. This is also consistent with the decrease in vertical stratification in the upper 1500 m in the Atlantic, Indian and Pacific sectors south of 30° S, as shown in Fig. <xref ref-type="fig" rid="F5"/>.  The available potential energy, however, has not yet reached an equilibrium state at the end of the simulation, as <inline-formula><mml:math id="M66" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> continues to increase.</p>
      <p id="d2e1930">The tendency of <inline-formula><mml:math id="M67" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="F4"/>) is affected by the terms <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, representing the mean wind energy input, and by <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, representing conversion of eddy potential to eddy kinetic energy.  An increase in <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, e.g. due to a more zonal flow with steeper isopycnals, increases <inline-formula><mml:math id="M71" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula>. In contrast, an increase in <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> reflects enhanced eddy generation through baroclinic instability, transferring more energy from <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and thus reduces <inline-formula><mml:math id="M75" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> over time. Figure <xref ref-type="fig" rid="F4"/> shows both a mean reduction of <inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, although the reduction in <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is larger (Fig. <xref ref-type="fig" rid="F4"/>c and d).  The increase in <inline-formula><mml:math id="M79" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> at the end of the simulation is therefore not driven by enhanced mean wind energy input, but instead is a consequence of changes in the density field associated with the AMOC collapse. Additionally, <inline-formula><mml:math id="M80" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> primarily exhibit a reduced amplitude of variability rather than a shift in mean magnitude (Fig. <xref ref-type="fig" rid="F4"/>b).</p>
      <p id="d2e2153">The relatively zonal background ACC flow starts to meander more after the AMOC collapse, which is reflected in the increase of the non-zonality parameter (<inline-formula><mml:math id="M82" display="inline"><mml:mi mathvariant="italic">ζ</mml:mi></mml:math></inline-formula>, Fig. <xref ref-type="fig" rid="F4"/>e). This increase is consistent with the reduction in mean wind energy input over time, as the correlation between the zonal wind forcing and the zonal mean flow weakens. While an increased non-zonal flow is typically associated with enhanced eddy activity, this is not reflected in an overall increase of <inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The non-zonality parameter loses its multidecadal variability entirely after the AMOC collapse, suggesting that its increase is not primarily driven by variability in the eddy generation and mean wind energy input. Mean flow changes likely also play a role, e.g. a reduction in the mean ACC strength or a shift in its position could lead to increased meandering of the zonal flow.</p>

      <fig id="F5" specific-use="star"><label>Figure 5</label><caption><p id="d2e2191">Depth profiles of the squared Brunt–Väisälä frequency (<inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) area-averaged in the <bold>(a)</bold> Atlantic sector (60° W–25° E), <bold>(b)</bold> the Indian sector (25–150° E), and <bold>(c)</bold> the Pacific sector (150° E–60° W) of the Southern Ocean (90–30° S). <bold>(d–f)</bold>: Similar to <bold>(a–c)</bold> but now showing the difference between model year (500–600) and (1–100).</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f05.png"/>

        </fig>

      <p id="d2e2227">Following the framework established in earlier studies <xref ref-type="bibr" rid="bib1.bibx13 bib1.bibx21 bib1.bibx16" id="paren.55"/>, the SOM cycle can be divided into four distinct regimes (Fig. <xref ref-type="fig" rid="F6"/>a), where the vertical stratification plays a key role in setting the timescale of this SOM cycle <xref ref-type="bibr" rid="bib1.bibx31" id="paren.56"/>.  Note that the quantities are now centered (zero mean) and normalised by their standard deviation, to more clearly see the phase differences between the different terms. Regime A corresponds to a low-energy state with a relatively zonal ACC, starting at the minimum of the total potential energy <inline-formula><mml:math id="M85" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> and ending at the minimum of the total kinetic energy <inline-formula><mml:math id="M86" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula>.  In regime B, <inline-formula><mml:math id="M87" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> increases as the zonal flow is accelerated by the wind work, leading to a maximum of <inline-formula><mml:math id="M88" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula>.  Regime C represents the high-energy state, spanning from the maximum of <inline-formula><mml:math id="M89" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> to the maximum of <inline-formula><mml:math id="M90" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula>.  During this period, the flow undergoes enhanced baroclinic instability, leading to an increase in the generation of eddies by the mean flow. The <inline-formula><mml:math id="M91" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> accumulated in regimes A and B is now converted to eddy kinetic energy.  This enhanced eddying flow rearranges the flow field, making it less zonal, thereby disrupting the correlation between the surface ocean velocity and the wind stress. As a result, the wind energy input quickly decreases.  Finally, regime D is characterised by declining <inline-formula><mml:math id="M92" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M93" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula>. As the storage of <inline-formula><mml:math id="M94" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> becomes exhausted, the conversion of <inline-formula><mml:math id="M95" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> to <inline-formula><mml:math id="M96" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula> begins to diminish as well.  This, combined with the reduction in wind work, drives the flow back to its low-energy state, thereby completing the cycle.</p>

      <fig id="F6" specific-use="star"><label>Figure 6</label><caption><p id="d2e2327">Energetics for three different SOM cycles in the SO30 region. Time series of volume integrated (90–30° S) available potential energy (<inline-formula><mml:math id="M97" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula>), total kinetic energy (<inline-formula><mml:math id="M98" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula>), energy conversion of eddy potential energy to eddy kinetic energy (<inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>), mean energy input by the wind (<inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>) and a measure of the non-zonality of the flow field <inline-formula><mml:math id="M101" display="inline"><mml:mi mathvariant="italic">ζ</mml:mi></mml:math></inline-formula> for <bold>(a)</bold> SOM cycle 1 (model year 63–114), <bold>(b)</bold> SOM cycle 2 (model year 324–378) and <bold>(c)</bold> SOM cycle 3 (model year 500–600). All time series represent 5 year running averages. Note that each quantity <inline-formula><mml:math id="M102" display="inline"><mml:mi>X</mml:mi></mml:math></inline-formula> is normalised according to <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mtext>mean</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi>X</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi>X</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> is the standard deviation of the quantity in SOM cycle 1. The vertical lines divide the SOM cycle into the four regimes (A–D) according to <xref ref-type="bibr" rid="bib1.bibx13" id="text.57"/>, as described in Sect. <xref ref-type="sec" rid="Ch1.S3.SS3"/>. Note that SOM cycle 3 cannot easily be divided into these regimes.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f06.png"/>

        </fig>

      <p id="d2e2464">The temporal evolution for SOM cycle 2 and 3 are shown in Fig. <xref ref-type="fig" rid="F6"/>b and c, respectively. Note that we normalised the quantities as <inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mtext>mean</mml:mtext></mml:msub><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mrow><mml:mi>X</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, where we use the standard deviation of the first cycle as reference. Equation (<xref ref-type="disp-formula" rid="Ch1.E5"/>) shows that the rate of change of <inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and therefore <inline-formula><mml:math id="M107" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula>, is mainly influenced by <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Large transfers of potential to kinetic energy feed almost directly into the eddy kinetic energy field. Consistent with this, in all three SOM cycles, <inline-formula><mml:math id="M109" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M110" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>,<inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> are positively correlated with a lag varying between 1–5 years. The non-zonality parameter <inline-formula><mml:math id="M112" display="inline"><mml:mi mathvariant="italic">ζ</mml:mi></mml:math></inline-formula> loses its multidecadal oscillatory behaviour in SOM cycle 3, in contrast to the pronounced variability found during SOM cycles 1 and 2 (Fig. <xref ref-type="fig" rid="F6"/>a and b). During SOM cycle 1 and 2, the minima and maxima of <inline-formula><mml:math id="M113" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> lead the minima and maxima of <inline-formula><mml:math id="M114" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula> with an approximate phase difference of 90°. The phase offset between <inline-formula><mml:math id="M115" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M116" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula> vanishes completely in SOM cycle 3 due to the altered behaviour of <inline-formula><mml:math id="M117" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> as a consequence of stratification changes in the water column. Furthermore, a clear phase difference between <inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is found in SOM cycle 1, which is essential to sustain the SOM <xref ref-type="bibr" rid="bib1.bibx13 bib1.bibx21 bib1.bibx16" id="paren.58"/>. In SOM cycle 3, however, <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> begin to co-vary, with reduced phase differences between their minima and maxima.</p>
      <p id="d2e2709">Figure <xref ref-type="fig" rid="F6"/> shows the energetics integrated over the entire Southern Ocean. Performing the same analysis for the Atlantic sector alone yields a similar behaviour: during SOM cycles 1 and 2, the phase differences between the energy terms resemble those found in the SO30 region, while these phase relationships disappear during SOM cycle 3 (Fig. <xref ref-type="fig" rid="FA7"/>). In contrast, in the Pacific sector the emergence of the SOM-P cycle is not accompanied by clear phase differences during SOM cycle 3 that are consistent with the established framework of <xref ref-type="bibr" rid="bib1.bibx13" id="text.59"/> (Fig. <xref ref-type="fig" rid="FA8"/>). This suggests that, unlike in the Atlantic sector, the SOM-P may not be strongly influenced by eddy–mean flow interactions. In conclusion, the reorganization of the Southern Ocean density field leads to a fundamental change in the mechanical energy budget, particularly affecting the phase relationships between <inline-formula><mml:math id="M122" display="inline"><mml:mi>P</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M123" display="inline"><mml:mi>K</mml:mi></mml:math></inline-formula>, and between <inline-formula><mml:math id="M124" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. As these phase relationships are essential for sustaining the SOM, their alteration due to the AMOC collapse leads to the disappearance of the SOM cycle in the Atlantic sector.</p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Changes in Southern Ocean deep convection</title>
      <p id="d2e2785">Changes in stratification likely influence deep convection across the Southern Ocean and the exact role of deep convection in the SOM variability is not completely clear <xref ref-type="bibr" rid="bib1.bibx16" id="paren.60"/>. The reason is that convection is parameterised (using the KPP mixing scheme in POP), which provides enhanced mixing without explicitly resolving vertical velocities. Hence, the contribution by deep convection cannot be assessed using the mechanical energy pathways <xref ref-type="bibr" rid="bib1.bibx16" id="paren.61"/>. A recent study by <xref ref-type="bibr" rid="bib1.bibx10" id="text.62"/>, based on the analysis of a high-resolution CESM simulation, found only weak evidence for atmosphere–ocean feedbacks contributing to Southern Ocean multidecadal variability and instead attributed this variability primarily to oceanic processes. They propose that the SOM mechanism operates as part of a coupled oscillator involving Southern Ocean deep convection events, with salinity upwelling east of Maud Rise playing a crucial role. These findings support the conclusion of <xref ref-type="bibr" rid="bib1.bibx16" id="text.63"/> that deep convection can also play a substantial role in sustaining the SOM.</p>
      <p id="d2e2800">Based on the largest differences in the maximum and variance of the mixed layer depth (MLD) between model years 500–600 and 1–100 (Fig. <xref ref-type="fig" rid="F7"/>a and b), four regions are identified for further analysis.  Similar to <xref ref-type="bibr" rid="bib1.bibx16" id="text.64"/>, we define the Weddell Gyre to Kerguelen Plateau (WGKP) region as 80–50° S and 35° W–80° E (green outlined region in Fig. <xref ref-type="fig" rid="F7"/>b).  The brown-outlined region in the eastern Indian sector south of Australia, extending from 70–50° S and from 80–150° E, is hereafter referred to as AU.  The convective region highlighted in magenta, located at longitudes aligned with New Zealand and spanning 70–62° S and 160° E–170° W, is hereafter denoted as NZ.  Finally, the blue-outlined western Pacific region, extending from 70–50° S and 110–60° W, is hereafter referred to as PA.</p>

      <fig id="F7" specific-use="star"><label>Figure 7</label><caption><p id="d2e2812">Mixed layer depth (MLD) and potential density (PD) properties in the SO30 region. Difference in the MLD between model year 500–600 and model year 1–100 of the <bold>(a)</bold> MLD maximum, and <bold>(b)</bold> variance in the SO30 region. The outlined regions denote the WGKP (green), the AU (brown), the NZ (magenta), and the PA (blue) region. <bold>(c, d)</bold>: The area-averaged PD profiles in the four convective regions time-averaged over <bold>(c)</bold> model year 1–100, and <bold>(d)</bold> model year 500–600.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f07.png"/>

        </fig>

      <p id="d2e2837">The area-averaged potential density (PD) profiles of the four regions are shown in Fig. <xref ref-type="fig" rid="F7"/>c and d for model year 1–100 and model year 500–600, respectively.  The stratification over the upper 2000 m is relatively weak for the NZ and WGKP regions, whereas the AU and PA regions are stronger stratified (Fig. <xref ref-type="fig" rid="F7"/>c).  Following the AMOC collapse, stratification increases in the NZ and WGKP regions, while the opposite is true for the AU and PA regions (Fig. <xref ref-type="fig" rid="F7"/>d).  A stronger (weaker) stratification reduces (increases) the MLD, which is found for the NZ and WGKP (AU and PA) regions.</p>
      <p id="d2e2846">To make the latter more explicit, we present the maximum MLD and Brunt-Väisälä frequency differences (relative to the first 100 model years) over the four regions in Fig. <xref ref-type="fig" rid="F8"/>. The stratification in the WGKP region strongly increases in the upper 100 m, decreases in the layer just below (down to 250–500 m), and increases again at depths down to 2000 m (Fig. <xref ref-type="fig" rid="F8"/>b). The NZ region exhibits an overall increase in stratification, with the strongest anomalies occurring in the upper 100 m.  In contrast, the AU and PA regions show an overall decrease in stratification in the upper 1000–1500 m, and an increase at greater depths.</p>
      <p id="d2e2853">The stratification changes in the convective regions are related to a salinity-dominated reorganization of the water-column structure following the AMOC collapse (Fig. <xref ref-type="fig" rid="FA9"/>).  The increased stratification in the deeper layers of the AU and PA regions, and in the intermediate layers of the NZ and WGKP regions, can be linked to a reduced poleward advection of warm and saline Circumpolar Deep Water (CDW) after the AMOC has weakened. Furthermore, a downward displacement or reorganization of Antarctic Intermediate Water (AAIW), identified by its salinity minimum, leads to reduced vertical salinity gradients causing weakening of the stratification. This mechanism explains the reduced stratification in the upper <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1500</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula> of the AU and PA regions, and the weakening of stratification in the WGKP region between roughly 100 and 250–500 m. Although the reduced stratification barely penetrates into the WGKP region (Fig. <xref ref-type="fig" rid="FA9"/>), it dominates over the otherwise increasing stratification in the same depth range. The stratification changes north of the NZ convective region show a similar structure to those in the WGKP region.</p>
      <p id="d2e2874">Although the stratification weakening over the AU and PA regions induces a slightly deeper mixed-layer (Fig. <xref ref-type="fig" rid="F8"/>c and d), the stratification remains sufficiently strong such that the MLD responses are limited. A weak multidecadal oscillation arises after the collapse of the AMOC with comparable periods to that of the SOM-P index (Fig. <xref ref-type="fig" rid="FA10"/>c and d). In contrast, the stratification over the NZ region remains relatively weak compared to the other three regions (Fig. <xref ref-type="fig" rid="F7"/>c and d), making this region the most prone to the deepest MLD events after the AMOC collapse. The onset of deep convection with strong multidecadal variability (Fig. <xref ref-type="fig" rid="FA10"/>a) in this region is closely linked to the stratification anomalies in the upper 100 m after the AMOC collapse (Figs. <xref ref-type="fig" rid="F7"/>a).</p>

      <fig id="F8" specific-use="star"><label>Figure 8</label><caption><p id="d2e2889">Maximum MLD (black line) and area-averaged <inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> anomalies (with respect to mean <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> over the first 100 model years) in the <bold>(a)</bold> NZ, <bold>(b)</bold> WGKP, <bold>(c)</bold> AU, and <bold>(d)</bold> PA convective regions.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f08.png"/>

        </fig>

      <p id="d2e2934">Up to the AMOC collapse, strong MLD changes occur in the WGKP region with a period closely following that of the SOM index (Fig. <xref ref-type="fig" rid="FA10"/>b). Over these 400 years, the MLD in the NZ region is deep (<inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">800</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula>) but its variability is relatively small (Fig. <xref ref-type="fig" rid="FA10"/>a). Deep convection events in the WGKP convective region follow a convection–restratification mechanism <xref ref-type="bibr" rid="bib1.bibx16 bib1.bibx7 bib1.bibx19" id="paren.65"/>. Heat originating from the inflow of relatively warm North Atlantic Deep Water (NADW) is transported into the Weddell Sea by the westward return flow in the southern branch of the Weddell Gyre, where it remains effectively trapped within the gyre circulation. The accumulation of heat at mid-depth levels destabilizes the water column and can eventually trigger deep convection. Once the mid-depth heat reservoir is depleted, convection shuts down (Fig. <xref ref-type="fig" rid="F8"/>b). The multidecadal recharge of this heat reservoir depends on both the AMOC and the Weddell Gyre circulation <xref ref-type="bibr" rid="bib1.bibx16" id="paren.66"/>, and is closely related to the SOM variability as generated by the eddy-mean flow interaction mechanism described in the previous section. The ACC is modulated by these convective episodes, with the meridional pressure gradient weakening during non-convective phases due to gradual mid-depth warming of waters south of the ACC, and strengthening during convective phases as these waters cool. This variability in the pressure gradient leads to a corresponding weakening or strengthening of the ACC, typically with a lag of a few years (Fig. <xref ref-type="fig" rid="FA11"/>).</p>
      <p id="d2e2966">The stratification over the WGKP region is relatively weak compared to the AU and PA regions (Fig. <xref ref-type="fig" rid="F7"/>), but increases due to the reduced inflow of NADW. As a result, the water column cannot support any deep convection (<inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">1000</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:mrow></mml:math></inline-formula>) events anymore after the AMOC collapse. At the same time, stratification anomalies in the upper 100 m start to appear again over the NZ region, predominantly salinity-driven (not shown), and are apparently sufficient to initiate convection and support relatively strong MLD changes (Fig. <xref ref-type="fig" rid="F8"/>a), which in turn affect the Drake Passage transport. After deep convection ceases in the WGKP region and the SOM cycle vanishes, a pronounced oscillatory signal still persists in the Drake Passage transport with a period similar to that of the SOM-P index (Fig. <xref ref-type="fig" rid="FA1"/>). Deep convection in the NZ region now leads the multidecadal oscillations in the Drake Passage transport (Fig. <xref ref-type="fig" rid="FA11"/>).</p>
      <p id="d2e2991">The occurrence of deep convection events have been linked to an overall strengthening of the ACC, as they facilitate the conversion of potential to kinetic energy, thereby energizing the ocean circulation <xref ref-type="bibr" rid="bib1.bibx42" id="paren.67"/>. Indeed, we find an overall decrease in mean strength of the ACC (Fig. <xref ref-type="fig" rid="F1"/>c), consistent with a decrease in <inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="F4"/>d) and the termination of deep convection events in the WGKP region.</p>
      <p id="d2e3025">This shift in Southern Ocean deep convection from the Atlantic to the Pacific sector is closely linked to the behaviour of the SOM-P index, which starts to exhibit pronounced multidecadal variability around the same time deep convection in the NZ region starts (Fig. <xref ref-type="fig" rid="F9"/>b). The convective episodes in the NZ region now lead the oscillations in the SOM-P index, in a similar way the minima and maxima of the WGKP convective episodes led the minima and maxima of the SOM-index (Fig. <xref ref-type="fig" rid="F9"/>a). Whereas the SOM mechanism involves a combination of eddy–mean flow interactions and deep convection in the WGKP region, the oscillations emerging after the AMOC collapse cannot be explained by the first mechanism, as its signature is not detectable in the mechanical energy budget over the SO30 region. Instead, the SOM-P variability has a purely convective origin and in this way, the Pacific sector becomes the primary source region for multidecadal variability of the Southern Ocean origin when the AMOC has collapsed.</p>

      <fig id="F9" specific-use="star"><label>Figure 9</label><caption><p id="d2e3034"><bold>(a)</bold>: SOM-index (blue), and the maximum MLD in the WGKP region (red). <bold>(b)</bold>: SOM-P index (green), and the maximum MLD in the NZ region (orange). Note that all time series are normalised and mean-centered, and a moving average of 20 years has been applied.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f09.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <label>4</label><title>Conclusions</title>
      <p id="d2e3057">In the strongly-eddying POP model, multidecadal intrinsic variability appears which is not found in the non-eddying version of the same model <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx16 bib1.bibx34" id="paren.68"/>. The same variability, referred to as the Southern Ocean Mode (SOM), occurs in the Community Earth System Model version with a strongly eddying ocean component <xref ref-type="bibr" rid="bib1.bibx30 bib1.bibx1 bib1.bibx37 bib1.bibx10" id="paren.69"/>. It is important to understand the mechanisms of this intrinsic variability in more detail, in addition to other mechanisms which have been suggested, as it is potentially relevant to interpret observed multidecadal Antarctic sea-ice variability <xref ref-type="bibr" rid="bib1.bibx24" id="paren.70"/>.</p>
      <p id="d2e3069">In this study, we use the same strongly-eddying POP version as in <xref ref-type="bibr" rid="bib1.bibx21" id="text.71"/> to study the effect of the AMOC on the SOM. Previous studies have shown that the SOM introduces multidecadal variability (of a few Sv) in the AMOC strength at 26° N caused by northward Rossby wave propagation in the Atlantic Ocean <xref ref-type="bibr" rid="bib1.bibx30" id="paren.72"/>. We demonstrated here that the SOM owes its existence to the density field in the Southern Ocean which is affected by the AMOC. A strong weakening of the AMOC induces substantial changes in the Southern Ocean density structure, leading to the disappearance of the SOM in the Atlantic sector and the emergence of the SOM-P in the Pacific sector. Although a complete understanding of the underlying mechanisms and pathways would require detailed heat- and freshwater budget analyses, our results show consistent salinity-driven stratification changes associated with a reduced poleward advection of CDW and deepening or reorganization of AAIW.</p>
      <p id="d2e3078">An analysis of the terms in the mechanical energy balance shows that eddy-mean flow interactions weaken under a decreasing AMOC strength and that phase differences between the input of the wind (<inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>), and the baroclinic conversion term (<inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>P</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">e</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>) decrease. This disrupts the coupling between eddy generation by baroclinic instability, jet zonality, and wind input. Furthermore, a weakening of the AMOC increases the stratification in the WGKP region, mainly due to reduced upper layer salinities associated with a reduced inflow of NADW, thereby weakening the deep convection events in this region. The primary source of convection appears to shift to the Pacific sector, where deep convection events begin to emerge only after the AMOC has collapsed. These convective events in the Pacific now cause the oscillatory behaviour of the Drake Passage. Although not studied here, this is also expected to affect variability in the Weddell and Ross Gyre circulations <xref ref-type="bibr" rid="bib1.bibx16" id="paren.73"/>.</p>
      <p id="d2e3125">The horizontal and vertical density structure of the Southern Ocean is thus modified in a way that weakens eddy–mean flow interactions and shifts the primary source of deep convection, leading to the disappearance of the SOM. However, despite being very localized, convection in the Pacific sector remains sufficiently strong to sustain a mode of multidecadal variability, namely the SOM-P. Although the exact role of convection in driving multidecadal oscillations in the Southern Ocean remains uncertain, this study also underscores the importance of deep convection events in shaping Southern Ocean multidecadal variability in climate models <xref ref-type="bibr" rid="bib1.bibx10" id="paren.74"/>.</p>
      <p id="d2e3132">While this study is based on an ocean-only model, atmospheric variability is likely to play a role. Although <xref ref-type="bibr" rid="bib1.bibx10" id="text.75"/> found only weak evidence for atmosphere–ocean feedbacks contributing to Southern Ocean multidecadal variability, multidecadal variability in Southern Ocean temperatures or sea-ice extent may influence large-scale climate modes such as the Interdecadal Pacific Oscillation (IPO) through atmospheric teleconnections <xref ref-type="bibr" rid="bib1.bibx1" id="paren.76"/>. Conversely, atmospheric variability, including changes in sea level pressure patterns such as the Amundsen Sea Low <xref ref-type="bibr" rid="bib1.bibx3" id="paren.77"/>, may feed back onto the ocean circulation and variability. This highlights the importance of understanding intrinsic multidecadal variability in the Southern Ocean and its potential coupling to the atmosphere.</p>
      <p id="d2e3144">Although the SOM cannot be clearly identified in the historical record <xref ref-type="bibr" rid="bib1.bibx17" id="paren.78"/>, its presence in the CESM <xref ref-type="bibr" rid="bib1.bibx31 bib1.bibx10" id="paren.79"/>, and the consistency of its underlying mechanism with that of a mode of multidecadal variability identified in a quasi-geostrophic model <xref ref-type="bibr" rid="bib1.bibx13" id="paren.80"/> provide strong support that the SOM is a dynamically meaningful feature in the present-day ocean. The analysis here has clearly demonstrated a strong connection between the SOM and the AMOC, with pronounced changes in multidecadal variability, ocean density field, and deep convection following an AMOC collapse. These changes have significant implications for the mean state of the Southern Ocean, including a marked cooling near the base of the Antarctic ice shelf. This, in turn, affects Antarctic sea-ice variability and basal melt, suppresses deep convection in the Weddell Sea, and may affect teleconnections with other ocean basins.</p>
</sec>

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

<app id="App1.Ch1.S1">
  <label>Appendix A</label><title>Additional figures</title>

      <fig id="FA1"><label>Figure A1</label><caption><p id="d2e3170">Wavelet (Morlet) power spectra for <bold>(a)</bold> the ACC transport, <bold>(b)</bold> the SOM index, and <bold>(c)</bold> the SOM-P index. Black contours indicate power significant at the 95 % level relative to an AR(1) red-noise background. The vertical red line marks the onset of the AMOC collapse, and the white dashed lines indicate the cone of influence.</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f10.png"/>

      </fig>

<fig id="FA2"><label>Figure A2</label><caption><p id="d2e3193">Hövmoller diagram of depth- and zonally-averaged (300–700 m, 55–5° W) <bold>(a)</bold> temperature and <bold>(b)</bold> salinity anomalies with respect to the first 100 model years.</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f11.png"/>

      </fig>

      <fig id="FA3"><label>Figure A3</label><caption><p id="d2e3213">Wavelet (Morlet) power spectra for the quadratically detrended AMOC strength from <bold>(a)</bold> model year 0–415, and for <bold>(b)</bold> model year 450–600. Black contours indicate power significant at the 95 % level relative to an AR(1) red-noise background, and the white dashed lines indicate the cone of influence.</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f12.png"/>

      </fig>

<fig id="FA4"><label>Figure A4</label><caption><p id="d2e3233">Linear density decomposition in the Atlantic sector. Zonal-averaged (60° W–25° E) <bold>(a)</bold> temperature-driven and <bold>(b)</bold> salinity-driven density changes (model year (500–600) minus model year (1–100)). <bold>(c)</bold> Linearised density anomaly, obtained as the sum of the temperature- and salinity-driven contributions. <bold>(d)</bold>: Reconstruction error of the linearised density anomaly relative to the actual density anomaly.</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f13.png"/>

      </fig>

      <fig id="FA5"><label>Figure A5</label><caption><p id="d2e3258">Temperature, salinity, meridional density gradient and zonal velocity differences in the Indian sector. Zonal-averaged (25–150° E) <bold>(a)</bold> temperature, <bold>(b)</bold> salinity, <bold>(c)</bold> meridional density gradient and <bold>(d)</bold> zonal velocity differences in the upper 2500 m before and after the AMOC collapse (model year (500–600) minus model year (1–100)). In <bold>(c)</bold>, the solid (dashed) black lines denote isopycnals of model year 1–100 (500–600). Plotted isopycnals are referenced to 5° N and the displayed (from top to bottom) ones are: 1025.1 (1025.2), 1026.5 (1026.9), and 1027.6 (1027.5) <inline-formula><mml:math id="M134" 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> for model year 1–100 (500–600). In <bold>(d)</bold>, the vertical dashed lines denote the mean ACC latitude band for model year 1–100.</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f14.png"/>

      </fig>

<fig id="FA6"><label>Figure A6</label><caption><p id="d2e3309">Temperature, salinity, meridional density gradient and zonal velocity differences in the Pacific sector. Zonal-averaged (150° E–60° W) <bold>(a)</bold> temperature, <bold>(b)</bold> salinity, <bold>(c)</bold> meridional density gradient and <bold>(d)</bold> zonal velocity differences in the upper 2500 m before and after the AMOC collapse (model year (500–600) minus model year (1–100)). In <bold>(c)</bold>, the solid (dashed) black lines denote isopycnals of model year 1–100 (500–600). Plotted isopycnals are referenced to 5° N and the displayed (from top to bottom) ones are: 1025.6 (1025.6), 1027.0 (1026.9), and 1027.6 (1027.6) <inline-formula><mml:math id="M135" 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> for model year 1–100 (500–600). In <bold>(d)</bold>, the vertical dashed lines denote the mean ACC latitude band for model year 1–100.</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f15.png"/>

      </fig>

      <fig id="FA7"><label>Figure A7</label><caption><p id="d2e3358">Energetics for three different SOM cycles in the Atlantic sector. Similar to Fig. <xref ref-type="fig" rid="F6"/>, but now for the Atlantic sector (90–30° S, 60° W–25° E).</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f16.png"/>

      </fig>

<fig id="FA8"><label>Figure A8</label><caption><p id="d2e3374">Energetics for three different SOM cycles in the Pacific sector. Similar to Fig. <xref ref-type="fig" rid="F6"/>, but now for the Pacific sector (90–30° S, 150° E–60° W).</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f17.png"/>

      </fig>

      <fig id="FA9"><label>Figure A9</label><caption><p id="d2e3389">Zonally averaged <italic>N</italic><sup>2</sup> anomalies in SO30 convective regions. <bold>(a)</bold> Zonally averaged (150–170° E) <inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> in the NZ convective region (model year (500–600) minus (1–100)). <bold>(b)</bold> Same as <bold>(a)</bold>, but now zonally averaged over the WGKP convective region (35–80° W), <bold>(c)</bold> for the AU convective region (80–150° E), and <bold>(d)</bold> for the PA convective region (110–160° W). The solid (dashed) black lines denote zonally averaged isopycnals of model year 1–100 (500–600). Plotted isopycnals are (from top to bottom): 1027.0, 1027.5, and 1027.7 <inline-formula><mml:math id="M137" 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>. The grey vertical lines denote the meridional boundaries of the respective convective regions.</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f18.png"/>

      </fig>

<fig id="FA10"><label>Figure A10</label><caption><p id="d2e3453">Wavelet (Morlet) power spectra for the maximum MLD in <bold>(a)</bold> the NZ convective region, <bold>(b)</bold> the WGKP convective region, <bold>(c)</bold> the AU convective region, and <bold>(d)</bold> the PA convective region. Black contours indicate power significant at the 95 % level relative to an AR(1) red-noise background. The vertical red line marks the onset of the AMOC collapse, and the white dashed lines indicate the cone of influence.</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f19.png"/>

      </fig>

      <fig id="FA11"><label>Figure A11</label><caption><p id="d2e3478">Drake Passage transport (blue), and the maximum MLD in the WGKP region (red) and NZ region (orange). A moving average of 20 years has been applied to all time series.</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/1965/2026/os-22-1965-2026-f20.png"/>

      </fig>


</app>
  </app-group><notes notes-type="codedataavailability"><title>Code and data availability</title>

      <p id="d2e3495">The processed model output and relevant scripts to generate the results are available via <xref ref-type="bibr" rid="bib1.bibx27" id="text.81"/> (<ext-link xlink:href="https://doi.org/10.5281/zenodo.20539702" ext-link-type="DOI">10.5281/zenodo.20539702</ext-link>).</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d2e3507">EJVS, RMvW, and HAD conceived the ideas presented in this study. EJVS performed the analysis and wrote the paper. RMvW and HAD contributed to writing the paper.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e3513">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d2e3519">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. The authors bear the ultimate responsibility for providing appropriate place names. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.</p>
  </notes><ack><title>Acknowledgements</title><p id="d2e3525">Emma J. V. Smolders is funded by Utrecht University. René M. van Westen and Henk A. Dijkstra are funded by the European Research Council through the ERC-AdG project TAOC (PI: Dijkstra, project 101055096). The model simulation and the analysis of all the model output was conducted on the Dutch National Supercomputer Snellius within NWO-SURF project 2024.013. We thank Michael Kliphuis (IMAU, UU) for carrying out these simulations and his support in analysing the data.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d2e3530">This research has been supported by the Utrecht University (grant-no. BN.000732.1).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e3536">This paper was edited by Katsuro Katsumata and reviewed by Quentin Dalaiden and one anonymous referee.</p>
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