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  <front>
    <journal-meta><journal-id journal-id-type="publisher">BG</journal-id><journal-title-group>
    <journal-title>Biogeosciences</journal-title>
    <abbrev-journal-title abbrev-type="publisher">BG</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Biogeosciences</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1726-4189</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/bg-23-6447-2026</article-id><title-group><article-title>Towards circularity in shellfish aquaculture: stimulating mussel shell dissolution in marine sediments</article-title><alt-title>Stimulating mussel shell dissolution in marine sediments</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Goossens</surname><given-names>Cedric</given-names></name>
          <email>cedric.goossens@uantwerpen.be</email>
        <ext-link>https://orcid.org/0000-0002-6161-5979</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2">
          <name><surname>Bouillon</surname><given-names>Steven</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-7669-2929</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Meysman</surname><given-names>Filip J. R.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-5334-7655</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3 aff4">
          <name><surname>van  de Velde</surname><given-names>Sebastiaan J.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-9999-5586</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Geobiology Research Group, University of Antwerp, Wilrijk, 2610, Belgium</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Division of Soil and Water Management, Katholieke Universiteit Leuven, Heverlee, 3001, Belgium</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Department of Marine Science, University of Otago, Ōtepoti Dunedin, 9016, Aotearoa New Zealand</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Earth Sciences New Zealand, Te Whanganui-a-Tara Wellington, 6021, Aotearoa New Zealand</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Cedric Goossens (cedric.goossens@uantwerpen.be)</corresp></author-notes><pub-date><day>17</day><month>September</month><year>2026</year></pub-date>
      
      <volume>23</volume>
      <issue>18</issue>
      <fpage>6447</fpage><lpage>6464</lpage>
      <history>
        <date date-type="received"><day>21</day><month>May</month><year>2026</year></date>
           <date date-type="rev-request"><day>1</day><month>June</month><year>2026</year></date>
           <date date-type="rev-recd"><day>18</day><month>August</month><year>2026</year></date>
           <date date-type="accepted"><day>9</day><month>September</month><year>2026</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2026 Cedric Goossens 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://bg.copernicus.org/articles/23/6447/2026/bg-23-6447-2026.html">This article is available from https://bg.copernicus.org/articles/23/6447/2026/bg-23-6447-2026.html</self-uri><self-uri xlink:href="https://bg.copernicus.org/articles/23/6447/2026/bg-23-6447-2026.pdf">The full text article is available as a PDF file from https://bg.copernicus.org/articles/23/6447/2026/bg-23-6447-2026.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e130">Ocean alkalinity enhancement (OAE) is receiving considerable attention as a carbon dioxide (<inline-formula><mml:math id="M1" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) removal strategy, and novel approaches to increase the total alkalinity (<inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) of the surface ocean are being explored. In bivalve aquaculture, calcification during shell growth consumes <inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, thus leading to <inline-formula><mml:math id="M4" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions. After consumption, shells are typically landfilled or incinerated, which can generate additional <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions. Here, we investigate how the <inline-formula><mml:math id="M6" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> footprint of shellfish aquaculture can be reduced by using bivalve shells as a resource for mineral-based OAE. The idea is to grind the calcium carbonate (<inline-formula><mml:math id="M7" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) shells to increase the reactive surface area and distribute them into permeable, oxygen-rich sediments, where their dissolution produces <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> that could then compensate the <inline-formula><mml:math id="M9" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emitted during calcification. To evaluate this concept, we conducted microcosm incubations of sediments amended with crushed mussel shells (<inline-formula><mml:math id="M10" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 8 <inline-formula><mml:math id="M11" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">wt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula>), and monitored the sediment geochemistry and sediment-water exchange over 24 weeks. Control sediments exhibited low and constant <inline-formula><mml:math id="M12" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution rates (<inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M14" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.9 <inline-formula><mml:math id="M15" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.5 <inline-formula><mml:math id="M16" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) and <inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fluxes (<inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mtext>AT</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M19" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 3.2 <inline-formula><mml:math id="M20" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.1 <inline-formula><mml:math id="M21" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</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">2</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). In contrast, shell-amended sediments showed markedly higher <inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mtext>AT</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values, which exhibited a transient response modulated by oxygen and organic matter availability. Initially, shell dissolution was restricted, most likely by oxygen availability due to the intense mineralization of shell-associated organic matter. Subsequently, following gradual sediment reoxygenation, dissolution rates increased, reaching a maximum <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> of 22.7 <inline-formula><mml:math id="M25" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2.6 <inline-formula><mml:math id="M26" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> after 9 weeks, corresponding to a measured <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mtext>AT</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> of 43.0 <inline-formula><mml:math id="M28" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 6.0 <inline-formula><mml:math id="M29" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. After that, <inline-formula><mml:math id="M30" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution rates declined as organic matter availability decreased, approaching control rates, with a slightly elevated <inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> of 2.2 <inline-formula><mml:math id="M32" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.1 <inline-formula><mml:math id="M33" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at the end of the experiment. After 24 weeks, <inline-formula><mml:math id="M34" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 6 % of the initial shell mass had dissolved, and extrapolation of the dissolution rate at the end of the experiment suggests that complete dissolution would require <inline-formula><mml:math id="M35" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 38 years. Our results suggest that organic matter availability limits <inline-formula><mml:math id="M36" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution in the permeable sediment investigated. This constraint, however, can be alleviated by targeting environments with high organic matter deposition for in-situ applications, such as sediments beneath mussel farms, thereby promoting mussel aquaculture circularity.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Belgian Federal Science Policy Office</funding-source>
<award-id>RV/21/DEHEAT</award-id>
</award-group>
<award-group id="gs2">
<funding-source>Fonds Wetenschappelijk Onderzoek</funding-source>
<award-id>S000619N</award-id>
</award-group>
<award-group id="gs3">
<funding-source>Universiteit Antwerpen</funding-source>
<award-id>BOF</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="d2e579">Climate stabilization requires direct carbon dioxide removal (CDR) from the atmosphere alongside conventional mitigation strategies that prevent new emissions (Gasser et al., 2015; IPCC, 2023; Sanderson et al., 2016). As a consequence, CDR research has gained considerable traction over the last few years (Lück et al., 2025; Minx et al., 2024). Marine CDR options are receiving increased attention due to the large <inline-formula><mml:math id="M37" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> buffering capacity of the ocean, which has taken up about 26 % of the global anthropogenic emissions since 1850 (Friedlingstein et al., 2025). The amount of <inline-formula><mml:math id="M38" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> that can be stored in the ocean is largely controlled by total alkalinity (<inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), which is a measure of the excess of proton acceptors (bases) over proton donors (acids) in solution (Dickson, 1981; Zeebe and Wolf-Gladrow, 2001). An increase in <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> causes the carbonate system to respond by dissociating dissolved <inline-formula><mml:math id="M41" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to bicarbonate (<inline-formula><mml:math id="M42" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) and carbonate (<inline-formula><mml:math id="M43" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula>), resulting in an increased uptake of atmospheric <inline-formula><mml:math id="M44" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Ocean alkalinity enhancement (OAE) represents one of the proposed marine CDR methods, and aims to establish higher oceanic <inline-formula><mml:math id="M45" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> uptake by artificially increasing <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> levels in the surface ocean (Oschlies et al., 2023; Renforth and Henderson, 2017).</p>
      <p id="d2e700">In recent years, a number of OAE approaches have been investigated in which minerals (silicates and carbonates) are added to coastal sediments (Fuhr et al., 2022, 2023, 2024, 2025). These minerals subsequently undergo a slow weathering process, which releases <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Up until now, most attention has gone towards purposely mined minerals, such as the silicate mineral olivine (e.g., Flipkens et al., 2023; Geerts et al., 2025; Hangx and Spiers, 2009; Meysman and Montserrat, 2017; Montserrat et al., 2017). Yet, mining operations require energy, generate environmental impacts, and are challenging to rapidly scale, as new mining sites require long permitting trajectories. Therefore, an alternative option is to consider minerals for OAE that are sourced from side and waste streams from existing industrial activities (Bullock et al., 2021). One such activity is bivalve aquaculture. During shell formation, bivalves remove dissolved inorganic carbon (DIC) from the water to form calcium carbonate (<inline-formula><mml:math id="M48" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>). Yet, like any form of carbonate formation, this process also removes <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, as the precipitation of 1 <inline-formula><mml:math id="M50" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mol</mml:mi></mml:mrow></mml:math></inline-formula> of <inline-formula><mml:math id="M51" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> consumes 2 <inline-formula><mml:math id="M52" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mol</mml:mi></mml:mrow></mml:math></inline-formula> of <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and 1 <inline-formula><mml:math id="M54" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mol</mml:mi></mml:mrow></mml:math></inline-formula> of DIC:

          <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M55" display="block"><mml:mrow><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow><mml:mo>↔</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:mrow></mml:math></disp-formula></p>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e837"><bold>(a)</bold> Thermodynamic equilibrium plot of alkalinity (<inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) as a function of dissolved inorganic carbon (DIC) superimposed on contours of partial pressure of <inline-formula><mml:math id="M57" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M58" display="inline"><mml:mrow class="chem"><mml:mi>p</mml:mi><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) at 15 <inline-formula><mml:math id="M59" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> and a salinity of 35. Black dot: initial seawater concentration. Calcification (vector 1) reduces <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and DIC in a <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> ratio, which increases <inline-formula><mml:math id="M62" display="inline"><mml:mrow class="chem"><mml:mi>p</mml:mi><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and leads to <inline-formula><mml:math id="M63" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> degassing to the atmosphere. Carbonate dissolution (vector 2) increases <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and DIC in a <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> ratio, which decreases <inline-formula><mml:math id="M66" display="inline"><mml:mrow class="chem"><mml:mi>p</mml:mi><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and leads to <inline-formula><mml:math id="M67" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> uptake from the atmosphere. <bold>(b)</bold> Conceptual scheme illustrating the life cycle of bivalve shells from aquaculture (using mussels as example). Bivalves remove <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and dissolved inorganic carbon (DIC) from seawater to form calcium carbonate shells (<inline-formula><mml:math id="M69" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>), a process that releases <inline-formula><mml:math id="M70" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. After harvest and consumption, shell waste is typically incinerated (with associated <inline-formula><mml:math id="M71" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emission and landfill of <inline-formula><mml:math id="M72" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">CaO</mml:mi></mml:mrow></mml:math></inline-formula>-containing ashes) or directly landfilled. The dashed arrows depict the circular route investigated here. Crushed shells are spread onto shallow sediments, where <inline-formula><mml:math id="M73" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution generates <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and leads to atmospheric <inline-formula><mml:math id="M75" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> uptake. The overall process offsets the <inline-formula><mml:math id="M76" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> released during shell growth.</p></caption>
        <graphic xlink:href="https://bg.copernicus.org/articles/23/6447/2026/bg-23-6447-2026-f01.png"/>

      </fig>

      <p id="d2e1090">Overall, carbonate formation results in an increase in the partial pressure of <inline-formula><mml:math id="M77" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M78" display="inline"><mml:mrow class="chem"><mml:mi>p</mml:mi><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) in seawater (Fig. 1a; Frankignoulle et al., 1994, 1995). In shallow coastal environments, where bivalve aquaculture typically takes place, rapid equilibration of the elevated <inline-formula><mml:math id="M79" display="inline"><mml:mrow class="chem"><mml:mi>p</mml:mi><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> with the atmosphere will result in outgassing of most of the <inline-formula><mml:math id="M80" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> produced during <inline-formula><mml:math id="M81" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> formation. As such, bivalve production induces a release of <inline-formula><mml:math id="M82" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> into the atmosphere (Pernet et al., 2025).</p>
      <p id="d2e1164">With a current global production of over 17 million <inline-formula><mml:math id="M83" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:math></inline-formula> of bivalves per year (FAO, 2024, 2025), bivalve aquaculture generates considerable <inline-formula><mml:math id="M84" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions associated with calcification (<inline-formula><mml:math id="M85" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 4 million  <inline-formula><mml:math id="M86" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">t</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). Life cycle assessments (LCAs) of bivalve aquaculture typically do not account for <inline-formula><mml:math id="M87" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions from calcification (see Ray et al., 2018 and references therein), thus resulting in an underestimation of its climate impact. When taken into account, calcification may account for up to 90 % of the total emissions (Ray et al., 2018; Thrane, 2004). Moreover, shell waste is typically disposed of as general waste, either through landfilling or incineration. While landfilling retains the <inline-formula><mml:math id="M88" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> mineral phase, incineration can result in additional <inline-formula><mml:math id="M89" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions because <inline-formula><mml:math id="M90" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> thermally decomposes into calcium oxide (<inline-formula><mml:math id="M91" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">CaO</mml:mi></mml:mrow></mml:math></inline-formula>, quicklime) and <inline-formula><mml:math id="M92" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> at high temperatures (Fig. 1b):

          <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M93" display="block"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:mi mathvariant="normal">CaO</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e1304">Following incineration, the resulting ash may be disposed of in landfill sites. Under these conditions, some <inline-formula><mml:math id="M94" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">CaO</mml:mi></mml:mrow></mml:math></inline-formula> may subsequently react with <inline-formula><mml:math id="M95" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> to reform <inline-formula><mml:math id="M96" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>; however, the extent of this carbonation remains uncertain and depends strongly on landfill conditions.</p>
      <p id="d2e1337">In this study, we explore an alternative destination for the <inline-formula><mml:math id="M97" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>-containing shells after consumption. The core idea is to offset <inline-formula><mml:math id="M98" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions associated with calcification (Eq. 1) by reintroducing mussel shells into the marine environment and stimulating shell dissolution (Fig. 1b). The key question is whether the mussel shells will effectively dissolve, and if so, under which conditions and over which timeframes. The precipitation and dissolution of <inline-formula><mml:math id="M99" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> are controlled by the <inline-formula><mml:math id="M100" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> saturation state of seawater (Zeebe and Wolf-Gladrow, 2001) and the reactive surface area of the <inline-formula><mml:math id="M101" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> minerals. Since surface waters are typically oversaturated with respect to <inline-formula><mml:math id="M102" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, dissolution generally does not occur in the water column (Kleypas, 2011; Morse and Mackenzie, 1990). However, <inline-formula><mml:math id="M103" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution is possible in the pore water of marine sediments under specific conditions, in a process referred to as metabolic carbonate dissolution, in which <inline-formula><mml:math id="M104" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> generated by aerobic mineralization of organic matter builds up in the pore water until undersaturation is achieved and <inline-formula><mml:math id="M105" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> starts to dissolve (Aller, 1982; Archer et al., 1989; Emerson and Bender, 1981; Lunstrum and Berelson, 2022; Morse et al., 1985; Subhas et al., 2022):

          <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M106" display="block"><mml:mrow><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">HCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:mrow></mml:math></disp-formula>

        The above reaction equation also succinctly summarizes the conditions that promote metabolic <inline-formula><mml:math id="M107" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution: (1) permeable sediments that enable deep oxygen penetration; (2) sediments sufficiently rich in organic matter, which drives metabolic dissolution; and (3) low ambient <inline-formula><mml:math id="M108" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> concentration, thereby limiting buffering from background <inline-formula><mml:math id="M109" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (Goossens et al., 2026). Dissolution efficiency could further be improved by grinding shells to a finer size to increase their reactive surface area and enhance their intrinsic dissolution rate. Likewise, the sediments should be located within shallow waters with a well-mixed water column as to allow rapid <inline-formula><mml:math id="M110" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> equilibration with the atmosphere.</p>
      <p id="d2e1538">Here, we assessed the potential for enhanced sedimentary dissolution of <inline-formula><mml:math id="M111" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> shells derived from the blue mussel (<italic>Mytilus edulis</italic>), a species that dominates shellfish aquaculture in Belgium and the Netherlands (FAO, 2025). Previous studies on biogenic shell dissolution (see Gazeau et al., 2013 for an overview) have considered a range of taxa, including oysters (Waldbusser et al., 2011; Welladsen et al., 2010), clams (Green et al., 2004, 2009; McClintock et al., 2009), limpets (McClintock et al., 2009), and snails (Nienhuis et al., 2010), but only a limited number focused on sedimentary environments (Green et al., 2004, 2009). Furthermore, relatively little attention has been given to mussel shells; the few studies that address their dissolution primarily focus on ocean acidification experiments using chemically altered (sea)water conditions (Carlson et al., 2025; Cubillas et al., 2005; Ericson and Ragg, 2022; Gazeau et al., 2007; Melzner et al., 2011). Here, we address this gap by performing laboratory flux incubations with permeable, <inline-formula><mml:math id="M112" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>-poor coastal sediments amended with crushed blue mussel shells.</p>

      <fig id="F2" specific-use="star"><label>Figure 2</label><caption><p id="d2e1569"><bold>(a)</bold> Map of the Belgian part of the North Sea (BPNS), showing the sediment collection site (Bruggen en Wegen) and the mussel farming site (Westdiep Sea Farm). An overview map of the North Sea is provided with the location of the BPNS in red. <bold>(b)</bold> Experimental setup, consisting of 3 control chambers and 3 treatment chambers amended with crushed mussel shells. Chamber and sediment dimensions are displayed in <inline-formula><mml:math id="M113" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula>. <bold>(c)</bold> Chamber top lids contained 3 sampling ports: one was used for an oxygen probe, and the other two for subsampling of the overlying water. Arrows indicate water flow during subsampling: subsamples were taken from one port, while replacement water was added through the other port. <bold>(d)</bold> Stirring disk rotation induced pore-water exchange through a radial pressure gradient. Arrows indicate pore-water flow through the sediment column.</p></caption>
        <graphic xlink:href="https://bg.copernicus.org/articles/23/6447/2026/bg-23-6447-2026-f02.png"/>

      </fig>

</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Materials and Methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Sediment collection and incubation setup</title>
      <p id="d2e1612">Sediment was collected from a shallow site in the southern North Sea along the Belgian coast (station “Bruggen en Wegen Oostende”, 51.28300° N 2.92133° E; Fig. 2a) on 20 March 2023. The location is a dredge deposit site characterized by permeable sediment. Sediment was collected using a Van Veen grab sampler, transported to the laboratory, homogenized and stored in the dark at stable room temperature (18–22 <inline-formula><mml:math id="M114" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>) with 20 <inline-formula><mml:math id="M115" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> of overlying seawater until further use. While the sediment was not sieved prior to incubation, visual inspection during homogenization and sediment sampling did not reveal any presence of macrofauna. Air pumps were installed to keep the overlying seawater oxygenated. A subsample of sediment was taken for analysis of grain size distribution and porosity. Natural seawater was used as overlying water in the sediment incubations. This seawater was collected from the Eastern Scheldt (The Netherlands) and filtered through a sand filter (0.5 <inline-formula><mml:math id="M116" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mm</mml:mi></mml:mrow></mml:math></inline-formula>) to remove macrofauna. Blue mussels (<italic>Mytilus edulis</italic>) were sourced from the supermarket and originated from a hanging culture at the Westdiep Sea Farm, a mussel farming site <inline-formula><mml:math id="M117" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5 <inline-formula><mml:math id="M118" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> off the Belgian coast at 15 <inline-formula><mml:math id="M119" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> water depth in the southern North Sea (51.16975° N, 2.63104° E; Fig. 2a). Mussel tissue was manually removed, shells were rinsed with fresh water and dried overnight in a drying oven at 60 <inline-formula><mml:math id="M120" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>. Dried shells were ground with an ultra-centrifugal mill (ZM 200, Retsch) and the fraction that passed a 0.25 <inline-formula><mml:math id="M121" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mm</mml:mi></mml:mrow></mml:math></inline-formula> sieve was retained. The potential influence of fine shell particles on sediment permeability therefore cannot be completely ruled out. Ground shell samples were collected for analysis of organic and inorganic carbon concentration.</p>
      <p id="d2e1686">The sediment microcosms were adapted for the closed incubation of permeable sediments following a well-known flux chamber design (Huettel and Gust, 1992). The flux chambers consisted of polymethyl methacrylate (PMMA) core barrels (19 <inline-formula><mml:math id="M122" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> inner diameter, 30 <inline-formula><mml:math id="M123" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> height) fitted with a top and bottom lid (Fig. 2b and c). Top lids were equipped with a stirring disk (14 <inline-formula><mml:math id="M124" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> diameter), which mixes the overlying seawater and also creates a radial pressure gradient that drives advective pore-water exchange in the permeable sediment (Fig. 2d; Huettel and Gust, 1992). Three sampling ports were installed in the top lids (Fig. 2c): one was used for a fiber-optical oxygen probe (FireSting OXROB10, PyroScience), and the other two for subsampling of the overlying seawater during the incubation.</p>
      <p id="d2e1713">The experimental setup consisted of 6 flux chambers: 3 replicate control chambers were filled solely with natural sediment (<inline-formula><mml:math id="M125" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 13 <inline-formula><mml:math id="M126" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula>), while 3 replicate treatment chambers were filled with a base layer of natural sediment (<inline-formula><mml:math id="M127" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 11 <inline-formula><mml:math id="M128" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula>) and a top layer of natural sediment (<inline-formula><mml:math id="M129" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 2 <inline-formula><mml:math id="M130" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula>) mixed with 100 <inline-formula><mml:math id="M131" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi></mml:mrow></mml:math></inline-formula> of ground shells, to achieve a concentration of <inline-formula><mml:math id="M132" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 8 <inline-formula><mml:math id="M133" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">wt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula> of added shell material in the mixed top layer. Solid-phase samples for the analysis of total, organic, and inorganic carbon (and its stable isotope composition, i.e. <inline-formula><mml:math id="M134" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> values) were collected from the surface sediment in the control and treatment chambers. Oxygenated filtered seawater (<inline-formula><mml:math id="M135" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 4.2 <inline-formula><mml:math id="M136" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">L</mml:mi></mml:mrow></mml:math></inline-formula>) was added to the chambers at the start of the incubation. Top lids were installed and chambers were placed in a closed container filled with water to ensure a dark and stable environment.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Solute flux incubation</title>
      <p id="d2e1825">Consecutive flux sessions were performed to quantify the uptake or release of solutes across the sediment-water interface by monitoring their accumulation in the overlying water. A total of 11 flux incubation sessions were conducted over the course of 24 weeks (each flux session lasted <inline-formula><mml:math id="M137" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 10 <inline-formula><mml:math id="M138" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">d</mml:mi></mml:mrow></mml:math></inline-formula>). Before each flux session, the overlying water in the flux chamber was replaced in order to start a new monitoring period of solute accumulation. Each flux session consisted of two parts: a short “closed” part (<inline-formula><mml:math id="M139" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 3 <inline-formula><mml:math id="M140" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">d</mml:mi></mml:mrow></mml:math></inline-formula>) and a longer “open” part (<inline-formula><mml:math id="M141" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 7 <inline-formula><mml:math id="M142" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">d</mml:mi></mml:mrow></mml:math></inline-formula>), as further detailed below. Throughout the session, the rotating disks were set at 80 rounds per minute (<inline-formula><mml:math id="M143" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">rpm</mml:mi></mml:mrow></mml:math></inline-formula>) to stimulate advective pore-water exchange with the overlying water while not disturbing the sediment (i.e., no resuspension). The total time of a single incubation was adjusted to prevent excessive solute concentration build-up (i.e., to avoid saturation effects and secondary mineral precipitation). Before each session, oxygen optodes were calibrated using a two-point calibration with seawater at 0 % (saturated with <inline-formula><mml:math id="M144" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">Na</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) and 100 % (bubbled with air pumps) <inline-formula><mml:math id="M145" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> saturation.</p>
      <p id="d2e1909">In the first “closed” part of the incubation session, atmospheric exchange was prevented by closing the gas-tight top lids. The aim was to obtain <inline-formula><mml:math id="M146" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and DIC fluxes, which necessitate isolation from the atmosphere. Closed incubations lasted until the <inline-formula><mml:math id="M147" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> saturation had dropped from <inline-formula><mml:math id="M148" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 100 % at the start to <inline-formula><mml:math id="M149" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 60 % to prevent excessive disturbance of the balance between aerobic and anaerobic processes in the sediment (which may influence <inline-formula><mml:math id="M150" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution). Water samples (25 <inline-formula><mml:math id="M151" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mL</mml:mi></mml:mrow></mml:math></inline-formula>) were taken from one sampling port, while simultaneously replacing the sampled volume with stock seawater through the other port (Fig. 2c). Sampling was done at variable time intervals (5 time points), with samples collected after every <inline-formula><mml:math id="M152" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 8 % decrease in <inline-formula><mml:math id="M153" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> saturation. Oxygen concentrations were continuously monitored at one-second intervals with the optode. Samples for dissolved inorganic carbon (DIC, 12 <inline-formula><mml:math id="M154" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mL</mml:mi></mml:mrow></mml:math></inline-formula>) and the stable isotope composition of DIC (<inline-formula><mml:math id="M155" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula>, 6 <inline-formula><mml:math id="M156" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mL</mml:mi></mml:mrow></mml:math></inline-formula>) were filtered (Acrodisc Syringe Filter, 0.8/0.2 <inline-formula><mml:math id="M157" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>) and collected in glass exetainers, poisoned with 10 <inline-formula><mml:math id="M158" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">L</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">HgCl</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and stored upside down in the dark at 4 <inline-formula><mml:math id="M159" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d2e2057">After the closed incubation, chambers were opened and allowed to reoxygenate, and salinity was measured in the overlying water. In the subsequent “open” incubation, atmospheric exchange was enabled by opening the top lids and placing small bars between the chambers and the lids to keep the overlying water oxygenated. Water samples (60 <inline-formula><mml:math id="M160" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mL</mml:mi></mml:mrow></mml:math></inline-formula>) were taken directly from the overlying water at fixed time intervals (<inline-formula><mml:math id="M161" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 24 <inline-formula><mml:math id="M162" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">h</mml:mi></mml:mrow></mml:math></inline-formula> in between) with 5–6 time points in total. At every time point, salinity was measured in the overlying water (as to track potential evaporation). Samples for <inline-formula><mml:math id="M163" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (50 <inline-formula><mml:math id="M164" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mL</mml:mi></mml:mrow></mml:math></inline-formula>) and nutrients (9 <inline-formula><mml:math id="M165" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mL</mml:mi></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M166" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M167" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>) were filtered through a dual-layer filter (Acrodisc Syringe Filter, 0.8/0.2 <inline-formula><mml:math id="M168" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>), collected in plastic vials, and stored unpoisoned in the dark at 4 and <inline-formula><mml:math id="M169" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>20 <inline-formula><mml:math id="M170" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>, respectively. Both <inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and DIC samples were analyzed within the same week of collection or, at most, during the following week to ensure accurate monitoring of fluxes and minimize potential changes in sample composition during storage.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Pore-water sampling</title>
      <p id="d2e2184">At the end of the final flux session, 2 small core liners were inserted into the sediment and recovered for pore-water analysis. Cores were sectioned in an anaerobic glove box at 0.5 <inline-formula><mml:math id="M172" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> intervals for the 0–2 <inline-formula><mml:math id="M173" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> depth range, 1 <inline-formula><mml:math id="M174" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> intervals for the 2–6 <inline-formula><mml:math id="M175" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> depth range, and 2 <inline-formula><mml:math id="M176" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> intervals for the remaining depth. Pore water was extracted from sediment slices using rhizon samplers. Pore-water samples from one core liner were collected for Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) analysis (<inline-formula><mml:math id="M177" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>; 0.5 <inline-formula><mml:math id="M178" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mL</mml:mi></mml:mrow></mml:math></inline-formula>), stored in plastic tubes, diluted 10 times with 0.7 M <inline-formula><mml:math id="M179" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">HNO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and stored in the dark at 4 <inline-formula><mml:math id="M180" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>. Pore-water samples from the second core liner were collected for DIC and <inline-formula><mml:math id="M181" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula> (only samples <inline-formula><mml:math id="M182" display="inline"><mml:mo>≥</mml:mo></mml:math></inline-formula> 1 <inline-formula><mml:math id="M183" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mL</mml:mi></mml:mrow></mml:math></inline-formula> were retained), poisoned with 10 <inline-formula><mml:math id="M184" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">L</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msub><mml:mi mathvariant="normal">HgCl</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and stored upside down in exetainers in the dark at 4 <inline-formula><mml:math id="M185" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>.</p>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Analytical methods</title>
      <p id="d2e2338">Grain size distribution was determined using a laser diffraction particle size analyzer (Malvern 2000, Malvern Panalytical) with a precision of <inline-formula><mml:math id="M186" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 3 % relative standard deviation (RSD) for <inline-formula><mml:math id="M187" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">D</mml:mi><mml:mn mathvariant="normal">50</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M188" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 5 % for <inline-formula><mml:math id="M189" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">D</mml:mi><mml:mn mathvariant="normal">10</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M190" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">D</mml:mi><mml:mn mathvariant="normal">90</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. Porosity was derived from weight loss after freeze-drying, accounting for salt content in the pore water, which was assumed to be equal to the salt content in the overlying water.</p>
      <p id="d2e2388">Solid-phase samples were analyzed for total carbon and organic carbon content as well as <inline-formula><mml:math id="M191" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> values through combustion using an elemental analyzer (EA 1110, CE Instruments), connected via a Conflo IV Universal Continuous Flow Interface (Thermo Fisher Scientific) to an Isotope Ratio Mass Spectrometer (IRMS; Thermo Delta V Advantage, Thermo Fisher Scientific). Calibration was done using certified reference material IAEA-600 (<inline-formula><mml:math id="M192" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M193" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M194" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>27.77 ‰; carbon content <inline-formula><mml:math id="M195" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 49.49 %) and in-house standards Leucine (<inline-formula><mml:math id="M196" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M197" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M198" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>13.73 ‰; carbon content <inline-formula><mml:math id="M199" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 54.72 %) and Tuna (<inline-formula><mml:math id="M200" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M201" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M202" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>17.96 ‰; carbon content <inline-formula><mml:math id="M203" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 45.24 %), which were calibrated against IAEA-600. Values of <inline-formula><mml:math id="M204" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> are expressed relative to the international standard Vienna PeeDee Belemnite (VPDB), with a precision for carbon content of <inline-formula><mml:math id="M205" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 2 % (RSD) and <inline-formula><mml:math id="M206" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.08 ‰ (1 SD) for <inline-formula><mml:math id="M207" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>. To determine organic carbon content and <inline-formula><mml:math id="M208" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>, subsamples were weighed into Ag cups and acidified with <inline-formula><mml:math id="M209" display="inline"><mml:mrow class="chem"><mml:mi mathvariant="normal">HCl</mml:mi></mml:mrow></mml:math></inline-formula> (10 %, 40 <inline-formula><mml:math id="M210" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:mrow></mml:math></inline-formula> or until no further reaction was observed) to remove inorganic carbon. Solid-phase samples were analyzed for inorganic carbon content and associated <inline-formula><mml:math id="M211" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> composition using a Gasbench II coupled to an IRMS (Thermo Delta Plus XP, Thermo Fisher Scientific). Calibration was done using certified reference materials LSVEC (<inline-formula><mml:math id="M212" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M213" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M214" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>46.60 ‰) and NBS19 (<inline-formula><mml:math id="M215" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M216" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1.95 ‰) and in-house standards Merck (<inline-formula><mml:math id="M217" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M218" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M219" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>9.65 ‰) and Fluka (<inline-formula><mml:math id="M220" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M221" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M222" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2.36</mml:mn></mml:mrow></mml:math></inline-formula> ‰), which were calibrated against LSVEC and NBS19. Values were expressed relative to VPDB, with a precision of <inline-formula><mml:math id="M223" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 0.1 ‰ (1 SD).</p>
      <p id="d2e2706">Nutrients were analyzed using a continuous flow analyzer (SAN++, Skalar Analytical). Calibration was done using stock solutions made with <inline-formula><mml:math id="M224" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:mi mathvariant="normal">Cl</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M225" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">NaNO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, verified with diluted standard quality control solutions for <inline-formula><mml:math id="M226" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> (Merck Millipore, reference 1.19812.0500) and <inline-formula><mml:math id="M227" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> (Merck Millipore, reference 1.19811.0500), respectively. The precision (RSD) was 5.9 % (low range) and 0.8 % (high range) for <inline-formula><mml:math id="M228" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>, and 1.5 % (low range) and 1.4 % (high range) for <inline-formula><mml:math id="M229" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula>. Dissolved inorganic carbon was analyzed using a DIC analyzer (AS-C6L, Apollo SciTech) coupled to a trace gas analyzer (LI-7810, LICOR). Calibration was done using Dickson certified reference material (batch 209; DIC <inline-formula><mml:math id="M230" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 2060.05 <inline-formula><mml:math id="M231" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">mol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) with a precision (RSD) of 0.16 %. Alkalinity was analyzed using a titrator (Titrando 888, Metrohm) with a 1 <inline-formula><mml:math id="M232" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mL</mml:mi></mml:mrow></mml:math></inline-formula> buret. Calibration was done using Dickson certified reference material (batch 209; <inline-formula><mml:math id="M233" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M234" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 2210.40 <inline-formula><mml:math id="M235" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">mol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) with a precision (RSD) of 0.08 %. Dissolved pore-water <inline-formula><mml:math id="M236" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> was analyzed using an ICP-OES elemental analyzer (AVIO500; Perkin Elmer), using indium as internal standard and the precision was generally <inline-formula><mml:math id="M237" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 2.5 % (RSD).</p>
</sec>
<sec id="Ch1.S2.SS5">
  <label>2.5</label><title>Solute flux calculations</title>
      <p id="d2e2888">Sediment-water flux calculations were performed using the R-based software FLUXER, which also provides robust data quality checks (Hylén and van de Velde, 2025). Solute fluxes (<inline-formula><mml:math id="M238" display="inline"><mml:mi>F</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M239" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</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">2</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, normalized to sediment surface area) were determined from the linear regression of overlying water concentrations over time.

            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M240" display="block"><mml:mrow><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mi>A</mml:mi></mml:mfrac></mml:mstyle><mml:mo>⋅</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mtext>ow</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mtext>ow</mml:mtext></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:msub><mml:mi>H</mml:mi><mml:mtext>ow</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="normal">d</mml:mi><mml:msub><mml:mi>C</mml:mi><mml:mtext>ow</mml:mtext></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:mrow></mml:math></disp-formula>

          <inline-formula><mml:math id="M241" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mtext>ow</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the volume of the overlying water, <inline-formula><mml:math id="M242" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> is the surface area of the sediment, and <inline-formula><mml:math id="M243" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mtext>ow</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the concentration of the solute in the overlying water. The term <inline-formula><mml:math id="M244" display="inline"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mtext>ow</mml:mtext></mml:msub><mml:mo>/</mml:mo><mml:mi>A</mml:mi></mml:mrow></mml:math></inline-formula> can be replaced by the height <inline-formula><mml:math id="M245" display="inline"><mml:mrow><mml:msub><mml:mi>H</mml:mi><mml:mtext>ow</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> of the overlying water, which was measured once during each session (as the mean of 4 different locations along the circumference of the chamber). Solute concentrations were corrected for dilution resulting from sample volume replacement in both types of incubations before flux calculations. Daily measurement of salinity during open incubations indicated no effect of evaporation.</p>
      <p id="d2e3044">FLUXER assumes simple linear regression by default, but can switch to a quadratic regression model when non-linear trends are detected, for example due to saturation effects from dissolved compound buildup (Devol et al., 1997; Forja and Gómez-Parra, 1998). To evaluate whether a linear of quadratic regression model is appropriate, FLUXER uses the corrected Akaike Information Criterion (cAIC; Hurvich and Tsai, 1989). The regression model with the lowest cAIC was selected, and a difference of <inline-formula><mml:math id="M246" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 2 was considered to be meaningful (Burnham and Anderson, 2004).</p>
      <p id="d2e3054">For each model, FLUXER displayed five diagnostic graphs to ensure good model fit and assess whether assumptions for linear regression were fulfilled (Montgomery et al., 2012): (1) residuals versus fitted values, which provided information about data linearity; (2) scale-location plot, which provided information about homoscedasticity; (3) residuals versus time, which provided information about the randomness of errors; (4) normal Q-Q (quantile-quantile) plot, which provided information about the error distribution; and (5) influence plot, which helped to identify points that had a high influence on the model (i.e., outliers) using studentized deleted residuals (SDR), hat values and Cook's distance values as indicators. We refer the reader to the <italic>theoretical background</italic> section of FLUXER for a detailed discussion of how to interpret the diagnostic graphs (Hylén and van de Velde, 2025).</p>
</sec>
<sec id="Ch1.S2.SS6">
  <label>2.6</label><title><inline-formula><mml:math id="M247" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution rates</title>
      <p id="d2e3079">Carbonate dissolution rates were calculated using the Keeling plot method (Keeling, 1958, 1961; Pataki et al., 2003), which is based on an isotope mass balance. In closed incubations, the DIC concentration (<inline-formula><mml:math id="M248" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">mol</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">L</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) of the overlying water (<inline-formula><mml:math id="M249" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">ow</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) is the sum of the background DIC concentration at the start of the incubation (<inline-formula><mml:math id="M250" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and the source DIC concentration (<inline-formula><mml:math id="M251" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), which is added to the overlying water by sedimentary processes:

                <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M252" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E5"><mml:mtd><mml:mtext>5</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">ow</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E6"><mml:mtd><mml:mtext>6</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mo>(</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">ow</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">ow</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mo>(</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>⋅</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow><mml:mo>(</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo><mml:mo>⋅</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d2e3269">Combining Eqs. (5) and (6) gives a first-order equation in the measured values of <inline-formula><mml:math id="M253" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula> (‰) of overlying water (<inline-formula><mml:math id="M254" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">ow</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) over <inline-formula><mml:math id="M255" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">ow</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:math></inline-formula>.

            <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M256" display="block"><mml:mtable class="split" rowspacing="0.2ex" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">ow</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow><mml:mo>⋅</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msub></mml:mrow><mml:mo>-</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mfenced></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>⋅</mml:mo><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">ow</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

          The isotope ratios of source and background can be obtained by a linear regression. The intercept yields <inline-formula><mml:math id="M257" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Since there are two sedimentary processes that generate DIC, i.e., organic matter mineralization and <inline-formula><mml:math id="M258" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution, that each have a distinct isotopic signature, the relative contribution of each process to the total DIC can be derived.

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M259" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E8"><mml:mtd><mml:mtext>8</mml:mtext></mml:mtd><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>f</mml:mi><mml:mtext>OM</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E9"><mml:mtd><mml:mtext>9</mml:mtext></mml:mtd><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">PIC</mml:mi></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mtext>OM</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">POC</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d2e3556">The fraction of DIC generated by carbonate dissolution hence becomes:

            <disp-formula id="Ch1.E10" content-type="numbered"><label>10</label><mml:math id="M260" display="block"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:msub><mml:mi mathvariant="normal">DIC</mml:mi><mml:mi mathvariant="normal">s</mml:mi></mml:msub></mml:mrow><mml:mo>-</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">POC</mml:mi></mml:msub></mml:mrow></mml:mrow><mml:mrow><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">PIC</mml:mi></mml:msub></mml:mrow><mml:mo>-</mml:mo><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">POC</mml:mi></mml:msub></mml:mrow></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>

          In these equations, <inline-formula><mml:math id="M261" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M262" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>OM</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> are the fractions of total DIC derived from <inline-formula><mml:math id="M263" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution and organic matter mineralization, respectively, while <inline-formula><mml:math id="M264" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">PIC</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M265" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">POC</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are the isotopic compositions of <inline-formula><mml:math id="M266" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and organic matter. At saturation (<inline-formula><mml:math id="M267" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M268" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 1), the theoretical maximum <inline-formula><mml:math id="M269" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is 0.5 (50 %), corresponding to fully efficient metabolic carbonate dissolution, where half of the total DIC pool originates from organic matter mineralization and the other half from <inline-formula><mml:math id="M270" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution (Eq. 3). Finally, the <inline-formula><mml:math id="M271" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution rate (<inline-formula><mml:math id="M272" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M273" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, normalized to sediment surface area) and metabolic <inline-formula><mml:math id="M274" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution efficiency (MCDE, %) can be calculated from <inline-formula><mml:math id="M275" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and the measured DIC flux (<inline-formula><mml:math id="M276" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>) via:

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M277" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E11"><mml:mtd><mml:mtext>11</mml:mtext></mml:mtd><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E12"><mml:mtd><mml:mtext>12</mml:mtext></mml:mtd><mml:mtd><mml:mstyle displaystyle="true" class="stylechange"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mtext> MCDE</mml:mtext><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>⋅</mml:mo><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d2e3886">Note that our experimental setup precludes any external methane sources.</p>

<table-wrap id="T1" specific-use="star"><label>Table 1</label><caption><p id="d2e3892">Particulate organic carbon (POC), particulate inorganic carbon (PIC), and calcium carbonate (<inline-formula><mml:math id="M278" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) concentrations (assuming all PIC is <inline-formula><mml:math id="M279" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) of the sediments in the control and treatment chambers, as well as the added mussel shells. The <inline-formula><mml:math id="M280" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> isotopic compositions are also provided. Values for treatment chambers are based on the top layer (2 <inline-formula><mml:math id="M281" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula>) composition (sediment mixed with crushed mussel shells). Uncertainties of the chamber values are standard deviations based on triplicate chambers. Uncertainties of the mussel shell values are standard deviations based on 4 samples.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="6">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1"/>
         <oasis:entry colname="col2">POC (<inline-formula><mml:math id="M282" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">wt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M283" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">POC</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (‰)</oasis:entry>
         <oasis:entry colname="col4">PIC (<inline-formula><mml:math id="M284" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">wt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col5"><inline-formula><mml:math id="M285" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M286" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">wt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M287" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">PIC</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (‰)</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">Control chamber (<inline-formula><mml:math id="M288" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">0.08 <inline-formula><mml:math id="M289" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M290" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>23.9 <inline-formula><mml:math id="M291" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.6</oasis:entry>
         <oasis:entry colname="col4">0.95 <inline-formula><mml:math id="M292" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.20</oasis:entry>
         <oasis:entry colname="col5">7.92 <inline-formula><mml:math id="M293" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.67</oasis:entry>
         <oasis:entry colname="col6">0.5 <inline-formula><mml:math id="M294" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Treatment chamber (<inline-formula><mml:math id="M295" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">0.21 <inline-formula><mml:math id="M296" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.04</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M297" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>21.8 <inline-formula><mml:math id="M298" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.6</oasis:entry>
         <oasis:entry colname="col4">1.95 <inline-formula><mml:math id="M299" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.39</oasis:entry>
         <oasis:entry colname="col5">16.25 <inline-formula><mml:math id="M300" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 3.25</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M301" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.7 <inline-formula><mml:math id="M302" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.6</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Mussel shells</oasis:entry>
         <oasis:entry colname="col2">2.20 <inline-formula><mml:math id="M303" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.09</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M304" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>19.8 <inline-formula><mml:math id="M305" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.1</oasis:entry>
         <oasis:entry colname="col4">11.12 <inline-formula><mml:math id="M306" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.11</oasis:entry>
         <oasis:entry colname="col5">92.65 <inline-formula><mml:math id="M307" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 9.18</oasis:entry>
         <oasis:entry colname="col6"><inline-formula><mml:math id="M308" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>2.2 <inline-formula><mml:math id="M309" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.4</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Sediment properties</title>
      <p id="d2e4297">The natural sediment had a median grain size of 262 <inline-formula><mml:math id="M310" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> and porosity of 0.45 <inline-formula><mml:math id="M311" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.03 (<inline-formula><mml:math id="M312" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>) and can be classified as medium sand according to the Wentworth scale. Consistent with a permeable sediment, the organic carbon content was low (0.08 %), while the background level of inorganic carbon was also moderate (0.95 %). Particulate organic carbon (POC) and particulate inorganic carbon (PIC) concentrations of the different substrates used in the experiments (including the added mussel shells) and their corresponding <inline-formula><mml:math id="M313" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> values are summarized in Table 1.</p>

      <fig id="F3" specific-use="star"><label>Figure 3</label><caption><p id="d2e4344"><bold>(a)</bold> Oxygen fluxes (<inline-formula><mml:math id="M314" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). <bold>(b)</bold> Dissolved inorganic carbon fluxes (<inline-formula><mml:math id="M315" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). <bold>(c)</bold> Alkalinity fluxes (<inline-formula><mml:math id="M316" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mtext>AT</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>). Positive fluxes indicate fluxes into the overlying water (i.e., net production by the sediment), negative fluxes indicate fluxes into the sediment (i.e., net consumption by the sediment). Means are plotted with error bars representing standard deviations based on three replicate chambers. No <inline-formula><mml:math id="M317" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and DIC data were available for week 7, as only open incubations were performed during that week. <bold>(d)</bold> <inline-formula><mml:math id="M318" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> plot, comparing <inline-formula><mml:math id="M319" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M320" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>. <bold>(e)</bold> <inline-formula><mml:math id="M321" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> plot, comparing <inline-formula><mml:math id="M322" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mtext>AT</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M323" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>.</p></caption>
          <graphic xlink:href="https://bg.copernicus.org/articles/23/6447/2026/bg-23-6447-2026-f03.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Sediment-water exchange fluxes</title>
      <p id="d2e4500">Most incubations showed linear changes in overlying water solute concentrations over time (Figs. S1–S5 in the Supplement). An exception was observed during week 1, where <inline-formula><mml:math id="M324" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> accumulation in the treatment chambers was nonlinear, with the accumulation rate decreasing halfway through the incubation (Fig. S3). Similarly, <inline-formula><mml:math id="M325" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M326" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> concentrations in the treatment chambers displayed nonlinear trends during week 1 (Figs. S4 and S5): concentrations of <inline-formula><mml:math id="M327" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> remained constant in the beginning of the incubation, after which they increased, while <inline-formula><mml:math id="M328" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> concentrations increased at the beginning and decreased at the end.</p>
      <p id="d2e4566">Fluxes of <inline-formula><mml:math id="M329" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, DIC and <inline-formula><mml:math id="M330" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> were calculated by regression of overlying water concentrations with time, and showed good replication between replicates at each time point (Fig. 3a–c). Fluxes showed a clear difference between control (<inline-formula><mml:math id="M331" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M332" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M333" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>5.4 <inline-formula><mml:math id="M334" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.2 <inline-formula><mml:math id="M335" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M336" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M337" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 7.4 <inline-formula><mml:math id="M338" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0 <inline-formula><mml:math id="M339" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M340" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mtext>AT</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M341" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 3.2 <inline-formula><mml:math id="M342" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.1 <inline-formula><mml:math id="M343" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</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">2</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>; mean flux <inline-formula><mml:math id="M344" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> standard deviation over all replicate chambers and flux sessions) and treatment chambers (<inline-formula><mml:math id="M345" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M346" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M347" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>16.8 <inline-formula><mml:math id="M348" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 4.3 <inline-formula><mml:math id="M349" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M350" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M351" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 32.0 <inline-formula><mml:math id="M352" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 9.4 <inline-formula><mml:math id="M353" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M354" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mtext>AT</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M355" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 25.1 <inline-formula><mml:math id="M356" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 13.5 <inline-formula><mml:math id="M357" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</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">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>; Table S1 in the Supplement). While fluxes in the control chambers showed little variation over time, the treatment chambers displayed a clear temporal pattern. Both <inline-formula><mml:math id="M358" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (Fig. 3a) and DIC (Fig. 3b) fluxes were initially markedly higher than those of the control chambers, and gradually decreased over the course of the experiment, approaching fluxes of the controls towards the end. Fluxes of <inline-formula><mml:math id="M359" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> first increased with time until a maximum value of 48.0 <inline-formula><mml:math id="M360" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 6.4 <inline-formula><mml:math id="M361" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> was reached at week 7, after which they decreased and approached the fluxes of the controls towards the end (Fig. 3c). Fluxes of <inline-formula><mml:math id="M362" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M363" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> in the control chambers were negligible throughout all flux sessions (Table S1). In the treatment chambers, elevated <inline-formula><mml:math id="M364" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> effluxes were only observed during the first part of week 1 (<inline-formula><mml:math id="M365" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M366" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 5.1 <inline-formula><mml:math id="M367" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.5 <inline-formula><mml:math id="M368" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</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">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), after which they dropped below the detection limit (Table S1). A positive <inline-formula><mml:math id="M369" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> efflux was observed in the second part of week 1 (<inline-formula><mml:math id="M370" display="inline"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M371" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 5.8 <inline-formula><mml:math id="M372" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0 <inline-formula><mml:math id="M373" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</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">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>; Table S1), and in weeks 3 and 5, <inline-formula><mml:math id="M374" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> fluxes were still observed, although they were substantially lower (<inline-formula><mml:math id="M375" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 1 <inline-formula><mml:math id="M376" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</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">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). Finally, flux scatter plots revealed a clear additional DIC source in the treatment chambers beyond mineralization-derived DIC (Fig. 3d), as well as a proportionally greater increase in <inline-formula><mml:math id="M377" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> relative to DIC (Fig. 3e).</p>

      <fig id="F4" specific-use="star"><label>Figure 4</label><caption><p id="d2e5216"><bold>(a)</bold> Mean fraction of total DIC derived from <inline-formula><mml:math id="M378" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution (<inline-formula><mml:math id="M379" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) as determined using the Keeling plot method. Values are expressed as percentages. <bold>(b)</bold> Corresponding mean <inline-formula><mml:math id="M380" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution rates (<inline-formula><mml:math id="M381" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>). Values of <inline-formula><mml:math id="M382" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> were only calculated for positive values of <inline-formula><mml:math id="M383" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, as discussed in the main text. Error bars are standard deviations based on three replicate chambers.</p></caption>
          <graphic xlink:href="https://bg.copernicus.org/articles/23/6447/2026/bg-23-6447-2026-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title><inline-formula><mml:math id="M384" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution rates</title>
      <p id="d2e5316">Figure 4a and b and Table S2 show the derived <inline-formula><mml:math id="M385" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and corresponding <inline-formula><mml:math id="M386" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values across the experiment, while the corresponding MCDE values are provided in Table S2 (see Fig. S6 for all Keeling plots and Table S2 for all model intercepts and <inline-formula><mml:math id="M387" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> values). A temporal pattern was observed in the treatment chambers over the course of the experiment, with <inline-formula><mml:math id="M388" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M389" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> increasing over time, reaching a maximum of <inline-formula><mml:math id="M390" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M391" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 59.5 <inline-formula><mml:math id="M392" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 6.5 % (<inline-formula><mml:math id="M393" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M394" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 22.7 <inline-formula><mml:math id="M395" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 2.6 <inline-formula><mml:math id="M396" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) in week 9, followed by a gradual decrease towards a final <inline-formula><mml:math id="M397" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> of 17.3 <inline-formula><mml:math id="M398" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 12.7 % (<inline-formula><mml:math id="M399" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M400" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 2.2 <inline-formula><mml:math id="M401" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.1 <inline-formula><mml:math id="M402" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). In the control chambers, <inline-formula><mml:math id="M403" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> remained relatively stable over time, although some variability was observed both among replicate chambers and across incubation weeks. As the Keeling plot method combines measurements of both DIC and <inline-formula><mml:math id="M404" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula>, each with associated uncertainties, such variability is expected, particularly in control chambers, where concentration and isotopic composition changes over time are relatively small. The occurrence of negative <inline-formula><mml:math id="M405" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values in some control chambers indicated that the regression intercept fell outside the isotopic range defined by the <inline-formula><mml:math id="M406" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and organic matter end-members. This has no geochemical meaning, other than suggesting that little to no <inline-formula><mml:math id="M407" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution is occurring, and underscores the uncertainty that the Keeling plot approach inherently incorporates when variations in DIC and/or <inline-formula><mml:math id="M408" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula> are relatively modest. For this reason, <inline-formula><mml:math id="M409" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> was only calculated for chambers with positive <inline-formula><mml:math id="M410" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values (Fig. 4b).</p>
</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Pore-water geochemistry</title>
      <p id="d2e5627">We tracked the color changes in the sediment over time by taking photographs throughout the experimental period (Fig. S7). These images reveal a markedly different color evolution in control versus treatment, thus suggesting a different development of the geochemistry. In the controls, the sediment remained light-grey colored, and the only color change observed was the development of a thin (<inline-formula><mml:math id="M411" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 5 <inline-formula><mml:math id="M412" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mm</mml:mi></mml:mrow></mml:math></inline-formula>) orange layer just below the sediment-water interface (Fig. S7). This feature suggests remobilization of ferrous iron in deeper layers, which then precipitates out as iron (hydr)oxide upon upward diffusion and contact with <inline-formula><mml:math id="M413" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. In contrast, in the treatments, there was a far more notable color change, as the entire layer with mussel shell fragments became black over the course of the first 3 weeks, after which it gradually became grey again as the experiment progressed (Fig. S7).</p>

      <fig id="F5" specific-use="star"><label>Figure 5</label><caption><p id="d2e5658">Pore-water profiles. <bold>(a)</bold> Calcium (<inline-formula><mml:math id="M414" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). <bold>(b)</bold> Dissolved inorganic carbon (DIC). <bold>(c)</bold> Isotopic DIC composition (<inline-formula><mml:math id="M415" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula>). <bold>(d)</bold> <inline-formula><mml:math id="M416" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> plot, comparing <inline-formula><mml:math id="M417" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and DIC concentrations. Pore-water samples were only taken once at the end of the experiment, explaining the buildup of solutes in deeper anoxic layers, as further discussed in the main text.</p></caption>
          <graphic xlink:href="https://bg.copernicus.org/articles/23/6447/2026/bg-23-6447-2026-f05.png"/>

        </fig>

      <p id="d2e5737">Figure 5 displays the depth profiles of pore-water concentrations (<inline-formula><mml:math id="M418" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, DIC) and isotopic composition (<inline-formula><mml:math id="M419" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula>) recorded at the end of the experiment. Higher pore-water <inline-formula><mml:math id="M420" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> concentrations were observed in the treatment chambers as compared to the control chambers (Fig. 5a). In the control chambers, pore-water <inline-formula><mml:math id="M421" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> concentrations remained constant with depth, and were similar to the concentration of <inline-formula><mml:math id="M422" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 9.5 <inline-formula><mml:math id="M423" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mM</mml:mi></mml:mrow></mml:math></inline-formula> of the overlying seawater. In contrast, in the treatment chambers, dissolved <inline-formula><mml:math id="M424" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> markedly increased with depth, reaching 12–13 <inline-formula><mml:math id="M425" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mM</mml:mi></mml:mrow></mml:math></inline-formula> at 12 <inline-formula><mml:math id="M426" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> depth. Pore-water DIC profiles showed an increasing trend with sediment depth for both control and treatment chambers, but with a different shape and higher DIC concentrations observed in the treatment chambers (Fig. 5b). Profiles of <inline-formula><mml:math id="M427" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula> showed a decreasing trend in <inline-formula><mml:math id="M428" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> values with sediment depth in the control chambers. In the treatment chambers, however, <inline-formula><mml:math id="M429" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> values decreased in the top layer but then remained relatively stable below a depth of <inline-formula><mml:math id="M430" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 1 <inline-formula><mml:math id="M431" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> (Fig. 5c). Pore-water <inline-formula><mml:math id="M432" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> plots of <inline-formula><mml:math id="M433" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and DIC concentrations revealed a clear <inline-formula><mml:math id="M434" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> source in the treatment chambers, alongside higher DIC production (Fig. 5d).</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Mussel shell dissolution provides a significant additional <inline-formula><mml:math id="M435" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> source</title>
      <p id="d2e5973">Metabolic <inline-formula><mml:math id="M436" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution is thought to occur more efficiently in oxygenated sediments, where the aerobic mineralization of organic matter produces the <inline-formula><mml:math id="M437" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> that drives the pore water towards undersaturation (Archer et al., 1989; Emerson and Bender, 1981; Lunstrum and Berelson, 2022; Morse et al., 1985). To meet this condition, permeable sediment (medium sand; porosity 0.45) was used here in the experiment. While the natural sediment employed does contain a sizeable baseline amount of PIC (0.95 <inline-formula><mml:math id="M438" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.20 %; Table 1), low <inline-formula><mml:math id="M439" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fluxes were observed in the control chambers (Fig. 3c). Likewise, the Keeling plot analysis indicated low rates of metabolic carbonate dissolution (Fig. 4b). The mean <inline-formula><mml:math id="M440" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution rate of 0.9 <inline-formula><mml:math id="M441" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.5 <inline-formula><mml:math id="M442" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</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">2</mml:mn></mml:mrow></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> as observed in the controls, corresponds to an <inline-formula><mml:math id="M443" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> flux 1.8 <inline-formula><mml:math id="M444" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.0 <inline-formula><mml:math id="M445" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</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">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, thus providing <inline-formula><mml:math id="M446" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 56 % of the total measured <inline-formula><mml:math id="M447" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> flux of 3.2 <inline-formula><mml:math id="M448" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.1 <inline-formula><mml:math id="M449" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mmol</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">2</mml:mn></mml:mrow></mml:msup><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The low organic carbon content of the natural sediment (0.08 <inline-formula><mml:math id="M450" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 0.02 <inline-formula><mml:math id="M451" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">wt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula>; Table 1) resulted in low mineralization rates, as indicated by the low <inline-formula><mml:math id="M452" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> consumption rates (Fig. 3a), which are a proxy for total sedimentary organic matter mineralization (Glud, 2008; Jørgensen et al., 2022). The low <inline-formula><mml:math id="M453" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> production from mineralization thus constrained metabolic <inline-formula><mml:math id="M454" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution in the natural sediment.</p>

      <fig id="F6" specific-use="star"><label>Figure 6</label><caption><p id="d2e6211">Shell-amended chamber flux comparison of total <inline-formula><mml:math id="M455" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, which was measured directly in the overlying water, and <inline-formula><mml:math id="M456" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M457" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, which was derived using the Keeling plot analysis. <bold>(a)</bold> Mean weekly fluxes with standard deviations based on three replicate chambers. <bold>(b)</bold> <inline-formula><mml:math id="M458" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>:</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> plot, comparing the individual weekly total and <inline-formula><mml:math id="M459" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>-derived <inline-formula><mml:math id="M460" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fluxes per chamber.</p></caption>
          <graphic xlink:href="https://bg.copernicus.org/articles/23/6447/2026/bg-23-6447-2026-f06.png"/>

        </fig>

      <p id="d2e6294">In the treatment chambers, more favorable conditions for metabolic dissolution were established, as the added mussel shells still had a considerable amount of associated organic matter (2.20 <inline-formula><mml:math id="M461" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">wt</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">%</mml:mi></mml:mrow></mml:math></inline-formula>; Table 1), which stimulated organic matter mineralization, as reflected in the <inline-formula><mml:math id="M462" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, DIC and <inline-formula><mml:math id="M463" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fluxes (Fig. 3a–c). First, elevated <inline-formula><mml:math id="M464" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> fluxes in the treatment chambers suggest high mineralization rates driven by the organic matter associated with the shells, and thus an increased metabolic dissolution potential. Second, elevated DIC fluxes in the treatment chambers confirmed increased metabolic dissolution driven by the more intense mineralization (Fig. 3d). The Keeling plot analysis demonstrates there is a clear additional DIC source coming from <inline-formula><mml:math id="M465" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution in the treatment chambers (Fig. 4b), which is further supported by the higher <inline-formula><mml:math id="M466" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> and DIC pore-water concentrations observed in the treatment chambers (Fig. 5a, b, and d). It should be noted that pore-water samples were only taken once at the end of the experiment (24 weeks), which allowed for the downward buildup of these solutes over time. While enhanced <inline-formula><mml:math id="M467" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution only occurred in the shell-amended top layer in the treatment chambers, downward diffusion likely resulted in the elevated concentrations in the deeper anoxic layers. Likewise, the overlying water was replaced after every incubation, which enabled upward diffusive and advective transport of <inline-formula><mml:math id="M468" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Ca</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> into the overlying water, thus resulting in a lower buildup in the top layer. Third, high <inline-formula><mml:math id="M469" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fluxes in the treatment chambers (Fig. 3c and e)  also provide support for substantial <inline-formula><mml:math id="M470" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution, as 2 <inline-formula><mml:math id="M471" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mol</mml:mi></mml:mrow></mml:math></inline-formula> of <inline-formula><mml:math id="M472" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are produced per <inline-formula><mml:math id="M473" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mol</mml:mi></mml:mrow></mml:math></inline-formula> of <inline-formula><mml:math id="M474" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolved (Eq. 1). In addition, comparison of the <inline-formula><mml:math id="M475" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fluxes attributed to <inline-formula><mml:math id="M476" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution (as derived from the Keeling plot analysis) with the total <inline-formula><mml:math id="M477" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fluxes (as measured in the overlying water) revealed a strong linear correlation for nearly all flux sessions (Fig. 6a and b), demonstrating that <inline-formula><mml:math id="M478" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution was the dominant <inline-formula><mml:math id="M479" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> source in the treatment chambers. A small number of flux sessions (weeks 3, 11, and 13) deviated from this relationship, indicating the presence of additional <inline-formula><mml:math id="M480" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-generating or <inline-formula><mml:math id="M481" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-consuming processes. These processes are discussed in the following section.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Factors controlling metabolic <inline-formula><mml:math id="M482" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution</title>
      <p id="d2e6551">The observed geochemistry in the treatment chambers carries a clear signature of metabolic <inline-formula><mml:math id="M483" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution. Given that metabolic <inline-formula><mml:math id="M484" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution is constrained by the availability of oxygen, organic matter, and <inline-formula><mml:math id="M485" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (Eq. 3), an important question is which of these three factors acts as the primary limiting factor. Metabolic carbonate dissolution efficiencies (MCDE, Eq. 12) offer a useful metric to assess this issue. Efficiencies <inline-formula><mml:math id="M486" display="inline"><mml:mo>&lt;</mml:mo></mml:math></inline-formula> 100 % can be due to different processes: (1) the <inline-formula><mml:math id="M487" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> pool is either too small or not reactive enough for dissolution to fully utilize the potential of mineralization, (2) the pore water receives <inline-formula><mml:math id="M488" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> from anaerobic mineralization processes, which suppresses the undersaturation with respect to <inline-formula><mml:math id="M489" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (Soetaert et al., 2007), or (3) the acid (i.e. <inline-formula><mml:math id="M490" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) produced by aerobic mineralization is flushed out of the pore water by advective transport before it can drive the pore water towards undersaturation (Goossens et al., 2026). We now discuss these different factors in more detail.</p>
<sec id="Ch1.S4.SS2.SSS1">
  <label>4.2.1</label><title>Limitation by <inline-formula><mml:math id="M491" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> availability and reactivity</title>
      <p id="d2e6658">To assess whether <inline-formula><mml:math id="M492" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> availability limited dissolution in the treatment chambers, the total amount of <inline-formula><mml:math id="M493" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolved over the course of the experiment was calculated by integrating the <inline-formula><mml:math id="M494" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values obtained from the Keeling plot analysis over their respective incubation periods and the sediment surface area (Fig. 4b). This resulted in a total of 6.1 <inline-formula><mml:math id="M495" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.2 <inline-formula><mml:math id="M496" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi></mml:mrow></mml:math></inline-formula> of <inline-formula><mml:math id="M497" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolved, corresponding to 6.1 <inline-formula><mml:math id="M498" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.2 % of the initial shell mass that was added. These results suggest that <inline-formula><mml:math id="M499" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> availability most likely did not limit dissolution.</p>
      <p id="d2e6739">In addition to <inline-formula><mml:math id="M500" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> content, <inline-formula><mml:math id="M501" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution efficiency can also be limited by reactivity. When pore waters transition from over- to undersaturated conditions, carbonate minerals dissolve more readily at high-energy surface sites such as steps and kinks, which are more reactive than smoother surfaces (Adkins et al., 2021). In this experiment, mussel shells were freshly crushed, resulting in more high-energy surface sites relative to the natural <inline-formula><mml:math id="M502" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> present in the sediment. This suggests that <inline-formula><mml:math id="M503" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> reactivity was unlikely to be limiting carbonate dissolution in the shell-amended chambers.</p>

      <fig id="F7" specific-use="star"><label>Figure 7</label><caption><p id="d2e6788">Conceptual figure illustrating the three distinct phases observed after mussel shell amendment. Black dots represent mean metabolic <inline-formula><mml:math id="M504" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution efficiencies (MCDE) determined using the Keeling plot method. During phase 1, MCDE is limited by oxygen (<inline-formula><mml:math id="M505" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) availability. During phase 2, <inline-formula><mml:math id="M506" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution is limited by organic matter (OM) availability while occurring at maximum efficiency. During phase 3, dissolution efficiency is limited by OM availability, and both dissolution efficiencies and rates gradually approach those observed in sediments without added shells. In a real-world shell amendment scenario, however, metabolic <inline-formula><mml:math id="M507" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution would be continuously fueled by the supply of fresh OM from the water column, potentially driving the system back towards maximum efficiency.</p></caption>
            <graphic xlink:href="https://bg.copernicus.org/articles/23/6447/2026/bg-23-6447-2026-f07.png"/>

          </fig>


</sec>
<sec id="Ch1.S4.SS2.SSS2">
  <label>4.2.2</label><title>Limitation by anaerobic mineralization and pore-water flushing</title>
      <p id="d2e6851">Undersaturation of pore waters with respect to <inline-formula><mml:math id="M508" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is promoted by oxic conditions, which drive <inline-formula><mml:math id="M509" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> production through aerobic mineralization. In coarse sediments, this is stimulated by advection, which allows deeper oxygen penetration (Huettel and Gust, 1992) and increases the zone in which <inline-formula><mml:math id="M510" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> undersaturation can develop. The degree of undersaturation is further controlled by the pore-water residence time (PRT), which is the mean time that seawater remains within the sediment before being replaced by new overlying water. If the PRT is too short, acid produced by aerobic mineralization is flushed out before it can drive the pore water towards undersaturation. If the PRT is too long, <inline-formula><mml:math id="M511" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> from <inline-formula><mml:math id="M512" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution will accumulate and drive the pore water back towards saturation (Goossens et al., 2026).</p>
      <p id="d2e6909">Below the oxic zone, anaerobic mineralization generates <inline-formula><mml:math id="M513" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> instead of acidity, along with reduced metabolites (Soetaert et al., 2007). However, these reduced compounds are typically transported upward into the oxic zone, where their reoxidation produces acidity that lowers the <inline-formula><mml:math id="M514" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> saturation state of the pore water. This means that metabolic carbonate dissolution can occur directly via aerobic mineralization and indirectly via anaerobic mineralization coupled to reoxidation in the oxic zone (Dale et al., 2024). Iron sulfide precipitation, however, represents an exception to this process.

                  <disp-formula specific-use="gather" content-type="numbered"><mml:math id="M515" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E13"><mml:mtd><mml:mtext>13</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mn mathvariant="normal">2</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow><mml:mo>→</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">S</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E14"><mml:mtd><mml:mtext>14</mml:mtext></mml:mtd><mml:mtd><mml:mrow><mml:mstyle displaystyle="true" class="stylechange"/><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn><mml:mrow class="chem"><mml:mi mathvariant="normal">FeOOH</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">8</mml:mn><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow><mml:mo>→</mml:mo><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">Fe</mml:mi><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">7</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula>

            

              <disp-formula id="Ch1.E15" content-type="numbered"><label>15</label><mml:math id="M516" display="block"><mml:mtable rowspacing="0.2ex" class="split" displaystyle="true" columnalign="right left"><mml:mtr><mml:mtd><mml:mrow><mml:mn mathvariant="normal">15</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CH</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">8</mml:mn><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">SO</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mrow><mml:mn mathvariant="normal">2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msubsup></mml:mrow></mml:mrow></mml:mtd><mml:mtd><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn><mml:mrow class="chem"><mml:mi mathvariant="normal">FeOOH</mml:mi></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">16</mml:mn><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="normal">H</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd/><mml:mtd><mml:mrow><mml:mo>→</mml:mo><mml:mn mathvariant="normal">15</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">FeS</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">25</mml:mn><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula>

            During sulfate reduction, hydrogen sulfide (<inline-formula><mml:math id="M517" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">S</mml:mi></mml:mrow></mml:math></inline-formula>) is produced (Eq. 13). When <inline-formula><mml:math id="M518" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">S</mml:mi></mml:mrow></mml:math></inline-formula> reacts with reactive iron generated through iron reduction (Eq. 14), iron sulfides can precipitate (Eq. 15, shown for pyrite formation). This prevents the upward transport of <inline-formula><mml:math id="M519" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">H</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mi mathvariant="normal">S</mml:mi></mml:mrow></mml:math></inline-formula> and its subsequent reoxidation, resulting in a net source of <inline-formula><mml:math id="M520" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (Hu and Cai, 2011; Middelburg et al., 2020). Under such conditions, the efficiency of metabolic carbonate dissolution is reduced since a potential source of acidity from mineralization is removed.</p>
      <p id="d2e7222">Ultimately, the interplay between aerobic/anaerobic mineralization and pore-water exchange dictates whether pore waters become under- or oversaturated, thus controlling the MCDE. Throughout the experiment, three distinct phases can be distinguished (Fig. 7): phase one (weeks 1–9) was characterized by initially low MCDE values that gradually increased over time; phase two (weeks 9–15) was characterized by maximum MCDE values (<inline-formula><mml:math id="M521" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 100 %); and phase three (weeks 15–24) was characterized by decreasing MCDE values over time.</p>
      <p id="d2e7232">During the first phase of the experiment (weeks 1–9), intense mineralization took place, likely driven by the fresh organic matter associated with the mussel shells. This process was immediately visibly apparent, as during the first week, the top layer of the shell-amended sediment (where the mussel shell fragments had been added) turned black, indicative of sediment anoxia and potential iron sulfide formation (Fig. S7). The oxygen consumption in the treatment chambers was high, suggesting that the oxic zone was likely strongly diminished. Week 1 was also the only week during which we observed <inline-formula><mml:math id="M522" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> accumulation in the overlying water, suggesting that nitrification was inhibited, most likely by a lack of oxygen. In all ensuing flux sessions, the <inline-formula><mml:math id="M523" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> efflux from the sediment remained negligible (Table S1). In the latter part of week 1, oxic conditions apparently reestablished, as nitrification initiated, leading to a depletion of <inline-formula><mml:math id="M524" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NH</mml:mi><mml:mn mathvariant="normal">4</mml:mn><mml:mo>+</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> (Fig. S5) and a buildup of <inline-formula><mml:math id="M525" display="inline"><mml:mrow class="chem"><mml:msubsup><mml:mi mathvariant="normal">NO</mml:mi><mml:mn mathvariant="normal">3</mml:mn><mml:mo>-</mml:mo></mml:msubsup></mml:mrow></mml:math></inline-formula> (Fig. S4). Nitrification consumes <inline-formula><mml:math id="M526" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> by releasing protons, which likely contributed to the observed nonlinear <inline-formula><mml:math id="M527" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> accumulation in week 1. Anaerobic mineralization generates <inline-formula><mml:math id="M528" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, which elevates the <inline-formula><mml:math id="M529" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> saturation state in the pore water and thus likely contributed to the low MCDE (<inline-formula><mml:math id="M530" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 45 %) observed in week 1.</p>
      <p id="d2e7340">In the rest of the first phase (after week 1), the mineralization remained high (as indicated by high <inline-formula><mml:math id="M531" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and DIC fluxes; Fig. 3a and b), but the pore waters recovered from the initial “mineralization burst” and became gradually more oxygenated, stimulating metabolic <inline-formula><mml:math id="M532" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution (Eq. 3). As a result, the MCDE increased with time, until reaching its maximum value in week 9.</p>
      <p id="d2e7365">During the second phase (weeks 9–15), carbonate dissolution occurred at maximum efficiency in the shell layer. The <inline-formula><mml:math id="M533" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula> pore-water profiles taken at the end of the experiment indicated that organic matter (<inline-formula><mml:math id="M534" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M535" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M536" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>21.8 ‰) and <inline-formula><mml:math id="M537" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M538" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M539" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M540" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>0.7 ‰) contributed approximately equally to the pore-water DIC pool, as reflected by the constant <inline-formula><mml:math id="M541" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula> value of <inline-formula><mml:math id="M542" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M543" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>10 ‰ in the deeper sediment layers (Fig. 5c). While this end-point profile does not reveal when these processes occurred, it indicates that, overall, metabolic dissolution contributed substantially to the accumulated pore-water DIC. Given that <inline-formula><mml:math id="M544" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> values were highest during the second phase, this integrated signal is expected to be dominated by this period, during which the dissolution efficiency was highest (MCDE <inline-formula><mml:math id="M545" display="inline"><mml:mo>≈</mml:mo></mml:math></inline-formula> 100 %; Fig. 7). Maximum efficiencies also indicate that <inline-formula><mml:math id="M546" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mo>min⁡</mml:mo></mml:msub></mml:mrow></mml:math></inline-formula> in the shell layer was sufficiently large to overwhelm any potential effect of iron sulfide formation below the oxic layer on <inline-formula><mml:math id="M547" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d2e7523">In weeks 9–11, the MCDE even exceeded 100 % (Fig. 7). Theoretically, this is not possible when only metabolic dissolution is at play, but it can occur when an additional acid source is present. The observed MCDE <inline-formula><mml:math id="M548" display="inline"><mml:mo>&gt;</mml:mo></mml:math></inline-formula> 100 % are hence either related to uncertainty in their estimation, or they can also result from the transient reoxidation of a pool of iron sulfides, a process which generates acid and consumes <inline-formula><mml:math id="M549" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (Rimstidt and Vaughan, 2003). After week 9, the intensity of mineralization decreased, which may have caused an increased and deeper oxygenation, and hence, a reoxidation of previously accumulated iron sulfides, consistent with the observed offset between total <inline-formula><mml:math id="M550" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fluxes and <inline-formula><mml:math id="M551" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> fluxes attributed to <inline-formula><mml:math id="M552" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution (Fig. 6). The observed continuous transition of the sediment color from black to light grey is also consistent with this interpretation, as it suggests potential reoxidation of iron sulfides (Fig. S7).</p>
      <p id="d2e7577">During the third phase (weeks 15–24), MCDE decreased with time (Fig. 7). At this point, the most labile fraction of organic matter had been mineralized, leading to reduced mineralization rates and decreased <inline-formula><mml:math id="M553" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> consumption rates (Fig. 3a). At this point, <inline-formula><mml:math id="M554" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution likely became limited by organic matter availability, and dissolution rates decreased accordingly (Fig. 4b). The decreasing <inline-formula><mml:math id="M555" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mo>min⁡</mml:mo></mml:msub></mml:mrow></mml:math></inline-formula> could not generate sufficient acidity to drive the pore water fully towards undersaturation before being flushed, thereby reducing <inline-formula><mml:math id="M556" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M557" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mtext>carb</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and MCDE. Eventually, the treatment chambers appeared to evolve towards the control rates, with <inline-formula><mml:math id="M558" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mtext>diss</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> remaining slightly higher than in the control chambers (Fig. 4b).</p>
      <p id="d2e7647">At the end of the experiment, <inline-formula><mml:math id="M559" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution appeared limited by organic matter availability. We hence speculate that the addition of new fresh organic matter could again increase the dissolution rate and associated MCDE (Fig. 7). The latter aspect was not examined in the current experiment but provides a testable hypothesis for future studies.</p>
</sec>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Enhanced <inline-formula><mml:math id="M560" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution in the global aquaculture context</title>
      <p id="d2e7682">The flux incubations performed here provide an estimate for the areal <inline-formula><mml:math id="M561" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution rate and <inline-formula><mml:math id="M562" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> flux induced by enhanced mussel shell dissolution. These values can be used to arrive at a first-order estimate of the potential of bivalve dissolution approaches within an OAE context. When extrapolating our results to the global aquaculture context, we need to consider both <inline-formula><mml:math id="M563" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions associated with mussel shell aquaculture as well as <inline-formula><mml:math id="M564" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> sequestration obtained from a shell amendment scenario.</p>
      <p id="d2e7729">Global yearly <inline-formula><mml:math id="M565" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions (<inline-formula><mml:math id="M566" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:msub><mml:mrow class="chem"><mml:mi mathvariant="normal">CO</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>; <inline-formula><mml:math id="M567" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">t</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) associated with calcification in mussel aquaculture can be calculated as:

            <disp-formula id="Ch1.E16" content-type="numbered"><label>16</label><mml:math id="M568" display="block"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>m</mml:mi><mml:mtext>mussel</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mtext>shell</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub><mml:mo>⋅</mml:mo><mml:mi mathvariant="italic">ψ</mml:mi><mml:mo>⋅</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>

          In this, <inline-formula><mml:math id="M569" display="inline"><mml:mrow><mml:msub><mml:mi>m</mml:mi><mml:mtext>mussel</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> represents the total mass of harvested mussels from aquaculture (<inline-formula><mml:math id="M570" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">t</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), <inline-formula><mml:math id="M571" display="inline"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mtext>shell</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> denotes the shell fraction of the total mussel mass (<inline-formula><mml:math id="M572" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 29 %; Adler et al., 2024), <inline-formula><mml:math id="M573" display="inline"><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> represents the <inline-formula><mml:math id="M574" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> fraction of shells (92.65 %; Table 1), <inline-formula><mml:math id="M575" display="inline"><mml:mi mathvariant="italic">ψ</mml:mi></mml:math></inline-formula> is the molar ratio of <inline-formula><mml:math id="M576" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> released versus <inline-formula><mml:math id="M577" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> precipitated (Frankignoulle, 1994; Frankignoulle et al., 1994), and <inline-formula><mml:math id="M578" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M579" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> are the molar masses of <inline-formula><mml:math id="M580" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (44.01 <inline-formula><mml:math id="M581" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">mol</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) and <inline-formula><mml:math id="M582" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> (100.01 <inline-formula><mml:math id="M583" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">mol</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), respectively. Calculation of <inline-formula><mml:math id="M584" display="inline"><mml:mi mathvariant="italic">ψ</mml:mi></mml:math></inline-formula> was done using the CRAN:seacarb package in R software (Gattuso et al., 2024), with input parameters representative of surface seawater conditions: DIC <inline-formula><mml:math id="M585" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 2100 <inline-formula><mml:math id="M586" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">mol</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, salinity <inline-formula><mml:math id="M587" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 35, temperature <inline-formula><mml:math id="M588" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 15 <inline-formula><mml:math id="M589" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>, and atmospheric <inline-formula><mml:math id="M590" display="inline"><mml:mrow class="chem"><mml:mi>p</mml:mi><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M591" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 427 <inline-formula><mml:math id="M592" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">µ</mml:mi><mml:mi mathvariant="normal">atm</mml:mi></mml:mrow></mml:math></inline-formula> (Lan et al., 2023). This yielded a value of <inline-formula><mml:math id="M593" display="inline"><mml:mi mathvariant="italic">ψ</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M594" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 0.72. Blue mussel aquaculture has a global production of approximately 132 <inline-formula><mml:math id="M595" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kt</mml:mi></mml:mrow></mml:math></inline-formula> yr<sup>−1</sup> (FAO, 2025), and so, the <inline-formula><mml:math id="M597" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions linked to calcification are <inline-formula><mml:math id="M598" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 11.2 <inline-formula><mml:math id="M599" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kt</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Using the results obtained here, 6.1 <inline-formula><mml:math id="M600" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.2 % of the initial shell mass was dissolved after 24 weeks, and so the corresponding <inline-formula><mml:math id="M601" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> compensation over the same time period would be 6.1 % of the calcification-related emissions incurred during the growth phase (representing 686 <inline-formula><mml:math id="M602" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 135 <inline-formula><mml:math id="M603" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">t</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> globally). It should be noted, however, that at the end of the experimental period, the <inline-formula><mml:math id="M604" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution rate and corresponding <inline-formula><mml:math id="M605" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> flux in the treatment chambers were still higher than those in the control chambers, thus indicating that enhanced shell dissolution would still continue for a longer period. Assuming the dissolution rate stays constant in time, it would take <inline-formula><mml:math id="M606" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 38 years to completely dissolve the added mussel shell fragments, if we use the dissolution rate measured at the end of the experiment. Alternatively, if we use the average dissolution rate over the experiment, the dissolution timescale reduces to <inline-formula><mml:math id="M607" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 7 years. However, the extent to which crushed shells remain exposed to oxic conditions over these timescales depends on sediment accumulation rates, which typically range between 0.1 and 1 <inline-formula><mml:math id="M608" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">yr</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> in shelf environments (Restreppo et al., 2020), and oxygen penetration depths. Assuming an oxygen penetration depth of 2 <inline-formula><mml:math id="M609" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula>, corresponding to the thickness of the amended sediment layer in our experiment, this suggests that crushed shells may remain exposed to oxic conditions for <inline-formula><mml:math id="M610" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 2–20 years. Once buried below the oxic layer, precipitation may become favored again in oversaturated pore waters, thereby reducing the potential for continued enhanced mussel shell dissolution. Bioturbation, however, can substantially increase the depth of oxygen penetration through bio-irrigation (Aller, 1980; Meysman et al., 2006), and extend the residence time of crushed shells within the oxygenated zone. Considering an average bioturbated layer depth of 10 <inline-formula><mml:math id="M611" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi></mml:mrow></mml:math></inline-formula> (Boudreau, 1998), the residence time of crushed shells within this zone increases to <inline-formula><mml:math id="M612" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 10–100 years (Kuderer and Middelburg, 2024). Therefore, in bioturbated sediments, crushed shells may remain exposed to conditions favorable for metabolic dissolution long enough to approach complete dissolution.</p>
      <p id="d2e8329">Furthermore, our results clearly indicate that carbonate dissolution was limited by organic matter availability from week <inline-formula><mml:math id="M613" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 15 onward in our experimental setup, leading to lowered mineralization rates and decreased metabolic <inline-formula><mml:math id="M614" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution. Such a depletion of fresh organic matter is a direct consequence of the incubation procedure. In real-world application scenarios, fresh organic matter would be continuously supplied from the water column, especially during spring blooms. This would fuel metabolic <inline-formula><mml:math id="M615" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution, as conceptually illustrated in Fig. 7, and hence reduce the dissolution time of bivalve shell material. Consequently, dissolution under field conditions may proceed considerably faster than suggested by the estimates derived from our laboratory experiment, increasing the likelihood that complete dissolution occurs before permanent burial, even in sediments with limited bioturbation. As such, the potential of mussel-shell amendment as a strategy to compensate for aquaculture <inline-formula><mml:math id="M616" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions could be greater than suggested by our laboratory experiment. This interpretation is supported by a recent study, which simulated an application scenario of two types of biominerals to coastal sediments by means of a reactive transport model. These simulations showed that enhanced <inline-formula><mml:math id="M617" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> production from shell dissolution could be sustained for over 30 years before transitioning back to steady state (Biçe et al., 2025). Sensitivity analysis also confirmed the limiting effect of lowered mineralization rates on <inline-formula><mml:math id="M618" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution rates, supporting our findings that shell amendment would be most effective in environments with high organic matter degradation (Biçe et al., 2025).</p>
      <p id="d2e8396">Enhanced bivalve shell dissolution is most promising in <inline-formula><mml:math id="M619" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>-poor permeable sediments residing in shallow areas with high local primary production. Globally, <inline-formula><mml:math id="M620" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 70 % of the continental shelf sediments are classified as sandy (i.e. permeable; Burdige, 2007), while <inline-formula><mml:math id="M621" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 88 % is classified as <inline-formula><mml:math id="M622" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>-poor (Smith and Mackenzie, 2016), thus showing that the coastal environment has a large areal potential for OAE applications based on enhanced bivalve shell dissolution. Bivalve aquaculture produces approximately 12 million  <inline-formula><mml:math id="M623" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">t</mml:mi></mml:mrow></mml:math></inline-formula> of shell material per year (FAO, 2025), which at the concentrations employed here (8 % addition) would require <inline-formula><mml:math id="M624" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 5000 <inline-formula><mml:math id="M625" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">km</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> of new application area per year. This area only represents 0.04 % of the <inline-formula><mml:math id="M626" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>-poor, sandy sediments found on the global continental shelf, and hence, the space for application does not appear to be limiting.</p>
      <p id="d2e8473">Still, the selection of an application site for enhanced bivalve shell dissolution requires judicious consideration. Sandy sediments are generally low in organic matter content, and so their potential for metabolic <inline-formula><mml:math id="M627" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution is highly dependent on a continuous local input of organic matter (de Beer et al., 2005; Goossens et al., 2026). Therefore, sandy sites with a suitably increased flux of organic matter towards the seabed seem preferential. When the organic matter input is too low, metabolic carbonate dissolution becomes limited by organic matter. Likewise, when organic matter inputs are too high, metabolic carbonate dissolution can become oxygen limited. Intensified mineralization can deplete sediment oxygen and create sulfidic conditions, which may remove the presence of bioturbating infauna (Christensen et al., 2003), and promotes <inline-formula><mml:math id="M628" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> production by iron sulfide formation. Under such circumstances, <inline-formula><mml:math id="M629" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution shifts from being organic-matter-limited to being oxygen-limited. Finally, hydrodynamic conditions will determine the fate of added shell material. Resuspension events are common in shallow coastal environments, but their frequency and intensity depend strongly on local wave and current forcing (Guillén et al., 2002; Miles et al., 2013). Resuspension may have contrasting effects on shell dissolution: while physical disturbance can increase oxygen exposure and abrasion of shelf particles, it also increases exposure to oversaturated water and may redistribute particles away from the application area into environments with less favorable conditions for dissolution. Therefore, local sediment transport dynamics should be considered when selecting suitable application sites.</p>
      <p id="d2e8509">One potential application scenario could be to redistribute shell waste in or near mussel aquaculture environments, which are known to have induced high organic matter deposition rates (Christensen et al., 2003; Hargrave et al., 2008; Lavoie et al., 2024). This would also create direct compensation for the calcifying-induced <inline-formula><mml:math id="M630" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> emissions that are locally generated (i.e. within-project offsetting). Moreover, it could potentially also improve aquaculture conditions by releasing <inline-formula><mml:math id="M631" display="inline"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and increasing the seawater pH, although this effect will strongly depend on the residence time of the water at the site. Previous studies have investigated organic matter accumulation beneath mussel farms and its effect on the local sediment geochemistry, showing that the magnitude of the impact depends on multiple factors. While the mussel density determines the total organic matter flux from the water column, the distance from the farm and the local hydrodynamics control how much of this material is deposited within the sediment (e.g., Christensen et al., 2003; Cranford et al., 2007; Hargrave et al., 2008; Lacoste et al., 2018; Lavoie et al., 2024; McKindsey et al., 2011; Wilson and Vopel, 2015). This emphasizes the need to carefully characterize sediment conditions prior to mussel shell waste application. Optimal sites could be areas with low hydrodynamic forcing that are located near but not directly beneath mussel farms, allowing elevated organic matter deposition without inducing anoxia, or areas with high hydrodynamic forcing directly beneath mussel farms, where organic matter fluxes are high but sufficiently dispersed to prevent highly localized deposition.</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Summary and outlook</title>
      <p id="d2e8543">In this study, we investigated the dissolution of mussel shell waste in permeable sediments as a novel type of OAE approach, which aims for enhanced circularity and reduced emissions in bivalve aquaculture operation. While mussels (and bivalves in general) already have a low <inline-formula><mml:math id="M632" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> footprint per gram of protein compared to other food sources, this <inline-formula><mml:math id="M633" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> footprint could be lowered by dissolving the shells in marine conditions. Permeable sediment amended with crushed mussel shells exhibited significantly higher dissolution rates, driven by aerobic mineralization linked to organic matter associated with the shells. A transient dissolution pattern was observed, where initial oxygen limitation was followed by organic matter limitation. After 24 weeks of sediment incubation, 6.1 <inline-formula><mml:math id="M634" display="inline"><mml:mo>±</mml:mo></mml:math></inline-formula> 1.2 % of the initial shell mass had dissolved, which upon extrapolation provides a dissolution timescale of <inline-formula><mml:math id="M635" display="inline"><mml:mo>∼</mml:mo></mml:math></inline-formula> 38 years. Deploying mussel shell waste in natural sediments with high and continuous organic matter deposition, however, could increase the compensation potential and shorten the dissolution timescale. Potential application areas include mussel farms, which would allow for direct in-project <inline-formula><mml:math id="M636" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> compensation, with the potential of improving aquaculture conditions. Careful characterization of the sediment geochemistry prior to mussel shell waste application is crucial to ensure optimal conditions for <inline-formula><mml:math id="M637" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CaCO</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> dissolution.</p>
      <p id="d2e8605">While enhanced mussel shell dissolution seems feasible, it should be noted that the results presented here are derived from a controlled laboratory experiment. In contrast, natural sediments experience seasonal variation in temperature and organic matter deposition, are subject to variable hydrodynamic forcing (including storms), and experience infaunal activity such as bioturbation and bio-irrigation, all of which can influence oxygen availability or benthic mineralization rates. Bridging the gap between laboratory and field conditions will require experiments conducted under more realistic settings, such as large-scale mesocosms and eventually field trials. To date, OAE studies are heavily inclined towards modeling approaches. While models are crucial for exploring large-scale scenarios, their predictive capacity ultimately depends on experimental data, which is currently still largely lacking. In this study, we tested a single mussel shell loading in a single sediment type under controlled conditions. It remains unknown whether higher shell concentrations could yield a higher <inline-formula><mml:math id="M638" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> compensation potential, or how this potential might change in coarser sediments with deeper oxygen penetration. Future research exploring a range of shell waste types, loadings and sediment grain sizes in realistic field conditions is needed to identify the optimal conditions for enhanced shell dissolution. Finally, future assessments should integrate a full life-cycle perspective on shell reuse pathways, including emissions associated with shell collection, processing, transport, and application, to determine the net <inline-formula><mml:math id="M639" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> benefit of enhanced shell dissolution under realistic deployment scenarios.</p>
</sec>

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

      <p id="d2e8634">The code used for analysis in this study is available upon request. Interested parties may contact the corresponding author.</p>
  </notes><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d2e8640">The source data is publicly available on GitHub and archived on Zenodo at <ext-link xlink:href="https://doi.org/10.5281/zenodo.19632016" ext-link-type="DOI">10.5281/zenodo.19632016</ext-link> (Goossens, 2026).</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d2e8646">The supplement related to this article is available online at <inline-supplementary-material xlink:href="https://doi.org/10.5194/bg-23-6447-2026-supplement" xlink:title="pdf">https://doi.org/10.5194/bg-23-6447-2026-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d2e8655">CG conducted the experiment and was responsible for the data collection, analysis, and writing of the manuscript. SJVDV and FJRM were responsible for the conceptualization and supervision of the study. SB supervised analysis of solid phase and <inline-formula><mml:math id="M640" display="inline"><mml:mrow class="chem"><mml:msup><mml:mi mathvariant="italic">δ</mml:mi><mml:mn mathvariant="normal">13</mml:mn></mml:msup><mml:mi mathvariant="normal">C</mml:mi><mml:mtext>-</mml:mtext><mml:mi mathvariant="normal">DIC</mml:mi></mml:mrow></mml:math></inline-formula> samples. All authors contributed to the final manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e8678">At least one of the (co-)authors is a member of the editorial board of <italic>Biogeosciences</italic>. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d2e8687">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="d2e8693">The authors thank Gunter Flipkens and Nada Nasri for assistance during pore-water sampling, Greet Lembregts for assistance during pore-water sampling and analysis of samples, and Yannick Stroobandt for analysis of samples.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d2e8699">This research was supported by the RV/21/DEHEAT project from the Belgian Science Policy Office (BELSPO), a Strategic Basic Research (SBO) project (no. S000619N) from Research Foundation Flanders (FWO), and the Blue Cluster project (project no. HBC.2023.0496) from Flanders Innovation &amp; Entrepreneurship (VLAIO). Cedric Goossens was supported by a University Research Fund (BOF) of the University of Antwerp. Sebastiaan J. van de Velde acknowledges the New Zealand MBIE Strategic Science Investment Fund for support via the ESNZ Ocean-Climate Interaction programme.</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e8705">This paper was edited by Tyler Cyronak and reviewed by three anonymous referees.</p>
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