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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-18-2221-2021</article-id><title-group><article-title>Arctic Ocean acidification over the 21st century co-driven<?xmltex \hack{\break}?> by anthropogenic carbon increases and freshening<?xmltex \hack{\break}?> in the CMIP6 model ensemble</article-title><alt-title>Future Arctic Ocean acidification in CMIP6 models</alt-title>
      </title-group><?xmltex \runningtitle{Future Arctic Ocean acidification in CMIP6 models}?><?xmltex \runningauthor{J. Terhaar et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff2">
          <name><surname>Terhaar</surname><given-names>Jens</given-names></name>
          <email>jens.terhaar@climate.unibe.ch</email>
        <ext-link>https://orcid.org/0000-0001-9377-415X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Torres</surname><given-names>Olivier</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Bourgeois</surname><given-names>Timothée</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-9367-464X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Kwiatkowski</surname><given-names>Lester</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Climate and Environmental Physics, Physics Institute, University of Bern, Bern, Switzerland</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Oeschger Center for Climate Change Research, University of Bern, Bern, Switzerland</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>LMD/IPSL, Ecole Normale Supérieure/PSL Université, CNRS, Ecole Polytechnique, Sorbonne Université, Paris, France</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>NORCE Norwegian Research Centre and Bjerknes Centre for Climate Research, Bergen, Norway</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>LOCEAN/IPSL, Sorbonne Université, CNRS, IRD, MNHN, Paris, France</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Jens Terhaar (jens.terhaar@climate.unibe.ch)</corresp></author-notes><pub-date><day>1</day><month>April</month><year>2021</year></pub-date>
      
      <volume>18</volume>
      <issue>6</issue>
      <fpage>2221</fpage><lpage>2240</lpage>
      <history>
        <date date-type="received"><day>4</day><month>December</month><year>2020</year></date>
           <date date-type="accepted"><day>23</day><month>February</month><year>2021</year></date>
           <date date-type="rev-recd"><day>22</day><month>February</month><year>2021</year></date>
           <date date-type="rev-request"><day>17</day><month>December</month><year>2020</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2021 Jens Terhaar et al.</copyright-statement>
        <copyright-year>2021</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/18/2221/2021/bg-18-2221-2021.html">This article is available from https://bg.copernicus.org/articles/18/2221/2021/bg-18-2221-2021.html</self-uri><self-uri xlink:href="https://bg.copernicus.org/articles/18/2221/2021/bg-18-2221-2021.pdf">The full text article is available as a PDF file from https://bg.copernicus.org/articles/18/2221/2021/bg-18-2221-2021.pdf</self-uri>
      <abstract><title>Abstract</title>
    <p id="d1e140">The uptake of anthropogenic carbon (<inline-formula><mml:math id="M1" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) by the ocean leads to ocean acidification, causing the reduction of pH and the saturation states of aragonite (<inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>) and calcite (<inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>). The Arctic Ocean is particularly vulnerable to ocean acidification due to its naturally low pH and saturation states and due to ongoing freshening and the concurrent reduction in total alkalinity in this region. Here, we analyse ocean acidification in the Arctic Ocean over the 21st century across 14 Earth system models (ESMs) from the latest Coupled Model Intercomparison Project Phase 6 (CMIP6). Compared to the previous model generation (CMIP5), models generally better simulate maximum sea surface densities in the Arctic Ocean and consequently the transport of <inline-formula><mml:math id="M4" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> into the Arctic Ocean interior, with simulated historical increases in <inline-formula><mml:math id="M5" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in improved agreement with observational products. Moreover, in CMIP6 the inter-model uncertainty of projected changes over the 21st century in Arctic Ocean <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> averaged over the upper 1000 m is reduced by 44–64 %. The strong reduction in projection uncertainties of <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> can be attributed to compensation between <inline-formula><mml:math id="M10" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> uptake and total alkalinity reduction in the latest models. Specifically, ESMs with a large increase in Arctic Ocean <inline-formula><mml:math id="M11" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> over the 21st century tend to simulate a relatively weak concurrent freshening and alkalinity reduction, while ESMs with a small increase in <inline-formula><mml:math id="M12" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> simulate a relatively strong freshening and concurrent total alkalinity reduction. Although both mechanisms contribute to Arctic Ocean acidification over the 21st century, the increase in <inline-formula><mml:math id="M13" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> remains the dominant driver. Even under the low-emissions Shared Socioeconomic Pathway 1-2.6 (SSP1-2.6), basin-wide averaged <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> undersaturation in the upper 1000 m occurs before the end of the century. While under the high-emissions pathway SSP5-8.5, the Arctic Ocean mesopelagic is projected to even become undersaturated with respect to calcite. An emergent constraint identified in CMIP5 which relates present-day maximum sea surface densities in the Arctic Ocean to the projected end-of-century Arctic Ocean <inline-formula><mml:math id="M15" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory is found to generally hold in CMIP6. However, a coincident constraint on Arctic declines in <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M17" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is not apparent in the new generation of models. This is due to both the reduction in <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> projection uncertainty and the weaker direct relationship between projected changes in Arctic Ocean <inline-formula><mml:math id="M20" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and changes in <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <?pagebreak page2222?><p id="d1e397">Human activities such as the burning of fossil fuels, cement production, and land use change have released large amounts of carbon into the atmosphere that cause global warming. The ocean mitigates global warming by taking up around one-quarter of this anthropogenic carbon (<inline-formula><mml:math id="M23" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) <xref ref-type="bibr" rid="bib1.bibx34" id="paren.1"/>. However, the increase of carbon in the ocean causes ocean acidification, a process that decreases pH, carbonate ion (<inline-formula><mml:math id="M24" 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>) concentrations, and in consequence the calcium carbonate (<inline-formula><mml:math id="M25" 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 states of calcite and aragonite minerals <xref ref-type="bibr" rid="bib1.bibx48 bib1.bibx79" id="paren.2"/>. The Arctic Ocean is particularly vulnerable to ocean acidification due to its naturally high dissolved inorganic carbon concentrations, its low carbonate ion concentrations, and its thus naturally low saturation states <xref ref-type="bibr" rid="bib1.bibx79 bib1.bibx33 bib1.bibx36 bib1.bibx84 bib1.bibx2" id="paren.3"/>.</p>
      <p id="d1e448">In contrast to most of the global ocean, Arctic Ocean acidification is caused not solely by increasing <inline-formula><mml:math id="M26" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> concentrations <xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx114 bib1.bibx112 bib1.bibx113" id="paren.4"/> but also by freshening <xref ref-type="bibr" rid="bib1.bibx58 bib1.bibx76 bib1.bibx96 bib1.bibx14 bib1.bibx120" id="paren.5"/>. Fresh water from rivers, precipitation, and sea ice typically has much lower total alkalinity (<inline-formula><mml:math id="M27" 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 total dissolved inorganic carbon (<inline-formula><mml:math id="M28" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) concentrations than the ocean and therefore, in the absence of indirect impacts on other fluxes, dilutes both marine <inline-formula><mml:math id="M29" 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 <inline-formula><mml:math id="M30" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx121" id="paren.6"/>. As freshwater <inline-formula><mml:math id="M31" 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 <inline-formula><mml:math id="M32" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> concentrations are generally similar, freshwater fluxes into the ocean typically act to reduce the difference between <inline-formula><mml:math id="M33" 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 <inline-formula><mml:math id="M34" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, decreasing marine <inline-formula><mml:math id="M35" 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> concentrations and ocean pH <xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx5 bib1.bibx122 bib1.bibx115 bib1.bibx116 bib1.bibx121" id="paren.7"/>. In the Arctic Ocean, projected freshening over the 21st century is larger than in most other ocean regions due to ongoing sea ice melt, positive precipitation minus evaporation, and large river runoff <xref ref-type="bibr" rid="bib1.bibx82 bib1.bibx85 bib1.bibx96" id="paren.8"/>.</p>
      <p id="d1e583">Due to freshening and increasing <inline-formula><mml:math id="M36" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> concentrations, the Arctic Ocean is projected to be the first large-scale ocean region to become undersaturated with
respect to the metastable <inline-formula><mml:math id="M37" 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> polymorph aragonite (<inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>) <xref ref-type="bibr" rid="bib1.bibx98" id="paren.9"/>. Under the Representative Concentration Pathway 8.5 (RCP8.5) high-emissions scenario, Arctic Ocean mesopelagic waters may even become undersaturated with respect to the more stable <inline-formula><mml:math id="M39" 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> polymorph calcite (<inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>) before 2100 <xref ref-type="bibr" rid="bib1.bibx112" id="paren.10"/>. Aragonite and calcite undersaturation is likely to affect the growth, reproduction, and survival of calcifying organisms, such as sea butterflies <xref ref-type="bibr" rid="bib1.bibx19" id="paren.11"/> and foraminifera <xref ref-type="bibr" rid="bib1.bibx26" id="paren.12"/>, and could have ramifications for the wider Arctic ecosystem <xref ref-type="bibr" rid="bib1.bibx4 bib1.bibx56" id="paren.13"/>, including some of its most iconic predators, such as grey whales and walruses <xref ref-type="bibr" rid="bib1.bibx51 bib1.bibx2" id="paren.14"/>.</p>
      <p id="d1e668">Projections of Arctic Ocean acidification over the 21st century had considerable subsurface uncertainties in the simulations conducted as part of the Coupled Model Intercomparison Project Phase 5 (CMIP5) <xref ref-type="bibr" rid="bib1.bibx99 bib1.bibx112" id="paren.15"/>, with projected end-of-century basin-wide <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> in mesopelagic waters ranging from 0.61 to 1.05. This large uncertainty has been attributed to multiple factors, including variable inflow of Atlantic waters and their subsequent subduction; difficulties resolving the narrow passages between the Arctic Ocean and its surrounding basins; and differences in brine rejection during sea ice formation, which is critical to the formation of dense Arctic waters <xref ref-type="bibr" rid="bib1.bibx111" id="paren.16"/>.</p>
<sec id="Ch1.S1.SS1">
  <label>1.1</label><title>Emergent constraints on Arctic Ocean carbon uptake and acidification</title>
      <p id="d1e696">Emergent constraints are a suite of statistical techniques that relate observable trends or sensitivities across multi-model ensembles to differences in model projections in order to reduce future uncertainties <xref ref-type="bibr" rid="bib1.bibx1 bib1.bibx47" id="paren.17"/>. An elegant early application that demonstrates many of the principles of emergent constraints is that of <xref ref-type="bibr" rid="bib1.bibx46" id="text.18"/>. In their study of models that contributed to the Intergovernmental Panel on Climate Change's Fourth Assessment Report (AR4), Hall and Qu found a strong positive correlation between the magnitude of a model's snow albedo feedback on present-day seasonal timescales and under future climate change. They concluded that relevant model biases were consistent across these contrasting timescales and therefore observations of the seasonal snow albedo feedback could be used to constrain the ensemble range of the projected snow albedo feedback under climate change. Since the publication of Hall and Qu (2006), emergent constraint approaches have been applied extensively within the Earth sciences to constrain, amongst other things, projections of climate sensitivity <xref ref-type="bibr" rid="bib1.bibx17" id="paren.19"/>, Arctic sea ice extent <xref ref-type="bibr" rid="bib1.bibx8" id="paren.20"/>, precipitation extremes <xref ref-type="bibr" rid="bib1.bibx81 bib1.bibx27" id="paren.21"/>, carbon cycle feedbacks <xref ref-type="bibr" rid="bib1.bibx20 bib1.bibx117" id="paren.22"/>, and marine primary production <xref ref-type="bibr" rid="bib1.bibx63" id="paren.23"/>.</p>
      <p id="d1e721">Recently <xref ref-type="bibr" rid="bib1.bibx112" id="text.24"/> showed that an emergent constraint could be applied to CMIP5 projections of the Arctic Ocean <inline-formula><mml:math id="M42" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory and coincident acidification over the 21st century. As the <inline-formula><mml:math id="M43" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> increase in the Arctic Ocean is mainly driven by the inflow of <inline-formula><mml:math id="M44" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-rich waters from the Atlantic and their subsequent subduction in the Barents Sea <xref ref-type="bibr" rid="bib1.bibx73 bib1.bibx86 bib1.bibx87 bib1.bibx52 bib1.bibx97" id="paren.25"/>, the capability of each model to form dense surface waters in the Barents Sea was shown to strongly influence the future Arctic Ocean <inline-formula><mml:math id="M45" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory. By constraining simulated surface water densities with observations, uncertainties related to the end-of-century Arctic Ocean <inline-formula><mml:math id="M46" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100 were reduced by around one-third, and the best estimate under RCP8.5 was increased by 20 % to <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:mn mathvariant="normal">9.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.6</mml:mn></mml:mrow></mml:math></inline-formula> Pg C <xref ref-type="bibr" rid="bib1.bibx112" id="paren.26"/>. Along with the projected <inline-formula><mml:math id="M48" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory, uncertainties in the projected associated basin-wide Arctic Ocean acidification could also be reduced in CMIP5. It should be noted, however, that in CMIP5 projected freshening and reductions in alkalinity were of minor importance for Arctic Ocean acidification over the 21st century. Moreover, the models have been shown to underestimate historical freshwater fluxes (1992–2012) in the Arctic Ocean by around 50 % <xref ref-type="bibr" rid="bib1.bibx96" id="paren.27"/>, which suggests<?pagebreak page2223?> they might also have underestimated freshwater fluxes over the 21st century.</p>
      <p id="d1e815">Given that emergent constraints in many cases conflict with one another <xref ref-type="bibr" rid="bib1.bibx17 bib1.bibx12" id="paren.28"/> and can even be derived from data-mined pseudocorrelations <xref ref-type="bibr" rid="bib1.bibx16" id="paren.29"/>, it is critical to test published constraints, and the mechanisms that underpin them, across Earth system model (ESM) generations <xref ref-type="bibr" rid="bib1.bibx32 bib1.bibx47" id="paren.30"/>. The CMIP6 simulations provide such an opportunity <xref ref-type="bibr" rid="bib1.bibx89" id="paren.31"/>.</p>
</sec>
<sec id="Ch1.S1.SS2">
  <label>1.2</label><title>From CMIP5 to CMIP6 models and simulations</title>
      <p id="d1e838">During the transition from CMIP5 to CMIP6, ESMs have generally improved the simulation of ocean dynamics and marine biogeochemistry <xref ref-type="bibr" rid="bib1.bibx94" id="paren.32"/>. Across most ESMs, the horizontal and/or vertical resolution of ocean models has increased, which potentially has large effects on the representation of Arctic Ocean circulation, sea ice dynamics <xref ref-type="bibr" rid="bib1.bibx29" id="paren.33"/>, and the carbon cycle <xref ref-type="bibr" rid="bib1.bibx111" id="paren.34"/>. Ocean biogeochemical model components in CMIP6 also tend to have a more complex representation of the carbon and nutrient cycles than in CMIP5. In particular, the treatment of organic matter carbon cycling has generally evolved, with remineralization of particles in sediments now simulated in 10 out of 14 ESMs. These developments will likely have a large effect on simulating the Arctic Ocean biogeochemistry given that 50 % of the Arctic Ocean is made up of shelf seas <xref ref-type="bibr" rid="bib1.bibx50" id="paren.35"/>, where sedimentation and sediment remineralization are crucial components of the carbon and nutrient cycle <xref ref-type="bibr" rid="bib1.bibx15 bib1.bibx40" id="paren.36"/>. Furthermore, the external carbon and nutrient sources from glaciers, atmospheric deposition, and rivers are represented in more models in CMIP6 (Table <xref ref-type="table" rid="Ch1.T1"/>) <xref ref-type="bibr" rid="bib1.bibx94" id="paren.37"/>. Riverine inputs in particular have been shown to be of importance for present-day Arctic Ocean acidification <xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx109" id="paren.38"/> and its future changes <xref ref-type="bibr" rid="bib1.bibx110" id="paren.39"/>.</p>

<?xmltex \floatpos{t}?><table-wrap id="Ch1.T1" specific-use="star"><?xmltex \currentcnt{1}?><label>Table 1</label><caption><p id="d1e871">The CMIP6 ESMs used in this study with their ocean–sea ice and marine-biogeochemical (MBG) model components plus their biogeochemical (BGC) riverine input.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="3.8cm"/>
     <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="justify" colwidth="3.3cm"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Model</oasis:entry>
         <oasis:entry colname="col2">Ocean–sea ice</oasis:entry>
         <oasis:entry colname="col3">MBG</oasis:entry>
         <oasis:entry colname="col4">Riverine BGC fluxes</oasis:entry>
         <oasis:entry colname="col5">Data DOI</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">ACCESS-ESM1.5</oasis:entry>
         <oasis:entry colname="col2">MOM5, CICE4</oasis:entry>
         <oasis:entry colname="col3">WOMBAT</oasis:entry>
         <oasis:entry colname="col4">None</oasis:entry>
         <oasis:entry colname="col5">
                      <xref ref-type="bibr" rid="bib1.bibx126 bib1.bibx127" id="text.40"/>
                    </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">
                      <xref ref-type="bibr" rid="bib1.bibx128" id="paren.41"/>
                    </oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CanESM5</oasis:entry>
         <oasis:entry colname="col2">NEMO 3.4.1-LIM2</oasis:entry>
         <oasis:entry colname="col3">CMOC</oasis:entry>
         <oasis:entry colname="col4">None</oasis:entry>
         <oasis:entry colname="col5">
                      <xref ref-type="bibr" rid="bib1.bibx101 bib1.bibx102" id="text.42"/>
                    </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">
                      <xref ref-type="bibr" rid="bib1.bibx105" id="paren.43"/>
                    </oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CanESM5-CanOE</oasis:entry>
         <oasis:entry colname="col2">NEMO 3.4.1-LIM2</oasis:entry>
         <oasis:entry colname="col3">CanOE</oasis:entry>
         <oasis:entry colname="col4">None</oasis:entry>
         <oasis:entry colname="col5">
                      <xref ref-type="bibr" rid="bib1.bibx103 bib1.bibx104" id="text.44"/>
                    </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">(<xref ref-type="bibr" rid="bib1.bibx105" id="altparen.45"/>;<?xmltex \hack{\hfill\break}?> <xref ref-type="bibr" rid="bib1.bibx18" id="altparen.46"/>)</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CESM2</oasis:entry>
         <oasis:entry colname="col2">POP2-CICE5</oasis:entry>
         <oasis:entry colname="col3">MARBL-BEC</oasis:entry>
         <oasis:entry colname="col4">C, N, P, Fe, Si, <inline-formula><mml:math id="M51" 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></oasis:entry>
         <oasis:entry colname="col5">
                      <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx22" id="text.47"/>
                    </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">
                      <xref ref-type="bibr" rid="bib1.bibx25" id="paren.48"/>
                    </oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CESM2-WACCM</oasis:entry>
         <oasis:entry colname="col2">POP2-CICE5</oasis:entry>
         <oasis:entry colname="col3">MARBL-BEC</oasis:entry>
         <oasis:entry colname="col4">C, N, P, Fe, Si, <inline-formula><mml:math id="M52" 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></oasis:entry>
         <oasis:entry colname="col5">
                      <xref ref-type="bibr" rid="bib1.bibx23 bib1.bibx24" id="text.49"/>
                    </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">
                      <xref ref-type="bibr" rid="bib1.bibx25" id="paren.50"/>
                    </oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">CNRM-ESM2-1</oasis:entry>
         <oasis:entry colname="col2">NEMOv3.6-GELATOv6</oasis:entry>
         <oasis:entry colname="col3">PISCESv2-gas</oasis:entry>
         <oasis:entry colname="col4">C, P, <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></oasis:entry>
         <oasis:entry colname="col5">
                      <xref ref-type="bibr" rid="bib1.bibx92 bib1.bibx93" id="text.51"/>
                    </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">
                      <xref ref-type="bibr" rid="bib1.bibx106" id="paren.52"/>
                    </oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">GFDL-CM4<inline-formula><mml:math id="M54" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">MOM6, SIS2</oasis:entry>
         <oasis:entry colname="col3">BLINGv2</oasis:entry>
         <oasis:entry colname="col4">C, N, P, Fe, <inline-formula><mml:math id="M55" 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></oasis:entry>
         <oasis:entry colname="col5">
                      <xref ref-type="bibr" rid="bib1.bibx42 bib1.bibx43" id="text.53"/>
                    </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">(<xref ref-type="bibr" rid="bib1.bibx49" id="altparen.54"/>;<?xmltex \hack{\hfill\break}?> <xref ref-type="bibr" rid="bib1.bibx30" id="altparen.55"/>)</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">GFDL-ESM4<?xmltex \hack{\hfill\break}?>(<xref ref-type="bibr" rid="bib1.bibx31" id="altparen.56"/>; <?xmltex \hack{\hfill\break}?> <xref ref-type="bibr" rid="bib1.bibx100" id="altparen.57"/>)</oasis:entry>
         <oasis:entry colname="col2">MOM6, SIS2</oasis:entry>
         <oasis:entry colname="col3">COBALTv2</oasis:entry>
         <oasis:entry colname="col4">C, P, N, <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></oasis:entry>
         <oasis:entry colname="col5"><xref ref-type="bibr" rid="bib1.bibx60" id="text.58"/>,<?xmltex \hack{\hfill\break}?> <xref ref-type="bibr" rid="bib1.bibx53" id="text.59"/></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">IPSL-CM6A-LR</oasis:entry>
         <oasis:entry colname="col2">NEMOv3.6-LIM3</oasis:entry>
         <oasis:entry colname="col3">PISCESv2</oasis:entry>
         <oasis:entry colname="col4">C, N, P, Fe, Si, <inline-formula><mml:math id="M57" 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></oasis:entry>
         <oasis:entry colname="col5">
                      <xref ref-type="bibr" rid="bib1.bibx9 bib1.bibx10" id="text.60"/>
                    </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">
                      <xref ref-type="bibr" rid="bib1.bibx11" id="paren.61"/>
                    </oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MIROC-ES2L<?xmltex \hack{\hfill\break}?> <xref ref-type="bibr" rid="bib1.bibx45" id="paren.62"/></oasis:entry>
         <oasis:entry colname="col2">COCO</oasis:entry>
         <oasis:entry colname="col3">OECO2</oasis:entry>
         <oasis:entry colname="col4">N, P</oasis:entry>
         <oasis:entry colname="col5"><xref ref-type="bibr" rid="bib1.bibx44" id="text.63"/>, <?xmltex \hack{\hfill\break}?> <xref ref-type="bibr" rid="bib1.bibx107" id="text.64"/></oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MPI-ESM1.2-HR<?xmltex \hack{\hfill\break}?>(<xref ref-type="bibr" rid="bib1.bibx75" id="altparen.65"/>;<?xmltex \hack{\hfill\break}?> <xref ref-type="bibr" rid="bib1.bibx68" id="altparen.66"/>)</oasis:entry>
         <oasis:entry colname="col2">MPIOM</oasis:entry>
         <oasis:entry colname="col3">HAMOCC6</oasis:entry>
         <oasis:entry colname="col4">None</oasis:entry>
         <oasis:entry colname="col5"><xref ref-type="bibr" rid="bib1.bibx91" id="text.67"/>,<?xmltex \hack{\hfill\break}?> <xref ref-type="bibr" rid="bib1.bibx55" id="text.68"/></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MPI-ESM1.2-LR</oasis:entry>
         <oasis:entry colname="col2">MPIOM</oasis:entry>
         <oasis:entry colname="col3">HAMOCC6</oasis:entry>
         <oasis:entry colname="col4">None</oasis:entry>
         <oasis:entry colname="col5">
                      <xref ref-type="bibr" rid="bib1.bibx118 bib1.bibx119" id="text.69"/>
                    </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">
                      <xref ref-type="bibr" rid="bib1.bibx68" id="paren.70"/>
                    </oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MRI-ESM2<inline-formula><mml:math id="M58" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">MRICOM4</oasis:entry>
         <oasis:entry colname="col3">NPZD</oasis:entry>
         <oasis:entry colname="col4">None</oasis:entry>
         <oasis:entry colname="col5">
                      <xref ref-type="bibr" rid="bib1.bibx124 bib1.bibx125" id="text.71"/>
                    </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">
                      <xref ref-type="bibr" rid="bib1.bibx123" id="paren.72"/>
                    </oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">UKESM1-0-LL<?xmltex \hack{\hfill\break}?> <xref ref-type="bibr" rid="bib1.bibx95" id="paren.73"/></oasis:entry>
         <oasis:entry colname="col2">NEMO v3.6, CICE</oasis:entry>
         <oasis:entry colname="col3">MEDUSA-2</oasis:entry>
         <oasis:entry colname="col4">None</oasis:entry>
         <oasis:entry colname="col5"><xref ref-type="bibr" rid="bib1.bibx108" id="text.74"/>, <?xmltex \hack{\hfill\break}?> <xref ref-type="bibr" rid="bib1.bibx39" id="text.75"/></oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table><table-wrap-foot><p id="d1e874"><inline-formula><mml:math id="M49" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">a</mml:mi></mml:msup></mml:math></inline-formula> Only SSP2-4.5 and SSP5-8.5. <inline-formula><mml:math id="M50" display="inline"><mml:msup><mml:mi/><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:math></inline-formula> Only SSP5-8.5.</p></table-wrap-foot></table-wrap>

      <p id="d1e1528">In this study, we extend recent CMIP6 ocean biogeochemical assessments <xref ref-type="bibr" rid="bib1.bibx94 bib1.bibx64" id="paren.76"><named-content content-type="pre">e.g.</named-content></xref> and previous attempts to constrain projected Arctic Ocean <inline-formula><mml:math id="M59" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> uptake by
<list list-type="order"><list-item>
      <p id="d1e1549">assessing projections of the Arctic Ocean <inline-formula><mml:math id="M60" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory over the 21st century in CMIP6 simulations</p></list-item><list-item>
      <p id="d1e1564">exploring the role of <inline-formula><mml:math id="M61" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory increases and freshening in driving concurrent basin-wide ocean acidification in the Arctic Basin</p></list-item><list-item>
      <p id="d1e1579">revaluating previous emergent constraints on the Arctic Ocean <inline-formula><mml:math id="M62" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory and associated acidification using the CMIP6 model ensemble and multiple future-emissions scenarios.</p></list-item></list></p><?xmltex \hack{\newpage}?>
</sec>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Arctic Ocean</title>
      <p id="d1e1610">The Arctic Ocean was defined as the water north of the Fram Strait, the Barents Sea Opening, the Bering Strait, and the Baffin Bay following <xref ref-type="bibr" rid="bib1.bibx5" id="text.77"/>. This is consistent with the previously published emergent constraint on projected Arctic Ocean <inline-formula><mml:math id="M63" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and acidification <xref ref-type="bibr" rid="bib1.bibx112" id="paren.78"/>.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Earth system models</title>
      <p id="d1e1638">An ensemble of 14 ESMs from CMIP6 (Table <xref ref-type="table" rid="Ch1.T1"/>) was used with one ensemble member per model. All models follow the biogeochemical protocols
outlined in <xref ref-type="bibr" rid="bib1.bibx80" id="text.79"/>. Riverine input of <inline-formula><mml:math id="M64" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M65" 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> is included in six ESMs (Table <xref ref-type="table" rid="Ch1.T1"/>). The absence of <inline-formula><mml:math id="M66" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M67" 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> in riverine freshwater input causes an overly strong reduction of <inline-formula><mml:math id="M68" 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> concentrations and thus low-biased saturation states in coastal regions but is of minor importance on the pan-Arctic scale <xref ref-type="bibr" rid="bib1.bibx110" id="paren.80"/>. The spin-up length for each model varied between 500 years (IPSL-CM6A-LR) and 12 000 years (MPI-ESM1-2-LR) <xref ref-type="bibr" rid="bib1.bibx94" id="paren.81"/>.</p>
      <p id="d1e1715">For each model, monthly 3D fields of dissolved inorganic carbon, total alkalinity, dissolved inorganic phosphorus and silicon, temperature, and salinity were used. All 3D fields were regridded to the regular <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> grid with 33 depth levels used in the GLobal Ocean Data Analysis Project Version 2 (GLODAPv2) observational product <xref ref-type="bibr" rid="bib1.bibx65" id="paren.82"/> to add simulated changes of these variables over the 21st century to observations of the present-day mean state (see below).</p>
      <p id="d1e1741"><inline-formula><mml:math id="M70" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> was defined as the difference between annual means of dissolved inorganic carbon in the historical (1850–2014) simulations merged with the respective shared socioeconomic pathway (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5; 2015–2100; <xref ref-type="bibr" rid="bib1.bibx83" id="altparen.83"/>) and the concurrent pre-industrial control simulations of each model. Output from 13 models was available for SSP1-2.6, output from 12 models for SSP2-4.5 and SSP3-7.0, and output from 14 models for SSP5-8.5 (Table <xref ref-type="table" rid="Ch1.T1"/>).</p>
      <p id="d1e1759">Changes in <inline-formula><mml:math id="M71" 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> over the 21st century were calculated by subtracting changes in the pre-industrial control simulations from changes in the respective SSP. To quantify the effect of freshening on changes in <inline-formula><mml:math id="M72" 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>, the <inline-formula><mml:math id="M73" 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> anomalies for each model were further decomposed into changes resulting from freshening and from the combined effect of other biogeochemical processes by calculating the temporal evolution of salinity-corrected alkalinity with a reference salinity of 35 following <xref ref-type="bibr" rid="bib1.bibx67" id="text.84"/>. A zero-alkalinity endmember was assumed for fresh water. This assumption is correct for models with no alkalinity in fresh water but an overestimation for models with finite alkalinity concentrations in freshwater inputs (Table <xref ref-type="table" rid="Ch1.T1"/>). Unfortunately, information on<?pagebreak page2224?> alkalinity concentrations in fresh water is not available for all models. Moreover, with the available model output, we cannot quantify the individual contributions of land ice melt, sea ice melt, precipitation minus evaporation, and riverine input to freshwater changes. Thus, for simplicity a zero-alkalinity endmember was assumed for all models.</p>
      <p id="d1e1801">Ocean carbon chemistry variables in ESMs commonly exhibit mean state biases <xref ref-type="bibr" rid="bib1.bibx79 bib1.bibx99" id="paren.85"/>. Therefore, observations of <inline-formula><mml:math id="M74" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M75" 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>, dissolved inorganic phosphorus and silicon, temperature, and salinity from GLODAPv2 <xref ref-type="bibr" rid="bib1.bibx65" id="paren.86"/>, which is normalized to the year 2002, were used to calculate present-day <inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, pH, and <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> using the <italic>mocsy2.0</italic> routine <xref ref-type="bibr" rid="bib1.bibx78" id="paren.87"/> and the equilibrium constants recommended for best practices <xref ref-type="bibr" rid="bib1.bibx28" id="paren.88"/>. Future <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, pH, and <inline-formula><mml:math id="M81" 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> were calculated for each model as the sum of the simulated changes in <inline-formula><mml:math id="M82" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M83" 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>, dissolved inorganic phosphorus and silicon, temperature, and salinity from 2002 onwards and the observed quantities in 2002.</p>
      <p id="d1e1935">The present-day maximum sea surface density in the Arctic Ocean was calculated from monthly climatologies over 1986–2005, constructed from the respective salinity and<?pagebreak page2225?> temperature outputs of each model. Maximum sea surface density was calculated, as in <xref ref-type="bibr" rid="bib1.bibx112" id="text.89"/>, as the mean density of the densest 5 % of Arctic surface waters (95th-percentile waters) over all 12 months of the year.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Simulations</title>
      <p id="d1e1949">The simulations performed within CMIP5 were not forced with the same atmospheric <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> concentrations as the simulations performed under CMIP6. In CMIP5, historically observed atmospheric <inline-formula><mml:math id="M85" 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> concentrations were used from 1850 to 2005 <xref ref-type="bibr" rid="bib1.bibx70" id="paren.90"/>. From 2006 onwards, the <inline-formula><mml:math id="M86" 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> concentrations follow the different RCPs. In CMIP6, the historical period was extended until 2014, and thereafter <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> concentrations follow the different SSPs <xref ref-type="bibr" rid="bib1.bibx72" id="paren.91"/>.</p>
      <p id="d1e2003">The different land and energy use assumptions in the SSPs <xref ref-type="bibr" rid="bib1.bibx83" id="paren.92"/> compared to the RCPs <xref ref-type="bibr" rid="bib1.bibx77" id="paren.93"/> lead to higher atmospheric <inline-formula><mml:math id="M88" 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> trajectories over the 21st century for the Tier 1 SSPs <xref ref-type="bibr" rid="bib1.bibx72" id="paren.94"/> compared to their RCP counterparts <xref ref-type="bibr" rid="bib1.bibx70" id="paren.95"/>, which results in globally greater surface ocean acidification in CMIP6 compared to CMIP5 <xref ref-type="bibr" rid="bib1.bibx64" id="paren.96"/>. Historical atmospheric <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> concentrations were also refined with additional data available since CMIP5 <xref ref-type="bibr" rid="bib1.bibx71" id="paren.97"/>. This refinement did not change the average atmospheric <inline-formula><mml:math id="M90" 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> concentration from 1850 to 2005 (<inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:mrow class="chem"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>p</mml:mi><mml:msubsup><mml:mi mathvariant="normal">CO</mml:mi><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="normal">atm</mml:mi></mml:msubsup></mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> ppm) but did change annual <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> concentration for single years by up to <inline-formula><mml:math id="M93" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> ppm. Furthermore, global <inline-formula><mml:math id="M94" 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> concentrations were additionally provided as monthly latitudinally resolved concentrations, with model groups free to choose the forcing files they use <xref ref-type="bibr" rid="bib1.bibx71 bib1.bibx72" id="paren.98"/>.</p>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><?xmltex \opttitle{{$\protect\chem{C_{{ant}}}$} scaling}?><title><inline-formula><mml:math id="M95" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> scaling</title>
      <p id="d1e2139">The different atmospheric <inline-formula><mml:math id="M96" 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> trajectories over the 21st century between CMIP5 and CMIP6 complicates a comparison of simulated Arctic Ocean <inline-formula><mml:math id="M97" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventories between model generations. To nevertheless compare the simulated Arctic Ocean <inline-formula><mml:math id="M98" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, we used the commonly applied scaling approach that assumes that the change in marine <inline-formula><mml:math id="M99" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is proportional to the atmospheric <inline-formula><mml:math id="M100" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> concentration <xref ref-type="bibr" rid="bib1.bibx38 bib1.bibx74 bib1.bibx37 bib1.bibx41" id="paren.99"/>. Under this assumption, the <inline-formula><mml:math id="M101" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100 for each scenario (RCP8.5, SSP1-2.6, SSP2-4.5, SSP3-7.0) is linearly rescaled to that of SSP5-8.5 by multiplying the simulated Arctic Ocean <inline-formula><mml:math id="M102" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory under the respective scenario by the ratio of the mean atmospheric <inline-formula><mml:math id="M103" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> concentration from 1850 to 2100 in SSP5-8.5 and the respective scenario.</p>
      <p id="d1e2234">This approximation is likely imprecise when very different scenarios are compared, such as SSP1-2.6 and SSP5-8.5, as the effects of circulation changes, sea ice melt, and warming are not considered. However, when comparing scenarios with the same radiative forcing, such as SSP5-8.5 and RCP8.5, it permits a first-order comparison.</p>
</sec>
<sec id="Ch1.S2.SS5">
  <label>2.5</label><title>Observational constraints</title>
      <p id="d1e2246">As for the ESMs, the maximum sea surface density was calculated based on a monthly sea surface density climatology on a regular <inline-formula><mml:math id="M104" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> grid, which was constructed from observed monthly salinity and temperature climatologies in the World Ocean Atlas 2018 <xref ref-type="bibr" rid="bib1.bibx66 bib1.bibx129" id="paren.100"/>.</p>
      <p id="d1e2272">The density uncertainty was calculated from the temperature and salinity uncertainties that were reported by the World Ocean Atlas following standard propagation of uncertainty. The total uncertainty is a combination of (1) the standard deviations for sea surface density derived from published standard deviations of sea surface temperature and salinity for each grid cell and each month in the World Ocean Atlas 2018, and (2) the standard deviation from the weighted mean of the 95th-percentile-density waters <xref ref-type="bibr" rid="bib1.bibx112" id="paren.101"/>.</p>
</sec>
<sec id="Ch1.S2.SS6">
  <label>2.6</label><?xmltex \opttitle{Emergent constraints and probability density functions of {$\protect\chem{C_{{ant}}}$}}?><title>Emergent constraints and probability density functions of <inline-formula><mml:math id="M105" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula></title>
      <p id="d1e2297">To calculate the emergent constraint, first an ordinary least-squares regression was calculated between the simulated present-day maximum sea surface density and the Arctic Ocean <inline-formula><mml:math id="M106" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100 for each ESM of the CMIP6 model ensemble. The uncertainty range was estimated using the <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> prediction interval. In a second step the probability density function (PDF) from the observations was convoluted with the PDF from the linear regression, assuming a Gaussian distribution in both cases. The convolution of both PDFs is the constrained projection of the Arctic Ocean <inline-formula><mml:math id="M108" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory following previous studies <xref ref-type="bibr" rid="bib1.bibx20 bib1.bibx117 bib1.bibx63" id="paren.102"/>. The PDFs for unconstrained projections of the <inline-formula><mml:math id="M109" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory were calculated using equal weights for each model and assuming a Gaussian distribution.</p>
      <p id="d1e2346">Extending the analysis of <xref ref-type="bibr" rid="bib1.bibx112" id="text.103"/>, PDFs for the constrained projections of the <inline-formula><mml:math id="M110" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory were calculated not only for the year 2100 but for each year from 2002 to 2100 and not only for the highest-emission scenario (RCP8.5) but for the four SSPs (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5).</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><?xmltex \opttitle{Arctic Ocean {$\protect\chem{C_{{ant}}}$} inventory}?><title>Arctic Ocean <inline-formula><mml:math id="M111" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory</title>
<sec id="Ch1.S3.SS1.SSS1">
  <label>3.1.1</label><title>Multi-model mean</title>
      <?pagebreak page2226?><p id="d1e2398">Over the historical period from 1850 to 2005, the CMIP6 ESMs simulate an Arctic Ocean <inline-formula><mml:math id="M112" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> increase of <inline-formula><mml:math id="M113" display="inline"><mml:mrow><mml:mn mathvariant="normal">2.1</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.6</mml:mn></mml:mrow></mml:math></inline-formula> Pg C (inter-model standard deviation; Fig. <xref ref-type="fig" rid="Ch1.F1"/>a). Thus, the CMIP6 ESMs simulate an Arctic Ocean <inline-formula><mml:math id="M114" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2005 that is 36 % below the data-based estimate for the period from 1765 to 2005 of <inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:mn mathvariant="normal">3.3</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.3</mml:mn></mml:mrow></mml:math></inline-formula> Pg C <xref ref-type="bibr" rid="bib1.bibx113" id="paren.104"/>.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1"><?xmltex \currentcnt{1}?><?xmltex \def\figurename{Figure}?><label>Figure 1</label><caption><p id="d1e2455">Arctic Ocean <inline-formula><mml:math id="M116" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory over the 21st century. <bold>(a)</bold> Time series of multi-model mean Arctic Ocean <inline-formula><mml:math id="M117" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory over the 21st century for SSP1-2.6 (blue), SSP2-4.5 (green), SSP3-7.0 (orange), and SSP5-8.5 (red) with the respective standard deviation across the model ensemble (shading) (<inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">12</mml:mn></mml:mrow></mml:math></inline-formula>–14). The bars on the right side of panels indicate the inter-model standard deviation in the year 2100. <bold>(b)</bold> Time series of Arctic Ocean <inline-formula><mml:math id="M119" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory for each scenario after the emergent constraint is applied.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://bg.copernicus.org/articles/18/2221/2021/bg-18-2221-2021-f01.png"/>

          </fig>

      <p id="d1e2516">Over the 21st century the Arctic Ocean <inline-formula><mml:math id="M120" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory increases depending on the SSP. Following the low-emission pathway SSP1-2.6 leads to a projected Arctic Ocean <inline-formula><mml:math id="M121" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100 of <inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:mn mathvariant="normal">6.2</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.3</mml:mn></mml:mrow></mml:math></inline-formula> Pg C. With increasing atmospheric <inline-formula><mml:math id="M123" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> concentrations from SSP1-2.6 to SSP5-8.5, the projected Arctic Ocean <inline-formula><mml:math id="M124" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100 also increases, resulting in <inline-formula><mml:math id="M125" display="inline"><mml:mrow><mml:mn mathvariant="normal">8.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.7</mml:mn></mml:mrow></mml:math></inline-formula> for SSP2-4.5, <inline-formula><mml:math id="M126" display="inline"><mml:mrow><mml:mn mathvariant="normal">9.6</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.6</mml:mn></mml:mrow></mml:math></inline-formula> for SSP3-7.0, and <inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:mn mathvariant="normal">10.3</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2.2</mml:mn></mml:mrow></mml:math></inline-formula> Pg C for SSP5-8.5. The relatively large uncertainties across the model ensemble (17–21 %) result in an overlap of the simulated <inline-formula><mml:math id="M128" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventories in 2100 for SSP2-4.5, SSP3-7.0, and SSP5-8.5 within <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> SD.</p>
</sec>
<sec id="Ch1.S3.SS1.SSS2">
  <label>3.1.2</label><title>Constrained results</title>
      <p id="d1e2641">As was shown for RCP8.5 in the CMIP5 model ensemble <xref ref-type="bibr" rid="bib1.bibx112" id="paren.105"/>, a linear relationship between maximum sea surface density and the Arctic Ocean <inline-formula><mml:math id="M130" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100 is found across the CMIP6 model ensemble for all four of the SSPs (<inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.63</mml:mn></mml:mrow></mml:math></inline-formula>–0.72; Fig. <xref ref-type="fig" rid="Ch1.F2"/>a, c, e, and g). By deriving a similar relationship for the projected <inline-formula><mml:math id="M132" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in all years from 2000 to 2100 and combining this with observations of present-day sea surface density, the uncertainty of the projected Arctic Ocean <inline-formula><mml:math id="M133" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory can be reduced throughout the 21st century (Fig. <xref ref-type="fig" rid="Ch1.F1"/>b). The emergent relationship is significant over all years from 2015 to 2100 (<inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula>) and the <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> increases from 0.39 in 2014 to 0.63–0.72 in 2100 depending on the scenario. In the year 2100, this results in Arctic Ocean <inline-formula><mml:math id="M136" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory estimates of <inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mn mathvariant="normal">6.3</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.9</mml:mn></mml:mrow></mml:math></inline-formula> (SSP1-2.6), <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:mn mathvariant="normal">8.2</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula> (SSP2-4.5), <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:mn mathvariant="normal">9.8</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.1</mml:mn></mml:mrow></mml:math></inline-formula> (SSP3-7.0), and <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:mn mathvariant="normal">10.7</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.4</mml:mn></mml:mrow></mml:math></inline-formula> Pg C (SSP5-8.5) (Fig. <xref ref-type="fig" rid="Ch1.F2"/>b, d, f, and h). Thus, the emergent constraint is shown to slightly increase the CMIP6 multi-model mean projected <inline-formula><mml:math id="M141" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory for each SSP (<inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> % to <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula> %) and substantially reduce associated uncertainties (<inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">29</mml:mn></mml:mrow></mml:math></inline-formula> % to <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">31</mml:mn></mml:mrow></mml:math></inline-formula> %) resulting in greater separation of the SSPs (Fig. <xref ref-type="fig" rid="Ch1.F1"/>).</p>

      <?xmltex \floatpos{p}?><fig id="Ch1.F2" specific-use="star"><?xmltex \currentcnt{2}?><?xmltex \def\figurename{Figure}?><label>Figure 2</label><caption><p id="d1e2841">Emergent constraint on Arctic Ocean <inline-formula><mml:math id="M146" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100. Maximum Arctic Ocean sea surface density (95th percentile) and Arctic Ocean <inline-formula><mml:math id="M147" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100 for 12–14 ESMs for <bold>(a)</bold> SSP1-2.6 (blue), <bold>(c)</bold> SSP2-4.5 (green), <bold>(e)</bold> SSP3-7.0 (orange), and <bold>(g)</bold> SSP5-8.5 (red). The ordinary least-squares regressions (dashed lines) and the <inline-formula><mml:math id="M148" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> prediction intervals (shaded area) are shown for each SSP. Probability density functions before and after applying the emergent constraint for <bold>(b)</bold> SSP1-2.6, <bold>(d)</bold> SSP2-4.5, <bold>(f)</bold> SSP3-7.0, and <bold>(h)</bold> SSP5-8.5.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/18/2221/2021/bg-18-2221-2021-f02.png"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Ocean acidification</title>
<sec id="Ch1.S3.SS2.SSS1">
  <label>3.2.1</label><title>Multi-model mean</title>
      <p id="d1e2925">Over the 21st century, ocean acidification leads to a reduction in <inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="Ch1.F3"/>). Until around 2040, the reduction of both saturation states averaged over the upper 1000 m is independent of the SSP. From 2040 onwards, the rate of the reduction depends on the pathway, and by 2100 basin-wide <inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> averaged over the upper 1000 m reaches <inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.00</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.06</mml:mn></mml:mrow></mml:math></inline-formula> (SSP1-2.6), <inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.82</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula> (SSP2-4.5), <inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.66</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.04</mml:mn></mml:mrow></mml:math></inline-formula> (SSP3-7.0), and <inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.59</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula> (SSP5-8.5), while <inline-formula><mml:math id="M156" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> reaches <inline-formula><mml:math id="M157" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.56</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.09</mml:mn></mml:mrow></mml:math></inline-formula> (SSP1-2.6), <inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.29</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.08</mml:mn></mml:mrow></mml:math></inline-formula> (SSP2-4.5), <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.06</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.06</mml:mn></mml:mrow></mml:math></inline-formula> (SSP3-7.0), and <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:mn mathvariant="normal">0.92</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula> (SSP5-8.5).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3" specific-use="star"><?xmltex \currentcnt{3}?><?xmltex \def\figurename{Figure}?><label>Figure 3</label><caption><p id="d1e3074">Basin-wide Arctic Ocean calcium carbonate saturation states over the 21st century. Time series of multi-model mean basin-wide saturation states of aragonite from 2000 to 2014 (black) and from 2015 to 2100 for SSP1-2.6 (blue), SSP2-4.5 (green), SSP3-7.0 (orange), and SSP5-8.5 (red) averaged <bold>(a)</bold> from 0 to 1000 m, <bold>(c)</bold> from 0 to 50 m, <bold>(e)</bold> from 50 to 500 m, and <bold>(g)</bold> from 500 to 1000 m with <inline-formula><mml:math id="M161" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> SD (<inline-formula><mml:math id="M162" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">12</mml:mn></mml:mrow></mml:math></inline-formula>–14) shown as a shaded area. The differences when changing from historical simulations to the SSPs result from the different number of ensemble members that are available for each simulation. <bold>(b, d, f, h)</bold> The same time series but for calcite.</p></caption>
            <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://bg.copernicus.org/articles/18/2221/2021/bg-18-2221-2021-f03.png"/>

          </fig>

      <p id="d1e3121">The upper 1000 m of the Arctic Ocean is projected to be on average undersaturated with respect to aragonite by 2100 under all of the SSPs, with <inline-formula><mml:math id="M163" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> in SSP1-2.6 just below 1 (0.995). Vertically, the entire water column will be undersaturated with respect to aragonite in 2100 for all pathways but SSP1-2.6 (Fig. <xref ref-type="fig" rid="Ch1.F4"/>). Under this low-emissions pathway, Arctic Ocean waters above 500 m are projected to remain supersaturated with respect to aragonite, while those below 500 m are projected to be undersaturated. For the more stable calcium carbonate polymorph calcite, basin-wide Arctic Ocean undersaturation is only projected under SSP5-8.5. Under this high-emissions pathway, basin-wide undersaturation is projected for the water masses between 50 and 800 m.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4"><?xmltex \currentcnt{4}?><?xmltex \def\figurename{Figure}?><label>Figure 4</label><caption><p id="d1e3140">Vertical profile of basin-wide Arctic Ocean calcium carbonate saturation states, pH, and <inline-formula><mml:math id="M164" 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 2100. Multi-model mean vertical profiles of <bold>(a)</bold> aragonite and <bold>(b)</bold> calcite saturation states, <bold>(c)</bold> pH, and <bold>(d)</bold> <inline-formula><mml:math id="M165" 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 2100 for SSP1-2.6 (blue), SSP2-4.5 (green), SSP3-7.0 (orange), and SSP5-8.5 (red) averaged <bold>(a)</bold> with <inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> SD (<inline-formula><mml:math id="M167" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">12</mml:mn></mml:mrow></mml:math></inline-formula>–14) shown as a shaded area. Observed profiles in 2002 from GLODAPv2 are shown in black <xref ref-type="bibr" rid="bib1.bibx65" id="paren.106"/>.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://bg.copernicus.org/articles/18/2221/2021/bg-18-2221-2021-f04.png"/>

          </fig>

      <p id="d1e3216">Alongside declines in calcium carbonate saturation states, pH and <inline-formula><mml:math id="M168" 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> are also projected to change over the 21st century. Basin-wide averaged pH in the upper 1000 m decreases from 8.06 in 2002 to <inline-formula><mml:math id="M169" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.88</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.02</mml:mn></mml:mrow></mml:math></inline-formula> (SSP1-2.6), <inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.79</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.03</mml:mn></mml:mrow></mml:math></inline-formula> (SSP2-4.5), <inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.68</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.03</mml:mn></mml:mrow></mml:math></inline-formula> (SSP3-7.0), and <inline-formula><mml:math id="M172" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.61</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.03</mml:mn></mml:mrow></mml:math></inline-formula> (SSP5-8.5), while basin-wide averaged <inline-formula><mml:math id="M173" 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 the upper 1000 m increases to <inline-formula><mml:math id="M174" display="inline"><mml:mrow><mml:mn mathvariant="normal">739</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">38</mml:mn></mml:mrow></mml:math></inline-formula> (SSP1-2.6), <inline-formula><mml:math id="M175" display="inline"><mml:mrow><mml:mn mathvariant="normal">918</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">75</mml:mn></mml:mrow></mml:math></inline-formula> (SSP2-4.5), <inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:mn mathvariant="normal">1209</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">92</mml:mn></mml:mrow></mml:math></inline-formula> (SSP3-7.0), and <inline-formula><mml:math id="M177" display="inline"><mml:mrow><mml:mn mathvariant="normal">1428</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">124</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M178" 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> (SSP5-8.5). The lowest pH values and highest <inline-formula><mml:math id="M179" 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> values are projected to occur between 100 and 1000 m from the surface (Fig. <xref ref-type="fig" rid="Ch1.F4"/>).</p>
</sec>
<sec id="Ch1.S3.SS2.SSS2">
  <label>3.2.2</label><title>Emergent constraints on acidification</title>
      <?pagebreak page2228?><p id="d1e3376">The emergent relationship between observed maximum sea surface density and end-of-century Arctic Ocean acidification that was previously identified in CMIP5 models <xref ref-type="bibr" rid="bib1.bibx112" id="paren.107"/> does not exist anymore in the new CMIP6 model generation (Fig. <xref ref-type="fig" rid="Ch1.F5"/>). Despite the emergent constraint approach still functioning for projections of the Arctic Ocean <inline-formula><mml:math id="M180" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in CMIP6, this no longer translates into an emergent constraint for Arctic Ocean <inline-formula><mml:math id="M181" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M182" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. However, if all changes in ocean biogeochemistry with the exception of alkalinity, which is kept constant at observed levels from 2002 <xref ref-type="bibr" rid="bib1.bibx65" id="paren.108"/>, are considered when estimating changes in <inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, emergent relationships are still found between maximum sea surface density and <inline-formula><mml:math id="M185" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> across all SSPs (<inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.54</mml:mn></mml:mrow></mml:math></inline-formula>–0.73). When decreases in alkalinity (<inline-formula><mml:math id="M187" 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 also taken into account, <inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> decrease further, and the emergent relationship disappears (<inline-formula><mml:math id="M190" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula>–0.12).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><?xmltex \currentcnt{5}?><?xmltex \def\figurename{Figure}?><label>Figure 5</label><caption><p id="d1e3520">The CMIP6 ensemble relationship between end-of-century <inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and the <inline-formula><mml:math id="M192" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in the Arctic Ocean. Basin-wide <inline-formula><mml:math id="M193" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> averaged over the upper 1000 m with (orange) and without (blue) taking into account concurrent changes in alkalinity (<inline-formula><mml:math id="M194" 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>) against the Arctic Ocean <inline-formula><mml:math id="M195" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in the year 2100 for <bold>(a)</bold> SSP1-2.6, <bold>(a)</bold> SSP2-4.5, <bold>(c)</bold> SSP3-7.0, and <bold>(d)</bold> SSP5-8.5.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://bg.copernicus.org/articles/18/2221/2021/bg-18-2221-2021-f05.png"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Comparison between CMIP5 and CMIP6</title>
      <p id="d1e3606">Compared to ESMs from CMIP5, the new generation of ESMs (CMIP6) has improved in simulating the maximum Arctic Ocean sea surface density. Specifically, negative density biases have been reduced, and the inter-model range in maximum sea surface density has substantially decreased from 3.6 in CMIP5 <xref ref-type="bibr" rid="bib1.bibx112" id="paren.109"/> to 0.9 <inline-formula><mml:math id="M196" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> in CMIP6 (Fig. <xref ref-type="fig" rid="Ch1.F2"/>). As a result, the inter-model range of the <inline-formula><mml:math id="M197" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in the CMIP6 model ensemble is also reduced (Fig. <xref ref-type="fig" rid="Ch1.F2"/>). Moreover, without the negative maximum-sea-surface-density bias, the simulated multi-model mean Arctic Ocean <inline-formula><mml:math id="M198" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2005 is 61 % higher than the inventory that was simulated by the previous model generation (<inline-formula><mml:math id="M199" display="inline"><mml:mrow><mml:mn mathvariant="normal">1.3</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.7</mml:mn></mml:mrow></mml:math></inline-formula> Pg C) <xref ref-type="bibr" rid="bib1.bibx112" id="paren.110"/>.</p>
      <p id="d1e3671">At the end of the 21st century, the unconstrained simulated Arctic Ocean <inline-formula><mml:math id="M200" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory under SSP5-8.5 is 37 % larger and the uncertainty is 19 % smaller than the unconstrained simulated <inline-formula><mml:math id="M201" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100 under RCP8.5 (<inline-formula><mml:math id="M202" display="inline"><mml:mrow><mml:mn mathvariant="normal">7.5</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2.9</mml:mn></mml:mrow></mml:math></inline-formula> Pg C) <xref ref-type="bibr" rid="bib1.bibx112" id="paren.111"/>. After applying the constraint, the Arctic Ocean <inline-formula><mml:math id="M203" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100 under SSP5-8.5 (<inline-formula><mml:math id="M204" display="inline"><mml:mrow><mml:mn mathvariant="normal">10.7</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.4</mml:mn></mml:mrow></mml:math></inline-formula> Pg C) is 19 % larger than the constrained Arctic Ocean <inline-formula><mml:math id="M205" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory under RCP8.5 (<inline-formula><mml:math id="M206" display="inline"><mml:mrow><mml:mn mathvariant="normal">9.0</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.6</mml:mn></mml:mrow></mml:math></inline-formula> Pg C). This difference is of the same order of magnitude as the difference in prescribed atmospheric <inline-formula><mml:math id="M207" 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> concentration over the 21st century, which is higher in SSP5-8.5 (CMIP6) than RCP8.5 (CMIP5) <xref ref-type="bibr" rid="bib1.bibx70 bib1.bibx72" id="paren.112"/> and therefore results in greater surface ocean acidification for approximately the same radiative forcing <xref ref-type="bibr" rid="bib1.bibx64" id="paren.113"/>.</p>
      <?pagebreak page2229?><p id="d1e3775">To compare the emergent constraint across scenarios with different atmospheric <inline-formula><mml:math id="M208" 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> concentrations, the simulated Arctic Ocean <inline-formula><mml:math id="M209" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100 for each scenario was rescaled to SSP5-8.5 using the mean atmospheric <inline-formula><mml:math id="M210" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> concentration from 1850 to 2100 as a linear scaling factor (Fig. <xref ref-type="fig" rid="Ch1.F6"/>). The relationship remains robust (<inline-formula><mml:math id="M211" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.63</mml:mn></mml:mrow></mml:math></inline-formula>–0.74) for all five analysed scenarios. The slope of the emergent relationship is however substantially steeper in CMIP6 (9.4–12.6 <inline-formula><mml:math id="M212" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Pg</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">C</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:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) than in CMIP5 (3.3 <inline-formula><mml:math id="M213" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Pg</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">C</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:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>). However, the slope in CMIP5 increases to 8.9 <inline-formula><mml:math id="M214" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Pg</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">C</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:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> if the three CMIP5 models with particularly low maximum sea surface densities (<inline-formula><mml:math id="M215" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">27.5</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M216" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) are excluded (dotted line in Fig. <xref ref-type="fig" rid="Ch1.F6"/>). The resulting constrained estimate for the rescaled Arctic Ocean <inline-formula><mml:math id="M217" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory decreases from the low-emission scenario to the high-emission scenario from 12.3 to 10.7 Pg C. When comparing the two high-emission scenarios, the rescaled Arctic Ocean <inline-formula><mml:math id="M218" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventories are 10.7 (SSP5-8.5) and 10.4 Pg C (RCP8.5). The latter remains unchanged if the three CMIP5 models with particularly low maximum sea surface densities (<inline-formula><mml:math id="M219" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">27.5</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M220" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) are excluded.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6"><?xmltex \currentcnt{6}?><?xmltex \def\figurename{Figure}?><label>Figure 6</label><caption><p id="d1e3989">Arctic Ocean <inline-formula><mml:math id="M221" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100, rescaled to SSP5-8.5 atmospheric <inline-formula><mml:math id="M222" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> concentrations (see Methods), against maximum Arctic Ocean sea surface density (95th percentile) for SSP1-2.6 (blue diamonds; <inline-formula><mml:math id="M223" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.70</mml:mn></mml:mrow></mml:math></inline-formula>), SSP2-4.5 (green squares; <inline-formula><mml:math id="M224" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.63</mml:mn></mml:mrow></mml:math></inline-formula>), SSP3-7.0 (orange triangles; <inline-formula><mml:math id="M225" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.70</mml:mn></mml:mrow></mml:math></inline-formula>), SSP5-8.5 (red circles; <inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.72</mml:mn></mml:mrow></mml:math></inline-formula>), and RCP8.5 (purple stars; <inline-formula><mml:math id="M227" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.74</mml:mn></mml:mrow></mml:math></inline-formula>) <bold>(a)</bold> over the entire density range and <bold>(b)</bold> over the density range from 27.5 to 28.3 <inline-formula><mml:math id="M228" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. The simulated Arctic Ocean <inline-formula><mml:math id="M229" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2100 for each scenario (Fig. <xref ref-type="fig" rid="Ch1.F2"/>) was rescaled to SSP5-8.5 using the mean atmospheric <inline-formula><mml:math id="M230" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> concentration from 1850 to 2100 as a scaling factor. Linear fits use all available models for each scenario (coloured dashed lines). For RCP8.5 an additional fit is shown excluding the three models with density anomalies below 27.5 <inline-formula><mml:math id="M231" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <bold>(b)</bold> (dotted purple line; <inline-formula><mml:math id="M232" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.79</mml:mn></mml:mrow></mml:math></inline-formula>).</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://bg.copernicus.org/articles/18/2221/2021/bg-18-2221-2021-f06.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><?xmltex \opttitle{Arctic Ocean {$\protect\chem{C_{{ant}}}$} inventory}?><title>Arctic Ocean <inline-formula><mml:math id="M233" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory</title>
      <p id="d1e4207">Across the CMIP6 model ensemble, the Arctic Ocean <inline-formula><mml:math id="M234" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> storage over the 21st century is highly related to maximum sea surface densities (Fig. <xref ref-type="fig" rid="Ch1.F2"/>), which predominately occur in the Barents Sea <xref ref-type="bibr" rid="bib1.bibx73 bib1.bibx97 bib1.bibx112" id="paren.114"/>. The inter-model range in maximum sea surface density in the Barents Sea is mainly explained by differences in sea surface salinities (<inline-formula><mml:math id="M235" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.93</mml:mn></mml:mrow></mml:math></inline-formula>), which are influenced by brine rejection <xref ref-type="bibr" rid="bib1.bibx73 bib1.bibx130" id="paren.115"/> and the strength of inflowing, saltier Atlantic waters through the Barents Sea Opening (Fig. <xref ref-type="fig" rid="Ch1.F7"/>). Compared to CMIP5 models, the reduced negative bias of simulated maximum sea surface densities (Fig. <xref ref-type="fig" rid="Ch1.F6"/>) indicates model improvement in<?pagebreak page2230?> simulating the circulation of Atlantic and Arctic surface waters. Despite the reduced inter-model range, the robust relationship between maximum sea surface density and <inline-formula><mml:math id="M236" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> across model generations (Fig. <xref ref-type="fig" rid="Ch1.F6"/>) supports evidence that inflowing Atlantic waters through the Barents Sea Opening and their transformation into deep and intermediate waters via brine rejection are the dominant process governing Arctic Ocean <inline-formula><mml:math id="M237" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> increases <xref ref-type="bibr" rid="bib1.bibx73 bib1.bibx86 bib1.bibx87 bib1.bibx52 bib1.bibx97" id="paren.116"/>. The application of observational constraints to this emergent multi-model relationship in order to constrain the projected Arctic Ocean <inline-formula><mml:math id="M238" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory (Fig. <xref ref-type="fig" rid="Ch1.F2"/>) and focus efforts on model development therefore remains promising.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7"><?xmltex \currentcnt{7}?><?xmltex \def\figurename{Figure}?><label>Figure 7</label><caption><p id="d1e4292">Annual mean sea surface salinity in the Barents Sea and its neighbouring waters from <bold>(a)</bold> the World Ocean Atlas 2018 and from the CMIP6 model with the <bold>(b)</bold> highest (UKESM1-0-LL) and <bold>(c)</bold> lowest (CESM2-WACCM) maximum sea surface density and salinity. The 0 <inline-formula><mml:math id="M239" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> isotherm indicates approximately the extent of Atlantic waters (black solid line).</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://bg.copernicus.org/articles/18/2221/2021/bg-18-2221-2021-f07.png"/>

        </fig>

      <p id="d1e4322">However, the slope of the linear relationship between maximum sea surface density and the Arctic Ocean <inline-formula><mml:math id="M240" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory over the 21st century in the CMIP5 model ensemble (<inline-formula><mml:math id="M241" display="inline"><mml:mrow><mml:mn mathvariant="normal">3.3</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.6</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M242" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Pg</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">C</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:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, scaled to SSP5-8.5 atmospheric <inline-formula><mml:math id="M243" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> concentrations) is 3–4 times less than that in the CMIP6 model ensemble (<inline-formula><mml:math id="M244" display="inline"><mml:mrow><mml:mn mathvariant="normal">12.6</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2.6</mml:mn></mml:mrow></mml:math></inline-formula> for SSP1-2.6, <inline-formula><mml:math id="M245" display="inline"><mml:mrow><mml:mn mathvariant="normal">12.1</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2.8</mml:mn></mml:mrow></mml:math></inline-formula> for SSP2-4.5, <inline-formula><mml:math id="M246" display="inline"><mml:mrow><mml:mn mathvariant="normal">9.4</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.9</mml:mn></mml:mrow></mml:math></inline-formula> for SSP3-7.0, and <inline-formula><mml:math id="M247" display="inline"><mml:mrow><mml:mn mathvariant="normal">11.3</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2.0</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M248" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Pg</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">C</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:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> for SSP5-8.5) (Fig. <xref ref-type="fig" rid="Ch1.F6"/>). The reduced slope in the CMIP5 ensemble is mainly caused by three models with maximum surface density anomalies well below 27.5 <inline-formula><mml:math id="M249" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. When these three models are excluded, the remaining CMIP5 models follow a slope of <inline-formula><mml:math id="M250" display="inline"><mml:mrow><mml:mn mathvariant="normal">8.9</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2.2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M251" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Pg</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">C</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:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, in broad agreement with the CMIP6 model ensemble (Fig. <xref ref-type="fig" rid="Ch1.F6"/>). This suggests that the linear emergent relationship does not hold below a certain value of maximum sea surface density below which the impact on deep-water formation and subsequent <inline-formula><mml:math id="M252" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> storage in the Arctic Ocean is limited. However, as the two linear relationships happen to cross the observed maximum sea surface density at nearly the same location (Fig. <xref ref-type="fig" rid="Ch1.F6"/>), the constrained <inline-formula><mml:math id="M253" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory for the CMIP5 model ensemble remains almost entirely unchanged when the three low-density models are excluded.</p>
      <p id="d1e4545">Even without the low-density bias in the Barents Sea, the constrained Arctic Ocean <inline-formula><mml:math id="M254" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2005 in CMIP6 remains 36 % below the data-based estimate <xref ref-type="bibr" rid="bib1.bibx113" id="paren.117"/>. This underestimation is partly due to the different definition of <inline-formula><mml:math id="M255" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in data-based estimates and ESMs. While the historical simulations in CMIP5 and CMIP6 typically start in 1850, data-based estimates account for all <inline-formula><mml:math id="M256" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> since 1765. This leads to an underestimation of the global ocean <inline-formula><mml:math id="M257" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory by ESMs of around 30 % <xref ref-type="bibr" rid="bib1.bibx13" id="paren.118"/> and of around 20 % in the Arctic Ocean <xref ref-type="bibr" rid="bib1.bibx111" id="paren.119"/>. Even if we increased the constrained Arctic Ocean <inline-formula><mml:math id="M258" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in 2005 by 20 %, an underestimation of around 16 % would remain compared to the data-based estimate. This underestimation of the data-based estimate suggests that all ESMs are missing additional pathways of <inline-formula><mml:math id="M259" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> entry into the Arctic Ocean, other than the principal pathway via the Barents Sea. Indeed, small-scale density flows along continental slopes can be observed in different regions of the Arctic Ocean <xref ref-type="bibr" rid="bib1.bibx86 bib1.bibx54" id="paren.120"/> but cannot be simulated by the coarse resolution of most ESMs. Thus, the constrained estimates of the Arctic Ocean <inline-formula><mml:math id="M260" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory presented here are likely still a lower boundary.</p>
      <p id="d1e4638">Recent observation of dilution of <inline-formula><mml:math id="M261" 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 <inline-formula><mml:math id="M262" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in surface waters of the Amerasian Basin caused by freshening have led to the hypothesis that continuous freshening might turn the Arctic Ocean from a sink of <inline-formula><mml:math id="M263" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> into a source over the 21st century <xref ref-type="bibr" rid="bib1.bibx120" id="paren.121"/>. However, observations in the Eurasian basins, which receive more saline Atlantic water and less freshwater input, still show increases of <inline-formula><mml:math id="M264" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> concentrations <xref ref-type="bibr" rid="bib1.bibx114" id="paren.122"/> over a depth of 1500 m in the last 20 years. The CMIP5 and CMIP6 model ensembles both simulate continuous accumulation of <inline-formula><mml:math id="M265" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the Arctic Ocean under all SSPs (Fig. <xref ref-type="fig" rid="Ch1.F1"/>), suggesting that the subduction of <inline-formula><mml:math id="M266" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>-rich Atlantic waters in the Barents Sea remains larger than any loss of <inline-formula><mml:math id="M267" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in surface waters over the 21st century. Nevertheless, the reduction of the storage rate of <inline-formula><mml:math id="M268" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> under SSP5-8.5 (Fig. <xref ref-type="fig" rid="Ch1.F1"/>) in combination with constantly increasing atmospheric <inline-formula><mml:math id="M269" 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> concentrations <xref ref-type="bibr" rid="bib1.bibx83" id="paren.123"/> indicates that dilution may reduce the capacity of the Arctic Ocean to store further <inline-formula><mml:math id="M270" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as suggested by <xref ref-type="bibr" rid="bib1.bibx120" id="text.124"/>.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Arctic Ocean acidification</title>
<sec id="Ch1.S4.SS2.SSS1">
  <label>4.2.1</label><?xmltex \opttitle{$\Omega _{{\text{arag}}}$ and $\Omega _{{\text{calc}}}$, pH, and {$\protect\chem{\mathit{p}CO_{2}}$} in 2100}?><title><inline-formula><mml:math id="M271" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M272" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, pH, and <inline-formula><mml:math id="M273" 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 2100</title>
      <p id="d1e4819">Even under the most optimistic scenario assessed (SSP1-2.6), the Arctic Ocean will become on average undersaturated with respect to aragonite, with possible consequences for calcifying organisms <xref ref-type="bibr" rid="bib1.bibx19" id="paren.125"/> and the food chain <xref ref-type="bibr" rid="bib1.bibx4 bib1.bibx56" id="paren.126"/>. In this scenario only water masses above 500 m remain supersaturated this century. These findings are in good agreement with idealized estimates of <inline-formula><mml:math id="M274" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M275" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> that project the future <inline-formula><mml:math id="M276" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory based on the transient time distribution method and observed CFC-12 concentrations <xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx113" id="paren.127"/>.</p>
      <p id="d1e4865">In addition to widespread Arctic Ocean undersaturation with respect to aragonite, water masses between 50 and 800 m are even projected to become undersaturated with respect to calcite by the end of the century under<?pagebreak page2231?> SSP5-8.5. Calcite undersaturation in Arctic Ocean subsurface waters will likely further enhance the pressure on the Arctic Ocean ecosystem as calcite-forming organisms, such as foraminifera <xref ref-type="bibr" rid="bib1.bibx26" id="paren.128"/> and coccolithophores <xref ref-type="bibr" rid="bib1.bibx59" id="paren.129"/>, experience potential impacts on growth and survival.</p>
      <p id="d1e4874">Furthermore, the projected increases in <inline-formula><mml:math id="M277" 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> (Fig. <xref ref-type="fig" rid="Ch1.F4"/>c and d) alongside projected increases in its seasonal amplitude <xref ref-type="bibr" rid="bib1.bibx69 bib1.bibx62" id="paren.130"/> are likely to lead to hypercapnic conditions that might directly affect the growth and survival of Arctic fish <xref ref-type="bibr" rid="bib1.bibx35 bib1.bibx90 bib1.bibx61" id="paren.131"/> under high-emissions scenarios.</p>
</sec>
<sec id="Ch1.S4.SS2.SSS2">
  <label>4.2.2</label><title>Driving processes of acidification</title>
      <p id="d1e4906">The CMIP6 model ensemble shows astonishingly good agreement with respect to projections of Arctic Ocean acidification over the 21st century. Compared to the CMIP5 model ensemble, the uncertainties in projected <inline-formula><mml:math id="M278" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> averaged over the upper 1000 m in 2100 have been reduced from 0.13 to 0.04–0.06, and those for <inline-formula><mml:math id="M279" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> from 0.21 to 0.05–0.09.</p>
      <p id="d1e4931">The main reason for the reduced uncertainty appears to be that the ESMs that have a lower maximum sea surface density and that thus take up less <inline-formula><mml:math id="M280" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the Arctic Ocean over the 21st century (Fig. <xref ref-type="fig" rid="Ch1.F2"/>) are the same models that simulate a stronger reduction in <inline-formula><mml:math id="M281" 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> (Fig. <xref ref-type="fig" rid="Ch1.F8"/>). To explain this negative correlation between <inline-formula><mml:math id="M282" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> uptake and reductions in <inline-formula><mml:math id="M283" 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>, we propose the following mechanism: over the 21st century, melting of sea ice, land ice, and increased river runoff are projected to freshen the Arctic Ocean <xref ref-type="bibr" rid="bib1.bibx58 bib1.bibx76 bib1.bibx96" id="paren.132"/> and to reduce <inline-formula><mml:math id="M284" 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> (Fig. <xref ref-type="fig" rid="Ch1.F8"/>) <xref ref-type="bibr" rid="bib1.bibx120" id="paren.133"/>. In the CMIP6 ensemble, this freshening and reduction of <inline-formula><mml:math id="M285" 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> tends to be stronger in models with lower sea surface salinities and densities; i.e. the models that simulate less inflow of saline Atlantic waters, such as CESM2-WACCM (Fig. <xref ref-type="fig" rid="Ch1.F7"/>), have lower Barents Sea surface salinity and density, weak deep-water formation, and therefore less <inline-formula><mml:math id="M286" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> storage (Fig. <xref ref-type="fig" rid="Ch1.F2"/>). In contrast, models with a larger inflow of saline Atlantic water have stronger deep-water formation, greater <inline-formula><mml:math id="M287" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> storage, less freshening, and a smaller reduction in <inline-formula><mml:math id="M288" 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>. This compensation then results in a similar simulated reduction of <inline-formula><mml:math id="M289" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M290" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> over the 21st century across all models in the CMIP6 ensemble, through either a reduction in <inline-formula><mml:math id="M291" 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> or an increase in <inline-formula><mml:math id="M292" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>. Other possible drivers, such as changes in temperature and salinity, are likely of minor importance given the relatively good correlation between the projected <inline-formula><mml:math id="M293" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory and basin-wide reduction of <inline-formula><mml:math id="M294" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M295" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> over the 21st century when <inline-formula><mml:math id="M296" 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> is not taken into account (<inline-formula><mml:math id="M297" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.54</mml:mn></mml:mrow></mml:math></inline-formula>–0.73).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F8"><?xmltex \currentcnt{8}?><?xmltex \def\figurename{Figure}?><label>Figure 8</label><caption><p id="d1e5158">CMIP6 basin-wide changes in alkalinity (<inline-formula><mml:math id="M298" 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>) averaged over the upper 1000 m from 2002 to 2100 caused by freshwater dilution (blue) and changes in biogeochemistry (green) against the Arctic Ocean <inline-formula><mml:math id="M299" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory for <bold>(a)</bold> SSP1-2.6, <bold>(b)</bold> SSP2-4.5, <bold>(c)</bold> SSP3-7.0, and <bold>(d)</bold> SSP5-8.5. <inline-formula><mml:math id="M300" 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> anomalies were decomposed by calculating the temporal evolution of salinity-corrected alkalinity following <xref ref-type="bibr" rid="bib1.bibx67" id="text.134"/>.</p></caption>
            <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://bg.copernicus.org/articles/18/2221/2021/bg-18-2221-2021-f08.png"/>

          </fig>

      <p id="d1e5217">In the CMIP5 model ensemble, this compensation effect did not exist, and projected saturation states and pH were mainly driven by the projected <inline-formula><mml:math id="M301" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> storage in each model <xref ref-type="bibr" rid="bib1.bibx112" id="paren.135"/>, with changes in <inline-formula><mml:math id="M302" 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>, temperature, and salinity being of minor importance. The relatively small changes in <inline-formula><mml:math id="M303" 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> in CMIP5 compared to CMIP6 might have been caused by an underestimation of Arctic Ocean freshening over the 21st century given that the CMIP5 models also underestimated historical Arctic Ocean freshening by around 50 % in the Arctic Ocean <xref ref-type="bibr" rid="bib1.bibx96" id="paren.136"/>. In the CMIP6 model ensemble this negative bias with respect to freshwater fluxes and subsequent dilution of <inline-formula><mml:math id="M304" 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> appears to have been reduced. This is probably a consequence of better representation of riverine fluxes as well as increased model resolution and hence improved circulation <xref ref-type="bibr" rid="bib1.bibx94" id="paren.137"/>.</p>
      <p id="d1e5274">To estimate the likely impacts of <inline-formula><mml:math id="M305" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> increases and <inline-formula><mml:math id="M306" 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> decreases to Arctic Ocean acidification over the 21st century, one can assess their relative contributions to acidification in constrained estimates of end-of-century <inline-formula><mml:math id="M307" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (dotted line in Fig. <xref ref-type="fig" rid="Ch1.F5"/>). In SSP5-8.5 for example, increasing <inline-formula><mml:math id="M308" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">T</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> along with changes in temperature and salinity reduce <inline-formula><mml:math id="M309" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> from 1.38 to 0.75, while decreasing <inline-formula><mml:math id="M310" 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> further reduces this to 0.59. Thus, the future storage of <inline-formula><mml:math id="M311" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> in the Arctic Ocean still remains the main driver of Arctic Ocean acidification, with acidification further enhanced by decreases in <inline-formula><mml:math id="M312" 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>.</p>
</sec>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <?pagebreak page2232?><p id="d1e5379">Earth system models tend to have improved their performance in the Arctic Ocean from CMIP5 to CMIP6. The negative bias with respect to present-day maximum sea surface density is substantially reduced in CMIP6, and the historical <inline-formula><mml:math id="M313" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory is closer to the data-based estimate <xref ref-type="bibr" rid="bib1.bibx113" id="paren.138"/>. Furthermore, the inter-model range of projected <inline-formula><mml:math id="M314" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M315" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and the <inline-formula><mml:math id="M316" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory have been reduced. Uncertainties in the future <inline-formula><mml:math id="M317" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory under four shared socioeconomic pathways can be further reduced by applying the previously identified emergent constraint between present-day maximum Arctic Ocean sea surface density and the future <inline-formula><mml:math id="M318" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory <xref ref-type="bibr" rid="bib1.bibx112" id="paren.139"/>.</p>
      <p id="d1e5455"><xref ref-type="bibr" rid="bib1.bibx47" id="text.140"/> define “confirmed” emergent constraints as fulfilling the following criteria: (1) a plausible mechanism, (2) verification of that mechanism, and (3) out-of-sample testing. The mechanism underpinning the relationship between maximum sea surface densities and the projected <inline-formula><mml:math id="M319" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory in the Arctic Ocean is consistent with observations and has been verified in an ocean-only model at different resolutions <xref ref-type="bibr" rid="bib1.bibx112" id="paren.141"/>. The testing of this emergent constraint in the CMIP6 ensemble can be considered out of sampling, although the extent of model independence between generations remains questionable <xref ref-type="bibr" rid="bib1.bibx57 bib1.bibx88" id="paren.142"/>. Despite the overall emergent constraint on projected Arctic Ocean <inline-formula><mml:math id="M320" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> being similar between CMIP6 and CMIP5, the change in the multi-model emergent relationship indicates that further validation is required. Specifically, it appears that the linear relationship between maximum sea surface densities and the projected <inline-formula><mml:math id="M321" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory breaks down in models with extremely low-biased sea surface densities, highlighting a potential limitation to this emergent constraint that requires further assessment.</p>
      <p id="d1e5499">While the mechanisms underlying emergent constraints on the future Arctic Ocean <inline-formula><mml:math id="M322" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> inventory appear to be consistent between CMIP5 and CMIP6, this is not the case for the previously identified emergent constraint on ocean acidification variables (<inline-formula><mml:math id="M323" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M324" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, pH, and <inline-formula><mml:math id="M325" 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 the CMIP6 model ensemble, projected model uncertainties in <inline-formula><mml:math id="M326" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>arag</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M327" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ω</mml:mi><mml:mtext>calc</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>, pH, and <inline-formula><mml:math id="M328" 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> are dramatically reduced compared to the uncertainties in CMIP5 and are driven not only by the increase in <inline-formula><mml:math id="M329" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> but also by a reduction in <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> due to pan-Arctic freshening. A weak inflow of saline Atlantic waters in ESMs results not only in lighter surface waters and less <inline-formula><mml:math id="M331" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> storage over the 21st century but also in a stronger reduction of alkalinity caused by a stronger freshening. A strong Atlantic inflow, however, appears to limit freshening and reductions in alkalinity but results in greater <inline-formula><mml:math id="M332" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> storage. Although both <inline-formula><mml:math id="M333" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> storage and alkalinity reductions contribute considerably to Arctic Ocean acidification, our results suggest that <inline-formula><mml:math id="M334" display="inline"><mml:mrow class="chem"><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mi mathvariant="normal">ant</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> remains the dominant process. In the CMIP5 model ensemble, the influence of freshening on emergent constraints on acidification variables might have been of limited importance because (a) freshening was largely underestimated <xref ref-type="bibr" rid="bib1.bibx96" id="paren.143"/> and (b) differences in simulating the inflow of Atlantic waters through the Barents Sea Opening were considerably larger across the model ensemble <xref ref-type="bibr" rid="bib1.bibx112" id="paren.144"/>. Thus, the absence of an emergent constraint on projected Arctic acidification in CMIP6 could be viewed as a consequence of successful model development. Indeed, there is clearly no need for such constraints when models are in broad agreement.</p>
      <p id="d1e5657">Independent of the driving mechanism, the projected Arctic Ocean acidification over the 21st century has possibly grave consequences for the wider Arctic Ocean ecosystem <xref ref-type="bibr" rid="bib1.bibx36 bib1.bibx84 bib1.bibx2" id="paren.145"/>. Under all socioeconomic pathways, the upper 1000 m of the Arctic Ocean will be on average undersaturated with respect to aragonite. Thus, keystone species like the sea butterfly (aragonitic pteropod <italic>Limacina helicina</italic>) may lose most to all of their suitable habitat in the Arctic Ocean <xref ref-type="bibr" rid="bib1.bibx19" id="paren.146"/>. However, under the low-emissions pathway SSP1-2.6 aragonite undersaturation is projected to be avoided in the upper 500 m of the water column, providing a potential refuge. Under the high-emissions pathway SSP5-8.5, water masses between 50 and 800 m are additionally projected to become undersaturated with respect to calcite. While isolated regions of the surface Arctic Ocean that are strongly influenced by riverine inputs are already seasonally undersaturated with respect to calcite <xref ref-type="bibr" rid="bib1.bibx5" id="paren.147"/>, subsurface Arctic waters would be the first to exhibit annually averaged and basin-wide calcite undersaturation over a depth of several hundred metres. Vertically migrating organisms that form calcite shells and skeletons, such as coccolithophores <xref ref-type="bibr" rid="bib1.bibx59" id="paren.148"/> and foraminifera <xref ref-type="bibr" rid="bib1.bibx26" id="paren.149"/>, may lose their natural refugia to which they migrate during the day <xref ref-type="bibr" rid="bib1.bibx7" id="paren.150"/>. These hostile conditions for calcifying organisms will likely cause their decline, with unknown consequences for the wider Arctic food web <xref ref-type="bibr" rid="bib1.bibx4 bib1.bibx56" id="paren.151"/> and its iconic species <xref ref-type="bibr" rid="bib1.bibx51 bib1.bibx2" id="paren.152"/>.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d1e5692">The Earth system model output used in this study is available via the Earth System Grid Federation (<uri>https://esgf-node.ipsl.upmc.fr/projects/esgf-ipsl/</uri>, last access: 31 March 2021). For further information, please see Table 1. Observations from the World Ocean Atlas 2018 (<uri>https://www.nodc.noaa.gov/OC5/woa18/</uri>, last access: 3 January 2020; <xref ref-type="bibr" rid="bib1.bibx66 bib1.bibx129" id="altparen.153"/>) and GLODAPv2 (<uri>https://www.nodc.noaa.gov/ocads/oceans/GLODAPv2_2019/</uri>, <xref ref-type="bibr" rid="bib1.bibx65" id="altparen.154"/>) are available via the National Oceanic and Atmospheric Administration.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d1e5713">The study was led by JT, who made the figures and wrote the initial manuscript. TB and LK provided help for the analyses and interpretation of the results. OT processed the CMIP6 model data (download, regridding). All authors contributed to the final manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d1e5719">The authors declare that they have no conflict of interest.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <?pagebreak page2233?><p id="d1e5725">The work reflects only the authors' view; the European Commission and their executive agency are not responsible for any use that may be made of the information the work contains.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e5731">We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP. For CMIP the US Department of Energy's Program for Climate Model Diagnosis and Intercomparison provided coordinating support and led the development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. We also thank the IPSL modelling group for the software infrastructure, which facilitated CMIP6 analysis.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d1e5736">This research has been supported by the Horizon 2020 (4C (grant no. 821003), CRESCENDO (grant no. 641816), and COMFORT (grant no. 820989)), the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (grant no. PP00P2_170687), the Agence Nationale de la Recherche (grant no. ANR-18-ERC2-0001-01), and the Norges Forskningsråd (grant no. 275268).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d1e5742">This paper was edited by Jean-Pierre Gattuso and reviewed by Scott C. Doney and Claudine Hauri.</p>
  </notes><ref-list>
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    <!--<article-title-html>Arctic Ocean acidification over the 21st century co-driven by anthropogenic carbon increases and freshening in the CMIP6 model ensemble</article-title-html>
<abstract-html><p>The uptake of anthropogenic carbon (C<sub>ant</sub>) by the ocean leads to ocean acidification, causing the reduction of pH and the saturation states of aragonite (Ω<sub>arag</sub>) and calcite (Ω<sub>calc</sub>). The Arctic Ocean is particularly vulnerable to ocean acidification due to its naturally low pH and saturation states and due to ongoing freshening and the concurrent reduction in total alkalinity in this region. Here, we analyse ocean acidification in the Arctic Ocean over the 21st century across 14 Earth system models (ESMs) from the latest Coupled Model Intercomparison Project Phase 6 (CMIP6). Compared to the previous model generation (CMIP5), models generally better simulate maximum sea surface densities in the Arctic Ocean and consequently the transport of C<sub>ant</sub> into the Arctic Ocean interior, with simulated historical increases in C<sub>ant</sub> in improved agreement with observational products. Moreover, in CMIP6 the inter-model uncertainty of projected changes over the 21st century in Arctic Ocean Ω<sub>arag</sub> and Ω<sub>calc</sub> averaged over the upper 1000&thinsp;m is reduced by 44–64&thinsp;%. The strong reduction in projection uncertainties of Ω<sub>arag</sub> and Ω<sub>calc</sub> can be attributed to compensation between C<sub>ant</sub> uptake and total alkalinity reduction in the latest models. Specifically, ESMs with a large increase in Arctic Ocean C<sub>ant</sub> over the 21st century tend to simulate a relatively weak concurrent freshening and alkalinity reduction, while ESMs with a small increase in C<sub>ant</sub> simulate a relatively strong freshening and concurrent total alkalinity reduction. Although both mechanisms contribute to Arctic Ocean acidification over the 21st century, the increase in C<sub>ant</sub> remains the dominant driver. Even under the low-emissions Shared Socioeconomic Pathway 1-2.6 (SSP1-2.6), basin-wide averaged Ω<sub>arag</sub> undersaturation in the upper 1000&thinsp;m occurs before the end of the century. While under the high-emissions pathway SSP5-8.5, the Arctic Ocean mesopelagic is projected to even become undersaturated with respect to calcite. An emergent constraint identified in CMIP5 which relates present-day maximum sea surface densities in the Arctic Ocean to the projected end-of-century Arctic Ocean C<sub>ant</sub> inventory is found to generally hold in CMIP6. However, a coincident constraint on Arctic declines in Ω<sub>arag</sub> and Ω<sub>calc</sub> is not apparent in the new generation of models. This is due to both the reduction in Ω<sub>arag</sub> and Ω<sub>calc</sub> projection uncertainty and the weaker direct relationship between projected changes in Arctic Ocean C<sub>ant</sub> and changes in Ω<sub>arag</sub> and Ω<sub>calc</sub>.</p></abstract-html>
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