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  <front>
    <journal-meta><journal-id journal-id-type="publisher">OS</journal-id><journal-title-group>
    <journal-title>Ocean Science</journal-title>
    <abbrev-journal-title abbrev-type="publisher">OS</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Ocean Sci.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1812-0792</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/os-22-2425-2026</article-id><title-group><article-title>Thermohaline gradients and frontal regimes in the  northwestern Tropical Atlantic</article-title><alt-title>Thermohaline gradients and frontal regimes in the northwestern Tropical Atlantic</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Napolitano</surname><given-names>Dante C.</given-names></name>
          <email>dante.napolitano@univ-brest.fr</email>
        <ext-link>https://orcid.org/0000-0001-9857-9724</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>Gula</surname><given-names>Jonathan</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-0876-9557</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3 aff4">
          <name><surname>Coadou-Chaventon</surname><given-names>Solange</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Speich</surname><given-names>Sabrina</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-5452-8287</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Rocha</surname><given-names>Cesar B.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff6">
          <name><surname>McWilliams</surname><given-names>James C.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff7">
          <name><surname>Zhang</surname><given-names>Dongxiao</given-names></name>
          
        <ext-link>https://orcid.org/0000-0001-5788-911X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Carton</surname><given-names>Xavier</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Univ. Brest, CNRS, Ifremer, IRD, Laboratoire d’Océanographie Physique et Spatiale (LOPS), IUEM,  29280, Plouzané, France</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Institut Universitaire de France (IUF), Paris, France</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>LMD/IPSL, ENS, PSL University, École Polytechnique, Institut Polytechnique de Paris, Sorbonne Université,  CNRS, Paris, France</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>Department of Marine Sciences, University of Gothenburg, Gothenburg, Sweden</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Instituto Oceanográfico, Universidade de São Paulo, São Paulo, Brazil</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>Department of Atmospheric and Ocean Sciences, University of California Los Angeles, Los Angeles, California, USA</institution>
        </aff>
        <aff id="aff7"><label>7</label><institution>CICOES/University of Washington and NOAA Pacific Marine Environmental Laboratory, Seattle, Washington, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Dante C. Napolitano (dante.napolitano@univ-brest.fr)</corresp></author-notes><pub-date><day>13</day><month>August</month><year>2026</year></pub-date>
      
      <volume>22</volume>
      <issue>4</issue>
      <fpage>2425</fpage><lpage>2447</lpage>
      <history>
        <date date-type="received"><day>13</day><month>April</month><year>2026</year></date>
           <date date-type="rev-request"><day>22</day><month>April</month><year>2026</year></date>
           <date date-type="rev-recd"><day>9</day><month>July</month><year>2026</year></date>
           <date date-type="accepted"><day>2</day><month>August</month><year>2026</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2026 Dante C. Napolitano et al.</copyright-statement>
        <copyright-year>2026</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026.html">This article is available from https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026.html</self-uri><self-uri xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026.pdf">The full text article is available as a PDF file from https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e192">At the edge of the Amazon River plume, stirring by the North Brazil Current (NBC) and its eddies creates sharp surface thermohaline gradients on horizontal scales of <inline-formula><mml:math id="M1" display="inline"><mml:mi mathvariant="script">O</mml:mi></mml:math></inline-formula> (1–100) <inline-formula><mml:math id="M2" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>. This study provides a comprehensive picture of these gradients and fronts associated with the region's distinctive dynamics. Saildrone observations show that the plume amplifies density gradient variability at all scales from 1–100 <inline-formula><mml:math id="M3" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>, with frontal sharpness up to <inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:mn mathvariant="normal">75</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math></inline-formula> stronger inside the plume than outside, with differences reaching <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mn mathvariant="normal">100</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math></inline-formula> at scales below 3 <inline-formula><mml:math id="M6" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>. Density gradients are partially reinforced or compensated by temperature-salinity variations, with net frontogenesis observed in both regions. To expand in-situ observations, we use a 1 <inline-formula><mml:math id="M7" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> resolution CROCO (Coastal and Regional Ocean COmmunity model) simulation to assess the spatial distribution of surface fronts and their spatio-temporal variability. We characterize three distinct frontal regimes: (i) broken-up fronts parallel to shore occupy the plume core over the continental shelf, (ii) thin elongated fronts associated with NBC-plume interactions connect nearshore and offshore regions, and (iii) pools of anisotropic fronts driven by the seasonal mixed-layer cycle are present offshore. Salinity dominates density gradients throughout the year north of 15° N, whereas near-shore fronts exhibit seasonal shifts in temperature-salinity dominance linked to the Amazon discharge seasonality and NBC strength. Within the plume, freshwater filaments stirred by NBC rings systematically generate density-compensated fronts on their inner edge and reinforced fronts on their outer rim, a pattern with implications for energy cascades and tracer export.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Agence Nationale de la Recherche</funding-source>
<award-id>ANR-19-JPOC-0004-05</award-id>
<award-id>ANR-19-CE01-0002-01</award-id>
</award-group>
<award-group id="gs2">
<funding-source>Région Bretagne</funding-source>
<award-id>ANR-19-JPOC-0004-05</award-id>
</award-group>
<award-group id="gs3">
<funding-source>Office of Naval Research</funding-source>
<award-id>N00014-23-1-2226</award-id>
</award-group>
<award-group id="gs4">
<funding-source>Centre National d’Etudes Spatiales</funding-source>
<award-id>CNES 19-1 2021</award-id>
</award-group>
<award-group id="gs5">
<funding-source>Horizon 2020</funding-source>
<award-id>81757</award-id>
</award-group>
<award-group id="gs6">
<funding-source>Grand Équipement National De Calcul Intensif</funding-source>
<award-id>2023-A0090112051</award-id>
</award-group>
<award-group id="gs7">
<funding-source>National Aeronautics and Space Administration</funding-source>
<award-id>NH17ZDA001N-EVS3)</award-id>
</award-group>
<award-group id="gs8">
<funding-source>Fundação de Amparo à Pesquisa do Estado de São Paulo</funding-source>
<award-id>2023/10506-0</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d2e264">The Amazon River reigns absolute as the largest river discharge into the ocean, with an annual average of <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M9" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Sv</mml:mi></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M10" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">Sv</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">6</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M11" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:msup><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) of freshwater entering the northwestern Tropical Atlantic <xref ref-type="bibr" rid="bib1.bibx65 bib1.bibx18" id="paren.1"/>. The offshore propagation of low sea surface salinity (SSS) from the Amazon Plume into the Tropical Atlantic has been observed from drifting buoys and satellite data <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx68 bib1.bibx63" id="paren.2"><named-content content-type="pre">e.g.,</named-content></xref>. This propagation is controlled by the seasonality of the Amazon outflow as well as the North Brazil Current <xref ref-type="bibr" rid="bib1.bibx26 bib1.bibx17" id="paren.3"><named-content content-type="pre">NBC;</named-content></xref>. Influenced by the Amazon Plume, an expanding low-SSS band spreads northwestward in winter and spring <xref ref-type="bibr" rid="bib1.bibx68" id="paren.4"><named-content content-type="pre">e.g.,</named-content></xref>; in summer and fall, the Amazon waters detach from the slope and loop northeastward with the NBC retroflection <xref ref-type="bibr" rid="bib1.bibx27" id="paren.5"><named-content content-type="pre">e.g.,</named-content></xref>. As a consequence of the spread of low salinity, a barrier layer driven by Amazon waters occupies a large part of the northwestern Tropical Atlantic <xref ref-type="bibr" rid="bib1.bibx52 bib1.bibx19 bib1.bibx71" id="paren.6"><named-content content-type="pre">e.g.,</named-content></xref>, with local and large-scale effects on climate <xref ref-type="bibr" rid="bib1.bibx41 bib1.bibx33 bib1.bibx62 bib1.bibx60" id="paren.7"><named-content content-type="pre">e.g.,</named-content></xref> and biogeochemical processes <xref ref-type="bibr" rid="bib1.bibx90 bib1.bibx35 bib1.bibx34" id="paren.8"><named-content content-type="pre">e.g.,</named-content></xref>.</p>
      <p id="d2e364">The strongest density gradients in the ocean are found at the edge of river plumes <xref ref-type="bibr" rid="bib1.bibx89" id="paren.9"><named-content content-type="pre">e.g.,</named-content><named-content content-type="post">and references therein</named-content></xref>. From 4–20° N, the Amazon water spreads over the shelf break and intersects the warm and salty NBC, with mesoscale and submesoscale dynamics dictating near-surface motions <xref ref-type="bibr" rid="bib1.bibx29 bib1.bibx68" id="paren.10"><named-content content-type="pre">e.g.,</named-content></xref>. The sharpest gradients at scales ranging from <inline-formula><mml:math id="M12" display="inline"><mml:mi mathvariant="script">O</mml:mi></mml:math></inline-formula> (0.1–100) <inline-formula><mml:math id="M13" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>
<xref ref-type="bibr" rid="bib1.bibx68 bib1.bibx62 bib1.bibx84" id="paren.11"/> are generated due to the stirring of the river plume by NBC rings <xref ref-type="bibr" rid="bib1.bibx42 bib1.bibx29" id="paren.12"><named-content content-type="pre">e.g.,</named-content></xref>. These submesoscale fronts are important for modulating air–sea interactions <xref ref-type="bibr" rid="bib1.bibx83" id="paren.13"><named-content content-type="pre">e.g.,</named-content></xref>, biogeochemical processes <xref ref-type="bibr" rid="bib1.bibx30" id="paren.14"><named-content content-type="pre">e.g.,</named-content></xref>, and the energy cascade <xref ref-type="bibr" rid="bib1.bibx80 bib1.bibx95" id="paren.15"><named-content content-type="pre">e.g.,</named-content></xref>. However, the challenges of observing and simulating small scales have historically hindered the understanding of such complex environments.</p>
      <p id="d2e418">In the present study, we use state-of-the-art observations from the EUREC4A-OA campaign and a 1 <inline-formula><mml:math id="M14" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> resolution numerical simulation to quantify surface thermohaline gradients and characterize frontal regimes in the Amazon Plume region.  One objective is to provide a comprehensive picture of the surface gradients and fronts in the Amazon Plume region at different scales. Specifically, we ask: (1) How does the plume modify the scale-dependence and magnitude of density gradients? (2) What is the relative role of temperature and salinity in driving frontogenesis? (3) Do the NBC and its mesoscale dynamics contribute to the spatiotemporal distribution of these fronts? To reach our goals, we revisit in-situ observations from <xref ref-type="bibr" rid="bib1.bibx81" id="text.16"/> and <xref ref-type="bibr" rid="bib1.bibx16" id="text.17"/> to analyze density gradients at fine scales. Then, using outputs from a numerical model, we discuss the spatial distribution of fronts and spatio-temporal control mechanisms.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>The EUREC4A-OA campaign</title>
      <p id="d2e443">Saildrone USVs – Uncrewed Surface Vehicles navigating with near real-time course correction <xref ref-type="bibr" rid="bib1.bibx93 bib1.bibx23" id="paren.18"><named-content content-type="pre">e.g.,</named-content></xref> – sampled the <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1500</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M16" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> long <italic>boulevard de tourbillons</italic> region off the Amazon shelf during the EUREC4A-OA campaign <xref ref-type="bibr" rid="bib1.bibx77 bib1.bibx81" id="paren.19"><named-content content-type="post">see saildrones' trajectory in Fig. <xref ref-type="fig" rid="F1"/>a</named-content></xref>. This eddy corridor connects the South and North Atlantic western boundary currents through the NBC rings, which detach from the NBC retroflection and travel toward the Caribbean Sea (Fig. <xref ref-type="fig" rid="F1"/>a). In EUREC4A-OA, four of these saildrones were piloted in formation, approximately parallel to each other, equipped with a near-surface Seabird SBE37 Microcat CTD and a 300 <inline-formula><mml:math id="M17" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kHz</mml:mi></mml:mrow></mml:math></inline-formula> RD Instruments ADCP, to adaptively sample across the mesoscale eddies and submesoscale features in this region. The CTD and ADCP were mounted on the saildrones at 0.5 and 2 <inline-formula><mml:math id="M18" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> below the waterline, respectively. The ADCP first bin was set at 6 <inline-formula><mml:math id="M19" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>. <xref ref-type="bibr" rid="bib1.bibx49" id="text.20"/> detail the post processing of the EUREC4A-OA Saildrone data, which resulted in 1 <inline-formula><mml:math id="M20" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> CTD (nominal accuracy of <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M22" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M24" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">mS</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">cm</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> for temperature and conductivity, respectively) and 5 <inline-formula><mml:math id="M25" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula> ADCP (<inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M27" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">cm</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) averages. For additional details on the fleet course and in-situ sampling during the campaign, see <xref ref-type="bibr" rid="bib1.bibx16" id="text.21"/>. More on Saildrone instrumentation and observations from different campaigns are available in e.g., <xref ref-type="bibr" rid="bib1.bibx92" id="text.22"/> and <xref ref-type="bibr" rid="bib1.bibx9" id="text.23"/>.</p>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e632"><bold>(a)</bold> The EUREC4A-OA saildrone campaign (17 January 2020–23 February 2020), with the saildrones' averaged trajectory in gray. The drones navigated the region of the North Brazil Current retroflection and the northwestern-propagating rings. The inset map shows the average sea surface salinity (SSS) from SMAP (Soil Moisture Active Passive mission) during EUREC4A-OA and a blowout of the saildrones trajectory, which <bold>(b)</bold> sampled regions inside the plume (blue) and outside (red). <bold>(c)</bold> Temperature–Salinity <inline-formula><mml:math id="M28" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M29" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> diagram of the EUREC4A-OA campaign, with colors representing points within the plume (blue) and outside (red). Keys: cSEC: central branch of the South Equatorial Current; NBC: North Brazil Current; NECC: North Equatorial Counter Current.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f01.png"/>

      </fig>

      <p id="d2e663">To compare processes inside and outside the Amazon Plume, we initially derive the position of the plume, bounded by the 36 isohaline, from satellite SSS data <xref ref-type="bibr" rid="bib1.bibx55" id="paren.24"><named-content content-type="pre">SMAP – Soil Moisture Active Passive mission;</named-content></xref>. While other authors use a more conservative approach <xref ref-type="bibr" rid="bib1.bibx57 bib1.bibx33" id="paren.25"><named-content content-type="pre">; e.g.,</named-content></xref>, we choose a wider threshold as in <xref ref-type="bibr" rid="bib1.bibx16" id="text.26"/>, which comprises a larger area under the plume influence <xref ref-type="bibr" rid="bib1.bibx58" id="paren.27"><named-content content-type="pre">e.g.,</named-content></xref>. We then refine the limits of the plume using the high-resolution saildrone SSS measurements to separate <sc>plume</sc> and <sc>outside</sc> (Fig. <xref ref-type="fig" rid="F1"/>b). This definition leads to a plume similar to that defined in <xref ref-type="bibr" rid="bib1.bibx16" id="text.28"/>: our <sc>plume</sc> region is virtually the same as Coadou-Chaventon's (2024) “Amazon” region, whereas the region <sc>outside</sc> roughly corresponds to the author's “Upstream” and “Downstream” areas combined. Overall, this definition suffices in isolating the core <sc>plume</sc> processes from those on the <sc>outside</sc>, both embedded in warm waters brought by the NBC (Fig. <xref ref-type="fig" rid="F1"/>c).</p>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Observed surface gradients</title>
      <p id="d2e720">The along-track measurements obtained by the saildrones provide a multi-scale overview of the surface properties, while drones sailing parallel allow the quantification of 2D gradients. We computed the mean values and gradients simultaneously over a mean trajectory between the four saildrones (see inset in Fig. <xref ref-type="fig" rid="F1"/>a) from 17 January 2020–23 February 2020. The final resolution of the dataset over the mean trajectory is <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>s</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M31" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:mn mathvariant="normal">2.5</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math></inline-formula> the saildrones' mean along-track resolution). With data from the four drones, we follow the method in <xref ref-type="bibr" rid="bib1.bibx76" id="text.29"/> to obtain temperature (<inline-formula><mml:math id="M33" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>), salinity (<inline-formula><mml:math id="M34" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula>), horizontal velocities <inline-formula><mml:math id="M35" display="inline"><mml:mi>u</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M36" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula>, and their corresponding gradients over this trajectory. Briefly, we gather the measurements of 3–4 saildrones (depending on their mutual distances, on average <inline-formula><mml:math id="M37" display="inline"><mml:mrow><mml:mn mathvariant="normal">2.5</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1.0</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M38" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>) within a moving 8 <inline-formula><mml:math id="M39" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula><inline-formula><mml:math id="M40" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula>120 <inline-formula><mml:math id="M41" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">min</mml:mi></mml:mrow></mml:math></inline-formula>-radius circle around the reference trajectory points. The size of the moving circle allows us to avoid temporal variability contaminating the averaged data in each circle, obtaining <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:mn mathvariant="normal">138.8</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">37.9</mml:mn></mml:mrow></mml:math></inline-formula> synoptic measurements <xref ref-type="bibr" rid="bib1.bibx16" id="paren.30"><named-content content-type="pre">for the saildrones, the synoptic scale is <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:mo>≃</mml:mo><mml:mn mathvariant="normal">40</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M44" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>; cf.</named-content></xref> per iteration, i.e., every time the circle moves. At each iteration, we fit a set of linear functions of the form

          <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M45" display="block"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mo>∂</mml:mo><mml:mi>x</mml:mi></mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mi>x</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:msub><mml:mo>∂</mml:mo><mml:mi>y</mml:mi></mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:mi>y</mml:mi><mml:mo>-</mml:mo><mml:mover accent="true"><mml:mi>y</mml:mi><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:mrow></mml:mfenced><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

        which provide the mean <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> values, alongside the zonal and meridional gradients <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>x</mml:mi></mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>y</mml:mi></mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi></mml:mrow></mml:math></inline-formula>. We solve Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>) for <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>v</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> at every point of the mean trajectory by applying a least squares plane fit to all (<inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:math></inline-formula>) observations within the moving circle <xref ref-type="bibr" rid="bib1.bibx9" id="paren.31"><named-content content-type="pre">cf.</named-content></xref>. These gradients are gradually smoothed by increasing <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:math></inline-formula> and the radius of the circle proportionally. Our choice is set for the smallest resolved scale under an accepted error threshold.</p>
      <p id="d2e1022">Saildrone instrumentation errors are documented in <xref ref-type="bibr" rid="bib1.bibx93 bib1.bibx94" id="text.32"/>. The uncertainty of observed density gradients could also be affected by e.g., variations in the fleet formation, time lag between drones, and dominant winds over along-current sampling. The choice of the mean trajectory resolution (1 <inline-formula><mml:math id="M52" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>) and the size of the moving circle (8 <inline-formula><mml:math id="M53" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>) reduce these and other associated errors, particularly in derived quantities. Still, we estimate the errors of the coefficients in Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>) by calculating the formal least-square uncertainties. For density gradients, we adopt a 95 % confidence interval for temperature and salinity gradients; in other words, we discard gradients smaller than twice their associated error, which removes 7 % of the 1 <inline-formula><mml:math id="M54" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>-binned data.</p>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Along-track density gradients</title>
      <p id="d2e1061">Saildrone along-track density observations allow us to assess the plume influence over multiple length scales through the computation of along-track gradients over a broad range of horizontal scales <inline-formula><mml:math id="M55" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula>. Figure <xref ref-type="fig" rid="F2"/> shows, on logarithmic scale, along-track absolute density gradients <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mi mathvariant="italic">ρ</mml:mi></mml:mrow></mml:math></inline-formula>, subsampled along the mean trajectory of the saildrones from scales between 1 and 100 <inline-formula><mml:math id="M57" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mo>,</mml:mo><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="normal">…</mml:mi><mml:mo>,</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">100</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M59" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>). A histogram counts occurrences per scale of <inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mi mathvariant="italic">ρ</mml:mi></mml:mrow></mml:math></inline-formula> (summing 100 % for each <inline-formula><mml:math id="M61" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula>), where bin values of the gradients can also be translated into a buoyancy frontal sharpness <inline-formula><mml:math id="M62" display="inline"><mml:mrow><mml:mi mathvariant="script">B</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mo>|</mml:mo><mml:mi mathvariant="normal">∇</mml:mi><mml:mi>b</mml:mi><mml:msup><mml:mo>|</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx36" id="paren.33"><named-content content-type="pre">e.g.,</named-content></xref>, with buoyancy <inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:mi>b</mml:mi><mml:mo>≡</mml:mo><mml:mo>-</mml:mo><mml:mi>g</mml:mi><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">ρ</mml:mi><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M64" display="inline"><mml:mi>g</mml:mi></mml:math></inline-formula> is the acceleration due to gravity and <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> is the reference mean density). This means, for example, that <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">5</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M67" 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">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> corresponds to <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:mi mathvariant="script">B</mml:mi><mml:mo>∼</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">13</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M69" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>.</p>

      <fig id="F2" specific-use="star"><label>Figure 2</label><caption><p id="d2e1308">Observed magnitude of surface along-track density gradients per horizontal scale <inline-formula><mml:math id="M70" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula> along the saildrones' trajectory <bold>(a)</bold> <sc>outside</sc> and <bold>(b)</bold> inside the Amazon <sc>plume</sc>. Colors represent the percentage of gradients for a given scale <inline-formula><mml:math id="M71" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula> (each column sum up to 100 % for every <inline-formula><mml:math id="M72" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula>) and dashed lines represent the buoyancy frontal sharpness <inline-formula><mml:math id="M73" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> reached for given density gradient thresholds.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f02.png"/>

        </fig>

      <p id="d2e1358">Analyzing the saildrone observations from scales between 1 and 100 <inline-formula><mml:math id="M74" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> reveals that along-track density gradients intensify rapidly when approaching smaller scales, where more sharp buoyancy fronts are present <xref ref-type="bibr" rid="bib1.bibx81" id="paren.34"><named-content content-type="pre">dashed lines in Fig. <xref ref-type="fig" rid="F2"/>a and b; also reported by</named-content><named-content content-type="post">using this dataset</named-content></xref>. These stronger gradients with increasing spatial resolution are consistent with previous numerical simulations <xref ref-type="bibr" rid="bib1.bibx56 bib1.bibx3" id="paren.35"><named-content content-type="pre">e.g.,</named-content></xref>. 
<sc>Outside</sc> the plume, the strongest density gradients range from <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:mi mathvariant="script">B</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">14</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M76" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> for <inline-formula><mml:math id="M77" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>≤</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M78" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>, decaying to <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">16</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M80" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> around <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M82" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> corresponding to weak large-scale horizontal density gradients <xref ref-type="bibr" rid="bib1.bibx91" id="paren.36"><named-content content-type="pre">Fig. <xref ref-type="fig" rid="F2"/>a; see also</named-content><named-content content-type="post">Fig. 3c</named-content></xref>. This latter value is similar to that of the <xref ref-type="bibr" rid="bib1.bibx44" id="text.37"/> global chart of lateral buoyancy gradients at low-resolution. Within the <sc>plume</sc>, fronts with <inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:mi mathvariant="script">B</mml:mi><mml:mo>≥</mml:mo><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">14</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M84" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> are numerous at all scales (Fig. <xref ref-type="fig" rid="F2"/>b). The fronts reach sharpness values of <inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:mi mathvariant="script">B</mml:mi><mml:mo>≥</mml:mo><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">13</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M86" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at 10 <inline-formula><mml:math id="M87" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> or less, in a combination of strong gradients and small scales, with peaks of <inline-formula><mml:math id="M88" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> of <inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">11</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M90" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at 1 <inline-formula><mml:math id="M91" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="F2"/>b). Such gradients were reported in very high-resolution numerical simulations (<inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">150</mml:mn></mml:mrow></mml:math></inline-formula>–500 <inline-formula><mml:math id="M93" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>), which produced fronts as sharp as <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:mi mathvariant="script">B</mml:mi><mml:mo>∼</mml:mo><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">14</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M95" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> in the North Atlantic <xref ref-type="bibr" rid="bib1.bibx80" id="paren.38"/>, <inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:mi mathvariant="script">B</mml:mi><mml:mo>∼</mml:mo><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">12</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M97" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> in the Gulf Stream <xref ref-type="bibr" rid="bib1.bibx36" id="paren.39"/> and even sharper <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">11</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula> in the Mississippi River plume <xref ref-type="bibr" rid="bib1.bibx5 bib1.bibx7" id="paren.40"/>.</p>
      <p id="d2e1790">Considering the 10 % strongest fronts, <inline-formula><mml:math id="M99" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> is on average <inline-formula><mml:math id="M100" display="inline"><mml:mrow><mml:mn mathvariant="normal">75</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math></inline-formula> stronger within the <sc>plume</sc> than in the <sc>outside</sc>. The largest differences (up to <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:mn mathvariant="normal">100</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math></inline-formula>) occur at small scales (). Besides their difference in magnitude, the variance of the buoyancy sharpness increases toward smaller scales both <sc>outside</sc> and within the <sc>plume</sc> (see Appendix A). The <inline-formula><mml:math id="M102" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> variance <sc>outside</sc> increases linearly from <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">31</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M104" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at <inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M106" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">28</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M108" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M110" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>. In the <sc>plume</sc>, the <inline-formula><mml:math id="M111" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> variance grows abruptly for <inline-formula><mml:math id="M112" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M113" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>, from <inline-formula><mml:math id="M114" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">28</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M115" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> to about <inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">23</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M117" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> at <inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M119" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d2e2050">This shift between the two regions suggests that frontogenesis driven by ageostrophic motions may be amplified by density gradients within the <sc>plume</sc>; such processes display high-vorticity and strain and are related to a recently observed shift from an inverse to a direct energy cascade on scales smaller than 10 <inline-formula><mml:math id="M120" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>
<xref ref-type="bibr" rid="bib1.bibx4" id="paren.41"><named-content content-type="pre">cf.</named-content><named-content content-type="post">although not independent from seasonality and location</named-content></xref>. We remind that, at large scales (<inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M122" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>), results should be interpreted with caution, since the effects of temporal variability are non-negligible for <inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>≳</mml:mo><mml:mn mathvariant="normal">40</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M124" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx16" id="paren.42"><named-content content-type="pre">i.e., the local synoptic scale;</named-content></xref>. The accuracy of the results could also be impacted by the direction in which the saildrones cross the fronts and changes in the fleet route, which are not considered in this study.</p>
      <p id="d2e2115">Having established that the plume dramatically amplifies density gradients, particularly at scales below 10 <inline-formula><mml:math id="M125" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>, we now examine the respective roles of temperature and salinity gradients in setting up density gradients through frontogenesis, and how temperature–salinity (<inline-formula><mml:math id="M126" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M127" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula>) relations act to partially compensate or reinforce the density gradients.</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Compensation, reinforcement, and frontogenetic tendency</title>
      <p id="d2e2148">A density gradient may be dominated by a temperature or a salinity gradient. Furthermore, both may combine to reinforce the density gradient or otherwise compensate each other to reduce it <xref ref-type="bibr" rid="bib1.bibx82 bib1.bibx24" id="paren.43"><named-content content-type="pre">cf.</named-content></xref>. The relation between these <inline-formula><mml:math id="M128" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M129" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients can be quantified by the Turner angle

            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M130" display="block"><mml:mrow><mml:mtext>Tu</mml:mtext><mml:mo>=</mml:mo><mml:mi>arctan⁡</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>(</mml:mo><mml:mi mathvariant="script">R</mml:mi><mml:mo>)</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          which replaces the infinite scale of the density ratio

            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M131" display="block"><mml:mrow><mml:mi mathvariant="script">R</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          by a finite one <xref ref-type="bibr" rid="bib1.bibx24" id="paren.44"/>. The density ratio in Eq. (<xref ref-type="disp-formula" rid="Ch1.E3"/>) evaluates the combined effect of the variation of temperature (<inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula>) and salinity (<inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:math></inline-formula>) on density gradients, where <inline-formula><mml:math id="M134" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M135" display="inline"><mml:mi mathvariant="italic">β</mml:mi></mml:math></inline-formula> are the thermal expansion and haline contraction coefficients, respectively. This ratio is positive (negative) for compensated (reinforced) gradients, with <inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:mtext>Tu</mml:mtext><mml:mo>=</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mi mathvariant="script">R</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>) representing fully compensated gradients. The Turner angle has recently been used to assess the effect of large freshwater discharges on oceanic density gradients <xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx78 bib1.bibx21 bib1.bibx22" id="paren.45"><named-content content-type="pre">e.g.,</named-content></xref>. In the present work, we compute Tu for the <inline-formula><mml:math id="M138" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M139" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients within 95 % confidence interval (see Sect. <xref ref-type="sec" rid="Ch1.S3"/>).</p>
      <p id="d2e2311">Regardless of their <inline-formula><mml:math id="M140" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M141" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> origin, the sharpening of buoyancy gradients indicates <italic>frontogenesis</italic> <xref ref-type="bibr" rid="bib1.bibx54 bib1.bibx53" id="paren.46"/>. The weakening of such fronts indicates <italic>frontolysis</italic>. <xref ref-type="bibr" rid="bib1.bibx54" id="text.47"/> derived the advective frontogenetic tendency for buoyancy,

            <disp-formula id="Ch1.E4" content-type="numbered"><label>4</label><mml:math id="M142" display="block"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msup><mml:mi>b</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:mfenced><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msup><mml:mi>u</mml:mi><mml:mi>j</mml:mi></mml:msup></mml:mrow></mml:mfenced><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>j</mml:mi></mml:msub><mml:msup><mml:mi>b</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:mfenced><mml:mo>-</mml:mo><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msup><mml:mi>b</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:mfenced><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:mi>w</mml:mi></mml:mrow></mml:mfenced><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>z</mml:mi></mml:msub><mml:mi>b</mml:mi></mml:mrow></mml:mfenced><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          in which the compact index notation <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>i</mml:mi><mml:mo>,</mml:mo><mml:mi>j</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> span <inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, with the horizontal velocity <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:msup><mml:mi>u</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi>v</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> and horizontal derivatives indicated by <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mo>∂</mml:mo><mml:mi>x</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mo>∂</mml:mo><mml:mi>y</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Since we only have surface buoyancy from the saildrones, the vertical derivative <inline-formula><mml:math id="M147" display="inline"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>z</mml:mi></mml:msub><mml:mi>b</mml:mi></mml:mrow></mml:math></inline-formula> is neglected, as is the second term on the right hand side of Eq. (<xref ref-type="disp-formula" rid="Ch1.E4"/>), where <inline-formula><mml:math id="M148" display="inline"><mml:mi>w</mml:mi></mml:math></inline-formula> is the vertical velocity. The equation thus reduces to the <italic>horizontal</italic> advective frontogenetic tendency, with buoyancy anomaly <inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>,

            <disp-formula id="Ch1.E5" content-type="numbered"><label>5</label><mml:math id="M150" display="block"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msup><mml:mi>b</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:mfenced><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msup><mml:mi>u</mml:mi><mml:mi>j</mml:mi></mml:msup></mml:mrow></mml:mfenced><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>j</mml:mi></mml:msub><mml:msup><mml:mi>b</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:mfenced><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          which is the leading order term of Eq. (<xref ref-type="disp-formula" rid="Ch1.E4"/>) <xref ref-type="bibr" rid="bib1.bibx7" id="paren.48"/>. We consider both CTD-derived buoyancy values at 0.5 <inline-formula><mml:math id="M151" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> and ADCP velocities at 6 <inline-formula><mml:math id="M152" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> as surface measurements.</p>
      <p id="d2e2627">To estimate errors of the frontogenetic tendency, we first obtain the uncertainties of velocity and buoyancy gradients prescribing an uncorrelated and homogeneous error of <inline-formula><mml:math id="M153" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.025</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M154" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M155" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx9" id="paren.49"><named-content content-type="pre"><inline-formula><mml:math id="M156" display="inline"><mml:mi>u</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M157" display="inline"><mml:mi>v</mml:mi></mml:math></inline-formula>;</named-content></xref> and <inline-formula><mml:math id="M158" display="inline"><mml:mrow><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">7</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M159" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (the mean standard error of <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msup><mml:mi>b</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>) for the saildrones. Adding the errors to Eq. (<xref ref-type="disp-formula" rid="Ch1.E5"/>), we apply basic rules for error propagation of multiplication and powers and normalize by the values of the corresponding gradients. The relative error

            <disp-formula id="Ch1.E6" content-type="numbered"><label>6</label><mml:math id="M161" display="block"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">σ</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msup><mml:mi>b</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:mfenced><mml:mo>+</mml:mo><mml:mi mathvariant="italic">σ</mml:mi><mml:mfenced open="(" close=")"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msup><mml:mi>u</mml:mi><mml:mi>j</mml:mi></mml:msup></mml:mrow></mml:mfenced><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

          with <inline-formula><mml:math id="M162" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϕ</mml:mi><mml:mtext>err</mml:mtext></mml:msub></mml:mrow><mml:mi mathvariant="italic">ϕ</mml:mi></mml:mfrac></mml:mstyle></mml:mrow></mml:math></inline-formula>, must be smaller than a threshold <inline-formula><mml:math id="M163" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>max⁡</mml:mo></mml:msub></mml:mrow></mml:math></inline-formula>. Since calculating <inline-formula><mml:math id="M164" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> involves multiple derivatives, we accept errors equivalent to 20 % of the inertial (<inline-formula><mml:math id="M165" display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula>) and buoyancy (<inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>) frequencies, for velocity and buoyancy gradients, respectively. We calculate <inline-formula><mml:math id="M167" display="inline"><mml:mi>f</mml:mi></mml:math></inline-formula> at each point of the trajectory and obtain an average <inline-formula><mml:math id="M168" display="inline"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> for <sc>plume</sc> and <sc>outside</sc> from shipboard in-situ data during the EUREC4A-OA campaign <xref ref-type="bibr" rid="bib1.bibx49" id="paren.50"/>. The maximum error in Eq. (<xref ref-type="disp-formula" rid="Ch1.E6"/>) becomes

            <disp-formula id="Ch1.E7" content-type="numbered"><label>7</label><mml:math id="M169" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>max⁡</mml:mo></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mfenced close=")" open="("><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">0.2</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi>N</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msup><mml:mi>b</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mo>+</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mn mathvariant="normal">0.2</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi>i</mml:mi></mml:msub><mml:msup><mml:mi>u</mml:mi><mml:mi>j</mml:mi></mml:msup></mml:mrow></mml:mfrac></mml:mstyle><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          After removing samples with errors larger than <inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>max⁡</mml:mo></mml:msub></mml:mrow></mml:math></inline-formula> (Eq. <xref ref-type="disp-formula" rid="Ch1.E7"/>), we keep 93 % of the Tu and 91 % of <inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>. Combining both, we build Fig. <xref ref-type="fig" rid="F3"/> using 88 % of samples at 1 <inline-formula><mml:math id="M172" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>.</p>

      <fig id="F3" specific-use="star"><label>Figure 3</label><caption><p id="d2e2986">Overview of observed gradients. <bold>(a)</bold> Schematic diagram mirroring gradients related to frontogenesis (top) and frontolysis (bottom). Radial distances represent the strength of <inline-formula><mml:math id="M173" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> [<inline-formula><mml:math id="M174" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>]. Azimuthal distances represent Turner angle Tu (clockwise from <inline-formula><mml:math id="M175" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> for frontogenesis and counterclockwise for frontolysis), where quadrants indicate if density gradients are driven by salinity (blue) or temperature (red) and if they compensate or reinforce each other. <bold>(b, c)</bold> Saildrone surface density variations at <inline-formula><mml:math id="M176" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.0</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M177" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> scale <sc>outside</sc> (<bold>b</bold>; 1964 samples) and inside the <sc>plume</sc> (<bold>c</bold>; 810 samples). Colors indicate the number of gradients sampled for each azimuthal and radial bin.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f03.png"/>

        </fig>

      <p id="d2e3073">Breaking down the density gradients observed at 1 <inline-formula><mml:math id="M178" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> reveals the role of temperature and salinity in their composition. We group the gradients along <inline-formula><mml:math id="M179" display="inline"><mml:mrow><mml:mtext>Tu</mml:mtext><mml:mo>]</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mo>;</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mo>[</mml:mo></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M180" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> [0–10<sup>−15</sup> <inline-formula><mml:math id="M182" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>], separating gradients undergoing frontogenesis and frontolysis. Finally, we add up their occurrences (counts) to present a comprehensive picture of the observed gradients in Fig. <xref ref-type="fig" rid="F3"/>.</p>
      <p id="d2e3154">Overall, frontogenesis is partially mirrored by frontolysis (Fig. <xref ref-type="fig" rid="F3"/>b and c). Nevertheless, our observations hint at net frontogenesis driven by the strongest <inline-formula><mml:math id="M183" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>, with maximum values of <inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">18</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M185" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>
<sc>outside</sc> and <inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">16</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M187" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> within the <sc>plume</sc>. <sc>Outside</sc>, the <inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">2000</mml:mn></mml:mrow></mml:math></inline-formula> observed buoyancy gradients typically show <inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup><mml:mo>≤</mml:mo><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">19</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M190" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, with temperature- and salinity-dominated gradients distributed throughout the range of Tu (Fig. <xref ref-type="fig" rid="F3"/>b). At large-scales, <xref ref-type="bibr" rid="bib1.bibx91" id="text.51"/> showed strong salinity influence over all the northwestern Tropical Atlantic. The higher occurrence of salinity dominance (<inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">4</mml:mn><mml:mo>&lt;</mml:mo><mml:mtext>Tu</mml:mtext><mml:mo>&lt;</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula>; see Fig. <xref ref-type="fig" rid="F3"/>a), even in the region <sc>outside</sc>, is likely due to a remnant plume from previous seasons <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx17 bib1.bibx28" id="paren.52"><named-content content-type="pre">e.g.,</named-content></xref>.</p>
      <p id="d2e3342">Mixed-layer instabilities and atmospheric forcing also play a role generating submesoscale fronts across the whole domain; locally, we assume that the NBC and the plume's influence are strong enough to intensify or reduce these effects significantly <xref ref-type="bibr" rid="bib1.bibx17" id="paren.53"><named-content content-type="pre">e.g.,</named-content></xref>. For example, in Fig. <xref ref-type="fig" rid="F3"/>, the co-occurrence of frontolysis and frontogenesis hints at a pattern typical of arched flows, with a confluent region followed by a diffluent one <xref ref-type="bibr" rid="bib1.bibx54" id="paren.54"><named-content content-type="pre">e.g.,</named-content></xref>. While only a handful of relatively strong gradients <inline-formula><mml:math id="M192" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup><mml:mo>≥</mml:mo><mml:mo>|</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">18</mml:mn></mml:mrow></mml:msup><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M193" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> are associated with frontogenesis <sc>outside</sc>, (Fig. <xref ref-type="fig" rid="F3"/>b), they become <inline-formula><mml:math id="M194" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">16</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> within the <sc>plume</sc> (Fig. <xref ref-type="fig" rid="F3"/>c). Not surprisingly, salinity gradients are largely dominant within the <sc>plume</sc>, and the distribution around <inline-formula><mml:math id="M195" display="inline"><mml:mrow><mml:mi mathvariant="script">R</mml:mi><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> highlights the large difference between the magnitude of temperature and salinity gradients. At 1 <inline-formula><mml:math id="M196" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M197" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> that reaches <inline-formula><mml:math id="M198" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>|</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">16</mml:mn></mml:mrow></mml:msup><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M199" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> is comparable to (model) values in the Mississippi River plume <xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx7" id="paren.55"><named-content content-type="post"><inline-formula><mml:math id="M200" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>x</mml:mi><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">500</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M201" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> resolution</named-content></xref> and in energetic Gulf Stream meanders <xref ref-type="bibr" rid="bib1.bibx54" id="paren.56"><named-content content-type="post"><inline-formula><mml:math id="M202" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M203" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula></named-content></xref>.</p>
      <p id="d2e3548">In the salinity-dominated Bay of Bengal, <xref ref-type="bibr" rid="bib1.bibx78" id="text.57"/> observations showed a shift from <inline-formula><mml:math id="M204" display="inline"><mml:mrow><mml:mi mathvariant="script">R</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> at 100 <inline-formula><mml:math id="M205" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> scales towards compensated fronts at 1 <inline-formula><mml:math id="M206" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> scale, attributing the compensation effect to the surface cooling of salinity dominated gradients at submesoscale. Within the Amazon Plume, <xref ref-type="bibr" rid="bib1.bibx16" id="text.58"/> found partially compensated <inline-formula><mml:math id="M207" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M208" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients dominant at different scales in the 20 % highest scale coefficients <inline-formula><mml:math id="M209" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M210" display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:math></inline-formula>. Taking every gradient at <inline-formula><mml:math id="M211" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M212" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>, the <inline-formula><mml:math id="M213" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula>-axis symmetry shows that partial reinforcement occurs almost as much as partial compensation (Fig. <xref ref-type="fig" rid="F3"/>b and c), and temperature-dominated gradients partially compensated by salinity (<inline-formula><mml:math id="M214" display="inline"><mml:mrow><mml:mi mathvariant="script">R</mml:mi><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula>), appear mostly <sc>outside</sc> (Fig. <xref ref-type="fig" rid="F3"/>b). Such partial compensation is ubiquitous in the global ocean <xref ref-type="bibr" rid="bib1.bibx72" id="paren.59"><named-content content-type="pre">e.g.,</named-content></xref>. Both within the <sc>plume</sc> and <sc>outside</sc>, observations also capture robust compensation (<inline-formula><mml:math id="M215" display="inline"><mml:mrow><mml:mi mathvariant="script">R</mml:mi><mml:mo>≃</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>), although less often (Fig. <xref ref-type="fig" rid="F3"/>b and c). To this point, our data allow us to only infer, based on the dynamics of the region, that this pattern could arise from the equatorial-warm NBC pushing fresh river water inbound the cooler and saltier Tropical Atlantic, creating freshwater filaments in a background of rather uniform temperature gradient. Such filaments present compensation on the warmer side of the filament and reinforcement on the colder one <xref ref-type="bibr" rid="bib1.bibx22" id="paren.60"><named-content content-type="pre">see e.g.,</named-content><named-content content-type="post">Fig. 8f for a cold filament with the same consequences for Tu</named-content></xref>.</p>
      <p id="d2e3704">When comparing statistics of observed frontogenesis, frontolysis, and Tu, matching probability density functions (pdfs) for frontogenesis and frontolysis with skewness <inline-formula><mml:math id="M216" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> and kurtosis <inline-formula><mml:math id="M217" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> show no predominance between <inline-formula><mml:math id="M218" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M219" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> nor between compensation and reinforcement <sc>outside</sc> (Fig. <xref ref-type="fig" rid="F4"/>a). High positive kurtosis within the <sc>plume</sc> further supports compensated and reinforced fronts heavily dominated by salinity (Fig. <xref ref-type="fig" rid="F4"/>b). Although modest, negative skewness points to slightly more compensation, becoming particularly important for fronts undergoing frontogenesis within the <sc>plume</sc>.</p>

      <fig id="F4" specific-use="star"><label>Figure 4</label><caption><p id="d2e3758">Statistics of observed Tu and <inline-formula><mml:math id="M220" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> at <inline-formula><mml:math id="M221" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M222" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>. <bold>(a, b)</bold> Pdf of Tu separated between gradients showing frontogenesis (red) and frontolysis (blue), for <bold>(a)</bold> <sc>outside</sc> and <bold>(b)</bold> the <sc>plume</sc>. <bold>(c, d)</bold> Inverse cumulative pdf of frontogenesis (red) and frontolysis (blue) for <bold>(c)</bold> <sc>outside</sc> and <bold>(d)</bold> the <sc>plume</sc>.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f04.png"/>

        </fig>

      <p id="d2e3830">There is a systematic predominance of frontogenesis over frontolysis in the range <inline-formula><mml:math id="M223" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>|</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:msup><mml:mo>|</mml:mo><mml:mo>&lt;</mml:mo><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup><mml:mo>&lt;</mml:mo><mml:mi mathvariant="script">O</mml:mi><mml:mo>|</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">18</mml:mn></mml:mrow></mml:msup><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M224" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, with up to more than 20 % of the gradients undergoing frontogenesis than frontolysis (Fig. <xref ref-type="fig" rid="F4"/>c and d). This persistent excess of frontogenesis over frontolysis implies that the region is not simply redistributing existing gradients, but actively sharpening them. Extreme <inline-formula><mml:math id="M225" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> observed within the <sc>plume</sc> likely drives convergent downwelling and subduction of surface tracers into the pycnocline <xref ref-type="bibr" rid="bib1.bibx13 bib1.bibx66" id="paren.61"><named-content content-type="pre">e.g.,</named-content></xref>.</p>
      <p id="d2e3912">Finally, the larger-than-expected ratio of reinforced fronts in the current analysis can be explained by <list list-type="bullet"><list-item>
      <p id="d2e3917">the evaluation of near-surface gradients compared to deeper gradients <xref ref-type="bibr" rid="bib1.bibx24" id="paren.62"><named-content content-type="pre">e.g.,</named-content></xref>, where unstable gradients are more likely to occur;</p></list-item><list-item>
      <p id="d2e3926">the use of every sampled gradient instead of a specific section <xref ref-type="bibr" rid="bib1.bibx78" id="paren.63"><named-content content-type="pre">e.g.,</named-content></xref> or a selection of a few % strong gradients <xref ref-type="bibr" rid="bib1.bibx16" id="paren.64"><named-content content-type="pre">e.g.,</named-content></xref>, where a bias can be introduced due to reinforced gradients becoming unstable and usually not producing <inline-formula><mml:math id="M226" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M227" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients as sharp as in compensated fronts <xref ref-type="bibr" rid="bib1.bibx22" id="paren.65"><named-content content-type="pre">e.g.,</named-content></xref>; and</p></list-item><list-item>
      <p id="d2e3959">the local dynamics driven by the interaction of the Amazon Plume and the NBC, which we discuss in more details later in this study.</p></list-item></list></p>
      <p id="d2e3962">So far, we have shown that density gradients intensify within the Amazon <sc>plume</sc>, especially at scales <inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M229" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>. There, fronts are salinity-dominated and partially compensated or reinforced by temperature, with local dynamics acting to sharpen them, resulting in net frontogenesis. <sc>Outside</sc> the plume, <inline-formula><mml:math id="M230" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M231" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients are weaker and more uniformly distributed in the <inline-formula><mml:math id="M232" display="inline"><mml:mrow><mml:mtext>Tu</mml:mtext><mml:mo>-</mml:mo><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> space, suggesting a competition between a remnant salinity-dominated surface layer and temperature fluctuations brought about by the seasonality of the NBC and local dynamics.</p>
      <p id="d2e4019">In the next section, we further explore gradients in the Amazon <sc>plume</sc> region using a numerical simulation to explore their spatial and temporal variability.</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>The numerical model</title>
      <p id="d2e4034">The model is CROCO <xref ref-type="bibr" rid="bib1.bibx75" id="paren.66"><named-content content-type="pre">Coastal and Regional Ocean COmmunity model, based on the Regional Oceanic Modeling System;</named-content></xref>. The simulation belongs to the GIGATL family <xref ref-type="bibr" rid="bib1.bibx37" id="paren.67"><named-content content-type="post">hereafter GIGATL1</named-content></xref> over the Atlantic Ocean with a nominal horizontal resolution of 1 <inline-formula><mml:math id="M233" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> and 100 terrain-following vertical levels. The simulation uses hourly CFSR <xref ref-type="bibr" rid="bib1.bibx73" id="paren.68"><named-content content-type="pre">Climate Forecast System Reanalysis;</named-content></xref> atmospheric forcing, a  turbulence closure scheme <xref ref-type="bibr" rid="bib1.bibx87" id="paren.69"/> for parameterization of vertical mixing, and SRTM30plus bathymetry <xref ref-type="bibr" rid="bib1.bibx8" id="paren.70"/>. The Amazon River input is a monthly climatology from <xref ref-type="bibr" rid="bib1.bibx18" id="text.71"/>. Barotropic tidal forcing at the boundaries and tidal potential and self attraction are from TPXO7.2 and GOT99.2b. Boundary conditions are from SODA <xref ref-type="bibr" rid="bib1.bibx14" id="paren.72"><named-content content-type="pre">Simple Ocean Data Assimilation;</named-content></xref>. GIGATL1 is initialized in July 2007 from the 3 <inline-formula><mml:math id="M234" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> simulation GIGATL3, which was in turn initialized with SODA in January 2004. GIGATL1 and GIGATL3 share the same configuration except for the horizontal resolution and initial condition. We draw snapshots and time series from 20 months of hourly surface output from the simulated years 2008 and 2009.</p>
      <p id="d2e4085">We first analyze a model snapshot exhibiting characteristics similar to those observed during the EUREC4A-OA campaign. The modeled plume on 25 March 2008, 6 <inline-formula><mml:math id="M235" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">h</mml:mi></mml:mrow></mml:math></inline-formula> partially occupies the 59–47° W, 4.5–15° N region where we conduct our analyses (Fig. <xref ref-type="fig" rid="F5"/>a). The chosen snapshot also captures the NBC retroflection next to the plume, a scenario depicted from satellite data during the campaign <xref ref-type="bibr" rid="bib1.bibx16" id="paren.73"><named-content content-type="pre">see inset map in Fig. <xref ref-type="fig" rid="F1"/>a and Fig. 1 from</named-content></xref>. The choice of a single snapshot to sample the <sc>plume</sc> and <sc>outside</sc> comes from the idea of minimizing plume-related processes being captured outside and vice-versa, since we use a simple salinity criterion to separate the regions. Rather than obtaining a direct comparison with the campaign (the modeled plume lags one month behind observations; see Appendix B), our focus is to show that the model is able to represent density gradients and <inline-formula><mml:math id="M236" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M237" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> relations similar to the observations.</p>

      <fig id="F5" specific-use="star"><label>Figure 5</label><caption><p id="d2e4128"><bold>(a)</bold> Model spatial distribution of buoyancy sharpness <inline-formula><mml:math id="M238" display="inline"><mml:mrow><mml:mi mathvariant="script">B</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mn mathvariant="normal">1</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle><mml:mo>|</mml:mo><mml:mi mathvariant="normal">∇</mml:mi><mml:mi>b</mml:mi><mml:msup><mml:mo>|</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> and the separation between <sc>plume</sc> and <sc>outside</sc> regions using the 0.25 quantile of the salinity distribution. <bold>(b)</bold> Latitudinal transects used to compute the magnitude of surface density gradients within the <sc>plume</sc> and <sc>outside</sc>.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f05.png"/>

      </fig>

      <p id="d2e4183">As for the observations, we start by comparing 1-D density differences along multiple zonal transects within the <sc>plume</sc> and <sc>outside</sc>, taken at 0.5° longitude and latitude intervals within the 59–47° W; 4.5–14.5° N region (Fig. <xref ref-type="fig" rid="F5"/>b). However, contrary to observations, in the model we adopt a varying salinity threshold to define the plume: the 0.25 quantile – one-fourth of the SSS probability distribution, hereafter <inline-formula><mml:math id="M239" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="script">Q</mml:mi><mml:mn mathvariant="normal">25</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> – which separates the strongest SSS gradients of the <sc>plume</sc> from the <sc>outside</sc> (see Appendix C). This moving threshold helps to capture the plume over a longer period than in the observations, while preserving its seasonal cycle.</p>
      <p id="d2e4212">The model reproduces the key observational signatures: stronger and more variable density gradients within the plume than outside, salinity dominance of fronts, and net frontogenesis both within the <sc>plume</sc> and <sc>outside</sc>. The main limitation is that the contrast between both regions is less pronounced in the simulation, owing to the model's effective resolution smoothing the sharpest submesoscale gradients and blurring the <sc>plume</sc> boundary. Keeping this in mind, we benefit from the model's spatial and temporal coverage to interpret the dynamical mechanisms behind the observed frontal characteristics.</p>
      <p id="d2e4224">Our detailed model analyses below begins by focusing on comparisons with observations collected by the saildrones.</p>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Modeled density gradients</title>
      <p id="d2e4234">Initially, we restrict our analysis and comparisons to a region similar to the one sampled by the saildrones, where the Amazon Plume and NBC are present (Fig. <xref ref-type="fig" rid="F5"/>a). On 25 March, a freshwater tongue penetrated the open ocean to the northwest, with a retroflecting NBC dragging low salinity (<inline-formula><mml:math id="M240" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">35.7</mml:mn></mml:mrow></mml:math></inline-formula>) to the northeast (Fig. <xref ref-type="fig" rid="F5"/>a; see also Fig. C3 in Appendix C). Strong <inline-formula><mml:math id="M241" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> occur within the <sc>plume</sc> along the continental shelf and over the recirculating branch of the NBC. Patches of strong <inline-formula><mml:math id="M242" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> stretch from the shelf, surrounding eddies and marking filaments on the path of the NBC retroflection. In the region <sc>outside</sc>, some strong <inline-formula><mml:math id="M243" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> detach from the plume and enter a second dynamical regime that extends from <inline-formula><mml:math id="M244" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">14</mml:mn></mml:mrow></mml:math></inline-formula>° N to the northern portion of the domain, away from the direct influence of the NBC.</p>
      <p id="d2e4291">With transects defined in Fig. <xref ref-type="fig" rid="F5"/>b, the per scale distributions in Fig. <xref ref-type="fig" rid="F6"/>a and b display <sc>plume</sc> and <sc>outside</sc> points from our snapshot. The modeled <inline-formula><mml:math id="M245" display="inline"><mml:mrow><mml:msub><mml:mo>∂</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mi mathvariant="italic">ρ</mml:mi></mml:mrow></mml:math></inline-formula> and associated <inline-formula><mml:math id="M246" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> are consistent with saildrone observations, with the model capturing extreme values in the same range as the observations. The model variability is also greater within the <sc>plume</sc> across the scales, even though differences are less striking than those reported by saildrone data. We attribute the weaker contrast between the two simulated regions to unresolved ageostrophic flows due to the model's horizontal resolution (partially resolving submesoscales in low latitudes), which hinders the divergent strain field directly related to submesoscale frontogenesis <xref ref-type="bibr" rid="bib1.bibx7" id="paren.74"/>. Additionally, model diffusion acting at scales up to the effective resolution of the model will likely smooth the sharpest gradients, consequently clouding the limits between <sc>plume</sc> and <sc>outside</sc>. Nevertheless, <inline-formula><mml:math id="M247" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> values in Fig. <xref ref-type="fig" rid="F6"/>b have been reported in other regions by previous regional modeling studies with at least twice the resolution <xref ref-type="bibr" rid="bib1.bibx36 bib1.bibx7" id="paren.75"><named-content content-type="pre">e.g.,</named-content></xref>, attesting to the unparalleled strength of gradients around river plumes <xref ref-type="bibr" rid="bib1.bibx89" id="paren.76"><named-content content-type="pre">e.g.,</named-content></xref>.</p>

      <fig id="F6" specific-use="star"><label>Figure 6</label><caption><p id="d2e4359">Magnitude of modeled surface density gradients, along latitudinal transects and per horizontal scale <inline-formula><mml:math id="M248" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula>, <sc>outside</sc> <bold>(a)</bold> and inside the Amazon <sc>plume</sc> <bold>(b)</bold>. Colors represent the percentage of gradients for a given scale <inline-formula><mml:math id="M249" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula> (each column sum up to 100 % for every <inline-formula><mml:math id="M250" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula>) and dashed lines represent the buoyancy frontal sharpness <inline-formula><mml:math id="M251" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> reached for given density gradient thresholds.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f06.png"/>

        </fig>

</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Compensation, reinforcement, and frontogenetic tendency in the model</title>
      <p id="d2e4417">From model outputs, we computed Tu using the two-dimensional horizontal temperature and salinity variations <inline-formula><mml:math id="M252" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M253" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:math></inline-formula>.  For <inline-formula><mml:math id="M254" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>, we decided to use the “horizontal” definition in Eq. (<xref ref-type="disp-formula" rid="Ch1.E5"/>) to constrain the analysis to the surface, which allows a (more) direct comparison with observations.</p>
      <p id="d2e4453">The representation of gradients in <inline-formula><mml:math id="M255" display="inline"><mml:mrow><mml:mtext>Tu</mml:mtext><mml:mo>-</mml:mo><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> space (Fig. <xref ref-type="fig" rid="F7"/>a) confirms the signature of both temperature and salinity <sc>outside</sc> (Fig. <xref ref-type="fig" rid="F7"/>b). The role of the Amazon Plume stands out by driving intense frontogenesis within salinity-dominated gradients <xref ref-type="bibr" rid="bib1.bibx51" id="paren.77"><named-content content-type="pre">Fig. <xref ref-type="fig" rid="F7"/>c; e.g.,</named-content></xref>. The separation between <sc>plume</sc> and <sc>outside</sc> in the model is not as extreme as in the observations, because smoothed gradients struggle to set the boundaries that separate the two regions. The model also encompasses every gradient in one region, notably displaying more temperature-dominated gradients within the <sc>plume</sc> compared to observations (Fig. <xref ref-type="fig" rid="F7"/>c). These gradients are mainly associated with the NBC (more on Sect. <xref ref-type="sec" rid="Ch1.S5"/>) and were virtually absent in the observations during the EUREC4A-OA campaign (Figs. <xref ref-type="fig" rid="F2"/>b and <xref ref-type="fig" rid="F3"/>c), but could be present in distinct saildrone trajectories on the outskirts of the plume. Still, the strongest frontogenetic gradients occur in the <sc>plume</sc>, heavily dominated by salinity.</p>

      <fig id="F7" specific-use="star"><label>Figure 7</label><caption><p id="d2e4509">Overview of modeled gradients. <bold>(a)</bold> Schematic diagram mirroring gradients related to frontogenesis (top) and frontolysis (bottom). Radial distances represent the strength of <inline-formula><mml:math id="M256" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>. Azimuthal distances represent Turner angle Tu (clockwise from <inline-formula><mml:math id="M257" display="inline"><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:mo>-</mml:mo><mml:mi mathvariant="italic">π</mml:mi></mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mfrac></mml:mstyle></mml:math></inline-formula> for frontogenesis and counterclockwise for frontolysis), where quadrants indicate if density gradients are driven by salinity (blue) or temperature (red) and if they compensate or reinforce each other. <bold>(b, c)</bold> Modeled surface density variations at <inline-formula><mml:math id="M258" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1.0</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M259" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> scale <sc>outside</sc> (<bold>b</bold>; 471276 samples) and inside the <sc>plume</sc> (<bold>c</bold>; 472332 samples); the region <sc>outside</sc> was randomly subsampled so the colorbar scale matches both regions.  Colors indicate the number of gradients sampled for each azimuthal and radial bin.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f07.png"/>

        </fig>

      <p id="d2e4586">In general, the model distributions respect the observations, with key features such as the salinity dominance within the <sc>plume</sc>, the homogeneity of the distribution <sc>outside</sc>, and net frontogenesis in both regions captured by the model. Model statistics show virtually the same Tu distribution for gradients undergoing frontogenesis or frontolysis (Fig. <xref ref-type="fig" rid="F8"/>a and b) and net frontogenesis (<inline-formula><mml:math id="M260" display="inline"><mml:mo lspace="0mm">∼</mml:mo></mml:math></inline-formula> 5 %–7 %; Fig. <xref ref-type="fig" rid="F8"/>c and d). In the <sc>plume</sc>, temperature-dominated gradients weigh on the tails of the model distributions (and yield negative kurtosis), although the salinity remains largely dominant, with a peak near zero. Negative kurtosis can also be explained by a tendency toward bimodality <xref ref-type="bibr" rid="bib1.bibx2" id="paren.78"><named-content content-type="pre">Fig. <xref ref-type="fig" rid="F8"/>b; cf.</named-content></xref>, with both the salinity of the Amazon Plume and the temperature of the NBC setting up gradients in the model.</p>

      <fig id="F8" specific-use="star"><label>Figure 8</label><caption><p id="d2e4619">Statistics of modeled Tu and <inline-formula><mml:math id="M261" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>. <bold>(a, b)</bold> Pdf of Tu separated between gradients showing frontogenesis (red) and frontolysis (blue), for <bold>(a)</bold> <sc>outside</sc> and <bold>(b)</bold> the <sc>plume</sc>. <bold>(c, d)</bold> Inverse cumulative pdf of frontogenesis (red) and frontolysis (blue), for <bold>(c)</bold> <sc>outside</sc> and <bold>(d)</bold> the <sc>plume</sc>.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f08.png"/>

        </fig>

      <p id="d2e4670">Even though the full terms are available from GIGATL1, analyses of <inline-formula><mml:math id="M262" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> are restricted to the surface. For the sake of completeness, we compared this approximation to the full terms of <inline-formula><mml:math id="M263" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>, which may, in extreme cases, modulate the fronts' intensity, but does not alter their spatial distribution (see Appendix D). This advocates for the efficiency of the observed strategy in capturing such features by sampling only their horizontal variability. Yet, strong stratification in this tropical region and the presence of the Amazon Plume can scale-up the vertical term and alter the ratio between frontogenesis and frontolysis. The effects of vertical terms are not detailed in this study.</p>
      <p id="d2e4695">Owing to a simulation capable of representing the magnitude and distribution of buoyancy gradients associated with the Amazon River plume over a wide range of conditions, we now proceed to the spatiotemporal analysis of the simulation to shed light on how the region's dynamics shape <inline-formula><mml:math id="M264" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M265" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> relations and fronts on the different <sc>plume</sc> and <sc>outside</sc> environments.</p>
</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Spatial distribution of surface fronts</title>
      <p id="d2e4728">At fine scales, the stirring and straining of tracers by mesoscale and submesoscale motions add to the low-frequency dynamics of the large scales <xref ref-type="bibr" rid="bib1.bibx48 bib1.bibx32" id="paren.79"><named-content content-type="pre">e.g.,</named-content></xref>. In the model, they control the spatial diversity of <inline-formula><mml:math id="M266" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M267" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients (Fig. <xref ref-type="fig" rid="F9"/>a), maintained by the joint action of the Amazon River plume and the NBC <xref ref-type="bibr" rid="bib1.bibx39" id="paren.80"/>. Their interaction gives rise to all <inline-formula><mml:math id="M268" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M269" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> relationships, producing different types of gradients (Fig. <xref ref-type="fig" rid="F9"/>a and b between 56–52° W; 8–10° N; see also Figs. <xref ref-type="fig" rid="F3"/> and <xref ref-type="fig" rid="F7"/>). On 25 March, a retroflecting NBC carrying warm waters rolls up a plume filament. Within the core of the impinging plume filament, the dominance of salinity gradients is striking (<inline-formula><mml:math id="M270" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle><mml:mo>&lt;</mml:mo><mml:mtext>Tu</mml:mtext><mml:mo>&lt;</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mi mathvariant="italic">π</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:mfrac></mml:mstyle></mml:mrow></mml:math></inline-formula>; Fig. <xref ref-type="fig" rid="F9"/>a). East of the plume, the NBC continues to advect freshwater northward, while the swirling motion associated with NBC rings folds gradients into layered structures characterized by alternating dominance of plume salinity and NBC temperature.</p>

      <fig id="F9" specific-use="star"><label>Figure 9</label><caption><p id="d2e4807">Spatial distribution of <bold>(a)</bold> the Turner Angle Tu and <bold>(b)</bold> the Frontogenetic Tendency of Buoyancy <inline-formula><mml:math id="M271" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> for the snapshot on 25 March 2008, 6 <inline-formula><mml:math id="M272" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">h</mml:mi></mml:mrow></mml:math></inline-formula>. The <sc>plume</sc> region is delimited by the isohaline representing the 0.25 quantile of the salinity probability distribution (dark blue and green lines).</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f09.png"/>

      </fig>

      <p id="d2e4844">Notably, the scenario shows the formation of an uncompensated front (Tu; Fig. <xref ref-type="fig" rid="F9"/>a) at the northern edge of the Amazon <sc>plume</sc> carried offshore by the NBC. Along the retroflecting current, <inline-formula><mml:math id="M273" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> surpassed by <inline-formula><mml:math id="M274" display="inline"><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> sets up a temperature-dominated, uncompensated front edge that delimits the NBC–plume interaction region (Fig. <xref ref-type="fig" rid="F9"/>a). Thus, fronts detaching from the near-shore region are unambiguously related to the NBC retroflection stirring the Amazon Plume. Within the core of the <sc>plume</sc>, in turn, both compensated and uncompensated fronts are now dominated by salinity. These fronts are still associated with the interaction of the NBC and the Amazon Plume, but occur mostly inside the <sc>plume</sc> (Fig. <xref ref-type="fig" rid="F9"/>a).</p>
      <p id="d2e4892">The frontogenetic tendency of buoyancy (Fig. <xref ref-type="fig" rid="F9"/>b) display distinct fronts over three domains, with particular dynamics and different geometry: <list list-type="custom"><list-item><label>i.</label>
      <p id="d2e4899">Shelf fronts: broken-up fronts parallel to shore occupy the core of the plume over the continental shelf. Strong <inline-formula><mml:math id="M275" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> of these fronts follow the coastal flow over the shelf <xref ref-type="bibr" rid="bib1.bibx12 bib1.bibx43" id="paren.81"/> and may be broken-up by processes acting on timescales shorter than the flow advection, such as interaction with normal-to-shore tidal currents <xref ref-type="bibr" rid="bib1.bibx12 bib1.bibx1" id="paren.82"><named-content content-type="pre">e.g.,</named-content></xref> and air–sea interactions <xref ref-type="bibr" rid="bib1.bibx78 bib1.bibx16" id="paren.83"><named-content content-type="pre">e.g.,</named-content></xref>;</p></list-item><list-item><label>ii.</label>
      <p id="d2e4927">NBC-plume interaction fronts: longer arched fronts associated with the NBC interacting with the plume connect the near-shore and oceanic region. They occur either within or at the border of the <sc>plume</sc>, as similarly shown by <xref ref-type="bibr" rid="bib1.bibx7" id="text.84"/> in the Mississippi plume, and are associated with curved filaments at the border of eddies and meanders <xref ref-type="bibr" rid="bib1.bibx47 bib1.bibx54" id="paren.85"/>; wavelike structures at the plume edge (<inline-formula><mml:math id="M276" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula>° W) could be associated with the strong internal tides that interact with the NBC <xref ref-type="bibr" rid="bib1.bibx85 bib1.bibx86" id="paren.86"><named-content content-type="pre">e.g.,</named-content></xref>;</p></list-item></list> a gap in frontal activity separates the plume and western boundary regions from the <list list-type="custom"><list-item><label>iii.</label>
      <p id="d2e4957">Offshore “submesoscale soup”: Away from the direct influence of the NBC (<inline-formula><mml:math id="M277" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">15</mml:mn></mml:mrow></mml:math></inline-formula>° N), the absence of a strong background strain field allows submesoscale fronts to develop with no preferred orientation, hence the isotropic spatial distribution of what are individually anisotropic (elongated) front structures, characteristic of a submesoscale “soup” away from the influence of the main flows <xref ref-type="bibr" rid="bib1.bibx76 bib1.bibx5 bib1.bibx79 bib1.bibx50" id="paren.87"><named-content content-type="pre">see e.g.,</named-content></xref>. These fronts are instead controlled by the seasonal mixed-layer cycle, intensifying in late winter and spring as shoaling mixed layers become unstable <xref ref-type="bibr" rid="bib1.bibx11 bib1.bibx70" id="paren.88"><named-content content-type="pre">e.g.,</named-content></xref>. A shift in frontal scales occurs from early to late spring (not shown), as larger fronts feed on smaller scales through the inverse energy cascade <xref ref-type="bibr" rid="bib1.bibx45 bib1.bibx20 bib1.bibx74 bib1.bibx61" id="paren.89"><named-content content-type="pre">e.g.,</named-content></xref>.</p></list-item></list></p>
      <p id="d2e4985">Although not quantified here, submesoscale fronts associated with frontogenesis at 1 <inline-formula><mml:math id="M278" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> scale also play a role in cascading energy from the submeso scale to smaller scales <xref ref-type="bibr" rid="bib1.bibx31" id="paren.90"/>. With a submesoscale resolving simulation, <xref ref-type="bibr" rid="bib1.bibx7" id="text.91"/> showed net frontogenesis associated with river plumes, with ageostrophic convergence near the surface dominating the dynamics of frontal sharpening. In our region, this process will complete (and likely at some point overcome) the classical frontogenesis <xref ref-type="bibr" rid="bib1.bibx40" id="paren.92"/> driven by the nondivergent mesoscale stirring due to the NBC.</p>
</sec>
<sec id="Ch1.S6">
  <label>6</label><title>Seasonality of <inline-formula><mml:math id="M279" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M280" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> compensation</title>
      <p id="d2e5028">The spatial distribution of Tu shows large areas dominated by salinity and not restricted to the <sc>plume</sc>. Temperature-dominated gradients also appear, mostly associated with remarkable flow structures driven by the NBC. Over these structures, a succession of compensated and reinforced density gradients appear to be related to the advection and stirring of freshwater filaments by the NBC <xref ref-type="bibr" rid="bib1.bibx22" id="paren.93"><named-content content-type="pre">Fig. <xref ref-type="fig" rid="F9"/>; see also, e.g.,</named-content></xref>. In the northern part of the domain, surface gradients can be dominated by salinity even 1200 <inline-formula><mml:math id="M281" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> away from the continental shelf. This relatively low salinity may be the result of older strong discharges still present in the region while slowly mixing with local waters <xref ref-type="bibr" rid="bib1.bibx59 bib1.bibx17" id="paren.94"><named-content content-type="pre">e.g.,</named-content></xref>. But how does low SSS reach as far as 20° N? Which processes are involved in the spatio-temporal distribution of gradients and how do they relate to density fronts? A Hovmöller diagram in Fig. <xref ref-type="fig" rid="F10"/>a illustrates the spatio-temporal evolution (propagation) of surface salinity versus temperature dominance over density gradients. Moreover, a timeseries of pdfs (Fig. <xref ref-type="fig" rid="F10"/>b) shows the temporal evolution of compensation and reinforcement on density by <inline-formula><mml:math id="M282" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M283" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients within the <sc>plume</sc>.</p>

      <fig id="F10" specific-use="star"><label>Figure 10</label><caption><p id="d2e5078"><bold>(a)</bold> Hovmöller diagram of the percentage of salinity (% Sal.) vs. temperature (% Temp.) dominance in the density ratio during the plume propagation northward (59–47° W; 6–18° N). Model time starts on 1 January 2008. <bold>(b)</bold> Daily timeseries of the probability density function of the percentage of compensation or reinforcement in the density ratio within the <sc>plume</sc> region.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f10.png"/>

      </fig>

      <p id="d2e5095">To construct Fig. <xref ref-type="fig" rid="F10"/>, we use Tu to quantify both the <inline-formula><mml:math id="M284" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M285" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> relations and their effects on density gradients. First, we calculate the percentage of salinity dominance in surface gradients (i.e., where <inline-formula><mml:math id="M286" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mtext>Tu</mml:mtext><mml:mo>|</mml:mo><mml:mo>&lt;</mml:mo><mml:mi mathvariant="italic">π</mml:mi><mml:mo>/</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula>), averaged longitudinally between 59–47° W. From 6–18° N, we binned <inline-formula><mml:math id="M287" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mtext>Tu</mml:mtext><mml:mo>|</mml:mo></mml:mrow></mml:math></inline-formula> in 0.05° intervals over 20 months of hourly-averaged snapshots, at 24 <inline-formula><mml:math id="M288" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">h</mml:mi></mml:mrow></mml:math></inline-formula> frequency (Fig. <xref ref-type="fig" rid="F10"/>a). Then, since Tu varies linearly, from the interpretation of Tu, it is possible to define the % of compensation or reinforcement in <inline-formula><mml:math id="M289" display="inline"><mml:mi mathvariant="script">R</mml:mi></mml:math></inline-formula> by interpolating Tu in each quadrant on a 0 %–100 % scale. For every snapshot, we select points where <inline-formula><mml:math id="M290" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mo>&lt;</mml:mo><mml:msub><mml:mi mathvariant="script">Q</mml:mi><mml:mn mathvariant="normal">25</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and repeat the computation to obtain daily pdfs.</p>
      <p id="d2e5180">Between 6–9° N, the prominent seasonality of salinity and temperature dominance reveals a competition between the NBC and the Amazon Plume. In Fig. <xref ref-type="fig" rid="F10"/>a, % Sal. is highly correlated with the Amazon Plume forcing <xref ref-type="bibr" rid="bib1.bibx18" id="paren.95"><named-content content-type="pre"><inline-formula><mml:math id="M291" 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>; cf.</named-content><named-content content-type="post">not shown</named-content></xref> and strongest from April to June. The weak discharge in autumn opens room for the NBC at low latitudes (Fig. <xref ref-type="fig" rid="F10"/>a). When the NBC is strongest <xref ref-type="bibr" rid="bib1.bibx43" id="paren.96"><named-content content-type="pre">e.g.,</named-content></xref>, the region between 6–9° N shows the highest % Temp., up to 70 %. The NBC influence rapidly fades offshore, and a north–south, quasi-stationary (<inline-formula><mml:math id="M292" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">80</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula>)% Sal. band appears from April on. Driven by a growing Amazon Plume, a secondary branch of % Sal. begins to expand offshore in late March <xref ref-type="bibr" rid="bib1.bibx33" id="paren.97"/>, at roughly 11–4 <inline-formula><mml:math id="M293" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="F10"/>a), consistent with previous drifter observations trapped within NBC rings <xref ref-type="bibr" rid="bib1.bibx69" id="paren.98"><named-content content-type="pre">e.g.,</named-content></xref>.</p>
      <p id="d2e5254">This propagating branch characterizes a “transition zone” (9–15° N) influenced by the advection of salinity gradients by the NBC and its associated mesoscale processes <xref ref-type="bibr" rid="bib1.bibx68 bib1.bibx33 bib1.bibx84" id="paren.99"/> and mean surface currents that drive the plume toward the north <xref ref-type="bibr" rid="bib1.bibx27" id="paren.100"><named-content content-type="pre">e.g.,</named-content></xref>. Strong fronts can be formed by the stirring of salinity gradients by the NBC retroflection and rings. Mesoscale stirring gives rise to gradients that can quickly evolve to submesoscale fronts by an exponential sharpening of those gradients <xref ref-type="bibr" rid="bib1.bibx38" id="paren.101"/>. Stirring and trapping of the plume by the NBC mesoscale activity could also explain the bifurcation of the % Sal. signal into a direct northward branch and a second branch that breaks off and slowly moves poleward after a virtually stationary period between 9 and 12° N, probably entrained within mesoscale structures <xref ref-type="bibr" rid="bib1.bibx62" id="paren.102"><named-content content-type="pre">Fig. <xref ref-type="fig" rid="F10"/>a; e.g.,</named-content></xref>. Indeed, low SSS anomalies (which drive density gradients in the area) were observed north of the NBC retroflection between June and November <xref ref-type="bibr" rid="bib1.bibx25" id="paren.103"><named-content content-type="pre">e.g.,</named-content></xref>. Low SSS anomalies in this region may be damped by evaporation <xref ref-type="bibr" rid="bib1.bibx27" id="paren.104"><named-content content-type="pre">e.g.,</named-content></xref>, although precipitation does not appear to reduce SSS <italic>within</italic> the plume <xref ref-type="bibr" rid="bib1.bibx33" id="paren.105"/>.</p>
      <p id="d2e5292">The northernmost part of the domain (15–18° N) shows the most persistent dominance of salinity on density gradients throughout the year. Away from the NBC and its associated (sub)mesoscale features, low SSS from the quasi-stationary branch is slowly mixed locally. A few months later, the secondary branch of the plume arrives. This high salinity dominance remains in the region until the onset of the “main branch” of the following year, and the number of fronts increases substantially in the transition zone (Fig. <xref ref-type="fig" rid="F9"/>b). Even with salinity dominance at the surface, the isotropic areas with anisotropic fronts show characteristics of a “submesoscale soup” <xref ref-type="bibr" rid="bib1.bibx5 bib1.bibx79" id="paren.106"><named-content content-type="pre">e.g.,</named-content></xref>, where fronts are linked to mixed-layer instabilities and the dynamics is fundamentally controlled by the mixed-layer cycle <xref ref-type="bibr" rid="bib1.bibx11" id="paren.107"><named-content content-type="pre">e.g.,</named-content></xref>.</p>
      <p id="d2e5307">The ensemble of <inline-formula><mml:math id="M294" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M295" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients within the <sc>plume</sc> exhibits a seasonal cycle in the distribution of compensated and reinforced fronts (Fig. <xref ref-type="fig" rid="F10"/>b). An expanding plume in spring is still mostly contained northwest along the coast and creates a SSS gradient from the shelf to the open ocean. Assuming salinity <inline-formula><mml:math id="M296" display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:math></inline-formula> largely dominates over <inline-formula><mml:math id="M297" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>T</mml:mi></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="F10"/>a), Tu is virtually zero and, in most density gradients, compensation or reinforcement can decrease or intensify them by only about 20 % (although Fig. <xref ref-type="fig" rid="F10"/>b does not distinguish salinity or temperature dominance), the rest being essentially driven by salinity <xref ref-type="bibr" rid="bib1.bibx51" id="paren.108"><named-content content-type="pre">Fig. <xref ref-type="fig" rid="F10"/>b – months June–August; see also</named-content></xref>.</p>
      <p id="d2e5365">In the first half of the year, warmer SST near the shelf presents a negative temperature gradient towards offshore <xref ref-type="bibr" rid="bib1.bibx25" id="paren.109"><named-content content-type="pre">e.g.,</named-content></xref>, which may reinforce density fronts associated with low SSS from the plume (Fig. <xref ref-type="fig" rid="F10"/>b – months February–May). From June to August, the transport by the NBC and its rings increases and pushes the plume to its maximum extent. In late fall and winter (October–December), a shift in the distribution towards compensation indicates the evolution of gradients within the <sc>plume</sc>. This is the period when compensation mechanisms through air–sea interaction will be most effective within the plume, for differential surface cooling will act due to a mixed-layer depth-dependent heat loss <xref ref-type="bibr" rid="bib1.bibx78 bib1.bibx16" id="paren.110"><named-content content-type="pre">e.g.,</named-content></xref>. Conversely, a positive heat flux in spring and summer would reinforce the salinity-dominated density gradients to the point where the unbalanced heat uptake leads to dominant temperature gradients on density. However, one must bear in mind that compensation and reinforcing are scale-dependent, so assumptions such as net seasonal heat fluxes involve processes other than mixed layer instabilities and air–sea heat fluxes acting on the mixed-layer depth, SSS, and SST <xref ref-type="bibr" rid="bib1.bibx78" id="paren.111"/>.</p>
      <p id="d2e5386">In the Mississippi River plume, <xref ref-type="bibr" rid="bib1.bibx6" id="text.112"/> showed an overall increase in the tails of Tu pdfs during winter. Moreover, the authors show with a Lagrangian framework that, even if an initial state presents a distribution of Tu centered at zero, a preference for compensated gradients arises over time. This shift occurs gradually during autumn, with a clear predominance of compensated gradients at the beginning of wintertime. We recall that our analysis considers only density gradients with SSS lower than <inline-formula><mml:math id="M298" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="script">Q</mml:mi><mml:mn mathvariant="normal">25</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, which can introduce a bias toward reinforced gradients: the mixing of “the old plume” usually creates higher SSS, and evolving fronts in this region can be removed from the analysis.</p>
      <p id="d2e5404">While air–sea interactions are known to induce compensation to the strongest <inline-formula><mml:math id="M299" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M300" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients at small scales in the Amazon Plume <xref ref-type="bibr" rid="bib1.bibx16" id="paren.113"/>, facing the gradients galore of the northwestern Tropical Atlantic brings a broader perspective related to the region's peculiar dynamics. Next, we suggest how these dynamics set up some <inline-formula><mml:math id="M301" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M302" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> relations observed in the region.</p>
</sec>
<sec id="Ch1.S7">
  <label>7</label><title>Interactions between the Amazon Plume and the NBC</title>
      <p id="d2e5446">In the previous sections, we showed regions with fronts related to the interaction between the Amazon Plume and the NBC. They are numerous near shore and broken up possibly due to further interactions with high-frequency processes. Offshore, elongated fronts drawn from this near-shore pool align with flow structures. They often come as freshwater filaments advected by the NBC that pierce through a higher salinity background (Fig. <xref ref-type="fig" rid="F11"/>a) and roll up into a warm-core NBC ring <xref ref-type="bibr" rid="bib1.bibx25" id="paren.114"><named-content content-type="pre">Fig. <xref ref-type="fig" rid="F11"/>b; e.g.,</named-content></xref>.</p>

      <fig id="F11" specific-use="star"><label>Figure 11</label><caption><p id="d2e5460">Interaction of the NBC and the Amazon Plume zoomed in from the model on 25 March 2008, 6 <inline-formula><mml:math id="M303" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">h</mml:mi></mml:mrow></mml:math></inline-formula>. <bold>(a)</bold> SA: Absolute salinity; <bold>(b)</bold> CT: Conservative Temperature; <bold>(c)</bold> Schematic of compensation (green) and reinforcement (orange) developing on opposite sides of the low-salinity filament; <bold>(d)</bold> contribution of salinity to density variation; <bold>(e)</bold> contribution of temperature to density variation; <bold>(f)</bold> Tu: Turner angle. The blowout of <inline-formula><mml:math id="M304" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M305" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients in <bold>(d–f)</bold> selects areas where <inline-formula><mml:math id="M306" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi><mml:mo>|</mml:mo><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M307" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, where thin black contours represent <inline-formula><mml:math id="M308" display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M309" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. In <bold>(d–f)</bold>, colors delimit regions of <inline-formula><mml:math id="M310" display="inline"><mml:mrow><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M311" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f11.png"/>

      </fig>

      <p id="d2e5611">From observations, we suggested that the interaction between the Amazon Plume and the NBC could induce a variety of Tu. Indeed, the resulting front sketched in Fig. <xref ref-type="fig" rid="F11"/>c shows compensation and reinforcement on opposite sides of the front. This asymmetry arises because the low-salinity filament is embedded in a warmer NBC temperature background. On the warm (inner) side of the filament, the temperature gradient opposes the salinity gradient, producing compensation. On the cooler (outer) side, temperature increases as salinity decreases toward the filament core, so they reinforce each other on the density gradient. The key driver is therefore the sign change in the salinity gradient across the filament, while the temperature gradient remains roughly uniform.</p>
      <p id="d2e5617">The blowout of <inline-formula><mml:math id="M312" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M313" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients in Fig. <xref ref-type="fig" rid="F11"/>d and e selects areas where <inline-formula><mml:math id="M314" display="inline"><mml:mrow><mml:mo>|</mml:mo><mml:mi mathvariant="italic">β</mml:mi><mml:mi mathvariant="normal">Δ</mml:mi><mml:mi>S</mml:mi><mml:mo>|</mml:mo><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">0.01</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M315" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. It further illustrates how salinity and temperature combine to sustain compensation and reinforcement at both sides of the arched filament (Fig. <xref ref-type="fig" rid="F11"/>f). Crossing the main filament, temperature gradients do not display a clear change in sign due to somewhat uniform west–east gradients. This pattern was briefly reported by <xref ref-type="bibr" rid="bib1.bibx22" id="text.115"/> in a cold filament in the Bay of Bengal and appears repeatedly during the formation of NBC rings on our simulation.</p>
      <p id="d2e5676">If one considers submesoscale fresh filaments developing at the edge of the plume, when considering all <inline-formula><mml:math id="M316" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M317" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> gradients this pattern of both compensation and reinforcement shall repeat over a large portion of the domain, yielding the zero-centered distributions of Tu due to the interaction with the plume and the NBC and/or local dynamics offshore. With the region being mainly frontogenetic, the set up of different fronts by the NBC–Amazon Plume interaction (e.g., Figs. <xref ref-type="fig" rid="F8"/> and <xref ref-type="fig" rid="F9"/>) could trigger distinct dynamical responses: while uncompensated fronts are unstable and act on the direct energy cascade and mixing <xref ref-type="bibr" rid="bib1.bibx72 bib1.bibx80" id="paren.116"><named-content content-type="pre">e.g.,</named-content></xref>, the more stable, (partially) compensated fronts can be strained for longer periods, shaping horizontal transport and maintaining their associated vertical fluxes <xref ref-type="bibr" rid="bib1.bibx72 bib1.bibx96" id="paren.117"><named-content content-type="pre">e.g.,</named-content></xref>. We call for future work to statistically address these mechanisms and their effects on the overall energy budgets of compensated and reinforced fronts. </p>
</sec>
<sec id="Ch1.S8" sec-type="conclusions">
  <label>8</label><title>Summary and Conclusions</title>
      <p id="d2e5717">An expanding Amazon River plume occupied the northwestern Tropical Atlantic during the EUREC4A-OA campaign <xref ref-type="bibr" rid="bib1.bibx68 bib1.bibx16" id="paren.118"><named-content content-type="pre">as seen in the SSS maps,</named-content></xref>. As expected for the transition period from low to high discharge <xref ref-type="bibr" rid="bib1.bibx27" id="paren.119"><named-content content-type="pre">e.g.,</named-content></xref>, the plume was relatively well developed, and saildrones sampled both the region <sc>outside</sc> and the interior of the <sc>plume</sc>. We observed the sharp increase in the magnitude of density gradients inside the <sc>plume</sc>, which translates into strong buoyancy gradients at <inline-formula><mml:math id="M318" display="inline"><mml:mi mathvariant="script">O</mml:mi></mml:math></inline-formula> (1–10) <inline-formula><mml:math id="M319" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>. Unsurprisingly, <inline-formula><mml:math id="M320" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M321" display="inline"><mml:mi>S</mml:mi></mml:math></inline-formula> relations show salinity-dominated density fronts within the <sc>plume</sc>. Perhaps more interestingly, these fronts display nearly equal contributions of compensation and reinforcement by temperature gradients. Moreover, net frontogenesis is observed both <sc>outside</sc> and within the <sc>plume</sc>.</p>
      <p id="d2e5779">Using a 1 <inline-formula><mml:math id="M322" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> resolution model, we explored how both the Tu and <inline-formula><mml:math id="M323" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> observed during EUREC4A-OA are spatially arranged when the Amazon Plume and the NBC interact.  The modeled region shows greater variability and extreme fronts in the <sc>plume</sc>, although the separation between <sc>plume</sc> and <sc>outside</sc> is less distinct in the simulation. Three different frontal regimes occur in the domain, one within the plume over the continental shelf, a second associated with stirring of the plume by the NBC, and a third offshore, typical of mixed-layer controlled submesoscale activity. Qualitatively detailing the interaction between the Amazon Plume and the NBC, we show that the mesoscale stirring of the plume by the NBC produces a patchy distribution of Tu, particularly during the formation of NBC rings, where freshwater filaments are rolled up into a NBC temperature background, generating compensated density fronts in the inner portion of the filament and reinforced fronts on the outer rim.</p>
      <p id="d2e5810">In the northwestern Tropical Atlantic, salinity gradients representative of sharp density gradients dominate the region up to 9° N driven by the seasonality of the Amazon runoff. When the river discharge is weakest and the NBC charges into the region, temperature gradients dominate. Stirring and advection of the plume by the NBC shape the fronts in the transition region from 9–15° N. North of 15° N, the distribution of surface gradients is dominated by salinity all year long, even though in this region their dynamics are most likely to follow the temperature-driven seasonality of submesoscale turbulence <xref ref-type="bibr" rid="bib1.bibx11 bib1.bibx70" id="paren.120"><named-content content-type="pre">e.g.,</named-content></xref>. The distribution of frontogenetic tendency suggests the northwestern Tropical Atlantic as a region of predominant frontogenesis, with both compensated and uncompensated density fronts mostly related to mesoscale low-salinity filaments stirred from the Amazon Plume by the NBC and submesoscale structures developing at the plume edge, with a clear seasonal cycle of compensation and reinforcement linked to the plume size and the NBC strength.</p>
      <p id="d2e5818">The frontal seascape described here, which is salinity-dominated, seasonally modulated, with coexisting compensated and reinforced fronts, has direct implications beyond physical oceanography. Compensated fronts, being more stable, sustain strong horizontal tracer gradients for longer periods, potentially influencing nutrient supply, phytoplankton patchiness <xref ref-type="bibr" rid="bib1.bibx35 bib1.bibx48" id="paren.121"><named-content content-type="pre">e.g.,</named-content></xref>, and ecosystem connectivity <xref ref-type="bibr" rid="bib1.bibx34" id="paren.122"><named-content content-type="pre">e.g.,</named-content></xref>. Reinforced fronts, being unstable, drive energetic downwelling that may export surface-enriched Amazon water below the pycnocline on short timescales <xref ref-type="bibr" rid="bib1.bibx88" id="paren.123"><named-content content-type="pre">e.g.,</named-content></xref>. Distinguishing these two populations of fronts may therefore be essential for understanding the plume's role in regional carbon and nitrogen budgets.</p>
      <p id="d2e5837">As numerical models continue to improve, they rely on data acquisition at high resolution to tackle current discrepancies and parameterizations for dynamics at small scales. The unprecedented datasets from campaigns such as EUREC4A-OA and other uncrewed vehicles in the global ocean <xref ref-type="bibr" rid="bib1.bibx64" id="paren.124"><named-content content-type="pre">meet them in a review by</named-content></xref>, together with state-of-the-art numerical modeling provide statistical confidence in studying derived quantities at <inline-formula><mml:math id="M324" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Our current effort is to explore the dynamics depicted from EUREC4A-OA small-scale observations to help improve the fine-scale ocean modeling of the Amazon Plume outflowing into the Atlantic. Such datasets need to be continuously exploited alongside new observational and modeling efforts to improve our assessment of the Amazon Plume region.</p>
</sec>

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

<app id="App1.Ch1.S1">
  <label>Appendix A</label><title>Observed Buoyancy Sharpness variance</title>
      <p id="d2e5875">In the <sc>outside</sc>, the <inline-formula><mml:math id="M325" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> variance gradually increases from <inline-formula><mml:math id="M326" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> up to 5 <inline-formula><mml:math id="M327" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>, whereas in the <sc>plume</sc> the major increase takes place at scales smaller than <inline-formula><mml:math id="M328" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M329" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="FA1"/>). The variance of the buoyancy frontal sharpness <inline-formula><mml:math id="M330" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> is greater in the <sc>plume</sc> at all observed scales.</p>

      <fig id="FA1"><label>Figure A1</label><caption><p id="d2e5946">Observed variance of the buoyancy frontal sharpness <inline-formula><mml:math id="M331" display="inline"><mml:mi mathvariant="script">B</mml:mi></mml:math></inline-formula> in the <sc>plume</sc> and in the <sc>outside</sc>.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f12.png"/>

      </fig>


</app>

<app id="App1.Ch1.S2">
  <label>Appendix B</label><title>Plume representation in the  model</title>
      <p id="d2e5978">Appendix B compares the poleward extension of the Amazon Plume of the model with the CATDS CEC SSS satellite product <xref ref-type="bibr" rid="bib1.bibx10" id="paren.125"/> and the ISAS climatology <xref ref-type="bibr" rid="bib1.bibx46" id="paren.126"/> in the 59–47° W; 6–19° N region where we conduct our analyses. The satellite data is a regional product for the Amazon region, which combines SMOS and SMAP data with an optimized interpolation scheme that yields a temporal resolution of 2–3 d and <inline-formula><mml:math id="M332" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M333" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> effective horizontal resolution. The ISAS17 release is a monthly climatology that combines Argo and Deep-Argo temperature and salinity data with other in-situ measurements between 2002 and 2017 to fill in gaps where Argo sampling is sparse or nonexistent. The ISAS product has 187 vertical levels between 0–5500 <inline-formula><mml:math id="M334" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> and a <inline-formula><mml:math id="M335" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M336" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> horizontal resolution.</p>
      <p id="d2e6032">We select the 36 isohaline in both model and the available datasets. This isohaline is used in the main text as a reference to identify the Amazon Plume edge in the observations. Then, we took the northernmost latitudinal point for each day (model, satellite), and month (climatology) as shown in Fig. <xref ref-type="fig" rid="FB1"/>.</p>
      <p id="d2e6037">The model presents a mean SSS comparable to that of the ISAS climatology but slightly overestimates the satellite SSS and underestimates its variability. This is due to a difference in the minimum SSS between the model and the satellite, with strong mixing coefficients leading to a rapid increase in the salinity at the points of river input. Strong mixing may also be related to a “delay” in the poleward displacement of the plume, with an <inline-formula><mml:math id="M337" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>-month difference between the observed and modeled plume reaching the same latitudes (Fig. <xref ref-type="fig" rid="FB1"/>). The northernmost position of the 36 isohaline in GIGATL1 shows a <inline-formula><mml:math id="M338" 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">0.80</mml:mn></mml:mrow></mml:math></inline-formula> (Pearson) linear correlation with the isohaline position depicted by satellite and 0.75 with the one from ISAS. It follows the pattern presented in <xref ref-type="bibr" rid="bib1.bibx33" id="text.127"/> for the evolution of the plume area. The latitudinal SSS profile of GIGATL1 is also well correlated with observations over time (0.87 for both satellite and ISAS). Therefore, even if not at the exact same period, our simulation can reproduce the SSS seasonal cycle as well as the strength of buoyancy gradients, which gave us confidence in carrying out the analyses in this study. We will address the noted discrepancies in future versions of the simulation.</p><fig id="FB1"><label>Figure B1</label><caption><p id="d2e6073">Northernmost position of the 36 isohaline between 14 March and 31 August from satellite (dark blue line mean with 80 % of the distribution in light blue), climatology (light yellow line), and model (red line). For the satellite data, five 18-month series (light grey lines) span data from 2016 to 2021. The monthly climatology is reorganized to display 18 months of data. The model years (March 2008–August 2009) are referenced due to the data used for forcing. Product keys: SAT – satellite product is a regional product distributed by CATDS CEC <xref ref-type="bibr" rid="bib1.bibx10" id="paren.128"/>, providing a combination of SMOS and SMAP sea surface salinity data; ISAS17 – stable (delayed time) Argo climatology distributed by Argo France <xref ref-type="bibr" rid="bib1.bibx46" id="paren.129"/>; GIGATL1 – CROCO numerical simulation <xref ref-type="bibr" rid="bib1.bibx37" id="paren.130"/>.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f13.png"/>

      </fig>

      <p id="d2e6091"><italic>Appendix B acknowledgments</italic>: We thank G. Reverdin and J. Boutin for the discussion of SSS products and for the CEC CATDS High Resolution V0 Sea Surface Salinity maps, produced by LOCEAN/IPSL (UMR CNRS/UPMC/IRD/MNHN) laboratory and ACRI-st company that participate to the Ocean Salinity Expertise Center (CECOS) of Centre Aval de Traitement des Données SMOS (CATDS). This product <xref ref-type="bibr" rid="bib1.bibx10" id="paren.131"/> is distributed by the Ocean Salinity Expertise Center (CECOS) of the CNES-IFREMER CATDS, Plouzane (France). ISAS temperature and salinity monthly gridded field products <xref ref-type="bibr" rid="bib1.bibx46" id="paren.132"/> are made freely available by SNO Argo France at LOPS Laboratory (supported by UBO/CNRS/Ifremer/IRD) and IUEM Observatory (OSU IUEM/CNRS/INSU) at <ext-link xlink:href="https://doi.org/10.17882/52367" ext-link-type="DOI">10.17882/52367</ext-link>.</p>
</app>

<app id="App1.Ch1.S3">
  <label>Appendix C</label><title>Adaptive definition of the plume in the simulation</title>
      <p id="d2e6114">To ensure numerical consistency and reduce the effect of numerics on variables at grid scales, gradients are smoothed in the model compared to the observed gradients at the same scales. This hinders the ability of the model to capture the abrupt changes marking the transition from the plume region to the outside.</p>
      <p id="d2e6117">In Fig. <xref ref-type="fig" rid="FC1"/>, we display the SSS gradient at the model grid scale. Those gradients, smoothed by a 50 <inline-formula><mml:math id="M339" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> rolling mean in both <inline-formula><mml:math id="M340" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M341" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula> directions, visually mark the separation from the plume and the outside regions. Here, we show contours of the 20 %-strongest mesoscale SSS gradients, which roughly coincide with the isohaline representing 25 % of the salinity probability distribution for each snapshot. This yields <inline-formula><mml:math id="M342" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">35.7</mml:mn></mml:mrow></mml:math></inline-formula> for the 25 March 2008, 6 <inline-formula><mml:math id="M343" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">h</mml:mi></mml:mrow></mml:math></inline-formula> snapshot discussed in the study. We also apply this 25 % threshold to retrieve the plume from snapshots daily and thus compute the percentage of density compensation and reinforcement (main text Fig. 8b).</p>

      <fig id="FC1"><label>Figure C1</label><caption><p id="d2e6167">Model surface salinity gradient on 25 March 2008, 6 <inline-formula><mml:math id="M344" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">h</mml:mi></mml:mrow></mml:math></inline-formula>. The plume region is delimited by the isohaline representing the 0.25 quantile of the salinity probability distribution (golden line). Purple lines represent the 20 % strongest mesoscale SSS gradient.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f14.png"/>

      </fig>


</app>

<app id="App1.Ch1.S4">
  <label>Appendix D</label><title>Advective Frontogenetic Tendency terms</title>
      <p id="d2e6194">We briefly evaluate the role of the vertical terms in the advective frontogenetic tendency of buoyancy equations by subtracting <inline-formula><mml:math id="M345" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> calculated from horizontal terms alone from the total <inline-formula><mml:math id="M346" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="FD1"/>.</p>
      <p id="d2e6221">Comparing snapshots from the simulation, the vertical terms modulate the magnitude of gradients, but the relative strongest differences [<inline-formula><mml:math id="M347" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">18</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M348" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>] are 2 orders of magnitude smaller than the strongest gradients [<inline-formula><mml:math id="M349" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">16</mml:mn></mml:mrow></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M350" display="inline"><mml:mrow class="unit"><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>] and representing 0.1 % (Fig. <xref ref-type="fig" rid="FD1"/>, right panels). Moreover, the spatial distribution of the gradients is unaltered, confirming that fronts are set up mainly by horizontal processes <xref ref-type="bibr" rid="bib1.bibx7" id="paren.133"/> and vertical processes either intensify or reduce their magnitude.</p><fig id="FD1"><label>Figure D1</label><caption><p id="d2e6300">Comparison between full and horizontal terms of the advective frontogenetic tendency for buoyancy. The green line represents the isohaline 35.7, i.e. the 25 % quantile of the surface salinity distribution. The gray box set the limits [59–47° W; 6–181.5° N] where the analysis was conducted. (From left to right) <inline-formula><mml:math id="M351" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula> with full terms from (4); difference between full and horizontal (5) <inline-formula><mml:math id="M352" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>; and the pdf of <inline-formula><mml:math id="M353" display="inline"><mml:mrow><mml:msup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msup></mml:mrow></mml:math></inline-formula>–<inline-formula><mml:math id="M354" display="inline"><mml:mrow><mml:msubsup><mml:mi mathvariant="italic">τ</mml:mi><mml:mi mathvariant="normal">H</mml:mi><mml:mi mathvariant="normal">b</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>.</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/2425/2026/os-22-2425-2026-f15.png"/>

      </fig>

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

      <p id="d2e6361">EUREC4A-OA Saildrone data <xref ref-type="bibr" rid="bib1.bibx77" id="paren.134"/> from NOAA and NASA/ATOMIC is freely available at <ext-link xlink:href="https://doi.org/10.13155/80129" ext-link-type="DOI">10.13155/80129</ext-link> and <uri>https://observations.ipsl.fr/aeris/eurec4a/#/</uri> (last access: 10 August 2026). SMAP data <xref ref-type="bibr" rid="bib1.bibx55" id="paren.135"/> can be obtained at  <ext-link xlink:href="https://doi.org/10.5067/SMP50-3SPCS" ext-link-type="DOI">10.5067/SMP50-3SPCS</ext-link> <xref ref-type="bibr" rid="bib1.bibx67" id="paren.136"/> and <uri>https://www.earthdata.nasa.gov/data/catalog/pocloud-smap-jpl-l3-sss-cap-8day-runningmean-v5-5.0</uri> (last access 11 August 2026). AVISO data can also be obtained via FTP at <uri>https://data.marine.copernicus.eu/product/SEALEVEL_GLO_PHY_CLIMATE_L4_MY_008_057/description</uri> (last access: 11 August 2026) and <ext-link xlink:href="https://doi.org/10.48670/moi-00145" ext-link-type="DOI">10.48670/moi-00145</ext-link>
<xref ref-type="bibr" rid="bib1.bibx15" id="paren.137"/>.  The source code of the simulation used in this study is available at <ext-link xlink:href="https://doi.org/10.5281/zenodo.4948523" ext-link-type="DOI">10.5281/zenodo.4948523</ext-link> <xref ref-type="bibr" rid="bib1.bibx37" id="paren.138"/>.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d2e6405">CRediT Taxonomy (<uri>https://publications.copernicus.org/services/contributor_roles_taxonomy.html</uri>) (last access: 10 August 2026): Co: Conceptualization; DC: Data Curation; FAn: Formal Analysis; FAc: Funding Acquisition; In: Investigation; Me: Methodology; PA: Project Administration; Re: Resources; Software: So; Su: Supervision; Va: Validation; Vi: Visualization; WOD: Writing Original Draft; WRE: Writing Review and Editing.</p>

      <p id="d2e6411">D. C. Napolitano: Co, FAn, In, Me, So, Va, Vi, WOD, WRE.  J. Gula: Co, FAn, FAc, In, Me, PA, Re, Su, Vi, WOD, WRE. S. Coadou-Chaventon: FAn, In, Me, So, WRE. S. Speich: DC, FAc, In, Me, PA, Re, Su, WRE. C. B. Rocha: DC, FAc, In, Me, Re, WRE.  J. C. McWilliams: In, Me, Re, WRE.  D. Zhang: FAc, In, Re, WRE. X. Carton: Co, FAc, In, Me, PA, Su, WOD, WRE.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e6418">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d2e6426">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. The authors bear the ultimate responsibility for providing appropriate place names. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.</p>
  </notes><ack><title>Acknowledgements</title><p id="d2e6432">We thank the French vessel research fleet and the captain and crew of RVs <italic>Atalante</italic>, <italic>Maria S. Merian</italic>, <italic>FS Meteor</italic>, and <italic>Ron Brown</italic>.  SS acknowledges the IPSL, the Chaire Chanel program of the Geosciences Department at ENS.  DCN thanks P. H. R. Calil and C. Whalen for discussions about the Turner Angle. Also A. Delpech, E. Capó, D. Dauhajre, J. Molemaker, P. Damien, and D. Hypolite for the warm hosting at UCLA and discussions with K. Srinivasan, R. Schubert, and C. Lemaréchal during this period.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d2e6449">The authors acknowledge support from Région Bretagne, the French National Agency for Research through the JPI Ocean and Climate program EUREC4A-OA (ANR-19-JPOC-0004-05) and DEEPER (ANR-19-CE01-0002-01), and the Office of Naval Research (ONR grant N00014-23-1-2226). Support for this project was also provided by the French National Space Center under project EUREC4A-OA (CNES 19-1 2021) and TOEddies and the European Union Horizon 2020 under Grant no. 817578 (TRIATLAS). This work was performed using HPC/AI resources from GENCI-TGCC (Grant no. 2023-A0090112051), from DATARMOR at Ifremer Brest France, and French research infrastructures AERIS and ODATIS. SCC is supported by a PhD grant from ENS Ulm. CBR acknowledges support from National Aeronautics and Space Administration (NASA NNH17ZDA001N-EVS3) and São Paulo Research Foundation (FAPESP 2023/10506-0).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e6456">This paper was edited by Mario Hoppema and reviewed by Maya Jakes and one anonymous referee.</p>
  </notes><ref-list>
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