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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-22-257-2026</article-id><title-group><article-title>Bottom mixed layer derivation and spatial variability over the central and eastern abyssal Pacific Ocean</article-title><alt-title>BML Pacific Ocean</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1 aff2">
          <name><surname>Kolbusz</surname><given-names>Jessica</given-names></name>
          <email>jess.kolbusz@uwa.edu.au</email>
        <ext-link>https://orcid.org/0000-0003-2779-451X</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Harrison</surname><given-names>Devin</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2 aff4">
          <name><surname>Jones</surname><given-names>Nicole</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" equal-contrib="yes" corresp="no" rid="aff5 aff6">
          <name><surname>O'Callaghan</surname><given-names>Joanne</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" equal-contrib="yes" corresp="no" rid="aff7">
          <name><surname>Sohail</surname><given-names>Taimoor</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>Bond</surname><given-names>Todd</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Stewart</surname><given-names>Heather</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1 aff2">
          <name><surname>Jamieson</surname><given-names>Alan</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>School of Biological Sciences, University of Western Australia, Crawley, Australia</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Oceans Institute, University of Western Australia, Crawley, Australia</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Kelpie Geoscience Ltd., Edinburgh, United Kingdom</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>School of Earth and Oceans, University of Western Australia, Crawley, Australia</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Department of Physics, University of Auckland, Auckland, New Zealand</institution>
        </aff>
        <aff id="aff6"><label>6</label><institution>Oceanly Science Limited, Wellington, New Zealand</institution>
        </aff>
        <aff id="aff7"><label>7</label><institution>School of Geography, Earth and Atmospheric Science, University of Melbourne, Melbourne, Australia</institution>
        </aff><author-comment content-type="econtrib"><p>These authors contributed equally to this work.</p></author-comment>
      </contrib-group>
      <author-notes><corresp id="corr1">Jessica Kolbusz (jess.kolbusz@uwa.edu.au)</corresp></author-notes><pub-date><day>22</day><month>January</month><year>2026</year></pub-date>
      
      <volume>22</volume>
      <issue>1</issue>
      <fpage>257</fpage><lpage>279</lpage>
      <history>
        <date date-type="received"><day>25</day><month>September</month><year>2025</year></date>
           <date date-type="rev-request"><day>6</day><month>October</month><year>2025</year></date>
           <date date-type="rev-recd"><day>5</day><month>December</month><year>2025</year></date>
           <date date-type="accepted"><day>13</day><month>January</month><year>2026</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2026 Jessica Kolbusz 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/22/257/2026/os-22-257-2026.html">This article is available from https://os.copernicus.org/articles/22/257/2026/os-22-257-2026.html</self-uri><self-uri xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026.pdf">The full text article is available as a PDF file from https://os.copernicus.org/articles/22/257/2026/os-22-257-2026.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e188">The bottom mixed layer (BML) of the abyssal ocean regulates heat exchange between the deep interior and seafloor, driving water–mass transformation and influencing global circulation. Spatial variability of the BML was examined in the under-sampled abyssal Pacific Ocean using surface-to-seafloor temperature and pressure observations over 4 months in 2023–2024. Given the typical decadal repeat rate of global hydrographic sections, subdecadal variability in the abyssal ocean has remained poorly resolved. Our observations contribute towards filling this gap for the central and eastern abyssal Pacific Ocean. Four methods were used to determine the BML thickness, with the threshold method providing the most reliable estimates. The mean BML thickness was (<inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:mn mathvariant="normal">226</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>±</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">172</mml:mn></mml:mrow></mml:math></inline-formula> m) with added repeat hydrographic sections providing context and additional data points. At each BML data point we determined the slope, the terrain roughness and the extracted predicted internal tide energy dissipation (over five different low-mode processes and high-mode local processes) at 50 <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> scales from publicly available datasets. These factors were input into a Random Forest Regressor (RF) model, the first time machine learning techniques have been applied to investigate BML thickness. The RF feature importance scores identified bottom depth, total internal tide energy dissipation, followed by slope, as the strongest predictors of BML thickness, revealing the importance of low-mode internal wave energy losses in this abyssal setting. Targeted and sustained observations near the seafloor at gateway regions of abyssal pathways are vital for understanding energy exchange that influences meridional overturning circulation. Our results highlight a regime where sustained low-mode internal tide energy loss, modulated by topographic slope and depth, governs the BML thickness in the abyssal Pacific. However, the rate at which BML thickness changes over time and the processes that cause these changes remain key unresolved factors.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d2e222">Nearly half the Pacific Ocean comprises abyssal zones that have experienced persistent warming in the past 30 years <xref ref-type="bibr" rid="bib1.bibx39" id="paren.1"/>. The bottom mixed layer (BML), a well-mixed region directly above the seafloor in the abyssal ocean <xref ref-type="bibr" rid="bib1.bibx5 bib1.bibx50" id="paren.2"/> is a critical interface where turbulent mixing facilitates exchange between the deep ocean interior and the seafloor, influencing water–mass transformation and global circulation. Dynamics within the BML are affected by internal wave activity <xref ref-type="bibr" rid="bib1.bibx96 bib1.bibx30" id="paren.3"/>, and near-boundary turbulence <xref ref-type="bibr" rid="bib1.bibx50 bib1.bibx86" id="paren.4"/>, impacting diapycnal mixing, deep-sea food web connectivity, and heat transport <xref ref-type="bibr" rid="bib1.bibx38" id="paren.5"/>. Additionally, the BML region may contribute to abyssal mixing, as the interplay of turbulent processes through internal tides and stratification here facilitates diapycnal mixing <xref ref-type="bibr" rid="bib1.bibx46" id="paren.6"/>, thereby helping to drive the meridional overturning circulation (MOC) <xref ref-type="bibr" rid="bib1.bibx91 bib1.bibx12 bib1.bibx18" id="paren.7"/>. MOC is sustained by the abyssal flow of North Atlantic Deep Water (NADW) and Antarctic Bottom Water (AABW), which transport dense water masses equatorward and poleward from their formation regions through the deep ocean. The pathways involved in the MOC have been broadly identified, with general consensus on their origins, particularly in the ventilation regions adjacent to Antarctica (AABW) and the Labrador Sea (NADW) <xref ref-type="bibr" rid="bib1.bibx18 bib1.bibx81" id="paren.8"/>. While the broad pathways of these abyssal waters are accepted, the detailed mechanisms by which they return to the surface through diapycnal mixing and upwelling remain active areas of research <xref ref-type="bibr" rid="bib1.bibx56 bib1.bibx86 bib1.bibx92 bib1.bibx12 bib1.bibx15" id="paren.9"/>. Regions of intense abyssal mixing over mid-ocean ridges and narrow inter-basin channels are key sites where stratification governs regional variability in the BML, current pathways and internal tide generation, connecting closely to abyssal pathways, while seafloor topography remains the primary control on BML thickness at the global scale <xref ref-type="bibr" rid="bib1.bibx25" id="paren.10"/>. However, the relative importance between topography, its spatial scales, and the dynamic processes within ocean basins dictating the BML thickness remains unclear <xref ref-type="bibr" rid="bib1.bibx88 bib1.bibx12" id="paren.11"/>.</p>
      <p id="d2e259">The strength of deep MOC in the Pacific Ocean has been historically underestimated due to a lack of data and its complex topographies, making simulations more challenging <xref ref-type="bibr" rid="bib1.bibx43 bib1.bibx69" id="paren.12"/>. Broadly, AABW enters the Pacific Ocean along the eastern side of the Tonga–Kermadec Ridge <xref ref-type="bibr" rid="bib1.bibx9" id="paren.13"/>, then narrows through the Samoan Passage <xref ref-type="bibr" rid="bib1.bibx3" id="paren.14"/> before bifurcating to the west and north towards the Japan Trench <xref ref-type="bibr" rid="bib1.bibx43" id="paren.15"/> (Fig. <xref ref-type="fig" rid="F1"/>). North of the Samoan Passage, there is also bottom water transport to the east and south of the Hawaiian Ridge. Around the Hawaiian Ridge, energetic baroclinic tides are generated over the rough seafloor, contributing to distinct differences in the eastern and western regions of the Pacific Ocean, with larger dissipation in the western Pacific <xref ref-type="bibr" rid="bib1.bibx27 bib1.bibx2" id="paren.16"/>. AABW transforms into North Pacific Deep Water (NPDW) while reaching the North Pacific. It is then further transformed through deep ocean mixing while traveling south and reinforcing subsurface stratification and linking to deep convection in the Southern Ocean <xref ref-type="bibr" rid="bib1.bibx82" id="paren.17"/>.</p>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e285"><bold>(a)</bold> Bottom water circulation pathways through the Pacific Ocean based on existing research <xref ref-type="bibr" rid="bib1.bibx43 bib1.bibx69 bib1.bibx27" id="paren.18"/> with <bold>(b)</bold> insert as the extent of the study region. AABW <inline-formula><mml:math id="M3" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> Antarctic Bottom Water, NPDW <inline-formula><mml:math id="M4" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> North Pacific Deep Water <bold>(b)</bold> Study region boundary, locations, and features, including a regional bathymetric grid. Orange triangles are the Trans-Pacific Transit Expedition deployment locations, with numbers as the site number within the associated leg. The R/V <italic>Dagon</italic> multibeam echosounder coverage is displayed in green. Note that Leg 1 is not used in this analysis. The GO-SHIP repeat hydrographic lines and deployment locations are marked with red circles (P16 and P02). Blue arrows are bottom water circulation pathways adapted from previous studies. Background regional bathymetry is from the Global Multi-Resolution Topography (GMRT) Synthesis <xref ref-type="bibr" rid="bib1.bibx78" id="paren.19"/>. Released CC BY 4.0 Deep <inline-formula><mml:math id="M5" display="inline"><mml:mo>|</mml:mo></mml:math></inline-formula> Attribution 4.0 International <inline-formula><mml:math id="M6" display="inline"><mml:mo>|</mml:mo></mml:math></inline-formula> Creative Commons.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f01.jpg"/>

      </fig>

      <p id="d2e341">While rough and variable topography can modulate the BML thickness (e.g. fracture zones  <xref ref-type="bibr" rid="bib1.bibx84" id="paren.20"/> and seamounts <xref ref-type="bibr" rid="bib1.bibx57" id="paren.21"/>) regions of the seafloor with broadly similar depths or geomorphology can nevertheless exhibit vastly different BML thicknesses due to differences in ocean dynamics such as boundary currents or abyssal transformations <xref ref-type="bibr" rid="bib1.bibx15 bib1.bibx31" id="paren.22"/>. Along continental shelf regions, it is on the order of 40–70 <inline-formula><mml:math id="M7" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> in the South China Sea <xref ref-type="bibr" rid="bib1.bibx51" id="paren.23"/> and 5–15 <inline-formula><mml:math id="M8" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> along the Northern California Shelf <xref ref-type="bibr" rid="bib1.bibx50" id="paren.24"/>. The mean BML thickness over different latitudes in the North Atlantic Basin has been reported as 30–60 <inline-formula><mml:math id="M9" 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.bibx53" id="paren.25"/>. Across the Drake Passage, it was found to be over 100 <inline-formula><mml:math id="M10" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>, similar to Gulf Stream regions <xref ref-type="bibr" rid="bib1.bibx85" id="paren.26"/>. These differences may also be due to methodology. For example, the region immediately north of the Puerto Rico Trench in the North Atlantic (21° N, 66° W) has a BML thickness reportedly ranging from 80–800 <inline-formula><mml:math id="M11" 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.bibx6" id="paren.27"><named-content content-type="pre">Fig. 9 in</named-content></xref>, 60–100 <inline-formula><mml:math id="M12" 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.bibx53" id="paren.28"><named-content content-type="pre">Fig. 2b in</named-content></xref> and 80 <inline-formula><mml:math id="M13" 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.bibx32" id="paren.29"><named-content content-type="pre">Fig. 1 in</named-content></xref> with the variation likely attributed to different methodology and spatial interpolation.</p>
      <p id="d2e438">The transfer of mass and momentum between the ocean interior and the seafloor occurs via the BML. Yet in most large-scale ocean circulation models, it is generally unrepresented. As a result, robust parameterizations of bottom boundary processes are essential <xref ref-type="bibr" rid="bib1.bibx49 bib1.bibx21" id="paren.30"/>. <xref ref-type="bibr" rid="bib1.bibx65" id="text.31"/> initially proposed a vertically integrated, one-dimensional framework to estimate diapycnal mixing rates averaged across the ocean interior. However, it has been subsequently found that mixing in the bottom boundary is inherently three-dimensional, shaped by turbulent processes influenced by topography and internal wave dynamics <xref ref-type="bibr" rid="bib1.bibx46 bib1.bibx74 bib1.bibx90" id="paren.32"/>. Simple bottom boundary layer parameterizations assume local, steady-state velocity shear and stratification relationships to simulate turbulent mixing and momentum transfer vertically, potentially neglecting variability in the BML thickness <xref ref-type="bibr" rid="bib1.bibx47" id="paren.33"/>. Recent improvements have incorporated wave-driven turbulence and terrain-following schemes <xref ref-type="bibr" rid="bib1.bibx4" id="paren.34"/>, some of which include profiles of diffusivity and viscosity in their parameterization <xref ref-type="bibr" rid="bib1.bibx21" id="paren.35"/>. Nevertheless, additional observations along the ocean's bottom boundary remain crucial, not only for validating models, but for resolving the spatial and temporal variability in the BML structure that underpins interior-seafloor exchange <xref ref-type="bibr" rid="bib1.bibx12 bib1.bibx18 bib1.bibx86 bib1.bibx92" id="paren.36"/>.</p>
      <p id="d2e463">The BML thickness is most commonly defined as the thickness above the seabed at which a variable (typically conservative temperature or density) deviates from the seafloor value by a specified threshold (also known as the “threshold method”). While we use a hydrographic definition of the mixed layer, it is important to note that this does not necessarily coincide with the dynamically active mixing layer defined by turbulence; distinguishing these layers is increasingly recognized as essential when inferring mixing intensity and water–mass transformation. While we refer to this as the bottom <italic>mixed</italic> layer, its thickness may reflect varied bottom boundary processes, not exclusively active mixing. It is inhomogeneous throughout the world's oceans, not only because of the varying depth and roughness of the seafloor but also because of the influence of differing oceanographic processes in each region. Different oceanographic conditions require varying thresholds to calculate the BML thickness. For instance, weakly stratified abyssal regions necessitate small density thresholds (<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</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="M15" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), while highly turbulent areas are better suited to larger threshold values <xref ref-type="bibr" rid="bib1.bibx6" id="paren.37"><named-content content-type="pre">Fig. 1 in</named-content></xref>, or sensitivity in the threshold value may be directly related to instrument noise <xref ref-type="bibr" rid="bib1.bibx50" id="paren.38"/>. To overcome sensitivity and subjectivity in threshold (or gradient) selections, approaches like the relative variance <xref ref-type="bibr" rid="bib1.bibx34" id="paren.39"/> and integrated methods <xref ref-type="bibr" rid="bib1.bibx33" id="paren.40"/> have been developed to provide more robust, non-arbitrary BML thickness estimates. The BML thickness serves as a useful proxy for characterizing diapycnal upwelling <xref ref-type="bibr" rid="bib1.bibx12 bib1.bibx84" id="paren.41"/>, nutrient transfer <xref ref-type="bibr" rid="bib1.bibx35" id="paren.42"/>, sediment transport <xref ref-type="bibr" rid="bib1.bibx16" id="paren.43"/> and the development of bottom boundary conditions and parameterizations in ocean models; therefore, the methods and outputs require diligent evaluation of their physical validity across spatial and temporal scales.</p>
      <p id="d2e528">Our first objective is to evaluate BML thickness methodological approaches suitable for data-poor regions of the ocean. We focus on four methods: the threshold method, the threshold-gradient method, a relative variance method, and a split-and-merge algorithm to derive the BML thickness and critique their use and relevance in an abyssal basin setting.  The second objective is to understand the BML variability across the central and eastern Pacific abyssal ocean, including assessment of the connection to internal tidal energy dissipation and bottom water pathways. To achieve these objectives, we collected surface-to-seafloor temperature-pressure profiles across the central and eastern Pacific Ocean and complemented them with publicly available repeat hydrographic datasets. As we show in the sections that follow, these data reveal new insights into the dynamics of the BML and its connection to broader abyssal processes.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Methods</title>
      <p id="d2e539">The Trans-Pacific Transit (TPT) Expedition occurred over six individual legs, with the duration of each leg approximately 21 <inline-formula><mml:math id="M16" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">d</mml:mi></mml:mrow></mml:math></inline-formula>, between June 2023 and January 2024 on Research Vessel (R/V) <italic>Dagon</italic> <xref ref-type="bibr" rid="bib1.bibx37" id="paren.44"/>. The vessel covered 20° longitude and 30° latitude over the central and eastern abyssal Pacific Ocean, including the Molokai and Clarion Clipperton fracture zones (Fig. <xref ref-type="fig" rid="F1"/>). Bathymetry and backscatter intensity data were acquired throughout the expedition using a hull-mounted Kongsberg EM124 multibeam echosounder. At each site, three autonomous landers were deployed in a roughly 2 <inline-formula><mml:math id="M17" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> equilateral triangle, acquiring a total of 73 surface-to-seafloor profiles of temperature and pressure (at a frequency of 2 <inline-formula><mml:math id="M18" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Hz</mml:mi></mml:mrow></mml:math></inline-formula> secured to the landers). These data are referred to here as “TPT profiles”. Conductivity, temperature and depth (CTD) sensor profiles from repeat Global Ocean Ship-Based Hydrographic Investigations Program (GO-SHIP) hydrographic sections, P16 and P02, provided observations within the study regions along meridional and zonal transects, respectively (see locations in Fig. <xref ref-type="fig" rid="F1"/>). The GO-SHIP sections were used in two ways: first, they were used to complete Gaussian mixture modelling (GMM), which was applied to the TPT profiles to generate modelled practical salinity (SP) profiles (see Methods section on GMM); second, they provided additional locations to derive the bottom mixed layer (BML) thickness. The BML derivation, followed by a random forest regressor, was applied to the GMM-derived TPT profiles and GO-SHIP profiles as one dataset and is detailed in the following sections.</p>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Data collection</title>
      <p id="d2e584">Three autonomous landers, <italic>Magna, Omma</italic> and <italic>Cranch</italic> included a baited camera system, Niskin bottles and a CTD sensor measuring at 1 or 0.1 <inline-formula><mml:math id="M19" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Hz</mml:mi></mml:mrow></mml:math></inline-formula> (SBE49 FastCAT, SeaBird Electronics, Bellevue, WA). The landers descended at an average speed of 0.8 <inline-formula><mml:math id="M20" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">s</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, spent up to 8 h on the seafloor, and then returned to the surface by releasing their ballast weights via an acoustic modem. On legs two to six, there was the addition of a temperature (<inline-formula><mml:math id="M21" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>) and pressure (<inline-formula><mml:math id="M22" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula>) logger (<inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:mtext>RBRduet</mml:mtext><mml:mo>|</mml:mo><mml:mtext>deep</mml:mtext></mml:mrow></mml:math></inline-formula>) mounted to the lander frame measuring at 2 <inline-formula><mml:math id="M24" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">Hz</mml:mi></mml:mrow></mml:math></inline-formula> with an accuracy of <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.002</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M26" 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 0.05 % full-scale respectively <xref ref-type="bibr" rid="bib1.bibx75" id="paren.45"/>. Due to the consistent high-frequency measurements of the <inline-formula><mml:math id="M27" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M28" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> sensors, and the inconsistent data collection of the CTDs, we have used the <inline-formula><mml:math id="M29" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M30" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> logger data and applied GMM to the profiles (see the following section). The Niskin bottles collected a water sample on the seafloor, which was analyzed with an 8400B Autosal Salinometer providing a bottom water practical salinity (SP) value. Leg one data was omitted from this study due to no <inline-formula><mml:math id="M31" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>–<inline-formula><mml:math id="M32" display="inline"><mml:mi>p</mml:mi></mml:math></inline-formula> loggers, and a total of 69 profiles were suitable for this study. The exact locations of deployments are in Table A1.</p>
      <p id="d2e719">GO-SHIP profiles were obtained through the CLIVAR and Carbon Hydrographic Data Office (CCHDO, <uri>https://cchdo.ucsd.edu/</uri>, last access: 24 November 2024) for repeat hydrographic Sects. P02 and P16 which form part of the GO-SHIP program. These were voyage numbers: <italic>31WTTUNES_3</italic>, <italic>325020060213</italic> and <italic>33R0150410</italic> for P16 and <italic>49K6K9401_1</italic>, <italic>318M200406</italic> and <italic>318M20130321</italic> for P02. Only profiles that exceeded 2000 <inline-formula><mml:math id="M33" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> and reached within 40 <inline-formula><mml:math id="M34" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> of the metadata bottom depth were used to calculate the BML thickness. Only one occupation along line P16 went north of 23° N, therefore north of this latitude was excluded for line P16. A gridded version of GO-SHIP dataset, GO-SHIP Easy Ocean provided by <xref ref-type="bibr" rid="bib1.bibx41" id="text.46"/>, and available from <ext-link xlink:href="https://doi.org/10.5281/zenodo.13315689" ext-link-type="DOI">10.5281/zenodo.13315689</ext-link> <xref ref-type="bibr" rid="bib1.bibx42" id="paren.47"/> was used to produce the background neutral density, <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and conservative temperature, <inline-formula><mml:math id="M36" display="inline"><mml:mi mathvariant="italic">θ</mml:mi></mml:math></inline-formula>, for Figs. <xref ref-type="fig" rid="F5"/> and <xref ref-type="fig" rid="F6"/>.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>Gaussian mixture modeling in <inline-formula><mml:math id="M37" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>-<italic>p</italic>-<italic>SA</italic> space</title>
      <p id="d2e814">Gaussian mixture modeling applications (GMM) can achieve unsupervised classification of the water column, identifying coherent patterns in the associated domains <xref ref-type="bibr" rid="bib1.bibx59" id="paren.48"/>.</p>
      <p id="d2e820">In three-dimensional space (<inline-formula><mml:math id="M38" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>-<italic>p</italic>-<italic>SA</italic>), the abyssopelagic zone occupies a relatively small volume <xref ref-type="bibr" rid="bib1.bibx28 bib1.bibx62" id="paren.49"/>. For hydrographic profiles close in proximity, this space is even tighter <xref ref-type="bibr" rid="bib1.bibx62" id="paren.50"/>. Considering this, gaussian mixture modeling applications (GMM) can be applied to automatically group variables of the water column into a distinct number of components, like clusters, revealing consistent patterns in the data <xref ref-type="bibr" rid="bib1.bibx59" id="paren.51"/>. GO-SHIP profiles in the study region (detailed in Sect. 2.1) were used to predict practical salinity (SP) from 2500 <inline-formula><mml:math id="M39" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> to the seafloor. Only profiles collected within the last 5 years and within 10° latitude and 10° longitude that exceeded 2000 <inline-formula><mml:math id="M40" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> were used for each site <xref ref-type="bibr" rid="bib1.bibx70 bib1.bibx59" id="paren.52"/>. To predict SP for each TPT temperature and pressure profile. Model selection used information-theory criteria, focusing on the covariance type and number of components in the model using the Gaussian Mixture <italic>scikit-learn</italic> Python package <xref ref-type="bibr" rid="bib1.bibx70" id="paren.53"/>. The maximum number of components was limited to 21. The covariance types were limited to each component having its own general covariance matrix or all components sharing the same general covariance matrix. The elbow method was used to determine the number of components in the model with a brief examination of the BIC value (Table A1). If the modeled SP output was physically unstable, the next best option was chosen. The modeled SP was compared with the measured SP from a seafloor water sample analyzed on the vessel using an 8400B Autosal Lab Salinometer (Table A1) with negligible differences found. A further detailed explanation and model details for each TPT profile are provided in Table A1.</p>
</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>BML thickness derivation</title>
      <p id="d2e879">Several methods exist for determining the BML thickness, as with the surface mixed layer thickness. The threshold method (TH) uses the depth at which the difference to the seafloor in either <inline-formula><mml:math id="M41" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula> or <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, potential density referenced to 4000 <inline-formula><mml:math id="M43" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">dbar</mml:mi></mml:mrow></mml:math></inline-formula> in this case, is less than a defined threshold value. These values range from 0.02 <inline-formula><mml:math id="M44" 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> <xref ref-type="bibr" rid="bib1.bibx50" id="paren.54"/>, 0.001 <inline-formula><mml:math id="M45" 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> <xref ref-type="bibr" rid="bib1.bibx29" id="paren.55"/>, 0.005 <inline-formula><mml:math id="M46" 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> <xref ref-type="bibr" rid="bib1.bibx53" id="paren.56"/> to <inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:mn mathvariant="normal">6</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M48" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx71" id="paren.57"/>. We used a threshold value of 0.003 <inline-formula><mml:math id="M49" 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> for the region. This value was chosen as it provided the highest mean quality index (QI) for the BML thickness (1) for all the TPT profiles when comparing threshold values of 0.001, 0.002, 0.003, 0.004, and 0.005 (Appendix B). A quality index was initially defined by <xref ref-type="bibr" rid="bib1.bibx52" id="text.58"/> as a value between 0 and 1 capturing the conservative temperature variability in 1.5 times the BML thickness compared to the variability over the BML thickness. In equation form:

            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M50" display="block"><mml:mrow><mml:msub><mml:mtext>QI</mml:mtext><mml:mtext>BML</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi>A</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>-</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mo>〈</mml:mo><mml:mi mathvariant="normal">Θ</mml:mi><mml:mo>〉</mml:mo><mml:mo>)</mml:mo><mml:msub><mml:mo mathsize="1.1em">|</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mtext>BML</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">Θ</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mo>〈</mml:mo><mml:mi mathvariant="normal">Θ</mml:mi><mml:mo>〉</mml:mo><mml:mo>)</mml:mo><mml:msub><mml:mo mathsize="1.1em">|</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mtext>BML</mml:mtext></mml:msub><mml:mo>×</mml:mo><mml:mn mathvariant="normal">1.5</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mrow></mml:math></disp-formula>

          where <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>(</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the standard deviation from the vertical mean <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:mo>〈</mml:mo><mml:mo>〉</mml:mo></mml:mrow></mml:math></inline-formula> conservative temperature from <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mtext>BML</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mtext>BML</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> is the BML thickness <xref ref-type="bibr" rid="bib1.bibx52 bib1.bibx33" id="paren.59"/>.</p>
      <p id="d2e1155">The threshold-gradient method (GR) is also used <xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx88" id="paren.60"/>. We defined this method as the thickness at which <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> over 20 <inline-formula><mml:math id="M56" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> intervals is less than a criterion of <inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</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="M58" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">kg</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> <xref ref-type="bibr" rid="bib1.bibx6" id="paren.61"/>, making the minimum BML thickness 10 <inline-formula><mml:math id="M59" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>.</p>
      <p id="d2e1235">Several techniques have been put forward over the last decade, including a relative variance (RV) method <xref ref-type="bibr" rid="bib1.bibx34" id="paren.62"/>, split-and-merge algorithms <xref ref-type="bibr" rid="bib1.bibx83" id="paren.63"/> and an integrated method <xref ref-type="bibr" rid="bib1.bibx33" id="paren.64"/> that combines several methods together. We included the RV method and the Douglas–Peucker (DP) algorithm method. The RV method relies on calculating the ratio between the standard deviation and the greatest variation of <inline-formula><mml:math id="M60" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula> or <inline-formula><mml:math id="M61" display="inline"><mml:mi mathvariant="italic">σ</mml:mi></mml:math></inline-formula> above the seabed. The location where the least relative variance occurs is identified as the upper boundary of the BML. The RV method is available through the original research <xref ref-type="bibr" rid="bib1.bibx34" id="paren.65"/>. The DP method is a split-and-merge technique that has been previously adopted to calculate the surface mixed layer <xref ref-type="bibr" rid="bib1.bibx83" id="paren.66"/>. The DP algorithm estimates a given profile by using a series of simplified line segments that represent large changes in slope or any abrupt changes in the profile. Therefore, the lowest part of the segment belongs to the BML. The DP algorithm is available within MATLAB and requires a <inline-formula><mml:math id="M62" display="inline"><mml:mi mathvariant="italic">ϵ</mml:mi></mml:math></inline-formula> value between 0 and 1 to determine the number of line segments <xref ref-type="bibr" rid="bib1.bibx1" id="paren.67"/>. We included 0.002 and 0.008 as two possible DP methods (DP2 and DP8, respectively) (Appendix B).</p>
      <p id="d2e1278">The integrated method put forward by <xref ref-type="bibr" rid="bib1.bibx33" id="text.68"/> focuses on the use of multiple methods (TH, the curvature method, <xref ref-type="bibr" rid="bib1.bibx52" id="altparen.69"/>; the maximum angle method, <xref ref-type="bibr" rid="bib1.bibx11" id="altparen.70"/>, and RV, <xref ref-type="bibr" rid="bib1.bibx34" id="altparen.71"/>), calculating the QI for each method, and then choosing the BML thickness with the highest QI <xref ref-type="bibr" rid="bib1.bibx32" id="paren.72"/>. Relying on QI-based selection of BML thickness from multiple methods produced highly variable results, even across nearby locations (within 3 <inline-formula><mml:math id="M63" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>). That is not to say this variation may not be real, but visual inspection was still needed to assess accuracy, and the variation was not consistent with global maps from either <xref ref-type="bibr" rid="bib1.bibx6" id="text.73"/> or <xref ref-type="bibr" rid="bib1.bibx32" id="text.74"/>. Therefore, unlike Huang's global integrated approach, the single threshold method that produced consistent results was more appropriate for our regional study, avoiding unnecessary and possibly unreal variability that ultimately required manual validation.</p>
      <p id="d2e1312">The suitability of the threshold value, despite sometimes having a lower QI, is shown in Fig. <xref ref-type="fig" rid="F2"/> at different locations with additional annotation in Fig. <xref ref-type="fig" rid="F2"/>c. At times, the QI did capture the BML thickness values that were unusable (e.g. small RV QI values in Fig. <xref ref-type="fig" rid="F2"/>f). However, on the upper scale, the highest QI value could provide an unlikely, significantly larger BML thickness than where the density gradient approached zero and appeared visually correct. For example, in Fig. <xref ref-type="fig" rid="F2"/>c for the profile on the left side, the highest QI was 0.78 and far from the visual BML thickness height. Considering all TPT and GO-SHIP profiles, consistency in the average values of each method (Fig. <xref ref-type="fig" rid="F4"/>) and their performance when assessed visually (Fig. <xref ref-type="fig" rid="F2"/>), using the threshold method consistently over the whole dataset, provided the most reasonable result.</p>

      <fig id="F2" specific-use="star"><label>Figure 2</label><caption><p id="d2e1329">Example profiles of <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and BML thickness outputs from <bold>(a)</bold>–<bold>(h)</bold>. Color and size of the marker correspond to the method and the quality index (QI) of the BML <bold>(a)</bold>. The map and inserts in <bold>(i)</bold>–<bold>(l)</bold> detail the locations of the profiles shown in the respective subplot. Grey map shows the study region with GEBCO bathymetry and sites (key in <bold>i</bold>; see Fig. <xref ref-type="fig" rid="F1"/> for more detail), the red region the extent of the figure and black points indicating all profiles used. Blue circles are GO-SHIP, with light blue indicating profiles used but not displayed, and black triangles are TPT locations. <bold>(a)</bold> P16 GO-SHIP profiles in 2002 between 0 and 0.5° N and <bold>(b)</bold> in 2015 between 12 and 13° N, <bold>(c)</bold> P02 GO-SHIP profiles in 2022 between 135 and 136° W and <bold>(d)</bold> in 2022 between 124 and 123° W. <bold>(e)</bold> TPT voyage Leg 3 Site 4, <bold>(f)</bold> Leg 2 Site 3, <bold>(g)</bold> Leg 4 Site 5, and <bold>(h)</bold> Leg 5 Site 1. Panel <bold>(c)</bold> includes a line of visual interpretation and the exact values of the quality index, as also indicated by the marker size at the BML thickness for each method.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f02.jpg"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Random Forest Regression</title>
      <p id="d2e1407">We considered bathymetric parameters (terrain roughness index (TRI) and slope) and dynamic parameters (internal tide energy dissipation and depth) within a Random Forest Regressor (RF) to disentangle patterns in the BML thickness. Machine learning techniques have been used to estimate the surface mixed layer depth, however this the first time it has been applied to the BML <xref ref-type="bibr" rid="bib1.bibx36 bib1.bibx20" id="paren.75"/>. The RF machine learning technique, included as the <italic>RandomForestRegressor</italic> scikit package in Python <xref ref-type="bibr" rid="bib1.bibx70" id="paren.76"/> is a ensemble machine learning estimator that combines the outputs of multiple decision trees to increase predictive accuracy and control overfitting. Each decision tree is trained on the dataset using a bootstrap aggregation technique, and the final prediction is obtained by averaging the outputs for regression <xref ref-type="bibr" rid="bib1.bibx8 bib1.bibx36" id="paren.77"/>. We randomly selected 80 % of the dataset to build each tree and the remaining 20 % of the dataset to test the model using <italic>train_test_split</italic> within scikit <xref ref-type="bibr" rid="bib1.bibx70" id="paren.78"/>. We modified the number of trees from 100 (default value) to 500 and 1000 for sensitivity testing (Table <xref ref-type="table" rid="T1"/>) with the random state of the <italic>train_test_split</italic> at 42, 0 or 1. The number of trees did not add significant computing time or signficantly alter the results, therefore we maximised the number of trees at <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1000</mml:mn></mml:mrow></mml:math></inline-formula> to further test different random subsets of the data with <italic>train_test_split</italic> then changed between 42, and 0 to 7. The random state was kept at 42 for the RF for all itterations.</p>

<table-wrap id="T1" specific-use="star"><label>Table 1</label><caption><p id="d2e1452">Random Forest performance for different numbers of estimators (<inline-formula><mml:math id="M66" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>), comparing models trained on all features vs. the top five features.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="7">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right" colsep="1"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="right"/>
     <oasis:thead>
       <oasis:row>
         <oasis:entry colname="col1"/>
         <oasis:entry rowsep="1" namest="col2" nameend="col4" align="center" colsep="1">All </oasis:entry>
         <oasis:entry rowsep="1" namest="col5" nameend="col7" align="center">Top 5 </oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Number of estimators (<inline-formula><mml:math id="M67" display="inline"><mml:mi>n</mml:mi></mml:math></inline-formula>)</oasis:entry>
         <oasis:entry colname="col2">1000</oasis:entry>
         <oasis:entry colname="col3">500</oasis:entry>
         <oasis:entry colname="col4">100</oasis:entry>
         <oasis:entry colname="col5">1000</oasis:entry>
         <oasis:entry colname="col6">500</oasis:entry>
         <oasis:entry colname="col7">100</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">(a) Train_test random state = 42</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.65</oasis:entry>
         <oasis:entry colname="col3">0.65</oasis:entry>
         <oasis:entry colname="col4">0.65</oasis:entry>
         <oasis:entry colname="col5">0.67</oasis:entry>
         <oasis:entry colname="col6">0.67</oasis:entry>
         <oasis:entry colname="col7">0.67</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">RMSE</oasis:entry>
         <oasis:entry colname="col2">97.1</oasis:entry>
         <oasis:entry colname="col3">97.4</oasis:entry>
         <oasis:entry colname="col4">95.7</oasis:entry>
         <oasis:entry colname="col5">93.9</oasis:entry>
         <oasis:entry colname="col6">93.7</oasis:entry>
         <oasis:entry colname="col7">93.5</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MAE</oasis:entry>
         <oasis:entry colname="col2">71.4</oasis:entry>
         <oasis:entry colname="col3">72.0</oasis:entry>
         <oasis:entry colname="col4">71.4</oasis:entry>
         <oasis:entry colname="col5">70.0</oasis:entry>
         <oasis:entry colname="col6">69.7</oasis:entry>
         <oasis:entry colname="col7">69.7</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">(b) Train_test random state = 0</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.62</oasis:entry>
         <oasis:entry colname="col3">0.62</oasis:entry>
         <oasis:entry colname="col4">0.60</oasis:entry>
         <oasis:entry colname="col5">0.63</oasis:entry>
         <oasis:entry colname="col6">0.63</oasis:entry>
         <oasis:entry colname="col7">0.64</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">RMSE</oasis:entry>
         <oasis:entry colname="col2">127.0</oasis:entry>
         <oasis:entry colname="col3">127.9</oasis:entry>
         <oasis:entry colname="col4">129.7</oasis:entry>
         <oasis:entry colname="col5">125.3</oasis:entry>
         <oasis:entry colname="col6">125.4</oasis:entry>
         <oasis:entry colname="col7">124.5</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">MAE</oasis:entry>
         <oasis:entry colname="col2">86.3</oasis:entry>
         <oasis:entry colname="col3">87.0</oasis:entry>
         <oasis:entry colname="col4">86.7</oasis:entry>
         <oasis:entry colname="col5">85.2</oasis:entry>
         <oasis:entry colname="col6">85.4</oasis:entry>
         <oasis:entry colname="col7">85.1</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">(c) Train_test random state = 1</oasis:entry>
         <oasis:entry colname="col2"/>
         <oasis:entry colname="col3"/>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
         <oasis:entry colname="col7"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1"><inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col2">0.54</oasis:entry>
         <oasis:entry colname="col3">0.54</oasis:entry>
         <oasis:entry colname="col4">0.54</oasis:entry>
         <oasis:entry colname="col5">0.56</oasis:entry>
         <oasis:entry colname="col6">0.56</oasis:entry>
         <oasis:entry colname="col7">0.54</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">RMSE</oasis:entry>
         <oasis:entry colname="col2">108.1</oasis:entry>
         <oasis:entry colname="col3">108.2</oasis:entry>
         <oasis:entry colname="col4">109.0</oasis:entry>
         <oasis:entry colname="col5">106.4</oasis:entry>
         <oasis:entry colname="col6">106.4</oasis:entry>
         <oasis:entry colname="col7">108.0</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">MAE</oasis:entry>
         <oasis:entry colname="col2">72.3</oasis:entry>
         <oasis:entry colname="col3">73.6</oasis:entry>
         <oasis:entry colname="col4">73.4</oasis:entry>
         <oasis:entry colname="col5">71.3</oasis:entry>
         <oasis:entry colname="col6">70.9</oasis:entry>
         <oasis:entry colname="col7">72.8</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d2e1842">As discussed in the Data Collection section, internal tide energy dissipation (<inline-formula><mml:math id="M71" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) for all (M2, S2 and K1) tidal constituents broken down into dissipation processes; low-mode wave-wave interactions, low-mode scattering by small-scale topography, low-mode interaction with critical slopes, low-mode shoaling and local dissipation of high modes was accessed through the paper by <xref ref-type="bibr" rid="bib1.bibx14" id="text.79"/>. These variables, alongside slope and TRI were chosen based on their accessibility and relevance to BML thickness <xref ref-type="bibr" rid="bib1.bibx77 bib1.bibx25 bib1.bibx51" id="paren.80"/>. Depth is a known contributor to the BML thickness <xref ref-type="bibr" rid="bib1.bibx32 bib1.bibx53" id="paren.81"/> as are bathymetric variables of slope and TRI <xref ref-type="bibr" rid="bib1.bibx5 bib1.bibx89 bib1.bibx73" id="paren.82"/>. The relative contribution of tidal dissipation mechanisms near the seafloor, therefore influencing the BML thickness has been discussed in literature <xref ref-type="bibr" rid="bib1.bibx14" id="paren.83"/>. When internal waves hit the seafloor, they lose energy through either scattering off small rough spots and losing energy, or reflecting or shoaling off topographic features, depending on their shape and height <xref ref-type="bibr" rid="bib1.bibx79 bib1.bibx64" id="paren.84"/>. These processes, along with others that are not as well understood, like wave capture and scattering by mesoscale eddies <xref ref-type="bibr" rid="bib1.bibx7" id="text.85"/>, <xref ref-type="bibr" rid="bib1.bibx72" id="text.86"/>, <xref ref-type="bibr" rid="bib1.bibx58" id="text.87"/>, can speed up the dissipation of tides and change the thickness of the bottom mixed layer. A grid point from each of the dissipation parameters was assigned to each GO-SHIP and TPT point using cKDTree in scipy for nearest-neighbor lookup <xref ref-type="bibr" rid="bib1.bibx87" id="paren.88"/>. This method constructs a binary space-partitioning tree applying axis-aligned hyperrectangles via the sliding midpoint rule <xref ref-type="bibr" rid="bib1.bibx55" id="paren.89"/>. This provides efficient nearest-neighbor queries by recursively improving the search space across coordinate axes to determine the nearest latitude and longitude grid point to the GO-SHIP and TPT observations.</p>
      <p id="d2e1898">Bathymetric variables (TRI, and slope) were compiled from the latest GEBCO 2024 Grid, including the standard deviation <xref ref-type="bibr" rid="bib1.bibx23" id="paren.90"/>. TRI and slope were calculated using the ArcGIS Geomorphometry <inline-formula><mml:math id="M72" display="inline"><mml:mi mathvariant="italic">&amp;</mml:mi></mml:math></inline-formula> Gradient Metrics toolbox with a neighbourhood of <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:mn mathvariant="normal">9</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">9</mml:mn></mml:mrow></mml:math></inline-formula> cells <xref ref-type="bibr" rid="bib1.bibx17" id="paren.91"/>. TRI is a useful derivative of bathymetric and topographic datasets in order to enable quantification of the spatial heterogeneity of the surface under investigation <xref ref-type="bibr" rid="bib1.bibx76" id="paren.92"/>. The TRI metric can be a valuable analytical tool for understanding the effect of landscape on processes, geomorphological evolution, and for habitat mapping and modeling regimes. For the extent of the study region (Fig. <xref ref-type="fig" rid="F1"/>) the slope and TRI were calculated at buffer zones of 25, 50, 100 and 200 <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> (Fig. <xref ref-type="fig" rid="FB3"/>). At each GO-SHIP and TPT data point, the TRI was extracted to assess the variation for different buffer zones. The RF was completed with the 50 <inline-formula><mml:math id="M75" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> buffer, as the resolution for the dissipation values was 50 <inline-formula><mml:math id="M76" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>. The depth for the GO-SHIP sites was taken as the “bottom depth” variable available in the datasets.</p>
      <p id="d2e1958">The GO-SHIP observations included multiple occupations as detailed in the Data collection section above. In some locations the exact latitude and longitude was covered in multiple years, although this is not spatially consistent throughout the observations. The profiles over the different occupations provide different BML thicknesses, however it is impossible to deduce the reasoning behind the differences at these yearly timescales as we know the BML thickness may change within a matter of hours <xref ref-type="bibr" rid="bib1.bibx88 bib1.bibx10" id="paren.93"/>. For this reason, we clustered the GO-SHIP observations within the RF using <italic>dbscan</italic> in scikit <xref ref-type="bibr" rid="bib1.bibx70" id="paren.94"/>. Geographic clustering was performed by converting the GO-SHIP latitude and longitude coordinates to radians and applying <italic>dbscan</italic> with a haversine metric and a 3 <inline-formula><mml:math id="M77" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> neighborhood radius to group nearby data points. For consistency between the TPT and GO-SHIP sites, TPT sites within a 3 <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> radius of one another (each leg and site) were averaged and GO-SHIP sites were averaged based on the 3 <inline-formula><mml:math id="M79" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> neighborhood radius from <italic>dbscan</italic>. Because the TPT SP values were corrected using nearby GO-SHIP profiles, the combined dataset may inherit some spatial imbalance towards the more regularly sampled GO-SHIP sections; however, both datasets occupy the same hydrographic regime and spatial scale, making them appropriate for joint analysis while acknowledging that this imbalance could introduce minor bias in the RF feature relationships.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>BML thickness</title>
      <p id="d2e2017">The average and median thickness of the BML using the TH method for all data points in the abyssal study region was 240 and 176 <inline-formula><mml:math id="M80" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> respectively, and the standard deviation was 200 <inline-formula><mml:math id="M81" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="F3"/>). The BML was inhomogeneous over the region, its thickness decreasing around continental slope regions approaching Mexico and the southern part of Hawaii. Between 15° S and 2° N the BML was below 200 <inline-formula><mml:math id="M82" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>. There was a distinct change between 2 and 15° N where the BML approximately doubled and reached a maximum of 799 <inline-formula><mml:math id="M83" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> crossing the Clarion Fracture Zone before decreasing to below 90 <inline-formula><mml:math id="M84" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> south of Hawaii. Along the zonal section of P02, the BML exhibited an approximately 50 % increase between 135 to 130° W and decreased to approximately 100 <inline-formula><mml:math id="M85" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> on approaching the continental slope. The TPT expedition data indicated generally similar patterns as the repeat hydrographic sections. These patterns excluded Leg 4 Site 7, where the BML was the largest of the TPT sites (Fig. <xref ref-type="fig" rid="F3"/>).</p>

      <fig id="F3"><label>Figure 3</label><caption><p id="d2e2075">Bottom mixed layer (BML) thickness (<inline-formula><mml:math id="M86" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>) derived from the threshold method (TH). It is calculated using the TPT Expedition profiles (triangles) and GO-SHIP profiles (circles). The TPT profiles are within 3 <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> of each other and therefore a standard deviation is included.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f03.png"/>

        </fig>

      <p id="d2e2100">To provide insight into the efficacy of the derivation methods, we calculated a QI <xref ref-type="bibr" rid="bib1.bibx52" id="paren.95"/> for each profile and its five possible BML thickness values (Fig. <xref ref-type="fig" rid="F4"/>). Visual inspection of the BML thickness estimates and their associated QI indicated that a higher QI and lower standard deviation do not always provide confidence in the BML value. TPT profiles within 3 <inline-formula><mml:math id="M88" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> of each other in Fig. <xref ref-type="fig" rid="F2"/>e had a higher QI for the GR and DP8 methods; however, the methods estimated very different BML thicknesses for very similar profiles. In contrast, the TH method, with lower QI values, was consistent among the profiles and appeared to capture the position of profile change under contrasting abyssal conditions sufficiently. For example, across all Fig. <xref ref-type="fig" rid="F2"/>e–h the TH BML thicknesses were in close proximity to one another. Additionally, the TH thickness corresponded with the visually identifiable thickness, despite the GR values being close in value to each other and of a high QI (Fig. <xref ref-type="fig" rid="F2"/>c). We therefore chose the TH method for all BML thickness values going forward due to its dependable performance when applied to both TPT and GO-SHIP profiles over different regions in the study area.</p>

      <fig id="F4"><label>Figure 4</label><caption><p id="d2e2126">Average bottom mixed layer (BML) thickness (<inline-formula><mml:math id="M89" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>) for the threshold method (TH), gradient method (GR), Douglas–Peuker method using an <inline-formula><mml:math id="M90" display="inline"><mml:mi mathvariant="italic">ϵ</mml:mi></mml:math></inline-formula>  of 0.002 (DP2), Douglas–Peuker method using an <inline-formula><mml:math id="M91" display="inline"><mml:mi mathvariant="italic">ϵ</mml:mi></mml:math></inline-formula> of 0.080 (DP8) and the relative variance method (RV). The BML thickness is calculated using the TPT Expedition profiles (orange) and GO-SHIP profiles (blue) with the length of the line indicating the range of the thickness. Bold values above the bars are the mean quality index (QI) and the italicised values are the standard deviation of the QI.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Spatial variability</title>
      <p id="d2e2165">On meridional transect P16 between 4 and 16° N, depths are over 5000 <inline-formula><mml:math id="M92" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>, and the BML thickness was at its greatest along the transect (Fig. <xref ref-type="fig" rid="F5"/>). The transition regions at 4 and 16° N appear to have the widest variation in BML over the different occupations. The TRI was low over the majority of this region, with increases near the Hawaiian Islands, over the Boudeuse Ridge (10° S) and other prominent seafloor features visible in the bathymetric data (Fig. <xref ref-type="fig" rid="F7"/>b and c). Similarly, the TRI reached a maximum across transect P02 when it crossed the Murray Fracture Zone and the Moonless Mountains before increasing towards the North American continental slope (see Fig. <xref ref-type="fig" rid="F1"/> for locations). TPT sites close to the major fracture zones and seamount chains had higher TRI and slope values over the 50 <inline-formula><mml:math id="M93" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> buffer range and exhibited patterns connecting them to the P16 and P02 lines spatially. The P02 transect had a higher BML thickness (<inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:mn mathvariant="normal">298</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mo>±</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">170</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M95" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>) compared to P16 (<inline-formula><mml:math id="M96" display="inline"><mml:mrow><mml:mn mathvariant="normal">175</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>±</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">157</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M97" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>) (Figs. <xref ref-type="fig" rid="F5"/> and <xref ref-type="fig" rid="F6"/>). Similar to P16, the sections of changes in BML thickness along P02 (<inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">500</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M99" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> from 136 to 129° W) broadly intersected with larger differences in BML thicknesses over the different occupations (Fig. <xref ref-type="fig" rid="F6"/>).</p>

      <fig id="F5" specific-use="star"><label>Figure 5</label><caption><p id="d2e2262">The P16 repeat hydrographic line nominally along 150° W with <bold>(a)</bold> conservative temperature (<inline-formula><mml:math id="M100" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>) with neutral density (<inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) as the white contours and the BML thickness for 2015 (green), 2006 (red), and 2002 (orange). Note the seafloor, <inline-formula><mml:math id="M102" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M103" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are from the gridded data product available from <xref ref-type="bibr" rid="bib1.bibx41" id="text.96"/> and therefore may not be an exact representation of the seafloor depth, <bold>(b)</bold> BML thickness above the seafloor with color representation as in <bold>(a)</bold>.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f05.png"/>

        </fig>

      <fig id="F6" specific-use="star"><label>Figure 6</label><caption><p id="d2e2322">The P02 repeat hydrographic line nominally along 30° N with <bold>(a)</bold> conservative temperature (<inline-formula><mml:math id="M104" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>) with neutral density (<inline-formula><mml:math id="M105" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) as the white contours and the BML thickness for 2002 (green), 2013 (red), and 2004 (orange). Note the seafloor, <inline-formula><mml:math id="M106" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">γ</mml:mi><mml:mi mathvariant="normal">n</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> are from the gridded data product available from <xref ref-type="bibr" rid="bib1.bibx41" id="text.97"/> and therefore may not be an exact representation of the seafloor depth, <bold>(b)</bold> BML thickness above the seafloor with color representation as in <bold>(a)</bold>.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f06.png"/>

        </fig>

      <fig id="F7" specific-use="star"><label>Figure 7</label><caption><p id="d2e2383">All GO-SHIP (circle) and TPT (triangle) site variables used for the Random Forest Regressor (RF). The top BML thickness figure is the same as Fig. <xref ref-type="fig" rid="F3"/> for reference. <bold>(a)</bold> Bottom depth (<inline-formula><mml:math id="M108" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>), <bold>(b)</bold> slope over a 50 <inline-formula><mml:math id="M109" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> radius (°), <bold>(c)</bold> terrain roughness index (TRI) over a 50 <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> buffer, <bold>(d)</bold> Td <inline-formula><mml:math id="M111" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> total internal tide energy dissipation (<inline-formula><mml:math id="M112" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), <bold>(e)</bold> SH <inline-formula><mml:math id="M113" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> low-mode dissipation from shoaling (<inline-formula><mml:math id="M114" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), <bold>(f)</bold> Ww <inline-formula><mml:math id="M115" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> low-mode dissipation from wave-wave interaction (<inline-formula><mml:math id="M116" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), <bold>(g)</bold> Cs <inline-formula><mml:math id="M117" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> low-mode dissipation from critical slopes (<inline-formula><mml:math id="M118" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>), <bold>(h)</bold> Sc <inline-formula><mml:math id="M119" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> low-mode dissipation from scattering (<inline-formula><mml:math id="M120" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) and <bold>(i)</bold> Hm <inline-formula><mml:math id="M121" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> high-mode dissipation from local processes (<inline-formula><mml:math id="M122" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>). Panels <bold>(d)</bold>–<bold>(i)</bold> are from <xref ref-type="bibr" rid="bib1.bibx14" id="text.98"/>. The background regional bathymetry is from the Global Multi-Resolution Topography (GMRT) Synthesis <xref ref-type="bibr" rid="bib1.bibx78" id="paren.99"/> Released CC BY 4.0 Deep <inline-formula><mml:math id="M123" display="inline"><mml:mo>|</mml:mo></mml:math></inline-formula> Attribution 4.0 International <inline-formula><mml:math id="M124" display="inline"><mml:mo>|</mml:mo></mml:math></inline-formula> Creative Commons. Note the colour scale is different in <bold>(d)</bold> compared with <bold>(e)</bold>–<bold>(i)</bold>.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f07.jpg"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Random Forest Regression</title>
      <p id="d2e2637">The TPT and GO-SHIP profiles were analysed together as part of a RF. As described in the Methods section, GO-SHIP data points within 3 <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> of one another were averaged together as a mean value to remove instances of temporal variability at unknown time scales. After the averaging, the number of GO-SHIP data points reduced from 335 to 301. The number of TPT data points was 29; therefore, a total of 330 points were used for the analysis. For each point, we extracted values of bottom depth (<inline-formula><mml:math id="M126" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>), slope, TRI, and internal tide energy dissipation values of low-mode wave-wave interactions, low-mode critical slope, low-mode scattering, low-mode shoaling, high-mode (<inline-formula><mml:math id="M127" display="inline"><mml:mrow><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">6</mml:mn></mml:mrow></mml:math></inline-formula>) local dissipation and total internal energy dissipation which is a sum of all the losses from the five processes (in <inline-formula><mml:math id="M128" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">W</mml:mi><mml:mspace linebreak="nobreak" width="0.125em"/><mml:msup><mml:mi mathvariant="normal">m</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) (Fig. <xref ref-type="fig" rid="F7"/>). The dissipation parameters are defined in depth by <xref ref-type="bibr" rid="bib1.bibx14" id="text.100"/>.</p>
      <p id="d2e2689">The feature with the highest importance score (<inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.4</mml:mn></mml:mrow></mml:math></inline-formula>) across all iterations of the RF was the bottom depth. For each variation of <italic>train test split</italic> sample data (i.e. <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:mtext mathvariant="italic">random_state</mml:mtext><mml:mo>=</mml:mo><mml:mn mathvariant="normal">42</mml:mn></mml:mrow></mml:math></inline-formula>, 0 or 1) chosen to train the RF, the same features with the highest importance were in the top 3. In order, these were the bottom depth, total dissipation and slope. The number of iterations (<inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1000</mml:mn></mml:mrow></mml:math></inline-formula>, 500 or 100) and the three most commonly used <italic>train test split</italic> values (<inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:mtext mathvariant="italic">random_state</mml:mtext><mml:mo>=</mml:mo><mml:mn mathvariant="normal">42</mml:mn></mml:mrow></mml:math></inline-formula>, 0 or 1) were sensitivity tested due to the relatively small number of data points. Reducing the predictor variables to include only the top 5 features, ranked by importance, increased the correlation coefficient, <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula>, by <inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0.02</mml:mn></mml:mrow></mml:math></inline-formula>, regardless of the number of iterations or the <italic>random_state</italic> value (Table <xref ref-type="table" rid="T1"/>). Similarly, the root mean squared error (RMSE) and mean average error (MAE) reduced an insignificant amount (<inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M136" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>) when including only the top 5 features (Table <xref ref-type="table" rid="T1"/>). The results from <inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1000</mml:mn></mml:mrow></mml:math></inline-formula>, 500 or 100 had comparable feature importance scores; therefore, only the results from <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1000</mml:mn></mml:mrow></mml:math></inline-formula>, all features and additional <italic>train test split</italic> values of <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:mtext mathvariant="italic">random_state</mml:mtext><mml:mo>=</mml:mo><mml:mn mathvariant="normal">42</mml:mn></mml:mrow></mml:math></inline-formula>, 0–7 were run and are shown in Figs. <xref ref-type="fig" rid="F8"/> and <xref ref-type="fig" rid="F9"/>. If we were to keep the <italic>random_state</italic> value as empty, which is the default, the sensitivity in altering the number of iterations would not be effectively tested. <italic>Train test</italic> values of <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:mtext mathvariant="italic">random_state</mml:mtext><mml:mo>=</mml:mo><mml:mn mathvariant="normal">42</mml:mn></mml:mrow></mml:math></inline-formula> and 0–7 were completed for <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1000</mml:mn></mml:mrow></mml:math></inline-formula> with the <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> and RMSE displayed in Fig. <xref ref-type="fig" rid="F9"/>. The nine sets of the RF residual model outputs are shown in Fig. <xref ref-type="fig" rid="F9"/>. The <inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> was between a minimum of 0.53 and a maximum of 0.77 and the RMSE had a minimum of 87.1 and a maximum of 127.</p>

      <fig id="F8" specific-use="star"><label>Figure 8</label><caption><p id="d2e2895">Feature importance scores for each feature output from the number of iterations <inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1000</mml:mn></mml:mrow></mml:math></inline-formula> for the <italic>train test split random_state</italic> values of the 80–20 data split for <bold>(a)</bold> 42 and <bold>(b–i)</bold> for 0–7 for the Random Forest Regressor. Bd <inline-formula><mml:math id="M145" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> bottom depth, S <inline-formula><mml:math id="M146" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> slope, TRI <inline-formula><mml:math id="M147" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> terrain roughness index, Td <inline-formula><mml:math id="M148" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> total internal tide energy dissipation, Sh <inline-formula><mml:math id="M149" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> low-mode dissipation from shoaling, Ww <inline-formula><mml:math id="M150" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> low-mode dissipation from wave-wave interaction, Cs <inline-formula><mml:math id="M151" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> low-mode dissipation from critical slopes, Sc <inline-formula><mml:math id="M152" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> low-mode dissipation from scattering and Hm <inline-formula><mml:math id="M153" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> high-mode dissipation from local processes.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f08.png"/>

        </fig>

      <fig id="F9" specific-use="star"><label>Figure 9</label><caption><p id="d2e2997">Spatial plots of the BML residual (m) (BML true–BML predicted) for the <italic>train test</italic> random_state values used to train the Random Forest Regressor with the number of iterations <inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1000</mml:mn></mml:mrow></mml:math></inline-formula>, generating a spread of the data for random_state equal to <bold>(a)</bold> 42 and <bold>(b–i)</bold> for 0–7. The correlation coefficient and the Root Mean Squared Error (RMSE) is displayed on each figure.</p></caption>
          <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f09.png"/>

        </fig>

      <p id="d2e3025">The different <italic>random_state</italic> values changed the ranking order of the feature importance scores, however the same features were within the top five, with the bottom depth always the highest. The slope and TRI are intrinsically linked due to their calculation from the same bathymetric dataset, with slope quantifying the local gradient over a 50 <inline-formula><mml:math id="M155" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> radius and TRI capturing the variability within a neighborhood, averaged over a 50 <inline-formula><mml:math id="M156" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> radius aligning with the spatial resolution the dissipation values, a 0.5° grid size. A surface may be steep but smooth, or flat yet jagged, drawing not always a strong correlation between the two. For example, there are sharp changes latitudinally, however, both TRI and slope are high and more gradual along the P02 line as part of the broad sloping region from the continental slope of Mexico to the center of the Pacific Ocean (Fig. <xref ref-type="fig" rid="F7"/>b and c). The western end of the P02 line has higher internal tidal dissipation compared to the more eastern half due to the presence of the Hawaiian Islands <xref ref-type="bibr" rid="bib1.bibx44" id="paren.101"/>. The full spatial extent of the dissipation parameters, not just at our data points, at 0.5° resolution are displayed and explained in <xref ref-type="bibr" rid="bib1.bibx14" id="text.102"/>. Overall, the internal tidal dissipation for each low-mode process (Fig. <xref ref-type="fig" rid="F7"/>e–h), and the total dissipation (Fig. <xref ref-type="fig" rid="F7"/>d), is highest between Hawaii and just north of the equator, intersecting with the region of higher BML along P16 aside from 15–20° N next to the Hawaiian Islands, where the BML decreases. This decrease overlaps with a slight decrease in bottom depth (Fig. <xref ref-type="fig" rid="F7"/>a).</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
      <p id="d2e3071">Density profiles over the central and eastern Pacific Ocean provide an inhomogeneous outlook of BML thickness variations at abyssal depths across plains and topographic features. Basin-scale expeditions such as the TPT voyages are frequently multidisciplinary in scope, with competing demands on vessel time. Incorporation of these profiles with the repeat GO-SHIP profiles provides increased understanding of the BML. Using RF methods, we found that bottom depth, total internal tide dissipation and slope are the highest-performing features to predict the BML thickness in this region. Because several predictors share spatial structure (e.g., bottom depth and total dissipation), the RF highlights associations rather than uniquely isolating independent physical drivers, and this limitation should be considered when interpreting the feature importance results <xref ref-type="bibr" rid="bib1.bibx80" id="paren.103"/>.</p>
      <p id="d2e3077">In the central and eastern Pacific abyssal ocean, the thickness of the BML was inhomogeneous with an average value of <inline-formula><mml:math id="M157" display="inline"><mml:mrow><mml:mn mathvariant="normal">226</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mo>±</mml:mo><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mn mathvariant="normal">172</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M158" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula>. The BML was calculated using the (<inline-formula><mml:math id="M159" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>) profiles through the threshold method (0.003 <inline-formula><mml:math id="M160" 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>) for the study region. There is no accepted standard methodology for calculating the BML thickness. It often depends on user-defined numerical values within those methods and depends on the region of interest. The integrated method proposed by <xref ref-type="bibr" rid="bib1.bibx33" id="text.104"/>, was used to calculate the BML depth globally, providing an average Pacific Ocean BML thickness of 64 <inline-formula><mml:math id="M161" 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.bibx32" id="paren.105"/>. We found that for our abyssal ocean context, using an integrated approach that combines multiple methods and calculates a QI to get the highest “quality” BML thickness generated spurious results for profiles within three kilometres of one another, making it difficult to compare BMLs estimated with different methods. Although the QI was calculated, visual interpretation was necessary to confirm the results, mirroring the approach taken within the integrated method where visual identification was still needed <xref ref-type="bibr" rid="bib1.bibx32" id="paren.106"/>. The variability in BML thickness is not unexpected given the variation in topographic features across the region, likely changes in friction velocity, and a wide longitudinal and latitudinal range <xref ref-type="bibr" rid="bib1.bibx88 bib1.bibx46" id="paren.107"/>. Profiles from the TPT Expedition broadly followed the same spatial patterns as those from the hydrographic sections and show similar spatial variations in BML thickness as <xref ref-type="bibr" rid="bib1.bibx6" id="text.108"/>.</p>
      <p id="d2e3143">In all instances, the RF identified the bottom depth, slope, total internal wave energy dissipation, TRI and low-mode wave-wave interactions as the most important predictors of the BML thickness in this Pacific Ocean abyssal setting. These results are physically intuitive, with the bottom depth constraining the maximum possible BML thickness, background stratification and the vertical extent available for turbulent mixing, which is consistent with past research <xref ref-type="bibr" rid="bib1.bibx48 bib1.bibx51 bib1.bibx53" id="paren.109"/>. Importantly, dissipation patterns in the de Lavergne et al. (2019) dataset are not set by depth, but by the distribution of internal tide energy sources, scattering pathways, and nonlinear wave–wave losses. Deep basins may accumulate low-mode energy and therefore show elevated dissipation, but this reflects remote energy propagation and decay rather than a mechanistic link to depth itself. Therefore, even where depth and dissipation appear spatially aligned in our RF model, this similarity arises from shared basin-scale structure rather than depth acting as a direct driver of turbulent energy loss.</p>
      <p id="d2e3149">The total internal wave energy dissipation value aggregates all internal tide dissipation mechanisms that drive turbulence <xref ref-type="bibr" rid="bib1.bibx14" id="paren.110"/>. On abyssal plains, where local topographic features are sparse, a substantial amount of this energy would likely originate remotely and dissipate gradually through sustained mixing events <xref ref-type="bibr" rid="bib1.bibx68" id="paren.111"/>. Therefore, the inclusion of low-mode wave-wave interactions as a predictor is especially significant. This variable refers to nonlinear energy transfers among long-wavelength internal tides. In regions with high low-mode wave-wave dissipation, this could lead to persistent near-bottom mixing that expands the BML thickness. This suggests that the BML thickness on the abyssal plain is of remote and sustained forcing origin, rather than high-mode breaking events <xref ref-type="bibr" rid="bib1.bibx14 bib1.bibx63" id="paren.112"/>. Although the study region lies predominantly within the abyssal plain, the terrain is not uniform. As shown by <xref ref-type="bibr" rid="bib1.bibx26" id="text.113"/> and Fig. <xref ref-type="fig" rid="F7"/>b and c, the region is interspersed with multiple features of abyssal plains, abyssal hills, and seamounts, creating heterogeneity in the TRI and slope. The observations north of Hawaii highlight where higher TRI and slope intersect with the smallest values of total internal tide dissipation and low-mode wave-wave interactions.</p>

      <fig id="F10" specific-use="star"><label>Figure 10</label><caption><p id="d2e3169">Conservative temperature (<inline-formula><mml:math id="M162" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>, °) – Absolute Salinity (SA, <inline-formula><mml:math id="M163" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">g</mml:mi><mml:mspace width="0.125em" linebreak="nobreak"/><mml:msup><mml:mi mathvariant="normal">kg</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>) plots for latitudinal sections of the P16 line for the 2015 occupation between 0–2° N (blue), 10–15° N (red) and 16–19° N (green). <bold>(a)</bold> Wider portion of the water column with the <bold>(b)</bold> limits outlined. In <bold>(a)</bold> the dashed contour lines show the potential density referenced to the 0 <inline-formula><mml:math id="M164" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">dbar</mml:mi></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M165" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>) and in <bold>(b)</bold> the dashed lines show the potential density referenced to 4000 <inline-formula><mml:math id="M166" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">dbar</mml:mi></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M167" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">σ</mml:mi><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>). <inline-formula><mml:math id="M168" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>-SA North Pacific water mass properties are shown in magenta <xref ref-type="bibr" rid="bib1.bibx22" id="paren.114"/> and the BML for the profile is displayed with a black X. NPIW <inline-formula><mml:math id="M169" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> North Pacific Intermediate Water, AAIW <inline-formula><mml:math id="M170" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> Antarctic Intermediate Water, NPDW <inline-formula><mml:math id="M171" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> North Pacific Deep Water, AABW <inline-formula><mml:math id="M172" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> Antarctic Bottom Water, used here interchangeably with Lower Circumpolar Deep Water (LCDW). Displayed and calculated with the TEOS-10 toolbox <xref ref-type="bibr" rid="bib1.bibx61" id="paren.115"/>.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f10.png"/>

      </fig>

      <p id="d2e3295">The TRI captures local bathymetric complexity at 50 <inline-formula><mml:math id="M173" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> scales, which enhances bottom drag and internal tide scattering, even where mean slopes may be weak, supporting thicker BMLs by maintaining sustained and patchy mixing close to the boundary layer <xref ref-type="bibr" rid="bib1.bibx67 bib1.bibx66" id="paren.116"/>. The slope of the topography within our study region is primarily of a subcritical regime; therefore, internal tides will refract and reflect weakly, allowing for persistent low-mode energy to mix over broader regions, rather than localized mixing. Between 4 and 15° N there is a small region where the low-mode critical slope dissipation increases (Fig. <xref ref-type="fig" rid="F7"/>g), and the BML thickness is large, suggesting the critical slope may be more important here. Nested within the same region is the highest total dissipation of the study region (4–7° N) where there is high local high-mode dissipation, low-mode wave-wave interactions and low-mode critical slope dissipation. The TRI and slope are small over this region, culminating in the BML thickness being slightly above the average. Similar connections to the slope and the TRI have been identified in the North Atlantic Ocean and the South China Sea <xref ref-type="bibr" rid="bib1.bibx53 bib1.bibx51" id="paren.117"/>.</p>
      <p id="d2e3314">Our results have highlighted differences in what factors drive the BML. Despite limited and sparsely located data points, it is clear that the BML thickness is a culmination of processes, both local and remote. The limited and spatially inconsistent data points meant we were unable to further the model to predict the BML without the RMSE at times equating to the predicted BML thickness. This correspondence between dissipation and hydrographic BML thickness further suggests that, in this region, the threshold-defined BML is not merely a passive hydrographic feature but may effectively capture the vertical extent over which mixing is dynamically active. Such alignment between hydrography and turbulence is rarely shown explicitly for the abyssal ocean and may point to an underappreciated sensitivity of BML structure to the local dissipation field. Despite the three highest importance features remaining consistent, the nine iterations of <italic>random_state</italic> values do not visually provide a clear picture of regions that are consistently lower or higher performing than others. This variability, combined with shared spatial patterns among some predictors, further underscores that the RF approach here is more diagnostic than predictive and should not be interpreted as uniquely isolating mechanistic controls. In addition, the reasonably high variation in <inline-formula><mml:math id="M174" display="inline"><mml:mrow><mml:msup><mml:mi>r</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> and RMSE values suggests that more observations are required for there to be less sensitivity in the results to which random selection of the data is chosen to train the model. The RF herein should be used to understand drivers but cannot be used predictively, which would require additional data points. However, in regions where there is a more dense and equal spread of CTD profiles, the publicly available datasets from <xref ref-type="bibr" rid="bib1.bibx14" id="text.118"/> and GMRT bathymetry <xref ref-type="bibr" rid="bib1.bibx78" id="paren.119"/> should be considered for usable predictive relationships. Prediction of the BML thickness was not in the scope of this study; however, we have shown the usefulness of publicly available datasets. Predictive relationships of the BML thickness would be useful for identifying regions of interest for internal wave-driven mixing at the ocean's bottom boundary, hydrodynamic model parameterisations and disentangling spatiotemporal variability in BML thickness within a given region.</p>
      <p id="d2e3337">At around 18° N, bottom water passes through the Horizon Passage (170° W) and flows around Hawaii <xref ref-type="bibr" rid="bib1.bibx54 bib1.bibx22 bib1.bibx40" id="paren.120"/>, intersecting where the BML was small and there was increased stratification in the water column above. This can be demonstrated by <inline-formula><mml:math id="M175" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>-SA profiles with increased fractions of North Pacific Intermediate Water (NPIW) from 16–19° N (Fig. <xref ref-type="fig" rid="F10"/>a) and more saline and cooler water at the seafloor within the BML, aligning with Antarctic Bottom Water (AABW) properties (Fig. <xref ref-type="fig" rid="F10"/>b). While the complete profiles between 0–2 and 10–15° N displayed visually similar water mass characteristics, the properties of the BML were distinct (X marks in Fig. <xref ref-type="fig" rid="F10"/>) with the equatorial seafloor BML fresher and warmer, indicating NPDW, compared to 10–15° N closer to the properties of AABW, and 16–19° N the most saline and coolest <xref ref-type="bibr" rid="bib1.bibx22" id="paren.121"/>. This region of water mass and inter-basin exchange highlights the difference between stratified regions of bottom water pathways (Fig. <xref ref-type="fig" rid="F1"/>) compared to low ocean interior stratification south of this region (curved <inline-formula><mml:math id="M176" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>-SA in Fig. <xref ref-type="fig" rid="F10"/>b, red and blue) and less variation in <inline-formula><mml:math id="M177" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>-SA space (Fig. <xref ref-type="fig" rid="F10"/>a) <xref ref-type="bibr" rid="bib1.bibx62 bib1.bibx27 bib1.bibx43" id="paren.122"/>. In essence, a more strongly stratified ocean interior likely suppresses mixing by reducing the turbulent diffusivity, even in regions where the turbulent kinetic energy dissipation may be high. Therefore, the buoyancy gradient remains difficult to overcome, resulting in a thinner BML in AABW regions compared to regions of NPDW at the equator <xref ref-type="bibr" rid="bib1.bibx88" id="paren.123"/>.</p>
      <p id="d2e3387">Consistent with previous analyses <xref ref-type="bibr" rid="bib1.bibx51 bib1.bibx53 bib1.bibx10" id="paren.124"/>, there are multiple processes influencing the BML thickness at abyssal basin scales. While the RF provides a quantitative approach to dissect the variations in BML thickness based on the features, the profiles are a single snapshot of the water column at that point in time. As exemplified by <xref ref-type="bibr" rid="bib1.bibx10" id="text.125"/> in the Clarion–Clipperton Fracture Zone, they were unable to define the diffusion processes of the suspended sediment within the BML, as additional short-term processes such as internal gravity waves were highlighted as likely influencing the results. In our case, the TRI and slope are single values over a 50 <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> buffer region, not including proximity and direction from features such as the Hawaiian Ridge, which may influence the formation of the BML and the water column in different ways; hence the inclusion of internal tidal dissipation from de Lavergne <xref ref-type="bibr" rid="bib1.bibx94 bib1.bibx19" id="paren.126"/>. Considering the broader consequences of BML dynamics for deep ocean mixing and overturning circulation, temporal variability in the BML over abyssal depths should be considered in future studies. For example, a mooring configuration both within the BML thickness and above, in a region of increased internal tide energy dissipation south of Hawaii and then at a similar depth to the north-east of Hawaii where the BML thickness is higher and dissipation is lower, while intersecting with a region of water mass transport. These locations transition from flat abyssal plains to the Hawaiian Islands, each with distinct BML patterns and drivers across <inline-formula><mml:math id="M179" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">6</mml:mn><mml:mi mathvariant="italic">°</mml:mi></mml:mrow></mml:math></inline-formula> of latitude. Increased observations of both direct mixing and far-field or wave-wave energy dynamics are required in this relatively dynamic, yet undersampled region of the abyssal Pacific Ocean.</p>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d2e3428">The BML is crucial for understanding diapycnal transport, which causes significant upward movement of deep-sea waters <xref ref-type="bibr" rid="bib1.bibx60 bib1.bibx18" id="paren.127"/> in the undersampled abyssal ocean. This research highlights the importance of abyssal seafloor regions, which are not typically categorized as dynamic, shifting in space and time. Through the application of four BML detection methods, we find that the commonly used threshold method provides the most consistent and interpretable estimates of BML thickness across large spatial scales. However, we have highlighted the necessity to test each method-specific parameter. We also show that GMM offers a useful approach for predicting essential ocean variables, such as salinity here, using publicly available data. The RF revealed BML thickness variation related primarily to bottom depth, followed by total internal tide energy dissipation and topographic slope.</p>
      <p id="d2e3434">Global studies of the BML using multiple methods seldom focus on the potential of variability over time <xref ref-type="bibr" rid="bib1.bibx32" id="paren.128"/>, while others aim to use a small range in time to comprehend processes such as sediment dispersal within the BML <xref ref-type="bibr" rid="bib1.bibx51" id="paren.129"/> reaching the conclusion of significant temporal variability long noted in literature <xref ref-type="bibr" rid="bib1.bibx24" id="paren.130"/>. The relative contributions of the mechanisms that control the BML thickness across the abyssal ocean and basin boundaries requires further investigation through increased continuous observations and modelling efforts with reduced interpolation. The role of abyssal circulation pathways and internal tide driven mixing is at the forefront of current research <xref ref-type="bibr" rid="bib1.bibx92 bib1.bibx86" id="paren.131"><named-content content-type="pre">e.g.</named-content></xref>, within which the formation of the BML forms a key component of the processes. Therefore, the present study highlights and encourages sustained observations of abyssal regions over the bottom boundary and ocean interior above. Such observations are particularly important around rough topography, specifically in the central and eastern Pacific, where the abyssal ocean is frequently overlooked. At present, the temporal scales of BML variability remain poorly understood. Determining these scales is essential for characterising how the BML is mediated by abyssal water–mass transformation and circulation.</p>
</sec>

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

<app id="App1.Ch1.S1">
  <label>Appendix A</label><title>Gaussian mixture modelling of TPT salinity profiles</title>

      <fig id="FA1"><label>Figure A1</label><caption><p id="d2e3464">Profiles over 2000 <inline-formula><mml:math id="M180" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> of TP4_MA3_5400 and GO-SHIP datasets for <bold>(a)</bold> modelled salinity (blue) compared to the measured GO-SHIP profiles (red) within the bounds and used for this GMM and <bold>(b)</bold> associated measured temperature (blue) and measured GO-SHIP profiles (red).</p></caption>
        
        <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f11.png"/>

      </fig>

      <p id="d2e3489">We applied Gaussian mixture modelling to achieve a modelled representation of the practical salinity (SP) from 2500 <inline-formula><mml:math id="M181" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> to the seafloor at each voyage deployment location (Table A1). Such unsupervised classifications have been completed for CTD profiles and Argo floats <xref ref-type="bibr" rid="bib1.bibx93 bib1.bibx95" id="paren.132"/>. All GO-SHIP profiles deeper than 5000 <inline-formula><mml:math id="M182" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math></inline-formula> and within 10° latitude and 10° longitude from the voyage site were used in scikit-learn package GaussianMixture (GMM) <xref ref-type="bibr" rid="bib1.bibx70" id="paren.133"/>. If there were 2 or less GO-SHIP profiles within the bounding box, it was expanded to 15° latitude and 15° longitude, otherwise the site was excluded.  Mixture models can be viewed as an extension of <inline-formula><mml:math id="M183" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula>-means clustering that integrates information regarding the covariance structure of the data alongside the centres of the latent Gaussian distributions. They are a probabilistic framework that assumes all data points are derived from a combination of a finite set of Gaussian distributions with unspecified parameters. Options within the package that were altered to get the optimal GMM model of SP were: <list list-type="bullet"><list-item>
      <p id="d2e3524"><italic>covariance_type</italic>: tied or full, default is full.</p></list-item><list-item>
      <p id="d2e3530"><italic>N_components</italic>: 1–21, number of mixture components.</p></list-item><list-item>
      <p id="d2e3536"><italic>random_state</italic>: 42, controls the generation of random samples.</p></list-item></list> The rest of the parameters were kept as default values. Each set of GO-SHIP data for the associated TPT voyage site was iterated through each covariance type for each number of components. The elbow method was then used to choose the number of components, whereby the increase in the number of components does not equate to an increase in the model performance (<inline-formula><mml:math id="M184" display="inline"><mml:mrow><mml:mtext>AIC</mml:mtext><mml:mo>/</mml:mo><mml:mtext>BIC</mml:mtext></mml:mrow></mml:math></inline-formula>). An example modelled SP profile over depth and associated <inline-formula><mml:math id="M185" display="inline"><mml:mi>t</mml:mi></mml:math></inline-formula>, in-situ temperature profiles are shown for <inline-formula><mml:math id="M186" display="inline"><mml:mrow><mml:mtext>TP</mml:mtext><mml:mn mathvariant="normal">4</mml:mn><mml:mi mathvariant="italic">_</mml:mi><mml:mtext>MA</mml:mtext><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">_</mml:mi><mml:mn mathvariant="normal">5400</mml:mn></mml:mrow></mml:math></inline-formula> in Fig. <xref ref-type="fig" rid="FA1"/>. The modelled seafloor salinity was then compared with a seafloor Niskin bottle salinity measurement at each site to provide a second validation of the profile. The water sample was analysed on the vessel using an 8400B Autosal Salinometer.</p>

<table-wrap id="TA1" specific-use="star"><label>Table A1</label><caption><p id="d2e3585">Station metadata and gaussian mixture model details for each location.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="8">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="right"/>
     <oasis:colspec colnum="3" colname="col3" align="right"/>
     <oasis:colspec colnum="4" colname="col4" align="right"/>
     <oasis:colspec colnum="5" colname="col5" align="right"/>
     <oasis:colspec colnum="6" colname="col6" align="right"/>
     <oasis:colspec colnum="7" colname="col7" align="left"/>
     <oasis:colspec colnum="8" colname="col8" align="right"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Station</oasis:entry>
         <oasis:entry colname="col2">Depth (m)</oasis:entry>
         <oasis:entry colname="col3">Lat (°)</oasis:entry>
         <oasis:entry colname="col4">Lon (°)</oasis:entry>
         <oasis:entry colname="col5">GO-SHIP files</oasis:entry>
         <oasis:entry colname="col6">Components</oasis:entry>
         <oasis:entry colname="col7">Covariance</oasis:entry>
         <oasis:entry colname="col8">Difference</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">TP2_CR1_5200</oasis:entry>
         <oasis:entry colname="col2">5202</oasis:entry>
         <oasis:entry colname="col3">17.424</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M187" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">151.997</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">73</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M188" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0047</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_CR2_5400</oasis:entry>
         <oasis:entry colname="col2">5384</oasis:entry>
         <oasis:entry colname="col3">14.808</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M189" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">148.371</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">83</oasis:entry>
         <oasis:entry colname="col6">14</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M190" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0027</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_CR3_5400</oasis:entry>
         <oasis:entry colname="col2">5310</oasis:entry>
         <oasis:entry colname="col3">10.635</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M191" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">144.672</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">84</oasis:entry>
         <oasis:entry colname="col6">15</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M192" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0019</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_CR4_5000</oasis:entry>
         <oasis:entry colname="col2">4988</oasis:entry>
         <oasis:entry colname="col3">5.181</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M193" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">144.780</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">62</oasis:entry>
         <oasis:entry colname="col6">15</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M194" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0033</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_CR5_4950</oasis:entry>
         <oasis:entry colname="col2">4944</oasis:entry>
         <oasis:entry colname="col3">4.470</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M195" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">145.870</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">62</oasis:entry>
         <oasis:entry colname="col6">15</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M196" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0075</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_CR7_4500</oasis:entry>
         <oasis:entry colname="col2">4588</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M197" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.926</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M198" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">144.014</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">36</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
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       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_MA3_5400</oasis:entry>
         <oasis:entry colname="col2">5140</oasis:entry>
         <oasis:entry colname="col3">10.630</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M200" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">144.689</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">84</oasis:entry>
         <oasis:entry colname="col6">15</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M201" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0030</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_MA4_5000</oasis:entry>
         <oasis:entry colname="col2">4992</oasis:entry>
         <oasis:entry colname="col3">5.194</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M202" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">144.793</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">62</oasis:entry>
         <oasis:entry colname="col6">15</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M203" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0024</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_MA5_4950</oasis:entry>
         <oasis:entry colname="col2">4992</oasis:entry>
         <oasis:entry colname="col3">4.482</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M204" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">145.883</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">62</oasis:entry>
         <oasis:entry colname="col6">16</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M205" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0089</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_MA7_4500</oasis:entry>
         <oasis:entry colname="col2">4563</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M206" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.913</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M207" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">144.028</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">36</oasis:entry>
         <oasis:entry colname="col6">13</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M208" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0030</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_OM1_5200</oasis:entry>
         <oasis:entry colname="col2">5219</oasis:entry>
         <oasis:entry colname="col3">17.437</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M209" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">151.994</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">73</oasis:entry>
         <oasis:entry colname="col6">13</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M210" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0030</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_OM2_5400</oasis:entry>
         <oasis:entry colname="col2">5385</oasis:entry>
         <oasis:entry colname="col3">14.791</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M211" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">148.376</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">83</oasis:entry>
         <oasis:entry colname="col6">13</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M212" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0030</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_OM3_5400</oasis:entry>
         <oasis:entry colname="col2">5197</oasis:entry>
         <oasis:entry colname="col3">10.648</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M213" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">144.685</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">84</oasis:entry>
         <oasis:entry colname="col6">15</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M214" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0030</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_OM5_4950</oasis:entry>
         <oasis:entry colname="col2">4944</oasis:entry>
         <oasis:entry colname="col3">4.487</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M215" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">145.866</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">62</oasis:entry>
         <oasis:entry colname="col6">16</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M216" display="inline"><mml:mn mathvariant="normal">0.0036</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP2_OM7_4500</oasis:entry>
         <oasis:entry colname="col2">4573</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M217" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.931</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M218" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">144.032</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">36</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M219" display="inline"><mml:mn mathvariant="normal">0.0056</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_CR1_4800</oasis:entry>
         <oasis:entry colname="col2">4875</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M220" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10.832</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M221" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">146.345</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">18</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M222" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0009</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_CR2_5100</oasis:entry>
         <oasis:entry colname="col2">5209</oasis:entry>
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         <oasis:entry colname="col4"><inline-formula><mml:math id="M224" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">147.826</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">22</oasis:entry>
         <oasis:entry colname="col6">18</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M225" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0036</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_CR3_4800</oasis:entry>
         <oasis:entry colname="col2">4760</oasis:entry>
         <oasis:entry colname="col3"><inline-formula><mml:math id="M226" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.630</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M227" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">150.330</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">46</oasis:entry>
         <oasis:entry colname="col6">13</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M228" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0029</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_CR4_4800</oasis:entry>
         <oasis:entry colname="col2">4881</oasis:entry>
         <oasis:entry colname="col3">3.178</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M229" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">153.505</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">60</oasis:entry>
         <oasis:entry colname="col6">9</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M230" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0010</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_CR5_4700</oasis:entry>
         <oasis:entry colname="col2">4816</oasis:entry>
         <oasis:entry colname="col3">6.649</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M231" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">156.946</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">68</oasis:entry>
         <oasis:entry colname="col6">6</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M232" display="inline"><mml:mn mathvariant="normal">0.0089</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_CR7_5200</oasis:entry>
         <oasis:entry colname="col2">5208</oasis:entry>
         <oasis:entry colname="col3">16.602</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M233" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">158.528</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">75</oasis:entry>
         <oasis:entry colname="col6">18</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M234" display="inline"><mml:mn mathvariant="normal">0.0100</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_MA1_5100</oasis:entry>
         <oasis:entry colname="col2">5083</oasis:entry>
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         <oasis:entry colname="col4"><inline-formula><mml:math id="M236" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">146.325</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">18</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M237" display="inline"><mml:mn mathvariant="normal">0.0063</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_MA2_5200</oasis:entry>
         <oasis:entry colname="col2">5226</oasis:entry>
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         <oasis:entry colname="col4"><inline-formula><mml:math id="M239" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">147.818</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">22</oasis:entry>
         <oasis:entry colname="col6">18</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M240" display="inline"><mml:mn mathvariant="normal">0.0029</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_MA3_4800</oasis:entry>
         <oasis:entry colname="col2">4835</oasis:entry>
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         <oasis:entry colname="col4"><inline-formula><mml:math id="M242" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">150.336</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">46</oasis:entry>
         <oasis:entry colname="col6">14</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
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       </oasis:row>
       <oasis:row>
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         <oasis:entry colname="col4"><inline-formula><mml:math id="M244" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">153.521</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">60</oasis:entry>
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         <oasis:entry colname="col8"><inline-formula><mml:math id="M245" display="inline"><mml:mn mathvariant="normal">0.0011</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_MA5_4600</oasis:entry>
         <oasis:entry colname="col2">4814</oasis:entry>
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         <oasis:entry colname="col5">68</oasis:entry>
         <oasis:entry colname="col6">6</oasis:entry>
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         <oasis:entry colname="col8"><inline-formula><mml:math id="M247" display="inline"><mml:mn mathvariant="normal">0.0020</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_OM1_5100</oasis:entry>
         <oasis:entry colname="col2">5101</oasis:entry>
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         <oasis:entry colname="col4"><inline-formula><mml:math id="M249" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">146.337</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">18</oasis:entry>
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         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M250" display="inline"><mml:mn mathvariant="normal">0.0012</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_OM4_4800</oasis:entry>
         <oasis:entry colname="col2">4873</oasis:entry>
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         <oasis:entry colname="col4"><inline-formula><mml:math id="M251" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">153.521</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">60</oasis:entry>
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         <oasis:entry colname="col8"><inline-formula><mml:math id="M252" display="inline"><mml:mn mathvariant="normal">0.0024</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP3_OM5_4600</oasis:entry>
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         <oasis:entry colname="col5">68</oasis:entry>
         <oasis:entry colname="col6">6</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M254" display="inline"><mml:mn mathvariant="normal">0.0011</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_CR2_5400</oasis:entry>
         <oasis:entry colname="col2">5437</oasis:entry>
         <oasis:entry colname="col3">20.688</oasis:entry>
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         <oasis:entry colname="col5">103</oasis:entry>
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         <oasis:entry colname="col7">tied</oasis:entry>
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       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_CR3_5400</oasis:entry>
         <oasis:entry colname="col2">5445</oasis:entry>
         <oasis:entry colname="col3">21.163</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M257" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">141.568</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">24</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M258" display="inline"><mml:mn mathvariant="normal">0.0029</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_CR4_5300</oasis:entry>
         <oasis:entry colname="col2">5319</oasis:entry>
         <oasis:entry colname="col3">21.563</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M259" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">136.898</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">14</oasis:entry>
         <oasis:entry colname="col6">10</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M260" display="inline"><mml:mn mathvariant="normal">0.0009</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_CR6_4700</oasis:entry>
         <oasis:entry colname="col2">4792</oasis:entry>
         <oasis:entry colname="col3">24.123</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M261" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">128.540</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">4</oasis:entry>
         <oasis:entry colname="col6">17</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M262" display="inline"><mml:mn mathvariant="normal">0.0009</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_CR7_4800</oasis:entry>
         <oasis:entry colname="col2">4873</oasis:entry>
         <oasis:entry colname="col3">26.825</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M263" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">124.635</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">4</oasis:entry>
         <oasis:entry colname="col6">17</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M264" display="inline"><mml:mn mathvariant="normal">0.0010</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_MA1_5200</oasis:entry>
         <oasis:entry colname="col2">5229</oasis:entry>
         <oasis:entry colname="col3">20.315</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M265" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">151.210</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">120</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M266" display="inline"><mml:mn mathvariant="normal">0.0004</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_MA2_5400</oasis:entry>
         <oasis:entry colname="col2">5476</oasis:entry>
         <oasis:entry colname="col3">20.688</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M267" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">146.264</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">103</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M268" display="inline"><mml:mn mathvariant="normal">0.0003</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_MA3_5400</oasis:entry>
         <oasis:entry colname="col2">5491</oasis:entry>
         <oasis:entry colname="col3">21.173</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M269" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">141.551</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">24</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M270" display="inline"><mml:mn mathvariant="normal">0.0003</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_MA4_5300</oasis:entry>
         <oasis:entry colname="col2">5335</oasis:entry>
         <oasis:entry colname="col3">21.560</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M271" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">136.917</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">14</oasis:entry>
         <oasis:entry colname="col6">10</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M272" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0017</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_MA5_5000</oasis:entry>
         <oasis:entry colname="col2">5105</oasis:entry>
         <oasis:entry colname="col3">23.647</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M273" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">133.339</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">5</oasis:entry>
         <oasis:entry colname="col6">18</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M274" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0019</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_MA6_4700</oasis:entry>
         <oasis:entry colname="col2">4786</oasis:entry>
         <oasis:entry colname="col3">24.138</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M275" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">128.551</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">4</oasis:entry>
         <oasis:entry colname="col6">17</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M276" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0019</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_MA7_4800</oasis:entry>
         <oasis:entry colname="col2">4906</oasis:entry>
         <oasis:entry colname="col3">26.841</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M277" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">124.623</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">4</oasis:entry>
         <oasis:entry colname="col6">17</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M278" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0019</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_OM1_5200</oasis:entry>
         <oasis:entry colname="col2">5232</oasis:entry>
         <oasis:entry colname="col3">20.297</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M279" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">151.208</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">120</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M280" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0015</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_OM2_5400</oasis:entry>
         <oasis:entry colname="col2">5445</oasis:entry>
         <oasis:entry colname="col3">20.704</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M281" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">146.272</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">103</oasis:entry>
         <oasis:entry colname="col6">17</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M282" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0014</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_OM3_5400</oasis:entry>
         <oasis:entry colname="col2">5438</oasis:entry>
         <oasis:entry colname="col3">21.181</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M283" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">141.568</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">24</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M284" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0010</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_OM4_5300</oasis:entry>
         <oasis:entry colname="col2">5367</oasis:entry>
         <oasis:entry colname="col3">21.577</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M285" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">136.909</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">14</oasis:entry>
         <oasis:entry colname="col6">10</oasis:entry>
         <oasis:entry colname="col7">full</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M286" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0005</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_OM5_5000</oasis:entry>
         <oasis:entry colname="col2">5148</oasis:entry>
         <oasis:entry colname="col3">23.647</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M287" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">133.358</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">5</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M288" display="inline"><mml:mn mathvariant="normal">0.0003</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_OM6_4700</oasis:entry>
         <oasis:entry colname="col2">4793</oasis:entry>
         <oasis:entry colname="col3">24.071</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M289" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">128.560</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">4</oasis:entry>
         <oasis:entry colname="col6">17</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
         <oasis:entry colname="col8"><inline-formula><mml:math id="M290" display="inline"><mml:mn mathvariant="normal">0.0003</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP4_OM7_4800</oasis:entry>
         <oasis:entry colname="col2">4934</oasis:entry>
         <oasis:entry colname="col3">26.824</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M291" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">124.615</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">4</oasis:entry>
         <oasis:entry colname="col6">17</oasis:entry>
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         <oasis:entry colname="col8"><inline-formula><mml:math id="M292" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0008</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP5_CR1_4300</oasis:entry>
         <oasis:entry colname="col2">4306</oasis:entry>
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         <oasis:entry colname="col4"><inline-formula><mml:math id="M293" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">124.368</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
         <oasis:entry colname="col5">4</oasis:entry>
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         <oasis:entry colname="col8"><inline-formula><mml:math id="M294" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0010</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
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         <oasis:entry colname="col5">4</oasis:entry>
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         <oasis:entry colname="col8"><inline-formula><mml:math id="M296" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0014</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
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       </oasis:row>
       <oasis:row>
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         <oasis:entry colname="col2">4310</oasis:entry>
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       </oasis:row>
       <oasis:row>
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       </oasis:row>
       <oasis:row>
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       </oasis:row>
       <oasis:row>
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       </oasis:row>
       <oasis:row>
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         <oasis:entry colname="col3">31.824</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M307" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">124.364</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
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         <oasis:entry colname="col8"><inline-formula><mml:math id="M308" display="inline"><mml:mn mathvariant="normal">0.0001</mml:mn></mml:math></inline-formula></oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP5_OM2_4600</oasis:entry>
         <oasis:entry colname="col2">4636</oasis:entry>
         <oasis:entry colname="col3">28.704</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M309" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">129.026</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
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       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">TP5_OM5_5200</oasis:entry>
         <oasis:entry colname="col2">5232</oasis:entry>
         <oasis:entry colname="col3">25.795</oasis:entry>
         <oasis:entry colname="col4"><inline-formula><mml:math id="M311" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">145.994</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
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         <oasis:entry colname="col8"><inline-formula><mml:math id="M312" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0012</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
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       <oasis:row>
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       <oasis:row>
         <oasis:entry colname="col1">TP6_MA5_4500</oasis:entry>
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         <oasis:entry colname="col3"><inline-formula><mml:math id="M328" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.632</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
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       <oasis:row>
         <oasis:entry colname="col1">TP6_OM4_4700</oasis:entry>
         <oasis:entry colname="col2">4651</oasis:entry>
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         <oasis:entry colname="col2">4465</oasis:entry>
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         <oasis:entry colname="col8"><inline-formula><mml:math id="M339" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.0008</mml:mn></mml:mrow></mml:math></inline-formula></oasis:entry>
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       <oasis:row>
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       <oasis:row>
         <oasis:entry colname="col1">TP6_OM7_4900</oasis:entry>
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         <oasis:entry colname="col5">18</oasis:entry>
         <oasis:entry colname="col6">11</oasis:entry>
         <oasis:entry colname="col7">tied</oasis:entry>
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   </oasis:tgroup></oasis:table></table-wrap>


</app>

<app id="App1.Ch1.S2">
  <label>Appendix B</label><title>Sensitivity analysis for threshold value (TH method) and <inline-formula><mml:math id="M346" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> value (DP method)</title>
      <p id="d2e6775">We used the collected profiles of temperature and pressure to test the optimal threshold value to use for the BML thickness derivation. We used the Quality Index methodology (Eq. 1 in the main text) to choose the appropriate threshold value based on <xref ref-type="bibr" rid="bib1.bibx52" id="text.134"/> as it was being applied to the same method. The conservative temperature of 0.003 <inline-formula><mml:math id="M347" 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> provided the highest mean QI for both the TPT voyage dataset and the GO-SHIP repeat hydrographic sections of P02 and P16 (Fig. <xref ref-type="fig" rid="FB1"/>).</p>

      <fig id="FB1" specific-use="star"><label>Figure B1</label><caption><p id="d2e6795">Histogram plots of the quality index values from the threshold BML height based on different threshold values of conservative temperature (<inline-formula><mml:math id="M348" display="inline"><mml:mi mathvariant="normal">Θ</mml:mi></mml:math></inline-formula>) for TPT profiles as <bold>(a)</bold> 0.001 <inline-formula><mml:math id="M349" 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>, <bold>(b)</bold> 0.002 <inline-formula><mml:math id="M350" 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>, <bold>(c)</bold> 0.003 <inline-formula><mml:math id="M351" 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>, <bold>(d)</bold> 0.004 <inline-formula><mml:math id="M352" 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 <bold>(e)</bold> 0.005 <inline-formula><mml:math id="M353" 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 for the GO-SHIP profiles as <bold>(f)</bold> 0.003 <inline-formula><mml:math id="M354" 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 <bold>(g)</bold> 0.005 <inline-formula><mml:math id="M355" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">°</mml:mi><mml:mi mathvariant="normal">C</mml:mi></mml:mrow></mml:math></inline-formula>.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f12.png"/>

      </fig>

      <p id="d2e6904">The Douglas–Peucker split-and-merge algorithm <xref ref-type="bibr" rid="bib1.bibx1" id="paren.135"/> reduces the number of points in a curve, approximating it by a series of points. An <inline-formula><mml:math id="M356" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> value between 0 and 1 is required to specify the similarity between the curve and the points, i.e. the smaller the epsilon, the more similar the curve. We tested three TPT Expedition profiles with <inline-formula><mml:math id="M357" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> values between 0.001 and 0.01 (Fig. <xref ref-type="fig" rid="FB2"/> for site <inline-formula><mml:math id="M358" display="inline"><mml:mrow><mml:mtext>TP</mml:mtext><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">_</mml:mi><mml:mtext>OM</mml:mtext><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">_</mml:mi><mml:mn mathvariant="normal">5400</mml:mn></mml:mrow></mml:math></inline-formula>). We chose <inline-formula><mml:math id="M359" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.002</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M360" display="inline"><mml:mrow><mml:mi mathvariant="italic">ε</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.008</mml:mn></mml:mrow></mml:math></inline-formula> as the two options with the most variability in results to calculate the BML height. This gave us methods DP02 and DP08 respectively.</p>

      <fig id="FB2" specific-use="star"><label>Figure B2</label><caption><p id="d2e6974">Douglas–Peuker Algorithm output (approximated, in blue) for different values of <inline-formula><mml:math id="M361" display="inline"><mml:mi mathvariant="italic">ε</mml:mi></mml:math></inline-formula> and original profile of <inline-formula><mml:math id="M362" display="inline"><mml:mrow><mml:mtext>TP</mml:mtext><mml:mn mathvariant="normal">2</mml:mn><mml:mi mathvariant="italic">_</mml:mi><mml:mtext>OM</mml:mtext><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">_</mml:mi><mml:mn mathvariant="normal">5400</mml:mn></mml:mrow></mml:math></inline-formula> in red as an example.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f13.png"/>

      </fig>

      <fig id="FB3" specific-use="star"><label>Figure B3</label><caption><p id="d2e7012">GO-SHIP (circle) and TPT (triangle) site variables of the <bold>(a–d)</bold> mean slope over 25, 50, 100 and 200 <inline-formula><mml:math id="M363" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> buffer zones respectively (deg) and the <bold>(e–h)</bold> standard deviation of slope over the 25, 50, 100 and 200 <inline-formula><mml:math id="M364" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> buffer zones respectively, <bold>(i–l)</bold> the mean normalised terrain roughness index (TRI) over the 25, 50, 100 and 200 <inline-formula><mml:math id="M365" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula> buffer zones respectively and <bold>(m–p)</bold> displaying the normalised standard deviation of the TRI.  For the multiple TPT sites within close proximity (3 <inline-formula><mml:math id="M366" display="inline"><mml:mrow class="unit"><mml:mi mathvariant="normal">km</mml:mi></mml:mrow></mml:math></inline-formula>), TRI and slope are on the centre point. The background regional bathymetry is from the Global Multi-Resolution Topography (GMRT) Synthesis Released CC BY 4.0 Deep <inline-formula><mml:math id="M367" display="inline"><mml:mo>|</mml:mo></mml:math></inline-formula> Attribution 4.0 International <inline-formula><mml:math id="M368" display="inline"><mml:mo>|</mml:mo></mml:math></inline-formula> Creative Commons <xref ref-type="bibr" rid="bib1.bibx78" id="text.136"/>.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/22/257/2026/os-22-257-2026-f14.jpg"/>

      </fig>


</app>
  </app-group><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d2e7089">GO-SHIP profiles were obtained through the CLIVAR and Carbon Hydrographic Data Office (CCHDO, <uri>https://cchdo.ucsd.edu/</uri>, last access: 29 November 2024) for cruise numbers: 31WTTUNES_3, 325020060213, 33R0150410, 49K6K9401_1, 318M200406 and 318M20130321. The gridded GO-SHIP product from <xref ref-type="bibr" rid="bib1.bibx41" id="text.137"/> was also accessed, used within figures and available on Zenodo at <ext-link xlink:href="https://doi.org/10.5281/zenodo.13315689" ext-link-type="DOI">10.5281/zenodo.13315689</ext-link> <xref ref-type="bibr" rid="bib1.bibx42" id="paren.138"/>. The temperature-pressure sensor observations collected over the Trans-Pacific Transit Expedition on board R/V <italic>Dagon</italic> are currently available on Zenodo at <ext-link xlink:href="https://doi.org/10.5281/zenodo.15536316" ext-link-type="DOI">10.5281/zenodo.15536316</ext-link> <xref ref-type="bibr" rid="bib1.bibx45" id="paren.139"/>. The global maps of internal tide generation and dissipation as outputs from <xref ref-type="bibr" rid="bib1.bibx14" id="text.140"/> are available from SEANOE at <ext-link xlink:href="https://doi.org/10.17882/58105" ext-link-type="DOI">10.17882/58105</ext-link> <xref ref-type="bibr" rid="bib1.bibx13" id="paren.141"/>.</p>
  </notes><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d2e7126">JK: Data curation, Formal Analysis, Investigation, Methodology, Writing – original draft, Writing – reviewing and editing. DH: Data curation, Writing – reviewing and editing. NJ: Methodology, Investigation, Writing – reviewing and editing. JO: Methodology, Writing – reviewing and editing. TS: Methodology, Writing – reviewing and editing. TB: Chief Scientist on Leg 3. HS: Chief Scientist on Leg 6. AJ: Chief Scientist on Leg 1, 2 and 5, Funding acquisition.  All authors reviewed the manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e7132">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="d2e7138">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="d2e7144">The authors would like to thank Inkfish LLC for their continuing support and logistics. We thank Captain Stuart Buckle, Captain Alan Dankool, Captain Jim Wales, Captain Ali Benarabi, the crew and the company onboard R/V <italic>Dagon</italic> for their crucial role in the successful completion of the Trans-Pacific Transit Expedition 2023–2024. Furthermore, we thank the hydrographic surveyors Jaya Roperez, Erin Heffron and Tion Uriam; and the science, submersible, and lander teams (Ryan Beecroft, Murray Blom, Bruce Brandt, Chris Corcos, Megan Cundy, Samuel Dews, Shane Eigler, Paul Fairclough, Brett Gonzalez, Andrew Henderson, Jeff Huck, Reuben Kent, Catriona Macdonald, Tim MacDonald, Alfredo Marchio, Shane Muhl, Georgia Nester, Gary Ogden, Alan Scott, Sarah Searson, Luke Siebermaier, Melanie Stott, Kate Wawatai, Brett Wilkins, Eddo Van Kolck, and Jennifer Wainwright).</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d2e7152">The author(s) declare that financial support was received for the research and/or publication of this article. This research was funded by the marine research organisation Inkfish LLC, as part of its Open Ocean Program. The funder was not involved in the study design, collection, analysis, interpretation of data, the writing of this article, or the decision to submit it for publication. Taimoor Sohail acknowledges funding from the Australian Research Council Discovery Project DP240101274.</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e7158">This paper was edited by Ilker Fer and reviewed by two anonymous referees.</p>
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