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  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">Ecological Safety of Coastal and Shelf Zones of Sea</journal-id>
      <journal-title-group>
        <journal-title>Ecological Safety of Coastal and Shelf Zones of Sea</journal-title>
      </journal-title-group>
      <issn publication-format="print">2413-5577</issn>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="publisher-id">20240303</article-id>

      <article-categories>
        <subj-group subj-group-type="article-type">
          <subject>Research Article</subject>
        </subj-group>
      </article-categories>

      <title-group>
        <article-title>Estimation of Carbon Dioxide Fluxes through the Surface of the Black Sea from Numerical Simulation Results</article-title>
      </title-group>

      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Dorofeev</surname>
            <given-names>V. L.</given-names>
          </name>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <email>viktor.dorofeev@mhi-ras.ru</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Sukhikh</surname>
            <given-names>L. I.</given-names>
          </name>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <email>l.sukhikh@gmail.com</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
      </contrib-group>

      <aff id="aff1">
        <institution>Marine Hydrophysical Institute of RAS</institution>
        <addr-line>Sevastopol</addr-line>
        <country country="RU">Russia</country>
      </aff>

      <pub-date date-type="pub" iso-8601-date="2024-09-25" publication-format="electronic">
        <day>25</day>
        <month>09</month>
        <year>2024</year>
      </pub-date>
      <volume>2024</volume>
      <issue>3</issue>
      <fpage>36</fpage>
      <lpage>48</lpage>

      <history>
        <date date-type="received" iso-8601-date="2024-01-25">
          <day>25</day>
          <month>01</month>
          <year>2024</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="2024-06-17">
          <day>17</day>
          <month>06</month>
          <year>2024</year>
        </date>
        <date date-type="accepted" iso-8601-date="2024-03-25">
          <day>25</day>
          <month>03</month>
          <year>2024</year>
        </date>
      </history>

      <permissions>
        <copyright-statement>Copyright © 2024, V. L. Dorofeev, L. I. Sukhikh</copyright-statement>
        <copyright-year>2024</copyright-year>
        <copyright-holder>V. L. Dorofeev, L. I. Sukhikh</copyright-holder>
        <ali:free_to_read xmlns:ali="http://www.niso.org/schemas/ali/1.0/"/>
        <license>
          <ali:license_ref xmlns:ali="http://www.niso.org/schemas/ali/1.0/">https://creativecommons.org/licenses/by-nc/4.0/</ali:license_ref>
        </license>
      </permissions>
      <self-uri xlink:href="https://ecological-safety.ru/en/repository/issues/2024/03/03/" xlink:title="Page of article">https://ecological-safety.ru/en/repository/issues/2024/03/03/</self-uri>

      <abstract>
        <p>Based on numerical simulation, the paper studies the spatiotemporal distribution of CO₂ fluxes through the free surface of the Black Sea. The basic equation for solving this problem is the three-dimensional evolutionary transport-diffusion equation for the concentration of dissolved inorganic carbon. The simulation uses hydrodynamic fields resulting from a previous physical reanalysis as input parameters. A model of the lower level of the Black-Sea ecosystem food chain is used to describe the influence of biological factors on the dissolved carbon dioxide distribution. The concentration and equilibrium partial pressure of dissolved carbon dioxide in the surface layer of the Black Sea were calculated from the numerical simulation results. It is shown that the time dependence of these quantities is highly seasonal. The seawater temperature significantly affects the solubility of carbon dioxide and therefore its fluxes. The equilibrium partial pressure of carbon dioxide averaged over the area of the Black Sea is minimal in January-February and maximal in June-July. Accordingly, in the warm season, the flux of carbon dioxide is directed mainly from the sea to the atmosphere; in the cold season, the sea mainly absorbs carbon dioxide. Biological factors also influence the CO₂ content in the sea. Thus, at the beginning of the year, a high concentration of phytoplankton is observed almost throughout the entire Black Sea water area, which is why the absorption of carbon dioxide predominates during photosynthesis. In summer, the release of carbon dioxide predominates due to plankton respiration and oxidation of organic matter. The simulation results are in fairly good agreement with in situ measurements of the partial pressure of dissolved carbon dioxide obtained during scientific cruises.</p>
      </abstract>

      <kwd-group>
        <kwd>carbonate system</kwd>
        <kwd>carbon dioxide</kwd>
        <kwd>partial pressure of carbon dioxide</kwd>
        <kwd>Black Sea</kwd>
        <kwd>marine ecosystem</kwd>
        <kwd>numerical simulation</kwd>
      </kwd-group>

      <funding-group>
        <funding-statement>The work was carried out under topic of state assignment of FSBSI FRC MHI FNNN-2023-0001. The authors thank the staff of the Biogeochemistry Department of the FSBSI FRC MHI for providing the results of field data processing.</funding-statement>
      </funding-group>

      <author-notes>
        <p><bold>About the authors:</bold></p>
        <p><bold>Viktor L. Dorofeev</bold>, Leading Research Associate, Marine Hydrophysical Institute of RAS (2 Kapitanskaya St., Sevastopol, 299011, Russian Federation), PhD (Phys.-Math.), ResearcherID: G-1050-2014, <email>viktor.dorofeev@mhi-ras.ru</email></p>
        <p><bold>Larisa I. Sukhikh</bold>, Research Associate, Marine Hydrophysical Institute of RAS (2 Kapitanskaya St., Sevastopol, 299011, Russian Federation), ResearcherID: M-4381-2018, <email>l.sukhikh@gmail.com</email></p>
        <p><bold>Contribution of the authors:</bold></p>
        <p><bold>Viktor L. Dorofeev</bold> – general scientific supervision of the study, formulation of the goals and objectives of the study, carrying out numerical simulations, analysis of the obtained results and their interpretation</p>
        <p><bold>Larisa I. Sukhikh</bold> – literature review, numerical simulations, analysis of the results</p>
        <p><italic>All the authors have read and approved the final manuscript.</italic></p>
      </author-notes>
    </article-meta>
  </front>

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  <back>
    <ref-list>
      <title>REFERENCES</title>
      <ref id="B1">
        <label>1.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Zhorov</surname><given-names>V.A.</given-names></name>
            <name><surname>Abakumova</surname><given-names>T.N.</given-names></name>
            <name><surname>Sovga</surname><given-names>E.E.</given-names></name>
            <name><surname>Lyashenko</surname><given-names>S.V.</given-names></name>
          </person-group>
          <article-title>On CO₂ Exchange between the Sea and the Atmosphere in Some Regions of the Black Sea</article-title>
          <source>Okeanologiya</source>
          <year>1981</year>
          <volume>21</volume>
          <issue>1</issue>
          <fpage>55</fpage>
          <lpage>62</lpage>
          <comment>(in Russian)</comment>
        </element-citation>
      </ref>
      <ref id="B2">
        <label>2.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Khoruzhiy</surname><given-names>D.S.</given-names></name>
            <name><surname>Konovalov</surname><given-names>S.K.</given-names></name>
          </person-group>
          <article-title>Diurnal Variation and Inter-Diurnal Changes of Carbonic Acid and Dissolved Inorganic Carbon Content in the Black Sea Coastal Waters</article-title>
          <source>Morskyy Gidrofizicheskiy Zhurnal</source>
          <year>2014</year>
          <issue>1</issue>
          <fpage>28</fpage>
          <lpage>43</lpage>
          <comment>(in Russian)</comment>
        </element-citation>
      </ref>
      <ref id="B3">
        <label>3.</label>
        <element-citation publication-type="book">
          <person-group person-group-type="author">
            <name><surname>Konovalov</surname><given-names>S.K.</given-names></name>
            <name><surname>Kondratev</surname><given-names>S.I.</given-names></name>
            <name><surname>Khoruzhiy</surname><given-names>D.S.</given-names></name>
            <name><surname>Medvedev</surname><given-names>E.V.</given-names></name>
            <name><surname>Moiseenko</surname><given-names>O.G.</given-names></name>
          </person-group>
          <article-title>Total Inorganic Carbon, Carbonate System and Carbon Dioxide Fluxes in the Coastal Zone of the Southern Coast of Crimea: Monitoring, Characteristics, Dynamics</article-title>
          <source>Monitoring of the Coastal Zone in the Black Sea Experimental Sub-Satellite Testing Area</source>
          <year>2014</year>
          <fpage>250</fpage>
          <lpage>271</lpage>
          <comment>(in Russian)</comment>
        </element-citation>
      </ref>
      <ref id="B4">
        <label>4.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Khoruzhii</surname><given-names>D.S.</given-names></name>
          </person-group>
          <article-title>Variability of Equilibrium Partial Pressure of Carbon Dioxide (pCO₂) and Concentration of Dissolved Inorganic Carbon (TCO₂) in the Black Sea Coastal Waters in 2010–2014</article-title>
          <source>Physical Oceanography</source>
          <year>2016</year>
          <issue>4</issue>
          <fpage>34</fpage>
          <lpage>46</lpage>
          <pub-id pub-id-type="doi">10.22449/1573-160X-2016-4-34-46</pub-id>
        </element-citation>
      </ref>
      <ref id="B5">
        <label>5.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Orekhova</surname><given-names>N.A.</given-names></name>
            <name><surname>Konovalov</surname><given-names>S.K.</given-names></name>
            <name><surname>Medvedev</surname><given-names>E.V.</given-names></name>
          </person-group>
          <article-title>Features of Inorganic Carbon Regional Balance in Marine Ecosystems under Anthropogenic Pressure</article-title>
          <source>Physical Oceanography</source>
          <year>2019</year>
          <volume>26</volume>
          <issue>3</issue>
          <fpage>225</fpage>
          <lpage>235</lpage>
          <pub-id pub-id-type="doi">10.22449/1573-160X-2019-3-225-235</pub-id>
        </element-citation>
      </ref>
      <ref id="B6">
        <label>6.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Silkin</surname><given-names>V.A.</given-names></name>
            <name><surname>Podymov</surname><given-names>O.I.</given-names></name>
            <name><surname>Lifanchuk</surname><given-names>A.V.</given-names></name>
          </person-group>
          <article-title>Biological Carbon Pump in the Black Sea</article-title>
          <source>Hydrosphere Ecology</source>
          <year>2022</year>
          <issue>2</issue>
          <fpage>69</fpage>
          <lpage>92</lpage>
          <pub-id pub-id-type="doi">10.33624/2587-9367-2022-2(8)-69-92</pub-id>
          <comment>(in Russian)</comment>
        </element-citation>
      </ref>
      <ref id="B7">
        <label>7.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Varenik</surname><given-names>A.V.</given-names></name>
            <name><surname>Kondratyev</surname><given-names>S.I.</given-names></name>
            <name><surname>Medvedev</surname><given-names>E.V.</given-names></name>
            <name><surname>Khoruzhii</surname><given-names>D.S.</given-names></name>
            <name><surname>Orekhova</surname><given-names>N.A.</given-names></name>
          </person-group>
          <article-title>Characteristics of State and Evolution of the Black Sea Hydrochemical Structure</article-title>
          <source>Physical Oceanography</source>
          <year>2023</year>
          <volume>30</volume>
          <issue>6</issue>
          <fpage>826</fpage>
          <lpage>850</lpage>
        </element-citation>
      </ref>
      <ref id="B8">
        <label>8.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Grégoire</surname><given-names>M.</given-names></name>
            <name><surname>Soetaert</surname><given-names>K.</given-names></name>
            <name><surname>Nezlin</surname><given-names>N.</given-names></name>
            <name><surname>Kostianoy</surname><given-names>A.</given-names></name>
          </person-group>
          <article-title>Modeling the Nitrogen Cycling and Plankton Productivity in an Enclosed Environment (The Black Sea) Using a Three-Dimensional Coupled Hydrodynamical-Ecosystem Model</article-title>
          <source>Journal of Geophysical Research: Oceans</source>
          <year>2004</year>
          <volume>109</volume>
          <issue>C5</issue>
          <fpage>C05007</fpage>
          <pub-id pub-id-type="doi">10.1029/2001JC001014</pub-id>
        </element-citation>
      </ref>
      <ref id="B9">
        <label>9.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Tsiaras</surname><given-names>K.P.</given-names></name>
            <name><surname>Kourafalou</surname><given-names>V.H.</given-names></name>
            <name><surname>Davidov</surname><given-names>A.</given-names></name>
            <name><surname>Staneva</surname><given-names>J.</given-names></name>
          </person-group>
          <article-title>A Three-Dimensional Coupled Model of the Western Black Sea Plankton Dynamics: Seasonal Variability and Comparison to SeaWiFS Data</article-title>
          <source>Journal of Geophysical Research: Oceans</source>
          <year>2008</year>
          <volume>113</volume>
          <issue>C7</issue>
          <fpage>C07007</fpage>
          <pub-id pub-id-type="doi">10.1029/2006JC003959</pub-id>
        </element-citation>
      </ref>
      <ref id="B10">
        <label>10.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Dorofeev</surname><given-names>V.L.</given-names></name>
          </person-group>
          <article-title>Modeling of Decadal Variations in the Black-Sea Ecosystem</article-title>
          <source>Physical Oceanography</source>
          <year>2009</year>
          <volume>19</volume>
          <issue>6</issue>
          <fpage>400</fpage>
          <lpage>409</lpage>
          <pub-id pub-id-type="doi">10.1007/s11110-010-9062-6</pub-id>
        </element-citation>
      </ref>
      <ref id="B11">
        <label>11.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Capet</surname><given-names>A.</given-names></name>
            <name><surname>Meysman</surname><given-names>F.J.R.</given-names></name>
            <name><surname>Akoumaniak</surname><given-names>I.</given-names></name>
            <name><surname>Soetaert</surname><given-names>K.</given-names></name>
            <name><surname>Grégoire</surname><given-names>M.</given-names></name>
          </person-group>
          <article-title>Integrating Sediment Biogeochemistry into 3D Oceanic Models: A Study of Benthic-Pelagic Coupling in the Black Sea</article-title>
          <source>Ocean Modelling</source>
          <year>2016</year>
          <volume>101</volume>
          <fpage>83</fpage>
          <lpage>100</lpage>
          <pub-id pub-id-type="doi">10.1016/j.ocemod.2016.03.006</pub-id>
        </element-citation>
      </ref>
      <ref id="B12">
        <label>12.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Aumont</surname><given-names>O.</given-names></name>
            <name><surname>Ethé</surname><given-names>C.</given-names></name>
            <name><surname>Tagliabue</surname><given-names>A.</given-names></name>
            <name><surname>Bopp</surname><given-names>L.</given-names></name>
            <name><surname>Gehlen</surname><given-names>M.</given-names></name>
          </person-group>
          <article-title>PISCES-v2: An Ocean Biogeochemical Model for Carbon and Ecosystem Studies</article-title>
          <source>Geoscientific Model Development</source>
          <year>2015</year>
          <volume>8</volume>
          <issue>8</issue>
          <fpage>2465</fpage>
          <lpage>2513</lpage>
          <pub-id pub-id-type="doi">10.5194/gmd-8-2465-2015</pub-id>
        </element-citation>
      </ref>
      <ref id="B13">
        <label>13.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Van den Meersche</surname><given-names>K.</given-names></name>
            <name><surname>Middelburg</surname><given-names>J.J.</given-names></name>
            <name><surname>Soetaert</surname><given-names>K.</given-names></name>
            <name><surname>Van Rijswijk</surname><given-names>P.</given-names></name>
            <name><surname>Boschker</surname><given-names>H.T.S.</given-names></name>
            <name><surname>Heip</surname><given-names>C.H.R.</given-names></name>
          </person-group>
          <article-title>Carbon Nitrogen Coupling and Algal-Bacterial Interactions during an Experimental Bloom: Modeling a ¹³C Tracer Experiment</article-title>
          <source>Limnology and Oceanography</source>
          <year>2004</year>
          <volume>49</volume>
          <issue>3</issue>
          <fpage>862</fpage>
          <lpage>878</lpage>
          <pub-id pub-id-type="doi">10.4319/lo.2004.49.3.0862</pub-id>
        </element-citation>
      </ref>
      <ref id="B14">
        <label>14.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Dorofeyev</surname><given-names>V.</given-names></name>
            <name><surname>Sukhikh</surname><given-names>L.</given-names></name>
          </person-group>
          <article-title>A Model for Monitoring the Evolution of the Black Sea Ecosystem on the Basis of Remote Sensing Data Assimilation</article-title>
          <source>International Journal of Remote Sensing</source>
          <year>2018</year>
          <volume>39</volume>
          <issue>24</issue>
          <fpage>9339</fpage>
          <lpage>9355</lpage>
          <pub-id pub-id-type="doi">10.1080/01431161.2018.1523589</pub-id>
        </element-citation>
      </ref>
      <ref id="B15">
        <label>15.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Dorofeev</surname><given-names>V.L.</given-names></name>
            <name><surname>Sukhikh</surname><given-names>L.I.</given-names></name>
          </person-group>
          <article-title>Studying Long-Term Variations in Black-Sea Ecosystem Based on the Assimilation of Remote Sensing Data in a Numerical Model</article-title>
          <source>Water Resources</source>
          <year>2019</year>
          <volume>46</volume>
          <issue>1</issue>
          <fpage>65</fpage>
          <lpage>75</lpage>
          <pub-id pub-id-type="doi">10.1134/S0097807819010032</pub-id>
        </element-citation>
      </ref>
      <ref id="B16">
        <label>16.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Grégoire</surname><given-names>M.</given-names></name>
            <name><surname>Raick</surname><given-names>C.</given-names></name>
            <name><surname>Soetaert</surname><given-names>K.</given-names></name>
          </person-group>
          <article-title>Numerical Modeling of the Central Black Sea Ecosystem Functioning During the Eutrophication Phase</article-title>
          <source>Progress in Oceanography</source>
          <year>2008</year>
          <volume>76</volume>
          <issue>3</issue>
          <fpage>286</fpage>
          <lpage>333</lpage>
          <pub-id pub-id-type="doi">10.1016/j.pocean.2008.01.002</pub-id>
        </element-citation>
      </ref>
      <ref id="B17">
        <label>17.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Dorofeev</surname><given-names>V.L.</given-names></name>
            <name><surname>Sukhikh</surname><given-names>L.I.</given-names></name>
          </person-group>
          <article-title>Analysis of Long-Term Variability of Hydrodynamic Fields in the Upper 200-Meter Layer of the Black Sea Based on the Reanalysis Results</article-title>
          <source>Physical Oceanography</source>
          <year>2023</year>
          <volume>30</volume>
          <issue>5</issue>
          <fpage>581</fpage>
          <lpage>593</lpage>
        </element-citation>
      </ref>
      <ref id="B18">
        <label>18.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Millero</surname><given-names>F.J.</given-names></name>
          </person-group>
          <article-title>The Marine Inorganic Carbon Cycle</article-title>
          <source>Chemical Reviews</source>
          <year>2007</year>
          <volume>107</volume>
          <issue>2</issue>
          <fpage>308</fpage>
          <lpage>341</lpage>
          <pub-id pub-id-type="doi">10.1021/cr0503557</pub-id>
        </element-citation>
      </ref>
      <ref id="B19">
        <label>19.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Takahashi</surname><given-names>T.</given-names></name>
            <name><surname>Sutherland</surname><given-names>S.C.</given-names></name>
            <name><surname>Wanninkhof</surname><given-names>R.</given-names></name>
            <name><surname>Sweeney</surname><given-names>C.</given-names></name>
            <name><surname>Feely</surname><given-names>R.A.</given-names></name>
            <name><surname>Chipman</surname><given-names>D.W.</given-names></name>
            <name><surname>Hales</surname><given-names>B.</given-names></name>
            <name><surname>Friederich</surname><given-names>G.</given-names></name>
            <name><surname>Chavez</surname><given-names>F.</given-names></name>
            <etal/>
          </person-group>
          <article-title>Climatological Mean and Decadal Changes in Surface Ocean pCO₂ and Net Sea-Air CO₂ Flux over the Global Oceans</article-title>
          <source>Deep-Sea Research II: Topical Studies in Oceanography</source>
          <year>2009</year>
          <volume>56</volume>
          <issue>8-10</issue>
          <fpage>554</fpage>
          <lpage>577</lpage>
          <pub-id pub-id-type="doi">10.1016/j.dsr2.2008.12.009</pub-id>
        </element-citation>
      </ref>
      <ref id="B20">
        <label>20.</label>
        <element-citation publication-type="paper-conference">
          <person-group person-group-type="author">
            <name><surname>Zabegaev</surname><given-names>I.A.</given-names></name>
            <name><surname>Medvedev</surname><given-names>E.V.</given-names></name>
          </person-group>
          <article-title>Equilibrium Partial Pressure of Carbon Dioxide in the Surface Water Layer of the Northern Black Sea Based on Direct Observations in 2017</article-title>
          <source>Seas of Russia: Fundamental and Applied Studies. Proceedings of the All-Russian Scientific Conference</source>
          <year>2019</year>
          <fpage>76</fpage>
          <lpage>78</lpage>
          <comment>(in Russian)</comment>
        </element-citation>
      </ref>
    </ref-list>
  </back>
</article>
