<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.3" xml:lang="en">
  <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">20230204</article-id>
      
      <article-categories>
        <subj-group subj-group-type="article-type">
          <subject>Research Article</subject>
        </subj-group>
      </article-categories>

      <title-group>
        <article-title>Variational Identification of the Initial Field of Chlorophyll A Concentration in the Transport Model according to Remote Sensing Data</article-title>
      </title-group>

      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Kochergin</surname>
            <given-names>V. S.</given-names>
          </name>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <email>vskocher@gmail.com</email>
          <xref ref-type="aff" rid="aff1"/>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Kochergin</surname>
            <given-names>S. V.</given-names>
          </name>
          <address>
            <country country="RU">Russian Federation</country>
          </address>
          <email>ko4ep@mail.ru</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">Russian Federation</country>
      </aff>

      <pub-date date-type="pub" iso-8601-date="2023-06-26" publication-format="electronic">
        <day>26</day>
        <month>06</month>
        <year>2023</year>
      </pub-date>
      <volume>2023</volume>
      <issue>2</issue>
      <fpage>61</fpage>
      <lpage>70</lpage>

      <history>
        <date date-type="received" iso-8601-date="2023-01-19">
          <day>19</day>
          <month>01</month>
          <year>2023</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="2023-05-03">
          <day>03</day>
          <month>05</month>
          <year>2023</year>
        </date>
        <date date-type="accepted" iso-8601-date="2023-03-16">
          <day>16</day>
          <month>03</month>
          <year>2023</year>
        </date>
      </history>

      <permissions>
        <copyright-statement>Copyright © 2023, V. S. Kochergin, S. V. Kochergin</copyright-statement>
        <copyright-year>2023</copyright-year>
        <copyright-holder>V. S. Kochergin, S. V. Kochergin</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/2023/02/04/" xlink:title="Page of article">https://ecological-safety.ru/en/repository/issues/2023/02/04/</self-uri>

      <abstract>
        <p>The work aims at construction of chlorophyll a fields based on variational assimilation of available satellite information for a few days in a transport model. Such information is the most real-time, but most often it has omissions (sometimes significant) in its structure due to the scattering effect of clouds, glares, etc. Therefore, obtaining reliable fields taking into account the available information for the Black Sea is an important and urgent task. In the numerical implementation of the transport model and variational method of measurement data assimilation, the results of calculations based on the MHI dynamic model for the Black Sea were used. In the numerical implementation of the variational assimilation algorithm, iterative gradient methods are used, and the solution of the adjoint problem is used to construct the gradient of the cost function in the parameter space. As a result of the calculations, a field of chlorophyll a concentration was obtained for almost the entire Black Sea area consistent with the measurement data. The paper implements a variational algorithm for the satellite information assimilation, which made it possible to obtain a chlorophyll a concentration field for the Black Sea area, taking into account incomplete coverage with observational data. The procedure can be used to determine concentration fields of various suspended substances in the sea based on data distributed over time and space.</p>
      </abstract>

      <kwd-group>
        <kwd>chlorophyll a concentration</kwd>
        <kwd>variational algorithm</kwd>
        <kwd>adjoint problem</kwd>
        <kwd>measurement data assimilation</kwd>
        <kwd>Black Sea</kwd>
        <kwd>space-time interpolation</kwd>
      </kwd-group>

      <funding-group>
        <funding-statement>The work was carried out under state assignment on topic FNNN-2021-0005 "Complex interdisciplinary studies of oceanologic processes which determine functioning and evolution of ecosystems in the coastal zones of the Black Sea and the Sea of Azov" (code "Coastal research").</funding-statement>
      </funding-group>

      <author-notes>
        <p><bold>About the authors:</bold></p>
        <p><bold>Vladimir S. Kochergin</bold>, Junior Research Associate, Marine Hydrophysical Institute of RAS (2 Kapitanskaya St., Sevastopol, 299011, Russian Federation), <bold>ORCID: 0000-0002-6767-1218</bold>, <bold>ResearcherID: AAG-4209-2020</bold>, <email>vskocher@gmail.com</email></p>
        <p><bold>Sergey V. Kochergin</bold>, Senior Research Associate, Marine Hydrophysical Institute of RAS (2 Kapitanskaya St., Sevastopol, 299011, Russian Federation), Ph.D. (Phys-Math.), <bold>ORCID: 0000-0002-3583-8351</bold>, <bold>ResearcherID: AAG-4206-2020</bold>, <email>ko4ep@mail.ru</email></p>
        <p><bold>Contribution of the authors:</bold></p>
        <p><bold>Vladimir S. Kochergin</bold> – problem statement, programme code writing and debugging, data preparation, analysis of calculation results, article text preparation</p>
        <p><bold>Sergey V. Kochergin</bold> – problem statement, analysis of calculation results, article text preparation</p>
        <p><italic>All the authors have read and approved the final manuscript.</italic></p>
      </author-notes>
    </article-meta>
  </front>

  <body>
    <p>Article text not included.</p>
  </body>

  <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>Demyshev</surname><given-names>S.G.</given-names></name>
          </person-group>
          <article-title>A Numerical Model of Online Forecasting Black Sea Currents</article-title>
          <source>Izvestiya, Atmospheric and Oceanic Physics</source>
          <year>2012</year>
          <volume>48</volume>
          <issue>1</issue>
          <fpage>120</fpage>
          <lpage>132</lpage>
          <pub-id pub-id-type="doi">10.1134/S0001433812010212</pub-id>
        </element-citation>
      </ref>
      <ref id="B2">
        <label>2.</label>
        <element-citation publication-type="book-chapter">
          <person-group person-group-type="author">
            <name><surname>Marchuk</surname><given-names>G.I.</given-names></name>
            <name><surname>Penenko</surname><given-names>V.V.</given-names></name>
          </person-group>
          <chapter-title>Application of Optimization Methods to the Problem of Mathematical Simulation of Atmospheric Processes and Environment</chapter-title>
          <person-group person-group-type="editor">
            <name><surname>Marchuk</surname><given-names>G.I.</given-names></name>
          </person-group>
          <source>Modelling and Optimization of Complex System</source>
          <publisher-loc>Berlin, Heidelberg</publisher-loc>
          <publisher-name>Springer</publisher-name>
          <year>2012</year>
          <volume>18</volume>
          <fpage>240</fpage>
          <lpage>252</lpage>
          <pub-id pub-id-type="doi">10.1007/BFb0004167</pub-id>
        </element-citation>
      </ref>
      <ref id="B3">
        <label>3.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Semenov</surname><given-names>E.V.</given-names></name>
            <name><surname>Mortikov</surname><given-names>E.V.</given-names></name>
          </person-group>
          <article-title>Problems of Operational Data Assimilation for Marginal Seas</article-title>
          <source>Izvestiya, Atmospheric and Oceanic Physics</source>
          <year>2012</year>
          <volume>48</volume>
          <issue>1</issue>
          <fpage>74</fpage>
          <lpage>85</lpage>
          <pub-id pub-id-type="doi">10.1134/S0001433812010124</pub-id>
        </element-citation>
      </ref>
      <ref id="B4">
        <label>4.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Zalesny</surname><given-names>V.B.</given-names></name>
            <name><surname>Agoshkov</surname><given-names>V.I.</given-names></name>
            <name><surname>Shutyaev</surname><given-names>V.P.</given-names></name>
            <name><surname>Le Dimet</surname><given-names>F.</given-names></name>
            <name><surname>Ivchenko</surname><given-names>B.O.</given-names></name>
          </person-group>
          <article-title>Numerical Modeling of Ocean Hydrodynamics with Variational Assimilation of Observational Data</article-title>
          <source>Izvestiya, Atmospheric and Oceanic Physics</source>
          <year>2016</year>
          <volume>52</volume>
          <issue>4</issue>
          <fpage>431</fpage>
          <lpage>442</lpage>
          <pub-id pub-id-type="doi">10.1134/S0001433816040137</pub-id>
        </element-citation>
      </ref>
      <ref id="B5">
        <label>5.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Shutyaev</surname><given-names>V.P.</given-names></name>
            <name><surname>Le Dimet</surname><given-names>F.-X.</given-names></name>
            <name><surname>Parmuzin</surname><given-names>E.</given-names></name>
          </person-group>
          <article-title>Sensitivity Analysis with Respect to Observations in Variational Data Assimilation for Parameter Estimation</article-title>
          <source>Nonlinear Processes in Geophysics</source>
          <year>2018</year>
          <volume>25</volume>
          <issue>2</issue>
          <fpage>429</fpage>
          <lpage>439</lpage>
          <pub-id pub-id-type="doi">10.5194/npg-25-429-2018</pub-id>
        </element-citation>
      </ref>
      <ref id="B6">
        <label>6.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Kochergin</surname><given-names>V.S.</given-names></name>
            <name><surname>Kochergin</surname><given-names>S.V.</given-names></name>
            <name><surname>Stashkov</surname><given-names>S.V.</given-names></name>
          </person-group>
          <article-title>Variational Assimilation of Satellite Data on Surface Concentration of Suspended Matter in the Azov Sea</article-title>
          <source>Sovremennye Problemy Distantsionnogo Zondirovaniya Zemli iz Kosmosa</source>
          <year>2020</year>
          <volume>17</volume>
          <issue>2</issue>
          <fpage>40</fpage>
          <lpage>48</lpage>
          <pub-id pub-id-type="doi">10.21046/2070-7401-2020-17-2-40-48</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>Demyshev</surname><given-names>G.S.</given-names></name>
            <name><surname>Dymova</surname><given-names>O.A.</given-names></name>
            <name><surname>Kochergin</surname><given-names>V.S.</given-names></name>
            <name><surname>Kochergin</surname><given-names>S.V.</given-names></name>
          </person-group>
          <article-title>Determination of Location of the Concentration Initial Field of a Possible Contamination Source in the Black Sea Water Area near the Gerakleiskiy Peninsula Based on the Adjoint Equations Method</article-title>
          <source>Physical Oceanography</source>
          <year>2020</year>
          <volume>27</volume>
          <issue>2</issue>
          <fpage>210</fpage>
          <lpage>221</lpage>
          <pub-id pub-id-type="doi">10.22449/1573-160X-2020-2-210-221</pub-id>
        </element-citation>
      </ref>
      <ref id="B8">
        <label>8.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Shutyaev</surname><given-names>V.P.</given-names></name>
          </person-group>
          <article-title>Methods for Observation Data Assimilation in Problems of Physics of Atmosphere and Ocean</article-title>
          <source>Izvestiya, Atmospheric and Oceanic Physics</source>
          <year>2019</year>
          <volume>55</volume>
          <issue>1</issue>
          <fpage>17</fpage>
          <lpage>31</lpage>
          <pub-id pub-id-type="doi">10.1134/S0001433819010080</pub-id>
        </element-citation>
      </ref>
      <ref id="B9">
        <label>9.</label>
        <element-citation publication-type="article">
          <person-group person-group-type="author">
            <name><surname>Harten</surname><given-names>A.</given-names></name>
          </person-group>
          <article-title>On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes</article-title>
          <source>SIAM Journal on Numerical Analysis</source>
          <year>1984</year>
          <volume>21</volume>
          <issue>1</issue>
          <fpage>1</fpage>
          <lpage>23</lpage>
          <pub-id pub-id-type="doi">10.1137/0721001</pub-id>
        </element-citation>
      </ref>
      <ref id="B10">
        <label>10.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Demyshev</surname><given-names>S.G.</given-names></name>
            <name><surname>Dymova</surname><given-names>O.A.</given-names></name>
          </person-group>
          <article-title>Numerical Analysis of the Mesoscale Features of Circulation in the Black Sea Coastal Zone</article-title>
          <source>Izvestiya, Atmospheric and Oceanic Physics</source>
          <year>2013</year>
          <volume>49</volume>
          <issue>6</issue>
          <fpage>603</fpage>
          <lpage>610</lpage>
          <pub-id pub-id-type="doi">10.1134/S0001433813060030</pub-id>
        </element-citation>
      </ref>
      <ref id="B11">
        <label>11.</label>
        <element-citation publication-type="paper-conference">
          <person-group person-group-type="author">
            <name><surname>Kallos</surname><given-names>G.</given-names></name>
            <name><surname>Nickovic</surname><given-names>S.</given-names></name>
            <name><surname>Papadopoulos</surname><given-names>A.</given-names></name>
            <name><surname>Jovic</surname><given-names>D.</given-names></name>
            <name><surname>Kakaliagou</surname><given-names>O.</given-names></name>
            <name><surname>Misirlis</surname><given-names>N.</given-names></name>
            <name><surname>Boukas</surname><given-names>L.</given-names></name>
            <name><surname>Mimikou</surname><given-names>N.G.S.J.P.</given-names></name>
            <name><surname>Sakellariadou</surname><given-names>G.</given-names></name>
            <name><surname>Papageorgiou</surname><given-names>J.</given-names></name>
            <name><surname>Anadranistakis</surname><given-names>E.</given-names></name>
            <name><surname>Manousakis</surname><given-names>M.</given-names></name>
          </person-group>
          <article-title>The Regional Weather Forecasting System SKIRON: An Overview</article-title>
          <source>Proceedings of the Symposium on Regional Weather Prediction on Parallel Computer Environments</source>
          <publisher-loc>Athens, Greece</publisher-loc>
          <publisher-name>University of Athens</publisher-name>
          <year>1997</year>
          <volume>15</volume>
          <fpage>109</fpage>
          <lpage>123</lpage>
        </element-citation>
      </ref>
      <ref id="B12">
        <label>12.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Arakawa</surname><given-names>A.</given-names></name>
            <name><surname>Lamb</surname><given-names>V.R.</given-names></name>
          </person-group>
          <article-title>A Potential Enstrophy and Energy Conserving Scheme for the Shallow Water Equations</article-title>
          <source>Monthly Weather Review</source>
          <year>1981</year>
          <volume>109</volume>
          <issue>1</issue>
          <fpage>18</fpage>
          <lpage>36</lpage>
          <pub-id pub-id-type="doi">10.1175/1520-0493(1981)109&lt;0018:APEACE&gt;2.0.CO;2</pub-id>
        </element-citation>
      </ref>
      <ref id="B13">
        <label>13.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Demyshev</surname><given-names>S.G.</given-names></name>
            <name><surname>Zapevalov</surname><given-names>A.S.</given-names></name>
            <name><surname>Kubryakov</surname><given-names>A.I.</given-names></name>
            <name><surname>Chudinovskikh</surname><given-names>T.V.</given-names></name>
          </person-group>
          <article-title>Evolution of the ¹³⁷Cs Concentration Field in the Black Sea after the Passage of the Chernobyl Cloud</article-title>
          <source>Russian Meteorology and Hydrology</source>
          <year>2001</year>
          <issue>1</issue>
          <fpage>37</fpage>
          <lpage>46</lpage>
        </element-citation>
      </ref>
      <ref id="B14">
        <label>14.</label>
        <element-citation publication-type="journal">
          <person-group person-group-type="author">
            <name><surname>Korotaev</surname><given-names>G.K.</given-names></name>
            <name><surname>Ratner</surname><given-names>Y.B.</given-names></name>
            <name><surname>Ivanchik</surname><given-names>M.V.</given-names></name>
            <name><surname>Kholod</surname><given-names>A.L.</given-names></name>
            <name><surname>Ivanchik</surname><given-names>A.M.</given-names></name>
          </person-group>
          <article-title>Operative System for Numerical Calculation of the Black Sea Hydrophysical Fields (Development Status and Prospects)</article-title>
          <source>Izvestiya, Atmospheric and Oceanic Physics</source>
          <year>2016</year>
          <volume>52</volume>
          <issue>5</issue>
          <fpage>542</fpage>
          <lpage>549</lpage>
          <pub-id pub-id-type="doi">10.1134/S0001433816050078</pub-id>
        </element-citation>
      </ref>
    </ref-list>
  </back>
</article>
