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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 xml:lang="en">Ecological Safety of Coastal and Shelf Zones of Sea</journal-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Экологическая безопасность прибрежной и шельфовой зон моря</trans-title>
        </trans-title-group>
      </journal-title-group>
      <issn publication-format="print">2413-5577</issn>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="publisher-id">20240102</article-id>
      <article-id pub-id-type="edn">EHKUET</article-id>
      
      <article-categories>
        <subj-group subj-group-type="toc-heading" xml:lang="ru">
          <subject>Научная статья</subject>
        </subj-group>
        <subj-group subj-group-type="article-type">
          <subject>Research Article</subject>
        </subj-group>
      </article-categories>

      <title-group>
        <article-title xml:lang="ru">Распределение возвышений морской поверхности в форме двухкомпонентной гауссовой смеси</article-title>
        <trans-title-group xml:lang="en">
          <trans-title>Distribution of Sea Surface Elevations in the Form of a Two-Component Gaussian Mixture</trans-title>
        </trans-title-group>
      </title-group>

      <contrib-group>
        <contrib contrib-type="author">
          <name-alternatives>
            <name xml:lang="en">
              <surname>Zapevalov</surname>
              <given-names>A. S.</given-names>
            </name>
            <name xml:lang="ru">
              <surname>Запевалов</surname>
              <given-names>А. С.</given-names>
            </name>
          </name-alternatives>
          <xref ref-type="aff" rid="aff1"/>
          <xref ref-type="corresp" rid="cor1"/>
          <email>sevzepter@mail.ru</email>
        </contrib>
        <contrib contrib-type="author">
          <name-alternatives>
            <name xml:lang="en">
              <surname>Knyazkov</surname>
              <given-names>A. S.</given-names>
            </name>
            <name xml:lang="ru">
              <surname>Князьков</surname>
              <given-names>А. С.</given-names>
            </name>
          </name-alternatives>
          <xref ref-type="aff" rid="aff1"/>
          <email>fizfak83@yandex.ru</email>
        </contrib>
      </contrib-group>

      <aff-alternatives id="aff1">
        <aff xml:lang="en">
          <institution>Marine Hydrophysical Institute of RAS</institution>
          <addr-line>Sevastopol</addr-line>
          <country>Russia</country>
        </aff>
        <aff xml:lang="ru">
          <institution>Морской гидрофизический институт РАН</institution>
          <addr-line>Севастополь</addr-line>
          <country>Россия</country>
        </aff>
      </aff-alternatives>

      <author-notes>
        <corresp id="cor1">
          <label>Контактная информация:</label>
          <email>sevzepter@mail.ru</email>
        </corresp>
      </author-notes>

      <pub-date date-type="pub" iso-8601-date="2024-03-25" publication-format="electronic">
        <day>25</day>
        <month>03</month>
        <year>2024</year>
      </pub-date>
      <issue>1</issue>
      <fpage>20</fpage>
      <lpage>30</lpage>

      <history>
        <date date-type="received" iso-8601-date="2023-07-06">
          <day>06</day>
          <month>07</month>
          <year>2023</year>
        </date>
        <date date-type="rev-recd" iso-8601-date="2023-09-03">
          <day>03</day>
          <month>09</month>
          <year>2023</year>
        </date>
        <date date-type="accepted" iso-8601-date="2023-12-27">
          <day>27</day>
          <month>12</month>
          <year>2023</year>
        </date>
      </history>

      <permissions>
        <copyright-statement xml:lang="ru">Copyright © 2024, Запевалов А. С., Князьков А. С.</copyright-statement>
        <copyright-statement xml:lang="en">Copyright © 2024, Zapevalov A. S., Knyazkov A. S.</copyright-statement>
        <copyright-year>2024</copyright-year>
        <copyright-holder xml:lang="ru">Запевалов А. С., Князьков А. С.</copyright-holder>
        <copyright-holder xml:lang="en">Zapevalov A. S., Knyazkov A. S.</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/repository/issues/2024/01/02/" xlink:title="Страница статьи">https://ecological-safety.ru/repository/issues/2024/01/02/</self-uri>

      <abstract xml:lang="ru">
        <p>Верифицирована аппроксимация функции плотности вероятностей возвышений морской поверхности двухкомпонентной гауссовой смесью. Для верификации использованы данные прямых волновых измерений, полученные на стационарной океанографической платформе, установленной в Черном море. Критерием корректности аппроксимации выбрана относительная ошибка ε отклонения модельной функции плотности вероятности от экспериментальной функции, рассчитанной по данным волновых измерений. Средняя по ансамблю ситуаций относительная ошибка 〈ε〉 мала, если значения нормированного на среднеквадратическую величину возвышения поверхности лежат в области 〈ε〉 &lt; 3. Среднеквадратическое отклонение относительной ошибки δ минимально при 〈ε〉 ≈ 0 и равняется 0.12, при 〈ε〉 = 3 возрастает до ~ 0.5. Показано, что ошибка 〈ε〉 имеет систематическую составляющую, которая зависит от отклонений третьего и четвертого статистических моментов от значений, соответствующих распределению Гаусса. Построена полуэмпирическая зависимость, позволяющая учесть эту составляющую. Отмечено, что точность аппроксимации можно повысить в 2–3 раза, исключив систематическую составляющую.</p>
      </abstract>
      
      <trans-abstract xml:lang="en">
        <p>The approximation of the probability density function of sea surface elevations by a two-component Gaussian mixture has been verified. For verification, the data of direct wave measurements obtained on a stationary oceanographic platform, installed in the Black Sea, were used. The approximation correctness criterion is the relative error ε of deviation of the model of probability densities function from the experimental function calculated from the measurement data. The average error ⟨ε⟩ over the ensemble of situations is small if | ε | &lt; 3. The standard deviation δ is minimal if | ε | ≈ 0 and is equal to 0.12, if | ε | = 3 then δ ≈ 0.5. It is shown that the error ⟨ε⟩ has a systematic component, which depends on the deviations of the third and fourth statistical moments from the values corresponding to the Gaussian distribution. A semi-empirical relationship has been constructed to take this component into account. It is noted that the approximation accuracy can be increased by 2–3 times by eliminating the systematic component.</p>
      </trans-abstract>

      <kwd-group xml:lang="ru">
        <kwd>гауссова смесь</kwd>
        <kwd>морская поверхность</kwd>
        <kwd>нелинейные волны</kwd>
        <kwd>статистический момент</kwd>
        <kwd>Черное море</kwd>
      </kwd-group>
      
      <kwd-group xml:lang="en">
        <kwd>Gaussian mixture</kwd>
        <kwd>sea waves</kwd>
        <kwd>surface elevation</kwd>
        <kwd>statistical moment</kwd>
        <kwd>Black Sea</kwd>
        <kwd>nonlinear waves</kwd>
      </kwd-group>

      <funding-group>
        <funding-statement xml:lang="ru">Работа выполнена в рамках госзадания ФГБУН ФИЦ МГИ по теме FNNN-2021-0004 «Фундаментальные исследования океанологических процессов, определяющих состояние и эволюцию морской среды под влиянием естественных и антропогенных факторов, на основе методов наблюдения и моделирования».</funding-statement>
        <funding-statement xml:lang="en">The work was performed under state assignment of Marine Hydrophysical Institute of RAS on topic FNNN-2021-0004 “Fundamental studies of oceanological processes which determine the state and evolution of the marine environment influenced by natural and anthropogenic factors, based on observation and modeling methods”.</funding-statement>
      </funding-group>
    </article-meta>
  </front>

  <body>
    <p>Текст статьи не включен.</p>
  </body>

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