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 <front>
  <journal-meta>
   <journal-id journal-id-type="publisher-id">Russian Journal of Earth Sciences</journal-id>
   <journal-title-group>
    <journal-title xml:lang="en">Russian Journal of Earth Sciences</journal-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Russian Journal of Earth Sciences</trans-title>
    </trans-title-group>
   </journal-title-group>
   <issn publication-format="online">1681-1208</issn>
  </journal-meta>
  <article-meta>
   <article-id pub-id-type="publisher-id">97252</article-id>
   <article-id pub-id-type="doi">10.2205/2026es001080</article-id>
   <article-id pub-id-type="edn">npdxnu</article-id>
   <article-categories>
    <subj-group subj-group-type="toc-heading" xml:lang="ru">
     <subject>ОРИГИНАЛЬНЫЕ СТАТЬИ</subject>
    </subj-group>
    <subj-group subj-group-type="toc-heading" xml:lang="en">
     <subject>ORIGINAL ARTICLES</subject>
    </subj-group>
    <subj-group>
     <subject>ОРИГИНАЛЬНЫЕ СТАТЬИ</subject>
    </subj-group>
   </article-categories>
   <title-group>
    <article-title xml:lang="en">On the Choice of Tidal Forcing at the Open Boundaries in a High-Resolution Regional Kara Sea Model</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>On the Choice of Tidal Forcing at the Open Boundaries in a High-Resolution Regional Kara Sea Model</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-0229-4191</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Мартьянов</surname>
       <given-names>Станислав Дмитриевич</given-names>
      </name>
      <name xml:lang="en">
       <surname>Martyanov</surname>
       <given-names>Stanislav Dmitrievich</given-names>
      </name>
     </name-alternatives>
     <email>martyanov.sd@gmail.com</email>
     <bio xml:lang="ru">
      <p>кандидат физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>candidate of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9334-3138</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Дворников</surname>
       <given-names>Антон Юрьевич</given-names>
      </name>
      <name xml:lang="en">
       <surname>Dvornikov</surname>
       <given-names>Anton Yurievich</given-names>
      </name>
     </name-alternatives>
     <bio xml:lang="ru">
      <p>кандидат физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>candidate of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-1190-3622</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Сеин</surname>
       <given-names>Дмитрий Владимирович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Sein</surname>
       <given-names>Dmitry Vladimirovich</given-names>
      </name>
     </name-alternatives>
     <bio xml:lang="ru">
      <p>кандидат физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>candidate of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-3"/>
     <xref ref-type="aff" rid="aff-4"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0009-0003-3270-4539</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Горчаков</surname>
       <given-names>Виктор Анатольевич</given-names>
      </name>
      <name xml:lang="en">
       <surname>Gorchakov</surname>
       <given-names>Victor Anatolievich</given-names>
      </name>
     </name-alternatives>
     <bio xml:lang="ru">
      <p>кандидат физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>candidate of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-5"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Институт Океанологии им. П.П. Ширшова РАН</institution>
     <city>Москва</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <city>Moscow</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Институт океанологии им. П.П. Ширшова РАН</institution>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-3">
    <aff>
     <institution xml:lang="ru">Институт океанологии им. П.П. Ширшова РАН</institution>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-4">
    <aff>
     <institution xml:lang="ru">Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research</institution>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research</institution>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-5">
    <aff>
     <institution xml:lang="ru">Институт океанологии им. П.П. Ширшова РАН</institution>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Shirshov Institute of Oceanology, Russian Academy of Sciences</institution>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <pub-date publication-format="print" date-type="pub" iso-8601-date="2026-04-28T12:58:29+03:00">
    <day>28</day>
    <month>04</month>
    <year>2026</year>
   </pub-date>
   <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-04-28T12:58:29+03:00">
    <day>28</day>
    <month>04</month>
    <year>2026</year>
   </pub-date>
   <volume>26</volume>
   <issue>1</issue>
   <elocation-id>ES1021</elocation-id>
   <history>
    <date date-type="received" iso-8601-date="2025-04-08T00:00:00+03:00">
     <day>08</day>
     <month>04</month>
     <year>2025</year>
    </date>
    <date date-type="accepted" iso-8601-date="2025-11-05T00:00:00+03:00">
     <day>05</day>
     <month>11</month>
     <year>2025</year>
    </date>
   </history>
   <self-uri xlink:href="https://rjes.ru/en/nauka/article/97252/view">https://rjes.ru/en/nauka/article/97252/view</self-uri>
   <abstract xml:lang="ru">
    <p>Tidal dynamics play an important role in Kara Sea circulation, influencing currents, sea ice formation, and biogeochemical processes. However, accurate numerical simulation of these processes in regional models depends on the choice of tidal forcing at open lateral boundaries. This study evaluates the performance of three tidal models – TPXO9, FES2014, and Arc2kmTM as sources of boundary forcing for a high-resolution regional Kara Sea model based on MITgcm numerical kernel. The goal is to identify the optimal tidal forcing that best aligns with observations from coastal stations. Numerical experiments have revealed significant discrepancies in tidal energy estimates among the models. The FES2014 model has shown the closest agreement to observations, while Arc2kmTM exhibits the largest errors. However, when used as boundary forcing in the regional Kara Sea model, Arc2kmTM yields the smallest errors in simulated tidal amplitude and phase. Overall, the regional model reproduces M2 tidal amplitudes well but introduces slight phase shifts in the southwestern part of the Kara Sea. Our findings emphasize that no single tidal model can be considered universally optimal. The choice depends on regional conditions and modeling objectives. For our regional model, Arc2kmTM is recommended as a source of tidal forcing at the open boundaries of the regional model, though global models like FES2014 remain viable alternatives. This work emphasizes the need for improved validation methods and highlights the challenges posed by limited observational data in the Arctic region.</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>Tidal dynamics play an important role in Kara Sea circulation, influencing currents, sea ice formation, and biogeochemical processes. However, accurate numerical simulation of these processes in regional models depends on the choice of tidal forcing at open lateral boundaries. This study evaluates the performance of three tidal models – TPXO9, FES2014, and Arc2kmTM as sources of boundary forcing for a high-resolution regional Kara Sea model based on MITgcm numerical kernel. The goal is to identify the optimal tidal forcing that best aligns with observations from coastal stations. Numerical experiments have revealed significant discrepancies in tidal energy estimates among the models. The FES2014 model has shown the closest agreement to observations, while Arc2kmTM exhibits the largest errors. However, when used as boundary forcing in the regional Kara Sea model, Arc2kmTM yields the smallest errors in simulated tidal amplitude and phase. Overall, the regional model reproduces M2 tidal amplitudes well but introduces slight phase shifts in the southwestern part of the Kara Sea. Our findings emphasize that no single tidal model can be considered universally optimal. The choice depends on regional conditions and modeling objectives. For our regional model, Arc2kmTM is recommended as a source of tidal forcing at the open boundaries of the regional model, though global models like FES2014 remain viable alternatives. This work emphasizes the need for improved validation methods and highlights the challenges posed by limited observational data in the Arctic region.</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>Kara Sea</kwd>
    <kwd>tide</kwd>
    <kwd>numerical modeling</kwd>
    <kwd>tidal forcing</kwd>
    <kwd>open boundary</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>Kara Sea</kwd>
    <kwd>tide</kwd>
    <kwd>numerical modeling</kwd>
    <kwd>tidal forcing</kwd>
    <kwd>open boundary</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="ru">The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation for IO RAS (theme No. FMWE2024-0028). This work used resources of the Deutsches Klimarechenzentrum (DKRZ) granted by its Scientific Steering Committee (WLA) under project ID ba1206.</funding-statement>
    <funding-statement xml:lang="en">The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation for IO RAS (theme No. FMWE2024-0028). This work used resources of the Deutsches Klimarechenzentrum (DKRZ) granted by its Scientific Steering Committee (WLA) under project ID ba1206.</funding-statement>
   </funding-group>
  </article-meta>
 </front>
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 </body>
 <back>
  <ref-list>
   <ref id="B1">
    <label>1.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Cai S., Long X., Liu H., et al. Tide model evaluation under different conditions // Continental Shelf Research. — 2006. — Vol. 26, no. 1. — P. 104–112. — https://doi.org/10.1016/j.csr.2005.09.004</mixed-citation>
     <mixed-citation xml:lang="en">Cai S., Long X., Liu H., et al. Tide model evaluation under different conditions // Continental Shelf Research. — 2006. — Vol. 26, no. 1. — P. 104–112. — https://doi.org/10.1016/j.csr.2005.09.004</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B2">
    <label>2.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Campin J.-M., Adcroft A., Hill C., et al. Conservation of properties in a free-surface model // Ocean Modelling. — 2004. — Vol. 6, no. 3/4. — P. 221–244. — https://doi.org/10.1016/s1463-5003(03)00009-x</mixed-citation>
     <mixed-citation xml:lang="en">Campin J.-M., Adcroft A., Hill C., et al. Conservation of properties in a free-surface model // Ocean Modelling. — 2004. — Vol. 6, no. 3/4. — P. 221–244. — https://doi.org/10.1016/s1463-5003(03)00009-x</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B3">
    <label>3.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Chantsev V. Y. and Danshina A. V. A calculation of the intra-annual dynamics of the Ob Bay hydrophysical regime with high spatial resolution // Fundamental and Applied Hydrophysics. — 2019. — Vol. 12, no. 3. — P. 55–64. — https://doi.org/10.7868/s2073667319030079 — (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Chantsev V. Y. and Danshina A. V. A calculation of the intra-annual dynamics of the Ob Bay hydrophysical regime with high spatial resolution // Fundamental and Applied Hydrophysics. — 2019. — Vol. 12, no. 3. — P. 55–64. — https://doi.org/10.7868/s2073667319030079 — (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B4">
    <label>4.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Codiga D. UTide Unified Tidal Analysis and Prediction Functions. — 2024. — URL: https://www.mathworks.com/matlabcentral/fileexchange/46523-utide-unified-tidal-analysis-and-prediction-functions</mixed-citation>
     <mixed-citation xml:lang="en">Codiga D. UTide Unified Tidal Analysis and Prediction Functions. — 2024. — URL: https://www.mathworks.com/matlabcentral/fileexchange/46523-utide-unified-tidal-analysis-and-prediction-functions</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B5">
    <label>5.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Egbert G. D. and Erofeeva S. Y. Efficient Inverse Modeling of Barotropic Ocean Tides // Journal of Atmospheric and Oceanic Technology. — 2002. — Vol. 19, no. 2. — P. 183–204. — https://doi.org/10.1175/1520-0426(2002)019&lt;0183:eimobo&gt;2.0.co;2</mixed-citation>
     <mixed-citation xml:lang="en">Egbert G. D. and Erofeeva S. Y. Efficient Inverse Modeling of Barotropic Ocean Tides // Journal of Atmospheric and Oceanic Technology. — 2002. — Vol. 19, no. 2. — P. 183–204. — https://doi.org/10.1175/1520-0426(2002)019&lt;0183:eimobo&gt;2.0.co;2</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B6">
    <label>6.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Gaspar P., Grégoris Y. and Lefevre J. A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: Tests at station Papa and long-term upper ocean study site // Journal of Geophysical Research: Oceans. — 1990. — Vol. 95, no. C9. — P. 16179–16193. — https://doi.org/10.1029/jc095ic09p16179</mixed-citation>
     <mixed-citation xml:lang="en">Gaspar P., Grégoris Y. and Lefevre J. A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: Tests at station Papa and long-term upper ocean study site // Journal of Geophysical Research: Oceans. — 1990. — Vol. 95, no. C9. — P. 16179–16193. — https://doi.org/10.1029/jc095ic09p16179</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B7">
    <label>7.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Grimaldi S., Salamon P., Disperati J., et al. River discharge and related historical data from the Global Flood Awareness System, v4.0. — European Commission, Joint Research Centre (JRC), 2022. — https://doi.org/10.24381/CDS.A4FDD6B9</mixed-citation>
     <mixed-citation xml:lang="en">Grimaldi S., Salamon P., Disperati J., et al. River discharge and related historical data from the Global Flood Awareness System, v4.0. — European Commission, Joint Research Centre (JRC), 2022. — https://doi.org/10.24381/CDS.A4FDD6B9</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B8">
    <label>8.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Hallberg R. Using a resolution function to regulate parameterizations of oceanic mesoscale eddy effects // Ocean Modelling. — 2013. — Vol. 72. — P. 92–103. — https://doi.org/10.1016/j.ocemod.2013.08.007</mixed-citation>
     <mixed-citation xml:lang="en">Hallberg R. Using a resolution function to regulate parameterizations of oceanic mesoscale eddy effects // Ocean Modelling. — 2013. — Vol. 72. — P. 92–103. — https://doi.org/10.1016/j.ocemod.2013.08.007</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B9">
    <label>9.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Harms I. H. A numerical study of the barotropic circulation in the Barents and Kara Seas // Continental Shelf Research. — 1992. — Vol. 12, no. 9. — P. 1043–1058. — https://doi.org/10.1016/0278-4343(92)90015-c</mixed-citation>
     <mixed-citation xml:lang="en">Harms I. H. A numerical study of the barotropic circulation in the Barents and Kara Seas // Continental Shelf Research. — 1992. — Vol. 12, no. 9. — P. 1043–1058. — https://doi.org/10.1016/0278-4343(92)90015-c</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B10">
    <label>10.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Hart-Davis M. G., Howard S. L., Ray R. D., et al. ArcTiCA: Arctic tidal constituents atlas // Scientific Data. — 2024. — Vol. 11, no. 1. — https://doi.org/10.1038/s41597-024-03012-w</mixed-citation>
     <mixed-citation xml:lang="en">Hart-Davis M. G., Howard S. L., Ray R. D., et al. ArcTiCA: Arctic tidal constituents atlas // Scientific Data. — 2024. — Vol. 11, no. 1. — https://doi.org/10.1038/s41597-024-03012-w</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B11">
    <label>11.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Howard S. L. and Padman L. Arc2kmTM: Arctic 2 kilometer Tide Model, 2021. — NSF Arctic Data Center, 2021. — https://doi.org/10.18739/A2PV6B79W</mixed-citation>
     <mixed-citation xml:lang="en">Howard S. L. and Padman L. Arc2kmTM: Arctic 2 kilometer Tide Model, 2021. — NSF Arctic Data Center, 2021. — https://doi.org/10.18739/A2PV6B79W</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B12">
    <label>12.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Jackett D. R. and McDougall T. J. Minimal Adjustment of Hydrographic Profiles to Achieve Static Stability // Journal of Atmospheric and Oceanic Technology. — 1995. — Vol. 12, no. 2. — P. 381–389. — https://doi.org/10.1175/1520-0426(1995)012&lt;0381:maohpt&gt;2.0.co;2</mixed-citation>
     <mixed-citation xml:lang="en">Jackett D. R. and McDougall T. J. Minimal Adjustment of Hydrographic Profiles to Achieve Static Stability // Journal of Atmospheric and Oceanic Technology. — 1995. — Vol. 12, no. 2. — P. 381–389. — https://doi.org/10.1175/1520-0426(1995)012&lt;0381:maohpt&gt;2.0.co;2</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B13">
    <label>13.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Jakobsson M., Mayer L., Coakley B., et al. The International Bathymetric Chart of the Arctic Ocean (IBCAO) Version 3.0 // Geophysical Research Letters. — 2012. — Vol. 39, no. 12. — https://doi.org/10.1029/2012gl052219</mixed-citation>
     <mixed-citation xml:lang="en">Jakobsson M., Mayer L., Coakley B., et al. The International Bathymetric Chart of the Arctic Ocean (IBCAO) Version 3.0 // Geophysical Research Letters. — 2012. — Vol. 39, no. 12. — https://doi.org/10.1029/2012gl052219</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B14">
    <label>14.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Janeković I. and Powell B. Analysis of imposing tidal dynamics to nested numerical models // Continental Shelf Research. — 2012. — Vol. 34. — P. 30–40. — https://doi.org/10.1016/j.csr.2011.11.017</mixed-citation>
     <mixed-citation xml:lang="en">Janeković I. and Powell B. Analysis of imposing tidal dynamics to nested numerical models // Continental Shelf Research. — 2012. — Vol. 34. — P. 30–40. — https://doi.org/10.1016/j.csr.2011.11.017</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B15">
    <label>15.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Jean-Michel L., Eric G., Romain B.-B., et al. The Copernicus Global 1/12◦ Oceanic and Sea Ice GLORYS12 Reanalysis // Frontiers in Earth Science. — 2021. — Vol. 9. — https://doi.org/10.3389/feart.2021.698876</mixed-citation>
     <mixed-citation xml:lang="en">Jean-Michel L., Eric G., Romain B.-B., et al. The Copernicus Global 1/12◦ Oceanic and Sea Ice GLORYS12 Reanalysis // Frontiers in Earth Science. — 2021. — Vol. 9. — https://doi.org/10.3389/feart.2021.698876</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B16">
    <label>16.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Kagan B. A., Sofina E. V. and Timofeev A. A. The Tidal Effect on Climatic Characteristics of the Kara Sea in the IceFree Period // Izvestiya, Atmospheric and Oceanic Physics. — 2019. — Vol. 55, no. 2. — P. 188–195. — https://doi.org/10.1134/s0001433819020087</mixed-citation>
     <mixed-citation xml:lang="en">Kagan B. A., Sofina E. V. and Timofeev A. A. The Tidal Effect on Climatic Characteristics of the Kara Sea in the IceFree Period // Izvestiya, Atmospheric and Oceanic Physics. — 2019. — Vol. 55, no. 2. — P. 188–195. — https://doi.org/10.1134/s0001433819020087</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B17">
    <label>17.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Kagan B. A. and Timofeev A. A. Simulation of surface and internal semidiurnal tides in the Kara Sea // Izvestiya, Atmospheric and Oceanic Physics. — 2017. — Vol. 53, no. 2. — P. 233–241. — https://doi.org/10.1134/s0001433817020050</mixed-citation>
     <mixed-citation xml:lang="en">Kagan B. A. and Timofeev A. A. Simulation of surface and internal semidiurnal tides in the Kara Sea // Izvestiya, Atmospheric and Oceanic Physics. — 2017. — Vol. 53, no. 2. — P. 233–241. — https://doi.org/10.1134/s0001433817020050</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B18">
    <label>18.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Kowalik Z. and Proshutinsky A. Y. The Arctic Ocean Tides // The Polar Oceans and Their Role in Shaping the Global Environment. — Washington, D. C. : American Geophysical Union, 2013. — P. 137–158. — https://doi.org/10.1029/gm085p0137</mixed-citation>
     <mixed-citation xml:lang="en">Kowalik Z. and Proshutinsky A. Y. The Arctic Ocean Tides // The Polar Oceans and Their Role in Shaping the Global Environment. — Washington, D. C. : American Geophysical Union, 2013. — P. 137–158. — https://doi.org/10.1029/gm085p0137</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B19">
    <label>19.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Leith C. E. Stochastic models of chaotic systems // Physica D: Nonlinear Phenomena. — 1996. — Vol. 98, no. 2–4. — P. 481–491. — https://doi.org/10.1016/0167-2789(96)00107-8</mixed-citation>
     <mixed-citation xml:lang="en">Leith C. E. Stochastic models of chaotic systems // Physica D: Nonlinear Phenomena. — 1996. — Vol. 98, no. 2–4. — P. 481–491. — https://doi.org/10.1016/0167-2789(96)00107-8</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B20">
    <label>20.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Li Q., Wu H., Yang H., et al. A numerical simulation of the generation and evolution of nonlinear internal waves across the Kara Strait // Acta Oceanologica Sinica. — 2019. — Vol. 38, no. 5. — P. 1–9. — https://doi.org/10.1007/s13131-019-1437-z</mixed-citation>
     <mixed-citation xml:lang="en">Li Q., Wu H., Yang H., et al. A numerical simulation of the generation and evolution of nonlinear internal waves across the Kara Strait // Acta Oceanologica Sinica. — 2019. — Vol. 38, no. 5. — P. 1–9. — https://doi.org/10.1007/s13131-019-1437-z</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B21">
    <label>21.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Losch M., Menemenlis D., Campin J.-M., et al. On the formulation of sea-ice models. Part 1: Effects of different solver implementations and parameterizations // Ocean Modelling. — 2010. — Vol. 33, no. 1/2. — P. 129–144. — https://doi.org/10.1016/j.ocemod.2009.12.008</mixed-citation>
     <mixed-citation xml:lang="en">Losch M., Menemenlis D., Campin J.-M., et al. On the formulation of sea-ice models. Part 1: Effects of different solver implementations and parameterizations // Ocean Modelling. — 2010. — Vol. 33, no. 1/2. — P. 129–144. — https://doi.org/10.1016/j.ocemod.2009.12.008</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B22">
    <label>22.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Lyard F. H., Allain D. J., Cancet M., et al. FES2014 global ocean tide atlas: design and performance // Ocean Science. — 2021. — Vol. 17, no. 3. — P. 615–649. — https://doi.org/10.5194/os-17-615-2021</mixed-citation>
     <mixed-citation xml:lang="en">Lyard F. H., Allain D. J., Cancet M., et al. FES2014 global ocean tide atlas: design and performance // Ocean Science. — 2021. — Vol. 17, no. 3. — P. 615–649. — https://doi.org/10.5194/os-17-615-2021</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B23">
    <label>23.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Marchesiello P., McWilliams J. C. and Shchepetkin A. Open boundary conditions for long-term integration of regional oceanic models // Ocean Modelling. — 2001. — Vol. 3, no. 1/2. — P. 1–20. — https://doi.org/10.1016/s1463-5003(00)00013-5</mixed-citation>
     <mixed-citation xml:lang="en">Marchesiello P., McWilliams J. C. and Shchepetkin A. Open boundary conditions for long-term integration of regional oceanic models // Ocean Modelling. — 2001. — Vol. 3, no. 1/2. — P. 1–20. — https://doi.org/10.1016/s1463-5003(00)00013-5</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B24">
    <label>24.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Marshall J., Adcroft A., Hill C., et al. A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers // Journal of Geophysical Research: Oceans. — 1997. — Vol. 102, no. C3. — P. 5753–5766. — https://doi.org/10.1029/96jc02775</mixed-citation>
     <mixed-citation xml:lang="en">Marshall J., Adcroft A., Hill C., et al. A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers // Journal of Geophysical Research: Oceans. — 1997. — Vol. 102, no. C3. — P. 5753–5766. — https://doi.org/10.1029/96jc02775</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B25">
    <label>25.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Martyanov S. D. High-Resolution Modeling of the Kara Sea Dynamics and Thermohaline Structure and Assessment of the Impact of Various River Runoff Forcing in the Model // Water Resources. — 2023. — Vol. 50, S3. — S323–S327. — https://doi.org/10.1134/s0097807823700525</mixed-citation>
     <mixed-citation xml:lang="en">Martyanov S. D. High-Resolution Modeling of the Kara Sea Dynamics and Thermohaline Structure and Assessment of the Impact of Various River Runoff Forcing in the Model // Water Resources. — 2023. — Vol. 50, S3. — S323–S327. — https://doi.org/10.1134/s0097807823700525</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B26">
    <label>26.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Martyanov S. D., Dvornikov A. Y., Gorchakov V. A., et al. Model estimates of the ecosystem contribution in the carbon dioxide exchange between the ocean and the atmosphere in the Barents Sea // Fundamental and Applied Hydrophysics. — 2017. — Vol. 10, no. 1. — P. 11–16. — https://doi.org/10.7868/S2073667317010026</mixed-citation>
     <mixed-citation xml:lang="en">Martyanov S. D., Dvornikov A. Y., Gorchakov V. A., et al. Model estimates of the ecosystem contribution in the carbon dioxide exchange between the ocean and the atmosphere in the Barents Sea // Fundamental and Applied Hydrophysics. — 2017. — Vol. 10, no. 1. — P. 11–16. — https://doi.org/10.7868/S2073667317010026</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B27">
    <label>27.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Martyanov S. D., Dvornikov A. Y., Ryabchenko V. A., et al. Investigation of the relationship between primary production and sea ice in the arctic seas: assessments based on a small-component model of marine ecosystem // Fundamental and Applied Hydrophysics. — 2018. — Vol. 11, no. 2. — P. 108–117. — https://doi.org/10.7868/s2073667318020107</mixed-citation>
     <mixed-citation xml:lang="en">Martyanov S. D., Dvornikov A. Y., Ryabchenko V. A., et al. Investigation of the relationship between primary production and sea ice in the arctic seas: assessments based on a small-component model of marine ecosystem // Fundamental and Applied Hydrophysics. — 2018. — Vol. 11, no. 2. — P. 108–117. — https://doi.org/10.7868/s2073667318020107</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B28">
    <label>28.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Mason E., Molemaker J., Shchepetkin A. F., et al. Procedures for offline grid nesting in regional ocean models // Ocean Modelling. — 2010. — Vol. 35, no. 1/2. — P. 1–15. — https://doi.org/10.1016/j.ocemod.2010.05.007</mixed-citation>
     <mixed-citation xml:lang="en">Mason E., Molemaker J., Shchepetkin A. F., et al. Procedures for offline grid nesting in regional ocean models // Ocean Modelling. — 2010. — Vol. 35, no. 1/2. — P. 1–15. — https://doi.org/10.1016/j.ocemod.2010.05.007</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B29">
    <label>29.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Morozov E. G., Kozlov I. E., Shchuka S. A., et al. Internal tide in the Kara Gates Strait // Oceanology. — 2017. — Vol. 57, no. 1. — P. 8–18. — https://doi.org/10.1134/s0001437017010106</mixed-citation>
     <mixed-citation xml:lang="en">Morozov E. G., Kozlov I. E., Shchuka S. A., et al. Internal tide in the Kara Gates Strait // Oceanology. — 2017. — Vol. 57, no. 1. — P. 8–18. — https://doi.org/10.1134/s0001437017010106</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B30">
    <label>30.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Morozov E. G., Paka V. T. and Bakhanov V. V. Strong internal tides in the Kara Gates Strait // Geophysical Research Letters. — 2008. — Vol. 35, no. 16. — https://doi.org/10.1029/2008gl033804</mixed-citation>
     <mixed-citation xml:lang="en">Morozov E. G., Paka V. T. and Bakhanov V. V. Strong internal tides in the Kara Gates Strait // Geophysical Research Letters. — 2008. — Vol. 35, no. 16. — https://doi.org/10.1029/2008gl033804</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B31">
    <label>31.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Nekrasov A. V. Energy of ocean tides. — Leningrad : Gidrometeoizdat, 1990. — 288 p. — (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Nekrasov A. V. Energy of ocean tides. — Leningrad : Gidrometeoizdat, 1990. — 288 p. — (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B32">
    <label>32.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Nguyen V. T. and Lee M. Effect of Open Boundary Conditions and Bottom Roughness on Tidal Modeling around the West Coast of Korea // Water. — 2020. — Vol. 12, no. 6. — P. 1706. — https://doi.org/10.3390/w12061706</mixed-citation>
     <mixed-citation xml:lang="en">Nguyen V. T. and Lee M. Effect of Open Boundary Conditions and Bottom Roughness on Tidal Modeling around the West Coast of Korea // Water. — 2020. — Vol. 12, no. 6. — P. 1706. — https://doi.org/10.3390/w12061706</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B33">
    <label>33.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Nurser A. J. G. and Bacon S. The Rossby radius in the Arctic Ocean // Ocean Science. — 2014. — Vol. 10, no. 6. — P. 967–975. — https://doi.org/10.5194/os-10-967-2014</mixed-citation>
     <mixed-citation xml:lang="en">Nurser A. J. G. and Bacon S. The Rossby radius in the Arctic Ocean // Ocean Science. — 2014. — Vol. 10, no. 6. — P. 967–975. — https://doi.org/10.5194/os-10-967-2014</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B34">
    <label>34.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Padman L. and Erofeeva S. A barotropic inverse tidal model for the Arctic Ocean // Geophysical Research Letters. — 2004. — Vol. 31, no. 2. — https://doi.org/10.1029/2003gl019003</mixed-citation>
     <mixed-citation xml:lang="en">Padman L. and Erofeeva S. A barotropic inverse tidal model for the Arctic Ocean // Geophysical Research Letters. — 2004. — Vol. 31, no. 2. — https://doi.org/10.1029/2003gl019003</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B35">
    <label>35.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Parkinson C. L. and Washington W. M. A large-scale numerical model of sea ice // Journal of Geophysical Research: Oceans. — 1979. — Vol. 84, no. C1. — P. 311–337. — https://doi.org/10.1029/jc084ic01p00311</mixed-citation>
     <mixed-citation xml:lang="en">Parkinson C. L. and Washington W. M. A large-scale numerical model of sea ice // Journal of Geophysical Research: Oceans. — 1979. — Vol. 84, no. C1. — P. 311–337. — https://doi.org/10.1029/jc084ic01p00311</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B36">
    <label>36.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Postlethwaite C. F., Morales Maqueda M. A., Fouest V. le, et al. The effect of tides on dense water formation in Arctic shelf seas // Ocean Science. — 2011. — Vol. 7, no. 2. — P. 203–217. — https://doi.org/10.5194/os-7-203-2011</mixed-citation>
     <mixed-citation xml:lang="en">Postlethwaite C. F., Morales Maqueda M. A., Fouest V. le, et al. The effect of tides on dense water formation in Arctic shelf seas // Ocean Science. — 2011. — Vol. 7, no. 2. — P. 203–217. — https://doi.org/10.5194/os-7-203-2011</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B37">
    <label>37.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Romanenkov D. A., Sofina E. V. and Rodikova A. E. Modeling of Barotropic Tide off the Southeastern Coast of the Kamchatka Peninsula in View of the Accuracy of Global Tidal Models in the Northwest Pacific Ocean //Fundamental and Applied Hydrophysics. — 2023. — Vol.16, no. 4. — P. 45–62. — https://doi.org/10.59887/2073-6673.2023.16(4)-4</mixed-citation>
     <mixed-citation xml:lang="en">Romanenkov D. A., Sofina E. V. and Rodikova A. E. Modeling of Barotropic Tide off the Southeastern Coast of the Kamchatka Peninsula in View of the Accuracy of Global Tidal Models in the Northwest Pacific Ocean //Fundamental and Applied Hydrophysics. — 2023. — Vol.16, no. 4. — P. 45–62. — https://doi.org/10.59887/2073-6673.2023.16(4)-4</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B38">
    <label>38.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Solano M., Canals M. and Leonardi S. Barotropic boundary conditions and tide forcing in split-explicit high resolution coastal ocean models // Journal of Ocean Engineering and Science. — 2020. — Vol. 5, no. 3. — P. 249–260. — https://doi.org/10.1016/j.joes.2019.12.002</mixed-citation>
     <mixed-citation xml:lang="en">Solano M., Canals M. and Leonardi S. Barotropic boundary conditions and tide forcing in split-explicit high resolution coastal ocean models // Journal of Ocean Engineering and Science. — 2020. — Vol. 5, no. 3. — P. 249–260. — https://doi.org/10.1016/j.joes.2019.12.002</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B39">
    <label>39.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Voinov G. N. Tidal phenomena in the Kara Sea. — Saint-Petersburg : Russian Geographical Society Publ., 1999. — 109 p. — (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Voinov G. N. Tidal phenomena in the Kara Sea. — Saint-Petersburg : Russian Geographical Society Publ., 1999. — 109 p. — (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B40">
    <label>40.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Voinov G. N., Golovin N. V., Kubyshkin N. V., et al. Approach to solving the problem of sea level forecasting off Cape Kamenny in the Ob’ Bay // Arctic and Antarctic Research. — 2023. — Vol. 69, no. 1. — P. 29–43. — https://doi.org/10.30758/0555-2648-2023-69-1-29-43 — (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Voinov G. N., Golovin N. V., Kubyshkin N. V., et al. Approach to solving the problem of sea level forecasting off Cape Kamenny in the Ob’ Bay // Arctic and Antarctic Research. — 2023. — Vol. 69, no. 1. — P. 29–43. — https://doi.org/10.30758/0555-2648-2023-69-1-29-43 — (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B41">
    <label>41.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Voinov G. N., Morozova O. A., Nesterov A. V., et al. Tides in the southern area of the Kara Sea in the vicinity of the Belyi island // Arctic and Antarctic Research. — 2020. — Vol. 66, no. 1. — P. 6–19. — https://doi.org/10.30758/0555- 2648-2020-66-1-6-19. — (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Voinov G. N., Morozova O. A., Nesterov A. V., et al. Tides in the southern area of the Kara Sea in the vicinity of the Belyi island // Arctic and Antarctic Research. — 2020. — Vol. 66, no. 1. — P. 6–19. — https://doi.org/10.30758/0555- 2648-2020-66-1-6-19. — (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B42">
    <label>42.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Voinov G. N. and Naumov A. K. The tides in the south-western Kara sea. Tides calibration method effects // Arctic and Antarctic Research. — 2017. — No. 4. — P. 98–115. — https://doi.org/10.30758/0555-2648-2017-0-4-98-115 — (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Voinov G. N. and Naumov A. K. The tides in the south-western Kara sea. Tides calibration method effects // Arctic and Antarctic Research. — 2017. — No. 4. — P. 98–115. — https://doi.org/10.30758/0555-2648-2017-0-4-98-115 — (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B43">
    <label>43.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Voinov G. N. and Piskun A. A. Tidal and storm surges levels variation at the Cape Kamenny (Gulf of the Ob) // Arctic and Antarctic Research. — 2019. — Vol. 65, no. 1. — P. 15–33. — https://doi.org/10.30758/0555-2648-2019-65-1-15-33 — (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Voinov G. N. and Piskun A. A. Tidal and storm surges levels variation at the Cape Kamenny (Gulf of the Ob) // Arctic and Antarctic Research. — 2019. — Vol. 65, no. 1. — P. 15–33. — https://doi.org/10.30758/0555-2648-2019-65-1-15-33 — (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B44">
    <label>44.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Voinov G. N. and Piskun A. A. Tidal and nontidal variations in the water level in the middle part of the Ob’ Bay // Arctic and Antarctic Research. — 2023. — Vol. 69, no. 3. — P. 272–289. — https://doi.org/10.30758/0555-2648-2023-69-3-272-289 — (In Russian).</mixed-citation>
     <mixed-citation xml:lang="en">Voinov G. N. and Piskun A. A. Tidal and nontidal variations in the water level in the middle part of the Ob’ Bay // Arctic and Antarctic Research. — 2023. — Vol. 69, no. 3. — P. 272–289. — https://doi.org/10.30758/0555-2648-2023-69-3-272-289 — (In Russian).</mixed-citation>
    </citation-alternatives>
   </ref>
  </ref-list>
 </back>
</article>
