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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">46585</article-id>
   <article-id pub-id-type="doi">10.2205/2019ES000662</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">Estimation of the wind-driven wave spectrum using a high spatial resolution coherent radar</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Estimation of the wind-driven wave spectrum using a high spatial resolution coherent radar</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Ermoshkin</surname>
       <given-names>A V</given-names>
      </name>
      <name xml:lang="en">
       <surname>Ermoshkin</surname>
       <given-names>A V</given-names>
      </name>
     </name-alternatives>
     <email>al-ermoshkin@yandex.ru</email>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Kapustin</surname>
       <given-names>I A</given-names>
      </name>
      <name xml:lang="en">
       <surname>Kapustin</surname>
       <given-names>I A</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Institute of Applied Physics of the Russian Academy of Sciences</institution>
     <country>ru</country>
    </aff>
    <aff>
     <institution xml:lang="en">Institute of Applied Physics of the Russian Academy of Sciences</institution>
     <country>ru</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Institute of Applied Physics of the Russian Academy of Sciences</institution>
     <country>ru</country>
    </aff>
    <aff>
     <institution xml:lang="en">Institute of Applied Physics of the Russian Academy of Sciences</institution>
     <country>ru</country>
    </aff>
   </aff-alternatives>
   <volume>19</volume>
   <issue>3</issue>
   <history>
    <date date-type="received" iso-8601-date="2021-10-29T12:50:45+03:00">
     <day>29</day>
     <month>10</month>
     <year>2021</year>
    </date>
   </history>
   <self-uri xlink:href="https://rjes.ru/en/nauka/article/46585/view">https://rjes.ru/en/nauka/article/46585/view</self-uri>
   <abstract xml:lang="ru">
    <p>The paper deals with experimental determination of the wind-driven wave spectrum by using the remote method of high-resolution coherent radar sensing of the water surface. The method is applied to the conditions of the fetch-limited wind wave growth, which is typical for enclosed waters and the sea nearshore, where the dominant wavelength is of the order of ten meters. The experiments were performed using a coherent X-band panoramic digital radar operating with the horizontal polarization for transmission and reception. The paper considers an algorithm used to form velocity images of the water surface from the data of coherent radar sensing on the basis of the phase angle difference method. The paper shows the possibility to recover wind wave spectra from the data on the Doppler shift of microwave radio waves. A theoretical justification and an experimental verification of the method are provided. Appearance of the third harmonic of the wind waves recovered from the radar sensing data of the spatio-temporal spectra of Doppler velocities is demonstrated for the first time. The functions that relate to the wave elevation spectra and the Doppler velocity spectra are determined. It is shown that the linear free-surface wave approximation is valid for the reconstruction of wave spectra. The temporal and spatial omnidirectional wave spectra obtained in the experiment are described well by the power model functions using the exponent factor of &amp;#x2212;4&quot; role=&quot;presentation&quot;&gt;-4</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>The paper deals with experimental determination of the wind-driven wave spectrum by using the remote method of high-resolution coherent radar sensing of the water surface. The method is applied to the conditions of the fetch-limited wind wave growth, which is typical for enclosed waters and the sea nearshore, where the dominant wavelength is of the order of ten meters. The experiments were performed using a coherent X-band panoramic digital radar operating with the horizontal polarization for transmission and reception. The paper considers an algorithm used to form velocity images of the water surface from the data of coherent radar sensing on the basis of the phase angle difference method. The paper shows the possibility to recover wind wave spectra from the data on the Doppler shift of microwave radio waves. A theoretical justification and an experimental verification of the method are provided. Appearance of the third harmonic of the wind waves recovered from the radar sensing data of the spatio-temporal spectra of Doppler velocities is demonstrated for the first time. The functions that relate to the wave elevation spectra and the Doppler velocity spectra are determined. It is shown that the linear free-surface wave approximation is valid for the reconstruction of wave spectra. The temporal and spatial omnidirectional wave spectra obtained in the experiment are described well by the power model functions using the exponent factor of &amp;#x2212;4&quot; role=&quot;presentation&quot;&gt;-4</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>Coherent radar</kwd>
    <kwd>Doppler velocity</kwd>
    <kwd>wind wave spectra</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>Coherent radar</kwd>
    <kwd>Doppler velocity</kwd>
    <kwd>wind wave spectra</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="en">This work was done by support of the Russian Science Foundation (Project RSF 18-77-00072).</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">
            
              Bass, F. G., I. M. Fuks (1972), Waves Scattering by Statistically Rough Surface, Nauka, Moscow (in Russian)
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Bass, F. G., I. M. Fuks (1972), Waves Scattering by Statistically Rough Surface, Nauka, Moscow (in Russian)
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B2">
    <label>2.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Battjes, J. A., T. J. Zitman, L. Y. Holthuijsen (1987), A reanalysis of the spectra observed in JONSWAP, J. Phys. Oceanogr., 17, p. 1288, https://doi.org/10.1175/1520-0485(1987)017&lt;1288:AROTSO&gt;2.0.CO;2
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Battjes, J. A., T. J. Zitman, L. Y. Holthuijsen (1987), A reanalysis of the spectra observed in JONSWAP, J. Phys. Oceanogr., 17, p. 1288, https://doi.org/10.1175/1520-0485(1987)017&lt;1288:AROTSO&gt;2.0.CO;2
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B3">
    <label>3.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Carrasco, R., J. Horstmann, J. Seemann (2017), Significant wave height measured by coherent X-band radar, IEEE Transactions on Geoscience and Remote Sensing, 55, no. 9, p. 5355-5265, https://doi.org/10.1109/TGRS.2017.2706067
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Carrasco, R., J. Horstmann, J. Seemann (2017), Significant wave height measured by coherent X-band radar, IEEE Transactions on Geoscience and Remote Sensing, 55, no. 9, p. 5355-5265, https://doi.org/10.1109/TGRS.2017.2706067
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B4">
    <label>4.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Dankert, H., J. Horstmann, W. Rosenthal (2005), Wind- and wave-field measurements using marine X-band radar-image sequences, IEEE Journal of oceanic engineering, 30, no. 3, p. 534-542, https://doi.org/10.1109/JOE.2005.857524
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Dankert, H., J. Horstmann, W. Rosenthal (2005), Wind- and wave-field measurements using marine X-band radar-image sequences, IEEE Journal of oceanic engineering, 30, no. 3, p. 534-542, https://doi.org/10.1109/JOE.2005.857524
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B5">
    <label>5.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Ermakov, S. A., I. A. Kapustin, I. A. Sergievskaya, O. V. Shomina, V. N. Kudryavtsev, B. Chapron, Y. Y. Yurovskiy (2014), On the Doppler Frequency Shifts of Radar Signals Backscattered from the Sea Surface, Radiophysics and Quantum Electronics, 57, no. 4, p. 239-250, https://doi.org/10.1007/s11141-014-9507-8
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Ermakov, S. A., I. A. Kapustin, I. A. Sergievskaya, O. V. Shomina, V. N. Kudryavtsev, B. Chapron, Y. Y. Yurovskiy (2014), On the Doppler Frequency Shifts of Radar Signals Backscattered from the Sea Surface, Radiophysics and Quantum Electronics, 57, no. 4, p. 239-250, https://doi.org/10.1007/s11141-014-9507-8
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B6">
    <label>6.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Hwang, P. A., M. A. Sletten, J. V. Toporkov (2010), A note on Doppler processing of coherent radar backscatter from the water surface: With application to ocean surface wave measurements, J. Geophys. Res., 115, p. C03026, https://doi.org/10.1029/2009JC005870
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Hwang, P. A., M. A. Sletten, J. V. Toporkov (2010), A note on Doppler processing of coherent radar backscatter from the water surface: With application to ocean surface wave measurements, J. Geophys. Res., 115, p. C03026, https://doi.org/10.1029/2009JC005870
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B7">
    <label>7.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Ivonin, D. V., V. A. Telegin, V. V. Bakhanov, A. V. Ermoshkin, A. I. Azarov (2011), Monitoring system of surface currents on the base of low-cost X-band radar. First application on the Black Sea, Russ. J. Earth. Sci., 13, p. ES2003, https://doi.org/10.2205/2011ES000507
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Ivonin, D. V., V. A. Telegin, V. V. Bakhanov, A. V. Ermoshkin, A. I. Azarov (2011), Monitoring system of surface currents on the base of low-cost X-band radar. First application on the Black Sea, Russ. J. Earth. Sci., 13, p. ES2003, https://doi.org/10.2205/2011ES000507
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B8">
    <label>8.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Lyzenga, D., O. Nwogu, D. Trizna, K. Hathaway (2010), Ocean wave field measurements using X-band Doppler radars at low grazing angles, 2010 IEEE International Geoscience and Remote Sensing Symposium, IEEE, Honolulu, HI, USA, https://doi.org/10.1109/IGARSS.2010.5650065
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Lyzenga, D., O. Nwogu, D. Trizna, K. Hathaway (2010), Ocean wave field measurements using X-band Doppler radars at low grazing angles, 2010 IEEE International Geoscience and Remote Sensing Symposium, IEEE, Honolulu, HI, USA, https://doi.org/10.1109/IGARSS.2010.5650065
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B9">
    <label>9.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Nekrasov, A. V., E. N. Pelinovskiy (eds.) (1992), Laboratory Manual in Ocean Dynamics, Gidrometeoizdat, Sankt-Petersburg (in Russian)
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Nekrasov, A. V., E. N. Pelinovskiy (eds.) (1992), Laboratory Manual in Ocean Dynamics, Gidrometeoizdat, Sankt-Petersburg (in Russian)
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B10">
    <label>10.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Nwogu, O. G., D. R. Lyzenga (2010), Surface-Wavefield Estimation From Coherent Marine Radars, IEEE Geoscience and Remote Sensing Letters, 7, no. 4, p. 631-635, https://doi.org/10.1109/LGRS.2010.2043712
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Nwogu, O. G., D. R. Lyzenga (2010), Surface-Wavefield Estimation From Coherent Marine Radars, IEEE Geoscience and Remote Sensing Letters, 7, no. 4, p. 631-635, https://doi.org/10.1109/LGRS.2010.2043712
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B11">
    <label>11.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Plant, W. J., G. Farquharson (2012), Origins of features in wave number-frequency spectra of space-time images of the ocean, J. Geophys. Res., 117, p. C06015, https://doi.org/10.1029/2012JC007986
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Plant, W. J., G. Farquharson (2012), Origins of features in wave number-frequency spectra of space-time images of the ocean, J. Geophys. Res., 117, p. C06015, https://doi.org/10.1029/2012JC007986
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B12">
    <label>12.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Pereslegin, S. V., Yu. P. Sinitsyn (2011), Interference synthetic-aperture radars for routine monitoring of ocean phenomena, Radiophysics and Quantum Electronics, 54, no. 6, p. 376-389, https://doi.org/10.1007/s11141-011-9298-0
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Pereslegin, S. V., Yu. P. Sinitsyn (2011), Interference synthetic-aperture radars for routine monitoring of ocean phenomena, Radiophysics and Quantum Electronics, 54, no. 6, p. 376-389, https://doi.org/10.1007/s11141-011-9298-0
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B13">
    <label>13.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Rosenberg, A. D., I. E. Ostrovskiy, V. I. Zel'dis, I. A. Leiykin, V. G. Ruskevich (1973), Determination of the energy-carrying part of the sea wave spectrum by the phase characteristics of the radio signal scattered by the sea), Izv. AN SSSR, FAO, 9, no. 12, p. 1323-1326 (in Russian)
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Rosenberg, A. D., I. E. Ostrovskiy, V. I. Zel'dis, I. A. Leiykin, V. G. Ruskevich (1973), Determination of the energy-carrying part of the sea wave spectrum by the phase characteristics of the radio signal scattered by the sea), Izv. AN SSSR, FAO, 9, no. 12, p. 1323-1326 (in Russian)
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B14">
    <label>14.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Slunyaev, A. V., A. V. Sergeeva (2012), Numerical Simulations and Analysis of Spatio-Temporal Fields of Rogue Waves, Fundamentsl and Applied Hydrophysics, 5, no. 1, p. 24-36
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Slunyaev, A. V., A. V. Sergeeva (2012), Numerical Simulations and Analysis of Spatio-Temporal Fields of Rogue Waves, Fundamentsl and Applied Hydrophysics, 5, no. 1, p. 24-36
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B15">
    <label>15.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Toporkov, J. V., M. A. Sletten (2017), Numerical simulations of range-resolved radar backscatter from evolving sea surface with floating targets, 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), IEEE, Fort Worth, TX, USA, https://doi.org/10.1109/IGARSS.2017.8127254
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Toporkov, J. V., M. A. Sletten (2017), Numerical simulations of range-resolved radar backscatter from evolving sea surface with floating targets, 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), IEEE, Fort Worth, TX, USA, https://doi.org/10.1109/IGARSS.2017.8127254
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B16">
    <label>16.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Trizna, D. B. (2011), Coherent Marine Radar Measurements of Ocean Surface Currents and Directional Spectra, OCEANS 2011 IEEE - Spain, IEEE, Santander, Spain, https://doi.org/10.1109/Oceans-Spain.2011.6003441
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Trizna, D. B. (2011), Coherent Marine Radar Measurements of Ocean Surface Currents and Directional Spectra, OCEANS 2011 IEEE - Spain, IEEE, Santander, Spain, https://doi.org/10.1109/Oceans-Spain.2011.6003441
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B17">
    <label>17.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">
            
              Young, I. R., W. Rosenthal, F. Ziemer (1985), A Three-Dimensional Analysis of Marine Radar Images for the Determination of Ocean Wave Directionality and Surface Currents, J. Geophys. Res., 90, no. C1, p. 1049-1059, https://doi.org/10.1029/JC090iC01p01049
            
          </mixed-citation>
     <mixed-citation xml:lang="en">
            
              Young, I. R., W. Rosenthal, F. Ziemer (1985), A Three-Dimensional Analysis of Marine Radar Images for the Determination of Ocean Wave Directionality and Surface Currents, J. Geophys. Res., 90, no. C1, p. 1049-1059, https://doi.org/10.1029/JC090iC01p01049
            
          </mixed-citation>
    </citation-alternatives>
   </ref>
  </ref-list>
 </back>
</article>
