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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">98455</article-id>
   <article-id pub-id-type="doi">10.2205/2026es001090</article-id>
   <article-id pub-id-type="edn">mmreka</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">Small Lakes Mixing by Surface Cooling: Efficiency Estimates</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Small Lakes Mixing by Surface Cooling: Efficiency Estimates</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/0000-0003-4150-2712</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Богданов</surname>
       <given-names>Сергей Рэмович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Bogdanov</surname>
       <given-names>Sergey Removich</given-names>
      </name>
     </name-alternatives>
     <email>Sergey.R.Bogdanov@mail.ru</email>
     <bio xml:lang="ru">
      <p>доктор физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>doctor 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/0000-0003-0313-6731</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Ефремова</surname>
       <given-names>Татьяна Владимировна</given-names>
      </name>
      <name xml:lang="en">
       <surname>Efremova</surname>
       <given-names>Tatjana Vladimirovna</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-1540-3788</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Пальшин</surname>
       <given-names>Николай Иннокентьевич</given-names>
      </name>
      <name xml:lang="en">
       <surname>Palshin</surname>
       <given-names>Nikolai Innocentjevich</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-3"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-1695-4872</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Здоровеннов</surname>
       <given-names>Роман Эдуардович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Zdorovennov</surname>
       <given-names>Roman Eduardovich</given-names>
      </name>
     </name-alternatives>
     <xref ref-type="aff" rid="aff-4"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Институт водных проблем Севера КарНЦ РАН</institution>
     <city>Петрозаводск</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Northern Water Problems Institute of the Karelian Research Centre of the Russian Academy of Sciences</institution>
     <city>Petrozavodsk</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Институт водных проблем Севера КарНЦ РАН</institution>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Northern Water Problems Institute of the Karelian Research Centre of the Russian Academy of Sciences</institution>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-3">
    <aff>
     <institution xml:lang="ru">Институт водных проблем Севера КарНЦ РАН</institution>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Northern Water Problems Institute of the Karelian Research Centre of the Russian Academy of Sciences</institution>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-4">
    <aff>
     <institution xml:lang="ru">Институт водных проблем Севера КарНЦ РАН</institution>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Northern Water Problems Institute of the Karelian Research Centre of the Russian Academy of Sciences</institution>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <pub-date publication-format="print" date-type="pub" iso-8601-date="2026-08-07T16:02:54+03:00">
    <day>07</day>
    <month>08</month>
    <year>2026</year>
   </pub-date>
   <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-08-07T16:02:54+03:00">
    <day>07</day>
    <month>08</month>
    <year>2026</year>
   </pub-date>
   <volume>26</volume>
   <issue>3</issue>
   <elocation-id>ES3008</elocation-id>
   <history>
    <date date-type="received" iso-8601-date="2025-05-06T00:00:00+03:00">
     <day>06</day>
     <month>05</month>
     <year>2025</year>
    </date>
    <date date-type="accepted" iso-8601-date="2025-11-25T00:00:00+03:00">
     <day>25</day>
     <month>11</month>
     <year>2025</year>
    </date>
   </history>
   <self-uri xlink:href="https://www.rjes.ru/en/nauka/article/98455/view">https://www.rjes.ru/en/nauka/article/98455/view</self-uri>
   <abstract xml:lang="ru">
    <p>The mixing of waterbodies and mixing efficiency estimates for different forcing mechanisms remain one of the main challenges in limnological studies, with a deep theoretical background and a wide range of practical applications. This paper examines the mixing that is triggered by surface cooling during the period of open water. The cooling often occurs at night and is largely determined by infrared radiation fluxes, in this regard, this type of forcing is usually positioned as the radiative mixing mechanism. To calculate the mixing efficiency η, an integral energy method was used, within which this parameter is defined as that portion of the external forcing that is spent on mixing itself, as opposed to viscous dissipation. Specific features of energy fluxes between different energy pools have been revealed for radiative type of forcing. For each identified mixing episode the changes of background potential energy were assessed, together with energy sink due to dissipation. Long-term temperature series for different depths at two small water bodies – a forest lake and a city pond – were used as initial data. Calculations carried out for several hundred mixing episodes showed that the mixing efficiency value, on average, significantly exceeds the canonical threshold 0.17. The correlation has also been identified between efficiency and CML thickness: vertical mixing resistance increases with CML deepening. This result introduces a new challenge to the “universality vs variability” dilemma: the efficiency may depend not only on the type and intensity of forcing, but also on the parameters of the initial temperature profile.</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>The mixing of waterbodies and mixing efficiency estimates for different forcing mechanisms remain one of the main challenges in limnological studies, with a deep theoretical background and a wide range of practical applications. This paper examines the mixing that is triggered by surface cooling during the period of open water. The cooling often occurs at night and is largely determined by infrared radiation fluxes, in this regard, this type of forcing is usually positioned as the radiative mixing mechanism. To calculate the mixing efficiency η, an integral energy method was used, within which this parameter is defined as that portion of the external forcing that is spent on mixing itself, as opposed to viscous dissipation. Specific features of energy fluxes between different energy pools have been revealed for radiative type of forcing. For each identified mixing episode the changes of background potential energy were assessed, together with energy sink due to dissipation. Long-term temperature series for different depths at two small water bodies – a forest lake and a city pond – were used as initial data. Calculations carried out for several hundred mixing episodes showed that the mixing efficiency value, on average, significantly exceeds the canonical threshold 0.17. The correlation has also been identified between efficiency and CML thickness: vertical mixing resistance increases with CML deepening. This result introduces a new challenge to the “universality vs variability” dilemma: the efficiency may depend not only on the type and intensity of forcing, but also on the parameters of the initial temperature profile.</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>mixing efficiency</kwd>
    <kwd>surface cooling</kwd>
    <kwd>external forcing</kwd>
    <kwd>background potential energy</kwd>
    <kwd>small lakes</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>mixing efficiency</kwd>
    <kwd>surface cooling</kwd>
    <kwd>external forcing</kwd>
    <kwd>background potential energy</kwd>
    <kwd>small lakes</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="ru">This research was supported by the federal budget within the framework of the state assignment FMEN-2026-0011 “Functioning of the ecosystem of Lake Onega and lake-river systems of its catchment area under conditions of climate change and anthropogenic impact”. The authors would like to thank G. E. Zdorovennova for helpful discussions and important comments.</funding-statement>
    <funding-statement xml:lang="en">This research was supported by the federal budget within the framework of the state assignment FMEN-2026-0011 “Functioning of the ecosystem of Lake Onega and lake-river systems of its catchment area under conditions of climate change and anthropogenic impact”. The authors would like to thank G. E. Zdorovennova for helpful discussions and important comments.</funding-statement>
   </funding-group>
  </article-meta>
 </front>
 <body>
  <p></p>
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