<!DOCTYPE article
PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.4 20190208//EN"
       "JATS-journalpublishing1.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" article-type="research-article" dtd-version="1.4" xml:lang="en">
 <front>
  <journal-meta>
   <journal-id journal-id-type="publisher-id">INTERNATIONAL AGRICULTURAL JOURNAL</journal-id>
   <journal-title-group>
    <journal-title xml:lang="en">INTERNATIONAL AGRICULTURAL JOURNAL</journal-title>
    <trans-title-group xml:lang="ru">
     <trans-title>МЕЖДУНАРОДНЫЙ СЕЛЬСКОХОЗЯЙСТВЕННЫЙ ЖУРНАЛ</trans-title>
    </trans-title-group>
   </journal-title-group>
   <issn publication-format="print">2587-6740</issn>
  </journal-meta>
  <article-meta>
   <article-id pub-id-type="publisher-id">110215</article-id>
   <article-id pub-id-type="doi">10.55186/25876740_2025_68_7_958</article-id>
   <article-categories>
    <subj-group subj-group-type="toc-heading" xml:lang="ru">
     <subject>Научное обеспечение и управление агропромышленным комплексом</subject>
    </subj-group>
    <subj-group subj-group-type="toc-heading" xml:lang="en">
     <subject>Scientific support and management of agrarian and industrial complex</subject>
    </subj-group>
    <subj-group>
     <subject>Научное обеспечение и управление агропромышленным комплексом</subject>
    </subj-group>
   </article-categories>
   <title-group>
    <article-title xml:lang="en">Long-term frost forecasting using machine learning methods in a precision farming system</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Долгосрочное прогнозирование заморозков с применением методов машинного обучения в системе точного земледелия</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/0009-0007-0833-7029</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Молин</surname>
       <given-names>Александр Евгеньевич</given-names>
      </name>
      <name xml:lang="en">
       <surname>Molin</surname>
       <given-names>Aleksandr Evgen'evich</given-names>
      </name>
     </name-alternatives>
     <email>a.molin@spbu.ru</email>
     <bio xml:lang="ru">
      <p>кандидат технических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>candidate of technical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-7059-4727</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Митрофанова</surname>
       <given-names>Ольга Александровна</given-names>
      </name>
      <name xml:lang="en">
       <surname>Mitrofanova</surname>
       <given-names>Olga Aleksandrovna</given-names>
      </name>
     </name-alternatives>
     <email>o.a.mitrofanova@spbu.ru</email>
     <bio xml:lang="ru">
      <p>кандидат технических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>candidate of technical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-7018-4667</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Буре</surname>
       <given-names>Владимир Мансурович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Bure</surname>
       <given-names>Vladimir Mansurovich</given-names>
      </name>
     </name-alternatives>
     <email>v.bure@spbu.ru</email>
     <bio xml:lang="ru">
      <p>доктор технических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>doctor of technical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-3"/>
    </contrib>
    <contrib contrib-type="author">
     <contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-1967-5126</contrib-id>
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Митрофанов</surname>
       <given-names>Евгений Павлович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Mitrofanov</surname>
       <given-names>Evgeniy Pavlovich</given-names>
      </name>
     </name-alternatives>
     <email>e.mitrofanov@spbu.ru</email>
     <bio xml:lang="ru">
      <p>кандидат технических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>candidate of technical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-4"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Санкт-Петербургский государственный университет</institution>
     <city>Санкт-Петербург</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Saint Petersburg State University</institution>
     <city>Saint-Petersburg</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Санкт-Петербургский государственный университет</institution>
     <city>Санкт-Петербург</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Saint Petersburg State University</institution>
     <city>Saint-Petersburg</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-3">
    <aff>
     <institution xml:lang="ru">Санкт-Петербургский государственный университет</institution>
     <city>Санкт-Петербург</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Saint Petersburg State University</institution>
     <city>Saint-Petersburg</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-4">
    <aff>
     <institution xml:lang="ru">Санкт-Петербургский государственный университет</institution>
     <city>Санкт-Петербург</city>
     <country>Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">Saint Petersburg State University</institution>
     <city>Saint-Petersburg</city>
     <country>Russian Federation</country>
    </aff>
   </aff-alternatives>
   <pub-date publication-format="print" date-type="pub" iso-8601-date="2025-12-15T00:00:00+03:00">
    <day>15</day>
    <month>12</month>
    <year>2025</year>
   </pub-date>
   <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2025-12-15T00:00:00+03:00">
    <day>15</day>
    <month>12</month>
    <year>2025</year>
   </pub-date>
   <issue>7</issue>
   <fpage>958</fpage>
   <lpage>962</lpage>
   <history>
    <date date-type="received" iso-8601-date="2025-09-13T00:00:00+03:00">
     <day>13</day>
     <month>09</month>
     <year>2025</year>
    </date>
    <date date-type="accepted" iso-8601-date="2025-10-15T00:00:00+03:00">
     <day>15</day>
     <month>10</month>
     <year>2025</year>
    </date>
   </history>
   <self-uri xlink:href="https://qje.su/en/nauka/article/110215/view">https://qje.su/en/nauka/article/110215/view</self-uri>
   <abstract xml:lang="ru">
    <p>Целью исследования являлось обучение и сравнительный анализ моделей машинного обучения (МО) и глубокого обучения (ГО) для долгосрочного прогнозирования минимальных суточных температур (заморозков) – ключевого агрометеорологического риска, влияющего на продуктивность сельскохозяйственных культур. Исследование выполнено на основе данных метеостанций Санкт-Петербурга и Ленинградской области. Для прогнозирования на год вперед, что соответствует потребностям оперативного агропроизводственного планирования (сроки сева, уборки, защитных мероприятий), использовались 8 методов: ForecasterAutoreg, Random Forest, Support Vector Regression (SVR), XGBoost, сверточная нейронная сеть (CNN), SimpleRNN, Gated Recurrent Unit (GRU) и Long Short-Term Memory (LSTM). Анализ проводился на двух датасетах: за периоды 1936-2024 и 1881-1995 годы. Качество моделей оценивалось по метрикам MAE, MSE, RMSE, R2 и скорректированному R2. Наиболее точные результаты на основном датасете (1936-2024) показала модель LSTM: MAE 2,9, MSE 14,661, R2 0,789. На архивных данных (1881-1995) лучшие метрики продемонстрировал метод SVR (MAE 3,461, R2 0,775). Установлено, что модели ГО (LSTM, GRU, CNN) в целом превосходят классические методы МО на современных данных. Метод LSTM признан наиболее эффективным для интеграции в системы точного земледелия и агромониторинга региона для заблаговременного планирования агротехнологических мероприятий по защите посевов от заморозков, оптимизации севооборотов и минимизации рисков потери урожая.</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>The purpose of the study was to train and compare machine learning (ML) and deep learning (DL) models for long-term forecasting of minimum daily temperatures (frosts) - a key agrometeorological risk affecting crop productivity. The study was based on data from weather stations in St. Petersburg and the Leningrad region. To predict the year ahead, which aligns with the needs of operational agricultural production planning (sowing dates, harvest timing, protective measures), 8 methods were used: ForecasterAutoreg, Random Forest, Support Vector Regression (SVR), XGBoost, Convolutional Neural Network (CNN), SimpleRNN, Gated Recurrent Unit (GRU) and Long Short-Term Memory (LSTM). The analysis was carried out on two datasets: for the periods 1936-2024 and 1881-1995. The quality of the models was assessed using the metrics MAE, MSE, RMSE, R2 and adjusted R2. The LSTM model showed the most accurate results on the main dataset (1936-2024): MAE 2.9, MSE 14.661, R2 0.789. The SVR method (MAE 3.461, R2 0.775) demonstrated the best metrics based on archived data (1881-1995). It has been established that DL models (LSTM, GRU, CNN) generally outperform classical ML methods based on modern data. The LSTM method is recognized as the most effective for integration into precision farming systems and agricultural monitoring in the region for the advance planning of agrotechnological measures to protect crops from frost, optimization of crop rotation systems, and minimization of crop loss risks.</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>долгосрочное агрометеорологическое прогнозирование</kwd>
    <kwd>заморозки</kwd>
    <kwd>методы машинного обучения</kwd>
    <kwd>методы глубокого обучения</kwd>
    <kwd>точное земледелие</kwd>
    <kwd>управление агропроизводством</kwd>
    <kwd>принятие решений в растениеводстве</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>long-term agrometeorological forecasting</kwd>
    <kwd>freezing</kwd>
    <kwd>machine learning methods</kwd>
    <kwd>deep learning methods</kwd>
    <kwd>precision farming</kwd>
    <kwd>agricultural management</kwd>
    <kwd>decision-making in crop production</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="ru">Исследование выполнено за счёт гранта Российского научного фонда № 24-21-00231, http://rscf.ru/project/24-21-00231.</funding-statement>
    <funding-statement xml:lang="en">The study was supported by the Russian Science Foundation grant No. 24-21-00231, https://rscf.ru/en/project/24-21-00231.</funding-statement>
   </funding-group>
  </article-meta>
 </front>
 <body>
  <p></p>
 </body>
 <back>
  <ref-list>
   <ref id="B1">
    <label>1.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">IPCC, 2012: Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation. A Special Report of Working Groups I and II of the Intergovernmental Panel on Climate Change [Field, C.B., V. Barros, T.F. Stocker, D. Qin, D.J. Dokken, K.L. Ebi, M.D. Mastrandrea, K.J. Mach, G.-K. Plattner, S.K. Allen, M. Tignor, and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, UK, and New York, NY, USA, 582 pp.</mixed-citation>
     <mixed-citation xml:lang="en">IPCC, 2012: Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation. A Special Report of Working Groups I and II of the Intergovernmental Panel on Climate Change [Field, C.B., V. Barros, T.F. Stocker, D. Qin, D.J. Dokken, K.L. Ebi, M.D. Mastrandrea, K.J. Mach, G.-K. Plattner, S.K. Allen, M. Tignor, and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, UK, and New York, NY, USA, 582 pp.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B2">
    <label>2.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Li X., Jiang D., Liu F. Winter soil warming exacerbates the impacts of Spring Low temperature stress on wheat // Journal of Agronomy and Crop Science. 2016. V. 202, no. 6. P. 554-563.</mixed-citation>
     <mixed-citation xml:lang="en">Li X., Jiang D., Liu F. Winter soil warming exacerbates the impacts of Spring Low temperature stress on wheat // Journal of Agronomy and Crop Science. 2016. V. 202, no. 6. P. 554-563.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B3">
    <label>3.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Mitrofanova O., Mitrofanov E., Blekanov I., Bure V., Molin A. Approach for long-term forecasting of frosts and droughts in smart agriculture // Agriculture Digitalization and Organic Production. ADOP 2024. Smart Innovation, Systems and Technologies, Springer, Singapore. 2024. V. 397. P. 35-46.</mixed-citation>
     <mixed-citation xml:lang="en">Mitrofanova O., Mitrofanov E., Blekanov I., Bure V., Molin A. Approach for long-term forecasting of frosts and droughts in smart agriculture // Agriculture Digitalization and Organic Production. ADOP 2024. Smart Innovation, Systems and Technologies, Springer, Singapore. 2024. V. 397. P. 35-46.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B4">
    <label>4.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Hua W., Heinemann P., He L. Frost management in agriculture with advanced sensing, modeling, and artificial intelligent technologies: A review // Computers and Electronics in Agriculture. 2025. V. 231. Article 110027.</mixed-citation>
     <mixed-citation xml:lang="en">Hua W., Heinemann P., He L. Frost management in agriculture with advanced sensing, modeling, and artificial intelligent technologies: A review // Computers and Electronics in Agriculture. 2025. V. 231. Article 110027.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B5">
    <label>5.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Eitzinger J., Daneu V., Kubu G., Thaler S., Trnka M., Schaumberger A., Schneider S., Tran T.M.A. Grid based monitoring and forecasting system of cropping conditions and risks by agrometeorological indicators in Austria – Agricultural Risk Information System ARIS // Climate Services. 2024. V. 34. Article 100478.</mixed-citation>
     <mixed-citation xml:lang="en">Eitzinger J., Daneu V., Kubu G., Thaler S., Trnka M., Schaumberger A., Schneider S., Tran T.M.A. Grid based monitoring and forecasting system of cropping conditions and risks by agrometeorological indicators in Austria – Agricultural Risk Information System ARIS // Climate Services. 2024. V. 34. Article 100478.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B6">
    <label>6.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Harilal G.T., Dixit A., Quattrone G. Establishing hybrid deep learning models for regional daily rainfall time series forecasting in the United Kingdom // Engineering Applications of Artificial Intelligence. 2024. V. 133. Article 108581.</mixed-citation>
     <mixed-citation xml:lang="en">Harilal G.T., Dixit A., Quattrone G. Establishing hybrid deep learning models for regional daily rainfall time series forecasting in the United Kingdom // Engineering Applications of Artificial Intelligence. 2024. V. 133. Article 108581.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B7">
    <label>7.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Guhan V., Raju A.D., Krishna R., Nagaratna K. Evaluating weather trends and forecasting with machine learning: Insights from maximum temperature, minimum temperature, and rainfall data in India // Dynamics of Atmospheres and Oceans. 2025. V. 110. Article 101562.</mixed-citation>
     <mixed-citation xml:lang="en">Guhan V., Raju A.D., Krishna R., Nagaratna K. Evaluating weather trends and forecasting with machine learning: Insights from maximum temperature, minimum temperature, and rainfall data in India // Dynamics of Atmospheres and Oceans. 2025. V. 110. Article 101562.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B8">
    <label>8.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Hossain M.A., Rahman Md M., Hasan S.S., Mahmud A., Bai L. Analysis and forecasting of meteorogical drought using PROPHET and SARIMA models deploying machine learning technique for southwestern region of Bangladesh // Environment and Sustainability Indicators. 2025. V. 27. Article 100761.</mixed-citation>
     <mixed-citation xml:lang="en">Hossain M.A., Rahman Md M., Hasan S.S., Mahmud A., Bai L. Analysis and forecasting of meteorogical drought using PROPHET and SARIMA models deploying machine learning technique for southwestern region of Bangladesh // Environment and Sustainability Indicators. 2025. V. 27. Article 100761.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B9">
    <label>9.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Hsu C.-C., Lin Y.-P. Incorporating long-term numerical weather forecast to quantify dynamic vulnerability of irrigation supply system: A case study of Shihmen Reservoir in Taiwan // Agricultural Water Management. 2024. V. 306. Article 109178.</mixed-citation>
     <mixed-citation xml:lang="en">Hsu C.-C., Lin Y.-P. Incorporating long-term numerical weather forecast to quantify dynamic vulnerability of irrigation supply system: A case study of Shihmen Reservoir in Taiwan // Agricultural Water Management. 2024. V. 306. Article 109178.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B10">
    <label>10.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Chen L., Liu X., Zeng C., He X., Chen F., Zhu B. Temperature prediction of seasonal frozen subgrades based on CEEMDAN-LSTM hybrid model // Sensors. 2022. V. 22. Article 5742.</mixed-citation>
     <mixed-citation xml:lang="en">Chen L., Liu X., Zeng C., He X., Chen F., Zhu B. Temperature prediction of seasonal frozen subgrades based on CEEMDAN-LSTM hybrid model // Sensors. 2022. V. 22. Article 5742.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B11">
    <label>11.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Zhang D., Ma Y., Jiang A., Ren Y., Lin J., Peng Q., Jin T. Long-term water temperature forecasting in fish spawning grounds downstream of hydropower stations using machine learning // Sustainability. 2025. V. 17. Article 4514.</mixed-citation>
     <mixed-citation xml:lang="en">Zhang D., Ma Y., Jiang A., Ren Y., Lin J., Peng Q., Jin T. Long-term water temperature forecasting in fish spawning grounds downstream of hydropower stations using machine learning // Sustainability. 2025. V. 17. Article 4514.</mixed-citation>
    </citation-alternatives>
   </ref>
  </ref-list>
 </back>
</article>
