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<article article-type="research-article" dtd-version="1.3" 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" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">gesj</journal-id><journal-title-group><journal-title xml:lang="en">GEOGRAPHY, ENVIRONMENT, SUSTAINABILITY</journal-title><trans-title-group xml:lang="ru"><trans-title>GEOGRAPHY, ENVIRONMENT, SUSTAINABILITY</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2071-9388</issn><issn pub-type="epub">2542-1565</issn><publisher><publisher-name>Russian Geographical Society</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.24057/2071-9388-2024-3564</article-id><article-id custom-type="elpub" pub-id-type="custom">gesj-3836</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>SPECIAL ISSUE «CATCHMENT EROSION AND POLLUTION PROBLEMS». Part 1. Catchment erosion and management</subject></subj-group></article-categories><title-group><article-title>A method of multi-site calibration of distributed hydrological models based on the Nash-Sutcliffe efficiency</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Gartsman</surname><given-names>Boris I.</given-names></name></name-alternatives><bio xml:lang="en"><p>Gubkina 3, Moscow, 119333</p><p>Prospekt Vernadskogo 4, Simferopol, 295007</p></bio><email xlink:type="simple">Gartsman@inbox.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Solomatine</surname><given-names>Dimitri P.</given-names></name></name-alternatives><bio xml:lang="en"><p>Gubkina 3, Moscow, 119333</p><p>Mekelweg 5, Delft, 2628CD, Netherlands</p><p>Westvest 7, Delft, 2611AX, Netherlands</p></bio><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Gubareva</surname><given-names>Tatiana S.</given-names></name></name-alternatives><bio xml:lang="en"><p>Gubkina 3, Moscow, 119333</p></bio><xref ref-type="aff" rid="aff-3"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>Water Problem Institute, Russian Academy of Sciences ; Vernadsky Crimean Federal University</institution><country>Russian Federation</country></aff><aff xml:lang="en" id="aff-2"><institution>Water Problem Institute, Russian Academy of Sciences ; Water Resources Section, Delft University of Technology ; Department of Hydroinformatics and Socio-Technical Innovation, IHE Delft Institute for Water Education</institution><country>Russian Federation</country></aff><aff xml:lang="en" id="aff-3"><institution>Water Problem Institute, Russian Academy of Sciences</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>15</day><month>01</month><year>2025</year></pub-date><volume>17</volume><issue>4</issue><fpage>76</fpage><lpage>87</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Gartsman B.I., Solomatine D.P., Gubareva T.S., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Gartsman B.I., Solomatine D.P., Gubareva T.S.</copyright-holder><copyright-holder xml:lang="en">Gartsman B.I., Solomatine D.P., Gubareva T.S.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://ges.rgo.ru/jour/article/view/3836">https://ges.rgo.ru/jour/article/view/3836</self-uri><abstract><p>Contemporary distributed hydrological models are detailed and mathematically rigorous, but their calibration and testing can be still an issue. Often it is based on the quadratic measure of the calculated and observed hydrographs proximity at one outlet gauge station, typically on the Nash-Sutcliffe model efficiency coefficient (NSE). This approach seems insufficient to calibrate a model with hundreds of spatial elements. This paper presents using a multi-dimensional estimator of modeling quality, being a natural generalization of the traditional NSE but which would aggregate data from several hydrological stations using Principal Component Analysis (PCA). The method was tested on the ECOMAG model developed for a sub-basin (24,400 km2, with 15 gauges) of the Ussuri River in Russia. The results show that the presented version of the multi-dimensional NSE with PCA in calibration of spatially-distributed hydrological models has a number of advantages compared to other methods: the reduced dimensionality without loss of important information, straightforward data analysis and the automated calibration procedure; objective separation of the deterministic signal from the noise, calibration using the “informational kernel” of data, leading to more accurate parameters’ estimates. Additionally, the introduced notion of the “compact” dataset allow to interpret physical-geographical homogeneity of the basins in mathematic manner, which can be valuable for hydrological zoning of the basins, hydrological fields analysis, and structuring the models of large basins. There is no doubt that further development and testing of the proposed methodology is advisable in solving spatial hydrological problems based on distributed models, such as managing a cascade of reservoirs, creating hydrological reanalyses, etc.</p></abstract><kwd-group xml:lang="en"><kwd>spatially-distributed hydrological models</kwd><kwd>multi-site calibration</kwd><kwd>multi-dimensional Nash-Sutcliffe coefficient</kwd><kwd>prediction for groups of sub-basins</kwd></kwd-group><funding-group><funding-statement xml:lang="en">This study was partly carried out under the grant from the Russian Science Foundation, No. 23-27-00236.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Ashu A.B. and Lee S.-I. (2023) Multi-Site Calibration of Hydrological Model and Spatio-Temporal Assessment of Water Balance in a Monsoon Watershed. 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