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<front>
<journal-meta>
<journal-id journal-id-type="publisher">EGUsphere</journal-id>
<journal-title-group>
<journal-title>EGUsphere</journal-title>
<abbrev-journal-title abbrev-type="publisher">EGUsphere</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">EGUsphere</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub"></issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/egusphere-2026-1787</article-id>
<title-group>
<article-title>Technical note: Machine learning metamodelling for global sensitivity analysis</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Yeste</surname>
<given-names>Patricio</given-names>
<ext-link>https://orcid.org/0000-0002-0546-9866</ext-link>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Melsen</surname>
<given-names>Lieke A.</given-names>
<ext-link>https://orcid.org/0000-0003-0062-1301</ext-link>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Brêda</surname>
<given-names>João Paulo L. F.</given-names>
<ext-link>https://orcid.org/0000-0002-8360-1308</ext-link>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Tacoronte</surname>
<given-names>Nicolás</given-names>
<ext-link>https://orcid.org/0000-0001-7329-7931</ext-link>
</name>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Saltelli</surname>
<given-names>Andrea</given-names>
</name>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
<xref ref-type="aff" rid="aff7">
<sup>7</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Vannucci</surname>
<given-names>Giulia</given-names>
</name>
<xref ref-type="aff" rid="aff8">
<sup>8</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Siciliano</surname>
<given-names>Roberta</given-names>
</name>
<xref ref-type="aff" rid="aff8">
<sup>8</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Bronstert</surname>
<given-names>Axel</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Institute of Environmental Science and Geography, University of Potsdam, Karl-Liebknecht-Straße 24–25, 14476 Potsdam, Germany</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>GFZ Helmholtz Centre for Geosciences, Potsdam, 14473, Germany</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Hydrology and Environmental Hydraulics Group, Wageningen University, Wageningen, The Netherlands</addr-line>
</aff>
<aff id="aff4">
<label>4</label>
<addr-line>Instituto de Pesquisas Hidráulicas, Universidade Federal do Rio Grande do Sul (IPH/UFRGS), Porto Alegre, Brazil</addr-line>
</aff>
<aff id="aff5">
<label>5</label>
<addr-line>Departamento de Física Aplicada, Universidad de Granada, Granada, Spain</addr-line>
</aff>
<aff id="aff6">
<label>6</label>
<addr-line>University Pompeu Fabra, Barcelona School of Management, Carrer de Balmes, 132, 08008, Barcelona, Spain</addr-line>
</aff>
<aff id="aff7">
<label>7</label>
<addr-line>Centre for the Study of the Sciences and the Humanities, University of Bergen, Parkveien 9, PB 7805, 5020, Bergen, Norway</addr-line>
</aff>
<aff id="aff8">
<label>8</label>
<addr-line>Department of Electrical Engineering and Information Technology, Polytechnic and Basic Sciences School, University of Naples Federico II, Via Claudio, 21, 80125 Napoli (NA), Italy</addr-line>
</aff>
<pub-date pub-type="epub">
<day>14</day>
<month>04</month>
<year>2026</year>
</pub-date>
<volume>2026</volume>
<fpage>1</fpage>
<lpage>26</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2026 Patricio Yeste et al.</copyright-statement>
<copyright-year>2026</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://egusphere.copernicus.org/preprints/2026/egusphere-2026-1787/">This article is available from https://egusphere.copernicus.org/preprints/2026/egusphere-2026-1787/</self-uri>
<self-uri xlink:href="https://egusphere.copernicus.org/preprints/2026/egusphere-2026-1787/egusphere-2026-1787.pdf">The full text article is available as a PDF file from https://egusphere.copernicus.org/preprints/2026/egusphere-2026-1787/egusphere-2026-1787.pdf</self-uri>
<abstract>
<p>Global sensitivity analysis (GSA) plays a central role in hydrologic modelling by supporting model understanding, diagnosis, and decision-making through the identification of influential and non-influential parameters and their interactions. Variance-based methods provide a rigorous framework for GSA but are often computationally expensive, as their estimation requires a large number of model evaluations. Metamodelling has therefore been widely adopted as a strategy to alleviate this issue, with recent advances in machine learning (ML) offering new opportunities to construct accurate and flexible surrogates for complex models. This technical note examines the practical relationship between Sobol&amp;rsquo; total-effect indices (&lt;em&gt;T&lt;sub&gt;i&lt;/sub&gt;&lt;/em&gt;) and feature importance measures derived from ML metamodels within a hydrologic modelling context. Building on theoretical results that link &lt;em&gt;T&lt;sub&gt;i&lt;/sub&gt;&lt;/em&gt; to permutation variable importance (PVI&lt;em&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/em&gt;) under independence assumptions, we provide systematic numerical evidence using three conceptual hydrologic models of varying complexity (HBV, HyMod, and VIC) applied to three headwater catchments in northern Germany, together with three ML metamodels: a random forest (RF), a neural network (NN), and a linear model (LM). The three metamodels were trained on Monte Carlo samples and used to estimate sensitivities through PVI&lt;em&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/em&gt; and SHapley Additive exPlanations (SHAP&lt;em&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/em&gt;). The results demonstrate that RF and NN metamodels reliably reproduce both the ranking and relative magnitude of &lt;em&gt;T&lt;sub&gt;i&lt;/sub&gt;&lt;/em&gt; using PVI&lt;em&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/em&gt; across all hydrologic models, providing clear empirical support for the theoretical connection between the two measures. In contrast, the performance of LM-based estimates depends strongly on the degree of linearity in the underlying model response. Mean absolute SHAP&lt;em&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/em&gt; values exhibit a consistent monotonic relationship with &lt;em&gt;T&lt;sub&gt;i&lt;/sub&gt;&lt;/em&gt; and preserve parameter rankings, while sample-specific SHAP&lt;em&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/em&gt; values enable a distributed evaluation of sensitivities across both the parameter space and the target variable space. Overall, this study highlights ML metamodelling as a computationally efficient and conceptually sound framework for GSA in hydrologic modelling and beyond.</p>
</abstract>
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<funding-group>
<award-group id="gs1">
<funding-source>Alexander von Humboldt-Stiftung</funding-source>
<award-id>Humboldt Research Fellowship for postdoctoral researchers</award-id>
</award-group>
</funding-group>
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