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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-2026-2912</article-id>
<title-group>
<article-title>SPatial Efficiency And Kmoments (SPEAK): Evaluating Spatial Consistency in (Semi)Distributed Rainfall&amp;ndash;Runoff Models</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Moreno</surname>
<given-names>Matías</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Mendoza</surname>
<given-names>Pablo</given-names>
<ext-link>https://orcid.org/0000-0002-0263-9698</ext-link>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Muñoz-Castro</surname>
<given-names>Eduardo</given-names>
<ext-link>https://orcid.org/0000-0002-0314-3563</ext-link>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
<xref ref-type="aff" rid="aff5">
<sup>5</sup>
</xref>
<xref ref-type="aff" rid="aff6">
<sup>6</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Zambrano-Bigiarini</surname>
<given-names>Mauricio</given-names>
<ext-link>https://orcid.org/0000-0002-9536-643X</ext-link>
</name>
<xref ref-type="aff" rid="aff7">
<sup>7</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Pizarro</surname>
<given-names>Alonso</given-names>
</name>
<xref ref-type="aff" rid="aff8">
<sup>8</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Independent Engineer and Researcher, Santiago, Chile</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Civil Engineering Department, Universidad de Chile, Santiago, Chile</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>Advanced Mining Technology Centre (AMTC), Universidad de Chile, Santiago, Chile</addr-line>
</aff>
<aff id="aff4">
<label>4</label>
<addr-line>WSL Institute for Snow and Avalanche Research SLF, Davos Dorf, Switzerland</addr-line>
</aff>
<aff id="aff5">
<label>5</label>
<addr-line>Climate Change, Extremes and Natural Hazards in Alpine Regions Research Center CERC, Davos Dorf, Switzerland</addr-line>
</aff>
<aff id="aff6">
<label>6</label>
<addr-line>Institute for Atmospheric and Climate Science, ETH Zurich, Zurich, Switzerland</addr-line>
</aff>
<aff id="aff7">
<label>7</label>
<addr-line>Department of Civil Engineering, Universidad de la Frontera, Temuco, Chile</addr-line>
</aff>
<aff id="aff8">
<label>8</label>
<addr-line>Department of Civil and Environmental Engineering, Universidad del Bío-Bío, Concepción, Chile</addr-line>
</aff>
<pub-date pub-type="epub">
<day>05</day>
<month>06</month>
<year>2026</year>
</pub-date>
<volume>2026</volume>
<fpage>1</fpage>
<lpage>30</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2026 Matías Moreno 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-2026-2912/">This article is available from https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2912/</self-uri>
<self-uri xlink:href="https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2912/egusphere-2026-2912.pdf">The full text article is available as a PDF file from https://egusphere.copernicus.org/preprints/2026/egusphere-2026-2912/egusphere-2026-2912.pdf</self-uri>
<abstract>
<p>We introduce the Spatial Efficiency and Kmoments (SPEAK) metric, a novel objective function for the spatial calibration of hydrological models. SPEAK is built on Kmoment-based statistics, including a Kmoment-based: i) correlation, ii) coefficient-of-variation ratio, and iii) probability density function. This novel formulation is explicitly designed to overcome key limitations of existing spatial performance metrics, such as sensitivity to binning strategies, grid resolution, and sample heterogeneity. By relying on distributional properties rather than grid-to-grid correspondence, SPEAK provides a statistically robust framework for evaluating spatial patterns in gridded hydrological variables. The proposed metric is implemented in both semi-distributed and fully distributed configurations of the TUW hydrological model and tested across 99 near-natural Chilean catchments that encompass strong climatic and physiographic gradients. Actual evapotranspiration (ETa) from GLEAM v4.2a is used as an independent spatial benchmark, allowing the assessment of model performance beyond streamflow reproduction. Calibration using SPEAK is compared with a conventional streamflow-only calibration based on the Kling-Gupta Efficiency (KGE) and an ETa-only calibration based on the Spatial Efficiency metric (SPAEF). Model performance is evaluated using the normalised root-mean-square error (NRMSE), the spatial Pearson correlation coefficient, the Fraction Skill Score (FSS), and sensitivity to catchment attributes. Results demonstrate that while streamflow-only calibration leads to satisfactory runoff simulations (KGE &amp;ge; 0.25 for all catchments and cases analysed; whereas the mean and median KGE are 0.80 and 0.85, respectively), it fails to reproduce the spatial patterns of ETa. When ETa is used as a calibration target, SPEAK consistently outperforms SPAEF, exhibiting lower NRMSE (number of catchments with lower NRMSE: 85 and 92 in fully and semi-distributed configuration, respectively), reduced internal component dispersion, and improved representation of spatial patterns across seasons and hydroclimatic zones. Importantly, SPEAK shows limited dependence on catchment characteristics. These findings highlight SPEAK as a methodologically robust spatial performance metric, with clear potential for improving the calibration and diagnosis of distributed hydrological models and other gridded environmental variables.</p>
</abstract>
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<funding-group>
<award-group id="gs1">
<funding-source>Agencia Nacional de Investigación y Desarrollo</funding-source>
<award-id>11240171</award-id>
<award-id>1212071</award-id>
<award-id>190018</award-id>
</award-group>
</funding-group>
</article-meta>
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