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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Ecol. Evol.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Ecology and Evolution</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Ecol. Evol.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2296-701X</issn>
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<publisher-name>Frontiers Media S.A.</publisher-name>
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<article-meta>
<article-id pub-id-type="doi">10.3389/fevo.2026.1763944</article-id>
<article-version article-version-type="Version of Record" vocab="NISO-RP-8-2008"/>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Spatiotemporal dynamics and driving factors of drought in the Yellow River Basin (Henan section): insights from TVDI analysis</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name><surname>Gu</surname><given-names>Zhijia</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>*</sup></xref>
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<contrib contrib-type="author">
<name><surname>Xu</surname><given-names>Gaohan</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
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<contrib contrib-type="author">
<name><surname>Feng</surname><given-names>Liu</given-names></name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
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<contrib contrib-type="author">
<name><surname>Li</surname><given-names>Yishan</given-names></name>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
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<contrib contrib-type="author">
<name><surname>Ji</surname><given-names>Keke</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
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<contrib contrib-type="author">
<name><surname>Reheman</surname><given-names>Maidinamu</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
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<aff id="aff1"><label>1</label><institution>School of Geographical Sciences, Xinyang Normal University</institution>, <city>Xinyang</city>,&#xa0;<country country="cn">China</country></aff>
<aff id="aff2"><label>2</label><institution>North&#x2013;South Transitional Zone Typical Vegetation Phenology Observation and Research Station of Henan Province</institution>, <city>Xinyang</city>,&#xa0;<country country="cn">China</country></aff>
<aff id="aff3"><label>3</label><institution>Business School, Xinyang Vocational and Technical College</institution>, <city>Xinyang</city>,&#xa0;<country country="cn">China</country></aff>
<aff id="aff4"><label>4</label><institution>Zhengzhou Lishui Foreign Language School</institution>, <city>Zhengzhou</city>,&#xa0;<country country="cn">China</country></aff>
<author-notes>
<corresp id="c001"><label>*</label>Correspondence: Zhijia Gu, <email xlink:href="mailto:guzhijia@xynu.edu.cn">guzhijia@xynu.edu.cn</email></corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-03-02">
<day>02</day>
<month>03</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2026</year>
</pub-date>
<volume>14</volume>
<elocation-id>1763944</elocation-id>
<history>
<date date-type="received">
<day>09</day>
<month>12</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>09</day>
<month>02</month>
<year>2026</year>
</date>
<date date-type="rev-recd">
<day>09</day>
<month>02</month>
<year>2026</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2026 Gu, Xu, Feng, Li, Ji and Reheman.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Gu, Xu, Feng, Li, Ji and Reheman</copyright-holder>
<license>
<ali:license_ref start_date="2026-03-02">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<sec>
<title>Introduction</title>
<p>Located in central China, the Yellow River Basin (Henan section) is a vital grain-producing region with extensive farmland. Its strategic central location also means its economic development is crucial for the stable growth of both Henan Province and the national economy. Nevertheless, persistent drought has long presented significant challenges to the region&#x2019;s agriculture, ecology, and economic development.</p>
</sec>
<sec>
<title>Methods</title>
<p>Based on TVDI (Temperature Vegetation Dryness Index) data from 2003 to 2022, this study investigated historical drought dynamics through Theil&#x2013;Sen Median and Mann&#x2013;Kendall trend analyses. Future drought tendencies were assessed using R/S analysis. Spatiotemporal influencing factors were further examined using Geographic Detector.</p>
</sec>
<sec>
<title>Results</title>
<p>Research results indicated that most areas of the region were experiencing drought conditions. From 2003 to 2022, drought intensified in the northeastern counties of Yuanyang, Fengqiu, Changyuan, Puyang, Fanxian, and Taiqian within the Yellow River Basin (Henan section), while drought conditions eased in the southwestern counties of Lingbao, Lushi, Luoning, Shanzhou District, and Jiyuan. Future trends in drought variation indicated that the southwestern part of the region showed potential for improvement in drought conditions, while drought conditions in the western areas were likely to worsen. The primary factors influencing the spatiotemporal variation of drought in this region were evapotranspiration, temperature, and rainfall.</p>
</sec>
<sec>
<title>Discussion</title>
<p>This study aimed to provide an in-depth analysis of the drought situation in the Yellow River Basin (Henan section), offering a reference to assist stakeholders in implementing timely drought mitigation measures, thereby reducing the impact of drought on agricultural production and the ecological environment.</p>
</sec>
</abstract>
<kwd-group>
<kwd>drought</kwd>
<kwd>geographic detector</kwd>
<kwd>Hurst exponent</kwd>
<kwd>TVDI (Temperature Vegetation Dryness Index)</kwd>
<kwd>Yellow River Basin (Henan section)</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declared that financial support was received for this work and/or its publication. This research was funded by Key Scientific and Technological Research Project of Henan Province, grant number 252102320245 and 242102320032, Key Research Projects of Higher Education Institutions in Henan Province, grant number 25A170004.</funding-statement>
</funding-group>
<counts>
<fig-count count="6"/>
<table-count count="4"/>
<equation-count count="14"/>
<ref-count count="41"/>
<page-count count="10"/>
<word-count count="6002"/>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Biogeography and Macroecology</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec id="s1" sec-type="intro">
<label>1</label>
<title>Introduction</title>
<p>Drought, a prolonged period of exceptionally dry weather resulting in a serious hydrological imbalance, ranks among the most widespread and impactful natural disasters globally (<xref ref-type="bibr" rid="B13">Field et&#xa0;al., 2012</xref>). It triggers a cascade of severe environmental consequences, including soil degradation, desertification, vegetation die-off, and an increased frequency of sandstorms and wildfires (<xref ref-type="bibr" rid="B16">Guo et&#xa0;al., 2017</xref>; <xref ref-type="bibr" rid="B33">Wang et&#xa0;al., 2023</xref>), thereby posing significant threats to ecosystems, agricultural productivity, and socioeconomic stability (<xref ref-type="bibr" rid="B1">Abbas and Ali, 2024</xref>; <xref ref-type="bibr" rid="B35">Wu et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B39">Zhu et&#xa0;al., 2025</xref>). Agricultural drought, a category of drought, results from an imbalance between crop water demand and available soil moisture, directly translating meteorological water shortages into agricultural losses (<xref ref-type="bibr" rid="B15">Guo et&#xa0;al., 2020</xref>; <xref ref-type="bibr" rid="B8">Chen et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B2">Alazba et&#xa0;al., 2025</xref>). It arises from an imbalance between crop water demand and soil water supply and is considered one of the direct consequences of meteorological drought (<xref ref-type="bibr" rid="B22">Liu and Li, 2024</xref>). Under global climatic and environmental change, China&#x2019;s status as a major agricultural nation renders its food systems especially susceptible to drought stress (<xref ref-type="bibr" rid="B31">Wang et&#xa0;al., 2019</xref>). Such conditions critically&#x2014;and often decisively&#x2014;limit rain-fed crop productivity. This is especially evident in the North China Plain, where a trend of declining rainfall has heightened the frequency of drought events, which often persist across consecutive seasons or even years (<xref ref-type="bibr" rid="B34">Wen et&#xa0;al., 2023</xref>).</p>
<p>Effective monitoring is fundamental to drought mitigation. While traditional ground-based methods for obtaining soil moisture data face significant challenges, their sparse observational networks limit reliable large-scale spatial assessment and forecasting (<xref ref-type="bibr" rid="B4">Almouctar et&#xa0;al., 2024</xref>). The advent of remote sensing has revolutionized this field by enabling synoptic, repetitive earth observation. Consequently, numerous remote sensing-based drought indices have been developed, such as the Vegetation Condition Index (VCI), the Soil Moisture Agricultural Drought Index (SMADI), and the Temperature Vegetation Dryness Index (TVDI). Among these, the TVDI, derived from the negative correlation between land surface temperature (LST) and vegetation indices (e.g., NDVI, EVI) in a feature space, offers distinct advantages for agricultural drought monitoring. It physically reflects soil moisture status, is particularly sensitive in vegetated and cropland areas, and leverages widely available MODIS data, ensuring operational feasibility and comparability across studies (<xref ref-type="bibr" rid="B5">Bai et&#xa0;al., 2017</xref>; <xref ref-type="bibr" rid="B27">Sandholt et&#xa0;al., 2002</xref>). This makes TVDI a robust tool for analyzing the spatiotemporal dynamics of drought. Therefore, it has been widely used in regional drought dynamic monitoring (<xref ref-type="bibr" rid="B40">Zormand et&#xa0;al., 2017</xref>; <xref ref-type="bibr" rid="B9">Chen et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B3">Ali et&#xa0;al., 2019</xref>; <xref ref-type="bibr" rid="B2">Alazba et&#xa0;al., 2025</xref>; <xref ref-type="bibr" rid="B41">Zou et&#xa0;al., 2025</xref>). It is now established as a principal indicator for assessing agricultural drought severity in China (<xref ref-type="bibr" rid="B30">Wan et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B17">Huang et&#xa0;al., 2025</xref>).</p>
<p>The Yellow River Basin is a vital ecological security barrier and a major socioeconomic corridorin China. Ecological conservation and high&#x2013;quality development of the basin has been designated as major national strategies. As a vital segment of the Yellow River Basin, the Henan section serves as a significant grain production base in China and encompasses multiple national key ecological function zones. Its role in promoting the holistic development of the entire Yellow River Basin is therefore indispensable (<xref ref-type="bibr" rid="B36">Yan et&#xa0;al., 2022</xref>). This region boasts a strategic geographical location, serving as a vital transportation nexus connecting North China, Central China, and the Southwest (<xref ref-type="bibr" rid="B24">Liu et&#xa0;al., 2023</xref>). It is also a key area under China&#x2019;s Western Development Strategy, playing a significant role in supporting the stable economic growth of both Henan Province and the nation as a whole part. Drought has long been a major constraint on production, livelihoods, and economic development in this region (<xref ref-type="bibr" rid="B38">Zhao et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B21">Li Y. et&#xa0;al., 2024</xref>). Despite the application of remote sensing for drought monitoring in broader contexts, a distinct knowledge gap persists regarding the long-term spatiotemporal patterns and the specific drivers of drought within the Yellow River Basin (Henan section). Existing studies often focus on single factors or short periods, lacking a comprehensive, long-term analysis that integrates climatic and anthropogenic drivers&#x2014;such as precipitation, temperature, evapotranspiration, and human activity indicators&#x2014;to explain drought dynamics in this ecologically and economically sensitive transition zone. To address this research gap, based on TVDI from 2003 to 2022, this study investigates the spatiotemporal dynamics and driving factors of drought in the Yellow River Basin (Henan section). Therefore, this study aimed to (1) characterize the spatiotemporal evolution of drought through Theil&#x2013;Sen Median, Mann&#x2013;Kendall trend analysis and R/S analysis; and (2) quantify the relative influence and interaction of key natural and anthropogenic driving factors using the geodetector. Our findings are expected to contribute to accurate drought monitoring and evaluation, provide a scientific basis for predicting future drought trends, and support the timely implementation of drought mitigation measures.</p>
</sec>
<sec id="s2" sec-type="materials|methods">
<label>2</label>
<title>Materials and methods</title>
<sec id="s2_1">
<label>2.1</label>
<title>Study area</title>
<p>The Yellow River Basin (Henan section) is located in the central part of China. Its geographical coordinates range from 33&#xb0;31&#x2032; N to 36&#xb0;22&#x2032; N, and from 110&#xb0;21&#x2032; E to 116&#xb0;05&#x2032; E. The main course of the river spans 711 km, the terrain tends to be higher in the southwest and lower in the northeast, with the lowest elevation of 35 m. The plain area in the eastern part of the study area belongs to the Huang Huai Hai alluvium plain in the eastern part of Henan Province, which is flat, rich in land resources and has a long history of farming (<xref ref-type="fig" rid="f1"><bold>Figure&#xa0;1</bold></xref>). Henan section accounts for 5.1% of the total drainage area of the Yellow River Basin (<xref ref-type="bibr" rid="B12">Fan, 2016</xref>). It is situated in the middle and lower reaches of the Yellow River, spanning the second and third terrain steps of China. The vegetation in the Henan section of the Yellow River Basin is dominated by cultivated crops, with farmland accounting for 76.51% of the total study area, followed by forestland, which makes up 13.79% (<xref ref-type="bibr" rid="B10">Cui et&#xa0;al., 2025</xref>). The increase in urban land use and the decrease in cultivated land in the future will both lead to an increase in TVDI, resulting in a higher degree of drought in urban areas. The region lies in a transitional zone between the temperate monsoon climate and the subtropical monsoon climate, characterized by four distinct seasons and precipitation concentrated mainly in the summer. The average annual temperature showed a significant increasing trend, with the fastest rates of increase observed in spring and autumn, while precipitation showed significant interannual variability (<xref ref-type="bibr" rid="B37">Yao et&#xa0;al., 2024</xref>). The study area is trending toward increased aridity. However, constrained by its natural geography and historical development, the region is characterized by an inadequate total water supply, uneven spatiotemporal distribution, and poor water quality. The region faces significant challenges in water resource management. Water use efficiency remains relatively low, with an agricultural irrigation efficiency coefficient of only 0.55&#x2014;well below advanced international standards. Meanwhile, the exploitation rate of water resources has reached 80%, far exceeding the internationally recognized warning threshold of 40% for river water resource development. As the population grows and the economy expands, the imbalance between water supply and demand is becoming increasingly acute. Water scarcity has emerged as a major constraint to the region&#x2019;s high-quality development.</p>
<fig id="f1" position="float">
<label>Figure&#xa0;1</label>
<caption>
<p>The location of the study area.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fevo-14-1763944-g001.tif">
<alt-text content-type="machine-generated">Colored elevation map of the Henan section of the Yellow River Basin in China, with county boundaries labeled, a legend for elevation ranges, river and basin markings, and two inset maps showing the location within China and surrounding provinces.</alt-text>
</graphic></fig>
</sec>
<sec id="s2_2">
<label>2.2</label>
<title>Data sources and preprocessing</title>
<p>The TVDI data in this paper is sourced from the 2003&#x2013;2022 annual 1 km resolution dataset of TCI, VCI, VHI, and TVDI for the Yellow River Basin (<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.57760/sciencedb.09116">https://doi.org/10.57760/sciencedb.09116</ext-link>) (<xref ref-type="bibr" rid="B28">Sha et&#xa0;al., 2024</xref>). The precipitation, temperature, and potential evapotranspiration data were obtained from the National Tibetan Plateau Data Center (<ext-link ext-link-type="uri" xlink:href="https://data.tpdc.ac.cn">https://data.tpdc.ac.cn</ext-link>), with a spatial resolution of 1 km. The Digital Elevation Model (DEM) data with a spatial resolution of 30m of the study area was obtained from the Geospatial Data Cloud (<ext-link ext-link-type="uri" xlink:href="https://www.gscloud.cn">https://www.gscloud.cn</ext-link>). Nighttime light data with a spatial resolution of 0.0042&#xb0; were acquired from the Data Center for Resources and Environmental Sciences, Chinese Academy of Sciences (<ext-link ext-link-type="uri" xlink:href="https://www.resdc.cn">https://www.resdc.cn</ext-link>). The 1 km resolution spatial distribution data of population density were obtained from the LandScan dataset (<ext-link ext-link-type="uri" xlink:href="https://landscan.ornl.gov">https://landscan.ornl.gov</ext-link>). All data were converted to Tiff format, the projection was converted to WGS-1984 coordinate system, and the spatial resolution was uniformly resampled to 1 km.</p>
</sec>
<sec id="s2_3">
<label>2.3</label>
<title>Methods</title>
<p>The structural flowchart of the study was shown in <xref ref-type="fig" rid="f2"><bold>Figure&#xa0;2</bold></xref>. The research methods employed in this study will be comprehensively elaborated in the current section.</p>
<fig id="f2" position="float">
<label>Figure&#xa0;2</label>
<caption>
<p>The structural flowchart of the study.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fevo-14-1763944-g002.tif">
<alt-text content-type="machine-generated">Flowchart illustrating the analysis process for drought using Temperature Vegetation Dryness Index, spatiotemporal dynamics, drought classification, statistical trend tests, spatial and temporal patterns, geographic detector, and Hurst exponent to assess driving factors and future drought trends.</alt-text>
</graphic></fig>
<sec id="s2_3_1">
<label>2.3.1</label>
<title>TVDI model</title>
<p>This study applied the TVDI model (<xref ref-type="disp-formula" rid="eq1">Equation 1</xref>) to inversion processing of remote sensing data. Based on the triangular distribution pattern observed in the NDVI&#x2013;LST scatter plot, <xref ref-type="bibr" rid="B27">Sandholt et&#xa0;al. (2002)</xref> revealed a significant negative correlation between LST and NDVI. As vegetation coverage increases, transpiration effects reduce surface temperatures, which led to the proposal of the TVDI. TVDI is calculated from vegetation indices and land surface temperature using the formula as follows:</p>
<disp-formula id="eq1"><label>(1)</label>
<mml:math display="block" id="M1"><mml:mrow><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>min</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>max</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>min</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<p>where <italic>t<sub>s</sub></italic> is surface temperature value (&#xb0;C). <italic>t<sub>smin</sub></italic> is the minimum surface temperature value of all grid values under the same vegetation cover condition. <italic>t<sub>smax</sub></italic> is the maximum surface temperature value of all grid values under the same vegetation cover condition.</p>
<p>The TVDI ranges from 0 to 1, serves as an indicator of surface soil moisture status. An increase in TVDI corresponds to decreased soil moisture and intensified drought severity, while a decrease indicates increased moisture and wetter conditions. Consequently, values closer to 1 represent more extreme drought, and values approaching 0 reflect higher moisture levels. In accordance with prior research and the prevailing conditions of the study area (<xref ref-type="bibr" rid="B29">Su et&#xa0;al., 2024</xref>), TVDI was categorized into five grades, as presented in <xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref>.</p>
<table-wrap id="T1" position="float">
<label>Table&#xa0;1</label>
<caption>
<p>TVDI&#x2013;based drought classification.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Grade</th>
<th valign="middle" align="center">Types</th>
<th valign="middle" align="center">TVDI</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="center">1</td>
<td valign="middle" align="center">Normal</td>
<td valign="middle" align="center">0&lt; TVDI&lt; 0.46</td>
</tr>
<tr>
<td valign="middle" align="center">2</td>
<td valign="middle" align="center">Mild drought</td>
<td valign="middle" align="center">0.46 &#x2264; TVDI&lt; 0.57</td>
</tr>
<tr>
<td valign="middle" align="center">3</td>
<td valign="middle" align="center">Moderate drought</td>
<td valign="middle" align="center">0.57 &#x2264; TVDI&lt; 0.76</td>
</tr>
<tr>
<td valign="middle" align="center">4</td>
<td valign="middle" align="center">Severe drought</td>
<td valign="middle" align="center">0.76 &#x2264; TVDI&lt; 0.86</td>
</tr>
<tr>
<td valign="middle" align="center">5</td>
<td valign="middle" align="center">Extreme drought</td>
<td valign="middle" align="center">0.86 &#x2264; TVDI&lt; 1.0</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s2_3_2">
<label>2.3.2</label>
<title>Theil&#x2013;Sen Median trend analysis and Mann&#x2013;Kendall significance test</title>
<p>This study first employed the Theil&#x2013;Sen Median trend analysis method to analyze the multi&#x2013;year TVDI within the region, clarifying its changing trends. Subsequently, the Mann&#x2013;Kendall significance test was applied to determine the statistical significance of these trends. The combination of these two methods (<xref ref-type="bibr" rid="B14">Guo et&#xa0;al., 2018</xref>; <xref ref-type="bibr" rid="B33">Wang et&#xa0;al., 2023</xref>) provides a more robust identification of changes in drought severity for the study area.</p>
<p>The Theil&#x2013;Sen Median trend analysis is a non&#x2013;parametric statistical method used to estimate data trends. This method is relatively insensitive to outliers in the data, offers strong robustness, and can more accurately reflect the overall trend. Furthermore, as long as the data exhibits a general trend, the Sen&#x2019;s slope estimate can provide a reasonable assessment of that trend. It is calculated as follows:</p>
<p>Given a set of points (<italic>x<sub>i</sub></italic>, <italic>y<sub>i</sub></italic>), where <italic>i</italic> = 1, 2, 3, &#x2026;, n. compute the slope (<italic>s<sub>ij</sub></italic>) for all possible pairwise combinations of points (<italic>x<sub>i</sub></italic>, <italic>y<sub>i</sub></italic>) and (<italic>x<sub>j</sub></italic>, <italic>y<sub>j</sub></italic>) (<italic>i</italic> &#x2260; <italic>j</italic>) (<xref ref-type="disp-formula" rid="eq2">Equation 2</xref>).</p>
<disp-formula id="eq2"><label>(2)</label>
<mml:math display="block" id="M2"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mrow><mml:mi>i</mml:mi><mml:mi>j</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<p>Arrange all the slopes(<italic>s<sub>ij</sub></italic>) in ascending order, and take the median as the Sen&#x2019;s slope estimate <italic>&#x3b2;</italic>. After obtaining the result <italic>&#x3b2;</italic>, if <italic>&#x3b2;</italic> &gt; 0, it indicates an increasing trend in the data from <italic>x<sub>i</sub></italic> to <italic>x<sub>j</sub></italic>; conversely, if <italic>&#x3b2;</italic> &lt; 0, it suggests a decreasing trend.</p>
<p>Mann&#x2013;Kendall test was used to test the significance of the change trend (<xref ref-type="bibr" rid="B26">Mann, 1945</xref>; <xref ref-type="bibr" rid="B19">Kendall, 1975</xref>). The Mann&#x2013;Kendall significance test is primarily used to determine whether a long&#x2013;term time series exhibits a statistically significant monotonic trend (upward or downward). The calculation procedure is as follows (<xref ref-type="disp-formula" rid="eq3">Equations 3</xref>&#x2013;<xref ref-type="disp-formula" rid="eq9">9</xref>):</p>
<p>It is assumed that the time series possesses no statistically significant monotonic trend, and that the data are structured in a random order. Given a time series <italic>x<sub>1</sub></italic>, <italic>x<sub>2</sub></italic>, &#x2026;, <italic>x<sub>n</sub></italic>, n = 1, 2, 3, &#x2026;, n. Compute the value of <italic>S</italic>:</p>
<disp-formula id="eq3"><label>(3)</label>
<mml:math display="block" id="M3"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mstyle></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq4"><label>(4)</label>
<mml:math display="block" id="M4"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mrow><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi></mml:mrow></mml:mstyle><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>,</mml:mo><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x2026;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq5"><label>(5)</label>
<mml:math display="block" id="M5"><mml:mrow><mml:mi>s</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>x</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mrow></mml:math>
</disp-formula>
<p>Calculate the expected value <italic>E(S)</italic> and variance <italic>Var(S)</italic> of <italic>S</italic>. When the sample size <italic>n</italic> is sufficiently large (<italic>n</italic> &gt; 10), the statistic <italic>S</italic> approximately follows a normal distribution. Its mean is <italic>E(s)</italic> = 0. A two&#x2013;tailed trend test is employed to determine the statistical significance of the change trend in the data series. Compute the test statistic <italic>Z</italic>:</p>
<disp-formula id="eq6"><label>(6)</label>
<mml:math display="block" id="M6"><mml:mrow><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mfrac><mml:mrow><mml:mi>S</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msqrt><mml:mrow><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msqrt></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mfrac><mml:mrow><mml:mi>S</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:msqrt><mml:mrow><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msqrt></mml:mrow></mml:mfrac><mml:mo>,</mml:mo><mml:mi>S</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mrow></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq7"><label>(7)</label>
<mml:math display="block" id="M7"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:munderover><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mi>i</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq8"><label>(8)</label>
<mml:math display="block" id="M8"><mml:mrow><mml:mi>v</mml:mi><mml:mi>a</mml:mi><mml:mi>r</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>S</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>5</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mn>18</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eq9"><label>(9)</label>
<mml:math display="block" id="M9"><mml:mrow><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>g</mml:mi><mml:mi>n</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mi>j</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:msub><mml:mi>I</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mrow></mml:mrow></mml:math>
</disp-formula>
<p>In the formula, <italic>n</italic> represents the length of the data, and <italic>TVDI<sub>i</sub></italic> and <italic>TVDI<sub>j</sub></italic> are the TVDI values in the TVDI time series corresponding to years <italic>i</italic> and <italic>j</italic>, respectively. In this study, |Z| greater than 2.58 indicates an extremely significant change trend. |Z|&#xa0;between 1.96 and 2.58 is considered significant change trend. |Z|&#xa0;between 1.65 and 1.96 is classified as slight significant. and |Z| less than 1.65 suggests no statistically significant trend. The specific criteria for determining the significance of trends are presented in <xref ref-type="table" rid="T2"><bold>Table&#xa0;2</bold></xref>.</p>
<table-wrap id="T2" position="float">
<label>Table&#xa0;2</label>
<caption>
<p>Trend analysis and significance evaluation.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">&#x3b2;</th>
<th valign="middle" align="center">Types</th>
<th valign="middle" align="center">Variation trend</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" rowspan="4" align="center"><italic>&#x3b2; &gt; 0</italic></td>
<td valign="middle" align="center">2.58 &#x2264; <italic>Z</italic></td>
<td valign="middle" align="center">Extremely significant increase</td>
</tr>
<tr>
<td valign="middle" align="center">1.96 &#x2264; <italic>Z</italic> &lt; 2.58</td>
<td valign="middle" align="center">Significant increase</td>
</tr>
<tr>
<td valign="middle" align="center">1.65 &#x2264; <italic>Z</italic> &lt; 1.96</td>
<td valign="middle" align="center">Slight significant increase</td>
</tr>
<tr>
<td valign="middle" align="center">0&#x2264; <italic>Z</italic> &lt; 1.65</td>
<td valign="middle" align="center">Not significant increase</td>
</tr>
<tr>
<td valign="middle" align="center"><italic>&#x3b2;</italic> = 0</td>
<td valign="middle" align="center">|Z|&lt; 1.65</td>
<td valign="middle" align="center">No change</td>
</tr>
<tr>
<td valign="middle" rowspan="4" align="center"><italic>&#x3b2;</italic> &lt; 0</td>
<td valign="middle" align="center">-1.65&lt; Z &#x2264; 0</td>
<td valign="middle" align="center">Not significant decrease</td>
</tr>
<tr>
<td valign="middle" align="center">-1.96&lt; <italic>Z</italic> &#x2264; -1.65</td>
<td valign="middle" align="center">Slight significant decrease</td>
</tr>
<tr>
<td valign="middle" align="center">-2.58&lt; <italic>Z</italic> &#x2264; -1.96</td>
<td valign="middle" align="center">Significant decrease</td>
</tr>
<tr>
<td valign="middle" align="center">Z &#x2264; -2.58</td>
<td valign="middle" align="center">Extremely significant decrease</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s2_3_3">
<label>2.3.3</label>
<title>Hurst exponent</title>
<p>Originally developed by British hydrologist <xref ref-type="bibr" rid="B18">Hurst (1951)</xref> and later refined by <xref ref-type="bibr" rid="B25">Mandelbrot and Wallis (1969)</xref>, the Hurst exponent method assesses the sustainability of time series data. This critical metric, derived from Rescaled Range (R/S) analysis, quantifies long&#x2013;term memory and persistence. By leveraging historical patterns, it enables predictions of future trends. The core principle is outlined below (<xref ref-type="disp-formula" rid="eq10">Equations 10</xref>&#x2013;<xref ref-type="disp-formula" rid="eq13">13</xref>).</p>
<p>Establish a time series of TVDI, <inline-formula>
<mml:math display="inline" id="im1"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:mi>I</mml:mi></mml:mrow><mml:mo stretchy="true">&#xaf;</mml:mo></mml:mover><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x3c4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, <italic>&#x3c4;</italic> = 1, 2, &#x2026;, n. Define the mean sequence of the time series:</p>
<disp-formula id="eq10"><label>(10)</label>
<mml:math display="block" id="M10"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:mi>I</mml:mi></mml:mrow><mml:mo stretchy="true">&#xaf;</mml:mo></mml:mover><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x3c4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mi>&#x3c4;</mml:mi></mml:mfrac><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>&#x3c4;</mml:mi></mml:munderover><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:mi>I</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mtext>t</mml:mtext><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#xa0;</mml:mo><mml:mi>&#x3c4;</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x22ef;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math>
</disp-formula>
<p>Calculate the accumulated deviation:</p>
<disp-formula id="eq11"><label>(11)</label>
<mml:math display="block" id="M11"><mml:mrow><mml:mi>X</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x3c4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>&#x3c4;</mml:mi></mml:munderover><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:mi>I</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:mi>I</mml:mi></mml:mrow><mml:mo stretchy="true">&#xaf;</mml:mo></mml:mover><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x3c4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mtext>&#xa0;&#xa0;&#xa0;&#xa0;</mml:mtext><mml:mi>&#x3c4;</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x22ef;</mml:mo><mml:mo>,</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mstyle></mml:mrow></mml:math>
</disp-formula>
<p>Establish a range sequence:</p>
<disp-formula id="eq12"><label>(12)</label>
<mml:math display="block" id="M12"><mml:mrow><mml:mi>R</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x3c4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>max</mml:mi></mml:mrow><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2264;</mml:mo><mml:mtext>t</mml:mtext><mml:mo>&#x2264;</mml:mo><mml:mi>&#x3c4;</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:mi>I</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mi>m</mml:mi><mml:mi>i</mml:mi><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>&#x2264;</mml:mo><mml:mtext>t</mml:mtext><mml:mo>&#x2264;</mml:mo><mml:mi>&#x3c4;</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:mi>I</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mtext>&#xa0;&#xa0;&#xa0;</mml:mtext><mml:mi>&#x3c4;</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x22ef;</mml:mo><mml:mo>,</mml:mo><mml:mtext>n</mml:mtext></mml:mrow></mml:math>
</disp-formula>
<p>Establish a standard deviation sequence:</p>
<disp-formula id="eq13"><label>(13)</label>
<mml:math display="block" id="M13"><mml:mrow><mml:mi>S</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x3c4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mi>&#x3c4;</mml:mi></mml:mfrac><mml:mstyle displaystyle="true"><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>t</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>&#x3c4;</mml:mi></mml:munderover><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:mi>I</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mover accent="true"><mml:mrow><mml:mi>T</mml:mi><mml:mi>V</mml:mi><mml:mi>D</mml:mi><mml:mi>I</mml:mi></mml:mrow><mml:mo stretchy="true">&#xaf;</mml:mo></mml:mover><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>&#x3c4;</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mstyle></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:msup><mml:mtext>&#xa0;&#xa0;&#xa0;</mml:mtext><mml:mi>&#x3c4;</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mo>&#x22ef;</mml:mo><mml:mo>,</mml:mo><mml:mtext>n</mml:mtext></mml:mrow></mml:math>
</disp-formula>
<p>If present <italic>R/S</italic> &#x221d; <italic>&#x3c4;<sup>H</sup></italic>, this indicates the existence of the Hurst phenomenon in the TVDI time series. The Hurst exponent (denoted as <italic>H</italic>) is quantitatively determined through least squares fitting.</p>
<p>The Hurst exponent (<italic>H</italic>) ranges from 0 to 1, with three distinct scenarios (<xref ref-type="bibr" rid="B6">Bhattacharya et&#xa0;al., 1983</xref>). <italic>H</italic> &gt; 0.5: Indicates persistent behavior in the time series. The <italic>H</italic> value approaching 1 indicates strong persistence, meaning the future trend is likely to continue the past direction. The <italic>H</italic> value of 0.5 signifies a random, uncorrelated series without a discernible trend. Conversely, the <italic>H</italic> value below 0.5 demonstrates anti&#x2013;persistence, suggesting the future trend is likely to reverse the past direction. To better understand the persistence of future TVDI change trends in the Yellow River Basin (Henan section), this study calculated the Hurst index of TVDI on a pixel&#x2013;by&#x2013;pixel basis. By integrating these results with the Sen&#x2019;s trend results that passed the significance test, the relationship between the future direction of drought changes and the past trend in the Yellow River Basin (Henan section) was determined.</p>
</sec>
<sec id="s2_3_4">
<label>2.3.4</label>
<title>Geographic detector</title>
<p>The geographic detector can analyze the influence of different independent variables on the spatial distribution pattern of specific dependent variables (<xref ref-type="bibr" rid="B32">Wang and Xu, 2017</xref>). It contains the following four detectors: factor detection, interaction detection, risk detection, and ecological detection.</p>
<p>1) Factor detector.</p>
<p>A factor detector could determine the effect of detecting the spatial heterogeneity of vegetation change. The spatial heterogeneity of X to Y could be expressed as <italic>q</italic> &#xd7; 100%, and the greater the number, the greater the influence of the detection factors on vegetation change (<xref ref-type="bibr" rid="B11">Deng et&#xa0;al., 2022</xref>), which is as follows (<xref ref-type="disp-formula" rid="eq14">Equation 14</xref>):</p>
<disp-formula id="eq14"><label>(14)</label>
<mml:math display="block" id="M14"><mml:mrow><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>&#x2212;</mml:mo><mml:mfrac><mml:mrow><mml:mstyle displaystyle="true"><mml:munderover><mml:mo>&#x2211;</mml:mo><mml:mrow><mml:mi>h</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>L</mml:mi></mml:munderover><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:msubsup><mml:mi>&#x3c3;</mml:mi><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></mml:mstyle></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:msup><mml:mi>&#x3c3;</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfrac></mml:mrow></mml:math>
</disp-formula>
<p>where q represents the influence of the factor on the dependent variable. h denotes the stratification of influencing factors. L indicates the number of sub-regions. N and N<sub>h</sub> are the sample sizes of the entire region and the h-th (h=1, &#x2026;, L) sub-region of the variable, respectively. <italic>&#x3c3;</italic><sup>2</sup><italic><sup>h</sup></italic> and <italic>&#x3c3;</italic><sup>2</sup> are represent the variances of the influencing factors for the entire region, h-th sub-region, respectively. A large <italic>q</italic> indicates a high explanation of the spatial heterogeneity (<xref ref-type="bibr" rid="B7">Chen et&#xa0;al., 2020</xref>).</p>
<p>2) Interaction detector.</p>
<p>Interaction detector was used to assess interaction between two factors. The <italic>q</italic> values of individual factors <italic>q</italic>(X1) and <italic>q</italic>(X2) were first calculated separately, and the value of two&#x2013;factor interaction <italic>q</italic>(X1&#x2229;X2) was calculated. Min (<italic>q</italic>(X1)<italic>, q</italic>(X2)) represents the minimum value between X1 and X2. Max(<italic>q</italic>(X1)<italic>, q</italic>(X2)) represents the maximum value between X1 and X2. The sum of X1 and X2 is <italic>q</italic>(X1) + <italic>q</italic>(X2). The interaction between X1 and X2 is <italic>q</italic>(X1&#x2229;X2). The results are defined by comparing the <italic>q</italic> value of individual factor and two&#x2013;factor interaction as shown in <xref ref-type="table" rid="T3"><bold>Table&#xa0;3</bold></xref>.</p>
<table-wrap id="T3" position="float">
<label>Table&#xa0;3</label>
<caption>
<p>Categories of factor interactions.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Foundation</th>
<th valign="middle" align="center">Interaction</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="center"><italic>q</italic>(X1&#x2229;X2)&lt; Min <break/>(<italic>q</italic>(X1)<italic>, q</italic>(X2))</td>
<td valign="middle" align="center">Nonlinear weakening: The interaction of two variables nonlinearly weakens the impacts of single variables.</td>
</tr>
<tr>
<td valign="middle" align="center">Min (<italic>q</italic>(X1)<italic>, q</italic>(X2)) &#x2264; <italic>q</italic>(X1&#x2229;X2) &#x2264; Max(<italic>q</italic>(X1)<italic>, q</italic>(X2))</td>
<td valign="middle" align="center">Single factor nonlinear weakening: The impacts of individual variables are weakened by the interaction, resulting in a single factor nonlinear weakening effect.</td>
</tr>
<tr>
<td valign="middle" align="center"><italic>q</italic>(X1&#x2229;X2) &gt; Max (<italic>q</italic>(X1)<italic>, q</italic>(X2))</td>
<td valign="middle" align="center">Double factor enhancement: The impact of single variables is enhanced by the interaction, resulting in a double factor enhancement effect.</td>
</tr>
<tr>
<td valign="middle" align="center"><italic>q</italic>(X1&#x2229;X2) = <italic>q</italic>(X1) + <italic>q</italic>(X2)</td>
<td valign="middle" align="center">Independence: The impacts of variables are assumed to be independent.</td>
</tr>
<tr>
<td valign="middle" align="center"><italic>q</italic>(X1&#x2229;X2) &gt; <italic>q</italic>(X1) + <italic>q</italic>(X2)</td>
<td valign="middle" align="center">Nonlinear enhancement: The effects of variables are enhanced in a non&#x2013;linear manner.</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Vegetation coverage, vegetation evapotranspiration, precipitation, temperature, elevation, slope gradient, population density, and nighttime light were selected. This study employed the factor detector and interaction detector within the Geodetector to analyze the influences of precipitation (PRE), temperature (TMP), evapotranspiration (ET), slope, GDP, nighttime light (NPP&#x2013;VIIRS), elevation (ELE), and population density (POP) on drought conditions (as represented by TVDI) in the Yellow River Basin (Henan section). The factor detector was used to identify their explanatory power.</p>
</sec>
</sec>
</sec>
<sec id="s3" sec-type="results">
<label>3</label>
<title>Results</title>
<sec id="s3_1">
<label>3.1</label>
<title>Spatiotemporal distribution characteristics of drought</title>
<sec id="s3_1_1">
<label>3.1.1</label>
<title>Spatial distribution characteristics of drought</title>
<p>Based on the spatial distribution of TVDI, the majority of the study area was experiencing drought conditions. Of the total area, 70.63% was classified as being in a state of moderate drought, followed by severe drought, which accounted for 19.28% (<xref ref-type="fig" rid="f3"><bold>Figure&#xa0;3</bold></xref>). Areas under normal conditions accounted for only 1.14% of the total study area. Mild drought areas were distributed along the periphery of these normal zones. Severe drought areas were concentrated in the northeastern part of Luoyang City, encompassing Yiyang County, Yichuan County, Song County, Mengjin County, the southeastern part of Xin&#x2019;an County, and Luolong District. Normal conditions were found only in small southwestern areas of Lingbao City in Sanmenxia City, marginal areas of Luanchuan County in Luoyang City, and the northern fringe of Jiyuan City.</p>
<fig id="f3" position="float">
<label>Figure&#xa0;3</label>
<caption>
<p>Spatial distribution of the mean annual TVDI in the Yellow River Basin (Henan section) from 2003 to 2022.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fevo-14-1763944-g003.tif">
<alt-text content-type="machine-generated">Choropleth map showing drought grades in a region, with areas color-coded as normal (dark green), mild drought (medium green), moderate drought (light green), severe drought (orange), and extreme drought (red). Severe and extreme droughts cluster centrally.</alt-text>
</graphic></fig>
</sec>
<sec id="s3_1_2">
<label>3.1.2</label>
<title>Temporal variation trend of drought</title>
<p>As illustrated in <xref ref-type="fig" rid="f4"><bold>Figure&#xa0;4a</bold></xref>, the TVDI trend from 2003 to 2022 exhibited pronounced spatial heterogeneity across the Yellow River Basin (Henan section). The entire region showed a general increasing gradient from southwest to northeast, which indicated a progressive intensification of drought conditions in that direction. Drought severity alleviated in the southwestern region, reflecting an improvement in conditions. In contrast, the northeastern region experienced a notable intensification of drought, and this worsening trend became increasingly evident. Through statistical analysis of the change trends across categories (<xref ref-type="fig" rid="f4"><bold>Figure&#xa0;4b</bold></xref>), the areal proportions corresponding to each grade level were derived. A decrease trend (including extremely significant decrease, significant decrease, slight significant decrease, and not significant decrease) in TVDI accounted for 41.17% of the study area, while a significant increase was observed in 15.82% of the region. Significant decrease trend of TVDI was primarily located in southern Lingbao, Lushi, Shanzhou, and northern Mianchi, Jiyuan City, Luoning County and northern Xin&#x2019;an County in Luoyang City, with small portions of southern Yiyang County, western Luanchuan County, southern Song County, and the border area between Yanshi and Yichuan, have shown a gradual improvement in drought conditions over the study period. The proportion of the area showing an increasing trend in TVDI was 56.7%. The central and northeastern parts of the study area demonstrated a significant increasing trend of TVDI. It is indicated that the drought in these areas was becoming more severe. A considerable portion (23.58%) of the study area was classified as experiencing an extremely significant increase.</p>
<fig id="f4" position="float">
<label>Figure&#xa0;4</label>
<caption>
<p>TVDI change trend <bold>(a)</bold> and significance of the change trend <bold>(b)</bold>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fevo-14-1763944-g004.tif">
<alt-text content-type="machine-generated">Panel (a) shows a color-coded map of an area with β values ranging from -0.0093 in dark blue to 0.0120 in red, indicating spatial data variation. Panel (b) presents the same region classified by significance of increase or decrease, with red tones for significant increases and blue for decreases, according to the legend. Both panels include scale bars and north arrows for orientation.</alt-text>
</graphic></fig>
</sec>
<sec id="s3_1_3">
<label>3.1.3</label>
<title>Prediction of future drought trends based on R/S analysis</title>
<p>The average Hurst exponent in the study area is 0.46, which may signal the end or reversal of drought conditions in the region. Hurst exponent values of less than 0.5 were observed in approximately 70% of the study area (<xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5a</bold></xref>). This implies that for the majority of the study area, the drought situation is expected to be the opposite of the past.</p>
<fig id="f5" position="float">
<label>Figure&#xa0;5</label>
<caption>
<p>The Hurst exponent <bold>(a)</bold> and future trends of TVDI <bold>(b)</bold>.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fevo-14-1763944-g005.tif">
<alt-text content-type="machine-generated">Panel (a) shows a geographic map with regions color-coded by Hurst index values, ranging from blue for low (0.19-0.35) to red for high (0.65-0.80). Panel (b) depicts the same area classified by future trend predictions, including different shades of green for decrease with varying persistence, shades of red and yellow for increase, and light blue for no change, as indicated by the legend. Both maps include scale bars and coordinate grids.</alt-text>
</graphic></fig>
<p>The increase (weak anti&#x2013;persistence) area accounts for the largest proportion of the area at 29.04%, primarily distributed in the central and northeastern parts of the study area. The decrease (weak anti&#x2013;persistence) area occupies the second&#x2013;largest proportion of the area at 26.55%, mainly located in the western part of the study area (<xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5b</bold></xref>). Drought conditions in these regions are expected to further alleviate. The increase (weak persistence and strong persistence) areas are mainly distributed in the northeastern part of the study area, accounting for 17.43% and 2.29% of the total area, respectively. Drought conditions in these regions are likely to further intensify in the future, primarily located in Wuzhi County and the southern part of Qinyang City in Jiaozuo City, the southwestern part of Yuanyang County in Xinxiang City, as well as Puyang County, Fan County, and Taiqian County. The areas classified as &#x201c;decrease (strong persistence)&#x201d; and &#x201c;decrease (weak persistence)&#x201d; account for relatively small proportions, primarily distributed in Lushi County of Sanmenxia City and certain parts of Jiyuan City. Drought conditions in these regions are expected to gradually improve in the future, and this alleviation trend is not temporary but demonstrates a certain degree of stability and long&#x2013;term persistence.</p>
</sec>
</sec>
<sec id="s3_2">
<label>3.2</label>
<title>Driving factors analysis of drought</title>
<sec id="s3_2_1">
<label>3.2.1</label>
<title>Analysis of single factor influence</title>
<p>To investigate the driving mechanisms behind changes in drought levels in the Yellow River Basin (Henan section), this study selected factors from three aspects: human activity factors, topographic factors, and climatic factors for each year. Geodetector was used to analyze the explanatory power of each factor on the drought severity in the Yellow River Basin (Henan section). The single&#x2013;factor detection results showed that the <italic>p</italic>&#x2013;values for evapotranspiration and temperature were less than 0.01, indicating that ET, TMP and PRE have a highly significant impact on the spatial distribution of drought in the Yellow River Basin (Henan section). From the <italic>q</italic>&#x2013;values in the <xref ref-type="table" rid="T4"><bold>Table&#xa0;4</bold></xref>, it can be observed that the differences in the explanatory power of the driving factors for drought in the Yellow River Basin (Henan section) are relatively small, though still notable. The analysis of <italic>q</italic>&#x2013;values revealed that ET held the greatest explanatory power for TVDI (<italic>q</italic>&#xa0;= 0.90), closely followed by TMP (<italic>q</italic> = 0.89) and PRE (<italic>q</italic> = 0.85). It indicates that ET, TMP and PRE are the dominant factors influencing TVDI in the Yellow River Basin (Henan section). NPP&#x2013;VIIRS has the lowest explanatory power for TVDI. Overall, changes in drought severity in the Yellow River Basin (Henan section) are primarily influenced by ET, TMP and PRE. Compared to topographic factors and human activities, climatic factors exhibit stronger explanatory power for environmental changes.</p>
<table-wrap id="T4" position="float">
<label>Table&#xa0;4</label>
<caption>
<p>Single&#x2013;factor detector analysis.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="middle" align="center">Statistical index</th>
<th valign="middle" align="center">GDP</th>
<th valign="middle" align="center">SLOPE</th>
<th valign="middle" align="center">ET</th>
<th valign="middle" align="center">TMP</th>
<th valign="middle" align="center">POP</th>
<th valign="middle" align="center">NPP&#x2013;VIIRS</th>
<th valign="middle" align="center">ELE</th>
<th valign="middle" align="center">PRE</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="middle" align="center"><italic>q</italic> value</td>
<td valign="middle" align="center">0.13</td>
<td valign="middle" align="center">0.24</td>
<td valign="middle" align="center">0.90</td>
<td valign="middle" align="center">0.89</td>
<td valign="middle" align="center">0.23</td>
<td valign="middle" align="center">0.10</td>
<td valign="middle" align="center">0.17</td>
<td valign="middle" align="center">0.85</td>
</tr>
<tr>
<td valign="middle" align="center"><italic>p</italic> value</td>
<td valign="middle" align="center">0.27</td>
<td valign="middle" align="center">0.16</td>
<td valign="middle" align="center">0.00</td>
<td valign="middle" align="center">0.00</td>
<td valign="middle" align="center">0.17</td>
<td valign="middle" align="center">0.58</td>
<td valign="middle" align="center">0.17</td>
<td valign="middle" align="center">0.00</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s3_2_2">
<label>3.2.2</label>
<title>Interaction analysis of driving factors</title>
<p>The Geodetector was employed in this section to analyze the interactions among driving factors on drought (<xref ref-type="fig" rid="f6"><bold>Figure&#xa0;6</bold></xref>). The interaction between TMP and POP demonstrated the strongest detection effect, reaching 0.99, which was higher than that of other combinations, followed by the interactions between ET and POP (0.98) and between PRE and POP (0.98). Although GDP, SLOPE, NPP&#x2013;VIIRS and ELE were not significant in the single&#x2013;factor detection, their explanatory power for the dependent variable increased when interacting with other factors. This indicates that the individual effects of these factors are not sufficient to influence the drought conditions in the study area. However, the geographical environment is a whole and the mechanism of drought occurrence is complex. The synergistic effect between the two factors will significantly affect the drought conditions in the region. Attention should be paid to this in the prevention and detection of drought. In summary, these driving factors all exerted varying degrees of influence on the drought levels in the study area, with significant differences observed in their explanatory power. The main factors influencing the drought in this region are the interaction of TMP, ET and PRE with POP. Meanwhile, other factors (such as GDP and SLOPE) interact with the meteorological factors, intensifying the drought severity in the Yellow River Basin (the Henan section).</p>
<fig id="f6" position="float">
<label>Figure&#xa0;6</label>
<caption>
<p>Interaction detection analysis of driving factors.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fevo-14-1763944-g006.tif">
<alt-text content-type="machine-generated">Heatmap chart showing q values in the range zero point one zero to zero point nine nine for pairs of eight variables: GDP, SLOPE, ET, TMP, POP, NPP-VIIRS, ELE, and PRE. Cells range from blue (low values) to red (high values), with higher correlations mostly shown in red, especially for TMP, ET, and POP, and lower correlations in blue between GDP, NPP-VIIRS, and ELE. A vertical color bar on the right indicates the q value gradient from zero point one zero (blue) to zero point nine nine (red).</alt-text>
</graphic></fig>
</sec>
</sec>
</sec>
<sec id="s4" sec-type="discussion">
<label>4</label>
<title>Discussion</title>
<p>Based on the analysis of TVDI, the results indicate that the majority of the study area was in astate of drought, with moderate drought being the dominant condition. Throughout the study period, drought conditions showed an overall trend of intensification, which is consistent with findings from previous research (<xref ref-type="bibr" rid="B38">Zhao et&#xa0;al., 2022</xref>; <xref ref-type="bibr" rid="B21">Li Y. et&#xa0;al., 2024</xref>). Drought severity in the Yellow River Basin (Henan section) exhibits significant spatial heterogeneity. Specifically, the southwestern region experiences relatively lower drought intensity, with projections indicating a mitigating trend in the future. In contrast, the northeastern region suffers from higher drought severity, which is expected to intensify further under future climatic conditions. The main factors influencing drought variation are ET, TMP, and PRE. From this perspective, the drought pattern in the study area is primarily dominated by natural factors. Besides, POP interact with meteorological factors can intensify the severity of drought in this region. The considerable population size leads to substantial water requirements for agriculture, industry, and household consumption. This demand places considerable strain on water resources, thereby increasing the region&#x2019;s vulnerability to more severe droughts.</p>
<p>The utilization of water resources is closely related to land use types and methods. The land use in the southwestern region is dominated by forest land and grassland, while cultivated land is the primary in the northeastern region (<xref ref-type="bibr" rid="B23">Liu et&#xa0;al., 2025</xref>). In areas with intensive cultivated land, vegetation coverage is low, soil structure is relatively fragile, and the exposed surface area is large. Within a certain period, the soil can absorb more solar radiation, leading to increased evaporation. Furthermore, in parts of the Yellow River Basin (Henan Section) characterized by dense construction land, a large population is concentrated, thereby exacerbating the already heightened risk of drought.</p>
<p>Agricultural irrigation can mitigate the adverse effects of drought to some extent. However, this region faces increasingly prominent challenges, including agricultural water scarcity, an imbalance between water supply and demand, aging irrigation infrastructure, and the urgent need to transform irrigation methods. To further address the issue of agricultural drought in the study area, water conservancy projects and measurement facilities should be upgraded and modernized. Optimizing and restructuring water management agencies requires establishing a practical communication mechanism. Integrated coordination of agricultural water-saving reforms can then enhance the effectiveness of the water management system and promote greater water use efficiency (<xref ref-type="bibr" rid="B20">Li G. et&#xa0;al., 2024</xref>).</p>
<p>However, certain limitations were associated with the use of TVDI in studying the spatiotemporal dynamics of drought in this region. TVDI was calculated based on remote sensing data with certain time intervals, it may not fully capture rapidly evolving drought events in the region, such as sudden&#x2013;onset droughts. Therefore, in terms of drought emergency monitoring and real&#x2013;time decision support, there are certain limitations in using TVDI data for drought monitoring in this area.</p>
<p>TVDI primarily reflects surface soil moisture conditions and has limited capacity to characterize deeper soil moisture, particularly in densely vegetated mountainous areas, where it may not fully capture the actual water stress experienced by the ecosystem. It is necessary to integrate multiple indices to jointly monitor drought conditions in the Yellow River Basin (Henan section), so as to achieve a more accurate assessment of regional drought status. Furthermore, this study only conducted a zonal analysis of drought conditions in the Yellow River Basin (Henan section) from 2003 to 2022 based on TVDI data, examining whether regional drought severity intensified or alleviated over time. While it provided a general reference for understanding drought patterns in the area, implementing specific measures to improve drought conditions in any particular zone requires more comprehensive monitoring and in&#x2013;depth analysis to enable precise and targeted actions.</p>
</sec>
<sec id="s5" sec-type="conclusions">
<label>5</label>
<title>Conclusions</title>
<p>This study employed the TVDI to monitor spatiotemporal drought variations in the Yellow River Basin (Henan section). The spatial distribution and temporal trends of drought were analyzed, along with the relationships between drought and meteorological factors, topographic factors, and human activities. The following main conclusions were obtained.</p>
<list list-type="order">
<list-item>
<p>Based on the spatial distribution of TVDI, most areas in the region were in a state of drought. Severe drought areas were concentrated in the northeastern part of Luoyang City. Only a few small areas were classified as normal regions, specifically the southwestern part of Lingbao City in Sanmenxia City, the marginal areas of Luanchuan County in Luoyang City, and the northern fringe of Jiyuan City, with TVDI values ranging from 0 to 0.46. Mild drought areas were distributed around the normal regions, with TVDI values between 0.46 and 0.57. All other areas in the region experienced moderate drought, with TVDI values ranging from 0.57 to 0.76.</p></list-item>
<list-item>
<p>The entire region exhibited a general increasing gradient in drought severity from the southwest to the northeast. The southwestern region experienced an alleviation of drought, reflecting an improvement in conditions. In contrast, the northeastern region witnessed a notable intensification of drought, a trend that became increasingly evident over the study period. These areas have high population density and concentrated cultivated land. Consequently, the adoption of water conservation practices and the scientific allocation of water resources are crucial for drought mitigation planning and management. Analysis using the Hurst exponent suggests that the future drought trend for the majority of the study area is expected to be opposite to that of the past. Notably, in the southwestern part of the study area, the drought situation in Sanmenxia City, Jiyuan City, and Luoning County is projected to worsen in the future. Since these are mountainous and hilly areas, the construction of water conservancy facilities and the improvement of the irrigation system will contribute to drought alleviation.</p></list-item>
<list-item>
<p>The main factors influencing drought conditions in the Yellow River Basin (Henan section) are ET, TMP, and PRE. Meanwhile, other factors such as POP interact with meteorological factors, which can intensify the severity of drought in this region.</p></list-item>
</list>
</sec>
</body>
<back>
<sec id="s6" sec-type="data-availability">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.</p></sec>
<sec id="s7" sec-type="author-contributions">
<title>Author contributions</title>
<p>ZG: Project administration, Writing &#x2013; original draft, Methodology, Funding acquisition, Writing &#x2013; review &amp; editing, Conceptualization. GX: Conceptualization, Writing &#x2013; review &amp; editing, Data curation. LF: Software, Writing &#x2013; review &amp; editing, Methodology. YL: Writing &#x2013; review &amp; editing, Software. KJ: Writing &#x2013; review &amp; editing, Supervision, Formal analysis. MR: Resources, Investigation, Writing &#x2013; review &amp; editing.</p></sec>
<sec id="s9" sec-type="COI-statement">
<title>Conflict of interest</title>
<p>The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p></sec>
<sec id="s10" sec-type="ai-statement">
<title>Generative AI statement</title>
<p>The author(s) declared that generative AI was not used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p></sec>
<sec id="s11" sec-type="disclaimer">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p></sec>
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