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  <front>
    <journal-meta><journal-id journal-id-type="publisher">TC</journal-id><journal-title-group>
    <journal-title>The Cryosphere</journal-title>
    <abbrev-journal-title abbrev-type="publisher">TC</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">The Cryosphere</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1994-0424</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/tc-20-4277-2026</article-id><title-group><article-title>Assessing spatial heterogeneity of active layer thickness over Arctic-foothills tundra, North Slope Alaska</article-title><alt-title>Assessing spatial heterogeneity of active layer thickness over Arctic-foothills tundra</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Du</surname><given-names>Jinyang</given-names></name>
          <email>jinyang.du@ntsg.umt.edu</email>
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Endsley</surname><given-names>K. Arthur</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2 aff3">
          <name><surname>Bakian Dogaheh</surname><given-names>Kazem</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Kimball</surname><given-names>John S.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Moghaddam</surname><given-names>Mahta</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Douglas</surname><given-names>Thomas A.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-1314-1905</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Melebari</surname><given-names>Asem</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Eskandari</surname><given-names>Sepehr</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff5">
          <name><surname>Kim</surname><given-names>Jinhyuk E.</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Whitcomb</surname><given-names>Jane</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Zhao</surname><given-names>Yuhuan</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff3">
          <name><surname>Henze</surname><given-names>Sophia</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>Numerical Terradynamic Simulation Group, W.A. Franke College of Forestry &amp; Conservation, University of Montana, Missoula, MT, 59812, USA</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, MI 481019, USA</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90089, USA</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>U.S. Army Cold Regions Research and Engineering Laboratory, Fort Wainwright, AK, 99703, USA</institution>
        </aff>
        <aff id="aff5"><label>5</label><institution>Department of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, MI, 48109, USA</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Jinyang Du (jinyang.du@ntsg.umt.edu)</corresp></author-notes><pub-date><day>7</day><month>August</month><year>2026</year></pub-date>
      
      <volume>20</volume>
      <issue>8</issue>
      <fpage>4277</fpage><lpage>4291</lpage>
      <history>
        <date date-type="received"><day>8</day><month>July</month><year>2025</year></date>
           <date date-type="rev-request"><day>11</day><month>August</month><year>2025</year></date>
           <date date-type="rev-recd"><day>20</day><month>July</month><year>2026</year></date>
           <date date-type="accepted"><day>21</day><month>July</month><year>2026</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2026 Jinyang Du 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://tc.copernicus.org/articles/20/4277/2026/tc-20-4277-2026.html">This article is available from https://tc.copernicus.org/articles/20/4277/2026/tc-20-4277-2026.html</self-uri><self-uri xlink:href="https://tc.copernicus.org/articles/20/4277/2026/tc-20-4277-2026.pdf">The full text article is available as a PDF file from https://tc.copernicus.org/articles/20/4277/2026/tc-20-4277-2026.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e210">Changes in active layer thickness (ALT) are used as an indicator of permafrost degradation. Increases in ALT can lead to increased greenhouse gas emissions, altered hydrology and ecology, ground instability, and a positive climate feedback. Quantifying ALT spatial heterogeneity remains challenging due to the influence of localized variations in terrain, microclimate, snow/soil properties, vegetation cover, and surface disturbances. It is also unclear how local ALT patterns and mechanisms (e.g., sub-meter to 10 m) scale up to broader landscape footprints (e.g., 10 to 1000 m) represented from global satellite observations and Earth system models. We assessed ALT spatial heterogeneity in the Arctic-foothills tundra within the North Slope of Alaska through intensive field sampling over four 90 m <inline-formula><mml:math id="M1" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 90 m plots, combined with multi-source remote sensing and machine learning (ML). Analysis using field observations and ML revealed that vegetation, surface wetness, subsurface rocks, and micro-topography exert strong influence on 5 m ALT variations, whereas terrain controls dominate (<inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">65</mml:mn></mml:mrow></mml:math></inline-formula> % contribution) at coarser 10 m spatial resolution. By leveraging centimeter-level optical-infrared drone imagery, we further generated 0.1 m ALT maps over a larger 5 km <inline-formula><mml:math id="M3" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 5 km region and examined ALT scaling effects. Our analysis showed a quadratic relationship in resolution-dependent uncertainties, characterized by a rapid increase in uncertainties at the sub-meter level (e.g., RMSE normalized by the standard deviation of 0.1 m ALT climbed by <inline-formula><mml:math id="M4" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> %), followed by another 10 % increase from 1 to 30 m resolution, and a more conservative error increase (<inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> %) from 30 to 1000 m resolution. Our study allows for improved interpretation of remote sensing and process-based ALT simulations for the changing Arctic by clarifying resolution-dependent uncertainties and underlying mechanisms.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>National Aeronautics and Space Administration</funding-source>
<award-id>80NSSC22K1238</award-id>
</award-group>
</funding-group>
</article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d2e266">Permafrost in the northern high latitudes is undergoing rapid changes driven by enhanced atmospheric warming at roughly four times the mean global rate (Rantanen et al., 2022). Complex environmental changes that accompany degrading permafrost include widespread earlier spring thawing and lengthening of the thaw season, shifts in seasonal snow cover properties, contrasting wetting and drying patterns, vegetation greening and browning, and increasing disturbances (Heijmans et al., 2022; Foster et al., 2022). Permafrost degradation, which involves active layer thickening, may lead to ground surface deformation (Du et al., 2019). In addition, thawing permafrost could potentially mobilize a vast reservoir of soil organic carbon previously stabilized in perennially frozen ground, resulting in accelerated soil decomposition and greenhouse gas emissions that may further amplify global warming (Turetsky et al., 2020; Schuur et al., 2022; Miner et al., 2022).</p>
      <p id="d2e269">Active layer thickness (ALT), defined as “the thickness of the layer of the ground that is subject to annual thawing and freezing in areas underlain by permafrost” (Lewkowicz et al., 2025), is an essential climate variable for monitoring permafrost degradation  (Smith and Brown, 2009). Accurate mapping of ALT spatial and temporal variability is critical for understanding impacts of climate change and disturbance on the permafrost energy balance, terrestrial water budget, organic matter decomposition, and land-atmosphere carbon exchange (Zhang et al., 2005; Schaefer et al., 2015; Garibaldi et al., 2022; Liu et al., 2024). ALT spatial patterns are closely linked to ambient air temperature at regional scales while demonstrating large spatial heterogeneity at local scales due to complex interactions with precipitation, vegetation, slope, aspect, soil and snow properties, topography, and disturbance (Leibman et al., 2012; Widhalm et al., 2017; Loranty et al., 2018; Chen et al., 2019; Garibaldi et al., 2022).</p>
      <p id="d2e272">Despite the importance of permafrost landscapes in monitoring and projecting Arctic-boreal system changes, there is only limited understanding of high-resolution (e.g., sub-meter to 10 m) ALT patterns and underlying driving factors over the highly heterogeneous permafrost regions due to a paucity of high-resolution ALT measurements. It is also unclear how local ALT patterns and its associated governing mechanisms scale up to the broader landscape when quantified at coarser spatial resolutions (e.g., 10 to 1000 m) using global satellite observations and regional process models (Yi et al., 2020). However, a better understanding of the high-resolution patterns, mechanisms, and their scaling effects is needed to clarify permafrost vulnerability and associated feedbacks to climate change, and to improve representation of the hydrological, ecological, and biogeochemical processes of Arctic ecosystems in global Earth system models as well as remote sensing inversion algorithms (Koven et al., 2013; Chen et al., 2019; Hantson et al., 2025).</p>
      <p id="d2e275">Remote sensing of ALT at high resolutions ranges from relatively direct electromagnetic retrievals from low frequency ground penetrating radar (GPR) to more indirect measures of surface topographic features from Light Detection and Ranging (LiDAR) (Gangodagamage et al., 2014) and soil freeze-thaw (FT) driven land surface deformations from Interferometric synthetic aperture radar (InSAR) measures (Schaefer et al., 2015). The distribution of ALT over ice-wedge polygon landscapes was empirically inferred using relevant topographic features quantified from LiDAR surface elevation measurements and data fusion approaches (Gangodagamage et al., 2014). In addition, the active layer heaves when frozen and subsides when thawed due to denser liquid water than ice. The seasonal vertical ground movement measured using InSAR is thus related to the ALT and ice/water content (Schaefer et al., 2015). Low-frequency (e.g., L- and P-band) microwave measurements are capable of penetrating through vegetation and soil layers and show strong potential for mapping active layer properties, including soil moisture and FT dynamics, organic matter content, and ALT (Tabatabaeenejad et al., 2014; Bakian-Dogaheh et al., 2025). This is due to the strong microwave sensitivity to the changes of soil dielectric properties, which are affected by soil moisture, texture, and freeze/thaw state (Kneisel et al., 2008; Du et al., 2019). In particular, the contrast in dielectric permittivity at the interface between thawed and frozen soil layers may lead to measurable microwave backscattering or reflection signals for estimating ALT (Kneisel et al., 2008). For example, retrieval algorithms were developed by exploiting airborne P-band radar data for ALT mapping in Alaska (Chen et al., 2019), which showed favorable retrieval accuracy for ALT up to <inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> cm. Another study on post-fire recovery in tundra regions further confirmed the unique sensitivity of low-frequency airborne radar in detecting the relatively fine-resolution heterogeneity in active layer conditions and post fire recovery that may be missing from coarser-resolution and higher-frequency satellite observations and model simulations (Yi et al., 2021). More recently, advanced physics-based computational radar retrieval algorithms have been developed to map the active layer soil organic matter and soil moisture profile of the Arctic-foothills tundra using P-band radar data (Bakian-Dogaheh et al., 2022). In sum, the remote sensing techniques provide information necessary to infer or model ALT.</p>
      <p id="d2e289">Considering its dependence on surface conditions (Kelley et al., 2004), ALT can also be indirectly inferred from optical vegetation observations and relatively high-frequency radar backscatter signals considering the ALT dependence on surface conditions using regression analysis (Kelley et al., 2004; Gangodagamage et al., 2014; Widhalm et al., 2017). Recent machine-learning based studies using airborne hyperspectral imaging data achieved meter-level ALT predictions over Interior Alaska with favorable accuracy (Zhang et al., 2021). Thus, complementary information available from multi-sensor and multi-resolution remote sensing provides the basis for developing more effective models and ALT retrievals capable of resolving local patterns and environmental linkages spanning Arctic-boreal permafrost landscapes (Brodylo et al., 2024; Hantson et al., 2025).</p>
      <p id="d2e292">Although remote sensing is a viable option for inferring ALT, it remains unclear how local ALT patterns and their governing mechanisms (e.g., sub-meter to 10 m) scale up to broader landscape footprints (e.g., 10 to 1000 m) represented by global satellite observations and Earth system models. Recent studies have begun to resolve multi-resolution ALT patterns using multi-sensor remote sensing (Brodylo et al., 2024; Hantson et al., 2025), but these efforts have been limited to Interior Alaska (Brodylo et al., 2024) and the Seward Peninsula (Hantson et al., 2025). For the Arctic-foothills tundra environment, dense in-situ sampling is extremely sparse, but is needed as a ground-truth benchmark for evaluating remote sensing retrievals and to quantify how uncertainty changes with spatial resolution. In addition, there is also a lack of multi-scale observations integrating field samples, high-resolution drone/airborne images, and satellite observations. Yet such measurements are essential to resolving how ALT patterns scale across resolutions. This study addresses this gap through a field experiment that integrated in-situ measurements with multi-scale remote sensing observations for the understudied Arctic tundra.</p>
      <p id="d2e295">The objectives of this study are to: (1) assess ALT spatial heterogeneity and scaling properties from 0.1 to 1000 m resolution within the tundra foothills region of the North Slope of Alaska; and to (2) assess the underlying environmental controls on ALT patterns manifesting at different resolutions and the potential influence of spatial resolution on regional permafrost remote sensing and modeling uncertainty.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Study Region</title>
      <p id="d2e306">Our study focused on the Imnavait Creek (68.6167° N, 149.3167° W) area within the Alaskan North Slope tundra foothills region (Fig. 1). The study region experiences a cold climate with a mean annual temperature of <inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">7.4</mml:mn></mml:mrow></mml:math></inline-formula> °C, ranging from an average of <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">17</mml:mn></mml:mrow></mml:math></inline-formula> °C in January to 9.4 °C in July (Schramm et al., 2007). Annual precipitation averages 340 mm, two-thirds of which falls as light rainfall during the summer (Schramm et al., 2007). The dominant vegetation consists of water-tolerant plants like tussock sedges and mosses, grasses and low shrubs (Schramm et al., 2007). Vegetation and soil patterns vary with slope, aspect, and drainage conditions, exhibiting a patchy distribution across the study domain (Hinkel and Nelson, 2003). The region is also characterized by diverse glacial landforms, including deposits, stream networks, and bedrock outcrops (Hinkel and Nelson, 2003). The region has gently rolling terrain, with elevations ranging from <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">750</mml:mn></mml:mrow></mml:math></inline-formula> to 980 m. Vegetation and soil patterns vary with slope, aspect, and drainage conditions, exhibiting a patchy distribution across the study domain (Hinkel and Nelson, 2003). The region is also characterized by diverse glacial landforms, including deposits, stream networks, and bedrock outcrops (Hinkel and Nelson, 2003). Increasing ALT was observed from both in-situ measurements at the Circumpolar Active Layer Monitoring (CALM) sites (<uri>https://www2.gwu.edu/~calm/data/north.htm</uri>, last access: 1 July 2025) and regional ALT records at 1 km resolution, which were generated using machine learning (ML) by combining in situ ALT observations with a suite of observational biophysical variables (Liu et al., 2024).</p>
      <p id="d2e342">The local study area consisted of four intensively sampled field plots (Plot 3, Plot 4, Plot 5, and Plot 6 in Fig. 1; 90 m <inline-formula><mml:math id="M10" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 90 m each) distributed across an elevation gradient along west facing hill slopes, and surrounded by a larger (5 km <inline-formula><mml:math id="M11" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 5 km) landscape domain used for analyzing ALT across different resolutions (Fig. 1; Table 1). The field plots are dominated by tussock-forming sedges and moss-lichen mats, along with scattered dwarf birch shrubs, and riparian grasses (Figs. 1–2, S1 in the Supplement). The common species identified near the ALT sampling points include dwarf birch (<italic>Betula nana</italic>), alpine blueberry (<italic>Vaccinium uliginosum</italic>), black bearberry (<italic>Arctous</italic> spp.), crowberry (<italic>Empetrum nigrum</italic>), and <italic>Arctostaphylos uva-ursi</italic>, among other less-recognizable species. Our soil coring samples indicated high organic matter content of the topsoil (0 to 10 cm depth) for Plots 3, 4 and 5, with the respective values of 77.3 %, 75.1 %, and 71.8 %, contrasting with a relatively low value of 45.5 % for Plot 6. In-situ measurements showed that ALT varies with terrain, vegetation cover types, and surface water conditions, with overall greater active layer thickness found at the higher-elevation Plot 6 (58 cm) than at the other plots (39 to 49 cm).</p>
      <p id="d2e375">Plot 3 and Plot 4 are located on west-facing downhill slopes characterized by gradual elevation changes (10 to 15 m across the plot), small water tracks, and scattered glacial erratics. Plot 3 is crossed by multiple drainage features that are transverse to the Kuparuk River (Fig. 1). These features are evident in the topography as well as the vegetation, with alternating bands of dwarf willow, grasses, and tussocks (Fig. S1a). Standing water is present in many places, particularly along the drainage channels. Plot 4 is more homogeneous in vegetation character and height, consisting mostly of grass tussocks and moss, with some larger glacial erratics present (Fig. S1b).</p>
      <p id="d2e378">Plots 5 and 6 are on the east side of the access road and are more level than Plots 3 and 4. Plot 5 is located at a valley bottom and is partitioned by Imnavait Creek, which winds directly through the middle of the plot. Shallow drainage channels transverse to Imnavait Creek are found on the west side of the plot, while the east side is upland and drier. Vegetation cover in Plot 5 follows the typical mix of grasses, mosses, and sedges, with some moss forming humps about 20 cm tall, while shrub density and height increase close to the creek. Along Imnavait Creek there are taller (0.5 to 1.0 m) birch shrubs and more grasses (Fig. S1c). Plot 6 is characterized by widespread subsurface rocks (Fig. 1) and overall short-statured grass-sedge tussocks and mosses, lichens, small bunchgrasses, <italic>Arctous</italic> spp., and alpine blueberry, interrupted by areas of bare rock and gravel (Fig. S1d). Bare areas are common in the center of the plot.</p>
      <p id="d2e385">As part of the NASA Arctic Boreal Vulnerability (ABoVE) field campaign, our study used the ABoVE standard projection, which is in the Canada Albers Equal Area projection, for data visualization and analysis (Loboda et al., 2017).</p>

<table-wrap id="T1" specific-use="star"><label>Table 1</label><caption><p id="d2e391">Summary of surface and soil conditions for the sampling plots. The ALT values were calculated from the probe-based measurements during 16–23 August 2024.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="5">
     <oasis:colspec colnum="1" colname="col1" align="justify" colwidth="3cm"/>
     <oasis:colspec colnum="2" colname="col2" align="justify" colwidth="3cm"/>
     <oasis:colspec colnum="3" colname="col3" align="justify" colwidth="3cm"/>
     <oasis:colspec colnum="4" colname="col4" align="justify" colwidth="3cm"/>
     <oasis:colspec colnum="5" colname="col5" align="justify" colwidth="3cm"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1" align="left">Name</oasis:entry>
         <oasis:entry colname="col2" align="left">Plot 3</oasis:entry>
         <oasis:entry colname="col3" align="left">Plot 4</oasis:entry>
         <oasis:entry colname="col4" align="left">Plot 5</oasis:entry>
         <oasis:entry colname="col5" align="left">Plot 6</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1" align="left">Elevation [m]</oasis:entry>
         <oasis:entry colname="col2" align="left">810</oasis:entry>
         <oasis:entry colname="col3" align="left">846</oasis:entry>
         <oasis:entry colname="col4" align="left">855</oasis:entry>
         <oasis:entry colname="col5" align="left">875</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1" align="left">Vegetation</oasis:entry>
         <oasis:entry colname="col2" align="left">dwarf willow, grasses, and tussocks</oasis:entry>
         <oasis:entry colname="col3" align="left">grass tussocks and moss</oasis:entry>
         <oasis:entry colname="col4" align="left">mix of grasses, mosses, and sedges</oasis:entry>
         <oasis:entry colname="col5" align="left">grass tussocks and mosses</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1" align="left">Topsoil organic matter content [%]</oasis:entry>
         <oasis:entry colname="col2" align="left">77.3</oasis:entry>
         <oasis:entry colname="col3" align="left">75.1</oasis:entry>
         <oasis:entry colname="col4" align="left">71.8</oasis:entry>
         <oasis:entry colname="col5" align="left">45.5</oasis:entry>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1" align="left">Unique characteristics</oasis:entry>
         <oasis:entry colname="col2" align="left">ephemeral, drainage features</oasis:entry>
         <oasis:entry colname="col3" align="left">homogeneous in vegetation character and height</oasis:entry>
         <oasis:entry colname="col4" align="left">located in a valley bottom and partitioned by Imnavait Creek</oasis:entry>
         <oasis:entry colname="col5" align="left">widespread subsurface rocks</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1" align="left">ALT [cm]</oasis:entry>
         <oasis:entry colname="col2" align="left">49</oasis:entry>
         <oasis:entry colname="col3" align="left">39</oasis:entry>
         <oasis:entry colname="col4" align="left">44</oasis:entry>
         <oasis:entry colname="col5" align="left">58</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e526">The study region encompasses an Arctic tundra area (68.6167° N, 149.3167° W; red dot in the inset) in the northern foothills of the Brooks Range, Alaska. The region consists of four intensively sampled plots (Plot 3, Plot 4, Plot 5, and Plot 6; 90 m <inline-formula><mml:math id="M12" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 90 m each) with their corresponding true-color RGB (red-green-blue) drone images displayed alongside for visual inspection only, and surrounded by a larger 5 km <inline-formula><mml:math id="M13" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 5 km study region (red rectangle) used for analyzing ALT scaling effects. The map was plotted using Canada Albers Equal Area Conic projection.</p></caption>
        <graphic xlink:href="https://tc.copernicus.org/articles/20/4277/2026/tc-20-4277-2026-f01.png"/>

      </fig>

      <fig id="F2" specific-use="star"><label>Figure 2</label><caption><p id="d2e551">The study region contains characteristic tundra vegetation types, including dwarf shrubs <bold>(a)</bold>, tussock-forming sedges <bold>(b)</bold>, moss-lichen mats <bold>(c)</bold>, and riparian grasses along watercourses <bold>(d)</bold>. The images (0.7 cm resolution) were acquired from a drone-based RGB camera.</p></caption>
        <graphic xlink:href="https://tc.copernicus.org/articles/20/4277/2026/tc-20-4277-2026-f02.jpg"/>

      </fig>

</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Data and Methods</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Data Sets</title>
      <p id="d2e587">Multi-resolution ALT mapping was performed using probe-based field measurements, high-resolution (centimeter level) drone-based optical-Infrared (IR) acquisitions, concurrent airborne L-band radar observations, Sentinel-2 satellite images, and ancillary digital elevation model (DEM) data.</p>
<sec id="Ch1.S3.SS1.SSS1">
  <label>3.1.1</label><title>Field Sampling</title>
      <p id="d2e597">Ground sampling activities were conducted within the field plots from 16–23 August 2024, which included probe-based ALT measurements, soil coring, and surface roughness measurements. Each plot (Fig. 1) contains 289 grid cells (containing 17 <inline-formula><mml:math id="M14" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 17 subpixels with 5 m <inline-formula><mml:math id="M15" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 5 m each) excluding a 2.5 m buffer zone along the plot edges. Probe-based ALT sampling was performed over every (or every other) grid cell. Three measurements (by inserting the probe in the active layer vertically until refusal) were taken randomly within each grid cell, unless the initial two measurements were less than 1.27 cm (0.5 inch) apart. Mechanical probing to the depth of refusal was used to determine the depth of the frost table. For Plot 5, samples were collected for every grid cell not covered by open water, whereas for Plot 6, sampling only covered about half of the area due to widespread shallow rocks. The readings were averaged to represent the ALT conditions for a given 5 m grid cell. Overall, approximately 1700 measurements were made, representing ca. 600 grid cells across the plots. Additional observations were made including vegetation types, occurrence of standing and running water, and appearance of subsurface rocks. Soil organic layer properties were also estimated from soil cores taken within the sampling plots (Sect. 2). Field measurement protocols followed previously established methods within the NASA ABoVE field campaign (Schaefer et al., 2021; Bakian-Dogaheh et al., 2022).</p>
</sec>
<sec id="Ch1.S3.SS1.SSS2">
  <label>3.1.2</label><title>Remote Sensing Data Sets</title>
      <p id="d2e622">For understanding ALT spatial heterogeneity, multi-resolution remote sensing measurements were collected from drone, piloted aircraft, and satellite platforms. Aerial surveys included drone-based optical-IR observations, and airborne L-band radar observations from the NASA Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR). The field and airborne data were collected under the ABoVE campaign, an intensive decadal field campaign focused on improving our understanding of climate-related impacts on Arctic and boreal systems in western North America (Miller et al., 2019).</p>
      <p id="d2e625">For this study, high-resolution ALT mapping relied on drone-based (DJI Matrice 210 v2) optical-IR observations from a DJI Zenmuse X7 RGB (red, green, blue) camera (0.7 cm resolution), a Micasense multispectral (blue, green, red, red-edge, near IR bands) camera (2.7 cm resolution), and a DEM (1.2 cm resolution) derived from the RGB imagery. These images were captured over each plot on 4 September 2024 by the ToolikGIS team from the Toolik Field Station of the University of Alaska Fairbanks. For capturing vegetation conditions and surface water signals, the Normalized Difference Vegetation Index (NDVI; Tucker, 1979) and the Normalized Difference Water Index (NDWI; McFeeters, 1996) were calculated respectively from the drone multispectral imagery. In addition, aspect and slope were calculated from the DEM. The drone-based optical images and products were aggregated to both 0.1 and 5 m resolutions through pixel averaging for supporting the ML and scaling analysis.</p>
      <p id="d2e628">For ALT mapping over the surrounding region at coarser spatial resolution, ESA Sentinel-2 satellite optical-NIR observations under clear-sky (cloud cover <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> %) conditions were composited over the summer months (15 June–15 August 2024) in Google Earth Engine (GEE). The NDVI and NDWI were derived using the Sentinel-2 observations at 10 m resolution. For understanding terrain controls on the regional ALT distribution, elevation, slope, and aspect data were derived from the ArcticDEM (Porter et al., 2018) and aggregated to 10 m resolution.</p>
      <p id="d2e641">To examine the possible contributions of airborne radar observations to ALT retrievals, the ML model (Sect. 3.2) for 5 m ALT mapping was augmented with additional UAVSAR L-band VV, HV and HH backscatter observations in a separate test. The UAVSAR data were acquired over the Imnavait study region on 21 August 2024 concurrent with the field measurements (Miller et al., 2024). However, the airborne radar data were not used in the scaling analysis, which primarily relied on drone optical imagery for providing centimeter-level details and Sentinel-2 observations for enabling large-area analysis.</p>
</sec>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Constructing Multi-resolution ALT Maps</title>
      <p id="d2e653">A multi-resolution approach was used for characterizing ALT spatial heterogeneity, understanding environmental driving factors, and quantifying resolution-dependent uncertainties in remote sensing retrievals. A data-driven Random Forest (RF) model was first trained to reconstruct ALT patterns at a 5 m resolution over the intensively sampled plots. This model was also used with 0.1 m predictors to generate the ALT maps at 0.1 m resolution. The 5 m ALT results were subsequently aggregated to 10 m resolution to train a second RF model, which was used to produce the 10 m ALT map over the surrounding region (Fig. 3).</p>
      <p id="d2e656">The RF method has been widely used with parameters determined through remote sensing to estimate land parameters such as soil moisture, vegetation optical depth, and ALT (Zhang et al., 2021; Du et al., 2024). The RF tree ensemble yields final regression results by combining individual predictions, resulting in improved accuracy and stability compared to a single tree (Breiman, 2001). Compared with alternative ML methods such as single decision trees, the RF demonstrates resilience to data noise and overfitting (Breiman, 2001).</p>

      <fig id="F3" specific-use="star"><label>Figure 3</label><caption><p id="d2e661">An overall flowchart of the machine learning (ML) based active layer thickness (ALT) mapping and analysis.</p></caption>
          <graphic xlink:href="https://tc.copernicus.org/articles/20/4277/2026/tc-20-4277-2026-f03.png"/>

        </fig>

      <p id="d2e671">For generating the baseline 5 m ALT maps over the sampling plots, the first RF model was trained using the local high-resolution drone optical-NIR imagery, which was aggregated to a coarser (5 m) resolution consistent with the spatial representativeness of the field sampling.  The RF target variable is ground-sampled ALT, and the model predictors (Table 2) were selected from different combinations of observations and indices. The model was trained using 80 % of the data and validated using 20 % of the data. Different sets of hyper-parameters (number of trees 10, 25, 50, 100 and minimum leaf population 1, 3, 5) were employed for tuning and evaluating the regression trees using GEE. The root mean square error (RMSE) and correlation coefficient (<inline-formula><mml:math id="M17" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula>) were calculated for performance evaluation. To reduce overfitting risks, the smaller (larger) value of tree number (minimum leaf population) was selected for prioritizing a relatively simple tree/forest structure if two hyper-parameter values led to similar performance (e.g., <inline-formula><mml:math id="M18" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> difference less than 0.005). The optimized RF hyper-parameters are 25 trees and a minimum leaf population of 3. The 5 m ALT outputs for the sampling plots from the first RF model were aggregated to 10 m resolution and used to train the second RF model. The second model was developed for regional ALT mapping by leveraging operational satellite data as model predictors. The predictors (Table 2) were selected from terrain features and Sentinel-2 observations. Following a similar dataset splitting and hyper-parameter tuning process, the best performing model was built with a relatively simple structure (10 trees, 1 minimum leaf population).</p>

<table-wrap id="T2" specific-use="star"><label>Table 2</label><caption><p id="d2e691">ML predictors for 0.1, 5, and 10 m ALT mapping and scaling analysis.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="6">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left" colsep="1"/>
     <oasis:colspec colnum="4" colname="col4" align="left"/>
     <oasis:colspec colnum="5" colname="col5" align="left"/>
     <oasis:colspec colnum="6" colname="col6" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry namest="col1" nameend="col3" colsep="1">Predictors for 0.1 and 5 m ALT mapping over sampling plots</oasis:entry>
         <oasis:entry namest="col4" nameend="col6">Predictors for 10 m ALT mapping over the 5 km <inline-formula><mml:math id="M19" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 5 km region</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Name</oasis:entry>
         <oasis:entry colname="col2">Spatial resolution</oasis:entry>
         <oasis:entry colname="col3">Drone sensor</oasis:entry>
         <oasis:entry colname="col4">Name</oasis:entry>
         <oasis:entry colname="col5">Spatial resolution</oasis:entry>
         <oasis:entry colname="col6">Data source</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Red</oasis:entry>
         <oasis:entry colname="col2">0.7 cm</oasis:entry>
         <oasis:entry colname="col3">RGB Camera</oasis:entry>
         <oasis:entry colname="col4">Elevation</oasis:entry>
         <oasis:entry colname="col5">2 m</oasis:entry>
         <oasis:entry colname="col6">ArcticDEM</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Green</oasis:entry>
         <oasis:entry colname="col2">0.7 cm</oasis:entry>
         <oasis:entry colname="col3">RGB Camera</oasis:entry>
         <oasis:entry colname="col4">Slope</oasis:entry>
         <oasis:entry colname="col5">2 m</oasis:entry>
         <oasis:entry colname="col6">ArcticDEM</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Blue</oasis:entry>
         <oasis:entry colname="col2">0.7 cm</oasis:entry>
         <oasis:entry colname="col3">RGB Camera</oasis:entry>
         <oasis:entry colname="col4">Aspect</oasis:entry>
         <oasis:entry colname="col5">2 m</oasis:entry>
         <oasis:entry colname="col6">ArcticDEM</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Red edge</oasis:entry>
         <oasis:entry colname="col2">2.7 cm</oasis:entry>
         <oasis:entry colname="col3">Multispectral Camera</oasis:entry>
         <oasis:entry colname="col4">NDVI</oasis:entry>
         <oasis:entry colname="col5">10 m</oasis:entry>
         <oasis:entry colname="col6">Sentinel-2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Near infrared</oasis:entry>
         <oasis:entry colname="col2">2.7 cm</oasis:entry>
         <oasis:entry colname="col3">Multispectral Camera</oasis:entry>
         <oasis:entry colname="col4">NDWI</oasis:entry>
         <oasis:entry colname="col5">10 m</oasis:entry>
         <oasis:entry colname="col6">Sentinel-2</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">NDVI</oasis:entry>
         <oasis:entry colname="col2">2.7 cm</oasis:entry>
         <oasis:entry colname="col3">Multispectral Camera</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">NDWI</oasis:entry>
         <oasis:entry colname="col2">2.7 cm</oasis:entry>
         <oasis:entry colname="col3">Multispectral Camera</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">Aspect</oasis:entry>
         <oasis:entry colname="col2">1.2 cm</oasis:entry>
         <oasis:entry colname="col3">RGB Camera</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
       </oasis:row>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Slope</oasis:entry>
         <oasis:entry colname="col2">1.2 cm</oasis:entry>
         <oasis:entry colname="col3">RGB Camera</oasis:entry>
         <oasis:entry colname="col4"/>
         <oasis:entry colname="col5"/>
         <oasis:entry colname="col6"/>
       </oasis:row>
       <oasis:row>
         <oasis:entry namest="col1" nameend="col3" colsep="1">Note: Drone images were acquired on 4 September 2024, and the predictors were processed to 0.1 and 5 m resolutions for the respective ALT mapping.</oasis:entry>
         <oasis:entry namest="col4" nameend="col6">Note: Terrain data were averaged to 10 m resolution; Satellite images were aggregated over the 2024 summer period from 15 June to 15 August.</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Assessing ALT Spatial Heterogeneity</title>
      <p id="d2e960">For studying the ALT spatial heterogeneity observed at different resolutions, the first RF model was applied to the drone-based optical-NIR observations aggregated to 0.1 m resolution. The 0.1 m ALT maps were generated as a fine-resolution benchmark for evaluating uncertainties in the coarser spatial resolution ALT maps. The 0.1 m ALT maps for the sampling plots were aggregated to 10 m resolution. By comparing the differences between the two maps for each 0.1 m pixel, the estimated RMSE of the 10 m product (referred hereafter as RMSE<sub>10 m</sub>) was obtained.</p>
      <p id="d2e976">For understanding the ALT variations over larger regions beyond the limited sampling plots, the second RF model was applied using Sentinel-2 and DEM data over the surrounding 5 km <inline-formula><mml:math id="M21" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 5 km area for generating the 10 m ALT regional map. A synthetic 0.1 m ALT map over the surrounding area was then generated using the 10 m ALT map derived from the second RF model and perturbed with noise with a normal distribution and RMSE<sub>10m</sub> standard deviation.</p>
      <p id="d2e998">Multiple ALT regional maps with spatial resolutions ranging from 0.2 to 1000 m were generated by aggregating the 0.1 m pixels of the synthetic map. The aggregation intervals were set as 0.1, 1, 10, and 100 m for deriving the respective maps at sub-meter, meter, decameter, and hectometer resolutions. The uncertainties of a given coarser-resolution map relative to the 0.1 m benchmark were then obtained by calculating their differences over each 0.1 m pixel and measured using two metrics, namely, the relative RMSE normalized by the ALT standard deviation of the 0.1 m data (RMSE <inline-formula><mml:math id="M23" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> SD) and the relative RMSE normalized by the mean ALT (RMSE <inline-formula><mml:math id="M24" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mean).</p>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Results</title>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Plot and Regional ALT Mapping</title>
<sec id="Ch1.S4.SS1.SSS1">
  <label>4.1.1</label><title>Field Sampling and Multi-source ALT Mapping for the Sampling Plots</title>
      <p id="d2e1038">The ALT values sampled across all plots have a mean of 45.9 cm and a standard deviation of 11.9 cm. Relatively low ALT (39.3 cm) was typically found in areas dominated by non-riparian shrubs, while larger ALT occurred in soils near standing water (61.0 cm), along creeks (78.2 cm) (e.g., Fig. 4i), and around rocks (70.0 cm) (e.g., Fig. 4m).</p>
      <p id="d2e1041">The resulting 5 and 0.1 m ALT maps were compared with the field measurements (Fig. 4). The 5 m ALT maps (Fig. 4b, f, j, n) captured the primary ALT patterns observed from the field measurements (Fig. 4a, e, i, m) including elevated ALT along the perimeter of Plot 3, consistently low ALT throughout Plot 4, high ALT values following the water tracks in Plot 5 (Fig. 4l), and generally deep ALT in Plot 6. The 0.1 m results revealed significantly finer variations (Fig. 4c, g, k, and o), resolving ALT patterns associated with small water tracks (e.g., Fig. 4k, l), discrete vegetation patches (Fig. 4c, d), and widespread clusters of underlying rocks (Fig. 4l, p) that were not discernible at 5 m resolution. Specifically, higher ALT values are visible along Imnavait Creek within Plot 5 (Fig. 4l), as shown by the red pixels in the field measurements (Fig. 4i), 5 m ML predictions (Fig. 4j), and 0.1 m ML results (Fig. 4k). However, field sampling revealed substantial ALT variation within individual 5 m grid cells, with a standard deviation of up to 32 cm as distance from the watercourse increases. These variations within individual 5 m grid cells are only resolved in the 0.1 m results (Fig. 4k), which distinguish the high ALT values along the creek (red pixels) from the lower values in adjacent areas (blue pixels). Similarly, the stripe patterns of ALT in Plot 4 associated with alternating bands of dwarf willow, grasses, and tussocks (Fig. 1; Sect. 2; Fig. 4d) are clearly defined in the 0.1 m predictions (Fig. 4c) but are not discernible in the 5 m results (Fig. 4b). For Plot 6 where overall high ALT is observed (Fig. 4m, n, and o), heterogeneity is only captured by the 0.1 m results (Fig. 4o). The pattern of interspersed lower-ALT (non-red) pixels within high ALT areas (Fig. 4o) is likely associated with widespread clusters of underlying rocks and complex vegetation cover observed in the field (Fig. 1; Sect. 2; Fig. 4p).</p>
      <p id="d2e1044">Considering the larger ALT variability and more diversified surface conditions at 0.1 m resolution relative to the 5 m resolution, the RF model trained using the limited 5 m data set may not be able to fully capture the 0.1 m ALT variations, leading to inconsistency of the overall ALT patterns between the 5 and 0.1 m results (e.g., Plot 4; Fig. 4e, f, g) and additional uncertainties in the multi-resolution analysis. In addition, the RF predictions tended to be centralized, which may underestimate larger ALT values (e.g., fewer dark red pixels with ALT higher than 65 cm in Fig. 4j and k than the measurements in Fig. 4i) and overestimate smaller ones relative to the measurements (e.g., dark blue pixels with measured ALT smaller than 35 cm in Fig. 4i but not in the ML predictions in Fig. 4j and k).</p>
      <p id="d2e1047">Overall, the first RF model was able to reproduce the sampled ALT at 5 m resolution with a RMSE of 6.53 cm and strong correlation (0.78). Among all the predictors, slope (17.40 %), red-edge reflectance (14.05 %), aspect (13.44 %), and NIR reflectance (12.64 %) were the most important features contributing to ALT predictions. The contributions from other predictors including green band (9.91 %), blue band (9.43 %), NDWI (8.48 %), red band (7.41 %), and NDVI (7.24 %) were also important. The RF model applied to the 0.1 m predictor features was able to capture the high-resolution ALT variability and details missed by coarser-resolution results. Additional assessments showed that DEM choice had a negligible impact on ML performance, whereas the use of airborne radar data enhanced performance (Sect. S1 in the Supplement).</p>

      <fig id="F4" specific-use="star"><label>Figure 4</label><caption><p id="d2e1053">Comparisons of ALT spatial patterns derived from field measurements (<bold>a, e, i, m</bold>; grey shading indicates areas without sampling), 5 m ML outputs <bold>(b, f, j, n)</bold>, and 0.1 m ML estimates <bold>(c, g, k, o)</bold>, and images acquired from drone-based RGB camera <bold>(d, h, l, p)</bold> for the intensively sampled plots. The map was plotted using Canada Albers Equal Area Conic projection.</p></caption>
            <graphic xlink:href="https://tc.copernicus.org/articles/20/4277/2026/tc-20-4277-2026-f04.png"/>

          </fig>

</sec>
<sec id="Ch1.S4.SS1.SSS2">
  <label>4.1.2</label><title>Satellite-based ALT Mapping over the Surrounding Region</title>
      <p id="d2e1082">For the second RF model, high accuracy (RMSE 1.63 cm, <inline-formula><mml:math id="M25" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> 0.97) was achieved for the 10 m ALT predictions over the sampling plots. Terrain factors collectively form the most important control on the ALT distributions at 10 m resolution (elevation 29.88 %, aspect 17.85 %, slope 17.16 %), while vegetation (NDVI 19.85 %) and surface wetness (15.26 %) conditions are relatively less important.</p>
      <p id="d2e1092">The model was then applied using Sentinel-2 observations over the larger region surrounding the sampling plots. The resulting regional ALT patterns are strongly influenced by local topography, which is consistent with the RF contribution analysis. The higher-elevation portions of the rolling terrain and gentle hill slopes generally have deeper ALT compared with the steeper slopes (Fig. 5a, d) whereas aspect has a secondary role (Fig. 5c).</p>

      <fig id="F5" specific-use="star"><label>Figure 5</label><caption><p id="d2e1097">Comparisons between ALT distributions at 10 m resolution derived from ML <bold>(a)</bold>, the synthetic ALT map at 0.1 m resolution <bold>(b)</bold>, terrain aspect <bold>(c)</bold>, slope <bold>(d)</bold>, and elevation <bold>(e)</bold> over a larger 5 km <inline-formula><mml:math id="M26" display="inline"><mml:mo>×</mml:mo></mml:math></inline-formula> 5 km area surrounding the sampling plots (black rectangles). The map was plotted using Canada Albers Equal Area Conic projection.</p></caption>
            <graphic xlink:href="https://tc.copernicus.org/articles/20/4277/2026/tc-20-4277-2026-f05.png"/>

          </fig>

</sec>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Resolution-dependent Uncertainties Analysis</title>
      <p id="d2e1138">The uncertainties associated with coarser-resolution results were calculated by comparing with the synthetic 0.1 m ALT map (Fig. 5b). Uncertainties increase as spatial resolution becomes coarser. However, this increase is most pronounced when moving from high resolutions (e.g., sub-meter to 1 m) and becomes smaller at coarser pixel sizes (e.g., 1000 m). The increase in ALT uncertainty at coarser spatial resolutions generally follows a quadratic functional form with best fit represented by a second-order polynomial; however, the accelerated error increase at sub-meter resolutions is better characterized by a different second-order polynomial (Fig. 6). The normalized uncertainties (RMSE <inline-formula><mml:math id="M27" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> SD) range from <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">68</mml:mn></mml:mrow></mml:math></inline-formula> % to 95 %, which suggests a majority of the 0.1 m variations are likely smoothed out when observed or modelled at coarser resolutions (e.g., 1000 m) (Fig. 6). However, the RMSE magnitudes are relatively small (<inline-formula><mml:math id="M29" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">9.6</mml:mn></mml:mrow></mml:math></inline-formula> % to 13.1 %) as compared to the 0.1 m ALT mean (Fig. 6).</p>

      <fig id="F6" specific-use="star"><label>Figure 6</label><caption><p id="d2e1170">ALT uncertainties change with spatial resolutions from 0.2 to 1000 m with a detailed subset analysis from 0.2 to 1 m (inset). The uncertainties were determined using the 0.1 m ALT benchmark and normalized by the standard deviation (left vertical axis) and mean (right vertical axis; fitted polynomial function) of the 0.1 m ALT values.</p></caption>
          <graphic xlink:href="https://tc.copernicus.org/articles/20/4277/2026/tc-20-4277-2026-f06.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S5">
  <label>5</label><title>Discussion</title>
      <p id="d2e1189">Recent studies have focused on resolving multi-resolution ALT patterns and their environmental linkages using multi-sensor remote sensing (Brodylo et al., 2024; Hantson et al., 2025). Compared with the existing studies, our study differs in three respects, which include (a) advancing from transect-based (1-dimensional) sampling to intensive 2-dimensional grid-cell sampling, which provided a more comprehensive representation of spatial variability to support multi-resolution analysis; (b) characterizing ALT patterns in the unique Arctic-foothills tundra environment, thereby complementing existing studies for Interior Alaska (Brodylo et al., 2024) and the Seward Peninsula (Hantson et al., 2025); and (c) quantifying resolution-dependent uncertainties in ALT retrievals, offering additional support for improved interpretation of multi-resolution ALT products derived from remote sensing and process-based simulations for the changing Arctic.</p>
<sec id="Ch1.S5.SS1">
  <label>5.1</label><title>Key Factors Controlling ALT Spatial Variations</title>
      <p id="d2e1199">Regional ALT dynamics at kilometer or coarser resolutions are primarily governed by air temperature, which affects surface temperature, and further influences soil thermal regimes and therefore active layer conditions (Gangodagamage et al., 2014; Peng et al., 2023). Local ALT variations at finer resolutions (sub-meter to 100 m) are highly complex (Gangodagamage et al., 2014) since soil thermal regimes are further modified by local environmental factors that fine-tune the microclimate. Here, vegetation conditions, snow cover properties, soil texture, soil moisture, surface water bodies, groundwater flow, micro-topography, and disturbances collectively determine the high-resolution ALT pattern (Gangodagamage et al., 2014; Grünberg et al., 2020; Rushlow et al., 2020; Clayton et al., 2021).</p>
      <p id="d2e1202">Consistent with previous studies, our field observations and RF estimates (Sect. 4.1.1) confirmed that greater ALT is most common in areas with standing water or adjacent to creeks (e.g., Plot 5; Fig. 4i, j, k, l), where wet conditions enhance soil thermal conductivity in foothills tundra (Grant et al., 2017; Clayton et al., 2021) despite increased latent heat required for thawing. Relatively larger ALT was also found in the vicinity of subsurface rocks (e.g., within 1 m distance) (e.g., Plot 6; Fig. 5j, k, l), whose high thermal conductivities facilitate heat propagation and summer thawing (Bonnaventure and Lamoureux, 2013). Relatively thinner ALT was recorded under shrubs, which likely cool the ground in summer through canopy shading (Lawrence and Swenson, 2011) and in winter through the thermal bridging effect (Domine et al., 2022). However, shrubs can also have a counteracting influence on ALT by promoting snow accumulation; whereby, the deeper snow layer insulates the ground, leading to warmer winter soil temperatures (e.g., Palmer et al., 2012; Morse et al., 2012; Kropp et al., 2020) which can result in a deeper active layer when this winter warming effect outweighs the summer shading effect of the shrubs (Way and Lapalme, 2021). A thick moss layer may also slow active layer thaw through its insulating capacity (Schuuring et al., 2024), though no specific descriptions of the moss layer were made in our sampling.</p>
      <p id="d2e1205">In the Imnavait Creek area, the thickness of the organic layer increases from hill crests to foot slopes. The thicker organic layer provides enhanced thermal insulation, leading to a shallower active layer downhill (Walker and Walker, 1996). Accordingly, Plots 3 and 4 on west-facing downhill slopes and Plot 5 in the valley bottom exhibited overall high soil organic matter content (<inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">75</mml:mn></mml:mrow></mml:math></inline-formula> %) and relatively low ALT (<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">44</mml:mn></mml:mrow></mml:math></inline-formula> cm). In contrast, the higher-elevation Plot 6 had lower organic matter (<inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">46</mml:mn></mml:mrow></mml:math></inline-formula> %) and a higher ALT (<inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">58</mml:mn></mml:mrow></mml:math></inline-formula> cm). Besides terrain-controlled organic matter distribution, topography also affects ALT through its impacts on runoff and drainage, soil temperature, snow properties, and vegetation types (Walker and Walker, 1996, Li et al., 2017). Accordingly, topography information including slope (17.40 %) and aspect (13.44 %) are among the most important factors shaping ALT variations in the ML- and drone-based analysis, while surface features including vegetation, water bodies, and soil properties determined from the multi-spectral reflectance and optical-NIR indices, all showed important contributions to the 5 m ALT predictions over the sampling plots (7.24 % to 14.05 %; Sect. 4.1.1).</p>
      <p id="d2e1248">For the ML- and satellite-based analysis, terrain factors (elevation, slope, and aspect) collectively dominate the ALT predictions (64.89 % contribution) at 10 m resolution. The broad ALT patterns over the surrounding region (Fig. 5a) largely align with terrain-driven variability (Sect. 4.1.2), as also observed in a previous study (Hinkel and Nelson, 2003). In general, south-facing slopes in the Northern Hemisphere receive more solar radiation than north-facing slopes, leading to warmer soil and larger ALT. However, the study region is characterized by gentle terrain slopes and west facing aspects (Fig. 5). Besides the terrain-controlled organic matter distribution observed over the Imnavait Creek area, direct solar radiation loading is higher around the hill tops and lower in downslope areas (Hinkel and Nelson, 2003), thus promoting larger ALT conditions in the uplands (Fig. 5). Topography therefore exerts a direct influence on the general thaw pattern as shown in the regional ML analysis.</p>
</sec>
<sec id="Ch1.S5.SS2">
  <label>5.2</label><title>ALT Resolution-dependent Uncertainties</title>
      <p id="d2e1259">Quantifying ALT uncertainties associated with varying spatial resolutions of observation and modeling is needed for determining the validity of remote sensing based ALT products, improving permafrost models and simulations, and understanding future climate-ecosystem-hydrology feedbacks (Hantson et al., 2025).  Our analysis revealed a greater increase in ALT spatial uncertainty at the sub-meter resolutions (e.g., RMSE <inline-formula><mml:math id="M34" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> SD climbed by <inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> %), followed by another 10 % increase from 1 to 30 m resolution, and a more conservative error growth (<inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> %) from 30 to 1000 m resolution. Additional variogram analysis on the 0.1 m ALT results further showed the range or correlation length can be as small as 0.86 m (e.g., upper-left part of the sampling area of Plot 3; Fig. 4c), suggesting that fine-structure active layer features can be quantified by the methodology. High resolution (e.g., meter or sub-meter level) observations are therefore needed for quantifying the high-resolution ALT heterogeneity, which is consistent with the findings from a discontinuous permafrost region in the Alaskan Seward Peninsula (Hantson et al., 2025).</p>
      <p id="d2e1289">On the other hand, the scaling effects follow a quadratic form represented by a second-order polynomial function (Fig. 6), which approaches greater error stability at coarser resolutions (e.g., 30 to 1000 m) and with relatively low RMSE <inline-formula><mml:math id="M37" display="inline"><mml:mo>/</mml:mo></mml:math></inline-formula> mean values (e.g., <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">13.4</mml:mn></mml:mrow></mml:math></inline-formula> %). These results indicate that while high-resolution heterogeneities are smoothed out at coarser resolutions, broader ALT patterns remain detectable from relatively coarser satellite observations (e.g., from Sentinel-2: Hantson et al., 2025; MODIS: Liu et al., 2024) and with acceptable error margins to reveal critical active layer dynamics and inform regional process models.</p>
</sec>
<sec id="Ch1.S5.SS3">
  <label>5.3</label><title>Regional and Temporal Representativeness of the Study</title>
      <p id="d2e1317">Based on the Circumpolar Arctic Vegetation Map (CAVM) (Raynolds et al., 2019), plot 3 and 4 belong to vegetation type G3 (Non-tussock sedge, dwarf-shrub, moss tundra) while plot 5 and 6 belong to vegetation type S1 (Erect dwarf-shrub, moss tundra), where G3 and S1 together represent 29.8 % <uri>https://www.sciencedirect.com/topics/agricultural-and-biological-sciences/treeline</uri> (last access: 1 July 2025). Accordingly, the model, parameter importance and scaling effects are more suitable for representing the Arctic G3 and S1 areas relative to other regions. However, the study area is also unique in its abundance of glacier deposits and low rolling terrain. For a more rigorous assessment of the applicability or transferability of the data-driven model for other regions, in-situ measurements over a few spatially-distributed regions within the Arctic would be necessary.</p>
      <p id="d2e1323">In addition, the ALT inter-annual variations are affected by many dynamic factors (e.g., air temperature, snow cover properties, and disturbances), which are not explicitly accounted for by the current model. Multi-season ALT measurements and inclusion of temporally variant predictors in the data-driven model would help extend the current approach and better capture the ALT inter-annual dynamics.</p>
</sec>
</sec>
<sec id="Ch1.S6" sec-type="conclusions">
  <label>6</label><title>Conclusions</title>
      <p id="d2e1335">This study represents a multi-resolution assessment of ALT spatial heterogeneity within the Arctic foothills of northern Alaska, a region characterized by continuous permafrost cover and relatively complex terrain within the Arctic domain. We employed a ML framework for ALT mapping ranging from local plot (0.1 m) to landscape (10 m) and regional (30 to 1000 m) levels using multi-resolution observations, including intensive field sampling, and drone, airborne and satellite remote sensing.</p>
      <p id="d2e1338">Our study showed that vegetation, soil, surface water, and topography are all key drivers of meter-resolution ALT patterns, while terrain topography becomes increasingly dominant in controlling ALT distribution at coarser resolutions. Resolution effect analysis further revealed a quadratic functional relationship describing the growth of resolution-dependent uncertainties in ALT mapping, indicating a rapid increase in uncertainty at sub-meter resolutions, a moderate error increase at intermediate (1 to 30 m) resolutions, and a more conservative increase at coarser (30 to 1000 m) resolutions representative of many global satellite and model based assessments. For areas where soil, vegetation, and terrain conditions are markedly different from the Arctic foothills tundra, their ALT scaling effects can be independently quantified through similar approaches from this study.</p>
</sec>

      
      </body>
    <back><notes notes-type="codedataavailability"><title>Code and data availability</title>

      <p id="d2e1345">The data that support the findings of this study are in the process of archival and will be openly available through the Oak Ridge National Laboratory Distributed Active Archive Center (ORNL DAAC) (<ext-link xlink:href="https://doi.org/10.3334/ORNLDAAC/2473" ext-link-type="DOI">10.3334/ORNLDAAC/2473</ext-link>, Bakian-Dogaheh et al., 2026). Code used in this study is available upon request.</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d2e1351">The supplement related to this article is available online at <inline-supplementary-material xlink:href="https://doi.org/10.5194/tc-20-4277-2026-supplement" xlink:title="pdf">https://doi.org/10.5194/tc-20-4277-2026-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d2e1360">JD wrote the manuscript. JD, KAE, KBD, AM, SE, JEK collected field data for analysis. JD, KAE, KBD, JSK, MM, TAD contributed to the design and conceptualization. All coauthors contributed to writing and editing of the manuscript. All coauthors have read and agreed to the published version of this manuscript.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e1366">The contact author has declared that none of the authors has any competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d2e1372">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. The authors bear the ultimate responsibility for providing appropriate place names. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.</p>
  </notes><ack><title>Acknowledgements</title><p id="d2e1378">This work was conducted at the University of Montana and University of Southern California with funding from the National Aeronautics and Space Administration (grant no. 80NSSC22K1238). The optical-IR drone images were collected by the Toolik GIS team. The UAVSAR images were provided through the NASA ABoVE airborne campaign.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d2e1383">This research has been supported by the National Aeronautics and Space Administration, Earth Sciences Division (grant no. 80NSSC22K1238).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e1390">This paper was edited by Regula Frauenfelder and reviewed by three anonymous referees.</p>
  </notes><ref-list>
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