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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-20-4787-2026</article-id><title-group><article-title>Field-validated imaging of decadal and seasonal changes in permafrost bedrock using quantitative electrical resistivity tomography (Zugspitze, Germany/Austria)</article-title><alt-title>Field-validated imaging of permafrost bedrock using quantitative ERT</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>Scandroglio</surname><given-names>Riccardo</given-names></name>
          <email>r.scandroglio@tum.de</email>
        <ext-link>https://orcid.org/0000-0002-5434-8382</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff2 aff3">
          <name><surname>Weber</surname><given-names>Samuel</given-names></name>
          
        <ext-link>https://orcid.org/0000-0003-0720-5378</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff4">
          <name><surname>Limbrock</surname><given-names>Jonas K.</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-0993-3646</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Krautblatter</surname><given-names>Michael</given-names></name>
          
        <ext-link>https://orcid.org/0000-0002-2775-2742</ext-link></contrib>
        <aff id="aff1"><label>1</label><institution>Technical University of Munich, Chair of Landslide Research, Munich, Germany</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>Climate Change, Extremes and Natural Hazards in Alpine Regions Research Center CERC, Davos, Switzerland</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>WSL Institute for Snow and Avalanche Research SLF, Davos, Switzerland</institution>
        </aff>
        <aff id="aff4"><label>4</label><institution>University of Bonn, Institute of Geosciences, Geophysics Section, Bonn, Germany</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Riccardo Scandroglio (r.scandroglio@tum.de)</corresp></author-notes><pub-date><day>31</day><month>August</month><year>2026</year></pub-date>
      
      <volume>20</volume>
      <issue>9</issue>
      <fpage>4787</fpage><lpage>4809</lpage>
      <history>
        <date date-type="received"><day>9</day><month>November</month><year>2025</year></date>
           <date date-type="rev-request"><day>21</day><month>November</month><year>2025</year></date>
           <date date-type="rev-recd"><day>29</day><month>June</month><year>2026</year></date>
           <date date-type="accepted"><day>6</day><month>July</month><year>2026</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2026 Riccardo Scandroglio 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/20/4787/2026/tc-20-4787-2026.html">This article is available from https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026.html</self-uri><self-uri xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026.pdf">The full text article is available as a PDF file from https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e128">Ongoing permafrost degradation in alpine regions requires monitoring methods that accurately decipher spatial and temporal dynamics. Electrical resistivity tomography (ERT) is widely applied in bedrock permafrost, yet its outputs are often interpreted only qualitatively. Quantitative evaluation of ERT results, however, is crucial for improving process understanding and enhancing predictions of permafrost-related slope instability. In this study, we present a 17-year monitoring of permafrost rock slopes on Mount Zugspitze (Germany/Austria) with monthly ERT campaigns. ERT data are combined with rock temperatures at four depths to establish field-based temperature–resistivity calibrations and to validate existing laboratory-derived relations. Both approaches agree well in the freezing range; however, field calibrations tend to yield higher resistivities at subzero temperatures and reveal substantial spatial heterogeneity. Incorporating reciprocal measurements refines the existing error model, increases image resolution, and improves the identification of subsurface features. Over 10 years, the measured rock temperature increased by 1 °C, accompanied by a 25 % decrease in resistivity. The permanently frozen surface decreased by 40 %, with degradation rates up to <inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.2</mml:mn></mml:mrow></mml:math></inline-formula> k<inline-formula><mml:math id="M2" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m yr<sup>−1</sup>. Extrapolating these trends would result in the loss of 65 % of permafrost within a decade. Thermal forcing controls the degradation; however, the observed conditions and projected increases in heatwaves suggest that newly unfrozen and connected fracture networks will enhance advective heat transport. This heat shortcut is expected to accelerate permafrost warming and thawing, thereby increasing the risk of slope instability. With these results, we demonstrate that ERT monitoring can yield high-quality quantitative insights into long-term permafrost evolution and effectively track bedrock permafrost degradation across both decadal and seasonal timescales.</p>
  </abstract>
    
<funding-group>
<award-group id="gs1">
<funding-source>Bayerisches Staatsministerium für Umwelt und Verbraucherschutz</funding-source>
<award-id>TUS01UFS-76976</award-id>
</award-group>
<award-group id="gs2">
<funding-source>International Graduate School of Science and Engineering</funding-source>
<award-id>n/a</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="d2e169">In the last few decades, air temperatures have reached unprecedented record values during repeated summer heatwaves, with consequences also underground. Warming of frozen ground is well documented at all latitudes and altitudes worldwide <xref ref-type="bibr" rid="bib1.bibx6 bib1.bibx81 bib1.bibx23 bib1.bibx59 bib1.bibx1" id="paren.1"/> with European mountain permafrost warming about 0.4 °C in the last 20 years <xref ref-type="bibr" rid="bib1.bibx17 bib1.bibx67" id="paren.2"/>. This degradation is projected to continue in response to climate change, but its magnitude and timing are uncertain, as the thermal response appears to be site-specific <xref ref-type="bibr" rid="bib1.bibx81" id="paren.3"/>. In fact, it depends on material, topography, surface characteristics, slope histories, permafrost type (warm vs. cold), and, most specifically, ice content <xref ref-type="bibr" rid="bib1.bibx53 bib1.bibx24 bib1.bibx13" id="paren.4"/>. Ice-poor bedrock permafrost, close to 0 °C, has recently experienced the strongest warming <xref ref-type="bibr" rid="bib1.bibx54" id="paren.5"/>. If ice is present, permafrost degradation appears to be non-linear due to latent heat effects <xref ref-type="bibr" rid="bib1.bibx26" id="paren.6"/>. Degrading permafrost has demonstrably increased slope instability <xref ref-type="bibr" rid="bib1.bibx44 bib1.bibx57" id="paren.7"/>, as shown by recent rockfalls, rock glacier acceleration, debris flows, and other cascading phenomena <xref ref-type="bibr" rid="bib1.bibx32 bib1.bibx72 bib1.bibx91 bib1.bibx13" id="paren.8"/>. Therefore, it needs to be closely monitored.</p>
      <p id="d2e197">Geophysics can support these investigations with deep and spatially extensive insights <xref ref-type="bibr" rid="bib1.bibx89" id="paren.9"/>. Electrical Resistivity Tomography (ERT) clearly detects permafrost due to the large resistivity contrasts between frozen and unfrozen conditions <xref ref-type="bibr" rid="bib1.bibx85 bib1.bibx64 bib1.bibx70" id="paren.10"/>. Focusing on mountain environments, ERT was introduced in the early 2000s <xref ref-type="bibr" rid="bib1.bibx88 bib1.bibx25" id="paren.11"/>. It quickly evolved into 2D surveys <xref ref-type="bibr" rid="bib1.bibx27 bib1.bibx37 bib1.bibx58" id="paren.12"/> with <xref ref-type="bibr" rid="bib1.bibx42" id="text.13"/> first applying it to bedrock permafrost, followed by 3D surveys <xref ref-type="bibr" rid="bib1.bibx75 bib1.bibx15 bib1.bibx78" id="paren.14"><named-content content-type="pre">e.g.,</named-content></xref>, and cross-borehole measurements <xref ref-type="bibr" rid="bib1.bibx73 bib1.bibx4" id="paren.15"/>. Repetition of measurements, i.e., time-lapse ERT, proved its capability to monitor permafrost changes <xref ref-type="bibr" rid="bib1.bibx29 bib1.bibx43 bib1.bibx74 bib1.bibx78" id="paren.16"/>. Fundamental for reproducibility is a robust setup <xref ref-type="bibr" rid="bib1.bibx38" id="paren.17"/>, but only recently have standard procedures been suggested <xref ref-type="bibr" rid="bib1.bibx28" id="paren.18"/>. The majority of time-lapse studies are composed of one single measurement per year at the end of summer for permafrost detection <xref ref-type="bibr" rid="bib1.bibx33 bib1.bibx71 bib1.bibx9" id="paren.19"><named-content content-type="pre">e.g.,</named-content></xref> and the repetition of surveys accounts only for 20 % of the studies <xref ref-type="bibr" rid="bib1.bibx28" id="paren.20"/>. Most of these were single repetitions <xref ref-type="bibr" rid="bib1.bibx52 bib1.bibx8" id="paren.21"><named-content content-type="pre">e.g.,</named-content></xref>, some monitoring occurred at irregular time intervals <xref ref-type="bibr" rid="bib1.bibx78 bib1.bibx19 bib1.bibx65" id="paren.22"/>, and only a few sites were regularly monitored <xref ref-type="bibr" rid="bib1.bibx62 bib1.bibx63" id="paren.23"/>. Although knowledge of the minimum permafrost extension at the end of summer is sufficient for most sites, hazardous locations require a higher temporal resolution to interpret site-specific, complex hydrothermal dynamics at depth <xref ref-type="bibr" rid="bib1.bibx43 bib1.bibx38 bib1.bibx68" id="paren.24"/>. This enables the evaluation of rock instabilities <xref ref-type="bibr" rid="bib1.bibx35 bib1.bibx18 bib1.bibx9" id="paren.25"/> to inform the development of effective geotechnical solutions and appropriate risk-reduction strategies <xref ref-type="bibr" rid="bib1.bibx7 bib1.bibx13" id="paren.26"/>. Automated time-lapse ERT can provide high temporal resolution <xref ref-type="bibr" rid="bib1.bibx38 bib1.bibx14" id="paren.27"/>. However, the analyses published so far are limited to 2 years or have significant gaps due to frequent technical failures <xref ref-type="bibr" rid="bib1.bibx30 bib1.bibx82 bib1.bibx36" id="paren.28"/>. Therefore, automated ERT has rarely been used to examine long-term trends in permafrost change <xref ref-type="bibr" rid="bib1.bibx28" id="paren.29"/>. The only known work presenting continuous decadal data at monthly resolution is by <xref ref-type="bibr" rid="bib1.bibx62" id="text.30"/> at the Schilthorn (CH).</p>
      <p id="d2e275">Quantification of permafrost changes can be obtained by calculating the average resistivity of the whole model <xref ref-type="bibr" rid="bib1.bibx29" id="paren.31"/> or only of the area of interest <xref ref-type="bibr" rid="bib1.bibx38" id="paren.32"/>. Quantitatively translating resistivity values into temperatures is a non-trivial task, as many factors influence the measurements <xref ref-type="bibr" rid="bib1.bibx43" id="paren.33"/>.  Laboratory calibration of bedrock samples was first introduced by <xref ref-type="bibr" rid="bib1.bibx43" id="text.34"/> and subsequently employed in several studies to enhance the interpretation of geophysical data in permafrost environments <xref ref-type="bibr" rid="bib1.bibx52 bib1.bibx18 bib1.bibx78" id="paren.35"><named-content content-type="pre">e.g.,</named-content></xref>, although without quantitative field validation. ERT validation is possible with borehole data <xref ref-type="bibr" rid="bib1.bibx88 bib1.bibx47 bib1.bibx14 bib1.bibx62 bib1.bibx20" id="paren.36"/> to constrain the interpretation of the results. While many studies report both borehole temperature data and ERT measurements, a direct comparison and validation between the two is rare in the literature. Only in recent studies, shallow borehole data have been used to calibrate automated ERT datasets: e.g., in arctic sediments <xref ref-type="bibr" rid="bib1.bibx10 bib1.bibx11" id="paren.37"/>. Further, to our knowledge, no study has validated laboratory-based calibrations in the field.</p>
      <p id="d2e302">Here, we present the first field-validated long-term temperature-resistivity monitoring over more than 10 years in bedrock permafrost. This database originates from a high-alpine location (Mount Zugspitze, Germany/Austria, 2800 m a.s.l.). It is unique due to its monthly resolution, the location of the electrodes in the permafrost core rather than on the surface, and the high-quality results achieved through manual measurements. Results are compared with those of <xref ref-type="bibr" rid="bib1.bibx43" id="text.38"/> to validate the methods and investigate the effects of climate change. This study aims to determine whether ERT monitoring can provide robust quantitative insights into long-term permafrost evolution and effectively capture bedrock permafrost degradation over both decadal and seasonal timescales. This overarching objective is explored through four key quantitative research questions: <list list-type="order"><list-item>
      <p id="d2e310">How reliable is laboratory calibration, and is it consistent with field calibration and observations?</p></list-item><list-item>
      <p id="d2e314">Do enhanced error models improve the reconnaissance of thermal processes in bedrock?</p></list-item><list-item>
      <p id="d2e318">What long-term trends and seasonal signals of permafrost degradation can be effectively captured with monthly resolution?</p></list-item><list-item>
      <p id="d2e322">At the Zugspitze, can we quantify permafrost extent, its degradation over a decade, and anticipate its future development?</p></list-item></list></p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Material and Methods</title>
<sec id="Ch1.S2.SS1">
  <label>2.1</label><title>Field site</title>
      <p id="d2e340">Measurements took place in the Kammstollen, a private tunnel beneath the E-W oriented ridge of Zugspitze (2962 m a.s.l., Fig. <xref ref-type="fig" rid="F1"/>a–b), located at the German-Austrian border. This mountain is part of the Northern Calcareous Alps, and its summit is composed of Upper Triassic carbonate rocks, mainly massive limestones of the Wetterstein Formation <xref ref-type="bibr" rid="bib1.bibx61" id="paren.39"/>. The thick-bedded, locally dolomitized rocks commonly exhibit fracturing and karstification due to dissolution, which are frequent and well documented on the nearby Plateau <xref ref-type="bibr" rid="bib1.bibx94 bib1.bibx93" id="paren.40"/>. Minor dolomite and occasional marl intercalations reflect depositional variability, while brecciated zones up to <inline-formula><mml:math id="M4" display="inline"><mml:mn mathvariant="normal">1</mml:mn></mml:math></inline-formula> m thickness are present in the summit area <xref ref-type="bibr" rid="bib1.bibx86" id="paren.41"/>. A prominent fault zone extends from the investigation area up to the summit <xref ref-type="bibr" rid="bib1.bibx31" id="paren.42"/>, but overall, the steep summit cliffs consist of comparatively pure, competent carbonate rocks. The study area is accessible year-round thanks to the infrastructure and logistical support of the research station, Scheefernerhaus (UFS), which is directly connected to the tunnel.</p>
      <p id="d2e365">Long-term meteorological records on the summit by the German Meteorological Service (DWD) are available since 1900 (Fig. <xref ref-type="fig" rid="F1"/>c). Air temperature increased drastically in the last 30 years, with mean temperatures in the last decade (2013–2022) reaching <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.3</mml:mn></mml:mrow></mml:math></inline-formula> °C, which is <inline-formula><mml:math id="M6" display="inline"><mml:mn mathvariant="normal">1.5</mml:mn></mml:math></inline-formula> °C warmer than the reference period 1961–1990. Additionally, 2011, 2020, 2022, and 2024 were the warmest years on record. Mean annual precipitation is more than <inline-formula><mml:math id="M7" display="inline"><mml:mn mathvariant="normal">2500</mml:mn></mml:math></inline-formula> mm of which 80 % is snowfall, but the steep north walls remain snow-free for most of the winter. The hydrological behavior of clefts at this location has been thoroughly measured for many years and interpreted by <xref ref-type="bibr" rid="bib1.bibx79" id="text.43"/>.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <label>2.2</label><title>State of the cryosphere at the Zugspitze</title>
      <p id="d2e405">The earliest records of permafrost on the Zugspitze date to the construction of its infrastructure <xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx40 bib1.bibx86" id="paren.44"/>. In recent years, 3D modeling has confirmed the possible presence of permafrost on the shaded and steep north side of the SW-NE ridge, which includes the site of this study, beginning at approximately 2350 m a.s.l., but suggests a rather warm permafrost <xref ref-type="bibr" rid="bib1.bibx66" id="paren.45"/>. Based on this modeling, one N-S borehole was drilled in 2007 by the Bavarian Environmental Agency (LfU) about 30 m under the summit to document permafrost presence and evolution under the summit cable car, at a distance of 700 m from our field site <xref ref-type="bibr" rid="bib1.bibx21 bib1.bibx22 bib1.bibx90" id="paren.46"/>. These measurements support the modeling, showing average core temperatures between <inline-formula><mml:math id="M8" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.2</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M9" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.7</mml:mn></mml:mrow></mml:math></inline-formula> °C, with a warming trend of 0.4 K in the last ten years. Modeling by <xref ref-type="bibr" rid="bib1.bibx21" id="text.47"/> forecasts the disappearance of this lens by 2070. <xref ref-type="bibr" rid="bib1.bibx43" id="text.48"/> conducted the first ERT monitoring in the tunnel in 2007, setting the basis for this study. The tunnel comprises a main tunnel (MT) and a side tunnel (ST). Ice accumulated across the entire ground of the side tunnel and in parts of the main tunnel, reaching a depth of up to 50 cm in some locations. Recently <xref ref-type="bibr" rid="bib1.bibx56 bib1.bibx57" id="text.49"/> conducted intense geophysical measurements and mechanical modeling to monitor an ice-controlled instability on the ridge 400 m from the tunnel. This location showed strongly degrading permafrost due to the thermal influence of the southern slope on a thin ridge. Other geophysical measurements in the area utilized passive seismic methods to document permafrost degradation <xref ref-type="bibr" rid="bib1.bibx50" id="paren.50"/> and relative gravimetry to detect mass changes associated with hydrology <xref ref-type="bibr" rid="bib1.bibx87" id="paren.51"/>. Finally, <xref ref-type="bibr" rid="bib1.bibx60" id="text.52"/> documented the dramatic recession of the three glaciers at the Zugspitze, which have been shrinking since the 1980s and could completely disappear within the next decade.</p>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e458"><italic>Study site overview.</italic> <bold>(a)</bold> Zugspitze summit, with the DWD meteorological station and the LfU borehole. In red, the main tunnel, going from the research station (UFS) at 2650 m a.s.l. (south) to the exit in the north slope at 2800 m a.s.l. © OpenStreetMap 2023. Open Data Commons Open Database License v1. <bold>(b)</bold> Zoom of the monitoring site showing the main and the side tunnel, the ERT electrodes, the temperature loggers, and the two temperature transects (A–A' and B–B'). In the background, one exemplary tomogram from <xref ref-type="bibr" rid="bib1.bibx43" id="text.53"/> shows the permafrost lens. A red line shows the approximate location of the fault zone. <bold>(c)</bold> Mean annual air temperature (MAAT) at the DWD station. The thick red line shows the 30-year backward moving mean, while the black lines show the average for the selected period. <bold>(d)</bold> The upper graph shows data availability for temperature loggers. For abbreviations, consult Table <xref ref-type="table" rid="T1"/>. The lower graph shows ERT data availability, with the percentage indicating the number of quadrupoles collected during fieldwork (100 % corresponds to 1310 quadrupoles).</p></caption>
          <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f01.png"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS3">
  <label>2.3</label><title>Monitoring setup</title>
      <p id="d2e495">The setup of our study is based on the feasibility study conducted in 2007 and 2008 by <xref ref-type="bibr" rid="bib1.bibx43" id="text.54"/> and remained constant to obtain comparable measurements. Monthly monitoring of electrical resistivity (<inline-formula><mml:math id="M10" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula>) commenced in 2014 and continues to this day. Measures were undertaken along 6 transects, with electrode distances of 4.6 and 1.5 m, using Wenner and Schlumberger arrays, for a total of 1310 quadrupoles. The monitoring settings are presented in the Supplement (Fig. S1), and a detailed description of the procedures is provided in <xref ref-type="bibr" rid="bib1.bibx43" id="text.55"/>. Resistivity data were primarily collected using an ABEM Terrameter LS, with alternating use of an ABEM SAS 1000 and SAS 300C before 2018. Contact resistance was improved by spraying the electrodes with saltwater shortly before the measurements, after our tests showed it did not affect the results. Electrodes that still had too high contact resistivity, mostly close to the active layer because of ice on or around the electrodes, were eventually excluded from the measurement. Problematic electrodes with rust or poor coupling have been consistently replaced. The final number of measured quadrupoles reached on average 90 % of the total, but was constantly above this average in the last 5 years (Fig. <xref ref-type="fig" rid="F1"/>d). Data were collected using a stacking of 2, increased to 4 in case of a measurement error above 1 %. Between 2017 and 2018, data availability and quality were limited due to repeated cable failures; therefore, 14 measurements from this period have been excluded from this analysis.</p>

<table-wrap id="T1" specific-use="star"><label>Table 1</label><caption><p id="d2e516">List of all temperature loggers. MT <inline-formula><mml:math id="M11" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> Main Tunnel, ST <inline-formula><mml:math id="M12" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> Side Tunnel.</p></caption><oasis:table frame="topbot"><oasis:tgroup cols="8">
     <oasis:colspec colnum="1" colname="col1" align="left"/>
     <oasis:colspec colnum="2" colname="col2" align="left"/>
     <oasis:colspec colnum="3" colname="col3" align="left"/>
     <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:colspec colnum="7" colname="col7" align="left"/>
     <oasis:colspec colnum="8" colname="col8" align="left"/>
     <oasis:thead>
       <oasis:row rowsep="1">
         <oasis:entry colname="col1">Transect</oasis:entry>
         <oasis:entry colname="col2">Name</oasis:entry>
         <oasis:entry colname="col3">Nr.</oasis:entry>
         <oasis:entry colname="col4">Type (Precision)</oasis:entry>
         <oasis:entry colname="col5">Location</oasis:entry>
         <oasis:entry colname="col6">Spacing</oasis:entry>
         <oasis:entry colname="col7">Time</oasis:entry>
         <oasis:entry colname="col8">Note</oasis:entry>
       </oasis:row>
     </oasis:thead>
     <oasis:tbody>
       <oasis:row>
         <oasis:entry colname="col1">A–A'</oasis:entry>
         <oasis:entry colname="col2">ST</oasis:entry>
         <oasis:entry colname="col3">4</oasis:entry>
         <oasis:entry colname="col4">Geoprecision M-Log 5W (<inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> °C)</oasis:entry>
         <oasis:entry colname="col5">Side tunnel (ST), rock</oasis:entry>
         <oasis:entry colname="col6">5 m</oasis:entry>
         <oasis:entry colname="col7">2019–2024</oasis:entry>
         <oasis:entry colname="col8">substitute UTL</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">B–B'</oasis:entry>
         <oasis:entry colname="col2">MT</oasis:entry>
         <oasis:entry colname="col3">20</oasis:entry>
         <oasis:entry colname="col4">iButton DS1922L (<inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> °C)</oasis:entry>
         <oasis:entry colname="col5">Main tunnel (MT), rock</oasis:entry>
         <oasis:entry colname="col6">4.6 m</oasis:entry>
         <oasis:entry colname="col7">2020–2024</oasis:entry>
         <oasis:entry colname="col8">new</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">B–B'</oasis:entry>
         <oasis:entry colname="col2">AT</oasis:entry>
         <oasis:entry colname="col3">3</oasis:entry>
         <oasis:entry colname="col4">Geoprecision M-Log 5W (<inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> °C)</oasis:entry>
         <oasis:entry colname="col5">Main tunnel (MT), air</oasis:entry>
         <oasis:entry colname="col6">46 m</oasis:entry>
         <oasis:entry colname="col7">2020–2024</oasis:entry>
         <oasis:entry colname="col8">new</oasis:entry>
       </oasis:row>
       <oasis:row>
         <oasis:entry colname="col1">–</oasis:entry>
         <oasis:entry colname="col2">RST</oasis:entry>
         <oasis:entry colname="col3">1</oasis:entry>
         <oasis:entry colname="col4">Geoprecision M-Log 5W (<inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.1</mml:mn></mml:mrow></mml:math></inline-formula> °C)</oasis:entry>
         <oasis:entry colname="col5">outside, rock</oasis:entry>
         <oasis:entry colname="col6">–</oasis:entry>
         <oasis:entry colname="col7">2022–2024</oasis:entry>
         <oasis:entry colname="col8">new</oasis:entry>
       </oasis:row>
     </oasis:tbody>
   </oasis:tgroup></oasis:table></table-wrap>

      <p id="d2e741">Hourly monitoring of rock temperature (<inline-formula><mml:math id="M17" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>) follows <xref ref-type="bibr" rid="bib1.bibx43" id="text.56"/> with updates and extensions as listed hereafter and in Table <xref ref-type="table" rid="T1"/>. Old loggers of Type UTL-1 were replaced with new Geoprecision loggers, offering higher accuracy and reliability. New loggers were installed along the main tunnel at a depth of 40 cm for rock and air temperature (MT and AT). One logger has been installed outside to measure rock surface temperature (RST) at 15 cm depth. The ST, AT, and RST loggers (Geoprecision) were calibrated at 0 °C by the manufacturer using a high-precision water triple-point cell, reaching a temperature stability of <inline-formula><mml:math id="M18" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.005</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow></mml:math></inline-formula> °C. This process ensures high accuracy and reproducibility in calibrating the measurement system. The iButton loggers (MT) were calibrated in an ice bath on multiple occasions throughout the study to account for drift effects. The analysis presented here focuses on the period after 2018, where complete data have been recorded. Data availability for temperature loggers is presented in Fig. <xref ref-type="fig" rid="F1"/>d.</p>
</sec>
<sec id="Ch1.S2.SS4">
  <label>2.4</label><title>Data analysis</title>
      <p id="d2e777">To analyze temperature dynamics, we linearly interpolated the four temperature measurements along the side tunnel (transect A–A') from 2019 to 2023, treating them as a borehole (Figs. <xref ref-type="fig" rid="F2"/> and <xref ref-type="fig" rid="F3"/>).</p>
      <p id="d2e784">Successively, <inline-formula><mml:math id="M19" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>-<inline-formula><mml:math id="M20" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> field calibration (Figs. <xref ref-type="fig" rid="F4"/>, <xref ref-type="fig" rid="F5"/>, and S6) was conducted by combining these temperature values with single apparent resistivity values from the closest quadrupole to each temperature logger (within a 0.3 m radius). Logger ST-5, located at a depth of 5 m below the surface, was excluded from the calibration because resistivity measurements at this location were only available during summer, resulting in an insufficient dataset for robust analysis. To validate the results, we analyzed the probability density function of the apparent resistivity before inversion (Fig. <xref ref-type="fig" rid="F6"/>).</p>
      <p id="d2e807">After field work, each database was imported into MATLAB. Winter measurements from December to June produced, on average, 4 negative resistivity measurements, which were excluded, while summer measurements showed none. Data were filtered using the coefficient of variability (CV, or VAR (%) according to ABEM) of the resistance, i.e., the standard deviation divided by the mean, as computed by the measuring instrument, to remove systematic errors. The threshold for the CV was set to 1 %, resulting in an average exclusion of 6 data points, mostly concentrated in the winter months.</p>
      <p id="d2e810">For the ERT inversion, we utilized an updated version of the software <italic>CRTomo</italic> <xref ref-type="bibr" rid="bib1.bibx34" id="paren.57"/>. This inversion algorithm fits a model <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="bold-italic">m</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> to the data <inline-formula><mml:math id="M22" display="inline"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> based on an adequate data error description <inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, instead of just minimizing the data misfit as commonly done. Data fit is achieved when the data misfit <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mtext>RMS</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> (root mean square) value is close to one, which indicates that the model reproduces the data within the expected error margins on average, as shown in Eq. (<xref ref-type="disp-formula" rid="Ch1.E1"/>) <xref ref-type="bibr" rid="bib1.bibx34" id="paren.58"/>

            <disp-formula id="Ch1.E1" content-type="numbered"><label>1</label><mml:math id="M25" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mtext>RMS</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mn mathvariant="normal">1</mml:mn><mml:mi>N</mml:mi></mml:mfrac></mml:mstyle><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mi mathvariant="normal">i</mml:mi><mml:mi>N</mml:mi></mml:munderover><mml:msup><mml:mfenced open="|" close="|"><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="bold-italic">m</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mstyle></mml:mfenced><mml:mn mathvariant="normal">2</mml:mn></mml:msup></mml:mrow></mml:msqrt><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula></p>
      <p id="d2e936">Following <xref ref-type="bibr" rid="bib1.bibx43" id="text.59"/>, we performed independent inversions without applying a time-lapse approach. Because time-lapse inversion can significantly influence results <xref ref-type="bibr" rid="bib1.bibx78" id="paren.60"/>, we aimed to minimize temporal constraints, such as those introduced by prior or initial inversions, that may bias the results. We argue that this approach enhances the robustness of our results, as consistent trends emerge without temporal regularization.</p>
      <p id="d2e945">Further on, the error model for the inversion was updated with new measurements. Image quality is highly dependent on the error estimates in the inversion: an overestimation smooths the image, reducing resolution, while an underestimation leads to artifacts <xref ref-type="bibr" rid="bib1.bibx5 bib1.bibx45 bib1.bibx80 bib1.bibx46 bib1.bibx84" id="paren.61"/>. The random error (<inline-formula><mml:math id="M26" display="inline"><mml:mi>e</mml:mi></mml:math></inline-formula>) can be quantified using the difference between normal (<inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">N</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) and reciprocal (<inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) resistivity measurements, although this is only a measure of precision and not accuracy <xref ref-type="bibr" rid="bib1.bibx45" id="paren.62"/> and does not represent the total experimental error. The error can be modeled as a linear function of the mean resistance <inline-formula><mml:math id="M29" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> (Eq. <xref ref-type="disp-formula" rid="Ch1.E2"/>), depending on an absolute (<inline-formula><mml:math id="M30" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula>) and a relative (<inline-formula><mml:math id="M31" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula>) term

            <disp-formula id="Ch1.E2" content-type="numbered"><label>2</label><mml:math id="M32" display="block"><mml:mrow><mml:mo>|</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">N</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">R</mml:mi></mml:msub><mml:mo>|</mml:mo><mml:mo>=</mml:mo><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mi>a</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:mi>R</mml:mi><mml:mo>.</mml:mo></mml:mrow></mml:math></disp-formula>

          To solve this, <xref ref-type="bibr" rid="bib1.bibx80" id="text.63"/> expresses <inline-formula><mml:math id="M33" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> as a function of <inline-formula><mml:math id="M34" display="inline"><mml:mi>e</mml:mi></mml:math></inline-formula>, removes obvious outliers (<inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:mi>e</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">10</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mi>R</mml:mi></mml:mrow></mml:math></inline-formula>), and obtains <inline-formula><mml:math id="M36" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M37" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> from the envelope of all remaining measurements. <xref ref-type="bibr" rid="bib1.bibx39" id="text.64"/> instead rejected only values of <inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:mi>e</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">100</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi><mml:mspace width="0.25em" linebreak="nobreak"/><mml:mi>R</mml:mi></mml:mrow></mml:math></inline-formula> and then divided the measurements into logarithmically equally sized bins. The standard deviations of the reciprocal errors in each bin were least-square fitted with the linear error model (Eq. <xref ref-type="disp-formula" rid="Ch1.E2"/>). <xref ref-type="bibr" rid="bib1.bibx46" id="text.65"/> adapted the approach of <xref ref-type="bibr" rid="bib1.bibx80" id="text.66"/> to fit the discrepancies between readings acquired at different times, proposing data error estimates for time-lapse measurements.</p>
      <p id="d2e1126">After updating the used error estimates, we computed a new inversion for all measurements, including those from 2007 published in <xref ref-type="bibr" rid="bib1.bibx43" id="text.67"/>, and analyzed temporal changes by classifying different areas of the tomogram, such as the active layer and permafrost core. Some authors manually define an area of interest  <xref ref-type="bibr" rid="bib1.bibx38" id="paren.68"/>, while others choose an automated algorithm <xref ref-type="bibr" rid="bib1.bibx12 bib1.bibx92" id="paren.69"/>. Here, the inversion results were clustered using the MATLAB <italic>k</italic>-means algorithm. The function analyzed all tomograms from 2014 to 2023 and computed, for each grid cell, the squared Euclidean distance to the cluster centroids (the cluster means). Cells were then categorized into the nearest centroid. The number of clusters <italic>k</italic> is defined by the user, and assignment is mutually exclusive. This approach converges to a local minimum, though lower minima may exist. In practice, the global minimum is approximated by running multiple replicates with random starting points. We used five cluster classes, based on the elbow method <xref ref-type="bibr" rid="bib1.bibx11" id="paren.70"/>, which evaluates the sum of squared distances between samples and their nearest cluster center as a function of the number of clusters. The optimal number is identified at the elbow of the resulting curve.</p>
</sec>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Results</title>
<sec id="Ch1.S3.SS1">
  <label>3.1</label><title>Characterization of thermal regime from temperature measurements</title>
      <p id="d2e1164">The temperature distribution in the tunnels indicates permafrost presence in transect A–A' (Fig. <xref ref-type="fig" rid="F2"/>). Due to repeated measurement gaps before 2019, it is not possible to determine longer temperature trends. Over the last five years, the increase in active layer thickness (ALT) from 8.5 to 10 m, combined with the overall rise in annual maximum temperatures, indicates permafrost degradation. The 10 m logger has now reached <inline-formula><mml:math id="M39" display="inline"><mml:mn mathvariant="normal">0</mml:mn></mml:math></inline-formula> °C and maintained this level for more than 2 months in summer 2023. It is likely to overcome this threshold in the next few years. No permafrost is recorded in transect B–B' (Fig. S2, Supplement), while seasonally frozen rock is recorded between electrodes E30 and E39. All loggers in the main tunnel recorded their maximum temperature in 2023, with a more pronounced increase in the area to the right of the side tunnel, specifically electrodes E32 to E41. Outside the tunnel, the mean annual rock surface temperature of the steep bedrock facing north is <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">1.7</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/></mml:mrow></mml:math></inline-formula> °C (RST-Logger, Fig. <xref ref-type="fig" rid="F3"/>c).</p>

      <fig id="F2" specific-use="star"><label>Figure 2</label><caption><p id="d2e1191"><italic>Temperature profile in the side tunnel.</italic> The location of the transect is visible in Fig. <xref ref-type="fig" rid="F1"/>b (profile A–A').</p></caption>
          <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f02.png"/>

        </fig>

      <p id="d2e1204">Ice on the ground of the main tunnel decreased between 2019 and 2021, especially in the area of the permafrost lens between electrodes E31 and E38 (Fig. S5). This decrease aligns with the temperature increases recorded by the loggers in the main tunnel. As documented by <xref ref-type="bibr" rid="bib1.bibx79" id="text.71"/>, large quantities of water from snowmelt are recorded in June and July in the northern part of the main tunnel (electrodes E1 to E20, <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">200</mml:mn></mml:mrow></mml:math></inline-formula> to 275 m). In the side tunnel, water accumulation on the ground is also common, but only at the end of summer and between the ST-5 and the north face. This water results from melting surface ice on the tunnel walls and from ice-filled fractures within the tunnel.</p>

      <fig id="F3" specific-use="star"><label>Figure 3</label><caption><p id="d2e1225"><italic>Temperature loggers and their correlation with external air temperature.</italic>
<bold>(a)</bold> Photo of the new ST-loggers and the old UTL-loggers. All sensors are located at a depth of 40 cm. The old loggers were replaced in  2019, with a one-year overlapping period. <bold>(b)</bold> Photos of the MT-loggers, also at a depth of 40 cm. <bold>(c)</bold> Photo of the RST logger on the north face, close to Electrode E30, at 10 cm depth. <bold>(d)</bold> Correlation between ST-loggers and external air temperature from the DWD station. <bold>(e)</bold> Correlation between AT-loggers and external air temperature.</p></caption>
          <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f03.jpg"/>

        </fig>

      <p id="d2e1251">The correlation between rock temperature inside the tunnel and air temperature outside is clear (Fig. <xref ref-type="fig" rid="F3"/>d), with correlation coefficients between 0.77 for the ST-5 logger at 5 m depth and 0.4 for the ST-20 logger at 20 m depth. As expected, with increasing depth, the time lag grows, reaching up to 75 d at 10–15 m. This represents the time required for the thermal signal to propagate to the permafrost core within the bedrock. The correlation between air temperatures inside and outside the tunnel is strong at electrode 30 (<inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">143</mml:mn></mml:mrow></mml:math></inline-formula> m), near one of the tunnel exits, but becomes absent for deeper loggers (Fig. <xref ref-type="fig" rid="F3"/>e), indicating the influence of additional processes at greater depths (e.g., solar radiation or snow cover from the south side slope). A comparison of ST-Loggers with the LfU-borehole <xref ref-type="bibr" rid="bib1.bibx21" id="paren.72"/>, which is installed on the summit, ca. 150–200 m higher than our site, shows that ST-5 and ST-10 are quite similar to the LfU-borehole measurements in summer. At the same time, winter temperatures are much lower in the LfU-borehole (Figs. S3 and S4).</p>
</sec>
<sec id="Ch1.S3.SS2">
  <label>3.2</label><title>Field calibration of the <inline-formula><mml:math id="M43" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>-<inline-formula><mml:math id="M44" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> relation</title>
      <p id="d2e1296">The newly collected thermal information, together with the ERT measurements, allows us to validate the temperature-resistivity (<inline-formula><mml:math id="M45" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>-<inline-formula><mml:math id="M46" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula>) laboratory calibration by <xref ref-type="bibr" rid="bib1.bibx43" id="text.73"/>, which was often used to interpret ERT field measurements so far <xref ref-type="bibr" rid="bib1.bibx52 bib1.bibx18 bib1.bibx78" id="paren.74"><named-content content-type="pre">e.g.,</named-content></xref>. Figure <xref ref-type="fig" rid="F4"/> shows that, despite differences in resistivity ranges, there is a high correlation between temperature and resistivity.</p>

      <fig id="F4" specific-use="star"><label>Figure 4</label><caption><p id="d2e1325"><italic>Temperature versus resistivity.</italic> Rock temperatures from the ST loggers in blue, and air temperatures from the DWD station in dotted green. In red, single quadrupole apparent resistivity measurements, prior to inversion, with reverse axis direction for simplifying comparison. Other periods are available in Fig. S6 of the Supplement.</p></caption>
          <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f04.png"/>

        </fig>

      <fig id="F5" specific-use="star"><label>Figure 5</label><caption><p id="d2e1339"><inline-formula><mml:math id="M47" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>-<inline-formula><mml:math id="M48" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> <italic>field calibration.</italic>
<bold>(a)</bold> All values from 2021 to 2024. <bold>(b)</bold> Calibration for ST-10, using only the values from the new <inline-formula><mml:math id="M49" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>-loggers, from 2019. In red is the interpolating line, in green is the lab calibration from <xref ref-type="bibr" rid="bib1.bibx43" id="text.75"/>. <bold>(c)</bold> Calibration lines for all loggers. In black, the average of logger ST-5, ST-10, and ST-20.</p></caption>
          <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f05.png"/>

        </fig>

      <p id="d2e1384">Resistivity varies from 30 to 120 k<inline-formula><mml:math id="M50" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m for ST-10, from 15 to 25 k<inline-formula><mml:math id="M51" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m for ST-15, and from 40 to 130 k<inline-formula><mml:math id="M52" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m for ST-20. These differences lead to a strong spreading of data when plotting all the values together (Fig. <xref ref-type="fig" rid="F5"/>a). Still, when analyzing each temperature logger separately, the correlation appears clear (Fig. <xref ref-type="fig" rid="F5"/>b and Fig. S7b–e). This suggests that the relation between resistivity and temperature can not be assumed to be unique for this transect. Logger ST-5 records only a few values below 0 °C: during the cold months, a thick ice cover in the tunnel limits electrode contact, whereas in the warm months, positive temperatures are measured. Therefore, ST-5 will be excluded from our analysis. The other loggers show a good linear fit: the best is at ST-10 (<inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.84</mml:mn></mml:mrow></mml:math></inline-formula>), whereas at ST-20 the fit is poor (<inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msup><mml:mi>R</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.41</mml:mn></mml:mrow></mml:math></inline-formula>). Resistivities decrease over time, possibly due to reduced ice content; therefore, an annual analysis could yield a better fit. Generally, most recorded data are close to the freezing point, which should be taken into consideration. Supercooling effects and similar phenomena from the calibration are not detectable in the field calibration due to the absence of freeze-thaw cycles in the permafrost core.</p>
      <p id="d2e1443">The freezing point at 29 k<inline-formula><mml:math id="M55" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m agrees with values from the laboratory, but in the field, resistivity increases at much stronger rates than laboratory experiments can reproduce. Field calibration results for ST-10 and ST-20 can be resumed in the “average” Eq. (<xref ref-type="disp-formula" rid="Ch1.E3"/>).

            <disp-formula id="Ch1.E3" content-type="numbered"><label>3</label><mml:math id="M56" display="block"><mml:mrow><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>=</mml:mo><mml:mo>(</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">106</mml:mn><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mo>±</mml:mo><mml:mn mathvariant="normal">49</mml:mn><mml:mo>)</mml:mo><mml:mspace linebreak="nobreak" width="0.25em"/><mml:mi>T</mml:mi><mml:mo>+</mml:mo><mml:mn mathvariant="normal">29</mml:mn></mml:mrow></mml:math></disp-formula>

          ST-15 shows much lower resistivity values than the other locations and behaves similarly to the laboratory calibration. This could depend on the degree of fracturing at this location.</p>
</sec>
<sec id="Ch1.S3.SS3">
  <label>3.3</label><title>Field validation of the <inline-formula><mml:math id="M57" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>-<inline-formula><mml:math id="M58" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> relation</title>
      <p id="d2e1509">To explain the big discrepancies in the field calibration, we analyze the rock that composes the tunnel. While the majority is made of compact rock (material A in Fig. <xref ref-type="fig" rid="F6"/>), short parts of the tunnel are highly fractured due to the fault zone (material B in Fig. <xref ref-type="fig" rid="F6"/>). As suggested by <xref ref-type="bibr" rid="bib1.bibx78" id="text.76"/>, we compare the probability density function of the apparent resistivity of all the measurements in the permafrost area (side tunnel). The ERT transect on the right (Fig. <xref ref-type="fig" rid="F6"/>d) presents only one peak, while on the left (Fig. <xref ref-type="fig" rid="F6"/>c) two peaks are visible. Supposing that each peak relates to a different rock type, this indicates the presence of two materials in the left area, as confirmed by field mapping (Fig. <xref ref-type="fig" rid="F6"/>a). The probability density curves for material A on the right side of the tunnel clearly show variations with time towards lower values. At the same time, smaller changes are recorded on the left for material A and no changes for material B. A combination of both materials would likely produce results similar to material B, as current follows the easiest path of lower resistivity; however, this should be further investigated.</p>

      <fig id="F6" specific-use="star"><label>Figure 6</label><caption><p id="d2e1528"><italic>Comparison of ERT raw data for the two resistivity transects in the permafrost area.</italic> <bold>(a)</bold> Photos from the tunnel. Material A, at electrode E36, is pure bedrock. Material B, at electrode E49, is mostly fine-grained material. A mix of materials A and B with fractures of variable width is also possible. <bold>(b)</bold> Areas of interest of the ERT transects in the side tunnel: violet for the left and yellow for the right transect. <bold>(c–d)</bold> Probability density functions of apparent resistivity of the whole transect for the warmest months. Data in subplot <bold>(c)</bold> show two peaks, indicating the presence of two main signatures, while data in subplot <bold>(d)</bold> shows only a single peak. The year 2023 recorded the lowest apparent resistivities in both cases.</p></caption>
          <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f06.jpg"/>

        </fig>

</sec>
<sec id="Ch1.S3.SS4">
  <label>3.4</label><title>Error model updating</title>
      <p id="d2e1562">During previous research at this site, <xref ref-type="bibr" rid="bib1.bibx43" id="text.77"/> analyzed 3000 reciprocal measurements according to <xref ref-type="bibr" rid="bib1.bibx39" id="text.78"/> and obtained values of <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">48</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M60" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">8</mml:mn><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula>. We recorded reciprocal measurements for four months in summer and autumn to validate these results and analyzed them using three methods, as described in <xref ref-type="bibr" rid="bib1.bibx80" id="text.79"/>, <xref ref-type="bibr" rid="bib1.bibx39" id="text.80"/>, and <xref ref-type="bibr" rid="bib1.bibx46" id="text.81"/>. All methods suggest that the previous absolute error (<inline-formula><mml:math id="M62" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula>) was strongly conservative. The newly computed value of <inline-formula><mml:math id="M63" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula> approaches zero (<inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:mi>a</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.22</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M65" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>), as Fig. <xref ref-type="fig" rid="F7"/> shows. The value of <inline-formula><mml:math id="M66" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> by <xref ref-type="bibr" rid="bib1.bibx43" id="text.82"/> appears to be correctly estimated: we obtained <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">7.5</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula> according to <xref ref-type="bibr" rid="bib1.bibx80" id="text.83"/>, or lower values (<inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">4</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula>) according to <xref ref-type="bibr" rid="bib1.bibx39" id="text.84"/> and <xref ref-type="bibr" rid="bib1.bibx46" id="text.85"/>. For the following analysis, we will use the error estimation from <xref ref-type="bibr" rid="bib1.bibx80" id="text.86"/>, as lower values of <inline-formula><mml:math id="M69" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula> can lead to overfitting in the tomograms.</p>

      <fig id="F7" specific-use="star"><label>Figure 7</label><caption><p id="d2e1713"><italic>Error model differences.</italic> <bold>(a)</bold> The new error model according to <xref ref-type="bibr" rid="bib1.bibx80" id="text.87"/>, where each dot represents a normal and a reciprocal measurement. <bold>(b)</bold> Relative differences between inversions with the old and the new error model for 2022. Resistivity values in log<inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:msub><mml:mi/><mml:mn mathvariant="normal">10</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="italic">ρ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. Numbers express the overall change as a percentage. <bold>(c)</bold> Zoom, subsection of <bold>(b)</bold> outlined in black. Comparison of the permafrost extension in July: The upper figure is obtained using the old error model; the middle figure, using the new model; and the lower figure shows the differences.</p></caption>
          <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f07.png"/>

        </fig>

      <p id="d2e1756">In Fig. <xref ref-type="fig" rid="F7"/>b, we present the inversion differences between the error model chosen for this study and the model previously used in <xref ref-type="bibr" rid="bib1.bibx43" id="text.88"/>, applied to the inversion of the ERT monitoring data from 2022. Using the updated error model, resistivities in the permafrost core (<inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">65</mml:mn></mml:mrow></mml:math></inline-formula> to 115 m) are higher in both winter and summer. The maximum differences occur from May to July, especially on the right side of the side tunnel (an increase of <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> %), while the smallest differences occur between January and April. An exception is represented by the area between <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M74" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> m right of the side tunnel (Fig. <xref ref-type="fig" rid="F7"/>c), which is very close to the rock surface. Here, resistivities are generally lower, with peaks during the warm months: this better represents the active-layer dynamics measured with temperature loggers. Considerable differences are also evident in the area corresponding to the fault zone crossing the permafrost body. The inversion with the updated error model reports lower resistivities along the fault axis; however, these values do not extend to the main tunnel, as field observations would suggest. The area between <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">150</mml:mn></mml:mrow></mml:math></inline-formula> and 200 m shows higher resistivity, but only in the winter months. The tunnel in this area is covered by concrete (indicating a more fractured bedrock), and it is seasonally covered by ice on the ground and walls. The tunnel surface (<inline-formula><mml:math id="M76" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>&lt;</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">25</mml:mn></mml:mrow></mml:math></inline-formula> m) shows smaller differences: frozen patches are found at different <inline-formula><mml:math id="M77" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula>-positions, but the most evident is at <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">135</mml:mn></mml:mrow></mml:math></inline-formula> m, which corresponds to one tunnel exit where snow normally accumulates in winter. Lower resistivities are produced by the inversion at <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">225</mml:mn></mml:mrow></mml:math></inline-formula> m from January to July, with new values reaching <inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> %.</p>
</sec>
<sec id="Ch1.S3.SS5">
  <label>3.5</label><title>Characterization of thermal regime from resistivity</title>
<sec id="Ch1.S3.SS5.SSSx1" specific-use="unnumbered">
  <title>Long-term signal</title>
      <p id="d2e1893">Figure <xref ref-type="fig" rid="F8"/> shows all ERT inversion results from 2007 to 2023 using the updated error model. This allows the detection of features, listed hereafter, that are confirmed by field observation (Fig. S10).</p>
      <p id="d2e1898"><list list-type="custom">
              <list-item><label>a.</label>

      <p id="d2e1903">The active layer is visible from 2014 on, at the right side of the tunnel next to the permafrost core (<inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> and 150 m). This feature follows the structure of the external slope and reaches minimum values from July to September.</p>
              </list-item>
              <list-item><label>b.</label>

      <p id="d2e1921">From December to April, a temporary frozen part appears at the center of the image  (<inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">150</mml:mn></mml:mrow></mml:math></inline-formula> to 200 m). This is an area of the tunnel with reduced rock thickness and a steep bedrock slope outside.</p>
              </list-item>
              <list-item><label>c.</label>

      <p id="d2e1939">The constantly unfrozen part between 200 and 250 m fits with a less steep debris-covered area outside the tunnel, which is snow-covered in winter.</p>
              </list-item>
              <list-item><label>d.</label>

      <p id="d2e1945">Some frozen patches can be found along the tunnel (<inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">25</mml:mn></mml:mrow></mml:math></inline-formula> m, lower border of each image), while they are present all year long in 2014 and 2016, decrease, up to disappearing, from 2018 onward.</p>
              </list-item>
              <list-item><label>e.</label>

      <p id="d2e1965">The fault zone crossing the permafrost is evident in all tomograms. This area exhibits lower resistivity than the surrounding area, with no clear thermal explanation.</p>
              </list-item>
              <list-item><label>f.</label>

      <p id="d2e1972">The constantly lower values at the beginning of the tunnel represent the area with the biggest distance to the north slope.</p>
              </list-item>
            </list>In addition to these features, measurement errors are also evident, thanks to the new error model, for example, in November 2020. For all inversions based on the new error model, RMS values range from 0.97 to 1, and the number of iterations ranges from 3 to 12, with an average of 6. Details are shown in Figure S9b. As expected, the smaller <inline-formula><mml:math id="M84" display="inline"><mml:mi>b</mml:mi></mml:math></inline-formula>-value of the updated (or new) error model leads to smaller data misfits and, consequently, to less smooth, slightly more detailed inversion results.</p>

      <fig id="F8" specific-use="star"><label>Figure 8</label><caption><p id="d2e1987"><italic>ERT inversion results.</italic> Tomograms from 2007 to 2023. On the left, the month of each tomogram. The color bar shown is valid for all tomograms. Bottom right: reference tomogram.</p></caption>
            <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f08.png"/>

          </fig>

      <p id="d2e1998">Long-term trends clearly present a reduction of the frozen areas, as confirmed by Fig. <xref ref-type="fig" rid="F9"/>. While frozen areas increased from 31 % to 40 % of the total area between 2007 and 2014, they drastically decreased from 2014 to 2020 to 25 %. This corresponds to a 40 % reduction compared to 2014. The last four years present little variation in the minimum frozen area. These trends are also visible in the winter months, but are less pronounced.</p>

      <fig id="F9" specific-use="star"><label>Figure 9</label><caption><p id="d2e2007">Long-term development of the frozen areas, from 2007 to 2023.</p></caption>
            <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f09.png"/>

          </fig>

      <fig id="F10" specific-use="star"><label>Figure 10</label><caption><p id="d2e2018"><inline-formula><mml:math id="M85" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula><italic>-means clustering.</italic>
<bold>(a)</bold> Classified tomogram. <bold>(b)</bold> Mean resistivities for each class on a logarithmic scale. On the left, the areas covered by each class are listed, and on the right, the corresponding gradients are shown. <bold>(c)</bold> Violin plot of all resistivity values included in one class.</p></caption>
            <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f10.png"/>

          </fig>

</sec>
<sec id="Ch1.S3.SS5.SSSx2" specific-use="unnumbered">
  <title>Image clustering of the tomograms with <inline-formula><mml:math id="M86" display="inline"><mml:mi>k</mml:mi></mml:math></inline-formula>-means</title>
      <p id="d2e2058">The best fit between the measurements and the previously analyzed features is obtained with <inline-formula><mml:math id="M87" display="inline"><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula>, as confirmed by the elbow method. The results are presented in Fig. <xref ref-type="fig" rid="F10"/>. Class 1 shows the highest <inline-formula><mml:math id="M88" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> values, which correspond to constantly frozen rock. This class has been remarkably consistent over the last 10 years and represents the core of the permafrost. Classes 2 and 3 include cells that are, respectively, mostly frozen and partially frozen, representing rapidly degrading permafrost and the active layer. Both classes are experiencing the strongest decrease in <inline-formula><mml:math id="M89" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> (<inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4200</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2330</mml:mn></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M92" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula> my<sup>−1</sup>, Fig. <xref ref-type="fig" rid="F10"/>b). Class 4 comprehends mostly unfrozen cells with a slightly decreasing 10-year trend and represents feature (c) of Fig. <xref ref-type="fig" rid="F8"/>. Class 5 encompasses the unfrozen area at the beginning of the tunnel, which has exhibited slightly increasing values over the past decade but has undergone constant development recently. The distribution of values in Fig. <xref ref-type="fig" rid="F10"/>c shows all values and not only the mean. In particular, values in class 2 are mostly frozen, while those in class 3 are half frozen and half unfrozen.</p>
</sec>
<sec id="Ch1.S3.SS5.SSSx3" specific-use="unnumbered">
  <title>Quantification of changes in permafrost extent</title>
      <p id="d2e2141">Knowing the grid size, we can estimate the size of the permanently frozen area. It covers circa 2000 m<sup>2</sup>, of which 700 m<sup>2</sup> is in class 1 (35 %) and 1300 m<sup>2</sup> is in class 2 (65 %). The external morphology suggests a vertical extension of the lens of 20–30 m, which would result in 40 000–60 000 m<sup>3</sup> of frozen rock. The remaining temporarily frozen and unfrozen areas (classes 3, 4, and 5) cover 5700 m<sup>2</sup>, about 75 % of the tomogram. Given the strong decreasing rates in the outer layer (class 2), up to 39 000 m<sup>3</sup> of permafrost are very likely to suffer irreversible thermal degradation, potentially leading to its disappearance. By linear extrapolation of the gradient computed in Fig. <xref ref-type="fig" rid="F10"/>b, we expect this process to happen within the following decade. This assumption significantly simplifies complex physical processes that are not necessarily linear and should therefore be considered with some degree of uncertainty. Still, given the actual development of climate change, the trend is unquestionable.</p>
</sec>
<sec id="Ch1.S3.SS5.SSSx4" specific-use="unnumbered">
  <title>Quantification of seasonal variations</title>
      <p id="d2e2207">To detect seasonal trends, we used the mean <inline-formula><mml:math id="M100" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> value across the entire ERT tomogram. The maximum values are recorded in April or May, the minimum around September (<inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula> month), as shown in Fig. <xref ref-type="fig" rid="F11"/>a. In the summer months, there is a clear shift in time towards lower values of <inline-formula><mml:math id="M102" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula>, while this is less evident in the winters, which present a higher variability. Resistivities in 2023 (dark red) indicate a prolonged winter with low values, a drastic drop in resistivities from June to July, and a long summer season with extremely low values from July to October. Comparing ten years of records reveals three distinct phases. The first is a gradual increase in resistivity from October to March/April. There is a sudden decrease between May and July, and finally, a stable phase with little variation in resistivity from August to October.</p>
      <p id="d2e2236">Seasonal averages in Fig. <xref ref-type="fig" rid="F11"/>b show that the resistivity decrease in the last ten years is more pronounced in the spring and summer months, reaching more than 0.9 k<inline-formula><mml:math id="M103" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m yr<sup>−1</sup>. Winter values are decreasing less than one-third of the rate. While winter and spring values vary widely from year to year, summer averages follow a clear linear trend.</p>
      <p id="d2e2260">Figure <xref ref-type="fig" rid="F11"/>c shows that the tomogram's mean <inline-formula><mml:math id="M105" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> is strongly correlated with the mean monthly air temperature with an hysteresis pattern. Resistivity responds to temperature changes with about a two-month delay, producing an elliptical path. The change in time (described by colors) shows the evolution over the last 10 years towards warmer air temperatures (<inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula> °C in summer), which led to lower resistivity (<inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">8</mml:mn></mml:mrow></mml:math></inline-formula> k<inline-formula><mml:math id="M108" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m). 2023 recorded the lowest value both for <inline-formula><mml:math id="M109" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> and MAAT: <inline-formula><mml:math id="M110" display="inline"><mml:mn mathvariant="normal">4.8</mml:mn></mml:math></inline-formula> °C and 19 k<inline-formula><mml:math id="M111" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m.</p>

      <fig id="F11" specific-use="star"><label>Figure 11</label><caption><p id="d2e2323"><italic>Seasonal changes of mean resistivity.</italic> Average value of the entire ERT tomogram, from 2014 to 2023. <bold>(a)</bold> Seasonal variation for all years. <bold>(b)</bold> Average values of 3 months, with trendline and gradient: February, March, and April in blue, May, June, and July in red, and August, September, and October in yellow. <bold>(c)</bold> Comparison of the tomogram mean resistivity with the mean monthly air temperature, measured at the DWD station on the summit, both values as a 3-month moving mean.</p></caption>
            <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f11.png"/>

          </fig>

</sec>
</sec>
</sec>
<sec id="Ch1.S4">
  <label>4</label><title>Discussion</title>
      <p id="d2e2353">We present 15 years of monthly ERT profiles and investigate permafrost dynamics in steep bedrock applying a newly developed temperature-resistivity (<inline-formula><mml:math id="M112" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>-<inline-formula><mml:math id="M113" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula>) field calibration, and an updated error model, compared to the first studies by <xref ref-type="bibr" rid="bib1.bibx43" id="text.89"/>. Newly available data, improvements in methods, and updated analyses have significantly enhanced the quantification of both short-term permafrost dynamics and long-term degradation.</p>
<sec id="Ch1.S4.SS1">
  <label>4.1</label><title>Linking temperature and electrical resistivity: comparison between laboratory and field observations</title>
      <p id="d2e2380">Precise knowledge of the <inline-formula><mml:math id="M114" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>-<inline-formula><mml:math id="M115" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> correlation is crucial for a correct interpretation of the thermal state of the permafrost core derived from resistivities. Many laboratory calibrations are nowadays available for different sites and materials <xref ref-type="bibr" rid="bib1.bibx28 bib1.bibx48" id="paren.90"><named-content content-type="pre">examples in</named-content></xref>, but most studies do not validate them quantitatively in the field <xref ref-type="bibr" rid="bib1.bibx52 bib1.bibx16" id="paren.91"><named-content content-type="pre">e.g.</named-content></xref>. Information at permafrost core depths is often missing, as few studies have compared field and laboratory measurements. <xref ref-type="bibr" rid="bib1.bibx62" id="text.92"/> previously conducted field calibration but did not compare it with laboratory values. <xref ref-type="bibr" rid="bib1.bibx68 bib1.bibx69" id="text.93"/> reported lower resistivity values in field measurements compared with laboratory calibrations, attributing this discrepancy to water pressure effects. To date, no field calibration procedures have been proposed.</p>
      <p id="d2e2414"><xref ref-type="bibr" rid="bib1.bibx41" id="text.94"/> demonstrates that resistivity behaves differently above and below the freezing point, a finding that we also observed at the ST-5m logger (see Fig. S7b). He could also show that the <inline-formula><mml:math id="M116" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula>-<inline-formula><mml:math id="M117" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula> gradient below the freezing point (<inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:mn mathvariant="normal">29.8</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">10.6</mml:mn></mml:mrow></mml:math></inline-formula> % °C<sup>−1</sup>) is, on average, ten times higher than that above the freezing point (<inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:mn mathvariant="normal">2.9</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">0.3</mml:mn></mml:mrow></mml:math></inline-formula> % °C<sup>−1</sup>). Our new field calibration yields similar values at the freezing point, but higher resistivity gradients at low temperatures. Similar results are obtained when comparing field calibration by <xref ref-type="bibr" rid="bib1.bibx62" id="text.95"/> with laboratory measurements by <xref ref-type="bibr" rid="bib1.bibx25" id="text.96"/>, or for laboratory measurements consistent for different types of rocks <xref ref-type="bibr" rid="bib1.bibx48" id="text.97"/>.</p>
      <p id="d2e2491">Assuming that laboratory measurements are typically performed on intact rock samples, it can be inferred that such results provide a reasonable approximation of a saturated rock matrix. Laboratory calibrations are typically performed on fully saturated samples, whereas field conditions often involve partial saturation, which can result in higher resistivity. In this case, the conditions we observe at the Zugspitze are always nearly fully saturated (<inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">90</mml:mn></mml:mrow></mml:math></inline-formula> %), except for the outer 8–10 cm of the rock surface <xref ref-type="bibr" rid="bib1.bibx76" id="paren.98"/>. In the specific setup where we measure from inside the gallery, meters to decameters from the rock wall, surface variations do not play an important role (compared to measurements with electrodes on the surface). The higher resistivity values observed in the field are likely attributable to the presence of ice within frozen discontinuities. However, the extraction of rock samples inevitably removes them from their in situ stress conditions, which may induce minor fracturing or the opening of pre-existing fractures, thereby potentially reducing the measured resistivity of the specimen.</p>
      <p id="d2e2507">Additionally, <xref ref-type="bibr" rid="bib1.bibx43" id="text.99"/> recorded supercooling effects just after the equilibrium freezing point (<inline-formula><mml:math id="M123" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.5</mml:mn></mml:mrow></mml:math></inline-formula> °C) during initial freezing in laboratory tests. Although these effects are not directly apparent in our dataset, an increase in the standard deviation of resistivity measurements is observed near the freezing point in the ST-5m logger data (see Fig. S7b), which may be linked to similar processes. It is important to note that such effects were only observed in the laboratory during the initial freezing phase and for very short periods, conditions that cannot be replicated with our setup.</p>
      <p id="d2e2524">Both field and laboratory calibrations at our site agree on the freezing point around 29 k<inline-formula><mml:math id="M124" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m; however, the interpretation of laboratory measurements above this point should be taken with caution. In fact, it is impossible to accurately reproduce the steadily variable alternation of bedrock, fractures, ice/water, and voids found in nature in a sample; however, this composition strongly influences ERT results. This is evident in the high variability of the calibration results presented here, despite our temperature loggers being just 5 m apart. For this reason, caution should be exercised when extrapolating the <inline-formula><mml:math id="M125" display="inline"><mml:mi>T</mml:mi></mml:math></inline-formula>-<inline-formula><mml:math id="M126" display="inline"><mml:mi mathvariant="italic">ρ</mml:mi></mml:math></inline-formula> relation to other locations, even within the same site. We suggest that field calibrations are totally valid only for the measured spot. Further limitations are a reduced temperature range in nature and the lack of freeze-thaw cycles when measuring permafrost. Recent studies confirm the presence of hysteresis effects in field measurements and demonstrate their importance in the energy balance of permafrost <xref ref-type="bibr" rid="bib1.bibx48 bib1.bibx51 bib1.bibx83" id="paren.100"/>.</p>
      <p id="d2e2551">Our measurements recorded resistivities greater than 200 k<inline-formula><mml:math id="M127" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m, values that exceed the laboratory calibration range. <xref ref-type="bibr" rid="bib1.bibx43" id="text.101"/> has explained these values in terms of ice presence, but not numerically proven. Our results indicate that laboratory calibration should be validated in the field and, if necessary, refined based on field data.</p>
</sec>
<sec id="Ch1.S4.SS2">
  <label>4.2</label><title>Influence of the error model on long-term ERT measurements</title>
      <p id="d2e2572">The chosen procedure, the filtering criteria for outliers, and the bin placement can affect the quantification of the error to varying degrees <xref ref-type="bibr" rid="bib1.bibx39 bib1.bibx84" id="paren.102"/>. Different arrays generate distinct error types, corresponding to different error models. Further complexity arises when multiple measurements are combined into a single dataset, as in this case. In addition, the reciprocal error may vary over time during long-term monitoring due to changing external conditions, such as seasonal fluctuations in water state or long-term variations in underground water content. Given these factors, the best inversion would theoretically require one error model per array and per epoch, which would be time-consuming during data acquisition. As a consequence, the use of reciprocal errors is very rare in field applications <xref ref-type="bibr" rid="bib1.bibx28" id="paren.103"/>. When reciprocal measurements are conducted, most studies use a uniform error level for all configurations and time steps to reduce the degrees of freedom <xref ref-type="bibr" rid="bib1.bibx46 bib1.bibx84" id="paren.104"/>, thereby ensuring consistency among results at different times <xref ref-type="bibr" rid="bib1.bibx43 bib1.bibx55" id="paren.105"/>, while other authors use a time-varying error model <xref ref-type="bibr" rid="bib1.bibx39" id="paren.106"/>. With the new computation of the error model suggested here, i.e., the drastic reduction of the absolute term <inline-formula><mml:math id="M128" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula>, we possibly introduce some artifacts in the inversion results. Still, the significant advantage is a substantial increase in resolution, enabling us to investigate permafrost degradation in much greater detail (see features in Fig. <xref ref-type="fig" rid="F8"/>).</p>
      <p id="d2e2600">As shown in Figure S9a, the updated error model has little impact on the RMS error, which remains within the same range (0.99–1), as expected, since this is the value minimized by the inversion algorithm. However, the number of iterations increases from 3–4 to 6, which was also foreseeable, since smaller errors require a more precise fit of the model to the data to achieve the same RMS values and therefore more iterations. Inspection of the RMS formulation (Eq. <xref ref-type="disp-formula" rid="Ch1.E1"/>) shows that, if <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mtext>RMS</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula> remains approximately constant, smaller values of the error <inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> result in a reduced data misfit (i.e., <inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mi>d</mml:mi><mml:mi mathvariant="normal">i</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="bold-italic">m</mml:mi><mml:msub><mml:mo>)</mml:mo><mml:mi mathvariant="normal">i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>). In our case, with the newly computed values of <inline-formula><mml:math id="M132" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula> (Fig. <xref ref-type="fig" rid="F7"/>), we observe smaller errors for <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mo>&lt;</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mn mathvariant="normal">4</mml:mn></mml:msup></mml:mrow></mml:math></inline-formula> <inline-formula><mml:math id="M134" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>, leading to stronger data weighting. This, in turn, allows for closer model adjustment, potentially improving the fit, though it also increases the risk of overfitting and introduces model artifacts, while reducing smoothing and enabling the resolution of finer-scale features.</p>
</sec>
<sec id="Ch1.S4.SS3">
  <label>4.3</label><title>Permafrost degradation according to ERT</title>
      <p id="d2e2691">New temperature calibrations and error models enable us to accurately interpret the inverted resistivities, particularly in the permafrost core. Results confirm the presence of permafrost near the melting point, and its degradation is readily quantifiable. Still, complex inter-annual behavior due to latent heat effects during thawing, seasonal water infiltration, and variable snow cover makes the processes highly non-linear <xref ref-type="bibr" rid="bib1.bibx26" id="paren.107"/> and therefore difficult to interpret. The degree of fracturing also seems to contribute to this non-linearity. A survey of fractured zones was already presented in <xref ref-type="bibr" rid="bib1.bibx43" id="text.108"/>, but the effects of the fault zone were neglected. Here, thanks to the new field calibration, differences are distinctly highlighted. Clustering, as suggested by <xref ref-type="bibr" rid="bib1.bibx12" id="text.109"/> and <xref ref-type="bibr" rid="bib1.bibx92" id="text.110"/>, also provided powerful insights in this direction. Thanks to simple algorithms, large amounts of data are used to detect similar patterns, yielding an objective, data-driven analysis. This allows for a more robust interpretation of results than the “user-defined areas of interest”, which are mostly rectangular, as previously used in the literature <xref ref-type="bibr" rid="bib1.bibx38" id="paren.111"/>.</p>
      <p id="d2e2709">Despite this complexity at high temporal and spatial resolution, when looking at slope scale over one decade, it is evident that ERT values strongly correlate with rock and air temperatures, as shown in Fig. <xref ref-type="fig" rid="F12"/>b. Mean resistivity of the tomograms decreases from 37 k<inline-formula><mml:math id="M135" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m in 2018 to 28 k<inline-formula><mml:math id="M136" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m in 2023 (<inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">25</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="italic">%</mml:mi></mml:mrow></mml:math></inline-formula>). The decrease is stronger from 2018 to 2021, whereas in the last 3 years it is less pronounced. Meanwhile, air temperatures have steadily increased since 2012, rising from <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.2</mml:mn></mml:mrow></mml:math></inline-formula> to <inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.2</mml:mn></mml:mrow></mml:math></inline-formula> °C.</p>
      <p id="d2e2762">This supports the theory that external thermal forcing and conductivity are the primary processes promoting permafrost degradation here. Contradicting trends, such as the increase in frozen areas between 2007 and 2014, as shown in Fig. <xref ref-type="fig" rid="F9"/>, can also be explained by thermal forcing (e.g., rising air temperatures). In fact, the hydrological year 2006/2007 recorded extreme temperatures, 1 °C warmer than the 30-year average. On the contrary, from 2007 to 2014, temperatures were mostly below the 30-year average (Fig. <xref ref-type="fig" rid="F12"/>b, inlet). Therefore, 2007 can be considered an anomaly, and the measurements from that year are not representative of the 2000–2010 decade.</p>

      <fig id="F12" specific-use="star"><label>Figure 12</label><caption><p id="d2e2772"><italic>External thermal forcing drives resistivity changes in the active layer.</italic>
<bold>(a)</bold> Resistivity ratio: class 1/class 2 in dark blue, class 1/class 3 in light blue. The red lines unite the minimum values for each year. Lower bars: mean annual air temperatures (MAAT) of hydrological years from 2014 to 2024. <bold>(b)</bold> The increase in overall mean resistivity (in red) is well explained by the increase in air temperature (in black). <bold>(c)</bold> Inlet: MAAT of hydrological years from 2001 to 2014. The following abbreviations are used: MMAT (monthly mean air temperature), mm10y – moving mean 10 years, mm12m – moving mean 12 months, mm36m – moving mean 36 months.</p></caption>
          <graphic xlink:href="https://tc.copernicus.org/articles/20/4787/2026/tc-20-4787-2026-f12.png"/>

        </fig>

      <p id="d2e2792">Analyzing the resistivity ratio between active layer and permafrost <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">PL</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">AL</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> as suggested by <xref ref-type="bibr" rid="bib1.bibx26" id="text.112"/>, we compare clustering class 1 with class 2 and class 1 with class 3 and focus on the maximum values of each year (Fig. <xref ref-type="fig" rid="F12"/>a). Although they varied, both ratios increased over the last 10 years. The ratio class 1/class 2 closely follows the trends of mean annual air temperature (MAAT): it decreased in 2018 and in 2021 after mild years, while it increased in all other years. In 9 out of the last 10 years, MAAT was above the long-term average of <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3.8</mml:mn></mml:mrow></mml:math></inline-formula> °C, with records reaching <inline-formula><mml:math id="M142" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.6</mml:mn></mml:mrow></mml:math></inline-formula> °C in 2019/2020 and 2022/2023. Excluding the possibility that the permafrost core has increased its resistivity (<inline-formula><mml:math id="M143" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">PL</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), this trend can be explained only by a decrease in resistivity in the active layer (<inline-formula><mml:math id="M144" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">AL</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), to a stronger degree than the decrease in the core, as confirmed by Fig. <xref ref-type="fig" rid="F10"/>b. Compared with Fig. <xref ref-type="fig" rid="F9"/>, it is remarkable that, although the number of frozen cells has not decreased since 2021, the ratio <inline-formula><mml:math id="M145" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">PL</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi mathvariant="italic">ρ</mml:mi><mml:mi mathvariant="normal">AL</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> increased in 2022 and 2023. This confirms that non-linear degradation processes are occurring in the active layer and that sudden degradation may occur in the next few years. On the contrary, it seems that class 1/class 3 have stabilized over the last four years, possibly indicating that degradation has already reached a stable level in these areas.</p>
      <p id="d2e2883">The resistivity ratio between the active layer and the permafrost in our data falls within the same range as reported by <xref ref-type="bibr" rid="bib1.bibx26" id="text.113"/>. However, while they observed a long-term decrease in this ratio, our results show a contradictory overall increase. This suggests that, at our site, the degradation of the active layer has not yet significantly impacted the permafrost core. Notably, our unconventional measurement setup–conducting measurements from the inside out rather than from the surface may influence this interpretation. In typical surface-based ERT surveys, accuracy decreases with depth due to the limited number of data points, resulting in higher confidence near the surface and lower confidence at greater depths. The configuration used here yields improved accuracy along the main tunnel (deep bedrock) and along the side tunnel (permafrost core), but provides lower resolution for the rest of the outside bedrock slope.</p>
</sec>
<sec id="Ch1.S4.SS4">
  <label>4.4</label><title>Lessons learned from over a decade of monitoring</title>
      <p id="d2e2898">After more than a decade of monitoring, we share key lessons learned from challenges like equipment malfunctions and data inconsistencies to improve future monitoring efforts and contribute to the scientific community. Long-term monitoring requires strict consistency in measurement parameters and procedures to ensure data comparability over time. However, when changes in software, hardware, or operational protocols are necessary or beneficial, it is advisable to implement an overlap period during which both the old and new setups are operated simultaneously. This overlap should be sufficiently long to capture variability across different environmental conditions, including both warm and cold periods.</p>
      <p id="d2e2901">Instruments deployed in humid environments are particularly susceptible to corrosion, which can compromise data quality and equipment longevity. Regular inspection and maintenance are therefore essential and require the continuous replacement of faulty or degraded electrodes. All components of the monitoring system, including cables, measurement units, and data loggers, should be routinely tested to promptly detect and address failures. Immediate, on-site verification of collected data – especially at remote locations – is strongly recommended to identify potential issues early. Quality control procedures – such as threshold checks, outlier detection, and trend analysis – in the data workflow can help identify inconsistencies early. Establishing clear criteria for data validation and flagging enhances the overall reliability of the dataset. In this context, optimizing and automating data analysis procedures can significantly enhance efficiency and reliability.</p>
      <p id="d2e2904">Comprehensive documentation, regular calibration (with redundancy where possible), and robust data management – including automated logging, standardized formats, and secure backups – are essential to ensure the accuracy, reproducibility, and long-term usability of monitoring data. We also encourage the publication of data in open-access repositories and active participation in collaborative initiatives such as the IPA Action Group IDGSP.</p>
</sec>
<sec id="Ch1.S4.SS5">
  <label>4.5</label><title>Future development of permafrost degradation and slope stability</title>
      <p id="d2e2915">At this site, permafrost degradation is mainly driven by thermal forcing, as shown in Fig. <xref ref-type="fig" rid="F12"/>b. Future heat waves are projected to increase in magnitude and frequency <xref ref-type="bibr" rid="bib1.bibx49" id="paren.114"/>. As a result, this trend is expected to persist in the coming decades, particularly for the active layer (cluster classes 2 and 3), although the permafrost core (class 1) will ultimately be affected as well. The fault crossing the tomogram, clearly visible thanks to the newly developed error model, may further accelerate degradation due to its high permeability. In fact, when unfrozen, it could allow large volumes of water to infiltrate, as demonstrated in <xref ref-type="bibr" rid="bib1.bibx79" id="text.115"/>, thereby introducing advective heat transport processes that compound the thermal degradation. Consequently, atmospheric forcing is expected to play a significant role in the dynamics of permafrost degradation; however, its influence remains difficult to quantify. Increasing the measurement frequency from April to July could provide valuable insights into the delayed thermal response of deep rock layers.</p>
      <p id="d2e2926">On steep slopes, the increase in rock temperatures is also linked to irreversible ice losses <xref ref-type="bibr" rid="bib1.bibx26" id="paren.116"/>. Although this is not expected to influence the hydrological cycle in alpine environments strongly, it has strong stability consequences for slope stability <xref ref-type="bibr" rid="bib1.bibx44" id="paren.117"/>. This might also be true for the analyzed area, where the fractured zones might be a source of new instabilities, given the almost vertical dip of this fracture area.</p>
      <p id="d2e2935">The current setup was not fully automated and, consequently, it does not enable real-time monitoring. The potential of automated ERT has been assessed in <xref ref-type="bibr" rid="bib1.bibx36" id="text.118"/>. The calibration and error estimates in this paper contribute to a more robust implementation of ERT in monitoring and early warning systems for critical infrastructure, e.g., mountain huts and cable car stations, where less-calibrated approaches are currently being tested. Fixed and automated ERT monitoring systems have been implemented on steep permafrost slopes (e.g., studies by <xref ref-type="bibr" rid="bib1.bibx2 bib1.bibx69" id="altparen.119"/>). In principle, such systems allow continuous resistivity measurements and could provide near-real-time insights into permafrost conditions. However, to our knowledge, these approaches have not yet reached a level of maturity that enables reliable operational use for early warning purposes. Achieving this would require developing robust automated workflows for both data acquisition and processing and establishing clearly defined early-warning criteria. Potential criteria could include thresholds for active-layer thickness or for resistivity values approaching the thawing point. It is important to remember that ERT-derived information alone is insufficient for early warning applications. It must be complemented by detailed geological characterization, including surface fracture mapping and, ideally, subsurface information obtained from boreholes <xref ref-type="bibr" rid="bib1.bibx69" id="paren.120"/> or tunnels to identify critical discontinuities and preferential ways for water flow. Furthermore, reliable quantitative interpretation of resistivity data requires field calibration over at least one complete freeze-thaw cycle and across multiple depths, as demonstrated in this study.</p>
</sec>
</sec>
<sec id="Ch1.S5" sec-type="conclusions">
  <label>5</label><title>Conclusions</title>
      <p id="d2e2957">This study compiles 109 ERT measurements collected over 17 years at monthly frequency from the Kammstollen Tunnel, 2800 m a.s.l. on Mount Zugspitze (Germany/Austria). Developing a field calibration of the temperature-resistivity relation, improving the inversion error model, and automatically clustering the results advance the understanding and quantification of permafrost degradation in steep rock slopes. <list list-type="bullet"><list-item>
      <p id="d2e2962">ERT field-based calibration with rock temperatures over five years validates laboratory-based calibrations, which have become a standard approach in the literature. While both methods show good agreement at the freezing point, field data reveal significantly higher resistivity values at subzero temperatures and highly variable results. This highlights the need for caution when interpreting tomograms based solely on laboratory calibration.</p></list-item><list-item>
      <p id="d2e2966">A correct estimation of measurement errors is essential for a correct inversion and interpretation of ERT data. Regular validation and update of the error model over time can significantly enhance the detection of thermal processes in long-term monitoring.</p></list-item><list-item>
      <p id="d2e2970">Mean resistivity of the tomogram shows a decrease of 25 % in the last 10 years, with more enhanced degradation in the summer months, where the overall decrease rates reach <inline-formula><mml:math id="M146" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.9</mml:mn></mml:mrow></mml:math></inline-formula> k<inline-formula><mml:math id="M147" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m yr<sup>−1</sup>.</p></list-item><list-item>
      <p id="d2e3003">Frozen cells decreased by almost 40 % in the same period, and the active layer suffered the strongest losses, with rates between <inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4.2</mml:mn></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">2.3</mml:mn></mml:mrow></mml:math></inline-formula> k<inline-formula><mml:math id="M151" display="inline"><mml:mi mathvariant="normal">Ω</mml:mi></mml:math></inline-formula>m yr<sup>−1</sup>.</p></list-item><list-item>
      <p id="d2e3046">The strong meteorological variability between years requires at least monthly monitoring in the summer and autumn months to precisely assess long-term degradation. Monitoring the spring and winter months is crucial for a comprehensive understanding of the processes and an accurate evaluation of the yearly trends.</p></list-item><list-item>
      <p id="d2e3050">The extent of the permafrost lens in 2023 can be estimated in 2000 m<sup>2</sup> (Class 1 and 2) – up to 60 000 m<sup>3</sup>. The actual degradation rates indicate that approximately 1300 m<sup>2</sup> (class 2) – up to 39 000 m<sup>3</sup> – will become unfrozen within the next decade. Still, degradation is not always linear, and this estimation does not account for thermal advection caused by infiltrating water <xref ref-type="bibr" rid="bib1.bibx79" id="paren.121"/>, which could entirely enhance this phenomenon.</p></list-item><list-item>
      <p id="d2e3093">The proposed resistivity-temperature monitoring allows a quantitative investigation of changes in the thermal regime of permafrost. Compared to previous studies, the results confirm the presence of the permafrost core, but indicate differences in its spatial extent, providing a more accurate representation of its dynamics.</p></list-item></list> These innovations enhance the ability to detect and predict permafrost degradation and the consequent bedrock instabilities with greater spatial and temporal precision. These findings help decision-makers assess the increasing risks posed by rising temperatures to both society and infrastructure.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability"><title>Data availability</title>

      <p id="d2e3101">All data analyses and visualizations for this study have been conducted in MATLAB. Data are available at the following link upon request: <ext-link xlink:href="https://doi.org/10.5281/zenodo.13839155" ext-link-type="DOI">10.5281/zenodo.13839155</ext-link> <xref ref-type="bibr" rid="bib1.bibx77" id="paren.122"/>.</p>
  </notes><app-group>
        <supplementary-material position="anchor"><p id="d2e3110">The supplement related to this article is available online at <inline-supplementary-material xlink:href="https://doi.org/10.5194/tc-20-4787-2026-supplement" xlink:title="pdf">https://doi.org/10.5194/tc-20-4787-2026-supplement</inline-supplementary-material>.</p></supplementary-material>
        </app-group><notes notes-type="authorcontribution"><title>Author contributions</title>

      <p id="d2e3119">RS designed the study, performed the field measurements, and conducted the data interpretation. JKL supported the inversion of ERT data, and SW supported the development of the manuscript and data interpretation. MK designed, financed, and supervised the study. RS prepared and revised the manuscript with final approval from all authors. SW and JKL improved the draft.</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e3125">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="d2e3131">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="d2e3137">Special thanks go to the Environmental Research Station Schneefernerhaus and Bayerische Zugspitzbahn Bergbahn AG for their logistical and financial support. We also express our gratitude to all colleagues from the Chairs of Landslide Research and Engineering Geology for their continuous assistance and productive exchanges. Massive thanks go to all the students who assisted in the field and provided valuable ideas, particularly Paul Schmid, Verena Soll, Saskia Brose, Frederik Reese, Leon Wassmann, Jonas Brixle, and Andrea Schmid. We also acknowledge the researchers who collected data prior to 2019, especially Saskia Eppinger, Tanja Schröder, and Philipp Mamot, as well as the Bavarian Environmental Agency (LfU), for the borehole data. We sincerely thank the Editor, Adam Booth, as well as the reviewers, Sebastian Uhlemann and an anonymous reviewer, for their constructive feedback, which has significantly improved this manuscript.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d2e3142">This research has been supported by the AlpSenseRely project, funded by the Bavarian State Ministry of the Environment and Consumer Protection (grant no. TUS01UFS-76976), and by the HydroPF project, funded by the TUM International Graduate School of Science and Engineering (IGSSE).</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e3148">This paper was edited by Adam Booth and reviewed by Sebastian Uhlemann and one anonymous referee.</p>
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