In order to calibrate our field measurements and evaluate the parameters (e.g., TC, θr) in the petrophysical model discussed above (Sect. 3), we conducted an electrical conductivity experiment on a granite rock sample collected from an outcrop at the study site. The cube-shaped granite sample (dimensions: 5×5×5cm3) was dried during 24 h at approximately 100 °C, then saturated under vacuum with degassed water. The saturated water conductivity was 0.016 Sm-1 at equilibrium at T=25°C. This value is representative of the conductivity of infiltrating water collected and measured in galleries at the AdM site (approximately 150 µScm-1 or 0.015 Sm-1, see Ben-Asher et al. (2026). The sample was left in the solution for several weeks to reach chemical equilibrium before performing the laboratory measurements. The sample was characterized by a very low measured porosity ϕ=0.014.

For thermal-resistivity analysis, the sample was placed in a heat-resistant insulating bag immersed in a thermostat bath (KISS K6 from Huber; dimensions: 210×400×546mm3; bath volume: 4.5 L). The temperature of the bath was controlled with a precision of 0.1 °C. Glycol was used as the heat carrying fluid (Coperey et al., 2019). Thin Carbon film electrodes were used for both current injections and potential measurement. The complex conductivity spectra were obtained over the temperature range of +10 to -10°C, using a high-precision impedance-meter ZEL-SIP04-V02 (Zimmermann et al., 2008). The resistivity measurements reported here are at a frequency of 1 Hz (Coperey et al., 2019).

ERT has been conducted over a four-years period (June 2020–December 2023). A total of three cables, each with 32 take-outs spaced 5 m (for a profile length of 155 m), were installed. The three cables were deployed downwards from the summit in three directions: North-West (NW), East (E) and South (S). The S profile starts at the South side and passes to the North–West side around mid-distance (see Fig. 1c and d). The cables were installed gradually (over a year) starting from NW side (installed in June 2020), then on the South side (installed in July and August 2020), and finally on the East side (installation finished in March 2021 because of snowpack in 2020 at this side). In order to ensure good electrical contact between electrodes and rock mass, stainless steel (A4/316) climbing bolts (Fischer 10mm×126mm) poured in salty bentonite were used and placed firmly in holes drilled in the rock. A specially designed jumper was used to attach each take-out to the bolt to ensure maximum contact. The resistivity cables were attached to anchors to minimize damage from rockfall and snow pressure.

A LS2-Terrameter (ABEM) with internal impedance of 20 MΩ was used for the data acquisition. The ERT device and control system for monitoring were deployed inside the summit station with network access, power connection, and overvoltage protection. Data acquisition was fully automated and remotely controlled since September 2021. Finally, the position of every electrode was measured using a differential GPS when the signal is available and a theodolite in steep areas. The measurements were carried out using a Wenner configuration, which provides a high signal-to-noise ratio and is widely used in mountain permafrost environments (Mollaret et al., 2020; Krautblatter and Hauck, 2007; Dahlin and Zhou, 2004). Each profile consists of 155 data points. An injected current ranging from 0.1–200 mA was applied, with a maximum stack number of 4 was applied to ensure a standard deviation of less than 5 % in the measured resistivity. The first measurements were performed in June 2020. Between June 2020 and September 2021, ERT measurements were repeated occasionally. Then the continuous measurements started in late September 2021 after developing an automated system of acquisition. Datasets were daily recorded for each profile (NW, S and E profiles).

A Contact Resistance (CR) test was performed before each series of measurements. A high contact resistance in the rock wall (>100kΩ) was encountered throughout the entire survey period, which posed a challenge to the quality and continuity of data acquisition. CR varies between a few kΩ and 10 000 kΩ. However, beyond a CR threshold, the ERT measurements lose their accuracy. Electrodes with high CR (>600kΩ) are excluded automatically by the LS2, leading to gaps in the pseudo-section of apparent resistivity. Special efforts were made to reduce CR and improve the electrode/rock contact, including the addition of salty water, using copper electrodes and duplicate electrodes. The latter one resulted in a significant and durable improvement in CR (one order of magnitude reduction in CR). Figure B1 shows the temporal evolution of CR at profiles S and NW, as well as gaps in the A-ERT measurements caused by cable defects. It also indicates the date of duplicate electrode installation, highlighting a reduction in contact resistance following installation.

The A-ERT ran into numerous software and hardware issues, resulting in unsystematic data gaps. The E face cable was severely damaged by a lightning strike, before being destroyed by an uncontrolled rock purge. Additionally, NW and S cables were both damaged by rockfalls, leading to significant data gaps (see Figs. 3 and B1). Repairing or replacing the damaged cables was not possible for several reasons (e.g., limited access to the cable path because of accumulated snowpack). Data acquisition on the Eastern side (E profile) encountered numerous challenges related to contact resistance, rockfalls and cable connections, resulting in long gaps and insufficient data for long time analysis or time-lapse inversion.

The apparent resistivities were calculated using the open-source package pyGIMLi (Rücker et al., 2017), which combines measured resistances and electrode positions. For datasets used in inversion, a systematic quality-control procedure was applied prior to processing. The primary selection criterion was the number of connected electrodes within each pseudo-section. Up to four unconnected electrodes (typically due to high contact resistance) were tolerated, depending on their positions, since electrode contributions are not equal in the pseudo-section. After selecting valid datasets, outlier removal was performed. To define appropriate filtering threshold, we individually analyzed representative pseudo-sections acquired in autumn and spring (completed datasets). As a result of this analysis, we filtered outliers out of the range (300 Ωm–20 kΩm) for data measured in summer and autumn, and out of range (300 Ωm–200 kΩm) for data measured in spring and winter. Table C1 (Appendix C) summarizes the data presented in this study. In most cases, more than 80 % of the originally recorded data points were retained in each pseudo-section after filtering.

The inversion of the electrical resistivity datasets was performed using the open-source package pyGIMLi (Rücker et al., 2017; Günther et al., 2006). The inversion uses a Gauss–Newton minimization algorithm of a cost-function penalizing the roughness of the electrical resistivity distribution on an irregular grid (Günther et al., 2006). In the absence of a reciprocal dataset to estimate errors in measurements, we used a linear error model which assumed 5 % relative error and absolute error 10-5. The parameters used in the inversion process are zWeight=10 and smoothness (lambda) equal one. The inversion parameter zWeight is chosen higher than one to enhance the vertical discontinuities and vertical structures (i.e., to better delineate the active layer and infrastructures), during the inversion process. Following Mollaret et al. (2020), an iterative process was conducted to select the smoothness parameter (lambda) that minimizes the data misfit of individual inversions of a reference dataset (dataset of 30 June 2020). The root-mean-square (RMS) error is evaluated at the end of each inversion and reported at the figures. In order to track the seasonal and interannual variations in the permafrost, a time-lapse inversion approach was employed. In this case, the reference model was moved along with the inversion so that the difference to the preceding step is constrained (Doetsch et al., 2015; Karaoulis et al., 2013).

Our interpretation of the ERT data starts with an analysis of the measured apparent resistivity data, which can provide insights into subsurface conditions. Figure 3 shows the temporal distribution of the measured apparent resistivities and the averaged apparent resistivity along the S-profile, with examples of time series of measured apparent resistivities obtained using various quadrupole configurations (ABMN), shown in different colors. The majority of measured apparent resistivities are distributed over three orders of magnitude (100 Ωm–100 kΩm), with few data points out of this range.

Figure 4 shows the variations in the average apparent resistivity associated with the same electrode distance or pseudo-depth for three selected datasets from two profiles (NW and S profiles). The data reveal the interannual and seasonal variations in the measured apparent resistivity, as well as the differences between the two sides. During frozen conditions at the surface (dataset from 12 April 2021), the apparent resistivity is almost the same on both sides (∼100-120kΩm near the surface), with only a slight decrease with depth at both sides. At the end of summer (dataset from 17 and 25 September 2021), the resistivity values are higher in 2021 than in 2020 on both sides, which correlates with climatic data indicating that 2021 was a cooler year, on average (see Fig. 2). Secondly, on the NW face, the average resistivities increase with depth (from ∼7kΩm to ∼12kΩm), while on the south side, the average resistivities decrease with depth (approximately 13 kΩm at shallow depth to ∼7kΩm at greater depth). This difference in trend between the two sides can be attributed to cooler conditions on the north-face, where permafrost appears at shallow depth, and warmer conditions on the south-face, characterized by a drained and thicker thawed active layer. This observation is consistent with the temperature measurements from boreholes BH-NW and BH-S (see Fig. A1).

In order to gain an overview of the internal structure of the study site based on the resistivity distribution, we carried out inversions of the first dataset acquired along two long profiles (NW + S and NW + E), using Wenner electrode arrays with 64 electrodes (Figs. 5 and 6). Figure 5 shows the electrical resistivity tomogram from late summer 2020 (26 August, 2020), where acquisition on both North–West and South sides (NW + S) was performed. The tomogram clearly reveals the site's internal structure, with low resistivity areas (warm-colored zones) indicating the relative positions of the infrastructure elements (elevator and galleries on both sides). It also shows the extent of the active layer (moderate resistivity areas near the surface), as well as the permafrost evidenced by high resistivity areas (represented in cool colors). Although the lower part of the tomogram appears similar on both the NW and S profiles, which is expected since they lie in rockwalls that are alike regarding slope and aspect (where the lowest part of the S profile is deployed on the NW face as well, see Fig. 1c), significant differences are evident in the upper part (i.e., above the gallery level). These differences highlight the contrast between the sun-exposed S face, composed of fractured granite (clearly visible in the field; see Fig. 1d) and exposed to strong insolation, leading to drier surface conditions and consequently higher electrical resistivity. In contrast, the shaded NW face mainly consisting of massive granite and less influenced by atmospheric heat flux, remains wetter and thus leads to lower resistivity close to surface. The upper part of the profile therefore reveals strong thermal gradient typical of high-alpine summits (Noetzli et al., 2007; Magnin et al., 2017). The high-resistivity area thus appears limited, likely due to the heat flux from the sun-exposed and warm face towards the close shaded-face.

Figure 6 provides an example of the resistivity tomogram for the combined NW and E profiles. This tomogram highlights the changes in resistivity associated with permafrost, active layer, and anthropogenic installation (such as the elevator and gallery (relatively far from the profile at the E side compared to S profile)). On the eastern side, a thick and desiccated active layer (>5m depth) is observed, with some resistive zones near the surface. Indeed, these resistive zones are likely fractured zones creating an unsaturated and air-filled zone and surrounded by moderate resistivity regions where fractures are filled or where water drainage is weak or absent.

In order to track the seasonal and interannual variations in the permafrost, a time-lapse inversion approach was employed to invert datasets for each profile (NW, S), while the data at the east profile was excluded from this analysis due to significant data gaps caused by poor electrical connection and cable malfunctions. Figure 7 shows the tomograms of resistivity distribution after a time-lapse inversion of selected datasets acquired along the NW profile at different time intervals. A more complete times series is presented in Appendix D, while the results from the south profile are discussed in Sect. 5.6. Spatial and temporal changes in resistivity can be observed, while the anomaly related to the gallery (the warm-colored area (low resistivity area)) remains relatively consistent over time. The permafrost layer associated with high resistivity, is observed in two zones, above and below the gallery. 2021 was, on average, cooler than both 2020 and 2022 in coherence with air temperature (Fig. 2), and this is reflected in the tomograms by a more prominent cool-colored zone (indicating colder conditions) in 2021 compared to data in 2020 (Fig. 7b and d). Additionally, there is a significant variation in the lower part of the tomograms in 2022 (Fig. 7e), which may be related to water infiltration in fractures that shortcut the heat transfer from the surface to depth (Hasler et al., 2011). However, this area is uncertain, as it is located at the border of the tomogram where sensitivity is low. In addition, the RMS error is high in this tomogram, indicating high uncertainties. Therefore, this information should be carefully considered and verified with further measurements focused on the zone of interest. Unlike Offer et al. (2025), no evidence of water pressurization was observed from the geophysical measurements on the NW face. This is most likely due to the distance between the monitored area and the water table laying at about 1000 m lower (Magnin and Josnin, 2021), and that leads to water drainage.

Instead of analyzing temporal resistivity changes in absolute terms, Fig. 7f–i illustrates the resistivity variation ratio between two subsequent measurements. This approach facilitates the tracking and visualization of small changes in resistivity. A value of 1 (represented in white color) corresponds to no change in resistivity between the two measurements (reflecting consistent thermal/hydrological conditions over time), while the blue color indicates that the resistivity increased over time, and the red color represents the inverse. It can be observed that seasonal variations are the most pronounced, as illustrated in Fig. 7g, h and i, compared to short-term fluctuations (see Fig. D2). The effects of freezing and thawing are marked by maximum variations near the surface (in the active layer). In contrast, over a short time interval (i.e., a few weeks), only minor variations are noted (e.g., Figs. 7f, D2b, e and j). The decrease in resistivity near the surface at approximately 3780 m, observed in Fig. 7i, could be related to water flow around the gallery, where water circulation and percolation in the galleries occurs every summer (Ben-Asher et al., 2026). Consequently, a specific water diversion system has been installed to protect tourists from these water flows. Furthermore, at approximately 3740 m, close to borehole BH-NW, we observe variations in resistivity, with values higher than in the surrounding zone, forming a vertical pattern visible in Figs. 7b, d, and e. These features coincide with open sub-vertical fractures that affect the temperature-depth profile in boreholes (Magnin et al., 2015b).

Inverted resistivities were extracted along profiles P1 and P2, corresponding to borehole BH-NW and a virtual borehole, respectively (see positions of P1 and P2 in Fig. 7a). The extracted resistivities (Fig. 8) show that the variation of resistivity with depth is more pronounced at P2 than at P1. This greater variation could be due to a higher water content in the active layer or a thicker active layer at P2 compared to P1. The greater thickness of the active layer in the upper section can be explained by the 3D heat transfer and the proximity of the shaded face (NW side) to the sun-exposed faces (S side) in the top part (Magnin et al., 2017), as well as the greater amount of direct sun-beams at the summit than in the more shaded lower parts of the face. The 3D effects are well visible at depth of P2, where resistivity decreases due to warmer conditions close to the opposite sun-exposed face. In the lower section at P1, the contrast between the resistivity in the active layer and that in the permafrost is not significant. This may be attributed to (i) reduced thermal variability because of snow accumulation in this zone (see Fig. 1c), where the snowpack acts as a thermal insulator, reducing temperature variability; (ii) the presence of fractures (as noted above) influencing the temperature-depth profile (see Fig. 7b, e and d). However, it is important to note that the ALT is about 2.7 m at the end of summer (based on BH-NW measurements; see Fig. A1), whereas, the smallest quadrupole spacing is 15 m, leading to effective depth around 2.55 m (Edwards, 1977), which is insufficient to fully capture the resistivity variations near the surface. Additionally, a slight decrease in permafrost resistivity is observed between 30 June 2020 and 30 June 2022. That is consistent with the observed permafrost warming at 10 m depth (Magnin et al., 2024). Finally, in 2021, resistivity values were higher in both the upper and lower parts (at P1 and P2) compared with 2020 and 2022, consistent with the temperature measurements (see Fig. 2, or details in Magnin et al., 2024).

Figure 9 presents the measurement results for the granite sample from the study site (labeled Sample AdM), alongside measurements of another granite sample (Sample Cosmiques) collected from a nearby site at the lower Cosmiques Ridge (Mont-Blanc massif, 3613 m a.s.l.), as reported by Duvillard et al. (2021). The experimental datasets are presented along with data fits, using Eqs. (1) for temperatures above the freezing point, and Eq. (2) for temperatures below the freezing point. The model proposed in Sect. 3 successfully fits the data above and below the freezing temperature, providing a proxy for connecting electrical conductivity or electrical resistivity measured in field to temperature.

Extracted resistivities at P1 are superimposed on the co-located borehole BH-NW, where temperature measurements are available. We are using these two datasets (i.e., temperature and resistivity measurements at the same location, BH-NW) to explore the potential for estimating temperature based on electrical resistivity measurements and to perform a quantitative evaluation of the temperature–resistivity relationship determined in a laboratory.

It is well established that when temperature>0°C (i.e., the case in the active layer), electrical resistivity depends on multiple factors, including porosity, water content, water salinity, Cation Exchange Capacity (CEC) and temperature (Revil et al., 2018). This multiple parameter dependance makes it difficult to accurately model or predict electrical resistivity, or to use it as a proxy for temperature estimation in the active layer. In contrast, under frozen conditions, resistivity of the medium is primarily controlled by the remaining unfrozen pore water, which is largely temperature dependent, while other parameters can be assumed relatively constant.

Based on this assumption, the resistivity values extracted from inverted model of resistivity were converted to temperature using the petrophysical model in Eq. (2) (Duvillard et al., 2021, 2018; Coperey et al., 2019). Figure 10 shows the measured temperature alongside the estimated temperature from ERT data, plotted against depth at different dates (in summer and autumn). A good agreement is observed between the measured and estimated temperature in frozen zone, with mean absolute error (MAE) less than 1 °C within the frozen zone (approximately from 2–2.5 to 10 m, depending on the date). These results suggest that the temperature distribution across the site can be reasonably estimated using this model, assuming that the medium is sufficiently homogeneous and that resistivity variations are predominantly controlled by temperature. Figure 11 illustrates the temperature distribution along the profile NW estimated from electrical resistivity measurements acquired at different dates between June 2020 and June 2022. The estimated temperatures consistent with previous analyses and highlight two permafrost zones located above and below the gallery. A clear temperature gradient with depth is observed on the 2D temperature sections, with positive temperatures around and in the infrastructure. It can also be observed that temperature decreases with depth, reaching values lower than -5°C in the zone where ERT sensitivity is low or absent (see lower part of profile NW Fig. 11). At greater depths, the reduced sensitivity affects the reliability of temperature estimates.

Finally, data collected under frozen surface conditions (i.e., measured in winter and early spring, when contact resistance is high) shows large discrepancy between the estimated and measured temperature and therefore cannot be reliably used for temperature estimation.

To go further in our analysis, Fig. 12 shows the extracted resistivity at P1 vs. temperature data measured in co-located BH-NW at different dates. Laboratory measurements on two granite samples (labeled Sample AdM and Sample Cosmiques) are also shown. Three key observations can be made: (i) Data collected in winter and spring (frozen conditions at surface), presented by blue symbols, show resistivity values higher than those expected from laboratory measurements, which aligns with the field observations reported by Maierhofer et al. (2024). This may be related to the salt segregation during freezing, which may enhance conductivity of pore water and consequently reduce resistivity of samples. (ii) At higher temperature (unfrozen conditions at surface), a linear trend is observed that aligns with laboratory measurements for part of datasets (e.g., datasets of 26 August 2020 and 17 September 2020). The difference in resistivity between field and laboratory data under unfrozen conditions could be attributed to the heterogeneity at the field scale and/or the difference in water content and water salinity between laboratory and field environments. Whereas laboratory measurements were conducted in saturated conditions (saturation was performed under vacuum using degassed water). (iii) Field data exhibit greater dispersion compared to laboratory data, which can be attributed to several factors, including 3D effects at the site, the influence of infrastructure and heterogeneity at different scales (from fractures scale to pore scale). In addition, there is a difference in resolution between the two field measurements: temperature measurements are local, while resistivity measurements account for a larger volume.

One of the objectives of this study was to assess hydrogeological dynamics. Due to gaps in the ERT time series, the analysis of times series did not yield conclusive information. Therefore, we selected specific datasets (nearly complete pseudo-sections) and compared the results of the time-lapse inversion to gather information about water infiltration and drainage. Although we could not precisely identify the infiltration and drainage pathways or the water table (which may be located at a lower altitude according to Magnin and Josnin, 2021) using ERT measurements, we observed several instances that serve as evidence of possible water flows.

Figure 13 shows the results of the time-lapse inversion of datasets along the S profile at various time intervals. The same inversion parameters were applied as those used to invert the datasets on the NW side (Fig. 7). In the upper part of the profile (i.e., above the gallery), we interpret that seasonal variations in resistivity are influenced by the presence of fractures, which control water flow pathways and, consequently the resistivity response throughout the seasonal cycle. This portion of the profile is exposed to strong insolation in summer, which dries the rock and fractures, leading to an increase in resistivity near the surface due to air-filled pores and fractures (e.g., Fig. 13b, c and l). Conversely, decreases in resistivity in this zone (e.g., Fig. 13a, d and g), can be attributed to higher water saturation caused by the circulation of snowmelt or rainfall water. Snowmelt on this side supplies substantial amounts of water throughout the thawing season (Ben-Asher et al., 2023). The conductive zone observed beneath the desiccated area (e.g., Fig. 13d and h) likely corresponds to zone of increased water saturation, as also reported by Sass (2004).

In the lower part of the S profile (i.e., below the gallery), the seasonal variations in permafrost resistivity are clearly observed and can be tracked over time, with no evidence of significant water flow or drainage in this zone. This portion of the S profile shares a similar sun exposure to the NW profile and therefore exhibits comparable dynamics, with the development of a thawed and more water saturated active layer than in the upper part, because it is less exposed to solar radiation, and it undergoes less desiccation than the south face sector.