Preconditioning of mountain permafrost towards degradation detected by electrical resistivity

Warming permafrost has been detected worldwide and is projected to continue during the next century by many modelling studies. In mountain regions, this can lead to potentially hazardous impacts on short time-scales by an increased tendency for slope instabilities. However, time scales of permafrost thaw and the role of the ice content are less clear, especially in heterogeneous mountain terrain, where ice content can vary between zero and supersaturated conditions over small distances. Warming of permafrost near the freezing point shows therefore complex inter-annual behaviour due to latent heat effects during thawing and the influence of the snow-cover, which is governed by highly non-linear processes itself. Here, we demonstrate a preconditioning effect within near-surface layers in mountain permafrost that causes non-linear degradation and accelerates thaw. We hypothesise that a summer heat wave, as has occurred in the Central European summers 2003, 2015 and 2022, will enhance permafrost degradation if the active layer and the top of the permafrost layer are already preconditioned, i.e. have reduced latent heat content. This preconditioning can already be effectuated by a singular warm year, leading to exceptionally strong melting of the ground ice. On sloping terrain this ice-loss can be considered as irreversible, as large parts of the melted water will drain during the process, and an equivalent build-up of ice in cold years does not happen on similar time-scales as the melting. We propose a simple geophysical approach based on electrical resistivity tomography surveys that can assess the state of preconditioning in the absence of boreholes. In addition, we will show that resistivity data from a total of 124 permafrost sites in the Andes, Europe, and Antarctic adhere to a distinct power law behaviour between unfrozen and frozen states, which confirms the consistent electrical behaviour of permafrost and active layer materials over a wide range of landforms and material composition.

The time scale of degradation and the role of the ice content for determining the strength and rate of permafrost thawing are still unclear.Non-linear processes related to snow cover, surface material and water infiltration, giving rise to non-conductive heat transfer processes, are emphasised in site-specific simulations (Gubler et al 2013, Scherler et al 2013, Ekici et al 2015, Phillips et al 2016, Westermann et al 2016, Pruessner et al 2018, Wicky and Hauck 2020), especially for mountain sites with generally low and spatially variable ice content and large spatiotemporal snow cover variability (Gisnås et al 2016, Marmy et al 2016, Haberkorn et al 2017).In mountain regions, these effects are complicated by threedimensional hydrological processes and interactions between snow melt, infiltration and drainage (e.g.Arenson et al 2010, Langston et al 2011, Evans et al 2015, Lüthi et al 2017), which may play an important role in the triggering of mass movements on steep permafrost slopes (Hasler et al 2011, Krautblatter et al 2013, Phillips et al 2016, Ravanel et al 2017, Mourey et al 2022).
Permafrost warming is usually monitored within 10-100 m deep boreholes, e.g.within international Global Terrestrial Network of Permafrost ((GTN-P), Biskaborn et al 2015; Permafrost and Climate in Europe (PACE), Etzelmüller et al 2020) or national (Switzerland, PERMOS 2023 andNorway, Isaksen et al 2022) networks.In the absence of boreholes, geophysical surveys and monitoring (e.g. through electrical resistivity tomography (ERT) measurements, (Mollaret et al 2019, Scandroglio et al 2021), but also using other techniques such as passive seismic, (Lindner et al 2021) or spectral induced polarisation, Maierhofer et al 2023) are the only means to indirectly assess the state and evolution of permafrost in the deeper subsurface.
Recent studies have suggested that the water content in the active layer and the ground ice content in the permafrost layer are the most important variables that determine how sensitive a permafrost environment reacts to climate warming (Marmy et al 2016, Clayton et al 2021).Both variables increase the latent heat content in the ground compared to dry and/or low-porous substrates.The present study attempts to target the analysis of these two variables using a simple non-invasive approach based on ERT measurements and shows that significant and sustained permafrost degradation can be facilitated by single extreme events, such as summer heat waves.

Electrical resistivity contrast between unfrozen active layer and permafrost
2.1.ERT Among geophysical measurement techniques, electrical methods are highly suitable to characterise structures in frozen materials and differentiate them from unfrozen materials, as a marked increase in electrical resistivity occurs at the freezing point.Hereby, ERT has become a very popular method, due to its comparatively short survey time, well-developed data processing routines and its wide applicability, even in very heterogeneous and rough mountain terrain (e.g.Maurer and Hauck 2007, Krautblatter et al 2010, Rödder and Kneisel 2012, Magnin et al 2015, Boaga et al 2020, Hilbich et al 2022, Kunz et al 2022).Consequently, it is now also used in a monitoring context where electrical resistivity changes can be related to freeze/thaw and permafrost degradation processes (temperature increase, ice content decrease; e.g.In ERT surveys, the electrical resistance of the ground is measured by passing a current between two electrodes and measuring the resulting potential difference between two further electrodes.By choosing different four-electrode combinations (quadrupoles) with different centre points and spacings along a survey line, a two-dimensional section is obtained, where large electrode spacings correspond to larger investigation depths.Multiplying the measured electrical resistances with a geometric factor that corresponds to the distance between the electrodes, an apparent resistivity distribution is obtained.The apparent resistivity distribution has to be inverted using suitable inversion algorithms to obtain the 'true' specific resistivity distribution along the modelled section.As with most geophysical techniques, the inverted resistivity model obtained is not unambiguous and depends on data quality, measurement geometry, and the choice of inversion parameters (e.g.Day-Lewis et al 2005, Flores-Orozco et al 2019).

Electrical resistivity of frozen and unfrozen materials
Several approaches have been suggested to link the bulk electrical resistivity of the ground with material properties relevant in permafrost studies such as water content, ice content, porosity and temperature.In general, it is assumed that electrolytic conduction is the dominant conduction process in Earth materials, which can be described by Archie's 2nd Law: where ρ and ρ w are the resistivity of the bulk material and the pore water, respectively, Φ is the porosity, S w is the saturation and n, m are material dependent parameters (Archie 1942).If the permafrost substrate is very dry or ion poor (leading to low pore water salinity and therefore high pore water resistivity), the measured bulk resistivities can be very high.In these cases, surface conduction processes (e.g.Sen et al 1988, Glover 2010) may play the dominant role and electrolytic conduction can be neglected.According to Duvillard et al (2018), in these cases, electrical resistivity can be derived from: with f w being the volumetric water content (f w = Φ S w ) and b = r g B CEC where r g is the grain density (in kg m −3 ), B the apparent mobility of the counterions for surface conduction (in m 2 V −1 s −1 ), and CEC is the cation exchange capacity (in C kg −1 ).
According to Duvillard et al (2018) and Mollaret et al (2020), equation ( 2) can be further simplified in the case of low pore water salinities (1/ρ w ≃ 0) to give: Finally, a geometric mean model (or random model) can be constructed, which assumes random distribution and orientation of subsurface components and weighs the resistivities of the soil constituents (rock, water, air and ice) according to their fractions (Glover 2010): where f denotes a volumetric fraction and the indices r, i, w and a stand for rock, ice, water and air, respectively.This model may be most appropriate in the general case, but does not address specific electrical conduction processes in the subsurface.Note that combinations of the above models have been applied as well (e.g.Mollaret et al 2020), but will not be treated here.

Electrical resistivity gradients
Equations ( 1)-( 4) can be re-written for the frozen and unfrozen state and the ratio between the frozen and unfrozen resistivities, ρ f and ρ u , would then approximately correspond to the resistivity gradient between the permafrost layer and active layer; assuming that the rock/soil material remains constant over the transition between the two layers.Of course, and especially in high mountain environments, the latter condition will often be violated due to the heterogeneity of the terrain.Note also that the resistivity of the frozen state will depend on temperature, as the resistivity will steadily increase with decreasing (negative) temperatures until most of the residual unfrozen water content has been frozen (Hauck 2002, Krautblatter et al 2010, Oldenborger and LeBlanc 2018, Tomaskovicova and Ingeman-Nielsen 2023).However, in most cases, the largest resistivity changes are observed close to the freezing point (e.g.Olhoeft 1978).
The resistivity ratio between frozen and unfrozen states for Archie's Law (equation ( 5)), the simplified surface conduction model (equation ( 6)) and the geometric mean model (equation ( 7)) can be expressed as: with the indices f and u denoting values for frozen and unfrozen states, respectively.The saturation in the unfrozen state, S u can hereby be transformed to unfrozen water content by the relation Note that porosity/rock content and air content are unchanged from the unfrozen to the frozen state, which is why they are eliminated from equations ( 5)-( 7) when taking the ratio.

Field data sets and results
To illustrate the above relationships and their relevance in the context of permafrost degradation, we use a large number of measured ERT data sets from multiple surveys on permafrost terrain in Europe (72 sites), the Central Andes of Chile and Argentina (45 sites), and the South Shetland Islands (Western Antarctic Peninsula Region, seven sites).In total, the data set consists of 124 individual ERT profiles (electrode spacing between 2 and 5 m, array configuration varying between Wenner, Wenner-Schlumberger and dipole-dipole), which were conducted as part of different research projects between 1998 and 2022.All measurements were taken in summer with a preference towards end-of-summer measurements, when the boundary between the active layer and the permafrost is clearly detectable by ERT measurements.Field sites cover many different substrates, including pure bedrock sites of different geology, fine-grained and coarse-grained sediments (e.g.colluvial slopes, but also blocky talus), but also special landforms such as rock glaciers and moraines.The estimated ice contents of the respective permafrost bodies range from a few per cent (in low-porosity bedrock) to high amounts of excess ice, i.e. close to 100%.Standardised data processing (filtering) and inversion of all datasets were conducted using the software package RES2DINV (Loke and Barker 1995) for data inversion.Measured resistances were hereby inverted accounting for the surface topography.Comparison studies using other inversion algorithms (CRTOMO (Kemna 2000), pyGIMLi/BERT (Rücker et al 2017)), did not yield fundamentally different results.To obtain representative values for the resistivity of active and permafrost layers we used the so-called zone-of-interest (ZOI) technique (after Hilbich et al 2022).In this approach, ZOIs are manually delineated in the tomogram in which an average of the inverted resistivity values within the ZOI is taken and assumed to be representative of a specific layer for each profile.By this, one mean representative value for ρ f and ρ u are obtained for each profile.We chose to define the ZOI for the permafrost close to the resistivity maximum and the ZOI for the active layer at the same horizontal distance but in the surface layer.Supplementary figure 1 illustrates this approach for two different cases of the data set.In cases of several landforms/substrates within the same profile, several ZOI's could be distinguished within one tomogram.
Figure 1 shows a synopsis of all ρ f and ρ u pairs of all 124 tomograms in our dataset plotted on a doublelogarithmic scale.The continuous straight line is hereby the 1:1 line, indicating equal resistivity values for unfrozen and frozen conditions, whereas the dashed lines mark resistivity ratios between frozen and unfrozen states of 10:1 and 100:1, for visualisation purposes.
While it has long been known that resistivity strongly increases upon freezing, it is nevertheless intriguing that most data in figure 1 show a common power law behaviour over a large range of resistivity values (double-logarithmic scale), independent of the very different landforms, substrates and therefore absolute resistivity values.Due to the very different materials and processes involved, care has to be taken when interpreting the data in a purely statistical sense (a correlation would yield an r 2 of 0.65 for a purely statistical relationship of y = 0.9143x + 0.9096, however, for different conduction processes).Note that the absolute values of permafrost resistivities range hereby from 10 2 to 10 6 Ωm, i.e. over five orders of magnitude.This large range also confirms that the mapping of permafrost substrates by relying on a specific resistivity threshold can be ambiguous, as has been emphasised in a recent study by Herring and Lewkowicz (2022).In contrast, it is the resistivity gradient between the active layer and the permafrost that suggests its presence and illustrates its development over time, as will be shown below.
In figure 2, the three petrophysical models of equations ( 5)-( 7) are included with varying values for the free parameter n (equation ( 5)) as well as the various formulations of the unfrozen water content/saturation in equations ( 5)-( 7) (S or f wu ).A similar dependency is obtained when varying the parameter b in equation ( 6) (not shown).It is shown that all models follow the same power law and, by using appropriate parameters, can explain the data almost equally well.This may explain why different equations can be used in practice to describe the unfrozen water content evolution upon freezing or temperature in a temporal monitoring context (e.g.Hauck 2002, Krautblatter et al 2010, Pellet et al 2016, Duvillard et al 2021).Without proper calibration data and a thorough understanding of the electrical conduction processes present at a specific field site, care has to be taken when quantitatively applying a certain model.However, when calibration data are present, figure 2 also shows that the very nature of the petrophysical relationship may seem of limited importance, as the mathematical form of the equations is similar, and all relationships are based on the same variable (water content) and one or several free calibration parameters.In the following we address the anticipated changes in the resistivity ratio between active layers and permafrost under climate warming and especially during and following an exceptionally hot summer.To illustrate the concept, we will show data from the long-term permafrost monitoring and PERMOS reference site Schilthorn (SCH) in the Swiss Alps (46.558N, 7.835E, 2910 m asl), where a geoelectrical monitoring was already established in 1999, which makes it the longest continuous time series worldwide of this type (Hauck 2002, Hilbich et al 2011, PERMOS 2023).

Preconditioning
Since the start of this time series several heat waves have occurred in the European Alps, amongst them the exceptionally warm summers 2003 (Schär 2004) and 2015 (Scherrer et al 2016), which led to the wellknown rock slope destabilisation effects as shown by  Gruber et al (2004), Ravanel et al (2017).Further heat waves have been observed in 2011, 2015, 2018and 2022(e.g. Orth et al 2016, Brunner et al 2019, Scherrer et al 2022), and are projected to increase in magnitude and frequency (Lin et al 2022).
For the station SCH (figure 3), the strong effect of the two warm summers 2003 and 2015 is clearly seen by the increased thaw layer depth.However, in both cases refreezing occurred in the following winter.Consequently, the temperature record did not give any indication of the development of a talik.Apart from the influence of the anomalous years 2003 and 2015, the active layer stayed constantly around 4-5 m until 2008, and around 5-7 m until 2016 (figure 3).Hilbich et al (2008a) showed for the 2003 heat wave that although temperatures (and therefore active layer thickness (ALT), see figure 3 for the years 2004 and 2016) did return to pre-heatwave values in the following year, the resistivities did not, but stayed at smaller values than before the occurrence of the heatwave.This was interpreted as being due to ground ice loss that could not be fully replaced in the following colder year.We argue that this ground ice loss has a non-linear effect on the future temperature evolution at a specific site by pre-conditioning the soil for faster seasonal thawing of the active layer in the following years.In a pre-conditioned subsurface, less heat is needed to thaw the seasonal ice, which usually acts as a thermal buffer.A subsequent heat wave would therefore reach deeper levels more easily due to the smaller latent heat of fusion necessary for the melting of the ice.
On the other hand, the thermal conductivity of ice is larger than for wet and especially for dry soil, so a loss of ground ice may also slow down the propagation of thawing.Clayton et al (2021) showed for field data from Alaska and Canada that the latent heat effect dominates for the active layer as a whole, whereas the conductivity effect dominates for the topmost cm of the soil.
In terms of resistivity evolution, the resistivity contrast between active layer and permafrost is expected to increase during a heatwave, as the permafrost layer is (yet) unaffected, but the active layer is wetter due to the melting ground ice.In addition, temperatures in the active layer are higher, which further decreases resistivity due to the temperature dependence of resistivity for positive temperatures  (e.g.Hauck 2002).In the year following a heat wave, the active layer temperatures may return to normal conditions, but the heat has further penetrated into the subsurface leading to a warming of the still frozen permafrost layer-which decreases the resistivity ratio.This effect is shown in figure 4 with the evolution of the resistivity ratio.The increase and subsequent decrease after the heat wave 2003 is clearly seen, similarly, but less strong for the heat wave in 2015.A strong increase has also been observed after the heat wave of 2022, with data from 2023 not yet available.Further increases in 2009 and 2017 coincides with strong increases in active layer thickness (see figure 3).
In the long-term and in a warming climate, we would expect a slow but continuous decrease in the resistivity ratio, while permafrost temperatures and unfrozen water content increase, and ice content and resistivity decrease.However, the resistivity of the active layer depends also on its moisture and especially on the drainage characteristics of the melting ground ice. Figure 5 shows the change of the resistivity ratio between permafrost body and active layer (averaged over the same ZOI's for the different years) for several field sites, where ERT surveys have been repeated after a long time period.A clear decrease can be seen for all profiles including SCH, despite the large interannual variability with an increasing ratio after the occurrence of heat waves.

Discussion and conclusion
Comparing the year-to-year variability of ALT (figure 3) with the geoelectrical monitoring data at Schilthorn, a preconditioning effect of an anomalously warm season can be inferred.After the extreme hot summer of 2003 in the European Alps, a strong resistivity decrease corresponding to a substantial ice loss is seen, especially at depths below 4-6 m accompanied with an increase in the resistivity ratio between the active layer and the permafrost.While the resistivity anomaly at larger depths persisted for several years, the borehole temperatures and active layer resistivity returned to normal values already the year after the 2003 anomaly (Hilbich et al 2008a).
The corresponding ice loss in deeper layers could not be compensated during most of the following years even in years with comparatively low air temperatures (i.e. the years 2004(i.e. the years , 2007(i.e. the years , 2013(i.e. the years and 2014(i.e. the years , see Hoelzle et al 2022)).As the smaller ice content (reduced latent heat content) also reduces the thermal buffer function of the active layer, such ice melt processes within permafrost caused by singularly extreme years can be seen as preconditioning of the subsurface towards irreversible (long-term) permafrost degradation, as each consecutive heat wave may easier penetrate to larger depths and accelerate permafrost thaw.
Hydro-thermal model simulations for this site confirm that the total water content decreases shortly after an extremely warm summer and cannot be completely compensated during the following years (Scherler et al 2013).They also suggest that a complete winter refreezing at this site seems unlikely as soon as the thaw depth reaches ∼14 m (Scherler et al 2013).After the hot summer of 2022 with an active layer thickness of almost 13 m (reached in December 2022), this situation may be reached very soon.
The preconditioning effect outlined in this study would imply that slope failures in permafrost areas (as discussed e.g. in Gruber and Haeberli 2007, Hasler et al 2012, Krautblatter et al 2013, Phillips et al 2016, Ravanel et al 2017, Deline et al 2021) would not necessarily occur only during or shortly after an extremely warm summer/autumn, but could also happen during the following years, if the ground was previously preconditioned.Water infiltration into the newly developed air voids and cracks and subsequent refreezing could increase the pore pressure and induce mechanical cracking and slope failure (Hasler et al 2012, Phillips et al 2016).A preconditioned subsurface would be much more vulnerable to additional heat or water transfer by e.g.heavy precipitation or snow melt events (Deline et al 2015, Savi et al 2021, Mourey et al 2022).Furthermore, this would imply that there is not necessarily a temporally close relation between heat waves and large rock slide activity from mountain permafrost regions (e.g.Gruber and Haeberli 2007).
In this study, we show that the resistivity contrast between the active layer and the permafrost follows a power law and is surprisingly stable over several orders of magnitude.Furthermore, the data can be explained by several petrophysical models that are primarily based on water content and additional free parameters, allowing the use of the resistivity ratio as an indicator for permafrost thaw.A high resistivity ratio (large contrast between active layer and permafrost resistivity) is usually observed for permafrost with high ice content (such as in rock glaciers or icecored moraines, see red triangles and blue stars in figure 1).Although heat waves tend to increase this ratio due to a short-term resistivity decrease in the wetter active layer, they lead to a stronger decrease of the ratio in the following years due to the accelerated thawing.We may therefore speculate that sites with low resistivity ratios have on average already been affected more often by preconditioning and degradation than sites with larger ratios.However, since resistivity is not only influenced by water, ice and temperature, but also by the electrical properties of the rock/soil matrix and the salinity of the pore water (i.e. the free parameters in the petrophysical models), a careful analysis of the site characteristics remains mandatory when interpreting resistivity changes over time.
We conclude that short-term, but extreme regional temperature anomalies, such as the Central European summers 2003, 2015 and 2022 will enhance sustained permafrost degradation by preconditioning the top of the permafrost layer, i.e. reducing its latent heat content.This preconditioning can already be effectuated by a singular warm season, leading to exceptionally strong melting of the ground ice in the near-surface layers.On sloping terrain and in the context of quasi-continuous climate warming, this ice-loss can be considered as irreversible, as a large part of the melted water will drain/evaporate during the process, and the build-up of an equivalent amount of ice in subsequent cold years does not happen on similar time-scales as the melting.This process probably applies mostly to sites with low to intermediate ice contents, where singular anomalies can lead to sustained ice loss even at larger depths.
The study is based on a compilation of a very extensive geophysical dataset that was obtained by several generations of researchers within our research group over the past 25 years.We would like to thank everybody who helped obtaining the data in the first place as well as specifically Coline Mollaret and Cécile Pellet, who were major driving forces in establishing the new IDGSP data base initiative.We would also like to thank two anonymous reviewers for their helpful comments and suggestions for our manuscript.This study has been supported by the Swiss National Science Foundation (Grant No. 200021L_178823).

Figure 1 .
Figure1.Log-log plot of electrical resistivity contrast between permafrost and active layer for 124 sites in the Andes (45 sites), the European Alps (55 sites) and Central Europe (eight sites), Norway (nine sites) and the Antarctic Peninsula Region (seven sites).Solid and dashed lines mark the 1-1 line and 10:1 and 100:1 resistivity ratio between permafrost and active layer, respectively.Red triangles mark active rock glaciers and blue stars mark ice-cored moraines/dead ice bodies.Note, that the x-and y-axis are shifted by one order of magnitude.

Figures 1
Figures 1 and 2 show temporally static data, i.e. each data point represents the permafrost conditions at a single time instance (usually at the end of the summer but in different years).Several ERT monitoring studies on permafrost have shown that changes in the subsurface conditions are well represented by changing resistivity values over time (e.g.Hilbich et al 2011, Oldenborger and LeBlanc 2018, Mollaret et al 2019, Farzamian et al 2020, Scandroglio et al 2021, Tomaškovic ˇová and Ingeman-Nielsen 2023).In the following we address the anticipated changes in the resistivity ratio between active layers and permafrost under climate warming and especially during and following an exceptionally hot summer.To illustrate the concept, we will show data from the long-term permafrost monitoring and PERMOS reference site Schilthorn (SCH) in the Swiss Alps (46.558N, 7.835E, 2910 m asl), where a geoelectrical monitoring was already established in 1999, which makes it the longest continuous time series worldwide of this type(Hauck 2002, Hilbich et al 2011, PERMOS 2023).Since the start of this time series several heat waves have occurred in the European Alps, amongst them the exceptionally warm summers 2003(Schär 2004) and 2015(Scherrer et al 2016), which led to the wellknown rock slope destabilisation effects as shown by

Figure 2 .
Figure 2. Same data as figure 1.In addition, three different petrophysical models were tested and shown by the red dashed lines: (a) Archie's law (electrolytic conduction, Archie 1942) with varying saturation exponent n, a small liquid water saturation in frozen state (S f = 0.05) and active layer water saturation of 0.15, (b) Archie's law with varying saturation values Su in the active layer, (c) geometric mean model (Glover 2010, Mollaret et al 2020) for varying unfrozen water content f wu, a very small liquid water content in frozen state (f wf = 0.05) and non-saline conditions (ρw = 100 ohm•m), (d) surface conduction model (Duvillard et al 2018) for different unfrozen water contents.

Figure 3 .
Figure 3. Active layer evolution at Schilthorn, Swiss Alps.Grey bars denote a comparatively higher uncertainty due to data gaps.Source: PERMOS.

Figure 4 .
Figure 4. Resistivity ratio between active layer and permafrost at Schilthorn, Swiss Alps over the full 25 year monitoring period.Resistivity values were taken from the inverted ERT model at the borehole location of BH51/98 and plotted as ratio between permafrost (resistivity at 10 m) and active layer (average resistivity between 0 and 2.5 m).Occurrence of specific heat waves are indicated.

Figure 5 .
Figure 5. Resistivity ratio between permafrost body and active layer as a function of time for different permafrost sites in the European Alps (see supplementary table 1).