Michael Krautblatter Dissertation Format

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1 Introduction

Rockfalls and rock avalanches linked to permafrost degradation are important hazards in high mountain regions worldwide [e.g., Geertsema et al., 2006; Fischer et al., 2006; Huggel et al., 2008; Allen et al., 2009; Deline et al., 2011; Ravanel et al., 2013]. In the Mont Blanc massif (MBM), more than 380 rockfalls were documented in 2003 and between 2007 and 2011 [Ravanel et al., 2010, 2011; Ravanel and Deline, 2013]. The MBM is a densely populated region with popular climbing routes, widespread infrastructure, and rockwalls that often exceed 1000 m height. Rockfalls and rock avalanches can pose a high risk to individuals and infrastructure in these areas, as seen in the 2–3 × 106 m3 Brenva rock avalanche in 1997 [Deline, 2001].

Rockwall destabilization has been linked to geological, geomorphological, hydrological, and thermal factors [Krautblatter and Moore, 2014]. Near-vertical rockwall permafrost destabilization, however, is not as well understood because the complex thermo-hydro-mechanic interplay is difficult to observe and model [Krautblatter et al., 2012]. Verleysdonk et al. [2011] identify the predisposition of warm sensitive permafrost systems to destabilization as an important mountain hazard, in a context of warming temperatures. Temperature changes in rock masses at subzero temperature, especially in the range of −5 to 0°C, significantly modify the mechanical properties of both the water-saturated rock and the ice-filled joints and encourage rockwall destabilization [Davies et al., 2001; Krautblatter et al., 2013]. The mapping and modeling of thermally sensitive permafrost has thus been recognized as a key objective in mountain permafrost research activities [Harris et al., 2001].

Numerical models used to map steep bedrock permafrost have revealed topoclimatic controls on the 3-D distribution of permafrost [Noetzli et al., 2007; Noetzli and Gruber, 2009]. However, these models could globally overestimate measured permafrost temperatures by +1 to +3°C on north and south slopes, respectively, due to rock fractures and snow distribution [Hasler et al., 2011]. The Alpine-wide Permafrost Index Map (APIM) is a 30 m resolution statistical model calibrated with ground surface temperature measurements, air temperature records, and computed incoming solar radiation [Boeckli et al., 2012a, 2012b]. The APIM also integrates findings from Hasler et al. [2011] to estimate permafrost occurrence at depth. The APIM can be used to estimate the spatial distribution of mountain permafrost in the MBM. Model validation in near-vertical rockwalls remains challenging for three main reasons: (i) the limited availability of data, (ii) the spatial heterogeneity of permafrost, and (iii) the resolution of models is often too coarse for direct comparison with in situ point measurements.

Electrical resistivity tomography (ERT) is a geophysical technique that measures electrical resistivity at depth along 2-D transects. The method can be applied to permafrost studies because of the difference in electric and dielectric properties of materials under frozen and unfrozen conditions [Scott et al., 1990]. The electrical resistivity of frozen rock, which can be solved by Archie's law [Archie, 1942], mainly depends on the pore volume, the degree of water saturation, the chemical properties of pore water, and the temperature of the rock [Kneisel et al., 2008]. ERT has been used to investigate mountain permafrost in Europe [e.g., Kneisel et al., 2008; Hauck et al., 2008; Hilbich et al., 2008] and in North America [e.g., Lewkowicz et al., 2011]. Krautblatter and Hauck [2007] demonstrated that ERT is generally capable of mapping and monitoring permafrost in rockwalls. As such, ERT may be appropriate for the validation of permafrost models as it can be conducted on scales that are similar to the resolution of the APIM model, for example.

ERT yields only qualitative information on the thermal state of materials when (i) pore volume, (ii) the degree of water saturation, and (iii) the chemical properties of pore water are poorly constrained (e.g., in a rock glacier). In such cases, quantitative information can be gained using ERT in combination with other geophysical methods (e.g., seismic P wave velocity) [Hauck et al., 2008]. In better constrained systems such as bedrock, where pore volume, the degree of water saturation, and chemical properties of pore water are defined and more homogeneous, temperature-resistivity relations of frozen bedrock can be derived in the laboratory [Krautblatter et al., 2010]. The applicability of ERT in near-vertical rockwall permafrost (NVRP) in characterizing permafrost distribution at a rock face scale and in validating distributed models of permafrost has not yet been demonstrated.

This paper describes a unique data set of seven ERT measurements from five NVRP sites in the MBM, two of which were repeated the following year. Laboratory testing on a rock sample was undertaken to identify the temperature-resistivity relationship in order to support the interpretation of field results. These measurements address three main questions: (i) Is ERT capable of characterizing permafrost distribution and its annual changes at a rock face scale in NVRP? (ii) Can ERT confirm that topography, snow distribution, and rock fractures are important controls on permafrost distribution in NVRP? (iii) Is ERT well suited for validating spatial models of permafrost distribution in NVRP?

2 Study Sites

2.1 Geological Settings of the Mont Blanc Massif

Located in the western European Alps, the MBM has an area of about 550 km2, approximately 30% of which is glaciated (Figure 1). Bordered by deep valleys, it culminates at 4810 m above sea level (asl) and provides a remarkable combination of peaks and crests standing well above 3000 m asl. The Variscan granitic batholith and related aplitic veins intruded into a metamorphic basement (orthogneisses, paragneisses, and metamorphic mafic rocks). Being fine grained near its SE contact, the granite becomes more porphyritic toward the massif core [Rolland et al., 2003; Leloup et al., 2005]. The massif is bounded by a wide shear zone in the NW and a thrust in the E and SE. Subvertical faults and shear zones have a fan-like arrangement [Bertini et al., 1985] and determine the distribution of the large spurs of massive granite and the main couloirs. At a larger scale, tectonic phases have broken up the rock with multiple planes and fractures with highly variable direction and density. Granites have typical porosities between 0.6 and 1% [Sousa et al., 2005] and are very hard and resistant to weathering, as evidenced by the number of extreme steep rockwalls and rock pinnacles in the MBM.

2.2 Permafrost Index Distribution

The APIM [Boeckli et al., 2012b] predicts the spatial distribution of permafrost in the MBM rockwalls using 1961–1990 mean annual air temperature (MAAT), potential incoming solar radiation (PISR), and the overall combined effects of rock fractures and snow (temperature offset from −2.5 to 0.5°C according to PISR). The mapped index classes indicate areas of warm and discontinuous permafrost where permafrost only exists in favorable conditions induced by dense fractures and thin snow accumulation (index from 0.1 to 0.5); areas of warm and more continuous permafrost, except in hard faces (index from 0.5 to 0.9); and areas of cold and continuous permafrost in all conditions (index ≥ 0.9). Each of these index classes covers a wide range of elevations. A 4 m resolution map, the CIP-MB (Carte d'Indice du Permafrost–Mont Blanc), has also been produced using the same modeling procedure as the APIM but with local MAAT input data to improve the permafrost index mapping at the local (rock face) scale [Magnin et al., 2015a]. Both the APIM and the CIP-MB predict the lower elevation boundaries of the 0.5 index class, which broadly corresponds to the presence of permafrost [Boeckli et al., 2012b], to be 2300 and 2700 m asl on north and south facing slopes, respectively.

2.3 Site Selection

The sites were first selected from the APIM and CIP-MB models. We focused on areas of discontinuous permafrost with index values from 0.1 to 0.5, where we could expect sharp contrasts in resistivity. As these areas were of limited occurrence and/or accessibility, we also considered areas with permafrost index values from 0.5 to 0.9, as well as the lower margins of ≥0.9 index areas. We performed measurements in only the Mont Blanc granite lithology to guarantee comparability between the surveyed sites, despite the fact that the index class from 0.1 to 0.5 occurs widely over the metamorphic basement.

Specific attention was paid to the subvertical topography and length of the chosen profiles in order to avoid debris-covered slopes and to guarantee sufficient penetration depth of the ERT. Finally, site selection was constrained by accessibility and safety sine qua non considerations which include helicopter drop, away from usual climbing routes and unstable areas.

2.4 Site Characteristics and Climatic Conditions During ERT Surveys

The study sites represent different aspects from NW to SE various permafrost indexes (Figure 2). The maximum elevation of the ERT profiles is between 2810 and 3350 m asl. Slope angles vary from near-vertical rockwalls to lower-grade rock faces and are slightly overhung at La Pointe Albert (Table 1). Les Grands Montets, La Pendant, and Le Gros Rognon stand out from glaciers as nunataks, whereas La Pointe Albert and Les Charmoz are surrounded by high rockwalls with limited glacier extension at their footwalls (Figure 1). Les Grands Montets is a wide and rounded, snow-covered summit in winter, contrasting with the sharp ridges of La Pointe Albert, Le Gros Rognon, and Les Charmoz (Figure 2). La Pendant has a pyramid-shaped geometry. The lower third of La Pointe Albert transect was located in a debris covered gully and the lower half of Le Gros Rognon transect on a snow-covered face.

Les Grands Montets3295NWHighly fractured, snow-covered in winter−5.311/10/12
Le Gros Rognon3350SECompact slab (80 m); snow covered and fractured (80 m)−5.620/10/12
La Pendant3000NWMassive blocks (30 m); fractured (120 m)−3.822/10/12
Les Charmoz2830NECompact slab−2.823/10/12
La Pointe Albert2810S (120 m)Compact slab (120 m); fractured, debris-covered gully (60 m)−2.820/09/13
SW (60 m)

MAAT at site locations (Table 1) is calculated from the 1993–2012 record in Chamonix (1042 m asl) and a mean lapse rate of −0.0053°C m−1 based on the air temperatures recorded by Météo France at Chamonix (1042 m asl) and the Aiguille du Midi (3842 m asl) from 2007 to 2013.

ERT measurements were conducted in October 2012 and September 2013. Both years were in the range of the 1993–2012 MAAT (+6.6°C in Chamonix), but 2012 was 0.5°C warmer than 2013, with warmer winter and spring: mean air temperature from December 2011 to June 2012 was +3.5°C, in contrast to +2.8°C from December 2012 to June 2013 (Figure 3a). The first survey was conducted at Les Grands Montets at the end of a period of stable and warm weather followed by a snow fall. The face was snow covered when the measurement was performed and air temperature dropped below −10°C at the Aiguille du Midi the following days (Figure 3b). However, the other 2012 measurements were done after this cooling episode during a warmer period with air temperature oscillating around 0°C. Air temperature during Les Charmoz and La Pointe Albert surveys in September 2013 was in the range of the one at Les Grands Montets in 2012 (−6.4°C at 3842 m asl); the warmest measurement day was at La Pendant in 2013 (+3.9°C).

3 Methods

3.1 Data Acquisition and Inversion

ERT field campaigns in NVRP require a high level of technical organization as poor electrical contacts can be expected [Krautblatter and Hauck, 2007]. Due to the subvertical working conditions of our study sites, redrilling and rewetting of electrodes along the survey line in case of bad electrical contact is restricted. The resistivity measurement had to be thoroughly prepared coincident to the installation of electrodes and cables. Two 80 m cables (160 m profile) and a total of 32 electrodes (5 m spacing) (Figure 4a) were connected to an ABEM Terrameter LS device. The electrodes are 10 mm thick and 120 mm long stainless screws. Salt water and metallic grease were used to improve electrical contacts. Cables were packed in advance in order to easily carry them while abseiling downward and installing the electrodes (Figure 4a). Choice of the electrode spacing is a compromise between expected depth of investigation, transect length, and resolution of the data: electrode spacing was set to 5 m, which yielded 160 m long survey lines with a depth of investigation of approximately 25 m exceeding the active layer thickness. Local variation of the rock surface (upper 10 cm that regularly dry out) is not visible at this resolution [Sass, 2005]. Thus, porosity, the degree of saturation, and pore water chemistry remain relatively constant at the scale of these ERT measurements, and changes in electrical conductivity are therefore assumed to be due to the freezing of pore water.

Despite the thorough electrode preparation and use of salt water, some electrodes were excluded as they did not provide sufficient contact. The maximum number of excluded electrodes was three in one array. In high-resistivity mediums such as these, the geometrical configuration of the profile is crucial. A Wenner electrode configuration with 155 datum points was used for the best signal-to-noise ratio, although it is less sensitive to weak signals [Kneisel, 2006; Hauck and Vonder Mühll, 2003]. The topography was measured with a Laser Technology TruPulse 200 rangefinder (accuracy: ±30 cm, ±0.25°, resolution: ±10 cm, ±0.1°) at La Pendant, La Pointe Albert, Les Grands Montets, and Les Charmoz. For Le Gros Rognon, the topography was calculated from topographical maps.

ERT profiles were inverted in RES2DINV software using a smoothness-constrained least squares method [Loke and Barker, 1996]. Mesh refinement to the half of the electrode spacing (2.5 m) and a robust inversion were chosen to deal with the expected strong contrasts in resistivity. Resistance values were converted into apparent resistivity (AR) from the measured ratio between potential differences and injected current multiplied with the Wenner geometric factor. AR values were checked for consistency prior to inversion. Five iterations of the inversions were found to have sufficient convergence without overfitting the data. Root-mean-square (RMS) errors range from 3.5% (Les Grands Montets) to 12.2% (Les Charmoz 2013). Smaller RMS errors do not always imply a more realistic model as more iteration will eventually overfit the model to the data [Hauck and Vonder Mühll, 2003]. RMS errors do not necessarily reflect the quality of the model in compact rock for two main reasons: the high-resistivity gradients that characterize steep alpine bedrock [Blaschek et al., 2008] and the anisotropy of fractured rocks are not resolved by 5 melectrode spacing [Linde, 2005], both leading to high RMS errors [Krautblatter, 2010]. Also, Krautblatter and Hauck [2007] found it difficult to minimize RMS errors in repeat ERT profiles of frozen rock, where freezing and thawing imply large changes from the baseline data set. To better assess the reliability of the inverted model, the spatial distribution of the uncertainties is analyzed using RES2DINV 3.32 tools which subdivide the profile into blocks depicting their respective uncertainty ranges. Model uncertainties were calculated with RES2DINV according to the model covariance matrix method described in Alumbaugh and Newman [2000]. Minimum and maximum models display average models plus or minus the model uncertainty.

3.2 Laboratory Calibration

Temperature-resistivity relationship have been measured in the Landslide Research Group freezing laboratory of the Technische Universität München using the approach described in Krautblatter et al. [2010]. A 45 × 30 × 20 cm granite block of homogeneous coarse-grained Mont Blanc granite that is representative for all sites has been sampled at Les Charmoz. It was immersed in water for several days until full saturation under atmospheric pressure, close to natural alpine conditions, as we assume that the rockwalls are fully saturated [Sass, 1998, 2005]. The sample was then coated with a thin plastic film to maintain its moisture and to obtain its chemical equilibrium with the pore water. Four Wenner-type four-electrode arrays with stainless steel electrodes of 5 mm in diameter were inserted in the middle section of the sample in 4 mm deep holes separated by a minimal distance of 8 cm, so that the medium depth of investigation (MDOI) half-space does not exceed the size of the rock sample (Figure 4b). The electric contact was improved with conductive grease, and measurements were performed with the same ABEM Terrameter LS device as in the field.

The sample was then placed into a 1.5 × 1 × 1 m freezing box insulated with polystyrene. The cooling device is a custom-made Fryka cooler with ventilation that is controlled by a 0.1°C accurate temperature probe in the cooling box. Ventilation was applied to avoid strong thermal difference between the air and the granite boulder and resulting thermal layering. Two thermometers of 0.03°C accuracy and 0.1°C resolution were placed in the block. Below the freezing point, as expected from prior measurements by Mellor [1973

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