The warming and subsequent degradation of mountain permafrost within alpine
areas represent an important process influencing the stability of steep slopes and
rock faces. The unstable and monitored slopes of Mannen (Møre and Romsdal
county, southern Norway) and Gámanjunni-3 (Troms and Finnmark county,
northern Norway) were classified as high-risk sites by the Norwegian
Geological Survey (NGU). Failure initiation has been suggested to be linked
to permafrost degradation, but the detailed permafrost distribution at the
sites is unknown. Rock wall (RW) temperature loggers at both sites have
measured the thermal regime since 2015, showing mean rock surface
temperatures between 2.5 and -1.6∘C depending on
site and topographic aspect. Between 2016 and 2019 we conducted 2D and 3D
electrical resistivity tomography (ERT) surveys on the plateau and directly
within the rock wall back scarp of the unstable slopes at both sites. In
combination with geophysical laboratory analysis of rock wall samples from
both sites, the ERT soundings indicate widespread permafrost areas,
especially at Gámanjunni-3. Finally, we conducted 2D thermal modelling
to evaluate the potential thermal regime, along with an analysis of
available displacement rate measurements based on Global Navigation
Satellite System (GNSS) and ground- and satellite-based interferometric
synthetic aperture radar (InSAR) methods. Surface air and ground
temperatures have increased significantly since ca. 1900 by 1
and 1.5 ∘C, and the highest temperatures have been measured and modelled
since 2000 at both study sites. We observed a seasonality of displacement,
with increasing velocities during late winter and early spring and the highest
velocities in June, probably related to water pressure variations during
snowmelt. The displacement rates of Gámanjunni-3 rockslide co-vary with
subsurface resistivity and modelled ground temperature. Increased
displacement rates seem to be associated with sub-zero ground temperatures
and higher ground resistivity. This might be related to the presence of
ground ice in fractures and pores close to the melting point, facilitating
increased deformation. The study demonstrates and discusses the possible
influence of permafrost, at least locally, on the dynamics of large rock
slope instabilities.
Introduction
Permafrost or permanently frozen ground is a globally widespread phenomenon
and covers ca. 15 % of the Northern Hemisphere land surface (Obu et al.,
2019). Permafrost is purely thermally defined, with ground temperatures
below 0 ∘C over at least 2 consecutive years (Williams and Smith, 1989). In southern Norway, permafrost is widespread above ca. 1500 m a.s.l. and in northern Norway above ca. 800 m a.s.l. (e.g.
Gisnås et al., 2016a). In steep rock walls, permafrost is located
several hundred metres lower then these values (Magnin et al., 2019),
and many rock faces in Norway are within or close to the mountain permafrost
limit. Furthermore, steep rock walls efficiently cool the ground and its
surroundings because of low or lacking snow cover (Myhra et
al., 2017), and they maintain strong thermal gradients in transition areas
compared to more snow-covered regions, forming environments of more intense
frost weathering (Myhra et al., 2019). While permafrost degradation in
the lowlands of the Arctic is mainly associated with ground ice melt (Hjort et al., 2018) and/or release of greenhouse gases (Schuur
et al., 2015; Davidson and Janssens, 2006; McGuire et al., 2010), slope
instability is the major concern in mountain areas (Haeberli et al.,
2010; Gruber and Haeberli, 2007). An increase in rockfall and rockslide
activity has been documented following atmospheric warming (Gruber and
Haeberli, 2007; Ravanel et al., 2010; Fischer et al., 2012; Frauenfelder et
al., 2018; Ravanel et al., 2017). Furthermore, the increase in sub-zero rock
temperatures reduces shear strength in steep slopes by affecting the
strength of intact rock, ice and rock–ice interfaces
(Krautblatter et al., 2013; Mamot et al., 2018). The specific
sensitivity of metamorphic rocks similar to those investigated in this study
for temperature-dependent weakening of the rock–ice interfaces has recently
been demonstrated (Mamot et al., 2021) and is complemented
by rock fatigue in zones with transitional rock freezing (Jia et
al., 2015; Mamot et al., 2018). Recently, large rockslide detachments in
Karrat Fjord, western Greenland, were associated with permafrost degradation
(Svennevig et al., 2020).
Large rockslides are the most destructive processes in terms of single-event
landslide disasters (Evans and DeGraff, 2002) and caused massive
destruction and loss of life in historic times, hitting waterbodies and
causing displacement waves or filling valley bottoms (Hermanns et al., 2013b, 2014; Svennevig et al., 2020). The Norwegian
Geological Survey has systematically mapped relevant areas over most of the
Norwegian high-relief land area for such potentially destructive unstable
slopes and classified them according to their risk (Hermanns et al.,
2013a; Majala et al., 2016). Seven unstable rock slopes have been identified
as high-risk objects based on their risk to cause loss of life and are
therefore permanently monitored. At least two of them are situated within
the permafrost realm or close to the lower limit of mountain permafrost in
Norway: Gámanjunni-3 in Kåfjord–Troms, northern Norway
(69.5∘ N, 20.6∘ E), and Mannen in Romsdalen, southern
Norway, (62.5∘ N, 7.8∘ E). Both sites were deglaciated
prior to the Younger Dryas (ca. 12 ka) and showed initial displacement long
after deglaciation, with calculated ages from ca. 7–8 ka at Mannen and ca. 6.6–4.3 ka at Gámanjunni-3 (overview in Hilger et al., 2021). Paleo-slip-rate variation during the Holocene and slip initialisation have been
discussed in relation to Holocene permafrost dynamics at these sites
(Böhme et al., 2019; Hilger et al., 2021), and it is demonstrated
that present movement rates are much higher than the estimated average
rates during the Holocene. While Vick et al. (2020) mostly relate these
instabilities to structurally controlled rock slope deformation, we
hypothesise that these higher rates might be influenced in addition by a
change in the ground thermal regime and thus permafrost dynamics since the
onset of atmospheric warming after the Little Ice Age (LIA).
This study evaluates the permafrost conditions and recent thermal
development in these two unstable slopes of Norway. We present updated
movement and rock wall temperature data, electrical resistivity tomography
(ERT) combined with seismic refraction tomography (SRT), and
numerical modelling of recent thermal behaviour of the unstable rock slopes.
Setting
The study focusses on two main sites monitored by the Norwegian Water and
Energy Directorate (NVE) since 2009 (Mannen) and 2016 (Gámanjunni-3) (Fig. 1) (Blikra et al., 2016). Both sites are located
at steep, glacially over-deepened valley sides and were presumably ice-free
during the Younger Dryas (e.g. Hughes et al., 2016), facilitating
thick permafrost aggradation during the late Pleistocene and early Holocene (Myhra, 2016; Hilger et al., 2021).
Gámanjunni-3 (Troms and Finnmark county)
Gámanjunni-3 is located in northern Norway on the west-facing slope of
the glacially eroded Manndalen valley. The instability consists of a
garnet-bearing quartz–mica schist from the Caledonian orogeny (Henderson
and Saintot, 2011). Gámanjunni-3 is interpreted as one instability of 26 Mm3 of rock (Figs. 1 and 2a). Two joint surfaces delimit a wedge in
the form of a large block which has already descended by 150 m. The two
sliding planes, oriented 217/51∘ and 305/58∘, are
dipping steeper than the slope, cutting the regional foliation, which is
oriented 312/8±13∘ (Böhme et al., 2019). The
movement vector of the wedge dips 45∘ with a rate of 5 cm a-1, while the toe moves shallower at 4 cm a-1. The rockslide is
moving as one wedge-shaped block that is heavily fractured in the lower
part, with a large boulder talus at the base and a lobate boulder
accumulation along the southern flank. This boulder accumulation forms a
rock-glacier-like landform (Figs. 1b and 2a) (Eriksen, 2018) and
is discussed in more detail later.
The mean annual air temperature (MAAT) was -3.2∘C during
2016–2020 on the top plateau at 1200 m a.s.l. The MAAT during the 1961–1990
normal period was -4.3∘C (Lussana et al.,
2018; Saloranta, 2012) and thus considerably cooler than in the recent years.
During the 4 years of meteorological data, mean annual precipitation was 655 mm. The ground is usually snow-covered from November until June, with an
approximate thickness of 1 m. The site lies in the discontinuous mountain
permafrost region of northern Norway, and permafrost has been modelled or
even measured within the slip face of the unstable rock slope (Magnin et
al., 2019; Farbrot et al., 2013; Gisnås et al., 2016a; Obu et al., 2019).
Mannen (Møre and Romsdal county)
The Mannen rockslide is situated in the Romsdalen valley on a north-facing
slope between 900 m and ca. 1300 m a.s.l. (Fig. 1). The glacially
over-steepened Romsdalen valley cuts through mountains comprised by gneisses
that formed during the Caledonian orogeny (Saintot et al., 2012). The
instability consists of an intensely folded high-grade metamorphic unit with
alternating sillimanite and kyanite layers, amphibolites, and pegmatites
(Saintot et al., 2012). There is an exposed slip surface or back
scarp building up a 20 m high rock wall and ending in a mostly snow-filled
deep rock fracture (Fig. 2b). The valley floor of Romsdalen is covered by
15 large postglacial rock slope failures. Below Mannen, six to nine rockslide
deposits are mapped, three of which occurred in the first millennia after the
deglaciation, and three to six slides are inferred to have been climatically triggered during a
climatic phase with increased precipitation following the Holocene Thermal
Maximum (Hilger et al., 2018). A smaller rockslide, Veslemannen, on the western
flank of Mannen occurred in September 2019 (Fig. 2b) after episodic
acceleration over several years, leading to numerous evacuations of the
local population living below Mannen (Kristensen et al.,
2021). Mannen was previously proposed as a translational failure
(Henderson and Saintot, 2007) and wedge failure (Dahle et al., 2010).
Two scenarios define the Mannen instability (Dahle et al., 2008), with
the largest having no detected movement. Scenario B is approximately 10 Mm3 of rock with displacements of 5 mm a-1 to north dipping
20∘. Scenario C has displacements of 2.5 cm a-1 dipping
60∘, which is steeper than the topographic surface, and possibly
sinking into a graben structure.
Since the installation in 2010, the meteorological station on top of the
Mannen plateau has measured an average annual precipitation of 1250 mm and mean
air temperature of -0.5∘C. During the last normal period of
1961–1990, the MAAT was -1.3∘C at the Mannen plateau.
Atmospheric warming is therefore evident at this site during the last
decades. The plateau is usually covered by a 2 to 3.5 m thick snow cover
during the period November–June. The site lies at the lower limit of
mountain permafrost, where permafrost can be expected in shaded patches or
deeper fractures (Magnin et al., 2019; Gisnås et al., 2014, 2016a; Westermann et al., 2013). Recent modelling for the small
rockslide Veslemannen indicated at least deep seasonal frost and a thermal
influence on the dynamics of the rockslide (Kristensen et
al., 2021).
Methods and data processing
This study uses various data series from different measurements related to
climate, rockslide movement, thermal regime and subsurface conditions. All
locations of the devices and profiles used in this study are given in Fig. 1.
Movement of the rock slopes
For Gámanjunni-3, the real-time monitoring was initiated in 2015 and includes Global
Navigation Satellite System (GNSS) antennas, crack meters, extensometer, a
laser to measure distances to a reflector plate, a meteorological station, a
ground-based interferometric synthetic aperture radar system (GB InSAR,
sensitive to displacement towards the valley floor along the radar
line of sight – LOS) and web cameras. In addition, three satellite corner
reflectors were installed in 2012, and their displacement measured along
satellite LOS (ascending: down and towards east, descending: down and
towards west) is currently being operationally monitored using Sentinel-1
satellite-based InSAR. A time series InSAR methodology based on the GSAR
software (Larsen et al., 2005; Lauknes et al., 2010; Eriksen et al., 2017)
was used to estimate displacement rates. From snow-free scenes with a
revisit period of 11 d acquired from ascending and descending satellite
geometry, two stacks of interferograms were produced using GSAR. Mean yearly
velocities from both TerraSAR-X stacks (2009–2014) were combined to a 2D
InSAR displacement vector surface (12×12 m ground resolution) with
enhanced sensitivity to displacement in the east–west up–down plane. For
details on processing, verification and limitations, see Eriksen et al. (2017).
For Mannen, the real-time monitoring was initiated late in 2009. The continuous
monitoring includes GNSS antennas, distance measurements with two lasers,
extensometers, two deep borehole instrumentations, a meteorological station,
web cameras and two GB InSAR systems. For this study, we use some selected
GNSS monitoring stations, the laser monitoring, the GB InSAR and the
satellite corner reflectors to evaluate changes in movements of the unstable
slopes. The location of the systems used in this study are given in Fig. 1b.
The distance laser sensor used at both sites is a Dimetix DLS-B 15, which
measures with an accuracy of 1.5±1 mm in good weather conditions. The
laser device registers 10 measurements per second, which are averaged
every 10 min. The distance measured is in LOS, which may deviate from the
true displacement vector direction, and daily averages are shown and used.
The Trimble NetR9 GNSS Reference Receiver with a Trimble Zephyr 2 antenna
measures position continuously and processes an average position every 12 h. The standard deviation calculated for a period between 1 August 2016 and
1 September 2020 is ±0.86 and ±0.69 mm in the north and east direction, respectively, and
±1.89 mm vertically. However, one of the permanent points located outside
the unstable section of the slope showed movement because of water intrusion
under the foundation; hence, the time series with reliable data is short.
All measurements included uncertainties and white noise in the data. To
reduce these effects, we calculated daily averages of movement rates and
filtered the data with a moving average filter, with variable window sizes.
This procedure allowed for identifications of long-term displacement trends
and possible seasonal variations of movement.
Measured and reconstructed rock wall temperatures
During 2015, five temperature data loggers (Geoprecision, M-Log5W-ROCK) were
installed in the back scarps of Gámanjunni-3 (three loggers) and Mannen (two
loggers), recording rock surface temperatures (RSTs) with a 2 h interval and
with an accuracy of ±0.05∘C (Magnin et al., 2019)
(Fig. 1b). The installation procedure followed the approach described by
Gruber et al. (2004). To avoid rapidly fluctuating surface
temperatures, sensors were placed at a depth of ca. 10 cm below the surface. We
also tried to place the loggers above ledges to minimise snow influence
(Magnin et al., 2019).
Automatic data loggers (Hobo and iButton) were placed on the
Gámanjunni-3 rockslide and rock glacier in 2013 and 2014, measuring
ground surface temperatures (GSTs), i.e. temperature below the snow cover,
and temperatures in air-filled voids between crushed blocks below the
surface (Eriksen, 2018). The GST loggers are distributed in three
clusters over the rockslide, with data points on the moving block, the rock
glacier and the toe area of the rockslide; they are maintained by NVE today
(Fig. 1). At the Mannen site, data loggers were placed on the plateau to
measure GST (Fig. 1) between fall 2015 and 2018. Below the plateau in the
upper part of Veslemannen, which failed in 2019, four TinyTag (Gemini) temperature
loggers were placed in fractures during two winter seasons in 2014–2015 and
2015–2016. The aim of these measurements was to record the temperature at
the interface between the ground surface and snow cover (bottom temperature of
snow – BTS) when the snow cover was established. These data provide
valuable additional thermal information on the rockslide and are used to
compare numerical temperature modelling and geophysical investigations for
permafrost mapping.
Both sites are equipped with automatic weather stations, measuring surface
air temperature (SAT), precipitation (P) and snow depth. To reconstruct
temperature development since the end of the LIA at the study sites in terms of both SAT and RST, two strategies are followed: first, we used gridded
climate data (daily SAT and P) available for all of Norway at a ground
resolution of 1 km since 1957. The dataset, in the following called
“seNorge”, is established by interpolation between meteorological stations
(Lussana et al., 2018) and is operationally updated daily. Secondly,
for the period before 1957 until the start of the meteorological observation
period, which is during the end of the 19th century in Norway, data
from the weather stations on site and the rock wall loggers were combined
with long-term series from nearby stations using simple or multiple linear
regressions. For Gámanjunni-3, a good correlation with the Tromsø
weather station was obtained (Fig. 1a), where the data series started in
1867. For the Mannen site, we used both the stations in Dombås and
Fokstua in central southern Norway (Fig. 1a), where SAT measurements reach
back to 1864 and 1923, respectively. We considered R2 scores of above
0.7 sufficient to use these datasets to derive upper boundary conditions
for the numerical modelling.
Laboratory analysis of rock properties
In order to relate the resistivity results of the geophysical surveys to the
freezing transition of specific rock types and approximate frozen rock
temperatures, six representative rock samples from the study sites were
tested in the freezing laboratory at the Technical University of Munich. The
two samples from Gámanjunni-3 are fine-grained greenish gneiss with
indicated schistosity (density (ρ) 3.1 g cm3,
porosity ca. 0.7 %). Some layers contain a significant high proportion of
feldspar. The one sample from Nordnesfjellet (10 km NW of Gámanjunni-3)
is a dark grey fine gneiss to quartz-rich mica schist (ρ=2.8 g cm3, porosity ca. 0.6 %). Minor slightly weathered but
closed clefts in different orientations and the anisotropy due to foliated
minerals account for certain deviations in the measured laboratory arrays.
These correspond to variations in the field where small-scale changes in
meta-sediment rock types appear. From Mannen, the three greenish to dark
grey gneiss samples are medium-grained with dark and light bands of biotite,
quartz and feldspar. The sample Mannen03 is coarser with a higher proportion
of feldspar minerals that are centimetres large and therefore pronounced white bands.
The method of the resistivity calibration follows Krautblatter et al.
(2010). The samples had a cuboid shape of ca. 20×20×30 cm and a mass of 20 to
45 kg. All blocks were submerged in undisturbed tap water
(473 µS cm-1 conductivity) in atmospheric pressure for at least 72 h to
approach close to natural fluid saturation and chemical equilibrium with the
pore-surrounding rock material. Each sample was equipped with three lines (L=21 cm) of four M6 stainless-steel screws in a Wenner-type array to
calculate resistivity assuming an undisturbed half-space measurement
geometry as the half-space with the median depth of investigation controlled
by electrode spacing is significantly smaller than the sample dimensions. To
overcome the challenge of loss of electrical contact upon freezing, the
electrodes were fitted tightly ca. 10 mm deep into the rock. Contact grease
was applied to the electrodes in order to further improve galvanic contact.
Two Greisinger GMH 3750 thermometers were put in each specimen (5 and 20 mm depths) to record both the near-rock surface temperature and the temperature
at the mean depth of investigation (Barker, 1989) every 30 s. We used
an ABEM Terrameter LS, operating in monitoring mode, to obtain resistivity
measurements every 15 min while the rock specimens were going through a
freeze–thaw cycle between 10 and -5∘C in a 1 m3 cooling box equipped with a specially designed Fryka
TK1041-LK-s ventilated cooling system controlled by a temperature probe
close to the sample. The cooling rate was controlled manually to not exceed
a temperature gradient of more than 1 K between the temperatures at the rock
surface and at the mean depth of investigation. We used a low minimum current of
0.1 mA and high maximum voltage of 600 V to allow measurements even at high
resistances supported by the high internal resistance of the ABEM
Terrameter. Variance between repeated measurements (stacks) in the critical
temperature interval of -2 to 2 ∘C was well below 1 %.
Field ERT and refraction seismic tomography
We used non-invasive geophysical surveys along profile lines in order to map
permafrost at the individual sites and provide information on possible
ice-rich or ice-poor zones in the ground. We used electrical resistivity
tomography (ERT) at all sites and in addition refraction seismic tomography
at Gámanjunni-3.
The electrical resistivity distribution of the subsurface is evaluated by
injecting a current and measuring the resulting electrical potential
differences along the profile. The investigation depth depends mainly on the
distances between the current electrodes employed along the profile and the
profile length, with larger distance giving greater penetration depth. The
obtained apparent resistivity measurements have to be inverted using
suitable inversion algorithms yielding the specific electrical resistivity
distribution along the 2D profiles. High electrical resistivity is normally
associated with either frozen conditions and ground ice occurrences or dry
blocky layers. Low electrical resistivity points to (high) liquid water
contents and unfrozen conditions (Hauck, 2002). At Gámanjunni-3,
ERT is combined with seismic tomography. Seismic shots along the profiles
produce P-waves, the velocity distribution and resulting travel times of which are
used and applied in a subsequent data inversion. The combination of ERT and
SRT is used to quantify to what extent the subsurface pores
are filled with ground ice, water or air (Hauck et al.,
2004; Mollaret et al., 2020) by applying the four-phase model (4PM) (Hauck et
al., 2011). The 4PM is based on both ERT and SRT
surveys. The combination of both methods is able to distinguish between ice
(high resistivity and medium P-wave velocities), water (low resistivity and
P-wave velocities) and air (high resistivity, low P-wave velocities). For
modelling details, we further refer to Hauck et al. (2011) and Mewes
et al. (2017).
Electrical resistivity tomograms included in this study. Provider
refers to the institution involved in the ERT survey. For G-NVE2 co-located
ERT and seismic profiles were re-analysed by Hauck and Hilbich (2018).
Site/nameLengthSpacingElevationProtocolInst.ProviderReference[m][m][m a.s.l.]G-NVE11150101080–522GradientPlus_1ABEM SAS4000NGUBöhme et al. (2016)G-NVE210359690–771Wenner, Schlumberger, seismicsAGI STINGNVEGSA (2016), Hauck and Hilbich (2018)G-EDY154051096–1166WennerABEM LSEDYTEM/UiOThis studyG-EDY26005970–1195WennerABEM LSEDYTEM/UiOThis studyG-TUM-S1 to –S430051180–1230WennerABEM LSTUMLeinauer (2017)G-TUM-E1 to –E440051220–1200WennerABEM LSTUMLeinauer (2017)M-NGU800101254–960ABEM SAS4000NGUDalsegg and Rønning (2012)M-TUM-scarp50051300–1250WennerABEM SAS1000TUMThis studyM-RW120051270–1245WennerABEM LSEDYTEM/UiOThis studyM-RW216021279–1252WennerABEM LSEDYTEM/UiOThis studyM-RW320051279–1236WennerABEM LSEDYTEM/UiOThis studyM-RW420051271–1238WennerABEM LSEDYTEM/UiOThis study
The ERT profiles at Gámanjunni-3 and Mannen were either located on the
plateaus, along the valley slopes or in the rock walls. In the rock walls we
used steel screws drilled into the bedrock as electrodes, while outside the
rock walls, normally steel rods were used. All measurements were carried out
during late summer. At the Gámanjunni-3 site, four major datasets were obtained between
2012 and 2019, while at the Mannen site, two major datasets were collected in 2012
and 2018, respectively. Locations and details of the profiles are given in
Fig. 1b and Table 1.
ERT data acquisition was conducted with ABEM Terrameters (SAS1000 or LS)
using Wenner or Wenner–Schlumberger protocols, with the Wenner protocol
providing the best signal-to-noise ratio in difficult rock wall terrains
(Dahlin and Zhou, 2004). All ERT profiles were inverted using common
inversion parameters within the software Res2Dinv (Loke and Barker,
1995). The colour coding followed the values obtained through the
temperature-dependent resistivity analysis performed in the freezing lab of
TUM (see Sect. 4.1), and three to five inversion iterations showed sufficient
convergence without overfitting. For profiles G-NVE1 and G-NVE2 at
Gámanjunni-3 (Fig. 1b) the 4PM was applied.
Bottom temperature of snow (BTS) survey
BTS measurement is a simple and rapid method to estimate the possibility of
permafrost conditions in the field. The principle is that during the late snow
season, under a snow cover of at least 80 cm or more, the temperature under
the snow cover is decoupled from the temperature in the atmosphere and is hence
governed by heat flow from the ground (Haeberli, 1973). BTS values
below -3∘C indicate a high probability of permafrost, while BTS
above -2∘C indicates no permafrost. This method has been widely
used and validated in mountain areas, especially since the 1980s, and has
also been used in Norwegian mountains for local permafrost mapping
(e.g. Isaksen et al., 2002; Brenning et al., 2005; Lewkowicz et al., 2012).
At both Gámanjunni-3 and Mannen BTS surveys were carried out on 9
and 1 March 2017, respectively (Fig. 1b). The survey was done using a
long stick with a thermistor mounted at the bottom. At each site the stick
is penetrated through the snow, and the BTS temperature is registered using
a standard multi-meter. At least two measurements are carried out at each
site to address small-scale variability.
Ground temperature modelling
The transient heat flow model CryoGrid 2D (Myhra et al.,
2017) solves the two-dimensional heat diffusion equation. The thermal
properties (e.g. volumetric heat capacity and thermal conductivity) depend on
temperature and material type. We used the MATLAB-based finite-element
method MILAMIN package (Dabrowski et al., 2008). CryoGrid 2D
models conductive processes, and thus non-conductive heat flow processes such as
convective water or airflow are neglected. The model domain is constructed
as a 2D slice through a slope up to a chosen depth. An unstructured
triangular mesh is generated for various subsurface thermal regions, i.e.
regions with a distinct combination of water (liquid and ice), mineral,
organic and air volumetric contents. The maximum allowed triangle area,
which is a measure of the spatial resolution, typically increases with
depth and is assigned to every thermal region. We used bedrock thermal
conductivity of 2.5 Wm-1 K-1 for both Mannen and Gámanjunni-3
slopes. Along the right and left boundaries we prescribe zero-flux boundary
conditions. The lower boundary (at a depth of 6000 m) is defined by a geothermal
heat flux of 50 m Wm-2 (Slagstad et al., 2009).
The upper boundary conditions are GST time series for the surface nodes. To
calculate GST at each node, we first used SAT extracted from seNorge for elevations
between the valley bottom and top plateau at both sites, where SAT is linearly
interpolated between the surface nodes, following a lapse rate of 6.4 ∘C km-1 for Mannen and 4.8 ∘C km-1 for
Gámanjunni-3 (Magnin et al., 2019). We subsequently estimate GST
using N factors between 0 and 1 that link SAT and GST, hence accounting for the surface
offset (Riseborough et al., 2008). The Nf factor describes the winter
surface offset due to snow coverage; values close to 1 indicate little to no
snow coverage, while values closer to 0 indicate a thick snow cover.
Nt factors relate surface offsets during summer, which depend on factors
such as vegetation cover, direct solar radiation and shading, albedo, and soil
moisture. We applied empirical results derived from snow studies in Norway,
relating Nf factors to annual mean snow height (Gisnas et al.,
2013, 2016a). In our modelling we assume Nf=1 for
steep rock walls (slope >60∘) that are frequently
snow-free, whereas values of 0.25–0.5 can be used on the mountain plateaus
(slope <30∘), where snow cover is thicker depending on
precipitation and wind redistribution (Gisnås et al., 2016a).
For the plateau, Nf was set to 0.5 on Gámanjunni-3 and 0.3 at Mannen
due to higher snow cover at the latter site. The intermediate values of
Nf are used at slope gradients between 30 and 60∘.
Temperature–resistivity plots of all successful test series for
rock samples from (a) Gámanjunni-3 and Nordnes as well as (b) the
Mannen plateau. The red rectangles denote the transition zone between frozen
and unfrozen conditions defined based on these laboratory tests. These calibrations are
used for plotting in Figs. 8, 9, 10, 12, B1 and B2.
The 2D geometry of the model domains has been extracted from a gridded 1 m digital elevation model (https://www.hoydedata.no, last access: 1 November 2020) along an approximately west–east
(Gámanjunni-3) or south-west to north-east transect (Mannen) (Fig. A1). There are normally larger temperature gradients close to the surface
than in deeper layers. Hence, we constructed nodes with a distance of 0.05 m at the upper boundary. The subsurface thermal regions are constructed
according to the geological profile for Gámanjunni-3 (Fig. 2) and our
mapping of surficial sediments along the profile using orthophotos for
Mannen (Fig. A1). We then applied a stratigraphy, i.e. volumetric contents
of the ground constituents, for the various surficial sediment classes at
both the surface and depth as presented in Westermann et al. (2013)
(Fig. A1).
For both sites, the model was initialised at deglaciation. When we assume
warm-based conditions at the bottom of the ice sheet (0 ∘C), we
used the methods to reconstruct deglaciation curves and climate data
described by Hilger et al. (2021). We ran the model yearly until
1 September 1873, then at weekly time steps, and in the period
1 January 2000–31 December 2018 at daily time steps.
Measured and reconstructed rock wall (RW) surface temperatures and
SAT on the plateaus at (a) Gámanjunni-3 and (b) Mannen in different
topographic aspects (N: north, for example). The temperature records show the
differences in topographic aspect, with higher differences during spring and
summer for the different aspects. (c) Reconstructed long-term annual
average RW temperature for selected RW loggers at Gámanjunni (Gá) and
Mannen (Ma) since 1870. The series show inter-annual variability and
increasing mean temperatures of 1 ∘C or above for the 150-year
period. The rockslide and RW temperature monitoring period since 2011 is
indicated by the shaded area and denotes some of the highest temperatures
during the 150-year period.
ResultsLaboratory analysis
The laboratory analysis relates rock temperatures to measured electrical
resistivity. The rock samples from Gámanjunni-3 showed a similar
pattern, with a sharp resistivity increase between 20 and 40 kΩm at
the equilibrium freezing temperature of ca. -0.5∘C (Fig. 3a). For
areas with electrical resistivity above this range we expect negative
temperatures, and below we expect unfrozen conditions. The rock samples from
Mannen revealed a sharp increase in resistivity below the equilibrium
freezing temperature of ca. -0.3∘C, depending on bedrock type and
freeze or thaw setting (Fig. 3b). The sharp increase in resistivity was
between 15 kΩm and close to 50 kΩm, a range we defined as
the transition zone between freezing and thawing conditions.
Gámanjunni-3Temperature monitoring and reconstruction
The three rock wall loggers at the unstable slope are all located at ca. 1200 m a.s.l. and oriented towards south (RW-S), north (RW-N) and north-west
(RW-NW) (Fig. 1). The RW-S site showed average rock surface
temperatures of 0.05 ∘C between 2015 and 2019, while the two
other loggers had clearly sub-zero temperatures of -1.6 and
-1.3∘C for RW-N and RW-NW, respectively (Fig. 4a). During the
same period mean SAT on the plateau was -3.1∘C, showing that
rock wall temperature was at least 1.5 ∘C higher than air
temperature. For the south-oriented rock wall, temperatures close to 3 ∘C higher than SAT on the plateau were recorded. The measured RW
temperatures represent a period of high temperatures in comparison to the
reconstructed RW temperatures since 1870, as shown in Fig. 4c. At
Gámanjunni-3, the north-exposed logger showed sub-zero mean annual RW
temperatures during the whole reconstruction period, while for RW-S positive
annual averages were mostly estimated since 2000, along with some years
during the 1930s. The reconstructed long-term series clearly demonstrate the
warming since the LIA, which increased by between 1 and 1.2 ∘C for Gámanjunni-3 and Mannen, respectively.
The GST loggers placed in the rockslide area (Fig. 1b) showed mostly
average annual temperatures below 0 ∘C, with some exceptions.
Average annual temperatures on the toe of the rockslide at ca. 750 m a.s.l.
revealed values between -1 and -1.5∘C, which
normally indicate high permafrost probability. On the rock glacier, annual
GST values are higher and between -1 and 0 ∘C. Close
to the moving block at ca. 1050 m a.s.l. a mean annual GST of -2∘C
is measured (Eriksen, 2018).
The few BTS measurements available (Fig. 1b) all showed values below
-3∘C. These observations altogether place the site in the
discontinuous mountain permafrost zone (Magnin et al., 2019; Farbrot et
al., 2013; Gisnås et al., 2016a).
Displacement measurements at Gámanjunni-3 (a–d) and Mannen
(e, f). (a) Cumulative displacement rates from the three satellite corner
reflectors on Gámanjunni-3, showing average annual displacement rates
between 35 and 47 mm a-1 along satellite radar LOS. (b) Residuals from the
linear trend for SAT2 (upper) and SAT3 (lower). We fitted a third-order
sinusoidal curve (red line) to the residual points. The fit indicates annual
variation and a trend towards negative residuals until 2018. (c) Cumulative
displacement along GB radar LOS derived at a total of 18 points dispersed over
the rockslide (RS) and rock glacier (RG) area (Fig. 1) based on GB InSAR. The
green shaded envelope shows the RS points, and the light blue envelope indicates
the RG points. Velocities between 10 and close to 600 mm a-1 are
encountered. (d) Average daily displacement averaged over a month along
GB radar LOS for one GB InSAR point at the rock glacier (blue bars) and a point at
the rockslide area (green bars). For each year the months between June and October are
shown. The graph shows the highest velocities early in the melting season and the
highest absolute velocities in 2017. (e) Mannen: cumulative displacement
rates for GNSS3 and Laser1, plotted with SAT since 2010. There are obvious
acceleration phases (some indicated by ellipses) during early summer
(May–June). (f) Residuals from the linear trend for Mannen Laser1 (red line)
against MAAT deviation between 2010 and 2020 (green bars) as well as snow depth
(purple bares) for the months March through May. There is a clear decrease
in displacement rates between 2013 and 2017, which seems to be related to higher
air temperatures and lower snow coverage.
For Gámanjunni-3, continuous laser and GNSS measurements are
available from 2018; however, the data are too short for assessing long-term
variations. The three satellite corner reflectors on site provided a
continuous data series since 2015 based on Copernicus Sentinel-1 data. They
show a homogenous movement of between 35 and 47 mm a-1 along satellite
radar LOS (Fig. 5a). The residuals from the linear trend clearly show
seasonal variations with higher velocities during early spring and summer,
with the largest negative residuals during winter 2017–2018 (Fig. 5b). Time
series derived from GB InSAR at all 18 points revealed velocity
variations between 160 and 580 mm a-1 along GB radar LOS for the 10
points on the rock glacier and between 12 and 290 mm a-1 for the 8
points in the rockslide area (Fig. 5c, d). The data showed a clear
seasonality, which is attributed to the insecurity of the data gathered when
the ground is snow-covered. Monthly velocities during the snow-free months
revealed in most cases (1) higher displacement rates early in the melting
season than later and (2) the highest summer velocities during 2017 for both
the rockslide and the rock glacier part of the instability (Fig. 5d).
According to the RW and SAT observations, 2017 was a particularly warm year,
and RW-S shows above-zero mean annual RW temperatures (Fig. 5c). The
distribution of velocity over the rockslide area shows relatively similar
velocities over most of the body including the sliding block of 40–80 mm a-1, decreasing rapidly towards the slide front at 600 m a.s.l.
(Eriksen et al., 2017) (Fig. 6a, b). The highest velocities are obtained
on the rock-glacier-like landform forming the southern part of the
instability, with surface velocities of >100 mm a-1 (Fig. 6b). GB InSAR revealed similar displacement patterns as the TerraSAR-X data
(Fig. 6a).
Numerical modelling
The temperature field revealed by the 2D temperature modelling clearly
showed permafrost conditions in the slopes of Gámanjunni-3 down to
600–700 m a.s.l. at the end of the 19th century, which includes most
of the moving unstable part of the slope (Fig. 7a). Since the end of the
LIA, permafrost has warmed and degraded at its lower boundaries (Fig. 7b),
and today probably only around half of the moving part of Gámanjunni-3 is
influenced by permafrost, while the lower parts are modelled to be
permafrost-free today (Fig. 7c). On the plateau, maximum snow cover is
around 1 m thick, while the steep rock walls
are snow-free. Snow cover and water content are sensible parameters for the
modelling, modulating the permafrost temperature and geometry, as shown in
the sensitivity tests provided in the Appendix (Fig. A2). A maximum
permafrost thickness of ca. 300 m is modelled, which is in agreement with
similar settings in which we measure deep permafrost temperatures, such as in
Tarfala in northern Sweden or Juvvasshøe in southern Norway
(Isaksen et al., 2001). The lower permafrost boundary is modelled
to be relatively stable during the 150-year period, demonstrating that
relative thick permafrost can be expected in places.
Modelled mean annual ground temperature for Gámanjunni-3 (a–c)
and Mannen (d–f) for three different years (1900, 1970 and 2018). The
stippled line denotes the instability at Gámanjunni-3 based on Böhme
et al. (2016). The black solid lines in the plots show the 0 ∘C isotherm. For parameterisation and sensitivity plots, see Figs. A1 and
A2.
Geophysical surveys
The two long profiles down the slope from the moving block at ca. 1050 m a.s.l. (G-NVE1, Fig. 8a) and along the slope at ca. 750 m a.s.l., crossing a
rock-glacier-like feature (G-NVE2, Fig. 8b), show consistent patterns (see
also Fig. B1b). General resistivity values of the unfrozen and intact
bedrock at depth seem to be around 1–10 kΩm. Surface resistivity
values in the downslope profile show a maximum of 700–900 m a.s.l.
(40–100 kΩm) and further decrease to below 2 kΩm towards
lower elevation (Fig. 8a). This altitudinal transition roughly coincides
with the numerical temperature modelling (see Fig. 7c). The profile G-NVE2
is oriented from south to north (Fig. 8b). Both profiles show maximum
resistive surface layers of up to 50 m in thickness. In combination with the
GST values by Eriksen (2018) and NVE this resistive near-surface
layer could indicate permafrost patches. The overall resistivity values
within the rock glacier are lower (10–20 kΩm), and the more
resistive surface layer is somewhat shallower (ca. 25 m) compared to the
rockslide part in the centre of the profile.
The 3D profiles (G-TUM-S1-S4 and G-TUM-E1-E4) on the plateau clearly
demonstrate the cooling influence of the NW-oriented rock wall, which
becomes less pronounced with distance from the rock wall (Figs. 9a–c, B1b). In addition, low-resistivity areas (<20 kΩm)
are visible, probably indicating thawed conditions associated with
water-filled fractures and cracks in prolongation of the exposed sliding
surfaces (Fig. 9a, b). These discontinuities oriented parallel and
perpendicular to the profiles may account for differences in overlapping
tomograms. The east-oriented profiles (TUM-E) are clearly influenced by the
SW-oriented rock wall, with generally lower resistivity compared to TUM-S
close to the NW-oriented rock wall (>60 kΩm) areas,
which are highly influenced by the rock walls (Figs. 10, B1c).
The G-EDY1 ERT profile crosses the south-exposed rock wall and shows lower
resistivity values close to the rock wall surface (<20 kΩm), decreasing towards the north side of Gámanjunni-3 (Fig. 10a). The
transition between the rock wall and the moving block below is covered by
blocky scree material and shows high resistivity (>100 kΩm) (Fig. 10a). The G-EDY2 ERT profile transverses the NW-oriented rock
wall, with higher resistivity at the surface, clearly indicating the
temperature differences between the two rock faces (Fig. 10b). Also here,
high-resistivity patches are found under the moving block and the cooled
rock wall, while lower resistivity values are found under the snow-covered
plateau (<15 kΩm) (Fig. 10b). The moving block is an area
of high resistivity, with either possible permafrost influence or the
presence of air-filled fractures. These higher values are also visible at a
cross-profile over the structure (G-TUM block) (Fig. 10c).
The long ERT profiles for Gámanjunni-3. The colour scale
follows the laboratory analysis shown in Fig. 3 and is a logarithmic
scale. (a) G-NVE1, showing high-resistivity layers down to ca. 700 m a.s.l.
(box). The dashed line indicates the possible transition to solid bedrock.
(b) G-NVE2, the cross-profile over the rock glacier and the lower rockslide
area, indicated by the red boxes. The circles in both profiles indicate
the location and mean annual GST in the vicinity of the profiles based on
Eriksen (2018) and subsequent measurements (Gudrun D. Majala, NVE, unpublished data, 2020).
They show sub-zero temperatures in areas with high-resistivity surface
layers and higher values below 700 m a.s.l. The part of the profile used
for the four-phase model (4PM) is indicated in both profiles (Fig. 11).
ERT surveys over the back scarp at Gámanjunni-3: (a) G-EDY1,
which is oriented over the exposed part of the slip surface. While the rock
wall shows low resistivity, there is a clear transition towards the scree
and the moving block with considerably higher resistivity. (b) G-EDY2, which
is placed over the north-western exposed part of the rock wall. There are
significantly higher resistivities in both the rock wall and plateau, illustrating
that this side is more influenced by the cooler rock wall. For both
profiles, the locations of the rock wall loggers are indicated as circles.
(c) G-TUM block oriented NW to SE over the moving block below the slip
face. The resistivity is relatively high in relation to the plateau and
below the block.
The combination of ERT and refraction seismic tomography within the 4PM
revealed clear patterns in relation to possible permafrost and ice
saturation (Fig. 11, Hauck and Hilbich, 2018). At the G-NVE2
ERT profile, considerable ice content values of up to 50 %–80 %
saturation suggest permafrost conditions. We also see heterogeneities in
vertical and horizontal directions along the profile line (Fig. 11b). The
overall water contents are mostly low, except a possible fracture zone at
depth (horizontal distance 180–230 m) (Fig. 11a), showing greater ERT
heterogeneities and low seismic velocities (Fig. C1b). Such a pattern is
normally associated with high subsurface air contents. This kind of low
P-wave velocity (i.e. high air contents) at greater depths is not common and
more prominently discussed in reports concerning the original seismic
and ERT results of the area (GeoExpert, 2016). Unfrozen surface layers
with no ice along G-NVE2 for the uppermost 5–10 m are further suggested by
the analysis, while the northern part of the profile shows a higher ice
saturation within the upper 30 m (Fig. 11b). Finally, overall dry
conditions are suggested by modelled high air contents near the surface. The
overall ice content is probably low even if the model indicates high
ice saturation. This is related to the low-porosity bedrock (porosity ca. 0.7 %, Leinauer, 2017) in accordance with resistivity
values of only ∼10 kΩm, which are more atypical for
high ice contents (Fig. C1b). We prescribed a laterally homogeneous
porosity model in the 4PM, which probably led to an overestimation of ice
saturations due to low-porosity bedrock in the right-hand side of the
profile.
Along the slope of the instability (G-NVE1) the results also suggest
permafrost conditions. This is especially evident for the upper part of the
profile (Fig. 11a). We also could identify an unfrozen surface layer, even
if this feature is less visible due to geometry reasons, and a fracture zone
characterised by high air contents (150–280 m horizontal distance, Fig. 11a). We also note that the values for the geophysical profiles at the
crossing points of the two profiles are quite correspondent. There, the
transition between predominantly high ice saturations and high water
saturations (which could be interpreted as a transition zone between frozen
and unfrozen conditions) is at around a depth of 40–50 m in both cases. However,
here we also prescribed a gradient model for porosity which was homogenous
along the profile, so such transitions in the data could also be due to
change in material properties. However, we are relatively confident of the
reliability of our analysis, as the 4PM resulted in similar values at the
cross-over area of both profiles.
The results indicate permafrost conditions in both profiles with at
least 30–50 m thickness. In addition, strong heterogeneities, especially
regarding de-compaction and fracture zones, have been found, indicating
significant air contents at larger depths, which is seldom found in
thermally stable mountain permafrost bodies.
Saturation of pore space determined using the four-phase model (4PM)
based on Hauck and Hilbich (2018) for (a) the long profile along
the slope G-NVE1 and (b) the transversal profile G-NVE2. The total
saturation values for ice, water and air are given in relation to the
porosity prescribed in the uppermost plots for the respective profiles. The
model clearly indicates high ice saturation in parts of both profiles, thus
suggesting the presence of permafrost. The potential fracture zone discussed
in the main text is indicated by the black boxes. The possible unfrozen
layer is indicated in (b), while the possible lower permafrost boundary is
indicated in (a) for G-NVE1. Note that the tomograms are subsets of G-NVE1
and G-NVE2 and thus shorter than the profiles shown in Fig. 8.
MannenTemperature monitoring and reconstruction
The two rock wall loggers are oriented towards north (RW-N) and east (RW-E) (Fig. 1c). Both loggers showed positive annual average
temperatures during 2015 and 2019 of 1.2 and 2.6 ∘C, respectively (Fig. 4b). During the same period, the mean
air temperature on the plateau was 0 ∘C, showing that rock wall
temperature was at least 1 ∘C higher than air temperature. The
reconstructed RW temperature series since 1970 revealed above-zero
temperatures in the rock wall, with an increasing trend (Fig. 4c). The
north-exposed rock wall certainly featured sub-zero temperatures in some
cold years, such as in 2011.
GST loggers distributed along the rock scarp (Fig. 1b) showed mean GST
between 0.9 and 1.6 ∘C, showing the warming influence of the
thick snow cover. The TinyTag loggers in Veslemannen (Fig. 1c) recorded BTS
in fractures between -1.3 and -1.8∘C in late April–early May 2015. In late April 2016 the BTS recorded was between 0 and -2.3∘C. The mean temperatures recorded by these loggers are not
representative, as they all lack complete annual data, but have to be around
0 ∘C on annual average. These data are described in more detail
in Kristensen et al. (2021). Most of the BTS measurements were
conducted close to the edge of the back scarp. While the BTS values were
mostly below -2∘C behind the north-exposed scarp, BTS values
above -2∘C dominate behind the east-oriented edge (Fig. 1c).
The data confirm that permafrost patches likely occur along the plateau edge
(Magnin et al., 2019).
Surface displacement
For the GNSS and laser station velocities, values between 14 and 20 mm a-1
have been recorded since the start of the monitoring in 2010 (Fig. 5e). The data
indicate higher displacement rates during the start (2010) and the last
years of measurements, with a slowdown between ca. 2013 and 2016 and a
subsequent increase (Fig. 5f). Between 2010 and 2013 southern Norway had
cold winters (MAAT of -1∘C on Mannen at 1200 m a.s.l.) (Fig. 5g), while after 2013 air temperatures increased by 1 ∘C on
average (MAAT =-0.1∘C between 2013 and 2020). The slowdown
of displacement rates between 2013 and 2016 seems to be associated with a
lower snow cover during the winters of these years (Fig. 5f). In terms of
seasonal variations the cumulative movement plots indicate a stepwise
pattern, with higher velocities during spring–summer and lower velocities
during fall–winter (Fig. 5f). This is different to what was observed at
Veslemannen, where velocity accelerations started during the snowmelt period but were
much higher and more variable in the fall period and after heavy
precipitation events (Kristensen et al., 2021).
The distribution of velocities over the moving slope body was derived from
GB InSAR and shows the highest velocities in the upper part just below the back
scarp and the plateau of >20 mm a-1 (Fig. 6c). This
high-velocity area defines scenario C for Mannen (Fig. 1c).
Simulated ground temperatures
The temperature field revealed by the 2D temperature modelling indicates
possible permafrost conditions in the steep part of the slope during the
onset of modelling at the end of the LIA, with permafrost thicknesses
between 50 and 100 m depending on model initialisation procedure (Fig. 7d)
and snow cover parameters (Fig. A2b). During the 150 years of the model
run, steady warming reduced and degraded the modelled permafrost. However,
isolated patches might still be possible in the steepest part with less
snow, depending on model parameterisation in terms of snow coverage and water
content in the model domain (Fig. A2b). Today, deep seasonal frost is
modelled in the steep parts, which is coincident with the rock wall
measurements in the back scarp (Figs. 7f, 4b). The plateau is heavily
snow-covered, and frost penetration is only possible laterally from the
snow-free steep slopes.
Geophysical surveys
The ERT profiles at Mannen show generally higher resistivity than at
Gámanjunni-3, probably related to different background resistivity of
the bedrock and less surficial sediment cover. The 1 km profile (M-NGU;
Dalsegg and Rønning, 2012) covers both the plateau and the steep unstable
slope, and it showed comparatively low resistivity (10–40 kΩm) at
depth (probably indicating the resistivity of the unfrozen intact bedrock),
and higher resistivity at and below the scarp close to the surface down to
ca. 1150 m a.s.l. (50–>100 kΩm) (Fig. 12a). These high-resistivity areas reveal crushed air-filled and well-drained bedrock and may
contain permafrost patches (Dalsegg and Rønning, 2012). The ERT
profile along the crest (M-TUM1-scarp) shows decreasing resistivity from NW to SE
(Fig. 12b). High resistivity (>100 kΩm, possibly
indicating frozen conditions at depth) is observed close to the rock wall,
while low resistivity (<30 kΩm) dominates in the south-east,
where the profile departs from the crest, and in the upper ca. 20 m of the
profile. The highest values (>300 kΩm) are observed
around a deep crack delimiting one of the moving blocks at Mannen, which
defines a fractured zone with high porosity and unsaturated conditions
(Fig. 12b).
The rock wall profiles (M-EDY1-4) mainly show resistivities below 40 kΩm,
also at depth, on the plateau and higher resistivity (>50 kΩm) over the back wall and over the fracture between the back scarp
and the moving block (Fig. 12c–f). Again, the highest values are measured
below the back scarp over large fractures, which contain much air and are
possibly partly snow-filled and possibly ice-filled. An exception is the M-EDY2
profile (Fig. 12d), with high resistivity also obtained on the
plateau. This profile has 2 m spacing, giving a higher resolution close to
the surface, and therefore the coarse and high-porosity block cover on the
plateau might result in higher resistivity values.
ERT surveys over the Mannen instability; for location see Fig. 1 and for survey parameters see Table 1. (a) Along-slope profile (M-NGU)
based on Dalsegg and Rønning (2012). The possible weakness zones
described in Dalsegg and Rønning (2012) are indicated by dashed
lines. The near-surface high-resistivity area is indicated by a box; it may
reveal crushed air-filled and well-drained bedrock and may contain
permafrost patches (Dalsegg and Rønning, 2012). (b) M-TUM-scarp
profile along the rim on the plateau of Mannen above the exposed slip
surface. A strong transition of resistivity is indicated by a red line and
interpreted as a deep fracture that may be water-filled. Panels (c) to (f) show the ERT
profiles (M-EDY1-4) over the rock wall from the plateau into the instability
at various locations (Fig. 1). The circles show the mean annual rock wall
temperatures in the two loggers on site. The exposed back fracture below the
slip surface is indicated by dashed lines, while the back scarp is indicated
by a red dotted line.
DiscussionHypothesis and uncertainties
Both Gámanjunni-3 and Mannen are considered to be high-risk unstable slopes
(Hermanns et al., 2013a; Majala et al., 2016) and are continuously
monitored. The movement was initiated several millennia after deglaciation, and
thus climatic changes have been discussed as a factor influencing the
dynamics of the instability (Hilger et al., 2021). Surface
exposure dating shows that the current displacements of the slopes are larger
than the Holocene average (Böhme et al., 2019; Hilger et
al., 2021), indicating atmospheric warming as a likely influencing factor.
For both sites, we therefore hypothesise that permafrost warming and/or
degradation might be a substantial explanation for the temporal displacement
pattern.
Our study combines a variety of methods, ranging from point observations
(e.g. rock wall temperature measurements) via local surveys (e.g.
geophysical measurements) to larger-scale modelling along an entire slope
setting (e.g. geothermal modelling). Each method has uncertainties and
includes different pre-conditions representing many pieces of a puzzle to
form a consistent picture. For example, the heat flow modelling represents
the lower extent of possible permafrost at Gámanjunni-3, as indicated in
the ERT surveys, but does not represent local thawed areas and variations
indicated by the ERT.
The methods used are independently of each other and may be contradictory in
places, but they result in an overall explainable pattern. The temperature
modelling does not account for fractures and other structures in a rockslide
area (e.g. where water can penetrate); CryoGrid 2D is a two-dimensional
model purely based on heat conduction, which results in a smoothed and
simplified version of reality (Myhra et al., 2017, 2019).
The ERT profiles were measured in rough terrain with often poor coupling,
and both the resistivity values and data noise are very sensitive to cracks
and fractures, strong topographic variations, and local water penetration.
This leads to high variability of resistivity and may produce inversion
artefacts, such as in the transition between plateau and rock wall at
Gámanjunni (Fig. 10), which is also represented by the partly high
root mean square errors (RMSEs) of the inverted tomograms, which vary between
6 % and 20 %. Therefore, comparing ERT and a more large-scale temperature
model is not meaningful on a local site level. Our ERT and 4PM results for
Gámanjunni-3 clearly show potentially frozen areas within the rockslide
area, disappearing downslope. The potentially frozen areas are at a depth
of ca. 30–50 m, which is close to the results of the temperature modelling at
these places. However, locally thawed areas in the rockslides and possible
taliks as indicated in the ERT are certainly realistic but cannot be
covered by the simplified heat flow model.
Permafrost conditions and recent ground thermal development
At Mannen, we do not measure subsurface RW or GST temperatures below
0 ∘C on an annual average at present, except for shaded locations
in fractures (Kristensen et al., 2021). Over the last 140
years, MAAT has increased, and since the cooling in the 1970s the temperature
rise was around 1.5 ∘C (Fig. 4c). Rock wall temperatures
oriented towards north must have had sub-zero surface temperatures during
several periods of the last 150 years, indicating permafrost development in
the past in shaded topographic settings (Fig. 4c). This confirms the
modelling by Magnin et al. (2019) and the results from Kristensen et al. (2021) for Veslemannen, which indicate sporadic permafrost zones at
Mannen in certain locations such as fractures, snow-free patches and in
shaded locations. It is also well documented that cracks and fractures in
rock walls locally significantly decrease ground temperatures (Magnin et
al., 2015a; Hasler et al., 2011). This is also supported by the ERT surveys
showing the highest resistivity values close to the rock wall and large
fractures (high porosity), which may be partly filled by ice (Fig. 12).
However, there are no observations of ice in the fractures as in the Jettan
rockslide in northern Norway, where permafrost is observed and probably
influences seasonal kinematic variations (Blikra and
Christiansen, 2014). The thermal modelling indicates that permafrost patches
could develop at and below the upper scarp and that the unstable area is
modelled as being cooler than the plateau (Fig. 7), a pattern also visible
in the long ERT profile (Fig. 12). The mountain plateau of Mannen can
hardly develop permafrost because of a very thick and long-lasting snow
cover.
For Gámanjunni-3, MAAT has risen over the last 140 years, and the rise
was around 1.8 ∘C since 1880. Estimated rock wall temperatures in
all orientations were mostly negative between 1880 and 2020. Since ca.
2000, however, the south-oriented rock wall has shown mean annual temperatures
close to or above 0 ∘C (Fig. 4c). Permafrost warming and
possible degradation might have accelerated since ca. 2000, which could
influence the geotechnical properties of the site. The ERT measurements
suggest permafrost at Gámanjunni-3, but resistivity differences between
topographic aspect and laterally over the plateau indicate changes in ice
content and ground temperature including the potential occurrence of taliks
(Krautblatter et al., 2010; Gruber and Haeberli, 2007, 2009). Those can form during general atmospheric warming, extreme warm years
or along water-filled fractures (Luethi et al., 2017). These processes
result in high resistivity variations (Hilbich et al., 2008; Krautblatter
and Hauck, 2007; Mollaret et al., 2019). This interplay, together with air
and water advection in fractures, produces a complicated thermal pattern,
which is not reproduced by our heat flow modelling. The pattern is further
highly modulated by snow cover, which in Scandinavian high-mountain settings
is highly variable due to wind redistribution (Gisnås et al.,
2014, 2016b). This redistribution of snow is the major
source for high spatial variability of surface temperatures (Haberkorn
et al., 2015), which can vary by several degrees Celsius (∘C) (Gisnås et
al., 2014; Marmy et al., 2016; Magnin et al., 2015a, b, 2017; Hasler et al., 2011; Haberkorn et al., 2017). However, ice-free
north-oriented rock walls show a cooling influence on the surrounding
subsurface.
In summary, for both sites, we can expect at least local permafrost
conditions, which are clearly more widespread at Gámanjunni-3 than at Mannen, and
warming with an accelerated pace during the last 2 decades, following
similar observations all over Europe (Etzelmüller et al., 2020).
Is there a coupling between the slope instability and permafrost dynamics?Spatial pattern of movement
The spatial distribution of surface displacement is slightly different
at the two sites. At Mannen, relatively high displacement rates of ca. 20 mm a-1 are measured in the upper part of the unstable slope, while low
velocities of <5 mm a-1 dominate the other parts (Fig. 6c).
At Gámanjunni-3 displacement rates of >50 mm a-1 are
registered over most of the mapped rockslide area, with some higher values
in the upper part. Maximum velocity values of >150 mm a-1
are observed in the rock glacier in the southern part of the area (Fig. 6a, b).
Displacement rates, ground temperatures and ERT results were related along
the ERT lines G-NVE1-2 and M-NGU (Fig. 13). At these sites GT is clearly
associated with measured resistivity, confirming the lab analysis and our
interpretation of possible permafrost at these sites (Fig. 13a, b). For
Gámanjunni-3 we observe a positive relationship between electrical
resistivity and displacement rates (more displacement when higher
resistivity) and associated lower displacement with higher ground
temperatures along the longitudinal profile over the rockslide mass (Fig. 13c, d).
At Mannen similar observations were made but are not that clear (Fig. 13f). This seems contradictory as permafrost is seen as a stabilising factor
for slopes (Gruber and Haeberli, 2007; Krautblatter et al., 2013). An
explanation for this behaviour can be found in e.g. Davies et al. (2001), who found factor-of-safety (FS) values below 1 for ice-filled
fractures close to the melting point and FS values at 1 or above when the
ice has melted or is very cold. The stability of both ice in fractures and
rock–ice interfaces strongly declines with increasing temperatures below
0 ∘C (Mamot et al., 2018). Both at Gámanjunni-3 and
Mannen possible ice occurrences are close to the melting point and thus
deformable.
It is important to note here that factors other than the presence or
absence of permafrost may govern the observed spatial differences in
displacement rates. Changes in the geo-mechanical behaviour may, for
example, cause similar variations of displacement rates as large unstable
slopes are typically controlled by pre-existing weak structures and their
reactivation by gravitational processes.
Relationship between resistivity,
modelled ground temperature (GT) and rockslide displacement rates along
selected profiles for Gámanjunni-3 and Mannen, binned in 50 m intervals.
At Mannen, poorer InSAR coverage restricted the analysis of the velocity–ERT
relationship. The black dotted line indicates the modelled 0 ∘C
line, while the grey area indicates the electrical resistivity transition
resolved from laboratory analysis (Fig. 3). (a) Relationship between
modelled ground temperature in three depths and extracted electrical
resistivity for four different depth areas for G-NVE1. The solid circles
display averages over all depths. The graph confirms the transition area for
permafrost around 800 m a.s.l. (b) The same as (a), but for Mannen (M-NGU).
Here there is also a higher resistivity with lower temperatures, but the
relationship is less clear. According to the modelling permafrost can be
expected above 1100 m a.s.l. (c) Relationship between elevation, displacement
rates and electrical resistivity for G-NVE1. ERT and displacement rates
co-vary, with a significant correlation of r=0.64. The red line shows the
crossing point for G-NVE2. (d) G-NVE1. Relationship between elevation,
modelled GT and electrical resistivity. We observe a negative relation
between GT and resistivity (r=-0.5). The red line shows the crossing point
for G-NVE2. (e) Cross-profile G-NVE2 over the rock glacier (dotted line) and
rockslide area at ca. 700 m a.s.l. Resistivity is lower and displacement rates
are much higher on the rock glacier than on the rockslide part, indicating
different modes of movement (see main text). The red line shows the crossing
point for G-NVE1 (f) M-NGU. Relationship between surface altitude, modelled
GT and resistivity. We observe a negative relationship between GT and
resistivity (r=-0.61), with lower GT and higher resistivity values along
the upper part of the steep slope. The location of the back scarp of the
unstable area is indicated with a circle.
This also applies when analysing the cross-profile (G-NVE2) at
Gámanjunni-3, which covered both the rock glacier and the rockslide.
Here, the geophysical surveys indicate that an unfrozen near-surface layer
(ice contents ∼0 in the uppermost 5–10 m) overlies frozen
areas. Further on, lower resistivity values at depths of 20–30 m are measured in
the rock glaciers than in the moving part of the rockslide, even if
velocities in the rock glacier landform are much higher (Fig. 13e). These
observations relate to different processes of movement in the two parts
of the instability. While in the rockslide the movement is influenced by
possible ice deformation due to inferred higher ice content with depth in
this part or block movement below a frozen layer, the rock glacier movement
seems governed by movement related to water–ice mixtures close to the
melting point, where shear strength is greatly reduced and ice deformation
increases (Arenson et al., 2002; Davies et al., 2001; Cicoira et al.,
2019).
The rock glacier has markedly higher velocities.
Such velocities are common for rock glaciers in alpine environments
(Kääb et al., 2007) and often facilitated by a block
motion within a deforming massive ice body (Arenson et al., 2002; Haeberli
et al., 1998, 2006; Cicoira et al., 2019; Kenner et al.,
2017). The ERT measurements show a local resistivity peak under the rock
glacier (at ca. 120 m distance, Fig. 8b), and GST loggers indicate permafrost
presence in the landform (Figs. 1b and 8b). A rock glacier in the
neighbouring valley from Gámanjunni-3 (Adjet rock glacier) had velocity
averages increasing from ∼4.9 to ∼9.8 m a-1 (2009–2016) and maximum velocities from ∼12 to
∼69 m a-1 (Eriksen et al., 2018). There,
permafrost warming, topographic controls, and increased water access to
deeper permafrost layers and internal shear zones have been used to explain
the kinematic behaviour at Adjet rock glacier (Eriksen et al., 2018).
The higher velocities of the rock glacier in relation to the rockslide mass
may indicate higher ice content or higher ground temperatures, influencing
rock glacier kinematics (Kääb et al., 2007; Ikeda et al.,
2008; Cicoira et al., 2019).
For Mannen the highest velocities and resistivity values are observed below the
back scarp and behind the large fracture present between the back scarp and
the unstable moving part of the slope. A similar setting is observed at
Jettan at Nordnesfjellet, which lies close to the Gámanjunni-3 site.
There, ground ice patches are observed in these cracks, governing movement
rates (Blikra and Christiansen, 2014). The ERT measurements
indicate very high resistivity values in this zone (>100 kΩm), indicating either air or snow–ice fill. However, there are no
direct observations of ice.
Temporal movement
The displacement measurements indicate a clear seasonal pattern in
Mannen based on GNSS and laser measurements, as well as a possible seasonal pattern
at Gámanjunni-3 based on the GB InSAR time series (Fig. 5). At both
sites, there seems to be an acceleration during late winter and spring, with
lower velocities during summer and fall. Wirz et al. (2014) found a
maximum displacement at Mattertal (Switzerland) during fall and early winter
and a minimum in spring. They point to meltwater infiltration and a phase
lag from GST of 2–4 months for landslide displacement. Weber et al. (2017) presented a series of 8 years of fracture kinematics at 3500 m a.s.l. on the steep and highly fractured Hörnligrat ridge (Matterhorn,
Swiss Alps). They showed that reversible displacements dominate in winter,
while irreversible enhanced fracture displacements are mainly observed in
summer, likely indicating thawing-related processes (e.g. meltwater
percolation into fractures). However, this behaviour can strongly differ
from one fracture to another as seen at the Aiguille du Midi at 3842 m a.s.l. in
France (Guillet et al., unpublished). A similar pattern is observed for
Veslemannen, where meltwater infiltration and thawing of seasonal frost along with
precipitation episodes are discussed (Kristensen et al.,
2021). The instability on the Zugspitze crest (Germany and Austria) shows
movements of ca. 20 mm a-1 and the highest displacement rates during summer,
with a reduction of up to 85 % during the remaining seasons
(Mamot et al., 2021). Gischig et al. (2011) found high
winter and low summer velocities at the Randa rock slope instability
(Switzerland) and no correlation with rainfall. They could reproduce this
pattern by thermomechanical modelling, whereby surface temperature governed
the variation. At the Jettan site near Gámanjunni-3, Blikra and
Christiansen (2014) documented ice in fractures and the highest velocities
during summer, probably caused by melting of ice patches in fractures.
The possible higher early spring and summer velocities and lower
displacement rates during fall and winter might be related to high water
input in the fractures due to snowmelt, causing hydraulic and/or hydrostatic
pressures and contributing to the melting of ice and snow in fractures formed
during the winter. During summer and fall, the fractures might be free of
ice and snow at the end of the melting season and water infiltration might have
less impact. The lower velocities at Mannen during years with lower snow
cover (Fig. 5f) also support this interpretation. However, only
thermomechanical modelling, like applied by Gishig et al. (2011) and
Mamot et al. (2021), may increase the understanding of how
this signal can influence rock mass deformation.
At both study sites, long-term Holocene displacement variations seem to be
related to climate signals (Hilger et al., 2021). These
observations also agree with other studies such as a study by Philips et al. (2017), who report on 6000-year-old ice sampled from a tension crack
associated with a rock pillar at Piz Kesch in the eastern Swiss Alps. The rock
pillar collapsed in 2014 and had a volume of around 150 000 m3.
Permafrost aggradation and degradation decrease the stability of intact
rocks by both weakening rock bonds (rock fatigue) and critical and
subcritical fracture propagation at sites with strongly varying cryostatic
and hydrostatic conditions (Draebing and Krautblatter,
2019; Voigtländer et al., 2018). There certainly has been a long-term
warming of our study sites since the LIA and an accelerated warming since
ca. 2000. This warming trend has been documented all over Europe
(Etzelmüller et al., 2020) and is responsible for permafrost
degradation in Norway (Borge et al., 2017), possibly influencing
both rock glacier velocities and landslide triggering (Eriksen et
al., 2018; Frauenfelder et al., 2018).
In summary, both sites show corresponding seasonality with increased early
summer velocities. Combined with the knowledge of at least discontinuous
permafrost to patchy permafrost at the sites, snow and ice melt processes
with associated water drainage in cracks are realistic explanations for a
possible seasonality. There is evidence that the recently measured higher
displacement rates in relation to Holocene values (Hilger et
al., 2021) may be related to a warmer atmosphere and can accelerate into
the future. The triggering of Veslemannen described in detail by Kristensen et al. (2021) might be a first sign.
For Gámanjunni-3, a rapid acceleration of the rock-glacier-like landform
forming the southern part of the rockslide is possible, as described for
various cases in the recent past in northern Norway (Eriksen et al.,
2018), in the European Alps (Delaloye et al., 2008) and in Central Asia (Kääb et al., 2021). It could possibly lead to the triggering of
secondary rockfalls or debris flow, as described elsewhere (Lugon and
Stoffel, 2010; Kummert et al., 2018), or movement can stop when the deforming
ice is melted out.
Conclusions
The following conclusions are drawn based on this study.
Temperature measurements, numerical modelling and geophysical soundings
indicate the existence of permafrost at both study sites: at
Gámanjunni-3 permafrost seems to extend down to 700 m a.s.l. today,
while at Mannen sporadic pockets of permafrost are possible.
Surface air and ground temperatures have increased significantly since ca. 1900
by 1 and 1.5 ∘C, and the highest temperatures have been
measured and modelled since 2000 at both study sites.
Displacement rates of Gámanjunni-3 rockslide co-vary significantly with
subsurface resistivity and modelled ground temperatures. Increasing
displacement rates seem to be associated with sub-zero ground temperatures
and higher ground resistivity. This might be related to the presence of
ground ice in fractures and pores close to the melting point, facilitating
increased deformation.
A seasonality of displacement has been observed, with increased velocities
during late winter and early summer at both sites. This pattern may be
linked to the timing of snowmelt and water infiltration, leading to high
water pressure. At Mannen, inter-annual variations may be related to snow
cover thickness.
The rock glacier associated with the Gámanjunni-3 rockslide shows 2 to
3 times higher velocities (>100 mm a-1) and lower
electrical resistivity than the rockslide part. The movement mechanisms are
clearly different for both systems, and a mixture of water and ice
contributing to the rock glacier movement is suggested.
The permafrost in the study sites has certainly warmed and probably degraded
since the LIA, with an accelerated pace since ca. 2000. This atmospheric and
associated permafrost warming might be a factor for the high measured
deformation rates in relation to the Holocene average.
A possible permafrost degradation and probable thawing at Gámanjunni-3
may result in the destabilisation of the upper part of the plateau south of
Gámanjunni-3, considerably increasing the susceptible volume for a
worst-case collapse scenario.
Thermal modelling
The thermal modelling requires a set of parameters and boundary conditions.
For our modelling we defined zones with crisp boundaries, defining surface
sediment cover, bedrock or fractured bedrock. For each of the zones a set of
material properties were defined, following the system in earlier
publications (e.g. Westermann et al., 2013). Most cover
sediments are quite coarse-grained, with no organic material (Fig. A1).
For Gámanjunni-3 we used a well-defined geological model to delineate
the rockslide (Böhme et al., 2016, 2019), while
for Mannen the instability is much less defined. In the latter surficial
material is thin, and bedrock at the surface in the slope and in the coarse blocks
at the plateau dominates. For the sensitivity analysis we varied forcing
air temperature, snow cover (by changing the Nf factor) and the
water content, but the latter only for Gámanjunni because of bedrock dominance
with assumed low water content for the Mannen site (Fig. A2). Permafrost
distribution and geometry vary with these parameters, indicating that
reality is probably somewhere in between. Especially for the Mannen site
located in the sporadic permafrost zone, the parameter variations show the
influence of less snow or cooler SAT on the possible permafrost presence at
the site (Fig. A2b).
The subsurface regions and parameterisation for the 2D thermal
modelling for (a) the Gámanjunni-3 and (b) Mannen profile. MTA: maximum
triangle area, which is a measure describing the spatial resolution of the
triangles in the employed finite-element method solver. The table shows the
stratigraphy chosen for the different regions, along with the depth
parameterisation and volumetric contents of water–ice, mineral, and organic and
air components following Westermann et al. (2013).
Sensitivity plots for the modelled ground thermal regime of (a)
Gámanjunni-3 and (b) Mannen. The main run is the presented run in Fig. 7, and the panels show modelled ground temperature in response to changes in
Nf factor (Nf 0.1 means that Nf is increased by 0.1;
Nf-0.1 means that Nf is decreased by 0.1), forcing SAT
(T1 ∘C means that SAT is increased by 1 ∘C; T–1 ∘C means that SAT is decreased by 1 ∘C) and water
content in the subsurface (50 % water means that water content is
halved and the remaining fraction is added to the mineral fraction; 200 % water means that water content is doubled by reducing the mineral
fraction). GT and permafrost geometry change in response to these
variations. It is noteworthy at Mannen that only small changes in snow or
forcing temperatures would produce considerably more permafrost in the
unstable area. Due to limited assumed sediment cover for the Mannen site, we
did no sensitivity plot for the water content in bedrock, which is low.
The main principles for the 4P model are (see Hauck et al., 2011 and
Mewes et al., 2017):
the electrical mixing rule (Archie's law, which was found empirically by
Archie, 1942, and later theoretically confirmed by e.g. Sen et al., 1981),
an extension to a four-phase medium of the seismic time-averaged approach for
P-wave velocities (modified after Timur, 1968) and
the necessary assumption that the sum of all volumetric fractions of the
ground is equal to 1.
Resistivity and seismic velocities for the 4PM at
Gámanjunni-3 for (a) G-NVE1 and (b) G-NVE2. Note that the profiles are
subsets of G-NVE1 and G-NVE2 and are thus shorter than shown in Figs. 8 and B1. Note also that the colours for the electrical resistivity do no
correspond to the colour scale derived from the laboratory analysis (Fig. 3) but are the original results first presented in Hauck and Hilbich (2018). The possible fracture zones mentioned in the paper
are indicated as a box, while the possible lower permafrost limit is drawn
as a line in (a).
Based on these principles, the 4PM uses the following equations to determine
the volumetric ice (fi), water (fw) and air content (fa) for
a given porosity model Φ (x, z) (Φ=1-fr; fr
being the rock content).
fa=vivavi-va1v-frvr+1vi(fr-1)-aρw(1-fr)nρ(1-fr)m1/n1vw-1vi
Here, a (1 in many applications), m (cementation exponent) and n
(saturation exponent) are empirically determined parameters (Archie, 1942),
ρw is the resistivity of the pore water, vr, vw,
va and vi are the theoretical P-wave velocities of the four components,
and ρ(x,z) and v(x,z) are the inverted resistivity and P-wave velocity
distributions, respectively.
The pore water resistivity (ρw) and the porosity Φ are the
most sensitive for the calculation of the ice and water content
(Hauck et al., 2011). As there is often a lack of borehole or
laboratory data, given exact information around these parameters, there is a
uncertainty involved in the modelling approach. This uncertainty has been
addressed in several publications and can be found in e.g. Pellet et al. (2016) and Mewes et al. (2017).
While Fig. 11 in the main text shows and discusses the results of the 4PM
for two profiles at Gámanjunni-3, Fig. C1 shows the original
inverted ERT and SRT tomograms of the two profiles.
Code and data availability
ERT profiles, measured rock surface temperatures, modelled ground temperatures, point velocity data from laser and GNSS, and velocity surfaces from GB-INSAR can be downloaded under 10.11582/2022.00004 (Etzelmüller, 2022). The long ERT profile from Mannen (M-NGU1) is available on request to the author. The corner reflector data and the TerraSAR-X data are available on request from Tom Rune Lauknes (NORCE). The climate data used can be retrieved from https://www.met.no/en/free-meteorological-data/Download-services. Code is available on request from the corresponding authors.
Author contributions
BE took the initiative for the study and coordinated the synthesis of the
various datasets. He wrote the first drafts of the paper and designed
most of the figures. JC carried out the numerical modelling of the ground
thermal regime at both sites, provided background information and modelling
results, and developed visualisation tools for the ERT profiles. SW developed
much of the principles of the numerical modelling code and supervised the
analysis. FM coordinated and participated in the field investigation of the
ground temperature and ERT rock wall surveys at both sites. PAD and EM
participated in the ERT surveys at Mannen and PAD and LR at
Gámanjunni-3. AA, LK and IS contributed on-site knowledge as well as
interpretation and displacement data from lasers, GNSS and GB InSAR on
behalf of NVE. BJ, JL and MK contributed to the laboratory analysis of the
bedrock samples at the Technical University of Munich (Germany) and ERT
profiles conducted in the field at both sites. RH and MB from NGU contributed
to a structural–geological model of the sites. CHa and CHi from the
University of Fribourg, Switzerland, applied the four-phase model and submitted
a report from the two long profiles at Gámanjunni-3. They also commented on
and improved the inversion and interpretation of all the other ERT profiles.
HØE provided and interpreted the TerraSAR-X data from Gámanjunni-3, along
with ground temperature logger data. TRL coordinated installation and
development of the satellite corner reflector processing chain and
supervised the TerraSAR-X InSAR processing. All authors contributed actively
to the final versions of the paper.
Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
The TerraSAR-X satellite dataset was provided through the German
Aerospace Centre (DLR) TerraSAR-X AO projects GEO0565 and GEO0764. The
satellite corner reflectors were initially funded by the Norwegian Space
Agency, and the processing of these data is now carried out as part of the
InSAR Norway ground motion service hosted by NGU (http://insar.ngu.no, last access: 21 January 2022). Jan Steinar Rønning from NGU provided raw data
for the ERT profile M-NGU at Mannen. Thanks for the extensive help in the field to go
NVE colleagues, in particular Anders Furuseth and Roald Elvenes at
NVE-Kåfjord, as well as Kjell R. Jogerud and Pål R. Hagen Røssevold at
NVE-Stranda. Lars Harald Blikra from NVE supported the study extensively.
Ove Brynhildsvoll, Jaroslav Obu, Juditha Schmidt, Erling Thokle Hovden,
Trond Eiken (UiO), Paula Hilger (Høyskolen i Vestlandet, Sogndal),
Regina Pläsken and Maximilian Reinhard (TUM) took part in fieldwork.
Finally, thanks for the very insightful reviews go to Oliver Sass and
Louise Vick, which improved the paper significantly.
Financial support
This study was part of the project “Cry35
oWALL – Permafrost slopes in Norway” (243784/CLE) funded
by the Research Council of Norway (RCN). Additional funding
was provided by the Norwegian Geological Survey (Trondheim),
the Department of Geosciences at the University of Oslo, the Norwegian
Water and Energy Directorate (NVE), the EDYTEM (Chambéry, France), and the Deutsche Forschungsgemeinschaft (DFG)
through the Technical University of Munich (TUM) International
Graduate School of Science and Engineering (IGSSE), GSC 81.
Review statement
This paper was edited by Arjen Stroeven and reviewed by Louise M. Vick and Oliver Sass.
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