TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-10-2865-2016Rock glaciers on the run – understanding rock glacier landform evolution and
recent changes from numerical flow modelingMüllerJohannjohann.mueller@geo.uzh.chVieliAndreashttps://orcid.org/0000-0002-2870-5921Gärtner-RoerIsabelleDepartment of Geography, University of Zurich, Zurich, 8004,
SwitzerlandJohann Müller (johann.mueller@geo.uzh.ch)23November2016106286528864February201629February20168July20165October2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://tc.copernicus.org/articles/10/2865/2016/tc-10-2865-2016.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/10/2865/2016/tc-10-2865-2016.pdf
Rock glaciers are landforms that form as a result of creeping mountain
permafrost which have received considerable attention concerning their
dynamical and thermal changes. Observed changes in rock glacier motion on
seasonal to decadal timescales have been linked to ground temperature
variations and related changes in landform geometries interpreted as signs of
degradation due to climate warming. Despite the extensive kinematic and
thermal monitoring of these creeping permafrost landforms, our understanding
of the controlling factors remains limited and lacks robust quantitative
models of rock glacier evolution in relation to their environmental setting.
Here, we use a holistic approach to analyze the current and long-term
dynamical development of two rock glaciers in the Swiss Alps. Site-specific
sedimentation and ice generation rates are linked with an adapted numerical
flow model for rock glaciers that couples the process chain from material
deposition to rock glacier flow in order to reproduce observed rock glacier
geometries and their general dynamics. Modeling experiments exploring the
impact of variations in rock glacier temperature and sediment–ice supply show
that these forcing processes are not sufficient to explain the currently
observed short-term geometrical changes derived from multitemporal digital
terrain models at the two different rock glaciers. The modeling also shows
that rock glacier thickness is dominantly controlled by slope and rheology
while the advance rates are mostly constrained by rates of sediment–ice
supply. Furthermore, timescales of dynamical adjustment are found to be
strongly linked to creep velocity. Overall, we provide a useful modeling
framework for a better understanding of the dynamical response and
morphological changes of rock glaciers to changes in external forcing.
Introduction
Rock glaciers and their dynamics have received much attention in permafrost
research and beyond, most prominently by the International Panel on Climate
Change (IPCC) in the context of impacts of a warming climate on high mountain
permafrost (IPCC, 2014). Time series of rock glacier movement in the European
Alps indicate that acceleration in permafrost creep in recent decades is
related to an increase in ground temperatures (Delaloye et al., 2010; PERMOS,
2013; Bodin et al., 2015). Furthermore, multitemporal geomorphometric
analysis has shown subsidence features and structural disintegration of
alpine rock glaciers, which are indicative of landform degradation and
destabilization (Kääb et al., 2007; Roer et al., 2008b; Bodin et al.,
2010; Springman et al., 2013; Micheletti et al., 2015). Many studies have
addressed the connection between mean annual air temperatures and rock
glacier dynamics from a descriptive point of view (Ikeda and Matsuoka, 2002;
Roer et al., 2005b; Delaloye et al., 2010; Springman et al., 2012) or have
used modeling approaches to assess rock glacier dynamics (Jansen and
Hergarten, 2006; Kääb et al., 2007; Springman et al., 2012). Most of
these studies focus on the impact of air or ground temperature on rock
glacier creep. Other authors stressed that rock glacier dynamics cannot
solely be explained by temperature variations and should integrate flow and
controlling environmental factors such as sediment supply dynamics and
landform characteristics (Roer et al., 2005b; French, 2007; Frauenfelder et
al., 2008). Rock glaciers have been defined as “lobate or tongue-shaped
bodies of perennially frozen unconsolidated material supersaturated with
interstitial ice and ice lenses that move down slope by creep as a
consequence of the deformation of ice contained in them and which are, thus,
features of cohesive flow” (Barsch, 1992, p. 176). Such a definition
includes information on form, material and process and, therefore, the
observable rock glacier characteristics are influenced by sediment and ice
input, permafrost conditions and the geomorphological setting, which in turn
control rheology and landform geometry (Barsch, 1996). Very few studies have
addressed rock glacier dynamics with such a holistic approach that includes
rock wall retreat, sediment and ice dynamics, and climate variations to gain
insight into the long-term evolution of rock glaciers (Olyphant, 1983;
Frauenfelder et al., 2008) and model validation was hampered by restricted
observational data.
Recent observations show signs of rock glacier destabilization such as
acceleration, subsidence features and structural disintegration (forming of
tension cracks) at several rock glacier landforms in the Swiss Alps
(Kääb et al., 2007; Roer et al., 2008b; Delaloye et al., 2011;
Lambiel, 2011; Springman et al., 2013; PERMOS, 2013; Kenner et al., 2014;
Bodin et al., 2015). These studies indicate that various factors can lead to
such degradation but a common triggering for all the cases has not been
identified. These potential factors are most likely connected to the complex
combination of the local topography, the thermal state of the permafrost
(climate-induced response), the existence and intrusion of liquid water
and/or variations in the sedimentation regime affecting the sediment load
during long-term landform evolution.
Numerous remote sensing techniques are available for acquiring data on
permafrost creep (see Haeberli et al., 2006, and Kääb, 2008, for an
extensive summary), high mountain geomorphometry (Bishop et al., 2003) and
high mountain sediment dynamics (Gärtner-Roer, 2012; Heckmann and
Schwanghart, 2013; Müller et al., 2014a). This provides the necessary
foundation for a holistic assessment strategy that includes the coupling of
relevant landforms and processes and in which sediment supply rates can be
quantified, ice volumes estimated and rock glacier rheologies derived
(Frauenfelder et al., 2008; Gärtner-Roer and Nyenhuis, 2010).
Here we present such a holistic analysis approach to assess long-term
rock glacier evolution and the impacts of variations in temperature, sediment
and ice supply on rock glacier geometry and movement. We apply a numerical
flow model to two rock glaciers in the Swiss Alps with different topographic,
morphometric and rheological characteristics. The modeling is motivated by
observations of topographic and kinematic changes for the two rock glaciers
revealing signs of degradation as presented in this study. The aim of the
modeling approach is to relate these changes to the long-term evolution and
short-term adaptation of rock glacier systems to changing environmental
factors and ultimately to a better understanding of the currently observed
dominant controls of geomorphological changes. We thereby consider
rock glaciers as an integral part of a coarse-debris cascading system in
periglacial environments.
Conceptual approach to high mountain periglacial systems
The topographic evolution of the rock glacier landform relies on the
production, transport and deposition of debris in the periglacial system and
the generation and integration of subsurface ice (Wahrhaftig and Cox, 1959;
Barsch, 1996). The development of rock glaciers is therefore dependent upon
the supply of debris from the source headwall(s) and the long-term
preservation of an ice matrix or ice-core-inducing creep (Morris, 1981). Rock
glaciers are also dynamic landforms that are influenced by the warming and
melting of ice and changes in sediment input. The variations in environmental
factors translate into observable changes in geometry and kinematics, which
can be interpreted as a sign of degradation and/or destabilization of these
periglacial landforms (Roer et al., 2008b; Springman et al., 2013).
Conceptual model of the dynamic evolution of a rock glacier system
(adapted from Fig. 1 in Müller et al., 2014a). Black arrows show the
sediment transport. t0, t1 and t2 show the rock glacier
surface geometries at different time steps resulting from variations in
environmental factors such as warming and a decrease of sediment–ice
input.
Figure 1 shows the theoretical concept of an idealized periglacial mountain
slope with a corresponding rock glacier system and builds the conceptual
basis for this study. Two main subsystems contribute to the temporal and
topographical development of the rock glacier landforms: the upper headwall
and talus slope system generate the sediments that are transported into the
lower rock glacier system. Besides the sediment input, the rock glacier
system is also controlled by the existence, generation and state of
subsurface ice and permafrost creep (see Fig. 1). The two subsystems differ
on the basis of several characteristics: topographic features, typical
landform(s) and the dominating mass transport processes. Back-weathering of
the exposed rock wall and resulting rockfall are the most effective mass
wasting processes (e.g., Krautblatter et al., 2012; Müller et al., 2014a)
and supply the entire system with sediment. Back-weathering rates and rock
wall dynamics are strongly influenced by the geological structures,
lithological conditions, the presence of moisture as well as the
characteristics and dynamics of cleft ice, which are in turn thermally
controlled (Hasler et al., 2012). The progressive accumulation of sediments
and ice on an inclined surface at the foot of the rock wall under permafrost
conditions leads to permafrost creep and the development of a rock glacier
(Barsch, 1992; Haeberli et al., 2006). The existence of ice and its
properties within the sediment obviously plays an important role in
controlling the rheology of the rock glacier and environmental changes
influence erosion and transport processes that result in topographical and
kinematic changes (White, 1973; Arenson et al., 2004; Haeberli et al., 2006).
We transfer this conceptual approach into a numerical flow model that
integrates the whole debris process chain and couples the different
subsystems and related mass fluxes. It assumes a uniform sediment and ice
input from the rock wall to an inclined surface, builds up a talus slope that
is supersaturated with ice and then starts to creep as a viscous nonlinear
media similar to ice. This rheological assumption has repeatedly been used
to assess rock glacier kinematics (Wahrhaftig and Cox, 1959; Olyphant, 1983;
Whalley and Martin, 1992; Barsch, 1996; Kääb et al., 2007;
Frauenfelder et al., 2008). A few studies (e.g., Olyphant, 1983; Wagner
1992; Leysinger Vieli and Gudmundsson, 2003; Frehner et al., 2015)
have demonstrated that such a rheology can in principal be used in a
numerical flow model for rock glaciers.
Recent observations of rock glacier change
The modeling work in this study is motivated by detailed observations of
geometric changes of two rock glacier systems, both in Switzerland. We
present in this section comprehensive new datasets of the two landforms: the
well-studied Murtèl rock glacier in the Engadine and the rock glacier
Huhh1 in the Turtmann valley. Both show changes in surface geometry and
kinematic behavior but have distinctly different landform characteristics
(see Table 1 for an overview). In order to assess the controlling mechanisms
of rock glacier evolution and potential degradation we use a “backward”
approach: we quantify and discuss distinct observed changes in surface
geometry and kinematics of the two rock glaciers, propose potential
controlling forcing factors (sediment and ice input as well as ground
temperature) and then assess these observations and related forcings with a
numerical creep model.
Characteristics of the two selected rock glaciers (excluding their
talus slopes). The data sources are cited in the text.
The first rock glacier site is the well-studied Murtèl (Hoelzle et al.,
2002; Haeberli et al., 2006; Springman et al., 2012) situated below the
northern face of Piz Corvatsch (3300 m a.s.l.) in the upper Engadine, in
the southeastern part of Switzerland (UTM, 563 131, 5 142 001; zone 32T).
The lithology mainly consists of granite and granodiorite. The density of the
in situ rock types is based on values given in the literature with a density
of 2650–2750 kg m-3 for granite and 2700–2800 kg m-3 for
granodiorite (Tarbuck et al., 2011), and studies on back-weathering at this
site have shown back-weathering rates of 2 mm a-1 (Müller et al.,
2014a). Murtèl is one of the best investigated rock glaciers and
observations from this permafrost site have been discussed in great detail
(see summary in Haeberli et al., 1998). As part of the PERMOS network
(Permafrost Monitoring Switzerland), parameters such as borehole
temperatures, ground surface temperatures (GSTs) and horizontal velocity have
been monitored since 1987 (Vonder Mühll et al., 2008). The borehole data
have revealed a layered internal structure with a shear horizon at 32 m
depth where almost all of the deformation takes place (Arenson et al., 2002;
Springman et al., 2012). Attempts to determine the age of this rock glacier
(Haeberli et al., 1999; Laustela et al., 2003) obtained an age of 5000 to
6000 a as a minimum value (Haeberli et al., 2003). These values were
calculated from present-day surface velocity fields assuming constant
environmental conditions over the rock glacier development (Kääb and
Vollmer, 2000; Frauenfelder and Kääb, 2000; Haeberli et al., 2003).
The rock glacier is characterized by rather slow creep velocity
(0.06–0.13 m a-1) and is considered a thick and ice-rich landform
with an average volumetric ice content of 60 % (Haeberli et al., 1998;
Arenson et al., 2002).
The annual elevation change of the two rock glacier systems for
Murtèl (period 1996–2007) and Huhh1 (period 2001–2012). The annual
rates are derived from multisensoral and multitemporal remote sensing
products (Table 2). For a detailed depiction of the structure of the
landforms see Supplement Fig. S1, where the orthophoto is shown without the
elevation change.
Huhh1 rock glacier, Turtmann valley, Valais
The second rock glacier is located in one of the hanging valleys of the
Turtmann valley, a tributary of the Rhône valley in southern Switzerland
(UTM 401 555, 5 115 642T; zone 32T). The valley's lithology mainly consists
of Palaeozoic gneisses and schists and based on this lithology rather
constant back-weathering rates of 2 mm a-1 are expected (Glade, 2005;
Krautblatter et al., 2012; Müller et al., 2014a). The valley stretches
from 2400 to 3278 m a.s.l and is characterized by steep rock walls, talus
cones, a glacier, several moraines of different ages and multiple active and
inactive rock glaciers (Roer and Nyenhuis, 2007). The focus within this study
lies on the rock glacier Huhh1, which can be considered a thin, moderately
fast moving rock glacier (see Table 1). This site is also part of the PERMOS
network and has undergone several scientific assessments (Rasemann,
2003;
Roer, 2005; Nyenhuis et al., 2005). There is no direct subsurface information
available but Gärtner-Roer (2012) used a semi-quantitative approach to
derive the rock glacier thickness and sediment storage assuming an ice volume
of 50–70 %. The age of the landform is estimated at
500–600 a using
the same approach as Haeberli et al. (2003) and Kääb and
Vollmer (2000), where the current velocity fields are assumed to be constant
over the rock glacier evolution time. Therefore the age estimates can be seen
as minimum ages.
Airborne and terrestrial remote sensing data available at the rock glacier sites.
Data typeMurtèlHuhh1Airborne remote sensingRC30 in 1996 (PERMOS)HRSC-A in 2001; Otto et al. (2007)(photogrammetry and airborneRC30 in 2002 (PERMOS)RC 30 in 2005; Roer (2005)laser scanning – ALS)ALS in 2003ALS in 2007; Müller et al. (2014a)RC30 in 2007 (PERMOS)ADS 40 in 2010; Müller et al. (2014a)ADS 80 in 2012; Müller et al. (2014a)Geodetic point surveys2009–2015 (annually)2001–2015 (annually)Observations of rock glacier dynamics
Complementary to the PERMOS-related kinematic monitoring, we used a
combination of remote sensing and terrestrial surveying methods to derive
multitemporal elevation and displacement data in order to assess changes in
geometry and creep.
The frequency distribution of annual vertical surface change
(m a-1) from DEM differencing in the talus slope–sedimentation area
of the two rock glacier systems. Both systems show negative mean values (red
lines). The black line refers to 0 m a-1 difference.
Multitemporal digital elevation models (DEMs) derived from
stereophotogrammetry and airborne laser scanning (ALS) are available for the
analysis between the years 1996 and 2007 for the Murtèl rock glacier. Five
high-resolution DEMs (also stereophotogrammetry and ALS) have been generated
in this study for the Turtmann valley between the years 2001 and 2010; the
technical details of these DEMs are given in Table 2. New elevation change
maps are derived from differencing of the DEMs over the periods 1996 and 2007
for Murtèl and 2001 and 2012 for Huhh1. The limitations concerning
processing, uncertainties and application of the different sensor systems are
presented in Kääb and Vollmer (2000), Roer et al. (2005d), Roer and
Nyenhuis (2007) and Müller et al. (2014b). The systematic error/trueness
(Menditto et al., 2007) of the remote sensing data was corrected using the
terrestrial geodetic survey points (tachymeter) as reference for the ALS and
the ALS data as reference for the photogrammetric DEM data, as presented in
Müller et al. (2014b). The spatial coverage of each reference dataset
allowed us to establish a slope-dependent detection limit derived from the
assessment ranging from 0.5 to 0.9 m (see also Müller et al., 2014b). The
availability of numerous multisensoral datasets enabled stacking,
investigating dense time steps and crosschecking products with different
precisions (terrestrial survey, ALS, photogrammetry), which led to a high
reliability of the DEM differencing and derived annual subsidence rates
(Winsvold et al., 2016).
Additionally, kinematic data are available for both rock glaciers from yearly
terrestrial geodetic surveys of approximately 20 points as described in
PERMOS (2013) and Roer (2005). Horizontal and vertical changes are quantified
annually with an accuracy of 1–2 cm. The vertical elevation change is
obtained by subtracting the surface-parallel component of the vertical
displacement from the total measured vertical displacement.
Based on the above DEMs, new elevation change maps have been derived for both
rock glaciers and the subsystem units of the main rock glacier body and
contributing talus slope have been identified (Fig. 2). This analysis (over
decadal time periods) showed distinct subsidence features of different
magnitudes on the entire rock glacier, most pronounced in the deposition area
(outline with green in Fig. 2) of the rock glacier. A more detailed assessment
of the subsidence shows a general lowering of the entire surface of the
rock glacier system of -0.02 m a-1 for the Murtèl rock glacier and
-0.09 m a-1 for the Huhh1 rock glacier. The spatial analysis of the
subsidence phenomenon depicts the strongest signal of annual lowering in the
deposition area (talus slope–sedimentation area; see Fig. 3) with an overall
average annual subsidence of -0.04 m a-1 for the Murtèl
rock glacier and -0.16 m a-1 for the Huhh1 rock glacier. Such
subsidence features, especially in the deposition area, have been interpreted
as signs of permafrost degradation (Roer et al., 2008a; Springman et al.,
2013; Bodin et al., 2015) and are assessed by the rock glacier evolution model
in Sect. 6.2.4. These observed subsidence rates are calculated considering
the uncertainties resulting from the DEM differencing (see Müller et al.,
2014b). Additional vertical displacement data from terrestrial surveys
conducted from 2001/2009 to 2015 corrected for slope parallel movement agree
with the results from the DEM differencing.
Theoretically, subsidence features can result from surface lowering by ice
melt (Phillips et al., 2009), reduced ice and sediment input, acceleration
of the entire landform (potentially thermally induced, leading to a
“creeping away” and thinning of the rock glacier from its feeding area) or,
most likely, a combination of the above (Roer et al., 2005b).
Our elevation change data also show the continuing advance of the
rock glacier front and the “furrow and ridge” structure. This shows that
the rock glacier continues to be active although it is probably no longer
fully connected to its sediment source and therefore not in an equilibrium
state with the current sedimentation and/or thermal state of the system.
Rock glacier evolution – modeling approach
We present here a quantitative rock glacier evolution modeling approach that
is based on the conservation of mass and includes the entire debris process
chain in high mountain environments (see Fig. 1).
Geomorphological setting
In order to initialize and evaluate the numerical model, it is necessary to
derive geometric information about the headwall, talus slope and
rock glacier. Therefore, the two rock glacier sites have been analyzed
according to the concept introduced in Sect. 2 for their along flow geometry
and the quantification of sediment input and sediment deposition.
Geomorphological mapping in the field as well as interpretation of DEMs and
orthophotos are used to identify the contributing headwall areas, deposition
areas and rock glacier landforms (see Fig. 2). Surface features (e.g., slope,
substrate) as well as velocity fields are further used to delimit the
different subsystems (Kääb et al., 1998; Roer et al., 2005a).
The DEMs served as basis for the geomorphometric analyses to determine
spatial dimensions, slope and surface geometry of the periglacial high
mountain systems.
Rock glacier creep modeling approach
A 1-D time-dependent numerical flow model is used to simulate the
evolution of the rock glacier surface, length and creep velocity along the
center flow line based on a given sediment–ice input and rock glacier
rheology. In this study we are not aiming to reproduce the exact evolution
or small-scale geometric features of the two chosen real-world rock glaciers,
but rather use the model to simulate the basic behavior of a rock glacier
body creeping down a slope and investigate the first-order dynamic response
of the geometry on changing external factors such as temperature and
sediment supply. Specifically, we will investigate potential causes for the
observed surface geometry changes (subsidence, front advance and velocity
variations) as set out above (Sect. 3.3).
Rock glacier creep
For our study we therefore reduce the rheology of the rock glacier to a body
of ice-bonded sediment that deforms and creeps like a nonlinear viscous
material under the influence of gravity, as proposed already in 1959 by
Wahrhaftig and Cox (1959) and applied similarly by Olyphant (1983) and
Frauenfelder et al. (2008). This rheology can be described by a Glen type
flow law (Glen, 1955) as typically used for glacier ice (Cuffey and
Paterson, 2010) which relates the strain rate ε˙
nonlinearly to the stress τ:
ε˙∝Aτn,
where n is a flow law exponent that is typically between 2 and 3 for frozen
material (Paterson, 2010) and A the rate factor describing the softness of
the rock glacier material. Such a constitutive relationship has been applied
and discussed in other studies on rock glacier creep (Olyphant, 1983; Whalley
and Martin, 1992; Whalley and Azizi, 1994; Barsch, 1996; Azizi and Whalley,
1996;
Kääb et al., 2007; Frauenfelder et al., 2008) and is further
supported by results from borehole measurements on real-world rock glaciers
and shear experiments in the laboratory on rock glacier material (including
Murtèl rock glacier; Arenson et al., 2002; Kääb and Weber, 2004;
Arenson and Springman, 2005; Frehner et al., 2015).
For simplification we assume the rock glacier material to be a homogenous
mixture of ice and sediment, meaning the rheological parameters such as the
rate factor A, flow exponent n and rock glacier material density
ρr do not change within the rock glacier body. This means that
we exclude any internal ice melting and consider the active layer
rheologically in the same way as the rock glacier material. However, from
boreholes we know that the rheology within rock glaciers is variable with
depth (Haeberli et al., 1998) and typically enhanced deformation in ice-rich
shearing zones are observed, for example, in the case of the Murtèl
rock glacier. Such shearing zones are typically near the bottom of the moving
body of the rock glacier, where shear stresses are highest and temperatures
the warmest, and thus they dominate the creep process. Consequently, potential
variations in rheology in the material above are not substantially changing
the nonlinear viscous creep behavior. The modeled flow is calibrated with
observed surface velocities (see Sect. 4.3) and is dominated by the rheology
of the material near the base and thus our modeling implicitly includes the
shear zone in its vertically averaged rheology. In addition, the rheology
within rock glaciers is generally poorly known and the assumption of a uniform
rheology is therefore justified for studying the first-order controls of
geometric changes.
We further simplify the problem to the case of an infinite sheet of uniform
thickness that creeps down an inclined plane (Cuffey and Paterson, 2010, also
known as the shallow ice approximation in glaciology) and thereby
neglect longitudinal stress gradients. As our focus is the evolution of the
surface and not the detailed stress field within the landform, according to
Leysinger Vieli and Gudmundsson (2004) this approximation is justified even
for relatively high length to thickness ratios such as occurring for
rock glaciers. For this 2-S case along a center flow line, the vertical strain
rate τ˙xz is directly related to the shear stress τxz
through
τ˙xz=A⋅τxzn,
where x is the horizontal coordinate along the center flow line and z the
vertical coordinate. The shear stress τxz is then given by the local
surface slope ∂s∂x and ice depth dz:
τxz=ρrg∂s∂xdz,
where ∂s∂x is the surface slope.
Integration of Eq. (2) over the rock glacier thickness results in a surface
flow speed us from deformation of the rock glacier material of
us=2An+1ρrg∂s∂xnhn+1
and accordingly a depth-averaged horizontal flow speed u‾ of
u‾=2An+2⋅ρg∂s∂xnhn+1.
Although this equation is in its form identical to the case of glacier ice
(Cuffey and Paterson, 2010), for rock glaciers the flow exponent n
and the rate factor A (referring to the material softness) are, due
to the presence of debris and water within the ice, not necessarily the same
(Moore, 2014) and may in reality thereby also vary with depth. From boreholes
and laboratory experiment flow law exponents of rock glaciers have been found
between n= 1.9 and 4.5 (mean n= 2.72) and increase linearly
with volumetric ice content cice of the sediment (Arenson and
Springman, 2005). For our relatively high ice contents (60 %) a value of
n= 3 equivalent to the case of ice seems justified and has been used
in earlier studies of Leysinger Vieli and Gudmundsson (2003) and Frauenfelder
et al. (2008).
The rate factor A is estimated from observed surface flow speeds by
inverting Eq. (3) for A but is known to be influenced by the material
temperature but also by other factors such as the moisture and debris content
(Cuffey and Peterson, 2010). Moisture content is known to vary with time and
temperature (Moore, 2014; Monnier and Kinnard, 2016) but we do not explicitly
include this in our model as such changes are poorly constrained. The
temperature-related effect from moisture is, however, implicitly included by
writing the rate factor of the rock glacier material as a product of the
temperature-dependent part A∗(T) and a scaling factor fA
accounting for the influence of the debris:
A=A∗(T)⋅fA.
This approach is in agreement with known rheological investigations (Paterson
and Budd, 1982; Arenson and Springman, 2005) and allows including a
temperature forcing in our modeling experiments. For the temperature-dependent part we use two approaches. Firstly, as done in Kääb et
al. (2007) we use the dependence on the temperature of pure ice, for which
A∗(T) increases exponentially with temperature (see Fig. 4;
Paterson and Budd, 1982).
Temperature dependence of the rate factor relative to the rate
factor at a reference temperature of -1.5 ∘C as derived for pure
ice (Paterson and Budd, 1982) and for rock glacier material (Arenson and
Springman 2005).
Secondly, and probably more realistic for rock glaciers, we follow the
description based on shearing experiments of frozen debris material of
Arenson (2005) which is given by
A∗(T)∝2T+1
for temperatures between -1 and -4 ∘C. Note that this second
version is at warm temperatures above -2 ∘C, as expected for our
two cases, more sensitive to temperature warming (Fig. 4). For both
approaches the temperature dependence is applied at a reference temperature
which refers approximately to the real mean annual temperature within the
rock glacier body.
Thickness evolution
The evolution of rock glacier thickness h and rock glacier surface elevation
s along the central flow line is calculated from the principle of mass
conservation, which takes for the 1-D representation the following form
(Oerlemans, 2001):
∂h∂t=ar-1w⋅∂u‾hw∂x,
where t is the time, ar is the rate of rock glacier material
accumulation or removal at the surface (> 0 for accumulation; in
m a -1), w the rock glacier width and u‾ the horizontal
and vertically averaged flow speed. The geometry of the rock glacier bed
transverse to flow is accounted for by assuming a parabolic valley
that is prescribed and here assumed to be uniform along the flow. This allows
the width of the rock glacier to vary with changing thickness; however, the effect
of side drag is not explicitly included but it is implicitly contained in the
scaling factor fA of the rate factor, which is calibrated on surface
displacements.
The evolution of the rock glacier thickness and surface is calculated
numerically on a regular grid with 10 m spacing along the center flow line.
Using a standard implicit finite-difference scheme (Oerlemans, 2001) the
surface evolution Eq. (8) is solved at each time step and for all grid points
from the depth-averaged material flux q‾=u‾⋅h⋅w and the material input ar at the rock glacier surface.
Observed and modeled rock glacier geometry after buildup. The along
flow bed topography used in the model and the modeled and observed (from
DEMs) rock glacier surfaces are shown. The vertical fine black lines mark the
boundary between the deposition area (talus slope) and the main rock glacier
lobe. Note that the model cannot replicate the exact geometry of the landform
due to the various simplifications but shows good agreement in length and
thickness of the rock glacier main body.
Model input and calibrationModel geometry
Approximate bedrock topographies are derived for both rock glaciers from the
DEMs and geomorphic mapping (Sect. 4.1) and we assume the bedrock to be
roughly parallel to the rock glacier surface. The shapes of the rock glacier
beds are approximated to two sections of constant slope that are
representative of the two respective rock glaciers. For both rock glaciers we
mapped the first 150 m of the distance along flow as deposition area and
apply there a spatially uniform material accumulation rate at the specified
sedimentation rate and ice content, whereas further downstream no mass is
added or lost at the surface. In the talus slope, where the material is
accumulated, we use a slope of 37∘ (which is slightly below the angle
of repose for unconsolidated talus slope material; Carson, 1977), which is
steeper than on the rock glacier part (12∘ for Murtèl and
27∘ for Huhh1, see Table 4). The respective dimensions and slopes for
the two rock glaciers are presented in detail in Table 1 and visualized in
Fig. 5.
Modeled evolution of surface geometry (a), absolute
thickness (b), horizontal velocity (c) along the central
flow line, terminus advance (d) and volume evolution (e)
for the rock glacier buildup (first 6000 a runtime) and for the successive
temperature perturbation experiment (temperature increase of 1 ∘C,
with -1.5 ∘C reference temperature). The black line shows the
state of the system before the temperature step change at 6000 a. The lines
are plotted at 100 a time intervals.
Specific model input parameters for the rock glaciers. The
sediment–ice input describes the volume of debris deposited on the
accumulation area per year. The rate factor A is derived from Eq. (11) and
the runtime of each rock glacier model is selected due to its approximated
age (see Sect. 3).
Comparison of the observed (obs.) and modeled (mod.) rock glacier
thickness and velocity for Murtèl and Huhh1 after 6000 years and 600
years, respectively.
Murtèl obs.Murtèl mod.Huhh1 obs.Huhh1 mod.Length280 m300 m310 m240 mThickness30 m28 m12 m16 mHorizontal velocity0.06–0.13 m a-10.06–0.09 m a-10.75–1.55 m a-10.63–0.79 m a-1Material input
The rock glacier material input rate ar at the surface is assumed
to be positive and uniform on the talus slope and, if not mentioned
otherwise, set to zero on the surface of the main rock glacier body. The
latter means that in general no sediment or ice is lost or gained at the
surface of the main rock glacier. The rock glacier material input at the
surface is estimated from the sediment input from the headwall to the talus
slope and its respective ice content, which is assumed to be constant in
time. The total amount of sediment produced at the headwall is calculated
from back-weathering rate and headwall area and is distributed equally over
the deposition area (talus slope–accumulation area). Based on in situ
measurements (Müller et al., 2014a) and previous studies (Glade, 2005;
Krautblatter, 2012), a back-weathering rate of 2 mm a-1 is used,
resulting in an annual sediment input over the entire talus slope of
0.006 m3 m-2 for Murtèl and 0.022 m3 m-2 for
Huhh1. Together with the ice content of the material the accumulation rate of
rock glacier material (sediment–ice mixture) is then calculated:
ar=as1-ci.
Based on field studies (Hoelzle et al., 2002) and previous approaches
(Gärtner-Roer, 2012) we use an estimated ice content ci of
60 % for both rock glaciers, which results in a rock glacier material input
rate that is 2.5 times higher than the pure sediment input rate.
Rock glacier density
We estimate the density of the rock glacier material (ρr) from the
percentage ice content (ci) and from the respective
densities of ice (ρi= 910 kg m-3) and the debris
material (ρd=2700 kg m-3), which we assume stay
constant in space and time:
ρr=(1-ci)⋅ρd-ci⋅ρi.
Estimating the rate factor <inline-formula><mml:math display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula>
Solving the equation describing surface ice flow from creep of a viscous
material (Eq. 4) for the rate factor A, we obtain
A=A∗(T)⋅fA=(n+1)us2hnτd=(n+1)us2hn+1ρrg∂s∂x.
Using observed surface flow speed data (us) we can then estimate
the corresponding rate factor A (respective fA for a given reference
temperature and temperature dependence model) for both rock glaciers. These
rate factor values are substantially lower than the values known for
pure ice at similar temperatures (Paterson and Budd, 1982;
-1.5 ∘C), which probably reflects enhanced mechanical resistance
from the sediment within the ice (Arenson and Springman, 2005).
Model experiments
The model is applied to the two selected rock glacier systems using the
landform-specific input parameters in Table 3 and the simplified geometries
described in Sect. 4.
Rock glacier buildup
The buildup experiment is documented for Murtèl in Fig. 6 (first
6000 a) and is qualitatively very similar for Huhh1 (shown in Supplement
Figs. S14 to S25). The model starts with an “empty” topography of bedrock
(bedrock topographies in Fig. 5). Initially, it builds up a homogenous
sediment–ice body in the talus slope which starts to creep and therefore
advances once it is thick enough and the shear stress high enough, which
occurs roughly after 600 a for Murtèl and 150 a for Huhh1. A
rock glacier body is then generated to a characteristic thickness while the
front keeps advancing at a roughly constant rate. This continuing advance is
a direct result of constantly adding mass at the top while no mass is removed
through melting. Further, the growth and geometry change of the rock glacier
landform mainly occurs through moving the rock glacier forward at the front.
The modeled advance rate is slightly below the surface speed of the main
rock glacier body. After a run time of 6000 a for the Murtèl rock glacier
and 600 a for Huhh1, which correspond to the ages of the landforms estimated
earlier, we obtain geometries (lengths and thicknesses) that are very close
to ones currently observed (Fig. 5 and Table 4). The actual furrow-ridge
structure of the landform cannot be replicated (Fig. 5) due to model design
but the overall geometry is well reproduced.
The modeled surface velocities on the main rock glacier lobes range between
0.06 and 0.09 m a -1 for Murtèl and between 0.63 and
0.79 m a -1 at Huhh1, which is in good agreement with the observed
values from long-term kinematic monitoring (see Table 1).
Note that the bedrock topography of the talus slope and rock glacier is
assumed to be of constant inclination. We defined the first 150 m of slope
as an idealized talus slope with an inclination of 37∘, which we
assumed to be the angle of repose for such unsorted and unconsolidated blocky
material (Carson, 1977). The general inclination of the bedrock topography
(see Table 1) below the rock glacier is derived from DEMs
where we assume the bedrock to be parallel to the rock glacier surface (see
Table 1). Figure 5 depicts the observed rock glacier front shapes and
positions slightly differently from the modeled ones as the real bedrock
geometries of the rock glaciers are more complex than the assumed uniform
mountain slopes. Also, the idealized talus slopes differ from the observed
geometries due to abovementioned simplification.
Perturbation modeling experiments
Starting with the rock glacier geometries from the buildup experiments (see
Sect. 5.1), we investigate the impact of variations in temperature and
material input on rock glacier dynamics. In a first phase we perform two
distinctly different perturbation experiments: in the first we increase the
temperature of the rock glacier body by 1 ∘C (Sect. 5.2.1) and in
the
second independent experiment we completely switch off the material supply to
the talus slope (Sect. 5.2.2). In a second step, we then combine these
perturbations in temperature and sediment supply. Atmospheric
warming is expected to influence both rock glacier temperatures and
consequently creep, as well as the production of sediment and incorporation
of subsurface ice, but quantification of the latter is highly uncertain
(Gruber, 2004; Fischer et al., 2010; Ravanel and Deline, 2011; Schneider et
al., 2012). We therefore run varying scenarios for the sediment and ice input
with the zero sediment supply being at the extreme end of the spectrum.
For the temperature experiments the chosen step temperature increase of
1 ∘C in the rock glacier depicts a potential warming scenario which
roughly refers to a 2 ∘C warming in GST
for a fixed position at the permafrost base. The 1 ∘C subsurface
warming is also consistent with current and expected future subsurface
warming trends based on borehole observations (PERMOS, 2013) and modeling
results in the next 50 a in the Swiss Alps (Marmy et al., 2015).
Multiplicative increase in rate factor A from a 1 ∘C
rock glacier warming for the different temperature relations of Arenson and
Springman (2005) and Paterson and Budd (1982) and varying rock glacier
reference temperatures.
Rock glacierChange in rate factorChange in rate factorreferenceA for Arenson andA for Paterson (1982)temperatureSpringman (2005)from a 1 ∘C warmingfrom a 1 ∘C warming-2 ∘C1.396 ⋅A1.254 ⋅A-1.5 ∘C1.705 ⋅A1.253 ⋅A-1 ∘C2.718 ⋅A1.252 ⋅A
Assuming relatively warm reference rock glacier temperatures between -1 and
-2 ∘C, as observed in the European Alps, the Arenson and Springman
(2005) temperature dependence gives an increase of the rate factor by a
factor of 1.4 to 2.7 (Table 5) for a 1 ∘C warming. The Paterson and
Budd (1982) temperature relation, however, shows almost no dependence on
rock glacier temperature and increases only by factor 1.25 with a
1 ∘C temperature increase. If not indicated otherwise, we
use the Arenson and Springman (2005) relation in the temperature warming
experiments.
The results for the simple temperature and sediment experiments are presented
in the following section only for Murtèl rock glacier but the results are
qualitatively similar (although of higher absolute magnitude) for the Huhh1
rock glacier. The more complex and realistic experiments combining variations
in temperature and sediment supply are presented for both rock glaciers later
in Sect. 5.2.3.
Temperature experiment
In a first experiment, a step temperature increase of the entire rock glacier
body of 1 ∘C is applied after rock glacier buildup (at 6000 a),
while the sediment supply is held constant. The reference temperature of the
rock glacier is set at -1.5 ∘C which results in a rate factor
increase by a factor of 1.7.
Figure 6 shows the modeled response of the surface geometry, landform
thickness and horizontal surface velocity of the Murtèl rock glacier along
the central flow line. For reference, the black line in Fig. 6 shows the state
of the rock glacier just after buildup (6000 a), immediately before the
temperature step change is introduced. The increase in the rate factor causes
an immediate speedup in horizontal flow of the entire landform by a factor
of about 2 (Fig. 6c, yellow lines), which then decays with time (orange to
red lines). As a result of the enhanced mass transport, the landform also
shows a distinct thinning of up to 0.02 m a -1 in the upper part of
the rock glacier and on the talus slope (Fig. 6b). At the front the
rock glacier continues to thicken and consequently advance, but at accelerated
rates as a consequence of enhanced flow speeds (Fig. 6d). With time, the
creep velocity, advance rate and thinning reduce and approach stable values
again after about 1000 a for Murtèl. We term in the following the time
it takes for this readjustment the “adjustment time”. This new state after
dynamic adjustment is, apart from the advancing front, stable and
characterized by a slightly faster creep velocity and a thinner rock glacier
body in order to transport the constant material supply from upstream.
Consistent with the creep velocity, the advance rate is also slightly
enhanced (Fig. 6d) whereas the volume grows at a constant rate throughout the
simulation, reflecting again the constant material supply and mass
conservation (Fig. 6e).
Modeled evolution of surface geometry (a), absolute
thickness (b), horizontal velocity (c) along the central
flow line, terminus advance (d) and volume evolution (e)
for Murtèl rock glacier when the material input is switched off at
6000 a, after the rock glacier buildup (-1.5 ∘C rock glacier
temperature). The black line shows the state of the system before the
switch-off of material supply at 6000 a. The lines are plotted at 100 a
time intervals.
Additional model simulations for other reference temperatures of the
rock glacier of -1 and -2 ∘C, show qualitatively very similar
results but the absolute rates of change scale proportionally to the
enhancement factors in the rate factor given in Table 5. The same experiments
for the Huhh1 rock glacier show quantitatively similar responses which are of
higher absolute magnitude and adjust within 100 a to a new quasi-stable
state also much faster.
Sediment experiment
In a second set of experiments, the influence of variations in sediment and
ice supply is investigated by varying the material input ar but keeping
the rock glacier temperature constant. Since there are no empirical data on
the impact of temperature increase on sedimentation and ice accumulation
rates, a range of changes in material supply rates has been explored.
Figure 7 shows the modeled response for an extreme example in which the ice
and sediment input is completely switched off after rock glacier buildup (at
6000 a). The results show that the rock glacier continues to creep downslope
and advance but with reduced velocities that start to decrease from upstream.
This slowdown is related to a thinning, reduced slope and driving stresses
in the upper part of the rock glacier as the downstream flowing mass is no
longer fully replaced by accumulation of material on the talus slope. The
rock glacier body essentially creeps downstream without any mass added or
removed, which is reflected well in the constant volume with time (dotted line
in Fig. 7e). The advance rates thereby decrease at relatively low rates. The
upper parts of the rock glacier react immediately to the change of material
input as this is where the sedimentation is taking place. Note that the
maximal thinning rates are only as high as the former material accumulation
rate (in case of Murtèl 0.006 m a -1, for Huhh1
0.022 m a -1).
Experiments with different perturbations in material input rates show
qualitatively similar changes but of reduced magnitude (Supplement Figs. S2
to S13) and are also evident in differing advance and volume growth rates
(Fig. 7d and e).
Combined experiment
As atmospheric warming is expected to influence both rock glacier temperatures
as well as ice and sediment production, we thus perform a third set of
experiments in which we combine the above perturbations.
All combined experiments. The creep rate change is implemented by
increasing the rate factor A (Eq. 6) and the change in material
accumulation by varying the accumulation rate ar (Eq. 9).
Model runCreep rateAccumulationchangechange1.4 ⋅A and 0 ⋅ Acc1.4 ⋅A0 ⋅ar1.4 ⋅A and 0.4 ⋅ Acc1.4 ⋅A0.4 ⋅ar1.4 ⋅A and 1 ⋅ Acc1.4 ⋅A1 ⋅ar1.4 ⋅A and 2 ⋅ Acc1.4 ⋅A2 ⋅ar1.7 ⋅A and 0 ⋅ Acc1.7 ⋅A0 ⋅ar1.7 ⋅A and 0.4 ⋅ Acc1.7 ⋅A0.4 ⋅ar1.7 ⋅A and 1 ⋅ Acc1.7 ⋅A1 ⋅ar1.7 ⋅A and 2 ⋅ Acc1.7 ⋅A2 ⋅ar2.7 ⋅A and 0 ⋅Acc2.7 ⋅A0 ⋅ar2.7 ⋅A and 0.4 ⋅ Acc2.7 ⋅A0.4 ⋅ar2.7 ⋅A and 1 ⋅ Acc2.7 ⋅A1 ⋅ar2.7 ⋅A and 2 ⋅ Acc2.7 ⋅A2 ⋅ar
Twelve scenarios were run for each rock glacier assuming three different
initial thermal states of each rock glacier (see Table 5), a potential warming
of 1 ∘C and four different scenarios concerning the material input
(see Table 6). The corresponding results are shown in the Supplement.
In Figs. 8 and 9 we show detailed results for both Murtèl and Huhh1
rock glacier for one representative perturbation experiment in which we used a
reference rock glacier temperature of -1.5 ∘C, an increase in
temperature of 1 ∘C (corresponding to a rate factor increase by
factor 1.7; Table 5) and a decrease of material input to 40 % of the
original value. We assume that warming and subsequent thawing of permafrost
in rock walls will lead to an increase in sediment
production in the short term but is expected to attenuate in the long term (Krautblatter et
al., 2013). Therefore we keep the material input from the rock wall constant but
reduce the ice contribution to the total material influx.
Modeled evolution of absolute thickness (a) and horizontal
velocities (b) of the Murtèl rock glacier introducing a
1 ∘C temperature increase (1.7 times increase in rate factor) and a
reduction in material input to 40 % after the rock glacier buildup
(6000 a, black line). The black lines in all plots depict the state of the
rock glacier as shown in Fig. 5 before the perturbations were introduced. The
lines are plotted at 100 a time steps.
The evolution of absolute thickness (a) and horizontal
velocities (b) of the Huhh1 rock glacier introducing a 1 ∘C
temperature increase (1.7 times increase in rate factor) and 40 % of the
initial material input after rock glacier buildup (600 a, black line). The
black lines in all plots depict the state of the rock glacier as shown in
Fig. 6 before the perturbations were introduced. The lines are plotted in
10 a steps.
Figures 8 and 9 illustrate the evolution of surface geometry and horizontal
velocities along the central flow line of Murtèl and Huhh1 rock glacier,
respectively. This combined experiment shows an upstream thinning of the
“initial” landform in the subsequent years (Figs. 8a and 9a) and a
substantial increase in horizontal velocities (Figs. 8b and 9b). The maximum
thinning rates occur within the first few decades of the experiment and
amount to 1.6 cm a-1 for Murtèl and 6 cm a-1 for Huhh1 (see
Fig. 11). A new stable geometry with advancing front is successively
approached, again within adjustment times of roughly 1000 and 100 a for
Murtèl and Huhh1, respectively. The final thickness and velocities of the
main rock glacier body are, however, very close to the initial values.
Rock glacier evolution of thickness, horizontal velocity, advance
and velocity after a 1 ∘C temperature increase and 40 % decrease
in material input after rock glacier buildup. The dynamic evolution is shown
for three points along the central flow line at 160, 200 and 400 m. The
rock glacier is assumed to have an initial temperature of -1.5 ∘C
Modeled maximum annual subsidence rates in the deposition area of
the rock glaciers in relation to the reference temperature and change in
material input and for the two temperature models of Arenson and Springman
(2005; black lines) and Paterson and Budd (1982; grey lines) immediately
after a 1 ∘C temperature step increase. Note the different scales
for subsidence for the two rock glaciers.
Figure 10 shows the more detailed temporal evolution of geometry and creep
velocity at three distinct positions on both rock glaciers. The rock glaciers
keep advancing throughout the simulation, with initially slightly enhanced
rates caused by the temperature increase and a successive slight slowing down
caused by the reduced material accumulation rates. The adjustment times of
Murtèl rock glacier are much lower compared to Huhh1, which was also shown
by the simple perturbation experiments.
The additional combined experiments with a 1 ∘C temperature increase
but variable reference temperatures and varying sediment supply rates show
qualitatively similar geometric and kinematic responses (see Supplement
Figs. S1–S24).
Subsidence
The sensitivity of the dynamic response to the initial temperature and to the
temperature-dependent model has been further analyzed for the combined
perturbation (1 ∘C warming, 60 % reduction in material input) in
a sensitivity modeling study (for detailed results see Supplement). As
subsidence is one of the observable quantities from repeated DEM analysis on
real rock glaciers, we summarized the results in terms of maximum thinning
rates in Fig. 11.
For the Paterson and Budd (1982) temperature relation, thinning rates are
almost independent of the reference rock glacier temperature, but they increase
with a reduction in material supply and reach maximum thinning rates of 1.8
and 6.5 cm a-1 for Murtèl and Huhh1, respectively. When using the
Arenson and Springman (2005) temperature model, thinning rates strongly
increase towards warmer rock glacier reference temperatures, reaching maximum
values of 3.4 and 12.5 cm a-1 for Murtèl and Huhh1, respectively.
DiscussionModeling approach and rock glacier buildup
Based on a continuum approach, our numerical model couples observed sediment
input rates and the rock glacier creep process in order to simulate the
evolution of creep velocities and surface geometry as well as their dynamic
interactions. This quantitative approach of coupling the relevant subsystems
(headwall, deposition area and rock glacier), although highly simplified, was
successful in building up the observed rock glacier geometries and related
kinematics (horizontal velocities) within the expected timescales (Table 1).
The basic dynamic behavior of a continuously advancing rock glacier body is
well reproduced, while the thickness of the main body remains roughly
constant.
The modeling of rock glacier buildup shows that besides topographical
factors such as slope, the long-term advance rates and horizontal velocity
are predominantly controlled by the rates of material accumulation and
rock glacier rheology, whereas the thickness of the main landform seems less
sensitive to material supply rates.
The match of observed to modeled velocities and thicknesses should, by model
construction, be expected (for similar surface slopes) given that the rate
factor A and therefore the viscosity of the rock glacier material has been
derived from such observed quantities (Eq. 11), but the agreement supports
our modeling approach. More importantly, the material input rates and
buildup times are fully independent estimates and it is therefore not
necessarily obvious to get the right rock glacier geometry at the prescribed
time.
Our modeled constant advance rates and consistency between modeled and
previously estimated rock glacier buildup times further supports the method
of back-calculating rock glacier age from current surface velocities
(Frauenfelder and Kääb, 2000; Kääb and Vollmer, 2000;
Haeberli et al., 2003). Even for the case of temperature perturbations,
advance rates of the front do not substantially change in the long term and
thus this “dating” methods seem still appropriate for alpine rock glaciers.
Advance rates are in the long term, however, affected by changes in material
supply rates. It remains to note that it is actually the vertically averaged
velocity, and not the surface velocity, that should match the advance rates.
Our modeled advance rates (derived from an assumed rheology with n= 3
in Eq. 5) corresponds in general to four-fifths of the surface velocity (e.g.,
modeled surface velocity on the main body of 0.065 m a -1 and an
advance rate of 0,054 m a -1 for Murtèl rock glacier).
Consequently, using surface velocities in back calculations of rock glacier
age may overestimate the age. For many real-world rock glaciers (including
Murtèl), rock glacier movement is dominated by deformation in a shear zone
near the base and thus surface and vertically averaged creep is almost
identical.
Strong simplifications have been made for our modeling approach such as using
a homogenous sediment–ice body of uniform temperature and rheology and a
spatially uniform and temporally constant material input. The successful
rock glacier buildup therefore supports the idea that despite such
simplifications rock glacier dynamics and evolution can be reduced to our
simple model approach, which is based on the historic concept of Wahrhaftig
and Cox (1959) and confirms earlier numerical modeling approaches of
Olyphant (1983) and Frauenfelder et al. (2008).
The nonlinear viscous Glen type flow law used here is also supported by
laboratory experiments (Arenson and Springman, 2005) and field observations
from boreholes (Arenson et al., 2002). However, in reality the involved flow
law parameters are, unlike the assumptions of our model, rarely constant in
space and time. The flow law exponent n has been found to increase with ice
content (Arenson et al., 2002; Arenson and Springman, 2005) and rock glacier
creep is mostly dominated by relatively thin shear layers with reduced
viscosity (Hoelzle et al., 2002; Haeberli et al., 2006; Buchli et al., 2013).
A more complex rheology of ice-debris mixtures could in theory and should in
the future be included in rock glacier creep models, but currently there is
very limited quantitative, field-based information available to constrain
more complex constitutive relationships. Especially the role of moisture and
the existence of unfrozen water appears to have a strong impact on the
properties ice–debris mixtures as temperature nears the melting point and
need to be further addressed (Moore, 2014) in establishing an adapted
flow law for rock glaciers. This becomes increasingly more complex as an
expected warming will not only influence the rheological properties of the
ice itself but also change the ratio of ice and debris by reducing the
volumetric ice content. A new ice–debris proportion will alter the viscosity
of the rock glacier in a spatially heterogeneous manner because melting
effects have been shown to be spatially diverse (Arenson and Springman, 2005;
Monnier and Kinnard, 2016). Moisture variations due to
precipitation events have been shown to impact rock glacier rheology in the short
term down to a few days (Wirz et al., 2016), whereas the impact of a changing
ice–water proportion is assumed to show its consequences in the long term.
Nevertheless, due to the fact that the creep is dominated near the base
within our model and that we have calibrated our model parameters to observed
geometry and velocities, we do not expect the general dynamical behavior and
involved timescales to be substantially different for other rheological
parameter choices. We see our highly reduced approach also as an advantage
for identifying the most essential controls and processes in rock glacier
evolution.
In our approach the geomorphological mapping of the different subsystems,
the quantification of sediment input rates, the ice content and the
horizontal velocities are the crucial observational constraints and
sufficient to set up a model of rock glacier evolution. However, the
simplicity of the model design does not, by construction, allow reproduction
of the exact small-scale features such as ridges and furrows of the two
chosen real-world rock glaciers (Frehner et al., 2015).
Dynamical adjustment to external forcing
The perturbation modeling experiments of applying a sudden change in
sediment input, material temperature or a combination of the two provide
useful insights into the dynamic and geometric adjustment of rock glaciers to
changes in external forcing and therefore also into potential mechanisms
that explain observed rock glacier degradation.
The two types of perturbation experiments show similarities but also clear
differences in the dynamic response. Both an increase in the rock glacier
temperature as well as a reduction in material input lead to a thinning of
the rock glacier and the talus slope, whereas the front keeps advancing
through thickening. Although the thinning is caused by different mechanisms
(lack of material supply from the rock wall or a runaway of mass through
creep acceleration), from an observational point of view the two forcing
mechanisms are difficult to distinguish. Importantly, the modeling shows a
pronounced thinning occurring in the upper parts of both rock glacier systems
(deposition area–talus slope).
The response in horizontal velocities are, for the two types of
perturbations, distinctly different. A reduction in material supply results
in a decrease of creep velocities from the top, whereas the temperature
increase leads to an immediate acceleration of the entire landform, although
in the long term the velocities return to almost pre-perturbation conditions
(see Figs. 6c and 7c). The temperature experiments show a brief increase in
the advance rates in the rock glaciers, but they subsequently return to similar
rates as before the perturbation. This occurs in contrast with a continuous
reduction of the advance rate during the decreased sediment supply
experiment. Therefore, temperature changes within the rock glacier show a
strong impact on short-term velocity variations whereas changes in the
material input determine the long-term advance rates and geometry. Similar
experiments by Olyphant (1983) and Frauenfelder et al. (2008) focused only on
combined experiments and could therefore not address the impact of the
individual forcings.
Dependence on rock glacier properties
Irrespective of the type of experiments, the absolute magnitude in response
(velocity change, thickness change or advance rate) is very different for the
two rock glaciers. Relative to the initial quantities, however
(pre-perturbation velocity, thickness or advance rates), the dynamic changes
are for both rock glaciers very similar (Fig. 10). This means that we should
expect dynamic changes of rock glaciers to be scalable by their geometric
(thickness) and kinematic characteristics (flow speed and advance rate). This
scalability is also in good agreement with the observational dataset of
multiannual creep variations of rock glaciers in the Swiss Alps (PERMOS,
2013). These show very similar normalized horizontal velocity variations as a
potential response to air temperature changes despite their distinctly
different characteristics (Delaloye et al., 2010 and PERMOS, 2013). Recent
continuous observations of creep velocities on rock glaciers in the Matter
Valley in the Swiss Alps confirm this finding even for seasonal timescales
(Wirz et al., 2016).
The modeled short-term increase in horizontal velocity for a 1 ∘C
warming in rock glacier body is also consistent with the observed speedup in
rock glacier creep of about 300 % in the year 2003/2004 with exceptional
snow conditions and a very warm summer (Delaloye et al., 2010).
Temperature dependence
Our temperature perturbation experiments assume an immediate warming of the
entire rock glacier due to an increase in air temperature and consequently
GST. This is, of course, an oversimplification because the vertical heat
transfer depends on the energy balance at the surface and heat transport
processes and thermal properties of the rock glacier material (Hanson and
Hoelzle, 2004). Heat transfer processes should potentially be implemented in
future studies (Kääb et al., 2007; Scherler et al., 2014). Hence we
consider our modeled warming rather as a simple way to investigate the
sensitivity to temperature increase.
For relatively thin rock glaciers such as Huhh1, a climatic warming could
affect the whole rock glacier thickness in timescales of a few years to
decades (Marmy et al., 2015). For thicker rock glaciers such as Murtèl,
it could take several decades to centuries for the temperature change to
reach the base where most of the deformation actually occurs. This implies
that thin, and consequently steep and fast, rock glaciers should be more
sensitive to warming from the surface.
The sensitivity to temperature warming is also enhanced for relatively warm
rock glaciers (with temperatures only a few degrees below freezing),
considering the most realistic model for temperature dependence of
rock glacier rheology by Arenson and Springman (2005). At -1.0 ∘C
rock glacier temperature, a warming of 1 ∘C results in a 2.7 times
increase in the rate factor (and hence creep velocity) whereas the same
warming at -2 ∘C results only in a 1.4 times higher rate factor.
Observed rock glacier temperatures in the Swiss Alps indicate already
relatively “warm” temperatures (close to zero degrees) and show a tendency
for further warming (PERMOS, 2013). Such a warming would further amplify the
response in acceleration. In contrast, when using a temperature dependence of
pure ice (Paterson and Budd, 1982), as done in an earlier attempt of modeling
the impact of temperature change on rock glacier creep (Kääb et al.,
2007), the sensitivity of creep to temperature warming is smaller (a
1 ∘C warming results in only a 1.25 times increase in rate factor)
and does not additionally increase towards warmer rock glacier temperatures
(Fig. 4). Thus, the impact of warming on creep acceleration could be bigger
than previously expected.
Adjustment timescales
The modeling shows that the “adjustment timescales” in thickness and
advance rates are for the faster and steeper Huhh1 rock glacier with 100 a,
an order of magnitude faster than the 1000 a of Murtèl rock glacier
(Figs. 6d and 7d). While in the literature such differences in adjustment
timescales have qualitatively been linked to the general rheology and mass
turnover, the controlling factors remain unquantified. A comparison to
theoretical considerations based on the kinematic wave theory developed by
Nye (1963) can be made for the material supply experiment. Besides the change
in material supply rate, the thickness adjustment depends mainly on the
traveling wave speed of the thickness perturbation and on its diffusion.
According to Nye (1963; and see also Hooke, 2005) the traveling wave speed
v0 is given by a multiple of the rock glacier flow speed and
specifically
v0=n+2⋅us.
The diffusion of the thickness perturbation is proportional to the
diffusivity which is given by
D0=n⋅qα=n⋅u‾hα,
where q is the ice flux and α the surface slope. For Murtèl and
Huhh1, this results in diffusivities of 30 and 53 m2 a-1, which
are as a result of very small creep velocities and low thicknesses much lower
compared to diffusivities of pure-ice glaciers.
Following Johannesson et al. (1989; see also Hooke, 2005, p. 376) the related
adjustment timescales of thickness changes to expand over the whole rock
glacier lobe then depend on a propagation timescale Tp and a
diffusion timescale Td. The propagation timescale is given by
Tp=L0v0=L0n+2⋅us,
where L0 is the length scale of the rock glacier lobe. This timescale is
inversely proportional to the horizontal velocity and consistent with our
modeling results means that a factor 10 difference in creep velocity between
Huhh1 and Murtèl rock glacier translates into a factor 10 difference in
adjustment time. For n= 3, lengths of 300 and 250 m and creep
velocities of 0.07 and 0.6 m a -1 for Murtèl and Huhh1, we obtain
adjustment timescales of 860 and 83 a, respectively. These theoretical values
agree in absolute and relative magnitude well with our modeled estimates.
The diffusion timescale is given by
Td=L02D0,
which results in 3000 and 1200 a for Murtèl and Huhh1, respectively,
for the thickness perturbation to spread over the entire landform and which
is substantially longer than the timescales derived above for the kinematic
wave propagation. These diffusion timescales are also much longer compared to
pure-ice glaciers and are consistent with the persistent occurrence of
morphological features of ridges and furrows on the surface of rock glaciers.
To conclude, the propagation timescale, and therefore the horizontal
velocity, is a simple and meaningful measure for rock glacier “adjustment
timescales”. The very similar adjustment timescales obtained for the
different types of perturbation experiments support the notion that this
propagation timescale Tp can be used as a general measure of
adjustment in creep dynamics to a step change in external forcing. Note that
the introduced adjustment timescale is not the same as the “volume response
time” for pure-ice glaciers for adjusting to a new climate (Johannesson,
1989) and should not be confused with a “reaction time” (time taken for a
rock glacier to show a detectable reaction on an external forcing).
Geometry change and subsidence
Regarding geometry, the modeled rock glaciers respond to both warming and
reduction in material input by a thinning of the landform that is fastest and
most pronounced in the deposition area and in the upper parts of the
rock glacier (Fig. 10). The front and therefore the landform as a whole
continues to advance, although at slightly differing speeds depending on the
applied perturbations (see Figs. 7b and 10a), even if the material input is
completely halted. The perturbation experiments can also be compared with the
observed subsidence data presented in Sect. 3 in order to investigate the
potentially controlling mechanisms of such geometry change. The observations
in Figs. 2 and 3 show a pronounced subsidence in the lower deposition area
and upper parts of the rock glaciers of roughly -0.05 m a -1 for the
Murtèl rock glacier and -0.16 m a -1 for Huhh1 rock glacier while
the lower rock glacier lobe shows relatively small or unchanging thicknesses
and an advancing front. Thus, the spatial patterns in modeled geometry
changes agree well with the observations. The absolute maximum rates of
modeled subsidence are for both rock glaciers between 2 and 10 times smaller
than the observed rates depending on the perturbation. These modeled rates
result from an immediate warming of 1 ∘C of the entire rock glacier
body, which is a rather extreme scenario. Further, the possible maximum rates
of thinning from a total switch off in material input rates are limited to
their pre-perturbation absolute values (0.006 m a -1 for Murtèl
and 0.022 m a -1 for Huhh1), which are also almost an order of
magnitude smaller than the observed subsidence rates.
Thus, we conclude that thinning due to thermally induced acceleration and a
reduction in material input are not sufficient to explain observed subsidence
patterns at Murtèl and Huhh1 rock glacier and that melt of subsurface ice
is additionally required for the observed volume loss. The process of
landform thinning, especially in the upper parts of the rock glacier, has been
described as a sign of degradation by Ikeda and Matsuoka (2002), Roer et
al. (2008b) and Springman et al. (2013). However, subsidence through melt of
subsurface ice remains poorly constrained through observations and our
process understanding and models linking them to external forcing are still
limited (Scherler et al., 2014) and therefore we did not include this process
in our flow modeling. In future work, internal ice melt (as a function of
temperature) could technically easily be included through a negative
accumulation term in the surface evolution Eq. (8) and an adjustment of the
mean density.
Conclusions
This study uses a numerical flow model based on the conservation of mass
within the cascading transport system of coarse debris to simulate the
long-term and current evolution of rock glacier surface geometry and velocity.
For a given sediment–ice input and rock glacier rheology, the model is able to
generate observed rock glacier geometries and creep velocities in realistic
timescales for two distinctly different rock glaciers. It is also capable of
reproducing the continuing advancing front through creep which is often
observed for rock glaciers (Barsch, 1996).
Climatic changes, especially increasing temperatures, are expected to
influence rock glacier dynamics in a profound way. Our modeling approach
allows not only for investigating the impact of a direct warming of the
rock glacier material by adjusting the rheology (rate factor) but also for
including the influence of changes in material input consisting of sediments
and ice. Changes in geometry and related kinematics in response to such
external perturbations can thereby be modeled and contribute towards a better
understanding of the evolution of rock glaciers. Note that effects of internal
ice melt or noncontinuous deformations such as the formation of tension
cracks are not included in the current version of the model. Our detailed
analysis of such perturbation experiments and modeling sensitivity studies
give the following insights on rock glacier dynamics:
Short-term changes in velocities and advance rates result from temperature
variations, whereas long-term geometric adaptations (thickness and advance
rates) are mainly influenced by material supply. We show that a 1 ∘C
temperature increase in rock glacier temperature can result in a 1.5–3 time
acceleration of horizontal velocity depending on the initial thermal state of
the rock glacier.
Both rock glacier temperature increase and reduction in material supply lead
to thinning, while for the latter the maximum thinning rates are limited by
the pre-perturbation material supply rate.
Irrespective of the perturbation, the rock glaciers keep advancing and remain
active although the thermal and sediment input conditions are not favorable
for their longevity, which is consistent with field observations.
Rock glaciers react spatially and temporally variably to changes in
environmental factors. Changes in temperature affect the entire landform but
the impact of material input variations is most pronounced in the
sedimentation area and upper parts of the rock glacier. Comparing the model
scenarios for localized topographic adaptations (subsidence) introduced by
warming and variations in sediment–ice supply to observed subsidence
features shows that these controlling factors are not sufficient to explain
the magnitudes observed for our two examples. This implies that other
processes such as melting of subsurface ice are responsible for subsidence
and need further investigation.
Although the absolute magnitudes in thinning and creep acceleration differ
between the two rock glaciers, the changes relative to the initial thickness
and creep velocity, respectively, are very similar thus indicating that
changes scale with their geometric and dynamic characteristics.
Based on most recent models of rock glacier rheology (Arenson and Springman,
2005), rock glaciers close to 0 ∘C likely show much stronger
reactions to thermal forcing than colder ones.
On the basis of our modeling and kinematic wave theory, we propose a typical
“timescale of dynamic adjustment” to external perturbations that is
given by the inverse of a few times the horizontal velocity of a rock glacier.
This timescale explains the order of magnitude difference in dynamic
adjustment of our two chosen rock glacier examples which amount to 1000 a for
Murtèl and 100 a for Huhh1.
The modeling approach presented here might serve as a useful tool to
determine the dynamic state of rock glaciers, their potential state of
degradation and related forcing mechanisms. The growing amount of
observations on geometric changes and rock glacier movements may thereby serve
as important constraints for such model assessments and serve as indicators
for the recent changes affecting periglacial high mountain systems.
Therefore, future monitoring strategies should specifically be designed to
detect spatially heterogeneous geometry changes and aim at observing entire
slope systems, in addition to focusing on single landforms.
Data availability
Data on rock glacier
kinematics are available from the PERMOS office upon request (see
http://www.permos.ch/data.html). The digital elevation models derived
from the RC30 sensor system at Murtél rockglacier 1996, 2002 and 2007 are
also part of the PERMOS dataset. The remaining DEMs are available upon
request from the authors.
The Supplement related to this article is available online at doi:10.5194/tc-10-2865-2016-supplement.
Acknowledgements
This study was conducted
within the SNF-Sinergia project TEMPS financed by the Swiss National Science
Foundation (project no. CRSII2 136279). Further support was granted by the
project X-sense 2 financed by the Swiss National Science Foundation and
funded by Nano-Tera.ch. The authors would like to thank all colleagues within
these projects for their valuable input during meetings and conferences.
Support from the PERMOS network (Permafrost Monitoring Switzerland) is also
thankfully acknowledged. We also thank Lukas U. Arenson and Christophe
Kinnard for their constructive comments. Edited by:
C. Hauck Reviewed by: L. Arenson and C. Kinnard
References
Arenson, L., Hoelzle, M., and Springman, S.: Borehole deformation
measurements and internal structure of some rock glaciers in Switzerland,
Permafrost Periglac., 13, 117–135, 2002.Arenson, L. U. and Springman, S. M.: Mathematical descriptions for the
behaviour of ice-rich frozen soils at temperatures close to 0 ∘C,
Can. Geotech. J., 42, 431–442, 10.1139/t04-109, 2005.Arenson, L. U., Johansen, M. M., and Springman, S. M.: Effects of volumetric
ice content and strain rate on shear strength under triaxial conditions for
frozen soil samples, Permafrost Periglac., 15, 261–271, 10.1002/ppp.498,
2004.Barsch, D.: Permafrost creep and rockglaciers, Permafrost Periglac., 3,
175–188, 10.1002/ppp.3430030303, 1992.
Barsch, D.: Rockglaciers: Permafrost Creep and Rockglaciers, Springer,
Berlin, 331 pp., 1996.Bishop, M. P., Shroder, J. F., and Colby, J. D.: Remote sensing and
geomorphometry for studying relief production in high mountains,
Geomorphology, 55, 345–361, 10.1016/S0169-555X(03)00149-1, 2003.Bodin, X., Rojas, F., and Brenning, A.: Status and evolution of the
cryosphere in the Andes of Santiago (Chile, 33.5∘ S.), Geomorphology,
118, 453–464, 10.1016/j.geomorph.2010.02.016, 2010.Bodin, X., Schoeneich, P., Deline, P., Ravanel, L., Magnin, F., Krysiecki,
J.-M., and Echelard, T.: Mountain permafrost and associated geomorphological
processes: Recent changes in the French Alps, J. Alp. Res., 103,
10.4000/rga.2885, 2015.Buchli, T., Merz, K., Zhou, X., Kinzelbach, W., and Springman, S. M.:
Characterization and Monitoring of the Furggwanghorn Rock Glacier, Turtmann
Valley, Switzerland: Results from 2010 to 2012, Vadose Zone J., 12,
1539–1663, 10.2136/vzj2012.0067, 2013.Carson, M. A.: Angles of repose, angles of shearing resistance and angles of
talus slopes, Earth Surf. Process., 2, 363–380, 10.1002/esp.3290020408,
1977.
Cuffey, K. M. and Paterson, W.: The physics of glaciers, 4th ed., Elsevier,
Amsterdam, 693 pp., 2010.Delaloye, R., Lambiel, C., and Gärtner-Roer, I.: Overview of rock glacier
kinematics research in the Swiss Alps, Geogr. Helv., 65, 135–145,
10.5194/gh-65-135-2010, 2010.
Delaloye, R., Morard, S., Barboux, C., Abbet, D., Gruber, V., Riedo, K., and
Gachet, S.: Rapidly moving rock glaciers in Mattertal, in: Mattertal – ein
Tal in Bewegung, edited by: Graf, C., Jahrestagung der Schweizerischen
Geomorphologischen Gesellschaft, St. Niklaus, 29 June–1 July, WSL,
Birmensdorf, 2011.Fischer, L., Amann, F., Moore, J. R., and Huggel, C.: Assessment of
periglacial slope stability for the 1988 Tschierva rock avalanche (Piz
Morteratsch, Switzerland), Eng. Geol., 116, 32–43,
10.1016/j.enggeo.2010.07.005, 2010.Frauenfelder, R. and Kääb, A.: Towards a palaeoclimatic model of
rock-glacier formation in the Swiss Alps, Ann. Glaciol., 31, 281–286,
10.3189/172756400781820264, 2000.Frauenfelder, R., Schneider, B., and Kääb, A.: Using dynamic modeling
to simulate the distribution of rockglaciers, Geomorphology, 93, 130–143,
10.1016/j.geomorph.2006.12.023, 2008.Frehner, M., Ling, A., and Gärtner-Roer, I.: Furrow-and-Ridge Morphology
on Rockglaciers Explained by Gravity-Driven Buckle Folding: A Case Study From
the Murtèl Rockglacier (Switzerland), Permafrost Periglac., 26, 57–66,
10.1002/ppp.1831, 2015.Gärtner-Roer, I.: Sediment transfer rates of two active rockglaciers in
the Swiss Alps, Geomorphology, 167–168, 45–50,
10.1016/j.geomorph.2012.04.013, 2012.
Gärtner-Roer, I. and Nyenhuis, M.: Volume estimation, kinematics and
sediment transfer rates of active rockglaciers in the Turtmann Valley,
Switzerland, in: Landform – structure, evolution, process control:
Proceedings of the International Symposium on Landform organised by the
Research Training Group 437, edited by: Otto, J.-C. and Dikau, R., Lecture
notes in earth sciences, 115, Springer, Berlin, 185–198, 2010.Glade, T.: Linking debris-flow hazard assessments with geomorphology,
Geomorphology, 66, 189–213, 10.1016/j.geomorph.2004.09.023, 2005.Glen, J. W.: The creep of polycristalline ice, P. R. Soc. London, 228,
519–538, 10.1098/rspa.1955.0066, 1955.Gruber, S., Hoelzle, M., and Haeberli, W.: Permafrost thaw and
destabilization of Alpine rock walls in the hot summer of 2003, Geophys. Res.
Lett., 31, L13504, 10.1029/2004GL020051, 2004.
Haeberli, W., Brandova, D. B. C., Egli, M., Frauenfelder, R., Kääb, A.,
Maisch, M., Mauz, B., and Dikau, R.: Methods for the absolute and relative
dating of rock-glacier surfaces in alpine permafrost, in: Permafrost:
Proceedings of the Eighth International Conference on Permafrost, 21-25 July
2003, Zurich, Switzerland, edited by: Phillips, M., Springman, S., and
Arenson, L. U., Lisse, Abingdon, 343–348, 2003.Haeberli, W., Hallet, B., Arenson, L., Elconin, R., Humlun, O., Kaab, A.,
Kaufmann, V., Ladanyi, B., Matsuoka, N., Springman, S., and Vonder Muhll, D.:
Permafrost creep and rock glacier dynamics, Permafrost Periglac., 17,
189–214, 10.1002/ppp.561, 2006.
Haeberli, W., Hoelzle, M., Kääb, A., Keller, F., Vonder Mühll,
D., and Wagner, S.: Ten years after drilling through the permafrost of the
active rock glacier Murtèl, Eastern Swiss Alps: answered questions and
new perspectives, in: Proceedings of 7th Interntional Permafrost Conference,
Yellowknife, Nordicana, 57, 403–410, 1998.Hanson, S. and Hoelzle, M.: The thermal regime of the active layer at the
Murtèl rock glacier based on data from 2002, Permafrost Periglac., 15,
273–282, 10.1002/ppp.499, 2004.Hasler, A., Gruber, S., and Beutel, J.: Kinematics of steep bedrock
permafrost, J. Geophys. Res., 117, F01016, 10.1029/2011JF001981, 2012.Heckmann, T. and Schwanghart, W.: Geomorphic coupling and sediment
connectivity in an alpine catchment – Exploring sediment cascades using
graph theory, Geomorphology, 182, 89–103,
10.1016/j.geomorph.2012.10.033, 2013.Hoelzle, M., Mühll, D. V., and Haeberli, W.: Thirty years of permafrost
research in the Corvatsch Furtschellas area, Eastern Swiss Alps: A review,
Norsk Geogr. Tidsskr., 56, 137–145, 10.1080/002919502760056468, 2002.
Hooke, R. L.: Principles of Glacier Mechanics, Cambridge University Press,
Cambridge, 371–381, 2005.Ikeda, A. and Matsuoka, N.: Degradation of talus-derived rock glaciers in the
Upper Engadin, Swiss Alps, Permafrost Periglac., 13, 145–161,
10.1002/ppp.413, 2002.
IPCC – Intergovernmental Panel on Climate Change: Climate Change 2013: The
Physical Science Basis.: Contribution of Working Group I to the Fifth
Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge
University Press, Cambridge, 2014.Jansen, F. and Hergarten, S.: Rock glacier dynamics: Stick-slip motion
coupled to hydrology, Geophys. Res. Lett., 33, L10502 ,
10.1029/2006GL026134, 2006.
Johannesson, T., Raymond, T. C., and Waddington, E. D.: Time-scale for
adjustment of glaciers to change in mass balance, J. Glaciol., 35, 355–369, 1989.Kääb, A.: Remote sensing of permafrost-related problems and hazards,
Permafrost Periglac., 19, 107–136, 10.1002/ppp.619, 2008.Kääb, A. and Vollmer, M.: Surface Geometry, Thickness Changes and
Flow Fields on Creeping Mountain Permafrost: Automatic Extraction by Digital
Image Analysis, Permafrost Periglac., 11, 315–326,
10.1002/1099-1530(200012)11:4<315:AID-PPP365>3.0.CO;2-J,
2000.Kääb, A. and Weber, M.: Development of transverse ridges on rock
glaciers: field measurements and laboratory experiments, Permafrost
Periglac., 15, 379–391, 10.1002/ppp.506, 2004.
Kääb, A., Gudmundsson, G. H., and Hoelzle, M.: Surface deformation of
creeping moutnain permafrost, Photogrammetric investigations on rockl glacier
Murtèl, Swiss Alps, in: 7th International Permafrost Conference
Proceedings, Yellowknife, USA, 531–537, 1998.Kääb, A., Frauenfelder, R., and Roer, I.: On the response of
rockglacier creep to surface temperature increase: Climate Change Impacts on
Mountain Glaciers and Permafrost, Global Planet. Change, 56, 172–187,
10.1016/j.gloplacha.2006.07.005, 2007.Kenner, R., Bühler, Y., Delaloye, R., Ginzler, C., and Phillips, M.:
Monitoring of high alpine mass movements combining laser scanning with
digital airborne photogrammetry, Geomorphology, 206, 492–504,
10.1016/j.geomorph.2013.10.020, 2014.Krautblatter, M., Moser, M., Schrott, L., Wolf, J., and Morche, D.:
Significance of rockfall magnitude and carbonate dissolution for rock slope
erosion and geomorphic work on Alpine limestone cliffs (Reintal, German
Alps), Geomorphology, 167–168, 21–34, 10.1016/j.geomorph.2012.04.007,
2012.
Krautblatter, M., Funk, D., and Günzel, F. K.: Why permafrost rocks become
unstable: a rock-ice-mechanical model in time and space, Earth Surf. Process.
Landforms, 38, 876–887, doi:10.1002/esp.3374, 2013.
Lambiel, C.: Le glacier rocheux déstabilisé de Tsaté-Moiry (VS)
caractéristiques morphologiques et vitesses de déplacement., in: La
géomorphologie alpine: Entre patrimoine et contrainte/actes du colloque
de la Société suisse de géomorphologie, 3–5 September 2009,
Olivone, edited by: Lambiel, C., Reynard, E., and Scappozza, C.,
Géovisions, 36, Institut de géographie de l'Univ. de Lausanne,
Lausanne, 211–224, 2011.
Laustela, M., Egli, M., Frauenfelder, R., Kaab, A., Maisch, M., and Haeberli,
W.: Weathering rind measurements and relative age dating of rockglacier
surfaces in crystalline regions of the Eastern Swiss Alps, in: Proceedings of
the 8th International Conference on Permafrost, edited by: Phillips, M.,
Springman, S. M., and Arenson, L. U., Zurich, 21–25 July, Swets &
Zeitlinger/Balkema, the Netherlands, 627–632, 2003.
Leysinger Vieli, G.-M. and Gudmundsson, G. H.: Evolution of rock glaciers and
alpine glaciers: A model – model approach, in: Permafrost: Proceedings of the
Eighth International Conference on Permafrost, 21–25 July 2003, Zurich,
Switzerland, edited by: Phillips, M., Springman, S., and Arenson, L. U., Lisse,
Abingdon, 2003.Leysinger Vieli, G. J.-M. C. and Gudmundsson, G. H.: On estimating length
fluctuations of glaciers caused by changes in climatic forcing, J. Geophys.
Res., 109, F01007, 10.1029/2003JF000027, 2004.Marmy, A., Rajczak, J., Delaloye, R., Hilbich, C., Hoelzle, M., Kotlarski,
S., Lambiel, C., Noetzli, J., Phillips, M., Salzmann, N., Staub, B., and
Hauck, C.: Semi-automated calibration method for modelling of mountain
permafrost evolution in Switzerland, The Cryosphere Discuss., 9, 4787–4843,
10.5194/tcd-9-4787-2015, 2015.Menditto, A., Patriarca, M., and Magnusson, B.: Understanding the meaning of
accuracy, trueness and precision, Accredit. Qual. Assur., 12, 45–47,
10.1007/s00769-006-0191-z, 2007.Micheletti, N., Lambiel, C., and Lane, S. N.: Investigating decadal-scale
geomorphic dynamics in an alpine mountain setting, J. Geophys. Res.-Earth,
120, 2155–2175, 10.1002/2015JF003656, 2015.Monnier, S. and Kinnard, C.: Interrogating the time and processes of
development of the Las Liebres rock glacier, central Chilean Andes, using a
numerical flow model, Earth Surf. Process., 41, 1884–1893,
10.1002/esp.3956, 2016.Moore, P. L.: Deformation of debris-ice mixtures, Rev. Geophys., 52,
435–467, 10.1002/2014RG000453, 2014.Morris, S. E.: Topoclimatic Factors and the Development of Rock Glacier
Facies, Sangre de Cristo Mountains, Southern Colorado, Arct. Alp. Res., 13,
329, 10.2307/1551039, 1981.Müller, J., Gärtner-Roer, I., Kenner, R., Thee, P., and Morche, D.:
Sediment storage and transfer on a periglacial mountain slope (Corvatsch,
Switzerland), Geomorphology, 218, 35–44, 10.1016/j.geomorph.2013.12.002,
2014a.Müller, J., Gärtner-Roer, I., Thee, P., and Ginzler, C.: Accuracy
assessment of airborne photogrammetrically derived high-resolution digital
elevation models in a high mountain environment, ISPRS J. Photogramm., 98, 58–69,
10.1016/j.isprsjprs.2014.09.015, 2014b.
Nye, J. F.: The response of a glacier to changes in the rate of nourishment
and wastage, P. R. Soc. London, 275, 87–112, 1963.
Oerlemans, J.: Glaciers and climate change, A.A. Balkema Publishers, Lisse,
148 pp., 2001.Olyphant, G.: Computer simulation of rock-glacier development under viscous
and pseudoplastic flow, Geol. Soc. Am. Bull., 94, 499,
10.1130/0016-7606(1983)94<499:CSORDU>2.0.CO;2, 1983.Otto, J.-C., Kleinod, K., Konig, O., Krautblatter, M., Nyenhuis, M., Roer,
I., Schneider, M., Schreiner, B., and Dikau, R.: HRSC-A data: a new
high-resolution data set with multipurpose applications in physical
geography, Prog. Phys. Geog., 31, 179–197,
10.1177/0309133307076479, 2007.Paterson, W. and Budd, W. F.: Flow parameters for ice sheet modeling,
Cold Reg. Sci. Technol., 6, 175–177, 10.1016/0165-232X(82)90010-6, 1982.
Permafrost in Switzerland 2008/2009 and 2009/2010, edited by: Noetzli, J.,
Glaciological Report (Permafrost), no. 10/11 of the Cryospheric Commission of
the Swiss Academy of Sciences, 80, 2013.Phillips, M., Mutter, E. Z., Kern-Luetschg, M., and Lehning, M.: Rapid
degradation of ground ice in a ventilated talus slope: Flüela Pass, Swiss
Alps, Permafrost Periglac., 20, 1–14, 10.1002/ppp.638, 2009.
Rasemann, S.: Geomorphometrische Struktur eines mesoskaligen alpinen
Geosystems, Dissertation, Bonner geographische Abhandlungen, 111, Asgard,
Sankt Augustin, 240 pp., 2004.Ravanel, L. and Deline, P.: Climate influence on rockfalls in high-Alpine
steep rockwalls: The north side of the Aiguilles de Chamonix (Mont Blanc
massif) since the end of the `Little Ice Age', The Holocene, 21, 357–365,
10.1177/0959683610374887, 2011.
Roer, I.: Rockglacier kinematics in a high mountain geosystem, Dissertation,
Bonner Geographische Abhandlungen 117, Bonn, 2005.
Roer, I., Avian, W., Kaufmann, V., Delaloye, R., Lambiel, C., and
Kääb, A.: Observations and considerations on destabilizing active
rock glaciers in the European Alps., in: Proceedings of the 9th International
Conference on Permafrost, University of Alaska, Fairbanks, Alaska, 29 June–3
July 2008, edited by: Kane, D. L. and Hinkel, K. M., Institute of Northern
Engineering, University of Alaska, Fairbanks, Fairbanks, Alaska, 1505–1510,
2008a.
Roer, I., Haeberli, W., Avian, M., Kaufmann, V., Delaloye, R., Lambiel, C.,
and Kääb, A.: Observations and considerations on destabilizing active
rock glaciers in the European Alps, in: Ninth International Conference on
Permafrost, 1505–1510, 2008b.
Roer, I., Kääb, A., and Dikau, R.: Rockglacier kinematics derived
from small-scale aerial photography and digital airborne pushbroom imagery,
Zeitschrift für Geomorphologie, 49, 73–87, 2005a.
Roer, I., Kääb, A., and Dikau, R.: Rockglacier acceleration in the
Turtmann valley (Swiss Alps): Probable controls, Norsk Geogr. Tidsskr., 59,
157–163, 2005b.
Roer, I., Kääb, A., and Dikau, R.: Rockglacier kinematics derived
from small-scale aerial photography and digital airborne pushbroom imagery,
Zeitschrift für Geomorphologie, 49, 73–87, 2005d.Roer, I. and Nyenhuis, M.: Rockglacier activity studies on a regional scale:
comparison of geomorphological mapping and photogrammetric monitoring, Earth
Surf. Process., 32, 1747–1758, 10.1002/esp.1496, 2007.Scherler, M., Schneider, S., Hoelzle, M., and Hauck, C.: A two-sided approach
to estimate heat transfer processes within the active layer of the
Murtèl–Corvatsch rock glacier, Earth Surf. Dynam., 2, 141–154,
10.5194/esurf-2-141-2014, 2014.Schneider, S., Hoelzle, M., and Hauck, C.: Influence of surface and
subsurface heterogeneity on observed borehole temperatures at a mountain
permafrost site in the Upper Engadine, Swiss Alps, The Cryosphere, 6,
517–531, 10.5194/tc-6-517-2012, 2012.Springman, S. M., Arenson, L. U., Yamamoto, Y., Mayer, H., Kos, A., Buchli,
T., and Derungs, G.: Multidisciplinary investigations on three rockglaciers
in the Swiss alps: Legacies and future perspectives, Geogr. Ann. A, 94, 215–243,
10.1111/j.1468-0459.2012.00464.x, 2012.
Springman, S. M., Yamamoto, Y., Buchli, T., Hertrich, M., Maurer, H., Merz,
K., Gärtner-Roer, I., and Seward, L.: Rock Glacier Degradation and
Instabilities in the European Alps: A Characterisation and Monitoring
Experiment in the Turtmanntal, CH, in: Landslide Science and Practice,
edited by: Margottini, C., Canuti, P., and Sassa, K., Springer Berlin Heidelberg,
Berlin, Heidelberg, 5–13, 2013.
Vonder Mühll, D., Noetzli, J., and Roer, I.: PERMOS – a comprehensive
monitoring network of mountain permafrost in the Swiss Alps., in: Proceedings
of the 9th International Conference on Permafrost, University of Alaska,
Fairbanks, Alaska, 29 June–3 July 2008, edited by: Kane, D. L., and Hinkel,
K. M., Institute of Northern Engineering, University of Alaska, Fairbanks,
Fairbanks, Alaska, 2008.Wagner, S.: Creep of alpine permafrost, investigated on the Murtèl rock
glacier, Permafrost Periglac., 3, 157–162, 10.1002/ppp.3430030214, 1992.Wahrhaftig, C. and COX, A.: Rock Glaciers in the Alaska Range, Geol. Soc. Am. Bull., 70, 383,
10.1130/0016-7606(1959)70[383:RGITAR]2.0.CO;2, 1959.Whalley, W. B. and Martin, H. E.: Rock glaciers: II models and mechanisms,
Prog. Phys. Geog., 16, 127–186, 10.1177/030913339201600201,
1992.Whalley, W. and Azizi, F.: Rheological models of active rock glaciers –
Evaluation, Critique and a possible test, Permafrost Periglac., 5, 37–51,
10.1002/ppp.3430050105, 1994.
White, S. E.: Rockfall, alluvial and avalanche in the Colorado front Range,
1961–1968, Arct. Alp. Res., 3, 77–97, 1973.Winsvold, S. H., Kaab, A., and Nuth, C.: Regional Glacier Mapping Using
Optical Satellite Data Time Series, IEEE J. Sel. Top. Appl. Earth Obs. Remote
Sens., 9, 1–14, 10.1109/JSTARS.2016.2527063, 2016.
Winsvold, S. H., Kaab, A., and Nuth, C.: Regional Glacier Mapping Using
Optical Satellite Data Time Series, IEEE J. Sel. Top. Appl. Earth Obs. Remote
Sens., 9, 1–14, 10.1109/JSTARS.2016.2527063, 2016Wirz, V., Gruber, S., Purves, R. S., Beutel, J., Gärtner-Roer, I.,
Gubler, S., and Vieli, A.: Short-term velocity variations of three rock
glaciers and their relationship with meteorological conditions, Earth Surf.
Dynam. 4, 103–123, 10.5194/esurf-4-103-2016, 2016.