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A Global View on Permafrost in Steep Bedrock
Stephan Gruber
Department of Geography, University of Zurich, Switzerland
Abstract
Mountainous topography covers a considerable proportion of the global permafrost region. There, temperature changes
and the degradation of permafrost in steep bedrock can evoke rapid geomorphic change, some of which may result innatural hazards. Due to the strong relief of most rock walls, corresponding events can have a long runout and transform
into cascading events, such as impact to lakes or the damming of rivers that propagate far below the periglacial zone. The
identication of areas that potentially have permafrost conditions in steep rock is the important rst step in the evaluation
of corresponding hazards. During the past decade, researchers have given considerable attention to permafrost in steep
bedrock, although most investigations have been conducted in the European Alps. This contribution provides a summary
of ndings related to the delineation of permafrost in rock walls. Based on this, simple considerations and data sources are
outlined that may help the application of current knowledge in remote mountain regions.
Keywords:bedrock slopes; mountains; steep terrain; global; hazard zonation; mapping.
Introduction
A signicant proportion of the global permafrost region
has mountainous topography (Gruber 2011a). Additionally,
coastal cliffs may be subject to permafrost conditions, and
changes to permafrost there can alter the stability of rock
faces perched high above valleys and thus pose a hazard to
human life and infrastructure (cf. Carey 2005). This may
occur indirectly through, for example, impacts to lakes that
may cause long-distance secondary events (cf. Geertsema &
Cruden 2008, Geertsema & Clague 2011). However, non-
stationarity, incomplete understanding of processes, and lack
of information on local surface and subsurface conditions
challenge corresponding hazard zonation. Here, the delineation
of permafrost rock slopes can serve as a proxy for areas thatmay require special attention or surveillance, as they are
prone to rapid changes in response to climate forcing (Gruber
2011b). Absent or minimal vegetation, a reduced snow cover,
and less important active-layer processes make permafrost in
steep rock a system that is simple enough for attempting an
extrapolation of ndings to environments not measured. In this
contribution, I summarize ndings on the spatial and temporal
variability of mean annual ground temperature (MAGT) and
permafrost in steep bedrock. These ndings, often based on a
narrow range of environmental conditions, are extended with
hypotheses for generalization to other environments. This is
intended to support the estimation of permafrost conditions in
steep rock globally, and to provide a framework to test andimprove them by means of measurement, experiment, and
observation. Unless stated otherwise, the investigations cited
have been performed in the European Alps.
Rock Temperature: Factors and Processes
Basic considerations
The energy uxes at and near the ground surface are shown
for the two conceptual end members of steep and homogenous
bedrock and a horizontal debris slope in Figure 1. Longwave
radiation is mostly affected by air temperature, moisture
content, and clouds. Turbulent uxes mostly depend on airtemperature and wind.
Solar irradiation, however, is strongly dependent on
cloudiness, sun-terrain geometry, and topography, and results
in a high degree of spatial differentiation. Figure 2 shows three
conceptual scales that determine ground temperatures. When
considering global patterns, differing climate conditions affect
the strength of the topographic inuence.
For example, in areas with more abundant clouds and diffuse
radiation, topographic differentiation is less pronounced than
in areas with few clouds and strong direct solar radiation. The
Figure 1. Schematic of energy balance at and near the ground
surface in steep bedrock (A) and gentle debris slopes (B).
Figure 2. Conceptual scales of inuence on ground temperatures.
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spatial differentiation of MAGT can be conveniently described
relative to mean annual air temperature (MAAT) using
(1)
Because MAAT is a commonly available climate variable,
dT helps to estimate local patterns relative to it. MAAT is
often subject to strong intra-annual variation, but dT for near-
vertical rock remains rather constant (cf. Noetzli & VonderMuehll 2010).
Near-vertical and compact rock
Near-vertical and compact rock faces exhibit a strong
topographic control on subsurface temperatures and a weak
thermal inuence of snow and active-layer processes typical
for debris-covered slopes (Fig. 1). Spatial patterns of dT are
dominated by direct solar radiation (cf. Hoelzle 1994) and
modied by rock albedo (cf. Hall 1997). For this reason,
they are a simple system to investigate and to then gradually
expand by considering additional processes. Gruber et al.
(2003) present a review of previous investigations and a
strategy for measuring in steep rock faces. Corresponding data
are available through PERMOS (cf. Noetzli & Vonder Muehll
2010) and a pan-Alpine inventory of permafrost evidence
(Cremonese et al. 2011). In near-vertical and compact rock,
MAGT is often measured 530 cm below the surface and
presumed to be equivalent to that just below the active layer.
Based on the work of Allen et al. (2009) summarizing 14
one-year time series from the Southern Alps of New Zealand
(44S), dT in sun-exposed slopes can be estimated to 4.5
6.5C. In the European Alps (46N), Boeckli et al. (2012)
estimated this to be 5.56C based on 57 locations and a
statistical model. A process-based modeling study (Gruber
et al. 2004) in the European Alps resulted in dT rangingfrom 6.5 to 9C. The model is driven by daily data that do
not resolve temperature differences between east and west
exposure. This may result from convective clouding in the
afternoon lowering the temperature on west-exposed faces by
reducing direct solar radiation. Generally, dT increases with
elevation due to more shortwave and less longwave radiation,
and with decreasing precipitation due to a higher amount of
direct radiation. Reection from surrounding snow-covered
slopes can locally increase shortwave irradiation and thus dT.
This effect is assumed to have affected dT at two measured
locations by 23C (cf. Allen et al. 2009). Without any solar
radiation, dT would become slightly negative due to longwave
loss.Summarizing this paragraph, dT likely ranges from 0 to 9C
in steep and compact rock at latitudes near 45, and varies
mostly as a function of solar radiation.
Surface heterogeneity and clefts
Most rock slopes differ from the near-vertical case because
micro-topography and fracturing promote patchy covers of
debris, snow, and ice (Gruber & Haeberli 2007). The thermal
inuence of snow, fractures, and active-layer processes can
thus contribute to the heterogeneity of dT. Safety issues
and the dominance of lateral heterogeneity in near-surface
measurements of MAGT, however, complicate corresponding
research. Gubler et al. (2011) found that MAGT on more
gentle slopes can already vary by up to 2.5C within an area of
10 m x 10 m. For heterogeneous bedrock slopes, this value is
likely often exceeded.
Using measurements at four depths down to 85 cm in
borings and deeper on thermistor strings lowered into clefts,
Hasler et al. (2011) estimated a local cooling effect of fractureson the order of 1.5C. This cooling resulting from ventilation
likely depends on cleft aperture and abundance, and its
functioning may resemble ventilation effects in coarse blocks
(cf. Harris & Pedersen 1998) or, in extreme cases, those in
ice caves (Obleitner & Sptl 2011, Schner et al. 2011). A
local lowering of dT by several C, even in shaded slopes,
thus appears possible in rare cases. For practical use, however,
an assumption of 12C cooling, increasing from shaded to
sun-exposed slopes, appears plausible for heterogeneous
conditions. Snow deposited in clefts may have an additional
cooling effect by consuming latent heat during melting. At
the same time, however, snow cover or inll can inhibit air
circulation and thus reduce the associated cooling (Hasler et
al. 2011). A thermal diode effect caused by seasonally varying
proportions of ice/water/air in pores and fractures can cause a
lowering of temperatures at depth (Gruber & Haeberli 2007)
similar to the thermal offset described for lowland permafrost
(cf. Smith & Riseborough 2002), but this has not been detected
in measurements (Hasler et al. 2011).
Snow and perennial ice
Snow on rock faces alters the coupling between the
atmosphere and subsurface and thus affects dT. It is usually
thinner and spatially and temporally more variable than in
gentle terrain. Due to difcult access, corresponding studiesare rare (cf. Wirz et al. 2011). Rock faces often extend far
above the equilibrium line of glaciers and receive much of their
precipitation in solid form. In those conditions, temperature
moderates the retention of snow because cohesive snow near
melting conditions is more likely to accumulate than cold
snow that is prone to be removed by wind and sliding. For
cold and shaded faces, this can cause a pronounced snow
cover during summer, whereas precipitation in winter barely
affects the bare and dark surfaces of ice and rock (cf. Gruber &
Haeberli 2007). Depending on the seasonality of precipitation,
snow during summer can be common in high-elevation
rock faces. For thin snow, the net warming through thermal
insulation during winter is reduced and the relative importanceof cooling through albedo and latent heat uptake during melt
becomes greater. Higher albedo decreases dT more strongly
on sun-exposed slopes, whereas the effect of latent heat can
cause a lowering of dT in all slope aspects.
Based on numerical experiments under the assumption of
laterally homogeneous snow cover, Pogliotti (2011) estimated
this cooling to have magnitudes of up to 2C with respect to
snow-free rock. In reality, this is further modied in laterally
heterogeneous and discontinuous snow cover because a lateral
interaction between snow-covered and snow-free rock facets
dT= MAGT- MAAT
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exists by heat conduction in rock as well as by radiative and
sensible exchange at the surface (cf. Neumann & Marsh 1998).
Based on distributed measurements of rock temperature,
Hasler et al. (2011) estimated the cooling effect of snow in
radiation-exposed faces to be up to 23C.
Ice faces, hanging glaciers, or surface lowering of glaciers
can inuence the temperature regime in steep rock and can
exhibit strong spatio-temporal variations (Fischer et al.
2011). While ice faces and hanging glaciers are diagnostic ofpermafrost conditions at their rock-ice interface, their absence
does not indicate the absence of permafrost. The occurrence of
cold rn (Suter et al. 2001, Suter & Hoelzle 2002, Hoelzle et
al. 2011), and thus hanging glaciers, follows differing patterns
than rock temperature because they are subject to higher albedo
and are affected by wind through snow transport. In gently
inclined parts of hanging glaciers, the percolation of water into
the rn and heat release at depth during refreezing can cause
zones of temperate rn and ice (Haeberli & Alean 1985). As
a consequence, an inference of temperature below ice cover
is difcult. For ice faces that are subject to minimal ow and
balance change, a cooling with respect to rock is likely for
sun-exposed slopes due to the inuence of albedo. For a north-
exposed ice face, Hasler et al. (2011) report approximately the
same mean annual temperature as in nearby rock.
Three-dimensional and transient effects
Spatial variation of surface conditions and their temporal
changes inuence permafrost bodies at depth (cf. Gold &
Lachenbruch 1973), and in mountain areas this is further
complicated by geometric effects (Kohl 1999, Gruber et al.
2004). The combination of a distributed MAGT model and
three-dimensional heat-transfer modeling of steep topography
(Noetzli et al. 2007) showed complicated permafrost bodies
with steeply inclined isotherms near peaks and ridges. Even insteady-state, permafrost can be induced below non-permafrost
terrain facets due to nearby cold slopes. Transient simulations
were performed with a similar setup (Noetzli & Gruber 2009)
and accounted for temperature changes during the past. This
revealed the importance of past climate and latent heat that
can lead to permafrost bodies persisting at depth below slopes
that today would be interpreted as permafrost-free. Because
of multi-lateral warming, the reaction of convex topography,
such as ridges or rock spurs, can be much faster than that of
at terrain (Noetzli & Gruber 2009). Several new boreholes
in steep rock and in ridges (Noetzli et al. 2010, Noetzli et al.
2008, Noetzli & Vonder Muehll 2010) support many of the
general ndings from the modeling studies.
The Global View: Estimating Spatial Patterns
of Rock Temperatures for Diverse Mountain
Ranges
In this section, simple approaches for estimating permafrost
occurrence in rock faces worldwide are proposed. It is
important to keep in mind that this is based on limited point
data from a restricted range of environmental conditions.
Furthermore, the derivation of such heuristics has an element
of subjectivity, especially where it involves the delineation of
permafrost zones.
Global distribution
For strongly shaded rock faces, the 0C long-term isotherm
of the MAAT is a good pointer to determine the elevation
above which permafrost must be expected, even though
permafrost may sometimes be found at lower elevation. Due
to the absence of better data, the zonation shown in Gruber
(2011a) can provide an approximation globally at about 1 km
resolution. While few rock faces are dominated by inversion
effects, inversions are important to consider in the choice
of local meteorological stations as possible alternatives.
As the extrapolation of MAAT in rugged terrain involvesconsiderable vertical distances, the choice of appropriate lapse
rates is important. If suitable ground measurements do not
exist, the lapse rate can be approximated based on model data
(Gruber 2011a) or regional radiosonde measurements. MAAT
data covering a period of several decades helps to minimize
the inuence of short-term uctuations. It is sometimes
necessary to account for longer-term transient effects that have
occurred during the past decades or centuries with respect to
the measurement period chosen (cf. Noetzli & Gruber 2009).
Topography and solar radiation
Topography inuences dT for individual slopes, mainly
through its geometric effect on incoming solar radiation.Generally, steeper and more rugged terrain causes a wider
range of dT than more gentle terrain. This effect, however,
is modied by latitude and the proportion of direct radiation.
As a rst approximation, a ruggedness index (e.g., Gruber
2011a) can be used to identify terrain tending to have a higher
proportion of steep and strongly shaded rock slopes. Locally,
the differentiation of slopes with respect to solar radiation can
be estimated based on the calculation of mean annual potential
solar irradiation and a decameter-resolution DEM (e.g., Farr et
al. 2007). This operation is routinely available in GIS software.
Figure 3. Latitude-dependency of maximum (solid) and minimum
(dashed) potential direct solar radiation received in rugged terrain.
The experiment shown spans slope angles 090, slope expositions
0180 (because east and west are identical in this respect), and has
no horizon shading.
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Latitude
Besides its effect on MAAT, latitude inuences the
maximum amount of total annual solar irradiation received by
the most suitably exposed slope. For this reason, the range of
dT is also likely to be affected by latitude (Fig. 3). Further,
the partitioning of radiation with topography changes with
latitude. Toward the poles, increasingly steep slopes receive
the highest amounts of radiation; near the tropics, rather gentleslopes receive the highest radiation input. Furthermore, the
sensitivity to cast shadowing by obstructed horizons increases
toward the poles with the prevalence of low solar elevation
angles.
Continentality
Continental (as opposed to maritime) climate is
characterized by comparably large seasonal thermal variations
and dryness, both generally caused by large distances from
major water bodies and altered by atmospheric circulation
patterns and rain-shadow effects. The dryness in continental
areas is usually accompanied by very high amounts of direct
solar radiation afforded by often cloud-free skies. BesidesMAAT, continentality is often used to describe spatial patterns
of cryosphere phenomena (e.g. Holmlund & Schneider 1997,
King 1986, Haeberli & Burn 2002, Shumskii 1964) and is
frequently characterized by a continentality index dened as
the average difference between the coldest and warmest month
at a location.
The continentality index shown in Figure 4 provides an
appreciation of its global patterns that may help to inform the
extrapolation of ndings from one mountain range to another.
The patterns of temperature range, the proportion of direct
sunlight, and precipitation are jointly described by the concept
of continentality. However, these affect rock temperature in
differing ways and often correlate much less than expected
when plotted based on gridded climate data. Until further
analyses help to disentangle these effects, the assumption of
subdued spatial differentiation of dT toward maritime areas
likely provides a good assumption. This effect of continentally
or precipitation on the degree of spatial differentiation due tosolar radiation is, however, not clearly detectable in current
measurements (cf. Allen et al. 2009, Boeckli et al. 2012) that
span only small gradients.
Surface characteristics
As a general rule, rough surfaces can be assumed to be colder
than smooth ones. Cooling is caused by a thin, intermittent,
and frequent snow cover and by air circulation in fractures or
debris.
At least qualitatively, the roughness of rock walls can be
assessed based on eld visits, photographs, aerial photographs,
or high-resolution satellite imagery. Increasingly, the imagery
freely available on GoogleEarth, for example, has sufcientresolution to provide valuable rst impressions.
Conclusion
Based on research from a narrow range of environmental
conditions and the consideration of what appear to be the
processes that govern permafrost distribution in steep bedrock,
I have proposed simple considerations to estimate permafrost
in rock walls worldwide. Besides the potential for practical
application, this contribution points to the wide range of
Figure 4. Continentality index derived from 20002010 mean monthly surface air temperatures based on ERA-Interim re-analysis data. Dark
areas are maritime; light areas are continental climate.
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environmental conditions that drive permafrost in steep terrain.
More systematic research in integrating local and regional
research to achieve a coherent understanding would be a good
avenue to progress beyond the heuristics presented here. Such
research would consolidate understanding by basing it on a
wider range of environmental conditions.
Acknowledgments
Over the past ten years, many colleagues and friends
have contributed toward the synthesis presented here.
These contributions have come not only through the works
referenced, but also though inspiring discussions and eld
campaigns. Among these are: Jeannette Ntzli, Andreas
Hasler, Marco Peter, Adrian Zgraggen, Lorenz Bckli, Jan
Beutel, Simon Allen, Martin Hoelzle, Ludovic Ravanel, Paolo
Pogliotti, Umberto Morra di Cella, Edoardo Cremonese, and
Reynald Delaloye. ECMWF ERA-Interim data used in this
study have been obtained from the ECMWF data server.
Michael Krautblatter is acknowledged for valuable and
insightful reviewer comments.
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