Permafrost distribution in steep slopes in Norway : measurements , statistical modelling and geomorphological implications

Permafrost in steep slopes has been increasingly studied since the early 2000s in conjunction with a 15 growing number of rock-slope failures, which likely resulted from permafrost degradation. In Norway, rockslope destabilization is a widespread phenomenon and a major source of risk for the population and infrastructure. However, the lack of precise understanding of the permafrost distribution in steep slopes hinders the assessment of its role in these destabilizations. This study proposes the first nation-wide permafrost probability map for the steep slopes of Norway (CryoWall map). It is based on a multiple linear regression 20 model fitted with multi-annual rock surface temperature (RST) measurements, collected at 25 rock-wall sites, spread across a latitudinal transect (59-69°N) over mainland Norway. The CryoWall map suggests that discontinuous permafrost widely occurs above 1300-1400 and 1600-1700 m a.s.l. in the north and south slopes of southern Norway (59°N), respectively. This lower altitudinal limit decreases in northern Norway (70°N) by about 500±50 m, with more pronounced decrease for south faces, in reason of the insolation patterns largely 25 driven by midnight sun in summer and polar night in winter. Similarly, the mean annual RST differences between north and south faces of similar elevation range around 1.5°C in northern Norway and 3.5°C in southern Norway. The CryoWall map is evaluated against direct ice observations in steep slopes and discussed in the context of former permafrost studies in various types of terrains in Norway. We show that permafrost can occur at much lower elevations in steep rock slopes than in other terrains, especially in north faces. We demonstrate 30 that the CryoWall map is a valuable basis for further investigations related to permafrost in steep slopes in both practical concerns and fundamental science. Earth Surf. Dynam. Discuss., https://doi.org/10.5194/esurf-2018-90 Manuscript under review for journal Earth Surf. Dynam. Discussion started: 4 February 2019 c © Author(s) 2019. CC BY 4.0 License.


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Permafrost processes affect rock-wall stability as much on short as on long time scales (days to millennia), by modifying the bedrock and ice-mechanical properties (Krautblatter et al., 2013). Permafrost aggradation provokes ice segregation processes, which prepare high-magnitude slope failure by favouring fracture propagation at depth (Matsuoka and Murton, 2008). Permafrost degradation can critically modify the shear strength of ice-filled fractures, with the most critical conditions being between -2 and 0°C (Davies et al., 2001).

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Water circulating in ice-free or partly ice-filled fractures could also accelerate the melting of ice in joints (Hasler et al., 2011a), while hydrostatic pressures caused by hydraulic permeability of ice-sealed fractures also adds to slope destabilization (Fischer et al., 2010). Rock-slope failures jeopardize infrastructures, activities and individuals in the either by direct hit or by potential secondary effects, such as displacement waves and catastrophic flooding through debris flows (e.g. Huggel et al., 2005;Romstad et al., 2009.

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Finally, rock fall and rock avalanches are essential agents of periglacial and paraglacial mass wasting processes (Ballantyne, 2002), and mass wasting and sediment transport sources in general (Korup, 2009). The role of the thermal regime as a significant driver for landscape forming processes has been emphasized recently (Berthling and Etzelmuller, 2011), and developed in modelling approaches to understand landscaping processes (e.g. Hales and Roering, 2007;Egholm et al., 2015). It is evident that the understanding of thermal regime within mountain 20 slopes, and its development during past and the future, has significant relevance for geomorphology.
In Norway, the glacially shaped deep valleys and fjords are prone to mass-wasting processes. Rock-slope failures from the oversteepened slopes and potential secondary effects, such as displacement waves, represent one of the most deadly natural hazards in the country (Furseth, 2006;Hermanns et al., 2012). Over the last 500 years, approximately 800 events and 500 fatalities have been recorded throughout the country, among which three 25 displacement waves, triggered by major rock-slope failures, caused the loss of 175 lives during the 20 th century (Furseth, 2006;Hermanns et al., 2013;. At present, more than 253 unstable rock slopes have been mapped systematically, and are partly monitored periodically by the Norwegian geological survey . At one of seven rock-slope instabilities, that are continuously monitored because of the potentially severe consequences in case of failure, direct observations allowed for a detailed assessment about the role of 30 permafrost in local rock-wall dynamics (Blikra and Christiansen, 2014). Many of these unstable slopes are most likely located at or above the lower boundary of altitudinal permafrost (Hilger et al., 2018). However, the lack of knowledge about its precise distribution in steep slopes precludes a systematic assessment of its role in the conditioning of rock slope failures.
Permafrost monitoring networks have been deployed in gentle mountain slopes and mires of northern and 35 southern Norway in the frame of national and international research programs (Ødegård et al., 1992;Harris et al., 2001;Christiansen et al., 2010;Isaksen et al., 2011;. Numerical models have been used to Earth Surf. Dynam. Discuss., https://doi.org /10.5194/esurf-2018-90 Manuscript under review for journal Earth Surf. Dynam. Discussion started: 4 February 2019 c Author(s) 2019. CC BY 4.0 License. assess the permafrost distribution at the national and Scandinavian scales (Westermann et al., 2013;Gisnås et al., 2013;2017). The study of permafrost in steep slopes in Norway has recently started with direct measurements of rock surface temperature (RST) in the high-elevated alpine areas of Jotunheimen and Hurrungane (Hipp et al., 2014). Myhra et al. (2017) have simulated the permafrost evolution since the end of the Little Ice Age (1880) to present, for steep mountain sites spread over a latitudinal transect over Norway. At the 5 national scale, a first-order estimation of the permafrost distribution in steep slopes has been proposed by Steiger et al., (2016), based on a straight forward empirical relationship between air and rock-wall surface temperatures. Finally, Frauenfelder et al. (2018) studied ground thermal and geomechanical conditions in a permafrost-affected rockslide site in Troms (northern Norway). It is likely that changing rock and ice-temperatures, due to general warming and in response to the extreme warm previous year, have played an important role in this detachment.

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Knowing the current distribution of permafrost is a prerequisite to assess its past, present and future variability, as well as to provide key-knowledge and tools to landuse-planners and geomorphologists. Thus, the lack of precise knowledge regarding the nation-wide distribution of steep slope permafrost is a major gap for both fundamental research and practical concerns. Therefore, we have monitored the RST at 25 measurement points, covering various aspects and elevations across a latitudinal transect of Norway to (i) characterize the thermal 15 regime in steep slopes, (ii) calibrate a statistical model of RST and (iii) map permafrost probability for steep slopes at the national scale. In this paper, we present (i) the measurement settings and strategy, (ii) the approaches for statistical modelling and permafrost probability mapping, and (iii) the permafrost distribution in steep slopes at the national scale and for local areas of interest.

2 Study area
The Norwegian mainland has a land area of c. 350000 km 2 , and is dominated by the mountain chain of the Scandes, stretching between 57 -71 °N through Norway and Sweden over a distance of more than 2000 km.
Scandinavia forms a tilted margin, with highest elevations found towards the western coast, decreasing towards the east and the Bothnian Sea. The area has undergone multiple glaciations during the Pleistocene, with the probably preserved under cold-based ice conditions during the major glaciations (e.g. Kleman et al., 1999).
Steep slopes and rock walls are mainly associated to four types of settings (e.g. Steiger et al., 2016): (i) steep valley sides associated to large U-shaped valleys which drained the ice sheets during the glaciations, (ii) rock 30 walls formed by local glaciations, mostly located along the western coast of the country and within the highest mountain regions of central southern Norway, (iii) rock walls associated to overthrusted nappes, such as in Hallingskarvet, and (iv) rock walls associated to steep river incisions, such as Alta canyon (Čávžu in Sami) in Finnmark. High-relief areas of Norway have experienced a high rock-slope failure activity throughout the late Pleistocene and Holocene, with a peak shortly after deglaciation (Böhme et al. 2015, Hermanns et al. 2017 In general, the lower limit of mountain permafrost in Scandinavia decreases from the western coast towards eastern Norway and north-western Sweden, while the glaciation limit increases from west to east (e.g. King, 1983King, , 1986Etzelmüller et al., 2003a). These gradients follow the climatic setting, with the maritime climate along the western coast (moist and high snow cover) gradually changing towards a more continental climate in the eastern parts of Norway (dry and less snow cover). In southern Norway, permafrost is mostly associated with 5 bedrock in mountain settings, with coarse ground moraines and regolith (Farbrot et al., 2013;Gisnås et al., 2013;2017;Christiansen et al., 2010;Westermann et al., 2013) with the lower limit of discontinuous permafrost decreasing from c. 1600 m a.s.l. in the west to c. 1200 m a.s.l. in the east (Etzelmüller et al., 2003a). In northern Norway, on the other hand, the permafrost limit decreases from 800-900 m a.s.l. in the western mountains of Troms county, to 200-300 m a.s.l. in more continental areas, where it is often found in depressions characterized 10 by peat plateaus (Borge et al., 2017).
The ongoing thawing and degradation of permafrost since the Little Ice Age (LIA) is likely to continue within the 21 st century, with the lower altitudinal limit projected to rise up to 1800-1900 m a.s.l. in southern Norway (Hipp et al., 2012). Projections at the national scale based on an equilibrium model suggest that stable permafrost 15 will be confined to 0.2% of mainland Norway by the end of the 21 st century while it occupies about 6-6.5% of the ground at present, and was extending over 14% of the ground at the end of the LIA (Gisnås et al., 2013). At present, we can expect considerable areas in Norway with thawing and degrading permafrost, which at greater depths is likely also a transient response to post-LIA warming.

Rock surface temperature monitoring
During the summers of 2015 to 2017, twenty-one temperature loggers (Geoprecision, M-Log5W-ROCK) were installed in eight mountain areas to record RST at a depth of 10 cm with a 2-h interval (Fig. 1). The installation procedure followed the approach described by Gruber et al. (2004a). Together with the remaining four out of five temperature loggers installed in 2010 in Jotunheimen (Hipp et al., 2014), a network of twenty-five 25 temperature loggers was available for this study. In order to represent a wide range of climate settings, they were distributed between 60.33° N and 69.46°N, 230 to 2320 m a.s.l., and in various aspects (Table 1, Fig. 2). Specific attention was paid to the topographical settings, to make sure that the loggers are not covered by snow during winter. This would make the recorded RST unsuitable for statistical modelling since it is unreliable to account for snow in such approaches. This is due to the high variability of snow in space and time in steep slopes, 30 resulting from the interactions between topographical and topoclimatic factors controlling the snow thickness, distribution and thermal properties, and that produce highly fluctuating thermal effects (Haberkorn et al., 2015;2017;Magnin et al., 2015a;2017a

Linear regression modelling and permafrost probability calculation
RST in steep slopes can be modelled by calculating the energy balance at the site (Gruber et al., 2004b), but for a regional survey with high spatial resolution, a statistical approach is better suited. From earlier investigations, it is widely accepted that RST is mainly related to incoming short-wave solar radiation and air temperature (Gruber et al., 2004b, Hipp et al., 2014. These two parameters are easily obtained over larger regions and with sufficient 5 spatial resolution, and thus available for multiple linear regression modelling. In a similar statistical approach, Boeckli et al. (2012a) have tested the role of precipitation and its seasonality, which have shown no significance.
In this study, we therefore predict the Mean Annual RST (MARST pred ) for the steep slopes of Norway as follows: where a is the MARST pred value when PISR and MAAT are equal to 0, PISR and MAAT are respectively the MARST pred ) are used to evaluate the suitability of the data sample for the linear regression model. We further performed a repeated ten-fold cross validation approach, which allows testing the model performance by

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partitioning the data set into ten sub-samples from which nine are used to fit the model while, one is kept to test the model (Gareth et al., 2014). The process is then repeated for each sub-sample and the means of the calculated R2, RMSE and MAE for each run are then provided to evaluate model performance (RM cv , RMSE cv and MAE cv ).
Ten folds balance the possible bias or high variability associated to respectively low and high fold numbers.
Finally, the probability of permafrost occurrence P(p) is expressed by the probability of MARST pred at a given 20 location to be ≤ 0°C. To calculate p, MARST pred is first transformed into a normal variable (MARST norm ) of mean µ = 0 and variance σ 2 = 1 with: In which µ pred and σ pred are the mean and standard deviation of MARST pred , respectively. The negative sign associated to MARST pred is necessary since we calculate the probability of MARST pred to be negative.

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In the final step, p is calculated using a logistic approximation of the cumulative normal distribution developed by Bowling et al. (2009):

Calculation of model variables
In order to ensure the suitability of the collected RST time series for linear modelling, a visual preliminary data control is performed. Daily means are computed from hourly records and plotted against local air temperature (AT) measurements (Fig. 3). Smoothing of the temperature curves and disconnection with AT oscillations are identified, since they indicate thick snow accumulation (Hanson and Hoelzle, 2004) which considerably 5 influences the RST (Magnin et al., 2015a;Haberkorn et al., 2015Haberkorn et al., : 2017. Daily RST data usually follows AT oscillations throughout the year (Fig. 3). In summer, the sensors, which are most exposed to solar radiation become warmer than both the air and the more shaded sensors. No obvious smoothing of the daily RST is found in the presented time series, making them all suitable for statistical modelling.
After this visual check, daily RST data are aggregated to mean annual values (MARST). For the eight loggers at

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Mannen, in Jotunheimen and in Alta, the records were interrupted by missing data. In order to calculate the MARST for the incomplete record the data gaps are filled by fitting a linear regression with local AT measurements (daily averages). For this, AT time series showing the best correlation with RST time series were chosen ( Table 2). The RST data processing provides 85 MARST measurement points to fit the regression model.
MAAT for the measurement period is calculated for each MARST point, using local meteorological records at 15 different elevations, from which a lapse rate is calculated. Similarly to the RST reconstruction, weather stations are chosen based on the best correlation between daily AT and RST records. To derive the most accurate MAAT during the RST measurement period, we calculate the lapse rate at a daily time step between relatively low-and relatively high-lying weather stations. When AT records are incomplete, an average lapse rate is calculated for the period of the gap (two months overlap on each side of the gap) and for each of the recorded years. This yields 20 a standard lapse rate value for the period of the gap, taking into account that lapse rate values can vary significantly throughout seasons. The meteorological data used to reconstruct MAAT at each of the MARST locations are presented in Table 3.
The PISR is then calculated for each MARST point at an hourly resolution over one year and considering a transmissivity of 100% (no atmosphere) using the Spatial Analyst tools of ArcGIS (© ESRI, Redlands, CA,

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USA). PISR is highly sensitive to topographical settings (sun-exposure, slope and viewshed), and thus highly dependent on the quality and coverage of the DEM. For the Mannen, Narvik, Flåm, Loen and one of the Kåfjord with the MARST, MAAT and PISR data used to fit the multiple linear regression model (Fig. S1, Tab. S1).

Permafrost mapping
MAAT and PISR are first mapped over the entire country based on the 10 m resolution DEM. The PISR is 5 calculated using the same parameters as for the model explanatory variable: hourly time step and 100% transmissivity. The MAAT is mapped using the SeNorge2 dataset, which is interpolated from in-situ temperature observations over grid point elevations at 1 km resolution (Lussana et al., 2017), and daily AT grids available from 1957. For the downscaling to a 10 m resolution, we first averaged daily AT data of the normal period 1981-2010 to generate a 1 km resolution MAAT raster. Then, for each 1 km grid cell, an average lapse rate is 10 calculated over a radius of 25 km (Fig 5). This regional lapse rate is then used to interpolate 1km MAAT grid to a 10 m resolution. The 25 km radius ensures a precision at the regional scale, representing the relatively high lapse rate of the maritime coasts and the relatively low lapse rates in the more continental areas, while smoothing local patterns and possible artefacts.
MARST pred and permafrost probability are then mapped by implementing Eq. (1) and (3) in a raster calculator.

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Since the model is only valuable for steep slopes with restricted snow and debris covers, the map is only produced for slopes > 40°, which is a conservative threshold above which a 10 m resolution DEM is expected to display steep slopes.

Permafrost classes and interpretation keys
The permafrost probability is calculated as a continuous variable ranging from 0 to 1 which is then classified into 20 four permafrost classes according to the international permafrost classification standards (Brown et al., 1997): Similarly to the Alpine-wide Permafrost Map covering the European Alps and its index interpretation keys (Boeckli et al., 2012b), the here proposed permafrost classes are interpreted against local bedrock settings ( result of the effect of sparse snow deposits preventing from heating of direct solar radiation and the effect of air ventilation in fractures, which acts as a shortcut between the cold atmosphere and the subsurface (Hasler et al., 2011b;Magnin et al., 2015a;2017a;Haberkorn et al., 2015). Sporadic permafrost suggests that permafrost exists only if the local settings are very favourable, meaning that the slope surface is substantially rugged and therefore more significantly covered by snow and debris. Finally, isolated permafrost refers to isolated and perennial ice 5 bodies found in open bedrock fractures at relatively low elevation.

Model variables and summary statistics
The lowest MARST registered over the measurement period (Tab. 4) is found at Juv_4, the second highest The lowest PISR value is at Fla_N, the most shaded sensor of the lowest latitude, and the highest one is at Adj_S, a high-elevated and south-exposed logger in northern Norway (Fig. 5).
At eleven loggers, the measurements directly suggest permafrost occurrence (negative MARST every year).

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Permafrost-free conditions (positive MARST every year) are suggested at nine loggers with recorded MARST consistently > 1°C, and possible permafrost, with MARST oscillating between -1 and 1.5°C is found at 5 loggers.
The presence of permafrost is nevertheless not excluded where positive MARSTs are recorded, because of the transient effect at depth from former colder periods (Noetzli and Gruber, 2009;Myhra et al., 2017), and a possible temperature offset (i.e. temperature difference between the surface and depth) resulting from the 20 fracturing and snow deposits (Hasler et al., 2011b).
The MARST difference between north-exposed and south-exposed faces is around 3.5°C in southern Norway . This difference between northern and southern Norway coincides with higher PISR values at north-exposed slopes of northern Norway, with for example 100 W.m -2 more at 25 Adj_N or Gam_N than at Fla_N or Man_N. Table 5 summarizes the statistics of the regression model. For most of the measurement points, the MARST is generally higher than the MAAT (Fig. 6a) and the difference between MARST and MAAT (surface offset) increases with increasing PISR (Fig. 6b), confirming previous studies of steep bedrock thermal characteristics (Boeckli et al., 2012a;Magnin et al., 2015a). The surface offset ranges from 0 to 4°C, the highest values being 30 found at the most sun-exposed sites (Fig. 6b). In some rare cases, the MARST is sligthly lower than the MAAT  where the highest peaks of Norway are located (Fig. 8b). West-facing slopes are generally predominant (30%), 10 while south-exposed faces are less frequent (20%), and north and east facing-slopes each represent a quarter of the steep slope surface area. However, this global pattern is not constant across latitudes, with for example, predominantly north-facing slopes between 65 and 67°N (Fig. 8a).
Continuous permafrost occupies about 2% of the rock wall surface area, discontinuous permafrost about 9% and sporadic permafrost about 20%, meaning that 31% of the rock wall surface area features a permafrost probability  permafrost classes according to latitude and aspect do not appear linear (Fig. 9) because the rock-wall distribution significantly controls this relationship (Fig. 8). However, there is a high correlation between the distribution of the 0°C isotherm (lower limit of discontinuous permafrost) and latitude (Fig. 10). The lower limit of permafrost decreases by about 60 m every degree northwards for north faces and almost 70 m for south facing 5 slopes.
The number of permafrost observations decreases with continentality ( Fig. 10) as most of the rock walls are found in the Caledonides close to the coast and in the interior mountain massifs of southern Norway such as Jotunheimen, Rondane or Dovrefjell (Fig. 11). In relation to continentality, the decrease in observations makes a statistical analysis of permafrost distribution poorly relevant. Nevertheless, we note that the lowermost 10 occurrences of discontinuous permafrost in north faces of southern Norway are found at the furthest distance from the sea, in Sølen, Sennsjøkampen, and the border with Sweden in the Nesjøen area ( Fig. 10 and 11). In northern Norway, the lowermost occurrences of discontinuous permafrost are not found near the coast, but further inland (about 25 to 50 km away from the sea, Fig. 11). At such distance, low-elevated rock walls (< 200 m a.s.sl.) are mostly found in river canyons, such as at the Alta, Reisa or Tana rivers (Fig. 11). It is also 15 noteworthy that in the general, the dominant areas of permafrost rock walls are located west of the main distribution of permafrost in Norway according to e.g. Gisnås et al. (2017).

Model evaluation
To evaluate the permafrost probability model, we compare the permafrost probability map for the steep slopes of 20 Norway, named "CryoWall map" in the following, to the rare permafrost evidences and studies in steep slopes of Norway. Unlike gentle slope permafrost, which produces typical landforms, such as rock glaciers or palsas and peat plateaus, permafrost in steep slopes only becomes evident by ice in rock fractures or failure scars. In northern Norway, Blikra and Christiansen (2014) observed sporadic permafrost in the fractures of the Jettan rock slide, extending from 400 to 800 m a.s.l., which is corroborated by the CryoWall map ( Fig. 11 and 12a). About  the CryoWall map (Fig. 12b).
In southern Norway, Etzelmüller et al. (2003b) report that ice was found during construction work in the 1950s at about 1500-1600 m in the bedrock of Gaustatoppen (1883 m a.s.l.), where the CryoWall map indicates discontinuous permafrost (Fig. 12c). Gaustatoppen is made of Precambrian quartzite, prone to macrogelivation and therefore to the producing of geometric blocks (Sellier, 1995). Combined with slopes rarely exceeding 55°, this results in a significant debris cover, favouring snow accumulation in winter and permafrost persistence, even with a relatively low probability value. Protruding rock outcrops also exists at Gaustatoppen, but they are generally highly fractured and covered by thin snow in winter, which makes them also favourable to permafrost persistence.

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In relation to the study by Steiger et al. (2016), this approach is an improvement as (i) we calibrate our model with observations and therefore account for the important influence of topographic aspect, (ii) we use an updated and improved spatial interpolation method for 2 m AT that has been used to build the SeNorge2 dataset (Lussana et al. 2017), (iii) we downscale AT using a regional lapse rate instead of using a standard and uniform one. The main pattern of steep-slope permafrost distribution is comparable, while locally deviations related to sun-

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Permafrost affecting steep rock slopes has mostly been studied in rock walls of the European Alps (45-46°N), where the lower limit of the isotherm 0°C lies around 2800±300 m a.s.l. in north faces and 3800±300 m a.s.l. in south faces (Gruber et al., 2004a;2004b;Magnin et al., 2015b). This difference of about 1000 m elevation between north and south faces is directly imputed to the solar radiation control, which results in a MARST difference reaching 8°C between the north and south faces of a same elevation. In British Columbia (Canada), 25 north faces are 4°C colder than south faces between 54°N and 59°N (Hasler et al., 2015). In the southern Alps of New Zealand, at 43°S, differences between north and south faces reaching a maximum of 5°C were reported (Allen et al., 2009). Our study presents MARST measurements at higher latitudes, where smaller and decreasing north-south differences with latitude are observed. This is the result of less and more direct solar radiation in south and north-facing slopes, respectively, which is reinforced at higher latitude due to the polar night in winter 30 and midnight sun during summer. This also explains the decreasing difference between the LAL limit of south and north faces towards lower latitudes (Fig. 9), where the south faces receive more solar radiation, unbalancing the air temperature controls, while the north facing slopes receive less direct solar radiation and are more directly controlled by air temperature. Despite the solar radiation control, which seems to be predominant in the RST patterns from local to continental scales, additional factors may also affect the RST. The snow that accumulate in various thicknesses in steep slopes has been recognized as a significant factor affecting the RST at the local scale, as it attenuate both, the winter cooling (Haberkorn et al., 2017) and the insolation heating in late winter and spring (Magnin et al., 2017b). In Norway, snow and frost coating (mainly due to atmospheric icing, i.e. high elevation rock walls that 5 are exposed to supercooled water in clouds and if combined with strong wind it can produce heavy ice accretions) are common in some of the high-elevation areas, and can provoke significant inter-annual variability of MARST in prevailing wind direction and preferential snow deposition (Frauenfelder et al. 2018). Furthermore, energy exchanges due to latent and sensible heat effects that are relatively more important in high-latitude and maritime settings than in more continental mountain areas possibly affect the RST patterns. In the same way, cloudiness, 10 that is generally more important in maritime settings, may also play an important role. This is evidenced by the relatively small north-south difference in the southern Alps of New Zealand that are at a rather low latitude but famous for their high precipitation rates. Such effects are not easily detectable by mean of visual control or statistical analysis and point out the need for more physic-based investigations in order to better understand their respective influence on MARST patterns and permafrost distribution. However, the good fit of observations with 15 the simple linear model indicates that such effects are only of minor relevance for Norway and do not strongly affect the overall permafrost distribution in steep slopes.

Permafrost characteristics in the steep slopes compared to other permafrost terrains in Norway
The distribution of permafrost has been estimated in various regions of southern and northern Norway by means of Bottom temperature of snow cover (BTS) measurements (Haeberli, 1973), rock glacier inventories, ground 20 temperature monitoring, geophysical soundings and numerical models.
In central southern Norway, the LAL of gentle slope permafrost decreases with continentality, being at c. 1500 m a.s.l. in Jotunheimen (Isaksen et al., 2002;, down to 1300 m a.s.l. in Dovrefjell at sites with no snow cover (Sollid et al., 2003;Isaksen et al., 2011;Westermann et al., 2013), and 1100 m a.s.l. in more eastern continental terrains in the Femunden region with a thin snow cover (Heggem et al., 2005;Westermann et 25 al., 2013;Gisnås et al., 2017). The CryoWall map confirms this decreasing elevation of the lower limit of permafrost across continentality ( Fig. 10 and 13). However, the LAL of permafrost in gentle slopes of Jotunheimen is close to the LAL of permafrost in south-facing rock walls, but 300-400 m higher than in the north-facing rock walls (Fig. 13). At the local scale, the transition between continuous and discontinuous permafrost is similar in north-exposed rock walls than in gentle slopes, while discontinuous permafrost in south-30 exposed rock-walls rather occurs in the continuous permafrost zone of for the surrounding gentle slopes (Fig.   S3a). In Dovrefjell further east, the LAL in gentle slopes rather corresponds to the lower LAL of north-exposed rock walls, while it is about 200-300 m lower than in south-exposed rock walls. But at the local scale, the transition between continuous, discontinuous and sporadic permafrost coincides remarkably well to the map based on BTS measurement (Isaksen et al., 2002) produced by Etzelmüller (unpublished), even for south-35 exposed rock walls (Fig. S3b). In eastern Norway, rock faces are rare and therefore evidences of permafrost in the north face of Sennsjøkampen, and above 1290 m a.s.l. in south, east and west faces of Sølen (Fig. 13).
This is generally higher than in surrounding slopes where permafrost generally occurs at much lower elevation (Heggem et al., 2005; Fig. S3c).
In northern Norway, the lower limit of permafrost in gentle slopes and flat terrains lies around 800-900 m a.s.l.

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in the coastal mountains of Troms county, such as in the Lyngen Alps (Farbrot et al., 2013, Steiger et al 2016, and decreases to 300-500 m a.s.l. in the coastal areas and mires in the inner part of Finnmark Farbrot et al., 2013;Borge et al., 2017). In the interior part of the Varanger peninsula the lower limit of permafrost in gentle slopes and flat terrains is around 400-450 m a.s.l. . Observations in the steep slopes of the Varanger peninsula ( Fig. 13) show, that permafrost can occur at lower elevations than in 10 gentle slopes in coastal Finnmark. The only rock faces existing in the inner part of Finnmark are mostly the river canyons, where discontinuous permafrost occurs between 100 and 600 m a.s.l. (Fig. 10 and 11), favoured by the high confinement and resulting low solar radiation input. The occurrence of permafrost may be underestimated in some places of continental areas due to local temperature inversion which are smoothed by the regional lapse rate calculation (e.g. Fig. 4).

Implications for landscape development in Norway
The CryoWall map confirms most of the previous findings in terms of permafrost occurrence and distribution in steep slopes inferred from visible ice or numerical modelling experiments. It is therefore a reliable basis to assess rock wall permafrost in Norway. The collected RST time series and CryoWall map may be used to model the permafrost evolution through time, using the predicted MARST or the measured RST as upper boundary 20 conditions for 1D or 2D simulation (Hipp et al., 2014;Magnin et al., 2017b). The permafrost models and the CryoWall map supports investigations on large-scale rock slope deformations, slope hazards such as rock falls and the assessment of geomorphological processes. To illustrate some of the research problems our map can contribute, we give some examples and analysis in the following.
Large-scale rock slope deformations in Norway -In the Norwegian mountains numerous sites, with large scale 25 instabilities are identified through systematic mapping and surveillance during the last years (e.g. Hermanns et al., 2012;Bunkholt et al., 2013;Oppikofer et al., 2015). Seven sites comprise a high hazard level, justifying installation of an early warning system, two of which have been equipped with RST loggers in this study. We now used the CryoWall map to assess permafrost occurrence at "critical slopes" inventoried by the Geological Survey of Norway (Oppikofer et al., 2015, http://geo.ngu.no/kart/ustabilefjellparti_mobil/). The database are permafrost slopes (probability > 0.5). The distribution of these critical slopes is displayed in the Supplement (Fig. S4). This preliminary investigation points out the critical slopes that may deserve further investigations on 5 the potential role of permafrost in their ongoing or possibly future destabilization, especially in the current context of climate change and permafrost degradation. As a further step, the hazard level could be statistically linked to the permafrost probability following a similar approach as the one conducted by (Ravanel et al., 2017) in the Mont Blanc massif.
Periglacial geomorphology -Rock glaciers and stable ice-cored moraines are the only landforms directly 10 indicating permafrost presence in mountain regions (e.g. Berthling ,2011, Haeberli 2000, Etzelmüller and Hagen 2005. These landforms are normally associated to steep slopes, at least in the vicinity. We used a rock glacier/stable ice-cored moraine inventory for Norway (Lilleøren and Etzelmuller, 2011) and compared adjacent rock walls of active rock glaciers to our results. We found that most rock walls associated to active rock glaciers or to cirques where ice-cored moraines emerge, were classified as discontinuous to continuous permafrost, at 15 least in their upper part (Fig. S5). This underpins the interest for studying the connection of permafrost rock walls and adjacent landforms which so far, to the author's knowledge, has not been directly addressed. Indeed, permafrost dynamics can influence material supply pattern to these landforms, as e.g. frost cracking varies greatly within and without permafrost environments (e.g. Hales and Roering, 2007).
Landscape development -It is evident that the understanding of thermal regime within mountain slopes, and its 20 development during past and the future, has a geomorphological relevance (Berthling andEtzelmuller, 2011, Hales andRoering, 2007). Frost weathering and stabilisation/destabilisation of slopes over long time scales due to climate variability and glaciation cycles work in concert, and in certain temperature bands. For example, the frost cracking window (e.g. Hallet et al., 1991;Hales and Roering, 2007) defines a narrow temperature band, in which frost weathering processes are most effective, resulting in ice segregation and subsequent rock falls. On 25 the other hand, deep permafrost aggragation/degradation weakens rock masses, with the possibility of largerscale slope destabilisation on longer time scales (e.g. Krautblatter et al., 2013). Moreover, steep rock walls, often snow free or with little snow cover can influence the thermal regime of adjacent areas due to lateral heat flux (Myhra et al., 2017), with the possibility to maintain large temperature gradients. All these processes influences material predication and erosion of mountain ranges and contribute to the periglacial realm being an important Norway.
-Discontinuous permafrost occupies 9% of the rock wall surface area and can be found in southern

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-The lower elevation limit of permafrost decreases by about 500±50 for between southern and northern Norway, with a more pronounced decrease for south-exposed slopes (-50m for every degree northwards for north-exposed slopes against -58 m for the south-exposed ones).
-The lower elevation limit of permafrost also decreases across continentality, with occurrences of discontinuous permafrost about 200 m lower in eastern Norway than in the west coast of southern

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Norway, and below 200 m a.s.l. in the river canyons of northern Norway.
-Steep slope permafrost generally occurs lower than in gentle mountain slopes in north faces, but at higher elevation in south faces. This pattern is nevertheless more or less pronounced depending on the regions of Norway.

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The CryoWall map will be made available after publication via the NIRD research data archive: https://archive.norstore.no/
Earth Surf. Dynam. Discuss., https://doi.org /10.5194/esurf-2018-90 Manuscript under review for journal Earth Surf. Dynam. Discussion started: 4 February 2019 c Author(s) 2019. CC BY 4.0 License. Figure 9. Distribution of the lower limit of each permafrost class according to elevation, aspect and latitude. The width of the boxes is proportional to the square-roots of the number of observations in the respective groups. The lowest and highest boundaries of the boxes respectively display the 1 st and 3 rd quartile (Q1 and Q3) of the observations. The lowest and highest whiskers respectively show Q1-((Q3-Q1)×1.5]) and (Q3+((Q3-Q1)×1.5)).

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The dots are the outliers.   Figure 12. Permafrost distribution at steep slope sites where permafrost has been previously observed in Norway (a. Blikra and Christiansen, 2014;b. Frauenfelder et al., 2018;Etzelmuller et al., 2003b). The CryoWall map has been combined with the 1 km resolution Nordic permafrost map (Gisnås et al., 2017) to display predicted permafrost in all types of terrains.