Modeling past and future alpine permafrost distribution in the Colorado Front Range

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1 Earth Surface Processes and Landforms Modeling Earth Surf. alpine Process. permafrost Landforms distribution 30, (2005) 1495 Published online in Wiley InterScience ( DOI: /esp.1205 Modeling past and future alpine permafrost distribution in the Colorado Front Range Jason R. Janke University of Southern Mississippi, Department of Geography Box 5051, Hattiesburg, MS 39406, USA *Correspondence to: J. R. Janke, Department of Geography Box 5051, University of Southern Mississippi, Hattiesburg, MS 39406, USA. Received 30 April 2004; Revised 21 October 2004; Accepted 19 November 2004 Abstract Rock glaciers, a feature associated with at least discontinuous permafrost, provide important topoclimatic information. Active and inactive rock glaciers can be used to model current permafrost distribution. Relict rock glacier locations provide paleoclimatic information to infer past conditions. Future warmer climates could cause permafrost zones to shrink and initiate slope instability hazards such as debris flows or rockslides, thus modeling change remains imperative. This research examines potential past and future permafrost distribution in the Colorado Front Range by calibrating an existing permafrost model using a standard adiabatic rate for mountains (0 5 C per 100 m) for a 4 C range of cooler and warmer temperatures. According to the model, permafrost currently covers about 12 per cent (326 1 km 2 ) of the entire study area ( km 2 ). In a 4 C cooler climate 73 7 per cent ( km 2 ) of the study area could be covered by permafrost, whereas in a 4 C warmer climate almost no permafrost would be found. Permafrost would be reduced severely by 93 9 per cent (a loss of km 2 ) in a 2 0 C warmer climate; however, permafrost will likely respond slowly to change. Relict rock glacier distribution indicates that mean annual air temperature (MAAT) was once at least some 3 0 to 4 0 C cooler during the Pleistocene, with permafrost extending some m lower than today. The model is effective at identifying temperature sensitive areas for future monitoring; however, other feedback mechanisms such as precipitation are neglected. Copyright 2005 John Wiley & Sons, Ltd. Keywords: permafrost; Front Range; climate change; rock glaciers Introduction Permafrost, or ground that remains at or below 0 C for at least two consecutive years, serves as an indicator of potential climate change (Harris et al., 2003). Relict landforms, such as sand wedges, patterned ground, pingo scars, or rock glaciers, provide historical information about where permafrost once existed (Frauenfelder et al., 2001). In the future, field monitoring of frozen ground will be vital as the active layer responds to global warming, shifting snow cover patterns, and change in vegetation land cover (Davis, 2001; Ishikawa, 2003). Other landforms related to permafrost occurrence may show a decline in activity as ice is removed or freeze thaw activity decreases. Permafrost mapping and modeling has been initiated in major mountain regions of the world (Keller, 1992; Hoelzle et al., 1993; Imhof, 1996; Frauenfelder et al., 1998; Etzelmüller et al., 2001; Gruber and Hoelzle, 2001; Lugon and Delaloye, 2001; Tannarro et al., 2001; Heginbottom, 2002; Guglielmin et al., 2003; Frauenfelder et al., 2003). In the Front Range (Figure 1), however, there is little precise information about permafrost distribution. A few studies have examined local distribution on Niwot Ridge (Ives, 1974; Greenstein, 1983). Since these field investigations were restricted in area, an attempt was made to model permafrost distribution using geographic information system (GIS) techniques and digital elevational model (DEM) variables based on rock glacier activity categories: (1) active = probable permafrost, (2) inactive = possible permafrost, and (3) fossil or relict = no current permafrost (Imhof, 1996; Janke, 2004). A multinomial logistic regression was built based on topoclimatic data (elevation and aspect) from rock glaciers to estimate the probability of permafrost occurence. The model showed promising results, correlating well with the 1 0 C mean annual air temperature (MAAT) isotherm and bottom temperature of winter snow (BTS) measurements less than 3 0 C (Janke, 2004). The purpose of this research is to investigate potential past and future distribution by calibrating the existing permafrost model for a 4 C range of temperatures.

2 1496 J. R. Janke Figure 1. Location of the study area in the Front Range of Colorado.

3 Modeling alpine permafrost distribution 1497 Paleoclimatic information Relict rock glacier distribution has been used to reconstruct previous cooler climates (Frauenfelder and Kääb, 2000). In Arizona and New Mexico, Barsch and Updike (1971) concluded that permafrost once extended as low as 2600 m during Wisconsin times. In the Tyrolean Alps, Kerschner (1985) found that relict rock glaciers became inactive approximately yrs B.P., thus permafrost at that time extended m lower than today with a 3 0 to 4 0 C lower mean annual air temperature (MAAT). In a region north of the Alps, Haeberli (1983) inferred that the permafrost limit was 3000 m lower than today during the extremely dry last glacial maximum in central Europe. In the Err- Julier area, Swiss Alps, Frauenfelder et al. (2001) used relict rock glaciers in conjunction with the PERMAMAP permafrost model to reconstruction conditions during the Younger Dryas and found that temperatures were once C cooler, depressing the permafrost limit by m. In the southern Carpathian Mountains, Urdea (1998) examined the evolution of permafrost from the Würm III period to the Little Ice Age, which suggested the lower limit of permafrost rose from 1480 to 2265 m over this period. In Greece, relict rock glaciers formed during the last glacial maximum indicate that MAATs were 8 9 C cooler, in agreement with paleoclimatic reconstructions (Hughes et al., 2003). Such paleoclimate reconstructions have not taken place in the Front Range using relict rock glacier extent. Temperature change models In polar regions of continuous and discontinuous permafrost, several attempts have been made to model areal change due to global warming. Nelson et al. (2002) combined results from a general circulation model (GCM) and digital permafrost maps to determine hazardous areas associated with increasing active layer thickness. Barsch (1993) suggested that by 2010 the southern limit of polar permafrost could shift some km northward from its present location if warming continues. In Canada, the southern limit of permafrost would shift some km north with a doubling of CO 2 and, if ground warming continues, permafrost in Tibet could disappear in the next 150 years (French, 1996). After combining climatic, soil, permafrost and climate permafrost interaction data in a GIS, Anisimov and Poliakov (2003) predicted that by per cent of artic permafrost would be reduced, with a per cent deeper seasonal thaw. Few attempts have been made to predict the extent of mountain permafrost in warmer climates. For the Upper Engadin, Swiss Alps, Hoelzle and Haeberli (1995) ran three temperature scenarios: (1) 0 6 C cooler, (2) 1 0 C warmer and (3) 3 0 C warmer. The cooling scenario showed a four per cent increase in permafrost occurrence, but the 3 0 C warming showed a 65 per cent loss. For the Qinghai-Xizang Plateau of China, a DEM, a permafrost base map and a coarse GCM were used to predict permafrost change. By 2009, 8 0 per cent of permafrost would be lost with 0 46 C warming; by 2049, an 18 5 per cent reduction in permafrost would occur with 0 78 C warming. At this stage, permafrost would retreat by 5 10 km along the Qinhai-Tibet highway. By 2099, 58 2 per cent of permafrost would be eliminated with 2 53 C warming (Li and Cheng, 1999; Wu et al., 2000). Observations in this area have shown a temperature increase since the 1970s (Wang and Jin, 2000). Future increases could cause a variety of slope stability issues (Haeberli and Beniston, 1998; Beniston, 2002). Potential effects of a warmer climate have not been examined in the Colorado Front Range. Study Area Description The study area ( km 2 ) covers a section of Rocky Mountain National Park located in the Front Range of northern Colorado (Figure 1). The topography is rugged with over 60 peaks rising above 3350 m and subdued with gently sloping tundra surfaces found above 3475 m (Figure 2). In the region south of Rocky Mountain National Park (Indian Peaks), interfluves usually extend east to west with Niwot Ridge being one of the most extensive (Ives and Fahey, 1971). The treeline is at about 3400 m, and a forest-tundra ecotone extends some 100 to 150 m above treeline. The climate resembles arctic conditions with daytime summer temperatures rarely exceeding 15 C (Elias, 1995). On Niwot Ridge, a series of long term ecological research (LTER) climatic stations have been established (Figure 2). Glacial history The Rocky Mountains were glaciated during three major events: (1) Pre-Bull Lake, (2) Bull Lake, and (3) Pinedale. The Bull Lake glaciation occurred before the Pinedale events, but the exact timing of the Bull Lake glaciation remains uncertain ( yrs B.P.), although two major Bull Lake stades have been identified, ending before

4 1498 J. R. Janke Figure 2. An oblique perspective of a section of the Indian Peaks wilderness located south of Rocky Mountain National Park. Locations of Long Term Ecological Research stations (points) on Niwot Ridge and rock glaciers in surrounding valleys (polygons) are shown draped on a digital orthophoto and a DEM yrs B.P. (Madole, 1976; Pierce, 1979; Richmond, 1986; Gosse et al., 1995). After a break of almost years, the Pinedale glaciation (Wisconsin glaciation) began shortly after the last (Sangamon) interglaciation ( yrs B.P.). On eastern slopes, Pinedale ice advanced by some km, whereas glaciers on the western slope extended some 33 km (Richmond, 1960). As far as Pinedale glaciation, events in Rocky Mountain National Park are restricted to just an earlier, more extensive event and a later Pinedale event (Elias, 1995), although some studies have identified three stades in the Front Range (Ray, 1940; Jones and Quam, 1944; Richmond, 1960). The most recent Pinedale advance started about yrs B.P. and reached a maximum around yrs B.P. when glacial Lake Devlin was dammed (Nelson et al., 1979; Madole, 1986; Caine, 2001). Deglaciation began about yrs B.P. (Harbor, 1984; Madole, 1986). However, similarities in radiocarbon dates, soil development, weathering features and altitude for Satanta Peak moraines, Triple Lakes moraines and sediments from Sky Pond designate a Younger Dryas event ( to yrs B.P.), marking the last major Pinedale advance (Benedict, 1973a; Davis, 1988; Menounos and Reasoner, 1997). Outcalt and MacPhail (1965) suggested that Pleistocene glaciers disappeared from the Front Range from 4500 to 7500 yrs B.P. during the Altithermal. Since then, neoglaciation has shown three major advances, but the timing remains inexact: (1) the Temple Lake Stade ( yrs B.P.), (2) the Arikaree Stade ( yrs B.P.) later renamed Audubon Stade, and (3) the Gannett Peak Stade ( yrs B.P.) later renamed Arapaho Peak Stade or the Indian Peaks equivalent to the Little Ice Age (Benedict, 1970; Mahaney, 1972; Benedict, 1973a; Davis, 1988). Glaciers during this period advanced from small, sheltered cirques, reaching a maximum around the mid-19th century (Richmond, 1960). The timing of rock glacier formation within the study area is not known. Galena Creek rock glacier, found in the Absaroka Range of Wyoming, seems to be consistent with the neoglacial record (Ackert, 1998). If velocities are extrapolated over the entire rock glacier surface, then age ranges from 4000 to 1200 years old (Clark et al., 1996;

5 Modeling alpine permafrost distribution 1499 Ackert, 1998; Konrad et al., 1999). However, given the slow rate of terminus movement, a decrease in velocity with depth, and isotopic composition of the ice-core, older ages may be more realistic (Clark et al., 1996; Cecil et al., 1998; Konrad et al., 1999). Within the Front Range, neoglacial dates have also been reported. On Arapaho rock glacier, an exposed ice-core revealed pollen, plant, and insect remains that were dated close to the end of the Audubon stade ( ± yrs B.P.) (Benedict, 1973b). Arapaho rock glacier has a sequence of lobes that are believed to be remnants of moraine material deposited from each neoglacial stade (Outcalt and Benedict, 1965; White, 1975; Benedict, 1985). As a result, most active and inactive rock glaciers are commonly thought to be a product of the late Holocene, whereas fossil rock glaciers formed during the late Pleistocene (Barsch, 1996). Methods Using aerial photographs, previous motion studies, and field investigations, rock glaciers were categorized into three types. Active rock glaciers were classified as those that are moving, contain ice, have a steep front slope and have pronounced ridges and furrows. Active rock glaciers are commonly thought to be an indicator of probable permafrost (Imhof, 1996). Inactive rock glaciers have ceased moving, may still contain ice, have a gentler frontal slope and surface topography, and are associated with possible permafrost. Fossil rock glaciers contain no ice, are not moving, and have vegetation on the surface, thus they do not indicate current permafrost presence, but are representative of past permafrost distribution (Barsch, 1996; Whalley and Martin, 1992). In ArcGIS, USGS DEMs with a 10 m resolution were obtained for the study area. Slope and aspect were calculated. The rock glacier file was then converted to a grid (10 m resolution), and zonal statistics, a GIS overlay method, were processed using the elevation and slope data. To correct for circular data ranging from 0 to 360, the mean aspect for each feature was calculated manually. The orientation measurements were then converted to vector space for each rock glacier. A multinomial logistic regression was formulated to predict current permafrost occurrence based on the aformentioned topoclimatic information for rock glacier activity classes (Figure 3). Analysis of the Wald statistics suggested that mean elevation, the sine of mean aspect, and the cosine of mean aspect provided sufficient parameters (all p < 0 03) for the regression model. Front Range rock glaciers present a dilemma when developing a permafrost model because they are transitional landforms that can be derived from both periglacial and glacial processes (Giardino and Vitek, 1987). Classifying rock glaciers according to activity fails to address the processes operating on rock glaciers. In the Front Range, the initial origin of rock glaciers is glacial because the area underwent glaciation. Rock glaciers in this region, therefore, may not truly be representative of permafrost. By definition, however, glacially derived rock glaciers contain ice that remains at or below 0 C, and fall within the broad thermal criteria required for permafrost existence. Using a standard adiabatic rate for mountains (0 5 C per 100 m), the model was calibrated for temperatures ranging from 4 C cooler to 4 C warmer (Barry, 1992). For each 0 5 C scenario, a separate multinomial logistic regression model was developed and processed in ArcGIS. Lake locations were masked from the analysis since the aspect of lakes is often characterized as flat ( 1 ) on DEMs, making classification difficult. Variability in precipitation and resulting change in snow cover as well as land cover change were omitted because at this point they are imponderable for past and future climates. It is likely that change in snow cover will affect active layer thickness; however, the model is designed to estimate the probability of permafrost occurrence at depth. Mean rock glacier probability scores were used to evaluate rock glacier sensitivity in different temperature regimes. Rock glacier locations were overlaid with permafrost maps for each 0 5 C temperature increment to determine mean probability scores. Rock glaciers were classified as active if they had a mean score greater than 75 per cent, inactive if they were in the 50 to 75 per cent range and relict if they were below 50 per cent. The number of rock glaciers falling into each activity class was summarized for each temperature scenario. Results Potential permafrost distributions for cooler and warmer climates are shown in Figures 4 and 5, respectively. The areal extent of permafrost scores greater than 50 per cent was summarized for each of the scenarios (Table I). Currently, permafrost covers about 12 per cent (326 1 km 2 ) of the entire study area ( km 2 ), while in a 4 C cooler climate 74 per cent ( km 2 ) of the study area could be covered by permafrost, about a 500 per cent increase in extent. In a 4 C warmer climate, almost no permafrost would be found (0 1 km 2 ). A temperature increase of even 0 5 C would reduce permafrost extent by km 2, a loss of 41 3 per cent. In fact, the initial warming scenarios show the most

6 1500 J. R. Janke Figure 3. Model used to predict past and future permafrost extent in the Front Range. loss between intervals ( km 2 ). Temperature sensitive areas (±0 5 C) along Niwot Ridge are illustrated in Figure 6. Even in a 2 0 C warmer climate, permafrost would be reduced by 93 9 per cent (a loss of km 2 ), a severe impact produced by a slight temperature increase. The time needed to thaw, however, would be much greater (French, 1996). Based on the current predicted extent, 80 per cent of rock glaciers fall within their current activity status (Table II). Nearly all rock glaciers (219 of 220) would lie in a zone of permafrost in a 3 0 to 4 0 C cooler climate, but if temperatures were to increase by 2 0 to 2 5 C, no rock glaciers would be considered active within the area of projected permafrost extent (Table II). In a 0 5 C cooler climate the model estimates that 32 more rock glaciers would become active, but if temperatures were to warm 13 additional rock glaciers would become inactive. Discussion Temperature change When interpreting these results, it should be kept in mind that permafrost and rock glaciers will respond slowly to changes in temperature, perhaps taking a few hundred years (French, 1996). Since rock glaciers have a coarse layer of

7 Modeling alpine permafrost distribution 1501 Figure 4. Predicted permafrost extent for cooler climates: (A) current conditions, (B) 0 5 C (C) 1 0 C, (D) 1 5 C, (E) 2 0 C, (F) 2 5 C (G) 3 0 C, (H) 3 5 C and (I) 4 0 C.

8 1502 J. R. Janke Figure 5. Predicted permafrost extent for warmer climates: (A) current conditions, (B) 0 5 C, (C) 1 0 C, (D) 1 5 C, (E) 2 0 C, (F) 2 5 C, (G) 3 0 C, (H) 3 5 C and (I) 4 0 C.

9 Modeling alpine permafrost distribution 1503 Figure 6. Example of potential change for areas surrounding Niwot Ridge.

10 1504 J. R. Janke Table I. Potential change for permafrost scores greater than 50 per cent Areal extent of permafrost scores Areal change Areal change Per cent change greater than Per cent of study from current from last from current Permafrost condition 50 per cent (km 2 ) area covered extent (km 2 ) interval (km 2 ) extent 4 0 C cooler C cooler C cooler C cooler C cooler C cooler C cooler C cooler Current condition C warmer C warmer C warmer C warmer C warmer C warmer C warmer C warmer Table II. Number of active, inactive and fossil rock glaciers within the projected permafrost extent in cooler and warmer climates Number of active Number of inactive Number of fossil rock glaciers rock glaciers rock glaciers Permafrost condition (x 75 per cent) (75 x 50 per cent) (x 50 per cent) 4 0 C cooler C cooler C cooler C cooler C cooler C cooler C cooler C cooler Current condition C warmer C warmer C warmer C warmer C warmer C warmer C warmer C warmer surface debris, the internal ice structure is protected from insolation and is further cooled by ventilation (Haeberli, 1985; Delaloye et al., 2003). As a result, a smoothed or lagged response to warming will most likely occur. This modeling approach assumes that active rock glaciers are adjusted to current climate, which may be misleading given the slow response time. Active rock glaciers may still be responding to Little Ice Age or late-holocene climatic events. It should also be noted that the predicted extent of permafrost in cooler climates might be extreme since alpine glaciers once filled the valleys, and currently active rock glaciers would have been overridden by ice. Sophisticated

11 Modeling alpine permafrost distribution 1505 glacial and permafrost reconstructions such as those that have been undertaken in the Swiss Alps are currently being implemented in the Front Range (Frauenfelder et al., 2001). Paleoclimatic reconstructions for the Front Range suggest that mean July temperatures were once C colder and that mean January temperatures were some C cooler as late as yrs B.P. (Elias, 1986, 1995). According to a mutual climatic range reconstruction from fossil beetles, mean July temperatures were only C cooler and mean January temperatures were some C cooler, indicating that deglaciation was occurring, possibly allowing now relict rock glaciers to form. Coupled with lower moisture during the late Pinedale, periglacial activity was high; thus, relict rock glaciers were probably once active during the Pleistocene (late Pinedale). The analysis indicates that mean annual temperatures were once some C cooler, with permafrost extending some m lower, than today. These results indicate that permafrost extended to slightly lower elevations than previously reported. Legg and Baker (1980) suggested that treeline was 500 m lower during the Pinedale with temperatures at least 4 C lower than today. At a nearby site, pollen records indicate the existence of tundra during mid-pinedale times, corresponding to a depression of treeline by 500 m and 3 0 C cooler temperatures (Elias, 2001). A relict rock glacier reconstruction in the Tyrolean and Swiss Alps also indicates similar results during the Younger Dryas ( C cooler) with a depressed lower limit of permafrost at m (Kerschner, 1985; Frauenfelder et al., 2001). The analysis also demonstrates the importance of appropriate topoclimates in order for rock glaciers to be active (Morris, 1981; Humlum, 1998; Sloan and Dike, 1998). For example, a 0 5 C temperature decrease might reactivate 32 rock glaciers with a 100 m lower elevation in permafrost limit if ample snowmelt and debris is available to form internal ice (Whalley and Martin, 1992). A 0 5 C temperature increase might deactivate 13 rock glaciers. Due to this variability, orientation must be an important variable for currently active rock glaciers since elevation of the permafrost limit has only changed by ±100 m. This sensitivity also exemplifies the close relationship between inactive and active forms, supporting a late-holocene formation for most rock glaciers. Although field measurements are sparse, permafrost in the Alps seems to be responding to warming, albeit more slowly than temperate glaciers. Compared to the rates in the 1970s, Gruben rock glacier has shown a two to three times greater subsidence rate in the warm 1980s to 1990s. Borehole temperature measurements on Murtèl I rock glacier have shown a temporal warming trend with depth (Haeberli, 1994). In the Front Range, a warming trend remains unclear. From 1952 to 1997, elevations above treeline have cooled, which would support permafrost aggradation, reduced active layer thickness, or possibly ice growth in some landforms (Pepin, 2000). If the current trend were to reverse, however, the model has shown that permafrost could eventually be adversely reduced. If the ice-rich bond of permafrost is removed, slope stability hazards will become more frequent, thus modeling potential change remains significant. Limitations Other than temperature, feedback mechanisms are left unchanged. An increase in winter precipitation could destroy permafrost by preventing cold air from reaching the ground. In fact, winter precipitation has increased by about 8 mm/ yr from 1980 to 2000, possibly eliminating some permafrost or increasing active layer thickness (Caine, 2002). An increase in summer snowfall events, however, could protect underlying permafrost from warm summer temperatures (Ives and Fahey, 1971; Williams and Smith, 1989; Harris and Corte, 1992). Since our understanding of temporal and spatial changes in precipitation remains uncertain, this variable was not incorporated. The lapse rate in the Front Range is also steepening (Pepin and Losleben, 2002). Since this trend is difficult to predict for past and future climates, lapse rates were assumed to be constant. Snowfall change and lapse rates need to be incorporated in processoriented models to better model change (Hoelzle et al., 2001). Therefore, the model assumptions are unrealistic in nature, but it does effectively illustrate temperature sensitive areas (Hoelzle and Haeberli, 1995). When considering paleoclimatic reconstructions, it is still necessary to date rock glaciers. Photogrammetric, radiocarbon, weathering rind, Schmidt-hammer rebound, lichenometry, and cosmogenic methods have shown recent success (Haeberli et al., 2003; Laustela et al., 2003). Once dates are available for Front Range rock glaciers, a more detailed account of landscape evolution could be undertaken, comparable to those that have take place in the Val Murgal, Upper Engadin, Swiss Alps (Maisch et al., 2003). Conclusions Relict rock glaciers indicate that MAAT was once at least some C cooler during the late Pleistocene with permafrost extending some m lower than today. Compared to pollen and tree paleoclimatic reconstructions,

12 1506 J. R. Janke the estimate presented here indicates a slightly more extensive permafrost zone. In a warmer climate, permafrost may continue to exist, but will slowly accumulate thicker active layers (French, 1996). The model has shown that a C temperature increase could dramatically reduce permafrost extent by about 95 per cent in the Front Range, although feedback mechanisms are neglected. As the ice that currently binds permafrost decays, the frequency of debris flows, rockfalls and other catastrophic events could increase. Acknowledgements Thanks should be given to the following funding agencies that provided these awards: a Doctoral Dissertation Improvement Award from the National Science Foundation (No. # ), a Geospatial Information and Technology Association Rocky Mountain Chapter Fellowship and a Colorado Mountain Club Fellowship. Special thanks to Nel Caine, John Pitlick, Tad Pfeffer, Mark Williams, Susan Berta, Babs Buttenfield and Jeremy Mennis for their help reviewing and insightful feedback. The manuscript also greatly benefited from an anonymous reviewer and Wilfried Haeberli. References Ackert RP A rock glacier/debris-covered glacier system at Galena Creek, Absaroka mountains, Wyoming. Geografiska Annaler Series A-Physical Geography 80A: Anisimov O, Poliakov V GIS assessment of climate-change impacts in permafrost regions. In Proceedings of the 8th International Conference on Permafrost, Phillips M, Springman S, Arenson L (eds). Balkema: Zurich; Barry RG Mountain Weather and Climate. Routledge: New York. Barsch D Periglacial geomorphology in the 21st century. Geomorphology 7: Barsch D Rockglaciers: Indicators for the Present and Former Geoecology in High Mountain Environments. Springer: Berlin. 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13 Modeling alpine permafrost distribution 1507 French HM The Periglacial Environment. Addison Wesley Longman: London, UK. Giardino JR, Vitek JD The significance of rock glaciers in the glacial periglacial landscape continuum. Journal of Quaternary Science 3: Gosse JC, Klein J, Evenson EB, Lawson B, Middleton R Beryllium-10 dating of the duration and retreat of the last Pinedale glacial sequence. Science 268: Greenstein L Alpine permafrost on Niwot Ridge based on indirect locational techniques. Master s Thesis, University of Colorado, Boulder. Gruber S, Hoelzle M Statistical modeling of mountain permafrost distribution: local calibration and incorporation of remotely sensed data. Permafrost and Periglacial Processes 12: Guglielmin M, Aldighieri B, Testa B PERMACLIM: a model for the distribution of mountain permafrost, based on climatic observations. Geomorphology 51: Haeberli W Permafrost glacier relationships in the Swiss Alps today and in the past. 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