Journal of Geophysical Research: Earth Surface

The influence of snow cover thickness on the thermal regime of Tête Rousse Glacier (Mont Blanc range, 3200 m a.s.l.): Consequences for outburst flood hazards and glacier response to climate change

Authors

  • A. Gilbert,

    Corresponding author
    1. Laboratoire de Glaciologie et de Géophysique de l'Environnement, UMR 5183, Université Joseph Fourier-Grenoble 1, CNRS, Grenoble, France
      Corresponding author: A. Gilbert, Laboratoire de Glaciologie, Université Joseph Fourier-Grenoble 1, CNRS, LGGE UMR 5183, BP 96, FR-38041 Grenoble CEDEX 09, France. (gilbert@lgge.obs.ujf-grenoble.fr)
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  • C. Vincent,

    1. Laboratoire de Glaciologie et de Géophysique de l'Environnement, UMR 5183, Université Joseph Fourier-Grenoble 1, CNRS, Grenoble, France
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  • P. Wagnon,

    1. Laboratoire de Glaciologie et de Géophysique de l'Environnement, UMR 5183, Laboratoire d'Étude des Transferts en Hydrologie et Environnement, UMR 5564, IRD, Université Joseph Fourier-Grenoble 1, CNRS, Grenoble, France
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  • E. Thibert,

    1. Unité de Recherche Erosion Torrentielle Neige et Avalanches, Institut National de Recherche en Sciences et Technologies pour Environnement et Agriculture, Saint-Martin-d'Heres, France
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  • A. Rabatel

    1. Laboratoire de Glaciologie et de Géophysique de l'Environnement, UMR 5183, Université Joseph Fourier-Grenoble 1, CNRS, Grenoble, France
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Corresponding author: A. Gilbert, Laboratoire de Glaciologie, Université Joseph Fourier-Grenoble 1, CNRS, LGGE UMR 5183, BP 96, FR-38041 Grenoble CEDEX 09, France. (gilbert@lgge.obs.ujf-grenoble.fr)

Abstract

[1] Tête Rousse Glacier (French Alps) was responsible for an outburst flood in 1892 that devastated the village of St Gervais-Le Fayet close to Chamonix, causing 175 fatalities. Changes in the hydrothermal configuration of the glacier are suspected to be the cause of this catastrophic outburst flood. In 2010, geophysical surveys of this glacier revealed a subglacial lake that was subsequently drained artificially. The processes controlling the thermal regime of the glacier have been investigated on the basis of measurements and snow/firn cover and heat flow models using meteorological data covering the last 200 years. Temperature measurements show a polythermal structure with subglacial water trapped by the cold lowest part of the glacier (−2°C). The modeling approach shows that the polythermal structure is due to temporal changes in the depth of the snow/firn cover at the glacier surface. Paradoxically, periods with negative mass balances, associated with warmer air temperature, tend to cool the glacier, whereas years with colder temperatures, associated with positive mass balances, tend to increase the glacier temperature by increasing the firnpack depth and extent. The thermal effect of the subglacial lake is evaluated and shows that the lake was formed around 1980. According to future climate scenarios, modeling shows that the glacier may cool again in the future. This study provides insights into the thermal processes responsible for water storage inside a small almost static glacier, which can lead to catastrophic outburst floods such as the 1892 event or potentially dangerous situations as in 2010.

1. Introduction

[2] In all mountainous glaciated area, polythermal structures can be observed on glaciers. Many studies have described this kind of glacier in the Alps [Eisen et al., 2009], Greenland [Loewe, 1966], Alaska [Rabus and Echelmeyer, 2002; Harrison et al., 1975], the Rockies [Paterson, 1972; Clarke and Goodman, 1975], the Himalayas [Maohuan, 1990; Gulley et al., 2009], the Peri-Antarctic Islands [Navarro et al., 2009], the Canadian Arctic [Copland et al., 2003; Blatter, 1987], Svalbard [Jania et al., 1996; Ødegard et al., 1992; Rippin et al., 2005], and the Scandinavian mountains [Holmlund and Eriksson, 1989]. In fact, all glaciers with wet accumulation areas [Paterson, 1994] and ablation areas with a mean annual temperature below zero are polythermal with a temperate accumulation area and a partially cold ablation area. This is a well-understood process caused by the refreezing of meltwater in the porous firnpack in the accumulation area, releasing latent heat that quickly removes the winter cold content while meltwater is evacuated by surface runoff in the ablation area [Hooke et al., 1983; Blatter and Hutter, 1991; Pettersson et al., 2003, 2007; Gusmeroli et al., 2012].

[3] Thus, in such glaciers, temperate ice (at the pressure melting temperature) coexists with cold ice. This structure affects mechanical [Aschwanden and Blatter, 2009; Copland et al., 2003] and hydrological [Skidmore and Sharp, 1999; Jansson, 1996; Boon and Sharp, 2003; Flowers and Clarke, 2002] properties within the glacier. Subglacial hydrology can be influenced by the thermal barrier formed by cold basal ice in the glacier tongue [Rippin et al., 2005; Copland et al., 2003], sometimes leading to potentially dangerous configurations of water storage when water is dammed by a cold ice barrier which can suddenly break. In the case of John Evans Glacier (Canada), it has been shown that basal water can be trapped at the cold/temperate ice interface and lead to local high water pressure [Copland et al., 2003]. This was also the case of Tête Rousse Glacier, which displays a polythermal structure and houses a subglacial water-filled cavity detected by field surveys carried out from 2007 to 2010 [Vincent et al., 2012; Legchenko et al., 2011] and artificially drained in September and October 2010 to avoid any possibility of a catastrophic outburst flood event. Vincent et al. [2012] have shown that the thermal regime of the glacier likely plays a key role in the formation of such a cavity. The modeling of processes that lead to such a polythermal structure is therefore a key issue to prevent subglacial lake outburst flood hazards. Furthermore, thermal regime of the glacier can change in response to climate change [Rabus and Echelmeyer, 2002; Pettersson et al., 2003; Wohlleben et al., 2009; Rippin et al., 2011; Gusmeroli et al., 2012]. The main objective of this study is to investigate the thermodynamic processes responsible for the polythermal structure of Tête Rousse Glacier under varying climate conditions in order to simulate thermal regime variations of the glacier. The aim is to improve our understanding of water storage inside the glacier and the associated lake outburst flood hazards.

[4] The data and model used are described in sections 2 and 3, respectively. Section 4 presents the results and the interpretation of the englacial temperature distribution in order to discuss the conditions that could lead to water storage inside the glacier (section 5). Section 6 explores the expected future changes of the thermal regime of Tête Rousse Glacier according to various climate scenarios and our conclusions are presented in section 7.

2. Study Site and Data

2.1. Study Site

[5] Tête Rousse Glacier is located in the Mont Blanc range (French Alps, 45°55′N, 6°57′E). The normal route to access the summit of the Mont Blanc crosses this glacier. Its surface area was 0.08 km2in 2007. This west-facing glacier is approximately 0.6 km long and extends from about 3300 m above sea level (a.s.l.) to 3100 m a.s.l. with a maximum thickness of 70 m [Vincent et al., 2010] (Figure 1). The size of the accumulation area varies significantly from one year to another. At the end of the hydrological year, the glacier may be completely snow covered or snow-free. The mean Equilibrium Line Altitude (ELA) observed over the last 20 years is around 3195 m (Figure 1). The mean annual air temperature measured by an automatic weather station in the vicinity of the glacier (3100 m a.s.l) over the period 1 July 2010 to 30 June 2011was −2.84°C.

Figure 1.

Map of Tête Rousse Glacier showing surface (blue contours) and bedrock topography (color scale) in 2007. The 1892 upper and lower cavities are represented in green and the 2010 cavity is plotted in black. Red points show the location of borehole temperature measurements. The black line is the longitudinal section used for 2-D temperature simulations. The bold dashed red line shows the approximate location of mean Equilibrium Line Altitude (ELA) over the last 20 years.

[6] One peculiarity of Tête Rousse Glacier comes from its location below the west face of the Aiguille du Goûter (3863 m a.s.l.) peak. Snow accumulation at the glacier surface comes partly from avalanches from this 500 m high face, which explains the high accumulation gradient observed in the upper reaches of the glacier. This location also results in considerable shading by surroundings slopes. This has been quantified by measuring the skyline elevation angle as a function of the azimuth angle at the center of the glacier and applying the calculation method proposed by Oerlemans [2001]. In comparison with solar radiation at the top of the atmosphere, shading reduces the mean annual direct solar radiation by −16% on Tête Rousse Glacier, with a maximum of −20% for winter daily means and a minimum of −9% during the ablation season (mid-May to mid-October).

2.2. Field Measurements

[7] All the field measurements used in this study will be briefly described here. The reader is invited to refer to Vincent et al. [2010, 2012] for more details.

2.2.1. Mass Balance and Surface Velocity

[8] Geodetic measurements were carried out in 1901 and 1950 using a theodolite and in 2007 using differential GPS instruments. The differences between the Digital Elevation Models (DEM) resulting from the 1901 and 2007 surveys show that the glacier thinned by 15 to 20 m on average over the whole period [Vincent et al., 2010].

[9] Surface ice-flow velocities were calculated at the end of the ablation season in 2007 and 2009 (September) from the displacement of five ablation stakes on a longitudinal section of the glacier. Ice-flow velocities range from 0.4 to 0.6 m yr−1 [Vincent et al., 2010]. In addition, many ice-flow velocity measurements were carried out between 1901 and 1903 [Mougin and Bernard, 1922]. These ice-flow velocities were also very low, ranging from 0.2 m yr−1 close to the edge of the glacier to 1.1 m yr−1 at the central flow line.

2.2.2. Bedrock Topography and Subglacial Lake Detection

[10] The bedrock topography of Tête Rousse Glacier was determined in 2007 from Ground Penetrating Radar (GPR) data using a 250 MHz shielded antenna [Vincent et al., 2010] and also from 20 direct borehole measurements conducted in summer 2010 (Figure 1, only shows the location of the boreholes with temperature sensors). Some uncertainties remain due to considerable radar energy dispersion in the deepest part of the glacier that prevents clear recognition of the radar returns from the ice/rock interface. Both methods (radar and boreholes) were used together to locate the glacier bedrock.

[11] GPR images from 2007 also show a peculiar pattern, with very clear, bright reflectors visible 40 m deep in the middle of the glacier, over a distance of 20 m along the central profile. These large reflectors are located approximately 170 m up from the snout. These reflectors suggest the possible presence of a subglacial water reservoir [Vincent et al., 2012]. In 2010, additional measurements on 18 cross sections and four longitudinal sections using 250 MHz and 100 MHz antennas confirmed the results obtained from 2007 measurements. Finally, 3-D images of the water reservoir inside the glacier were obtained by surface nuclear magnetic resonance imaging (SNMR) performed in 2009 [Legchenko et al., 2011]. The minimum total volume of water stored in the glacier was estimated to be 45,000 m3.

2.2.3. Temperature Profiles

[12] Figure 1 shows the location of seven thermistor chains installed in boreholes in July 2010 along a central longitudinal section of the glacier at 3141 m a.s.l. (34 m depth), 3159 m a.s.l. (57 m depth), 3168 m a.s.l. (65 m depth), 3176 m a.s.l. (70 m depth), 3181 m a.s.l. (70 m depth), 3186 m a.s.l. (66 m depth), and 3207 m a.s.l. (70 m depth). In each borehole, temperature was measured by the thermistors through the entire thickness of the ice. Boreholes were made by hot water drilling, resulting in a temporary local disturbance of englacial temperatures. Consequently, measurements were repeated five times between July and September 2010 (accuracy of ±0.1°C) to be sure that thermal equilibrium had been reached. Little change was observed between the last two measurements, 10 days apart (+/−0.1°C), indicating that thermal equilibrium had been reached.

2.3. Meteorological Data

[13] In order to simulate glacier surface changes, meteorological data over the two last century are required. The different sources for each kind of data are described below.

2.3.1. Air Temperature

[14] Daily maximum and minimum air temperatures on the glacier were reconstructed using data from the Lyon-Bron meteorological station located ∼200 km west of the glacier. These data are available from 1907 to present. Before this date, we used homogenized temperature data over the northwest Alps fromBöhm et al. [2001].

2.3.2. Precipitation

[15] Precipitation data are available from 1907 for Besse-en-Oisans meteorological station located ∼150 km south of the Mont Blanc range in the Grandes Rousses range at 1525 m a.s.l.Vincent et al. [2007a]found a good correlation between Besse-en-Oisans and Chamonix precipitation records (close to our study site) using 5-year running averages over the 1938–2007 period. We therefore decided to use the Besse-en-Oisans series rather than the closer Chamonix series because it began 31 years earlier. Surface accumulation was assessed from this precipitation record using a multiplication factor ranging from 1.5 to 3.3 depending on the location on the glacier. These factors were calibrated to fit the winter accumulation measured on Tête Rousse Glacier for the hydrological years 2007/2008, 2008/2009, and 2009/2010. Snow accumulation is strongly influenced by local effects which result in a negative gradient (−0.012 m w.e. m−1) from 3120 m a.s.l. to 3170 m a.s.l. and a positive gradient (+0.011 m w.e. m−1) from 3170 m a.s.l. to 3275 m a.s.l. Indeed, at an annual timescale, higher accumulation rates have been observed on the tongue of the glacier, mainly due to site effects (the lowest part of the tongue is surrounded by slopes, forming a basin that traps precipitation). Before 1907 we used homogenized precipitation data over the northwest Alps from Auer et al. [2007]. These data are inferred from instrument-based time series of monthly mean precipitation.

2.3.3. Radiation, Wind Speed, Humidity, and Cloudiness

[16] In addition to air temperature and precipitation, the Crocus model used for snow and firn thickness simulations (section 3.1) requires the following input meteorological data at an hourly timescale: 10-m wind speed, 2-m air relative humidity, incoming direct and diffuse solar radiation, incoming long-wave radiation, and cloudiness. These data are provided by the SAFRAN downscaled meteorological model [Durand et al., 1993] and are available from 1958 for each mountain range of the French Alps according to aspect and altitude (every 300 m). SAFRAN reanalysis assimilates large-scale meteorological fields obtained from meteorological modeling and local information provided by weather stations and direct observations at ski resorts [Durand et al., 1993]. In the vicinity of Tête Rousse Glacier, an automatic weather station has been operating at 3100 m a.s.l since 1 July 2010, recording 30-min averages of air temperature and relative humidity, wind speed and incoming solar and long wave radiation. Comparison between SAFRAN reanalysis and daily mean data from the weather station over July, August, and September 2010 shows good agreement in mean and daily variability for humidity and incoming direct radiation (n = 93 days and r2 = 0.66 and 0.80, respectively). We found r2 = 0.19 and r2= 0.23 for wind speed and long wave incoming radiation, respectively. Wind speed is effectively influenced by local topography and cannot be well represented by large-scale data. Similarly, long wave radiation depends on nebulosity which can also vary locally. Nevertheless, these data are used because we consider that mean variations over larger time scales are well represented. Indeed, long wave radiations trends mainly depend on air temperature trends which are well reconstructed by SAFRAN (comparison with the glacier station gives r2 = 0.95). Furthermore, mean cloudiness (that also influences long wave radiation) did not change too much over the period of interest [Durand et al., 2009].

[17] Before 1958, we consider that mean wind speed, air relative humidity, incoming direct and diffuse solar radiation, and cloudiness remain unchanged and we use a 10-year time series from 1958 to 1968 provided by SAFRAN reanalysis to reconstruct these data over the 1800–1958 period. Indeed, the relative humidity of the atmosphere can be considered to be roughly constant, even if air temperatures show large seasonal variations [Hartmann, 1994]. Analysis of year to year variations in wind speed from SAFRAN data does not indicate any specific trend and the mean wind speed is around 2.7 m s−1. SAFRAN reanalysis indicates that cloud cover has not significantly changed either, remaining at about 44%. This is also confirmed at a larger scale from the HISTALP data set [Auer et al., 2007]. Considering that atmospheric solar transmissivity mainly depends on cloud cover, we consider global radiation to be constant, neglecting dimming and brightening of solar radiation due to changes in atmospheric aerosol content. We assume the associated error to be negligible since, based on the long record from Davos (Switzerland) [Ohmura et al., 1989], global solar radiation has not presented any marked changes since 1949.

[18] Incoming long-wave radiation was estimated from air temperature, vapor pressure, and cloudiness using [Brutsaert, 1975]:

display math

where Lw (W m−2) is the incoming long-wave radiation,e (Pa) is the partial pressure of water vapor, T (K) is the air temperature, σ is the Stephan Boltzman constant (σ = 5.67 × 10−8 W m−2 K−4), n is the cloudiness (in tenths), and a and b are two dimensionless parameters. These parameters a and bwere tuned to obtain the best agreement between estimated hourly long-wave radiation derived fromequation (1) and SAFRAN data (r2 = 0.55 over one randomly selected year (2009) at an hourly time scale): a = 0.3 and b = 3.14. Tests performed on other years gave the same result.

2.4. Aerial Photographs and Satellite Images

[19] In order to assess the validity of the snow cover model (section 3) and to correct possible discrepancies, modeling results were compared with observations. Generally, the snowline on a glacier is easy to discern from aerial photographs and satellite images [Rabatel et al., 2005], as illustrated in Figure 2, and offers a good way to constrain our snow cover model. Thus the end-of-summer snow line was identified on Tête Rousse Glacier using 38 aerial photographs and satellite images (Table 1). These data cover the 1939–2009 period with an almost annual resolution since the early 1980s. All the aerial photographs and satellite images were geometrically corrected on the basis of the same image used as a reference (SPOT 5 image from 2003) and using a 25 m resolution DEM from the French National Geographical Institute (IGN). The snowline was delineated manually and its elevation was computed using the IGN DEM.

Figure 2.

Aerial photographs (1949 and 1970) and satellite images (2003 and 2008) of Tête Rousse Glacier in summer. For each year, the glacier outline in 2003 is indicated in red and the snow line in yellow.

Table 1. List of Aerial Photographs (From the French National Geographic Institute) and Satellite Images
Date SourcePath/RowScale or ResolutionSnow Cover on the Glacier (Partial or Total)Mean Snowline Elevation (m)
1939-07-03 Aerial PhotographN/A1:20,000T-
1949-09-04 Aerial PhotographN/A1:26,000P3200
1952-07-27 Aerial PhotographN/A1:25,000P3180
1958-07-31 Aerial PhotographN/A1:25,000T-
1961-08-29 Aerial PhotographN/A1:25,000T-
1966-09-08 Aerial PhotographN/A1:25,000T-
1970-09-17 Aerial PhotographN/A1:30,000T-
1979-09-05 Aerial PhotographN/A1:30,000T-
1982-09-26 Aerial PhotographN/A1:30,000T-
1984-07-09 Aerial PhotographN/A1:15,000T-
1984-08-31 Landsat 5 TM196–02830 mT-
1985-08-11 Landsat 5 TM195–02830 mT-
1986-09-09 Landsat 5 TM196–02830 mT-
1987-09-09 Landsat 5 TM196–02830 mP3150
1988-07-26 Aerial PhotographN/A1:30,000T-
1988-09-12 Landsat 4 TM195–02830 mP3160
1989-09-20 SPOT 1052–25810 mT-
1990-09-10 Landsat 5 TM195–02830 mP3180
1991-08-30 SPOT 2051–25810 mP3220
1992-08-05 Landsat 5 TM196–02830 mT-
1993-08-11 Aerial PhotographN/A1:20,000P3170
1993-09-02 Landsat 5 TM195–02830 mT-
1994-08-09 SPOT 3052–25810 mP3180
1998-08-30 SPOT 4052–25820 mP3150
1999-09-11 Landsat 7 ETM+195–02815 mT-
2000-08-01 Aerial PhotographN/A1:25,000T-
2000-08-26 SPOT 1051–25710 mP3180
2001-08-13 Aerial PhotographN/A1:25,000P3170
2001-07-30 Landsat 7 ETM+195–02815 mT-
2002-08-18 Landsat 7 ETM+195–02815 mT-
2003-08-23 SPOT 5051–2572.5 mP3200
2005-08-10 Landsat 7 ETM+195–02815 mP3150
2006-09-05 Aerial PhotographN/A1:20,000T-
2006-09-05 Landsat 7 ETM+196–02815 mT-
2007-07-31 Landsat 7 ETM+195–02815 mT-
2008-09-02 SPOT 5051–2575 mP3180
2009-08-15 SPOT 5052–25810 mP3200

3. Methodology: Numerical Modeling

[20] Englacial temperatures are derived from heat flow and water content modeling taking into account meltwater percolation through snow and firn as well as moisture diffusion in the temperate ice. This numerical modeling needs to simulate both spatial and temporal changes of the thickness and extent of snow and firn on the glacier. First, the thickness changes are modeled using the Crocus model (see section 3.1). Second, modeled firnpacks and snowpacks are used as inputs to the heat and water transfer models described in sections 3.2.1 and 3.2.2. The heat and water transfer models also work independently but water content and temperature are coupled at each time step as explained in section 3.2.3.

3.1. Snow and Firn Thickness Modeling

[21] The presence of snow affects the physical properties of the glacier surface layers. Indeed, thermal conductivity strongly depends on density. The porosity of snow also allows water percolation and storage at the snow/ice interface [Fountain and Walder, 1998]. Consequently, the heat input during the summer season strongly depends on the snow thickness. When the glacier surface is snow covered, heat is stored by percolation (and refreezing) of surface meltwater. Conversely, when the glacier surface is snow-free, this latent heat is lost due to meltwater runoff over the impermeable surface.

[22] To estimate snow thickness changes over the last 200 years, we use the Crocus snow model [Brun et al., 1989, 1992]. This one-dimensional multilayer physical model was initially developed for seasonal snow modeling and avalanche forecasting in the French Alps. It explicitly evaluates mass and energy exchanges between the snowpack and the low-level atmosphere at 15-min time steps as a function of meteorological conditions, including turbulent heat flux, moisture surface transfers, and ground heat flux. Crocus computes the heat transfer within the snowpack and also the grain types, snow temperature, density, and liquid-water content of each snow layer. Snow and firn albedo is derived from grain characteristics (optical diameter) and from the age of the surface layer. Crocus has been successfully applied to glaciers in the French Alps for mass balance modeling [Gerbaux et al., 2005]. As suggested by Gerbaux et al. [2005], we added a 200 m thick ice layer below the initial snow profile to start the simulations. The reason for this is that in the ablation zone where mass is lost yearly, an initial 200 m thick ice layer makes it possible to preserve ice throughout the simulation. The thickness of this ice layer does not have any influence on the results and is simply used to maintain the presence of ice below the snow. Ice albedo was set to 0.23 in the 0.3–0.8 μm band, 0.15 in the 0.8–1.5 μm band, and 0.06 in the 1.5–2.8 μm band, according to measurements performed on St Sorlin Glacier (French Alps) [Gerbaux et al., 2005]. In the accumulation zone, we consider that snow to ice compaction is completed when simulated firn density reaches 800 kg m−3. Indeed, Crocus is a seasonal snow model and it cannot reproduce the firn densification until the ice (913 kg m−3). We use the value of 800 km m−3 as threshold for the firn/ice transition. At the elevation of Tête Rousse Glacier, densification processes mainly come from percolation and refreezing of surface meltwater. Given that the firn is approximately 30 m thick at 3550 m a.s.l. in the Mont Blanc range [Vallon et al., 1976], we assume that the firn thickness is less (20 m) in the accumulation zone of Tête Rousse Glacier due to the lower elevation of the site.

[23] The Crocus model also calculates temperature, heat flow, and water percolation within the snowpack. However, Crocus is a one-dimensional model developed for seasonal snowpack simulations and therefore cannot be used to simulate the thermal regime of a glacier with a peculiar geometry. Consequently, only the snow thicknesses modeled by Crocus are used and the thermal regime of the glacier is modeled by the model presented below.

3.2. Heat Flow and Water Content Modeling

[24] Field temperature measurements performed along a longitudinal section (Figure 1) are assumed to be representative of the temperature distribution within the glacier. We assume that the relevant physical processes are laterally invariant and that the lateral heat fluxes coming from the glacier sides are negligible because the central longitudinal section we use is located ∼80–120 m from the glacier edges. Physical equations are integrated on a 2-D grid using the spectral element method [Patera, 1984] with tetragonal polygons. Temperature and water content are computed at a 8-h timescale and spatial resolution varies from 0.8 m to 2 m. We consider that glacier thickness remains constant over the whole 20th century (equal to the measured thickness in 2007 [Vincent et al., 2010]) and over the whole 19th century (equal to the measured thickness in 1901 [Mougin and Bernard, 1922]). This approximation does not influence modeled temperature since the changes in the glacier thickness (−15 m over 104 years) is not significant in comparison with heat transfer velocity by diffusive and advective processes.

3.2.1. Heat Flow Model

[25] The temperature field in the cold part of the glacier is calculated solving the heat transfer equation within a cold glacier (including ice, firn, and snow) which can be written as follows [Malvern, 1969; Hutter, 1983]:

display math

where T (K) is the temperature, ρ (kg m−3) is the density, Cp (J kg−1 K−1) is the specific heat and k (W m−1 K−1) is the thermal conductivity of the firn/ice, v (m s−1) is the glacier flow velocity vector, t (s) is the time, and Q (W m−3) is a volumetric heat source. Heat dissipation by ice deformation was neglected given that we observed very low ice-flow velocities. The heat source associated with the refreezing of percolating water is discussed insection 3.2.3 and is treated separately from the volumetric source, so Q is set to zero.

[26] Ice advection has been taken into account. For this purpose, the ice-flow velocities have been calculated using steady state three-dimensional full-Stokes simulation proposed byGagliardini et al. [2011]. For these numerical simulations, we used (1) the 1901 topography (maximum surface velocity of about 1.1 m yr−1) for the period 1800–1901 and (2) the 2007 topography (maximum surface velocity about 0.6 m yr1) for the period 1901–2010. For the period during which the subglacial water-filled cavity is present (seesection 4.2.2.), (3) we take into account of the water-filled cavity influence on the velocity field. In this way, the calculated surface velocities are in agreement with the measurements. However, heat advection due to firn densification is ignored because heat transport into the firn is largely dominated by meltwater percolation and refreezing. Furthermore, in this wet accumulation zone, densification is mainly due to refreezing of surface meltwater [Vallon et al., 1976] involving very fast densification of firn and therefore very low vertical advection.

[27] Changing snow thickness is included in the model by changing density profile each month supposing a constant surface elevation (to avoid a remesh calculation each month). Given that Crocus model is developed for seasonal snowpack, it is not able to simulate correctly firn densification into ice. Consequently, according to the fact that, at 3500 m a.s.l. in the Mont Blanc area, the firn density increases linearly as a function of depth [Vallon et al., 1976], density is updated every month from snow thicknesses modeled by Crocus using equation (3):

display math

where x (m) is the horizontal distance from the upper limit of the glacier, z (m) is the depth from the surface, zmax (m) is the maximum firn thickness (set to 20 m), ρsurf is the surface density (set to 400 kg m−3, in agreement with field observations), ρice is the ice density (913 kg m−3), and zsnow (m) is the snow thickness given by the Crocus model. Here zmax represent the firn thickness needed to transform firn into ice. Although Crocus model gives firn thickness superior to zmax, firn thickness cannot exceed this value. Indeed, Crocus model is not developed to simulate correctly firn densification into ice.

[28] Thermal conductivity is inferred from snow and firn density using the relationship provided by Sturm et al. [1997]:

display math

Ice conductivity is set to 2.1 W m−1 K−1 [Paterson, 1994]. Surface temperatures are inferred from air temperature using a constant lapse rate (Table 2) and determine the surface boundary condition. This approximation has shown good results in heat flow modeling carried out for the Col du Dôme, 1000 m above the study site [Vincent et al., 2007b], and for Mount Illimani (6350 m a.s.l.) in Bolivia [Gilbert et al., 2010]. At the glacier bedrock, the basal heat flux is assumed to be constant in time and space (flux boundary condition). Owing to local topography (Tête Rousse Glacier is located on a large spur on the west face of Aiguille du Goûter), the horizontal component of the heat flux through the bedrock between the south-facing side of the spur to the north-facing side is probably greater than the vertical component [Noetzli et al., 2007]. Consequently, since the basal flux is in any case low, we derived the basal flux from the basal temperature gradient observed at the borehole in the cold tongue of the glacier, yielding a value of 20 ± 10 × 10−3 W m−2. The englacial temperature in this borehole is not influenced by the subglacial lake, as opposed to the temperature in boreholes 2 and 3 (see section 4.2.2).

Table 2. List of Parameters Used in the Model
ParameterLabelValuesUnits
Heat Flow (Section 3.2.1)
Latent heat of ice fusionL3.35 × 105J kg−1
Basal fluxFb15 × 10−3W m−2
Thermal conductivityk[0.25; 2.1]W m−1 K−1
Specific heat of iceCp2.05 × 103J kg−1 K−1
Surface temperature lapse ratedT/dz−6.5 × 10−3K m−1
 
Surface Melting (Degree Days)
Degree day factorDday3.0 × 10−3m K−1 day−1
 
Water Content (Section 3.2.2)
Percolation velocityvz3.0 × 10−5m s−1
Residual saturationsr0.03 
Moisture diffusivityK5 × 10−4m2 s−1
Maximum water content in temperate iceωice10kg m−3
 
Snow Thickness (Crocus Model)
Precipitation correction factorP[1.5 3.3]-
Long wave radiation (cloudiness corrections)a; b0.3; 3.14-
 
Heat Flow/Water Content
Snow thicknesszsnowfrom Crocus modelm
Maximum snow thicknesszmax20m
Densityρ[400; 913]kg m−3

[29] Assuming a thermodynamic equilibrium between ice and water, the temperature of the water reservoir is set to 0°C. Note that this is consistent with our temperature measurements performed in 2010 in boreholes 4 and 5.

[30] When ice or firn become temperate, temperature is set to the melting point temperature T0 and liquid water can be stored (section 3.2.2).

3.2.2. Water Content Modeling

[31] Processes involving meltwater percolation from the surface and refreezing have a strong influence on englacial temperature [Greuell and Oerlemans, 1989; Lüthi and Funk, 2001; Vincent et al., 2007a, 2007b; Gilbert et al., 2010, Humphrey et al., 2012]. We therefore coupled our heat flow model with a model of water percolation within the snow/firn layers of the glacier and a model of moisture diffusion in the temperate ice [Hutter, 1982; Aschwanden and Blatter, 2009].

[32] We assume that the surface meltwater percolates vertically through the snow and firn at a constant velocity of 3.0 × 10−5 m s−1 as observed by Vallon et al. [1976] in the accumulation zone of the Mer de Glace (3550 m a.s.l., Mont Blanc range), although this value is somewhat higher than theoretical values for water percolation through homogeneous snow (values close to 10−6 m s−1 [Colbeck and Davidson, 1973]). Neglecting noncontinuous sources of water transport like water channels within the ice or crevasses, the transport equation for water is expressed as follow:

display math

where ω (kg m−3) is the water content, vz (m s−1) is the percolation velocity, ωadvec (kg m−3) is the water available for percolation, and K (m2 s−1) is the moisture diffusivity [Hutter, 1982] set to 5 × 10−4 m2 s−1 if ρ = ρice [Aschwanden and Blatter, 2009] and set to zero if ρ < ρice. We assume that cold or temperate ice is totally impermeable to liquid water percolation [Fountain and Walder, 1998]. Therefore vz is set to 0 as soon as the density sets by equation (3) reaches the ice density (913 kg m−3). As water is partly retained in the snow by capillarity [Colbeck and Davidson, 1973], we define:

display math

where ω (kg m−3) is the total water content, sr the residual saturation (ranging from 0.03 to 0.07 [Illangasekare et al., 1990]) and ωsat the maximum water content which depends on the snow porosity and related to snow density by:

display math

where ρwater is the water density and ρsnow (kg m−3) the snow density. If water content exceeds ωsat, we assume that this water is drained by runoff. In the temperate ice, maximum water content is set to 10 kg m−3 in temperate ice [Pettersson et al., 2004]. When this maximum water content is reached, we assume that water cannot enter anymore into the body of the glacier.

[33] Surface boundary condition is a water flux ωsource (kg m−2 s−1) coming from surface melting and we assume a zero-flux basal boundary condition. Surface melting is estimated from daily maximum air temperature by a degree-day model as done byVincent et al. [2007b]for the Col du Dôme in the Mont Blanc range because meteorological data like wind speed, direct and diffuse short-wave radiation, incident long-wave radiation, cloudiness, and relative humidity are not sufficiently accurate before 1958 (SAFRAN reanalysis data are not available, seesection 3.1) to apply a full energy balance model like Crocus.

3.2.3. Coupling Water Content and Temperature Field

[34] Water content is coupled with the heat flow model by assuming that water refreezes and produces latent heat in the cold firn at each time step. This induces a temperature increase given by:

display math

as long as the snow temperature T (K) remains below the ice melting point (where L (J kg−1) is the latent heat of fusion of ice). This total refreeze of the liquid water content results in ω = 0. If the temperature reaches the melting point T0, T is set equal to T0 and the content of water which remains liquid is given by:

display math

where ωi and Ti are the initial water content and firn temperature, respectively. Energy released when the refrozen meltwater is cooled to the temperature of the surrounding firn is not accounted for. Given that the firn temperature is not lower than −4°C (section 4), this source is therefore less than 5% of the latent heat (ratio between latent heat of fusion and energy lost by cooling the refrozen meltwater of 4 K) and its contribution can be neglected.

4. Results

[35] Englacial temperatures along a 2-D longitudinal section of Tête Rousse Glacier were simulated over the whole 1800–2010 period, using different data sets depending on the considered period (cf.section 2.2). At the beginning of the simulation period, in 1800, the glacier was considered to be uniformly cold (−2.5°C). This initial temperature corresponds to the mean simulated englacial temperature for the first 50 years. The initial snow thickness was arbitrarily set to 10 m at 3125 m a.s.l., 5 m at 3175 m a.s.l., 20 m at 3225 m a.s.l., and 20 m at 3275 m a.s.l. These choices do not affect simulated temperatures after 1850.

4.1. Snow Cover: Validation and Correction Using Satellite Images and Aerial Photographs

[36] The aerial photographs and satellite images show that the portion of the glacier covered by snow at the end of summer can vary from almost none to all (Figure 2 and Table 1). Indeed, the 1949 aerial photography shows that almost the whole surface of the glacier showed exposed ice on 4 September, whereas it was entirely snow covered from 1960 to 1990.

[37] Figure 3 shows that snowline elevations from the model and images/photographs are in good agreement over the period 1940–2010 except for 9 years (1984, 1986, 1987, 1989, 1992, 1993, 1999, 2001, 2002). Owing to the fact that snow and firn thicknesses are simulated during 200 years, potential model errors accumulate from year to year after each winter accumulation /summer melting cycle even if the model performs correctly for most of annual runs. Therefore hourly snow thicknesses modeled by Crocus are corrected by incorporating information from satellite images and aerial photographs. The aim of this correction is to have the best possible unbiased snow and firn thicknesses evolution since 200 years for our heat transport model. Thus in the event of disagreement between the model and the images/photographs, snow thickness is reinitialized at the date of the image/photograph. For such dates, the snow thickness at given elevation is deduced from the difference between that elevation and the snowline elevation, i.e., it is set to zero below the snowline and is calculated from the measured accumulation gradient used for precipitation corrections (see section 2.2) above the snowline. However, the glacier may often remain totally snow covered during the whole year, as shown in Figure 2 for 1970. In such a case, because images and photographs cannot provide any information on snow thickness, the images are only used to correct the Crocus model if it calculates an exposed ice surface on the glacier. Thus, in this case, we impose a minimum of 1 m of snow at 3160 m (where snow thickness is generally minimal) and we use the measured accumulation gradient to complete the snow cover thickness over the glacier.

Figure 3.

Modeled (bars) and observed (squares) snowline elevations. Modeled snowline elevations on the dates from Table 1 are shown after and before correction using aerial photographs and satellite images (red and green bars, respectively). Black squares are snowline elevations estimated from satellite images and photographs. For years without available satellite images or photographs, the snowlines modeled for 15 September are plotted. Note that differences between measurements and the corrected model results are due to the elevation resolution of the model (set to 20 m). A snowline at 3100 m means that the entire glacier is snow covered. There is no ablation zone during these periods.

[38] Snow cover modeling results presented in Figure 4show rapid and large changes of snow thickness over the last 200 years. From the beginning of the study period to 1878, the snow cover thickness on the glacier was lower than over the 20th century. Between 1878 and 1892, periods of positive mass balance increased the snowpack thickness by about 4 m (at 3175 m a.s.l.) to 10 m (at 3225 m a.s.l.). The snowpack then remained thick until 1930 and the glacier was snow covered all year-round with a thickness ranging from 3 to 20 m (except between 1921 and 1926). Owing to a period of strong negative mass balances during the forties, Tête Rousse Glacier quickly lost its snow cover to become snow-free on a large part of the glacier in 1949 (seeFigure 2). Snow cover increased again between 1955 and 1985 before returning to a state where permanent snow cover was limited to the highest part of the glacier (see Figure 3).

Figure 4.

Mean annual firn plus snow thicknesses on Tête Rousse Glacier modeled by Crocus at four different elevations (3275 m a.s.l. in black, 3225 m a.s.l. in red, 3175 m a.s.l. in green, and 3125 m a.s.l. in blue) for the period 1810–2010. The years 1892, 1949, and 1970 correspond to the date of the first outburst flood and the date of the two first photographs shown in Figure 2, respectively.

4.2. Thermal Regime

4.2.1. Comparison With Observations in 2010

[39] Measured and simulated temperature distributions for September 2010 along the longitudinal section are shown in Figure 5. Measurements and simulation are in very good agreement (Figure 5b) and show a polythermal structure with a cold tongue and temperate ice in the upper part of the glacier. Advection of temperate ice is not sufficient to impact significantly the cold temperature of the glacier tongue. Surface temperatures (between 0 and 10 m deep) are not plotted in Figure 5 given that they are influenced by seasonal changes. The temperate zone at the center of the glacier, between distance 280 m and 330 m, is due to the 55,000 m3 water reservoir drained in 2010 [Vincent et al., 2012] and fixed in the boundary conditions since 1980. The date of appearance of this water-filled cavity and its thermal influence will be discussed insection 4.2.2.

Figure 5.

(a) Modeled englacial temperatures in 2010 for Tête Rousse Glacier. Black dots show thermistor locations in the boreholes. (b) Comparison between measurements (blue dots) and simulation (black bold line) at each borehole. The borehole numbers are indicated in Figures 5a and 5b. The cold temperate transition surface (CTS) is indicated with a dashed line.

[40] We performed sensitivity tests for the main parameters of the model by comparing 2010 englacial temperatures simulated using a given set of reference parameters with temperatures obtained when varying each parameter from its maximum to its minimum values (Table 3) taken from the literature (see section 3.2) and/or field observations. Figure 6shows the results along a one-dimensional longitudinal profile at about 30 m depth (red dashed line inFigure 7a). The most sensitive parameters are the degree-day factor (red line), snow cover thickness (blue and dashed blue lines), and surface temperature (the air temperature gradient, black line). The other parameters (temperate ice porosity, water percolation velocities, basal flux, maximum snow thickness, residual water saturation in snow, and maximum water content in ice) are less sensitive and do not imply a temperature difference exceeding 0.5°C along the considered one-dimensional longitudinal profile. The sensitivity to snow cover is investigated by observing the impact of snow persistence throughout the year and snow thickness separately. Note that adding or removing just one meter of snow to the annual snowpack has the same impact as multiplying or dividing the snow thickness by two. Consequently, the persistence of snow all year-round, which turns into firn, is the most important process controlling the thermal regime of the glacier in comparison with winter snow thickness.

Table 3. List of Simulations Performed for Sensitivity Testa
Simulation NumbersModified ParametersNew Values
  • a

    One parameter is modified from Table 2 in each simulation.

1 and 2Fb0 and 30 × 10−3
3 and 4dT/dz−6 × 10−3 and −7 × 10−3
5 and 6Dday1 × 10−3 and 5 × 10−3
7vz3.0 × 10−6
8sr0.1
9 and 10ωice4 and 16
11 and 12zsnowzsnow = zsnow + 1 and zsnow = zsnow − 1
13 and 14zsnowzsnow = zsnow × 2 and zsnow = zsnow/2
15zmax40
Figure 6.

Simulated 30-m depth englacial temperatures along the central longitudinal section (red dashed line inFigure 7a) for different parameter sets. Squares represent the measurements (with borehole numbers from Figure 1) and the black dashed line shows model results using the reference parameter set (see Table 2). Other curves show the modeled englacial temperatures with other parameter values summarized in Table 3.

Figure 7.

(a) Differences in steady state temperature between the glacier with and without a subglacial lake. (b) Temperatures measured and modeled in borehole 3 for different dates of lake formation. Error bars represent measurements, the black bold line is the modeled temperature without the lake and the blue line is the modeled temperature with a lake at thermal equilibrium with the surface of the glacier. Purple, green, black, and red curves are the thermal states for a lake formed respectively in 2005, 2000, 1990, and 1980. (c) Borehole temperature measured and modeled along the red dashed line in Figure 7a for different dates of lake formation. The fit with red curve means that the lake was likely formed in 1980. Error bars represent measurements (with borehole numbers from Figure 1). The curve legend is the same as for Figure 7b.

[41] The tongue of the glacier remains cold irrespective of the parameter set used for the simulation. This means that current climatic conditions lead undoubtedly to a polythermal glacier. Transformation to a temperate glacier would require persistence of snow cover exceeding 7 to 8 m over the whole glacier surface for several consecutive years.

4.2.2. Thermal Influence of the Subglacial Water-Filled Cavity

[42] The temperature inside the subglacial water-filled cavity is set to 0°C assuming thermodynamic equilibrium between the liquid and solid phases. As surrounding ice temperature is negative (Figures 5a and 5b), heat conduction largely contributes to warming the glacier around the cavity. Because of the low velocity of heat transfer in ice, this warming effect is very dependent on the date on which the cavity formed, i.e., if thermal equilibrium has been reached or not. In this section, “steady state” or “thermal equilibrium” will mean that the subglacial lake no longer has an influence on ice temperatures change. We have therefore analyzed the thermal effect of the subglacial lake to answer two questions: Is the observed (2010) temperature field at steady state? How is the age of the cavity related to the observed temperatures?

[43] To investigate steady state conditions, we consider this subglacial cavity to be formed as far as possible in the past, i.e., in 1907 (beginning of the Lyon-Bron air temperature time series). Starting the simulation in 1907 allows us to make sure that a steady state is reached. Indeed, our simulations show that thermal equilibrium between the surface of the glacier and the 0°C zone is reached after 60 years. To determine how the subglacial lake modifies the temperature field at steady state, an additional simulation with no subglacial reservoir was performed. This simulation shows that the thermal effect of the subglacial reservoir in the surrounding cold ice is only significant (difference >0.1°C) at a distance less than 100 m downstream of the cavity and less than 70 m upstream of the cavity (due to ice-flow advection). A very small influence is therefore detected at borehole 1. Average temperatures at boreholes 2 and 3 increase by +0.5°C and +0.8°C, respectively (Figure 7a). Comparing the steady state simulation (cavity created in 1907) to the temperature profiles measured in boreholes 2 and 3 (Figures 7b and 7c), we note that the observed temperatures disagree with this steady state (r2 = 0.72). This suggests that thermal equilibrium between the surface and the cavity was not yet reached in the thermal state observed in 2010.

[44] From the previous conclusion, a remaining question is the age of the subglacial lake required to reach the temperatures observed in 2010. To determine this, the thermal effect of the 0°C volume was investigated by making it appear at different dates. Simulations were performed considering a subglacial water-filled cavity appearing in 2005, 2000, 1990, and 1980, respectively. The modeling experiments reported inFigures 7b and 7c show that temperatures measured in boreholes 2 to 6 can only be explained by a cavity that is 30 years old (r2 = 0.99).

[45] The dependency of this conclusion on the parameter values used in the simulation was checked with a sensitivity test. The temperature profile measured in borehole 1 is effectively sensitive to all model parameters (Figure 6) although it is very little thermally influenced by the water-filled cavity (Figure 7a). Thus, if we assume that the cavity appeared after 1980 and that the warming simulated in boreholes 2 to 6 is due to changing parameters, simulated temperatures in borehole 1 would have also been modified and would disagree with the data. This is not the case and leads us to conclude that our model parameters are well constrained by borehole 1 temperature data. Therefore temperature measurements in boreholes 2 to 6 suggest the existence of a subglacial water reservoir for 30 years. This result is obtained assuming constant cavity geometry, i.e., not taking into account any cavity growth. This means that the thermal influence of the cavity could be overestimated and that the cavity may have started to grow a few years before 1980.

4.2.3. Thermal Regime Variability Over the Last Two Centuries

[46] Figure 8 shows the temperature distribution at six different dates in 1860, 1892, 1920, 1950, 1980, and 2010. Simulated englacial temperatures in 1860 are not very sensitive to initial conditions in 1800 (cold glacier at −2.5°C throughout). Indeed, a simulation performed with an initial temperate glacier in 1800 gives similar results as of 1860 with the same extent of the temperate zone and less than a 1°C temperature difference in the cold zone. To set relevant boundary conditions, we also assume the existence of a supraglacial lake as of 1870, at the level of the upper cavity in 1892 [Vincent et al., 2010], and the existence of a subglacial cavity since 1980 as presented in section 4.2.2. Results show that the extent of the temperate part of such a small and thin glacier can change significantly over a 15- to 20-year period.Figures 9a, 9b, and 9c shows that the extent of the temperate part is clearly linked to the snow thickness on the glacier. Consequently, the expansions of temperate parts of the glacier are negatively correlated to air temperature variations. Higher accumulation can lead to temperate conditions at the glacier tongue as observed in the late 19th century (Figure 8). Although the central part of the glacier has remained cold over the whole period of simulation, the temperate part included as much as half of the total volume of the glacier in 1920 and 1980. Our simulations show that Tête Rousse Glacier has been a polythermal glacier since the beginning of our study period. This is in disagreement with the conclusion of Mougin and Bernard [1905]. These authors reported measurements performed at different times in the ice at 15 and 20 m depth at the level of the 1892 upper cavity (Figure 1) and concluded that the glacier was temperate in 1903. Their measurements were made 11 years after the 1892 event and were probably influenced by a local warming effect caused by meltwater infiltration into the old upper cavity, the inner central part of the glacier remaining cold.

Figure 8.

Englacial temperature for Tête Rousse Glacier for six different dates over the last 200 years.

Figure 9.

(a) Mean annual air temperature measured at Lyon-Bron meteorological station and extrapolated to Tête Rousse Glacier. (b) Mean englacial temperature of Tête Rousse Glacier (red curve) and proportion of the temperate part of the glacier (black curve). (c) Mean annual snow thickness simulated on Tête Rousse Glacier (black line) and mean winter snow accumulation (blue dashed line) from December to April.

[47] The past 25 years are known as a period of strong negative mass balances for Alpine glaciers, mainly explained by an increase in summer air temperatures [Vincent, 2002] (Figure 9a). A paradoxical consequence on Tête Rousse Glacier is the glacier cooling effect caused by reduction of the surface firn cover (Figures 9b and 9c). However, no trend in winter snow accumulation is observed (Figure 9c), which shows that the cooling effect mainly comes from increased summer melting (which reduces the firn thickness). The influence of winter snow precipitation is not significant in comparison to the influence of firn depth and extent. Our model clearly indicates that the temperate part of the glacier has shrunk over the last 25 years (Figure 9b). Thus deep temperate ice observed in the upper part of the glacier in 2010 is likely to come from the temperate accumulation zone simulated between 1955 and 1980 and is now cooling.

5. Discussion

5.1. Thermal Regime

[48] Simulations shows that the polythermal structure of the glacier is strongly influenced by the snow and firn cover which control englacial temperature distribution within the glacier. Two processes are involved here, the refreezing of meltwater (process a) and the thermal insulation provided by this snow and firn cover (process b). Process a releases latent heat that warms up the snowpack (and firnpack). This process occurs when surface meltwater percolates into the cold snowpack or when stored liquid water refreezes in winter. This process warms the snow and firn up to 0°C each year during summer and also stores energy by trapping liquid water which can potentially refreeze later. This mechanism does not appear on snow-free surfaces of the ablation area because, in this case, the surface meltwater is lost by runoff. Process b reduces the heat loss by thermal diffusion during winter as a function of snow/firn thickness. Owing to the extremely low thermal conductivity of the snow (values of ∼0.2 to 0.4 W m−1 K−1 [Sturm et al., 1997]), the upper snow/firn layers act as an insulating layer that efficiently limits the diffusion of the cold wave through the snowpack from the surface toward the older underlying layers. The efficiency of this process depends on the snow thickness. We show in our model that below 7 to 8 m, the firn formed during previous years always remains at 0°C and all the water stored sufficiently deep in the firn layers of the glacier cannot refreeze and keep the upper ice layer of the glacier temperate all year-round. The contribution of these two processes is not the same over the whole glacier surface because snow thickness is spatially variable. This can explain the observed thermal structure of Tête Rousse Glacier.

[49] The accumulation zone of Tête Rousse Glacier corresponds to a “wet snow” accumulation zone [Paterson, 1994, chapter 2], i.e., all the snow accumulated during winter reaches 0°C in summer mainly due to process a. After that, meltwater is lost by runoff or trapped by an impermeable surface (ice layer or interface between firn and ice). Consequently, in the accumulation zone, when the entire snowpack accumulated during winter has reached 0°C, water percolates through the firnpack down to the waterproof ice surface, forming a water-saturated layer at the firn/ice interface. Owing to latent heat released when it refreezes, this water-saturated layer keeps the upper ice layer of the glacier temperate. Furthermore, if the snow cover is sufficiently thick (>8 m), process b prevents refreezing of all the water stored in deep firn layers of the glacier and keeps the upper ice layer of the glacier temperate all year-round.

[50] In the ablation zone, because of the absence of snow/firn at the glacier surface during summer, the meltwater cannot be trapped and is evacuated by runoff over the impermeable ice surface. Therefore no latent heat can be released by refreezing and energy from process a is lost and does not warm up the glacier. Process b is also less efficient because the snow thickness does not exceed the winter accumulation.

[51] Consequently, englacial temperature strongly depends on the respective sizes of the accumulation and ablation zones which have significantly changed in the past as shown by our snow/firn thickness simulation over the last 200 years (Figure 4). As a consequence the polythermal structure of Tête Rousse Glacier observed in 2010 results from snow and firn thickness changes in the past.

[52] The consequence of the recent decreasing firn cover due to climate warming is a cooling of Tête Rousse Glacier. This result conflicts with most of the studies showing that glaciers are warming in a warming climate, not only in their accumulation zone [Vincent et al., 2007b; Gilbert et al., 2010; Hoelzle et al., 2011] but also in their ablation zone [Pettersson et al., 2003; Gusmeroli et al., 2012; Rabus and Echelmeyer, 2002]. Cooling may only occur in the vicinity of the fluctuating firn. In the case of Tête Rousse Glacier, due to its small elevation range (150 m), the whole glacier is located within the fluctuating firn zone, explaining why the entire glacier is cooling although air temperatures are rising. This specific behavior of Tête Rousse Glacier is due to its small size as well as its altitudinal location.

5.2. Water Storage in the Glacier

5.2.1. Case of the Outburst Flood in 1892

[53] In the analysis of the 1892 outburst flood, Vincent et al. [2010] concluded that water had been stored in a supraglacial lake formed in the 1860–1870s and covered afterward by the heavy annual snowfalls of the winters of the 1880s. Englacial and subglacial conduits may have drained the water toward the glacier terminus where a watertight cavity was formed in contact with the bedrock. However, the causes of the bursting of the terminus still remain unclear. Two possible explanations were considered by these authors. First, the glacier terminus could have burst due to the water pressure against the thinning ice roof of the lower cavity. Another possibility could be linked to a thermal regime change. Simulations performed in the present study support the second hypothesis.

[54] Indeed, most of the glacier was comprised of cold ice for more than 20 years before 1880 (Figure 8). This favored the formation of a supraglacial lake filled with meltwater trapped over an ice-impermeable surface [Boon and Sharp, 2003] in the context of a flat topography. Furthermore, the formation of the lower cavity required a cold tongue frozen to bedrock to avoid any water drainage through subglacial conduits [Vincent et al., 2010]. Between 1878 and 1892, successive years with positive mass balances were responsible for a sufficiently high snow accumulation to produce temperate conditions in the lower part of the glacier tongue (Figure 8, top right). The temperature rise of the glacier sole linked with snow accumulation was probably the process responsible for the 1892 rupture. However, the formation of the englacial conduits from the upper to lower cavity remains unclear for the case of cold ice as simulated in our study (between −1.5°C and −1°C here). Only mechanical fracturing of the ice could explain water drainage in such a case [Fountain and Walder, 1998; Van der Veen, 2007].

5.2.2. Cold/Temperate Interface: A Trap for Subglacial Water

[55] The processes explaining the subglacial water-filled cavity discovered in 2010 are different than those explaining the 19th century lake. Results presented insection 4.2.2tend to support the existence of a 30-year old internal cavity andFigure 8 shows that the upper part of Tête Rousse Glacier was generally made up of temperate ice over the last century. In this zone, surface meltwater can drain to the glacier bedrock through small englacial conduits or crevasses [Fountain and Walder, 1998; Fountain et al., 2005]. Water can also enter below the glacier along the rock-ice interface from the Aiguille du Goûter western face and form subglacial water streams. These streams can contribute to melting of the ice, creating channels descending along the sloping bedrock [Fountain and Walder, 1998] due to pressure-induced melting [Paterson, 1994, chapter 6]. This subglacial water is then trapped by the cold and impermeable lower part of the glacier, creating a water-filled cavity. How the cavity was formed remains unclear but high water pressure measured in 2010 in the cavity suggests mechanical processes involving hydraulically driven fracturing and ice deformation around a high water pressure zone [Vincent et al., 2012]. Energy transfer through the roof of the cavity, as low as −1.9 × 10−1 W m−2 according to our simulations, is not sufficient to refreeze the stored water. Indeed, with such an energy flux, refreezing of 1 m of the cavity wall would take ∼55 years (2 cm yr−1). Thus the location of the cavity observed in 2010 corresponds to the lowest elevation ever reached by the trapped water, which is the same as the location of the temperate part of the glacier at the end of the seventies. In case of regression of the temperate part as indicated by simulations over the last 30 years, the cavity cannot move upward and is progressively surrounded by cold ice as observed in 2010.

[56] The minimum volume of this subglacial water reservoir was estimated to be 45,000 m3 in 2010 [Legchenko et al., 2011; Vincent et al., 2012]. The roof of the northern part of the cavity was about 6 m below the surface and the hydrostatic water pressure was close to the overburden pressure [Vincent et al., 2012]. Consequently, to prevent the subglacial lake from outbursting, it was totally artificially drained in early fall 2010.

6. Future Evolution

[57] The future evolution of the thermal regime of Tête Rousse Glacier was investigated by testing two scenarios and assuming no change in the snow precipitation rate. Meteorological conditions over the next 30 years were considered similar to those of the last 10 years, except for air temperature, assumed to increase linearly at a rate of 2°C and 5°C per 100 years. The results for the two scenarios are very similar and only the first is reported in Figure 10. In both cases, the glacier will be totally in the ablation zone and will remain comprised of cold ice with a deeper residual temperate part in 2020 and entirely cold in 2040 (Figure 10). Despite strongly differing temperature conditions, both scenarios have roughly the same impact on the glacier thermal state. The greater surface warming for the +5°C scenario is partly counteracted by the effect of surface temperature cooling related to the greater diminution of snow cover extent for this scenario, leading to an overall similar effect on englacial temperatures for both scenarios. In conclusion, in the coming decades, the glacier will become completely cold, gradually preventing water from snowmelt to percolate through the glacier and therefore limiting the possibilities of subglacial water-filled cavity formation. Note that in both scenarios, we did not take into account glacier thinning that could accelerate cooling and the snow precipitation rate is maintained constant. According to our numerical modeling, a 30% increase in the precipitation rate could maintain the temperate part of the glacier. For atmospheric warming scenarios higher than +3°C from present, the local mean annual air temperature will be positive after 2080.

Figure 10.

Future temperature distributions for Tête Rousse Glacier in 2020 and 2040, assuming an air temperature warming of 2°C over the next 100 years and a constant precipitation rate.

7. Conclusion

[58] The thermal regime of Tête Rousse Glacier is characterized by a temperate accumulation area and a predominantly cold ablation area. This polythermal structure is explained by the presence of a wet accumulation area and a negative mean annual air temperature. This cover insulates the glacier in winter and warms it up to the melting point in summer by releasing latent heat from the refreezing of meltwater. The absence of a firn layer in the lower part leads the glacier to reach a temperature close to the local mean annual temperature (−2.8°C) below a depth of nearly 10 m which englacial temperature are not influenced by the seasonal temperature change. Owing to the very low glacier dynamics, the gravitational temperate ice advection from the upper part of the glacier cannot balance this thermal equilibrium likely present over the last 30 years. Heat flow modeling shows that each summer, snow and firn reach 0°C due to meltwater refreezing. Moreover, when the snow cover exceeds a thickness of 7–8 m, a water saturated layer subsists at the firn-ice interface during winter, maintaining the temperature of the surface layers at 0°C. Thus the englacial temperature distribution directly depends on the snow cover thickness distribution and changes. Simulations of snow cover and englacial temperatures over the last 200 years show that the glacier was cold before 1870 but then gradually warmed up until 1920 due to a snow thickness increase. During this period, the glacier was almost entirely temperate except for its central deeper part which remained cold. The 1892 outburst flood event may have been triggered by a change from cold to temperate conditions at the glacier tongue. The temperate part was large until 1980, allowing water to percolate through the glacier until becoming trapped at the cold-temperate interface. From the comparison of modeled and observed temperatures, we show that water had probably been stored for around 30 years in the subglacial water-filled cavity discovered inside the glacier in 2010. This confirms a probable cavity formation between 1970 and 1980. The future evolution of the thermal regime and the associated water storage of Tête Rousse Glacier depend on the future mass balance trend. According to atmospheric temperature increase scenarios of +2°C and +5°C for the coming century, snow cover will become very thin and spatially reduced and most of the glacier will become cold. Finally, assessment of the outburst flood hazard associated with the water cavity will require further investigations regarding the mechanisms of water percolation through temperate ice. Cavity formation, filling, and bursting will also need to be better understood. Dye tracing experiments will be performed in a near future to better understand the internal hydrological network of the glacier and the origin of the internal water cavity.

Acknowledgments

[59] This study was funded by Le Service de Restauration des Terrains en Montagne (RTM) of Haute Savoie (France), the city of Saint Gervais (France), and the Joseph Fourier University–Grenoble (Pôle TUNES program). Funding was also provided by the European “GlaRiskAlp” Alcotra Program. We thank P. Possenti for conducting the drilling operations and the USGS-EDC for providing free access to Landsat images. SPOT images were provided through the CNES/SPOT-Image ISIS program, contracts 405 and 435. Finally, we thank R. Böhm for providing the homogenized instrument temperature data going back to 1760 in the Alps and Météo-France – CNRS, CNRM-GAME/CEN for providing meteorological data for the twentieth century and the snow model Crocus. We also thank A. Gusmeroli, J. Walder, and an anonymous reviewer for helpful comments and suggestions, and we are grateful to H. Harder, who revised the English of this manuscript.