Ice ablation as evidence of climate change in the Alps over the 20th century

Authors


Abstract

[1] Over fifty years of cumulative annual mass balance data for several glaciers in the Alps shows similar fluctuations which seem to provide evidence of a common climatic signal. Separate winter and summer mass balance measurements from the Claridenfirn (glacier in Switzerland) since 1914 and the Sarennes glacier (France) since 1949 show that (1) the annual mass balance is primarily driven by the summer mass balance term and (2) melting rate variations with time are very similar for these two glaciers located 290 km apart. The increase in the ablation rate of 0.5 cm w.e. day−1 between the two periods 1954–1981 and 1982–2002 over these two glaciers corresponds to a 20 Wm−2 rise in the energy flux at the glacier surface. These results suggest that a common summer melting rate change may have affected the Alps as a whole. Detailed observations on the Sarennes glacier show that the origin of this strong increase in summer ablation since 1982 is not only a rise in the summer melting rate, but also an increase in the ablation period during the months of September and October.

1. Introduction

[2] Mountain glaciers are widely recognized as excellent indicators of climate change over recent centuries [e.g., IPCC, 2001; Oerlemans, 1986; Oerlemans and Fortuin, 1992; Haeberli, 1995]. In particular, glacier mass variations can be used to assess climate warming over the 20th century and possible anthropogenic influences. Unfortunately, available data becomes sparser as we go back in time. Documentation over the last few centuries is only available through snout position observations and with a limited number of glaciers worldwide [Oerlemans et al., 1998]. In spite of this limited knowledge of past glacier fluctuations, available data nevertheless reflects the changes of the Little Ice Age and shows that glaciers have been retreating since the middle of the 19th century. As an illustration, snout fluctuations over the last four centuries are shown in Figure 1 for four glaciers in the Alps. As for the Mont-Blanc area (Mer de Glace, Argentière and Bossons glaciers) and for the Bernese Alps (Unterer Grindelwaldgletscher), snout positions before 1870 were deduced from paintings and historical written reports on damage caused by glacier advances [Mougin, 1912; Zumbühl et al., 1983; Schmeits and Oerlemans, 1997]. These data as well as data from other locations in the Alps [Haeberli et al., 2002; Grove, 2001], show that between the end of the 16th century and the middle of the 19th century alpine glaciers were generally 0.8 to 1.6 km longer than now and that the major retreat took place during the 20th century. Moreover, the changes that took place during the Little Ice Age are recorded in most of the world's mountainous regions [Grove, 1988] even though this period is not always visible on temperature series reconstructed over the past 1000 years [e.g., Mann et al., 1998; Jones et al., 1998; Crowley, 2000].

Figure 1.

Front fluctuations of four glaciers in the Alps.

[3] Figure 1 points out significant trends in glacier length fluctuations over the past four centuries. However, these length variations cannot be directly interpreted in terms of climate change for the following main reasons: (1) snout positions are the result of complex ice flow dynamics which depend on climatic forcing over several previous decades [Paterson, 1994], (2) the dynamic response time of snouts is related to the size of the glacier, its geometry and other dynamic parameters, resulting in differences from one glacier to another [Nye, 1965; Johannesson, 1989]. For these reasons, high frequency fluctuations observed over the 20th century are not synchronous and not always visible for all glaciers, as can be seen in Figure 1. Conversely, mass balance fluctuations are direct climatic indicators as they directly record solid precipitation in the form of winter mass balance and surface energy fluxes via summer ablation [Oerlemans, 1993, 2001; Brathwaite, 1981]. Indeed, since most glaciers in the Alps are temperate (i.e., close to the pressure melting point [Paterson, 1994, p. 215]), the excess energy flux at the glacier surface in summer serves mainly for melting and is therefore recorded in the form of a mass change. Moreover, a previous study [Vincent, 2002] has shown that (1) in the Alps, winter mass balance fluctuations are essentially dependent on winter precipitation and summer mass balance fluctuations are strongly related to summer temperatures and (2) as a consequence, it is necessary to measure both winter and summer mass balance terms over a sufficiently long period to investigate long-term climate trends.

[4] Throughout the world, 10 continuous direct annual mass balance series go back beyond 1960 [Haeberli et al., 1998]. Unfortunately, precise knowledge of the two separate mass balance terms is generally available only through relatively recent measurements [Dyurgerov and Meier, 1999; Duygerov, 2002]. As for the Alps, there are only two data series for which these separate terms are known for more than 50 years. They come from two glaciers located 290 km apart. The main objective of this paper is to use these two long mass balance series to investigate the possibility of a common climatic signal throughout the Alps. This paper will first describe the available data (section 2). Second, the overall mass balance variations since the beginning of the 20th century will be compared for four selected glaciers in the Alps (section 3), revealing common fluctuations of these cumulative annual mass balances. Then, the origin of these common fluctuations will be studied through detailed analysis of winter and summer mass balance terms observed from the two oldest series in the Alps (section 4). Finally, the very high melting rate observed over the last 20 years will be analyzed in detail (section 5).

2. Description of Available Data

[5] In the Alps, the oldest mass balance series performed on the entire glaciated surface are for the Sarennes (1949), Hintereisferner (1953), Kesselwandferner (1953), Saint Sorlin (1957) and Sonnblickees (1959) glaciers. These annual mass balances are obtained from stakes inserted in ice in the ablation area and from drilled cores in the accumulation zone. Total cumulative annual mass balances of the Sarennes and Saint Sorlin glaciers have been extended to cover the entire 20th century using old maps with elevation contours and recent geodetic measurements [Vincent et al., 2000; Vincent, 2002; Torinesi et al., 2002]. For the Aletsch glacier, annual mass balances have been obtained since 1923 by an indirect method using hydrological data [Aellen and Funk, 1990; Müller-Lemans et al., 1994]. This method enables annual mass balances to be monitored using water flux measurements and precipitation data [Paterson, 1994, p. 35]. The Aletsch data have been checked against an independent method using old maps and photogrammetric measurements (Bauder and Funk, unpublished data, 2003).

[6] There are only two data series that contain separate series of winter and summer mass balance measurements over more than 50 years. The oldest series of direct winter and summer mass balance measurements in the world is from the Claridenfirn [Müller and Kappenberger, 1991; Müller-Lemans et al., 1994]. Although these measurements do not cover the entire surface of the glacier, stake readings and density measurements have been carried out since 1914 on two sites, one close to the equilibrum line, at 2700 m a.s.l., and the other in the accumulation zone at 2900 m a.s.l., in two very flat areas of the glacier. The stakes have been set up each year at exactly in the same locations; this positionning has been performed since 1914 from simple alignments with summits visible on the horizon. Consequently, the measurements are not influenced by any spatial variations. In this study, only measurements relative to the highest stake (2900 m a.s.l.) have been used because the series of the lowest stake are not complete. The second longest series of winter and summer mass balances in the Alps come from the Sarennes glacier. On this glacier, the separate mass balance terms have been measured since 1949 on the entire glaciated area from drilled cores and from five to seven stakes inserted in ice [Valla and Piedallu, 1997; Vincent and Vallon, 1997]. Since 1949, the observations have been made five to eight times per year between the beginning of June and the end of ablation season. Table 1 gives a short description of all these glaciers used in this study and Figure 2 shows their locations.

Figure 2.

Map of the Alps. The glaciers of Sarennes (Sar.), Saint Sorlin (Sor.), Alestch (Ales.), Claridenfirn (Clar.) and Hintereisferner (Hint.) are plotted on the map.

Table 1. List of the Glaciers Used in This Study With Their Topographical Characteristics and the Type of Mass Balance Measurements Available
 ClaridenfirnAletschHintereisfernerSaint SorlinSarennes
Location (latitude and longitude)46°40′N; 8°50′E46°30′N; 8°02′E46°48′N; 10°46′E45°10′N; 6°10′E45°07′N; 6°07′E
Surface area (km2)5.61278.330.5
Max. elevation (m)32404160371034003150
Min. elevation (m)25401556243027002850
Length (km)2.824.772.51
ExposureEastSoutheast to southEast to northeastNorth to eastSouth
Mean slope14°13°17°
Available mass balance surveyDirect winter and summer mass balance since 1914, at 2700 and 2900 m a.s.l.Indirect annual mass balance from hydrologic dataDirect annual mass balance since 1953Direct annual mass balance since 1957, winter and summer mass balance since 1993Direct winter and summer mass balance since 1949

3. Cumulative Mass Balance of Alpine Glaciers Over the 20th Century

[7] Direct cumulative mass balance of the Aletsch, Hintereisferner, Saint Sorlin and Sarennes glaciers are plotted in Figure 3a, from direct measurements (small dots and triangles). Moreover, total cumulative mass balances of the Aletsch, Saint Sorlin and Sarennes glaciers have been calculated using old maps with elevation contours and geodetic measurements (large triangles on Figure 3a). For the Saint Sorlin and Sarennes glaciers, the beginning of these series is 1906, although no data is available between 1906 and the mid-20th century. The Aletsch series starts in 1923 and the Hintereisferner series in 1953. Since the mass balance of this glacier is unknown over the first half of the 20th century, the first value of cumulative mass balance has been artificially set to −20 m w.e. in 1953 for easy reading on the graph. The 20th century averaged cumulative mass balances of these glaciers are very different and range from −0.33 m w.e. yr−1 for the Saint Sorlin glacier (1906–2002) to −0.62 m w.e. yr−1 for the Sarennes glacier (1906–2002), although these glaciers lie 3 km apart in the same mountain range and with similar climatic conditions [Vincent and Vallon, 1997]. This can be explained by the difference in their respective geometric and geographic characteristics, i.e., the size of the glaciers, altitude of the accumulation zones and exposure. The Sarennes glacier faces south and its maximum altitude is 3200 m a.s.l. (Table 1). From Figure 3a, it can be seen that this glacier has been strongly receeding in response to the climate of the 20th century. In order to reduce the effects of these trends, the 1953–1999 average rate of decrease has been removed, i.e., each glacier mass balance has been reduced by subtracting the 1953–1999 average mass balance of each glacier from the annual values (−0.62 m w.e. yr−1 for Sarennes, −0.45 m w.e. yr−1 for Hintereisferner, −0.32 m w.e. yr−1 for Aletsch and −0.33 m w.e. yr−1 for Saint Sorlin). The results shown in Figure 3b therefore show deviations in the cumulative mass balance from the 1953–1999 average value, a method that has been used widely in previous studies [Letreguilly and Reynaud, 1990; Six, 2000]. In addition to the previously mentioned glaciers, Figure 3b also includes data from Claridenfirn. Although the overall mass balance of the Claridenfirn remains unknown (see section 2), mass balance fluctuations can be determined from yearly measurements performed at a single stake (at 2900 m a.s.l.). Figure 3b must be interpreted in terms of the slopes of the curves: if the slope is positive (negative), mass balance is higher (lower) than the mass balance average 1953–1999. This graph shows a strikingly common feature between the respective behaviours of the Claridenfirn, Hintereisferner, Saint Sorlin and Sarennes glaciers. A common signal between the Saint Sorlin and Sarennes glaciers might be expected [Vincent and Vallon, 1997] as these glaciers are located only 3 kms apart, but the similarity between the Claridenfirn and Sarennes glacier located some 290 km apart is, on the other hand, more surprising.

Figure 3.

(a) Cumulative mass balance of 4 Alpine glaciers in meters of water equivalent; the Aletsch series starts in 1923 and the Hintereisferner series in 1953. The first value of Hintereisferner has been articially set to −20 m w.e. in 1953. (b) cumulative centered mass balance series of the same glaciers after the 1953–1999 average for each glacier has been substracted. The Claridenfirn has been added to Figure 3b.

[8] Mass balance fluctuations of the Aletsch glacier show some discrepancies, especially between 1957 and 1980. These discrepancies could be a consequence of a difference in climate between the western and eastern Alps. However, if this were the case, it would be surprising to obtain such good agreement between the Hintereisferner glacier and Claridenfirn east of Aletsch and the Sarennes and Saint Sorlin glaciers west of Aletsch. Note that the mass balance data for the Aletsch glacier comes from a hydrological method while that of the other glaciers is based on direct field measurements using stakes and drill cores. The hydrological method requires precipitation values over the entire drainage basin (including nonglaciated areas) and for this reason can lead to large uncertainties [Paterson, 1994, p. 35]. Although the Aletsch cumulative mass balance data have been checked using an independent method based on geodetic measurements, the resulting series is probably not as reliable as direct measurements.

4. Analysis of Winter and Summer Separate Mass Balances

[9] This section aims at comparing the two mass balance terms observed on these glaciers in order to clarify the common signal as shown in Figure 3b. Separate winter and summer mass balance observations over the last 50 years are available only for the Claridenfirn and Sarennes glacier (see section 2) and the following comparison is therefore limited to these glaciers. Furthemore, measurements at only one stake were selected on each glacier: the highest stake (at 2900 m a.s.l.) of Claridenfirn as explained in section 2, and a stake located in the middle of the Sarennes glacier (at 2900 m a.s.l.) and representative of the overall glacier mass balance [Vincent and Vallon, 1997]. The respective influences of winter and summer mass balances on the annual mass balance are shown in Table 2 by the explained variance percentages. These results show that the summer mass balance term represents by far the largest contribution to the annual mass balance. The comparison of the standard deviations of each mass balance term for these glaciers (Table 3) shows the respective variabilities and leads to the same conclusion. Note however that the winter mass balance contribution to the annual mass balance is greater on the Claridenfirn. These results are consistent with (1) the fact that Claridenfirn observations are from the accumulation zone only and (2) the decreasing variability of mass balance with elevation [Vallon et al., 1998].

Table 2. Explained Variance Between Mass Balance Terms for the Sarennes Glacier and Claridenfirn
 Winter Mass BalanceSummer Mass BalanceAnnual Mass Balance
Winter mass balance1Sarennes 0.4%Sarennes 30%
 Clariden 1%Clariden 42%
Summer mass balance 1Sarennes 76%
  Clariden 68%
Table 3. Standard Deviations of Mass Balance Terms
 ClaridenfirnSarennes
Winter mass balance standard deviation0.42 m w.e.0.44 m w.e.
Summer mass balance standard deviation0.56 m w.e.0.75 m w.e.
Annual mass balance standard deviation0.73 m w.e.0.90 m w.e.

[10] Over the last 50 years, mass balance parameters have been compared between the Sarennes glacier and Claridenfirn and the explained variance percentages are reported in Table 4. These results show that the summer mass balance explains by far the largest part of the annual mass balance correlation between these two glaciers. In the same manner as for Figure 3b, Figure 4 displays the cumulative winter and summer mass balance variations centered with respect to the 1954–1981 period. This figure must be interpreted similarly to Figure 3b, i.e., positive (negative) slope means that winter (or summer) mass balance is higher (lower) than the average 1954–1981 winter (or summer) mass balance. The 1954–1981 period was selected with regard to results obtained in a previous study [Vincent, 2002]. In that study, the 20th century was divided into four periods: two steady periods, 1907–1941 and 1954–1981, during which the mass of the glaciers remained almost constant, and two periods of loss, 1942–1953 and 1982–1999, marked by a sharp reduction in glacier mass. In any case, the choice of this reference period influences the slopes but does not change the time-dependent pattern of Figure 4. As would be expected from the explained variance results in Table 4, Figure 4a shows strong differences between winter mass balance on the Claridenfirn and Sarennes glacier. The winter mass balance for Claridenfirn shows no trend. On the other hand, that of Sarennes shows a strong positive trend over the last 20 years, in total opposition with the annual mass balance trend. Over this 1982–2002 period, the winter mass balance on Sarennes has increased by an average of 30 cm w.e./yr (+17% compared to the 1954–1976 average). Note that this increase began in 1977. The relationship between this winter increase and the winter precipitation evolution will be discussed at section 6.

Figure 4.

Cumulative winter and summer mass balance variations relative to the 1954–1981 period.

Table 4. Explained Variance Between Clariden and Sarennes Mass Balances
 Claridenfirn
Winter Mass BalanceSummer Mass BalanceAnnual Mass Balance
Sarennes   
Winter mass balance28%  
Summer mass balance (without correction) 37% 
Annual mass balance  49%

[11] The comparison between Sarennes and Claridenfirn summer mass balances (Figure 4b) shows a striking feature: the variation pattern is very similar until 1981 followed by strong differences in melting rates between 1982 and 2002. Could these differences be related to the mass balance measurement method, to local effects or to a regional climatic difference?

[12] First, the exact date of the measurements must be looked at. The observations at the Claridenfirn have been carried out generally between the 15th and the 30th of September (sometimes in October). Müller-Lemans et al. [1994] have corrected this series up to 1984 in order to obtain corrected mass balance and the date of the end of the melting season. These corrections on melting are small, generally less than 0.20 m w.e. From 1985 to 2002, the measurement dates have been retained and the mass balance measurements have been corrected to account for fresh snow effects. Conversely, mass balance measurements on the Sarennes glacier were performed 5 to 8 times over the melting season until the end of the melting season which can last until the end of October. In order to improve the comparison between these two glaciers, the Sarennes summer mass balances observations have been adjusted to the dates of Claridenfirn data. The interpolation procedure was relatively easy to carry out given the numerous observations on the Sarennes glacier. The corresponding results reported in Figure 4b show that ablation variations are now very similar between the Claridenfirn and Sarennes glacier and that the discrepancies mentioned above therefore came from the different measurement dates. In fact, the correlation between Sarennes and Claridenfirn annual ablation is hardly improved (R2 = 0.44), but the large bias during the last 20 years has been corrected. This means that the cumulative ablation, adjusted to the date of Claridenfirn data, follows the same trend, with very similar melting rate changes over the last 50 years.

[13] Second, the influence of the surface albedo must also be looked at. Although the melting rate increase at Sarennes and at Claridenfirn are now in very good agreement, the influence of albedo cannot be totally disregarded, since Sarennes mass balance observations are generally carried out in ablation zone. Nevertheless, as shown in the next section, the influence of albedo change is probably small since the ice ablation at Sarennes (from the stakes located in the middle of the glacier) usually begins after the end of August. In any case, the influence of albedo is not visible from these data.

[14] In Figure 5, average summer mass balances are reported over the four previously mentioned periods of the 20th century for Claridenfirn and only over the last two for Sarennes. Between 1954–1981 and 1982–2002, ablation from the 1st of June to September has increased similarly at Claridenfirn (0.77 to 1.36 m w.e.) and at Sarennes (1.88 to 2.48 m w.e.). This result suggests that a climate change may have affected the Alps as a whole (in summer). Moreover, from Sarennes measurements, it is obvious that over these last 20 years, ablation has persisted largely after the 1st of September as will be discussed in the next section.

Figure 5.

Mean summer mass balance (m w.e.) for Claridenfirn and Sarennes glacier. Dashed line shows Sarennes summer mass balance for Claridenfirn measurements date.

5. Origin of the High Ablation Over the Last 20 Years

[15] Owing to the very extensive mass balance observations on the Sarennes glacier, it is possible to determine (1) the exact respective periods of snow and ice ablation, (2) the ablation rates over each period on the glacier. For this purpose, the same measurements at only one stake on each glacier were selected, as described in section 4. Figure 6 (bottom) displays the mean ablation rate for snow and ice over the 1954–1981 and 1982–2002 periods for Sarennes. This Figure 6 shows that (1) the ablation rate on the Sarennes glacier increased significantly from 1954–1981 to 1982–2002 with regards to both snow and ice ablation periods. This rise ranges between 0.5 cm w.e. day−1 (snow ablation) and 0.3 cm w.e. day−1 (ice ablation). (2) the snow ablation rate increase on the Claridenfirn (0.57 cm w.e. day−1) is very similar to that observed on the Sarennes glacier. (3) consequently the snow ablation period on the Sarennes glacier has decreased by 4 days in spite of the increase of winter accumulation, as mentioned in the previous section. (4) the ice ablation period on this glacier has risen considerably from 27 to 43 days.

Figure 6.

Mean ablation rates at (a) Claridenfirn (upper stake at 2900 m a.s.l.) and (b) Sarennes glacier (stake at 2900 m a.s.l.) averaged over the periods 1954–1981 and 1981–2002.

[16] Therefore, the very large increase in summer ablation at Sarennes results from both higher ablation rates and a longer summer ablation period. Uncertainties result from the influence of solid precipitation at the beginning (June) and end (September and October) of the ablation period because such precipitation is capable of slowing down the ablation rate, although this effect does not seem to affect the average results. Finally, it seems that the role of the albedo change (snow/ice) cannot explain the discrepancy observed in Figure 4a, First because the ice ablation on the Sarennes glacier only starts after the mean date of 23rd of August, and Second, because the snow ablation duration is only reduced by 4 days.

[17] Using a latent heat of fusion of 334000 J kg−1, the snow and ice ablation rates (mm day−1) have been converted into energy (W m−2) assuming that the ablation is due only to melting (Table 5). Between 1954–1981 and 1982–2002, the energy variations are 20 and 11 W m−2 for the snow and ice ablation periods respectively.

Table 5. Snow/Ice Ablation Rate Converted Into Energy for the Sarennes Glacier
 1954–19811982–2002
Snow ablation rate (cm w.e. day−1)1.52.0
Energy required for snow ablation (W m−2)5777
Ice ablation rate (cm w.e. day−1)2.42.7
Energy required for ice ablation (W m−2)93104

6. Discussion

[18] The analysis of Claridenfirn and Sarennes mass balance terms allows to separate the respective influence of winter precipitation and summer energy balance over the annual balance. This analysis shows that the average annual mass balance is essentially driven by the summer mass balance and therefore by the summer surface energy balance. Nevertheless, the influence of winter accumulation can be strong over some periods and can affect the annual mass balance sign. For instance, winter and summer mass balance analysis shows that in the Western Alps, winter accumulation has been increasing since 1977 whereas the summer ablation rise only started in 1982. This six-year interval, for which annual mass balance was strongly positive, allowed the glaciers to swell and re-advance as can be seen in Figures 1 and 3. The winter mass balance trend observed from Sarennes observations is in agreement with the winter precipitation observed in the western Alps valleys from meteorological data, for instance at Besse en Oisans and Chamonix (Météo France data). Indeed, between 1954–1976 and 1977–1999, winter precipitation (October to May) increased by 10 cm w.e./yr at Besse en Oisans and Chamonix (+15%). These results confirm the findings relative to the ratios between winter mass balance and winter valley precipitation obtained in a previous study [Vincent, 2002]. Although these ratios depend on the sites and are strongly influenced by the topography of the glacier, they remain relatively constant with time and show that it can be easier to detect a small precipitation variation from winter accumulation on a glacier than from meteorological data.

[19] As seen in section 5, the large increase in summer ablation at Sarennes results from both higher ablation rates and a longer summer ablation period. The energy balance change between 1954–1981 and 1982–2002, resulting from snow and ice melting at Sarennes is in very good agreement with the results obtained in a previous study [Vincent, 2002, Table 2]. Given these values (Table 5), it is surprising that the ice ablation rate rise is less than the snow ablation rate rise, since the short wave radiation balance is strongly dependent on surface albedo. This might suggest that solar radiation has not increased or that its rise has affected only the snow ablation period (from June to the end of August). Nevertheless, this interpretation is subject to caution because solid precipitation can affect the ablation rate in September and October and it is possible that the ice ablation rates reported in Table 5 are underestimated. Moreover, as shown in a previous study [Vincent, 2002] based on energy balance analysis, the air temperature increase between 1954–1981 and 1982–2002 explains the largest part of the ablation rise. The observed regional air temperature rise (June to October) can be estimated at 1.2°C (45° latitude, 6° longitude) using homogenised data from a very extensive meteorological network [Böhm et al., 2001]. This rise does not affect only July and August (+1.6°C) but also September (+1.0°C) and October (+1.6°C). Consequently, it is not surprising that the melting season is longer.

7. Conclusions

[20] Cumulative mass balance analysis based on the longest direct mass balance measurements series available in the Alps indicates that cumulative mass balance fluctuations (centered values) are very similar, revealing a common climatic signal over the entire region. From the analysis of Claridenfirn and Sarennes mass balance terms, we can conclude that the average annual mass balance is essentially driven by the summer mass balance and therefore by the summer surface energy balance.

[21] The analysis of Claridenfirn and Sarennes summer mass balance data leads to the following conclusions: (1) the large increase in ablation over the last 2 decades is very similar on these two glaciers located 290 kms apart, and consequently, (2) it is likely that the summer climate changes which affect the glaciers are similar over the Alps as a whole. The detailed observations at Sarennes points out the origin of the strong increase in summer ablation: it results both from the rise in ablation rate and from the increase in summer ablation duration.

[22] In conclusion, this study highlights the representativeness of mass balance fluctuations over the Alps and shows very similar melting rate rises over the last two decades for two glaciers separated by a relatively large distance. Summer mass balance measurements are without a doubt the best way to obtain accurate and inexpensive energy balances over large areas with different altitudes and exposures. This method requires measurement of the winter mass balance from drilling cores and regular stake measurements throughout the summer until the end of the melting season.

Acknowledgments

[23] The authors would like to thank all those who took part in collecting the extensive field measurements on these glaciers. This study has been funded by Observatoire des Sciences de l'Univers de Grenoble (OSUG), by the French National Eclipse Program over the last two years and by the glaciological commission of the Swiss Academy of Sciences. The authors are very grateful to the anonymous reviewers whose comments significantly improved the quality of the manuscript.

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