Annals of Glaciology 52(58) 20111

Spatial distribution of surface ablation in the terminus ofRhonegletscher, Switzerland
Shin SUGIYAMA,1 Takeshi YOSHIZAWA,1;2 Matthias HUSS,3 Shun TSUTAKI,1;2
Daisuke NISHIMURA1;2
1

Institute of Low Temperature Science, Hokkaido University, Sapporo 060-0819, Japan
E-mail: sugishin@lowtem.hokudai.ac.jp
2
Graduate School of Environmental Science, Hokkaido University, Sapporo 060-0810, Japan3
Department of Geosciences, University of Fribourg, CH-1700 Fribourg, Switzerland
ABSTRACT. The spatial pattern of glacier surface melt was measured with a resolution of 20–100 mwithin a region extending 1 km up-glacier from the terminus of Rhonegletscher, Switzerland. The melt
rate was monitored from 6 July to 6 September 2009 using 44 ablation stakes. We also measured thesurface albedo near the stakes to investigate the importance of this parameter for the melt-rate
distribution. The melt rate varied from 32.8 to 71.9 mm w.e. d–1 in the study area. Our measurementssuggest that the spatial variation of the melt rate can be explained by (1) shading of the ice surface byneighbouring mountains, (2) surface albedo and (3) effects of microclimate (e.g. radiation from sidewalls) on the surface energy balance. The observed melt-rate distribution was compared to the results ofa temperature-index melt model, which takes into account shading of direct solar illumination but not
the other two effects. The model reproduces some important features of the field data, but its spatial
variations are generally less than the measured values. Our study shows the importance of albedo andother local conditions in the accurate estimation of the small-scale melt-rate distribution.

INTRODUCTION
Glacier melt plays a key role in the hydrology of glacierizedcatchments. Run-off from mountain glaciers is an importantresource for irrigation, hydropower generation and potablewater in mountainous regions (e.g. Schaefli and others,
2007; Huss and others, 2008b). Accurate quantification ofsnow and ice melt on glaciers is therefore crucial for humanactivities. Melting is also important for the mass balance of
mountain glaciers. Glaciers change their volume under the
influence of climate conditions (e.g. Huss and others, 2009),
and their mass loss significantly contributes to changes in
global sea level (e.g. Meier and others, 2007). To predict
future glacier evolution and its impact on human society, wemust be able to estimate their melt rates from projectedclimate variables.
Glacier melt can be computed by energy-balance models(e.g. Klok and Oerlemans, 2002; Hock and Holmgren,2005; Arnold and others, 2006). Solving the energy balanceof the glacier surface involves the capture of complex
processes, but such models require field observations thatare difficult to acquire. Alternatively, glacier melt is often
computed from air-temperature records by using temperature-index melt models (e.g. Braithwaite, 1995; Ohmura,
2001; Hock, 2003; Shea and others, 2009). Taking into
account the expected spatial distribution of solar radiation
improves computations of temporal and spatial glacier melt
patterns (e.g. Hock, 1999). Such models have been tested
against glacier discharge data, but their ability to reproduce
small-scale spatial melt variation has not been well studied
because high-resolution field data are lacking. Distributed
temperature-index melt models do include some geometrical effects which determine the amount of potential solar
radiation, such as shading by surrounding mountains andthe angle of incidence of the solar beam on the glaciersurface. Other key variables such as ice-surface albedo andwind-mediated sensible and latent heat exchanges are moredifficult to take into account, but are equally important.
Albedo is particularly important on mountain glaciers (e.g.
Oerlemans and others, 2009), but its spatial and temporalvariability is difficult to model; it must be measured on theglacier (e.g. Brock and others, 2000) or by using satellite
data (e.g. Klok and others, 2003).
To study spatial variations in glacier surface melt on thescale of tens of metres in the crucial region of a glacierterminus, we carried out field measurements on the terminusof Rhonegletscher, Switzerland. This paper reports surface
melt rate and albedo measurements from July to September
2009. Both variables varied substantially over the studied
area. The field data were compared with a distributed
temperature-index melt model to evaluate the ability of thelatter to reproduce small-scale melt patterns. The small-scale
melt pattern is especially important for Rhonegletscher,which is rapidly thinning under the influence of factors
related to proglacial lake formation. The non-uniform melt
rates on the surface of the glacier control the evolution of theterminus and future development of the lake.

METHOD
Study site
Rhonegletscher is a temperate valley glacier with a length of
9 km and an area of about 16 km2 in 2007 (Fig. 1a; Bauderand others, 2007). Having retreated 1700 m from 1878 to
2000, the glacier terminus is now at the top of a steep cliff(Sugiyama and others, 2007). Because the current terminus
is located over a depression in the bedrock, a new proglaciallake formed in 2005. The impact of this lake on the glacier isdrawing intense glaciological and public attention. The
terminus of the glacier is thinning at an increasing rate
(Sugiyama and others, 2008) as a result of rising air

2Sugiyama and others: Surface ablation in the terminus of Rhonegletscher

readings was 10–30 mm. Because the reading error accumulates when the stakes were redrilled, the accuracy in the
total melt was about 100 mm. The total melt over the study
period in the region was >2 m in ice thickness; thus, theerror in the mean melt rate was <5%. The readings wereconverted to water equivalent (w.e.) by assuming the densityof ice to be 900 kg m3 .

Albedo measurements
The surface albedo was measured between 1100 and 1600 h
on 5 August 2009 in the vicinity of the ablation stakes. The
cloud cover on that day was <10% according to visualobservation. The upward and downward radiation energies
were measured with an albedo meter (EKO Instruments MR21) and recorded with a datalogger (Hioki 3645). The
albedo meter was held 1 m from the ice surface, and theradiation was measured for at least 1 min. The albedo wascomputed from the radiation energies and incident angle ofthe solar radiation following the standard procedure (Jonsell
and others, 2003; Dewalle and Rango, 2008). The fluctuation in the radiation energies during the 1 min measurement period was <5% (1–2% in general), and the standard
deviation in the downward radiation energy over the entire
survey period was 4.5%.

Meteorological observations
Meteorological observations were carried out on the western
flank of the glacier at 2531 m a.s.l. (Fig. 1a) using an
automatic weather station (Vaisala WXT510), installed at aheight of 1.8 m from a rock surface, that measured airtemperature, precipitation, humidity and wind speed. Sensors measured these variables at 10 s intervals; mean values
were recorded every 5 min with a datalogger (Campbell
CR1000).

Melt modelFig. 1. (a) Map of Rhonegletscher with surface contour lines at
100 m intervals. The location of the automatic weather station(AWS) is indicated by a cross. (b) The study site indicated by the box
in (a). The locations of ablation stakes are indicated by filled circles.
The contour lines show surface elevation at intervals of 20 m. The
two proglacial lakes are indicated by the shaded areas. The
coordinates correspond to the official Swiss coordinate system.

temperature, elevated ice-flow speed (Tsutaki and others,2011) and rapid ice dissipation by melting and fragmentation into the lake. Our study site is the region extending
approximately 1 km upstream of the glacier from theterminus (Fig. 1b).

Surface melt measurements
The surface melt rate was measured by inserting aluminium
ablation stakes 2–4 m in length into the glacier (see Fig. 1b
for the stake locations). We installed 44 stakes in July 2009and monitored their lengths above the surface every 1–10
days. The stakes were redrilled before they melted out. The
mean melt rate was calculated over the entire study period
from 6 July to 6 September 2009. Because of ice surface
roughness and tilt of the stakes, the precision of individual

We used the following numerical model to compute twodimensional (2-D) snow and ice melt-rate (M (m w.e. d1 ))distributions over the study period on a regular grid of
25  25 m:
fM þ rs=i I Tm Tm > 0
M¼
,
ð1Þ
0
Tm  0where fM is a melt factor (m w.e. d1 8C1 ), rs and ri areradiation factors for snow and ice surfaces (m3 W1 d1 8
C1 ), I is the daily total potential solar radiation (W m2 ) and
Tm is daily mean temperature (8C). The temperature at theelevation of the gridcell is calculated from the weather
station data using a lapse rate of dT =dz. The snow/ice surface
condition is distinguished by monitoring snow depth
computed from modelled snowmelt and solid precipitation.
The above model is based on the distributed temperatureindex model reported by Hock (1999; see also Huss andothers, 2008a). The dependence of radiation efficiency on
surface inclination and shading by surrounding topography isquantified by computing I for each gridpoint from theincident angle of solar radiation and a digital elevation model(DEM), as described by Hock (1999). In the case of aconventional degree-day model, the second term in Equation (1) can be neglected and the parameter fM is called the‘degree-day factor’.
To apply the model to Rhonegletscher, the parameters fM
and rs=i in Equation (1) and dT =dz were calibrated so that

Sugiyama and others: Surface ablation in the terminus of Rhonegletscher

3

Table 1. The locations of the ablation stakes, albedos measured on
5 August 2009, measured (Mmeas ) and computed (Mcomp ) melt rates
from 6 July to 6 September 2009 and deviation of the computed melt
rates from the measurements, M ((Mcomp /Mmeas  1Þ  100%);
coordinates correspond to the official Swiss coordinate system
Stake

Fig. 2. (a) Daily mean air temperature (curve) and daily precipitation (bars) and (b) daily mean humidity (bold grey) and hourlymean wind speed. Dates are mm/dd.

(1) the mean misfit of computed total melt with the field data
was close to zero and (2) the root-mean-square error was
minimized. These parameters were assumed to be constantin space and time. We used a DEM constructed byphotogrammetrical evaluation of aerial photographs taken
in September 2007 (25 m resolution, 0.3 m accuracy)(Bauder and others, 2007). Daily mean air temperaturesfrom the above-mentioned weather station were used todrive the computation.

RESULTS
Meteorological data
Meteorological data obtained from 6 July to 6 September
2009 are shown in Figure 2. During the study period, themean air temperature was 6.98C, with a standard deviationof 3.518C, the total precipitation was 261.0 mm and themean wind speed was 4.0 m s1 . There was a snowfall event
during 17–18 July, resulting in a 0.05–0.1 m thick snow
cover on the glacier.

Surface melt
Figure 3a shows a map of the mean melt rate for the period 6
July to 6 September 2009. Ablation stake data are listed inTable 1. The mean melt rate over all measurement sites was
56.1 mm w.e. d1 , with a standard deviation of 7.5 mm w.e.
d1 . Measurements at the stakes were interpolated in spacewith cubic spline interpolation to obtain the overall spatial
distribution. The 2-D melt pattern shows substantial spatial
variation. Over an elevation range of only 100 m, the melt
rate varied by a factor of more than two. For example, there
is a spot of low melt in the upper reaches of the study area
(32.8 mm w.e. d1 at stake 23), and the melt rate is generally
smaller in the northeast part of the studied area. The greatest
melt was observed near the eastern margin at stake 2(71.9 mm w.e. d1 ). The melt pattern near the terminus is

1
2
3
5
6
7
8
9
10
11
12
13
14
15
16
17
21
22
23
24
25
26
30
31
32
33
34
35
36
37
38
39
40
41
42
48
53
54
56
59
T8
T9
T10
T11

Easting

Northingmm

672538672437672410672544672671672784672637672596672546672382672311672335672316672236672281672418672923672816672710672581672777672683672498672532672896672459672931673022672799672705672360672503672480672494672450672203672483672428672393672334672678672573672486672415159402159441159350159324
159355159319159257159198159149159141159171
159144
159233
159166
159145159248159960159930159911159903159471159544159840159642159378159564
159484159609159720159197
159246
159248159290159129159143159149159213
159200159291
159194159700159470159343
159207

Albedo

Mmeas

0.21
0.11
0.14
0.21
0.25
0.11
0.10
0.17
0.13
0.09
0.11
0.06
0.09
0.08
0.06
0.17
0.24
0.30
0.33
0.24
0.22
0.27
0.13
0.16
0.09
0.13
0.12
0.10
0.26
0.09
0.13
0.19
0.16
0.10
0.12
0.11
0.20
0.16
0.12
0.13
0.21
0.24
0.11
0.08

M

Mcomp
1

1

mm w.e. dmm w.e. d

%

58.21
71.93
60.68
59.17
54.07
56.18
59.44
64.02
54.94
55.02
45.87
60.56
67.43
52.33
61.80
60.31
46.74
44.27
32.81
53.27
49.06
53.13
52.40
55.05
59.69
64.35
40.73
50.01
47.90
57.70
62.52
62.38
62.71
55.86
59.30
54.58
46.79
62.20
60.82
53.93
58.50
59.23
53.49
68.59

55.27
54.89
54.90
58.61
55.84
56.19
57.21
58.37
60.34
62.50
59.65
59.97
55.79
56.00
59.37
58.85
49.66
50.58
51.08
52.06
53.53
54.55
53.32
55.24
53.34
54.55
51.65
50.61
53.37
53.58
56.56
60.15
58.79
60.98
62.65
53.27
60.37
59.61
55.69
57.19
54.26
55.42
57.63
58.95

–5.0
–23.7
–9.5
–0.9
3.3
0.0
–3.8
–8.8
9.8
13.6
30.0
–1.0
–17.3
7.0
–3.9
–2.4
6.2
14.2
55.7
–2.3
9.1
2.7
1.8
0.4
–10.6
–15.2
26.8
1.2
11.4
–7.1
–9.5
–3.6
–6.3
9.2
5.6
–2.4
29.0
–4.2
–8.4
6.1
–7.3
–6.4
7.7
–14.1

spatially complex. In general, the melt rate increases downglacier and from the glacier centre to the margins (Fig. 3a).
The spatial pattern of the melt rate was analysed bycomputing semivariance:ðhÞ ¼o2
1 XnMðxi Þ  Mðxj Þ ,NðhÞ NðhÞ

ð2Þ

where xi is the ith stake location and h is theso-calledover lagged distance. The sum is takenNðhÞ  ði, jÞ : h  50 m < jxi  xj j < h þ 50 m
( e . g .

4Sugiyama and others: Surface ablation in the terminus of Rhonegletscher

distance between the measurement sites is approximately h.
A plot of semivariance against the lagged distance is referred
to as a semivariogram, which demonstrates the similarity
between observations as a function of the distance between
the data (Fig. 3c). The semivariance is relatively large in the
distance range h < 200 m, showing relatively high local
variability in the melt rate. Its increase at h  400 m indicatesthat the correlation rapidly decreases at this distance.

AlbedoFigure 3b shows the 2-D distribution of surface albedo
measured on 5 August 2009. Individual measurements arelisted in Table 1. The albedo clearly decreases from thecentre to the margins and down-glacier towards the terminus. The highest albedo, 0.33, was observed in the upper
reaches at stake 23. The albedo drops below 0.2 in the area
below stakes 2, 5, 8 and 37. The lowest observed value was
0.06, on a debris-covered surface near the terminus at stakes
13 and 16. These albedos on Rhonegletscher are similar to
those measured near the terminus of other mountain glaciers.
Brock and others (2000) reported a value of approximately
0.1 at the terminus of Haut Glacier d’Arolla, Switzerland,
whereas Klok and others (2003) reported approximately 0.2
at Morteratschgletscher, Switzerland. Jonsell and others(2003) measured 0.06 as the lowest albedo in Storglaciären,
Sweden, at a sediment-covered site near the margin.
The semivariogram of the albedo shows features different
from that of the melt rate (Fig. 3c). The semivariance is small
at short lagged distances, indicating that the albedo values
are similar when they are compared within a small scale. It
progressively increases within the range 0 < h < 300 m,
which implies the albedo is spatially uncorrelated in theregion beyond 300 m.

Model results

Fig. 3. (a) Mean daily melt rates from 6 July to 6 September 2009 inmm w.e. d 1 . The contour intervals are 2 mm w.e. d 1 . The
locations of ablation stakes are indicated by circles. (b) Surface
albedos measured on 5 August 2009. The contour intervals are
0.02. (c) Semivariance computed for the observed melt rate () andalbedo ( ) variations. The tolerance in the lagged distance is 50 m.

Cressie, 1993). The semivariance, ðhÞ, represents themeasure of variance between the data separated by thelagged distance. For example, a low ðhÞ value indicates thata pair of observations are similar to each other when the

The model was calibrated to reproduce the observations
from 6 July to 6 September 2009. The best-fitting parametervalues were fM ¼ 1:50  104 m w.e. d1 8C1 , rs ¼ 1:32
105 m3 W1 d1 8C1 , ri ¼ 2:20  105 m3 W1 d1 8C1
and dT =dz ¼ 9:0  103 8C m1 . Figure 4 compares thecomputed melt rates at mesh gridpoints with the dataobtained at the ablation stakes (see also Table 1). The meandifference between the measured and computed melt rates
was –0.03 mm w.e. d1 , and the root-mean-square error was
6.7 mm w.e. d1 . The computed melt pattern reproduces
several important features of the observational data (Fig. 5a):the melt rate increases down-glacier and there is a low-melt
region in the northeast part. Nevertheless, the model
predicts weaker spatial variations overall, that is, the highand low melt rates are under- and overestimated, respectively. The discrepancy reaches –24% and +56% at stakes 2
and 23, respectively (Fig. 5b; Table 1). Moreover, thecalculated melt rate near the terminus increases from northto south, contrary to the observations.

DISCUSSION
Our measurements revealed a complex spatial melt patternover the terminus of Rhonegletscher. The mean melt rateduring the observation period at stake 2 was more thandouble that at stake 23. The melt rate generally increases
down-glacier, but the spatial variations cannot be explainedby surface elevation alone. Degree-day factors (DDFs) wereSugiyama and others: Surface ablation in the terminus of Rhonegletscher

5Fig. 4. Total surface melt from 6 July to 6 September 2009
computed using a melt model for all mesh gridpoints ( ) andmeasured in the field at the stakes (+). The length of the verticallines indicates the difference between the measured and computed
melt at the stake locations.

calculated for every ablation stake by linear regression of
cumulative melt on the sum of positive degree-days over theentire study period. Measured air temperature was extrapolated to the stake elevation using a lapse rate of
6:5  103 8C m1 . DDFs vary from 5.2 mm w.e. d1 8C1
to 11.2 mm w.e. d1 8C1 for stakes 23 and 2, respectively.
These values are within the range of previously reported
DDFs on ice surfaces (Braithwaite and Zhang, 2000; Hock,2003), but the extent of the spatial variation is greater thanthose obtained for other glaciers (Hock, 2003).
One of the reasons for this spatial variation is the surface
albedo. The melt rate was small at stake 23 because thealbedo was high, as shown in Figure 3a and b. The complex
melt pattern near the terminus also corresponds to thealbedo pattern. For example, the low albedo at stake T11
and high albedo at stake 53 coincide with large and small
melt rates, respectively. The albedo was lower near theglacier margins, consistent with the trend in melt rate,
because ice was contaminated by dark particles related tothe emergence of basal ice and the surface was covered withmore debris. A scatter plot of DDFs versus albedo at eachablation stake demonstrates the important influence ofalbedo on the melt rate (Fig. 6a). A linear regression of thedata yields a relationship between the DDF and albedo, ,
of: DDF¼ 8:2 þ 10:2, with a correlation coefficient of
r ¼ 0:49 and a p-value of 0.0006 (the probability ofobtaining jrj > 0:49 assuming the true correlation is zero).
Below the line connecting stakes 2, 5, 8 and 37, the albedo
dropped and the melt rate increased. In this region, thedecrease in albedo seems to be related to the presence of
crevasses. Meltwater washed away surface particles in thesmooth upper reaches, but surface water flow was impededin the heavily crevassed lower reaches (Fig. 7a). It should
also be noted that the crevassed surface traps more solar
radiation than a flat surface, which increases net energy
absorption in the region (Pfeffer and Bretherton, 1987).
The observed melt pattern cannot be explained with only
albedo variations, as implied by the different spatial

Fig. 5. (a) Melt rates (mm w.e. d1 ) computed for the period 6 July to
6 September 2009; and (b) relative deviations from the observed
values, ðMcomp =Mmeas  1Þ 100%. The locations of ablation stakes
are indicated by circles.

statistical features obtained by the semivariance analysis(Fig. 3c). Another important effect is shading by thesurrounding topography. A side-wall to the southeast of theglacier terminus shaded the eastern side of the study area forseveral hours each morning (Fig. 7b). The low-melt-rate
region around stakes 34 and 35 coincides with this area oflow potential radiation (Fig. 3a). This effect is taken into
account by the potential solar radiation term in the modeland is clearly recognizable in Figure 8. The reduced melt
rate was therefore reproduced by the computed melt pattern,although its magnitude was smaller than the observation.
Correlation of the DDF to the absorbed potential radiation(Ið1  Þ) is more significant (Fig. 6b; r ¼ 0:55 and
p ¼ 0:0001) than the correlation of the DDF to the albedo.
The very strong melt observed at stake 2 is difficult to
explain. Albedo increased towards the margins, but the melt
rate was greater near the western margin than on the otherside of the glacier. Seasonal variation in albedo is often
important in the ablation area (e.g. Brock and others, 2000),
but no significant change in surface conditions wasrecognized in this region over the study period. The surface

6

Sugiyama and others: Surface ablation in the terminus of Rhonegletscher

Fig. 6. (a) DDFs and surface albedos and (b) DDFs and absorbed
potential solar radiation, Ið1  Þ, obtained at the ablation stakes.
The lines are linear regressions of the data.

was steeply inclined towards the south in the western part of
the glacier, but the model, which includes the incident angleof solar radiation, does not produce a similar pattern. We
speculate that the increase in melt rate arises from theabsorption of longwave radiation emitted by the barebedrock on the western flank, which has been exposed by
the retreat of the glacier in this region (Fig. 7c). A similareffect has been observed at Franz Josef Glacier, New
Zealand (Ishikawa and others, 1992).
Comparing the field data to the computed results
confirms the ability of the distributed temperature-index
model to include the effects of potential solar radiation.
However, several important features in the spatial melt
distribution were insufficiently captured. It is clear from theobservation at stake 23, for example, that variations in ice
albedo are one of the most influential factors not included in
the model. Albedo can be included as an additional model
parameter (e.g. Pellicciotti and others, 2005); however, ourmeasurements show that its spatial variation is large andFig. 7. Photographs showing (a) the lower part of the study areafrom the southeast, (b) the upper part of the study area from thesouth and (c) the western margin of the glacier from the southwest.
The approximate locations of the ablation stakes are indicated. The
photographs were taken on (a) 16 July 2009, (b) 16 July 2009 at
0844 h and (c) 26 July 2008.

does not follow a predictable pattern (Fig. 3b). This implies
that albedo would have to be measured over the glacier,which is often not feasible. To compute an accurate estimateof total meltwater production in a region, simple temperature-index models should not be calibrated on singleablation-stake data; the data may be influenced by highsmall-scale variations in melt rate, as demonstrated by our
measurements.

Sugiyama and others: Surface ablation in the terminus of Rhonegletscher

7

Materials for the field campaign were loaned by the Sectionof Glaciology, Swiss Federal Institute of Technology (VAW),ETH Zürich. The manuscript was substantially improved byconstructive review comments provided by two anonymousreferees and the scientific editor, D. MacAyeal. This research
was funded by the Japanese Ministry of Education, Science,Sports and Culture, Grant-in-Aid, 20540418, 2008–10 and
the Global Center of Excellence Program, MEXT, Japan.

REFERENCES

Fig. 8. Potential solar radiation computed for 29 July 2009 (W m2 ).
The contour intervals are 5 W m2 .

CONCLUSION
We measured glacier surface melt in the terminus ofRhonegletscher at a resolution of 20–100 m. The surface
melt rate obtained at 44 stakes over the summer of 2009
showed significant spatial variability. The DDFs obtained
from the measured melt at the stakes over a 2 month period
ranged from 5.2 to 11.2 mm w.e. d1 8C1 within an area
extending 1 km from the glacier terminus. Part of thevariation can be plausibly explained by differences insurface albedo. Our measurements of albedo range from0.06 to 0.33, and the highest albedo coincided with low
melt rate. The albedo generally decreased from the glaciercentre to the margins, in agreement with the observed melt
rate variations. The influence of shading by surrounding
topography is evident from the field data. The melt rate
decreased in the northeast part of the study site, where thepotential solar radiation was smaller due to shading by
mountain ridges to the east of the glacier. However, somefeatures of the 2-D melt pattern are still difficult to explain.
The greatest melt rate was observed near the western
margin. Radiation from rock walls close to the glacier is apossible source of the heat energy.
We computed melt rates over the glacier surface using a
distributed temperature-index melt model. The model wascalibrated using the field data, and the computed spatial
melt pattern was compared to observations. The model
successfully reproduced the decrease in melt rate due to theshading. Geometrical effects can therefore be taken into
account by the model. The model results deviate from theobservations by +56% and –24% at the lowest and highest
melt rates, respectively. Care should therefore be taken
when using such models to investigate a spatial melt patternat high resolution. Model calibration should be carried out
with data sampled in a wide range of ice-surface albedo andother conditions in order to obtain accurate total melt.

ACKNOWLEDGEMENTS
We thank M. Funk, A. Bauder and members of the Rhonegletscher field campaign in 2009 for their help in the field.

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