Introduction
Mountain glaciers represent only 3 % of the ice volume on the Earth but
contribute significantly to sea level rise (e.g. Church et al., 2013; Gardner
et al., 2013; Jacob et al., 2012). In addition, millions of people partly
rely on glaciers, either for drinking water or agriculture or due to related glacier
hazards (Baraer et al., 2012; Chen and Ohmura, 1990; Immerzeel et al., 2010;
Kaser et al., 2010; Sorg et al., 2012; Soruco et al., 2015). The surface mass
balance (SMB) of glaciers is directly driven by the climate conditions;
consequently, glaciers are among the most visible proxies of climate change
(Dyurgerov and Meier, 2000; Haeberli and Beniston, 1998; Oerlemans, 2001;
Stocker et al., 2013). Measuring and reconstructing glacier SMB therefore
provides critical insights into climate change both at global and regional
scales (Oerlemans, 1994).
Systematic SMB monitoring programmes began in the late 1940s and early 1950s in
most of the European countries (e.g. France, Norway, Sweden, Switzerland).
Gradually, more glaciers have become monitored, reaching the present
worldwide figure of 440. However, this represents only a small sample of the
nearly 250 000 inventoried glaciers worldwide (Pfeffer et al., 2014). Among
the existing methods to quantify changes in glacier SMB, the well-established
glaciological method has become a standard, widely used worldwide, yielding
most of the reference datasets (World Glacier Monitoring Service, WGMS; Zemp
et al., 2015). Based on repeated in situ measurements, this method requires
intensive fieldwork. However, this method is unable to reconstruct the SMB of
unmonitored glaciers. The Global Terrestrial Network for Glaciers (GTN-G)
aims at increasing substantially the number of monitored glaciers to study
regional climate signal through changes in SMB. To reach this objective, the
development of methods complementary to the ground-based glaciological method
is therefore required. Since the 1970s, several methods have taken advantage
of satellite imaging to compute changes in glacier volume (Kääb
et al., 2005; Rabatel et al., 2017; Racoviteanu et al., 2008). Several
glacier surface properties have thus been used as proxies for volume
fluctuations – changes in surface elevation from differencing digital
elevation models (DEMs) (e.g. Belart et al., 2017; Berthier et al., 2016;
Gardelle et al., 2013; Ragettli et al., 2016; Shean et al., 2016);
end-of-summer snow line elevation from high spatial resolution optical images
(Braithwaite, 1984; Chinn et al., 2005; Meier and Post, 1962; Mernild et al.,
2013; Rabatel et al., 2005, 2008, 2016; Shea et al., 2013); mean regional
altitude of snow from low spatial resolution optical images (Chaponniere
et al., 2005; Drolon et al., 2016); or changes in the glacier surface albedo
from high temporal resolution images (Brun et al., 2015; Dumont et al., 2012;
Greuell et al., 2007; Greuell and Knap, 2000; Shea et al., 2013; Sirguey
et al., 2016). Widely used over icecaps or large ice masses, satellite
derived DEMs cannot yet be confidently used to compute annual or seasonal
SMB of mountain glaciers, although recent studies have revealed promising
results for determining SMB changes of large mountainous glacierized areas
(Belart et al., 2017; Ragettli et al., 2016). The method based on the
correlation between the regional snow cover and glacier SMB has shown
satisfying results to retrieve seasonal SMB, especially for the winter
period. This method was used for the quantification of 55 glaciers SMB in the
European Alps over the period 1998–2014 (Drolon et al., 2016). The method
based on the identification on high spatial resolution optical images of the
end-of-summer snow line altitude has shown encouraging results in the French
Alps, multiplying by 6 the available long-term annual SMB time series
(Rabatel et al., 2016), but needs to be automated to compute glacier SMB at
regional scales. In addition, monitoring glacier surface properties on the
daily or weekly basis and over large glacierized regions is still challenging
with high spatial resolution images. The current study is based on the albedo
method used in Dumont et al. (2012), Brun et al. (2015) and Sirguey
et al. (2016). Images from the MODerate resolution Imaging Spectroradiometer
(MODIS) are processed to compute daily albedo maps of 30 glaciers in the
French Alps over the period 2000–2015. Then we rely on the methodological
framework proposed by Sirguey et al. (2016) on Brewster Glacier (New
Zealand), looking at the relationships between annual and seasonal SMB and
the glacier-wide averaged surface albedo α‾. Our overall
objective is to study the relationships between glacier SMB and albedo by
(i) reconstructing the annual albedo cycle for 30 glaciers in the French Alps
for the period 2000–2015, (ii) linking the albedo signal to the summer
components of the SMB as well as to its annual values for 6 and 30 glaciers,
respectively, and (iii) assessing the sensitivity of the retrieved albedo towards
tuning parameters (cloud coverage threshold for images processing,
reliability of detected shadows). Section presents the available SMB
datasets used for the comparison and describes briefly the in situ automatic
weather stations (AWS) used to assess the quality of MODIS-retrieved albedo.
The method to retrieve albedo maps is described in Sect. . Results
are presented and discussed in Sects. and . The conclusion
gathers the main results of the study and provides perspectives for future
works.
Map of the region of interest with the studied glaciers shown in red
(numbers refer to Table 1). The four AWS used in the present study were set
up on Saint-Sorlin Glacier (no. 20). Adapted from Rabatel et al. (2016).
Study area and data
Site description
The study focuses on 30 glaciers located in the French Alps (Fig. 1). Each
glacier can be classified as a mountain glacier, extending over an altitudinal
range from around 1600 ma.s.l. (Argentière and Mer de Glace
glaciers) to 4028 ma.s.l. (Blanc Glacier), and located between the
coordinates 44∘51′′ to 46∘ N and
6∘09′′ to 7∘08′′ E. The
cumulative glacial coverage considered in the present study is
136 km2, i.e. half of the glacier surface area covered by
593 inventoried glaciers over the French Alps for the period 2006–2009
(Gardent et al., 2014).
List of studied glaciers, characteristics and albedo/mass balance
correlations over 2000–2015, except for summer coefficients (over
2000–2010). For localization, refer to Fig. 1. Bolded rows exhibit glaciers
where annual and summer in situ glacier-wide SMB data are available. The mask
size is expressed in number of pixels. To obtain the glacier mask area
in km2, one should multiply the mask size by 0.0625 km2.
Determination coefficients are expressed for each glacier. Note the units
of r2 (%), RMSE, P1 and P2 (mw.e.).
No.
Name
Mask size (pixel)
ba=P1aα‾amin+P2a
bs=P1sα‾sint+P2s
r2
RMSE
P1a
P2a
r2
RMSE
P1s
P2s
1
Tour
71
0.78
0.61
14.9
-7.8
2
Argentière
111
0.74
0.39
16.8
-8.4
0.76
0.27
12.3
-10.1
3
Talèfre
40
0.46
0.73
17.0
-8.0
0.46
0.69
15.9
-12.1
4
Mer de Glace
246
0.16
0.89
8.7
-5.8
0.69
0.31
15.3
-12.1
5
Tré La Tête
38
0.43
1.25
22.8
-10.0
6
Savinaz
7
0.23
1.27
12.3
-7.4
7
Gurraz
17
0.29
0.77
9.8
-5.8
8
Sassière
19
0.52
0.67
8.2
-4.9
9
Grande Motte
30
0.83
0.53
13.6
-6.5
10
Mulinet
18
0.33
0.62
7.7
-4.5
11
Grand Méan
11
0.44
0.64
7.8
-4.2
12
Arcelin
37
0.64
0.52
6.6
-3.7
13
Pelve
44
0.41
0.75
8.7
-5.7
14
Arpont
41
0.28
1.00
9.8
-5.8
15
Mahure
20
0.55
0.66
10.1
-5.1
16
Vallonnet
19
0.36
0.66
3.4
-2.0
17
Gebroulaz
23
0.62
0.45
9.1
-4.6
0.76
0.28
9.8
-7.9
18
Baounet
11
0.16
0.64
2.8
-2.5
19
Rochemelon
11
0.31
0.67
4.3
-2.8
20
Saint-Sorlin
31
0.86
0.37
13.8
-6.3
0.94
0.21
14.7
-11.0
21
Quirlies
15
0.6
0.54
11.4
-5.2
22
Mont De Lans
35
0.69
0.64
11.4
-5.4
23
Girose
60
0.7
0.43
9.1
-4.7
24
Selle
13
0.79
0.41
9.0
-4.4
25
Casset
7
0.73
0.47
8.9
-4.6
26
Blanc
44
0.82
0.29
7.9
-3.9
0.72
0.26
9.2
-7.3
27
Vallon Pilatte
7
0.68
0.56
16.0
-7.2
28
Rouies
14
0.72
0.68
18.0
-7.8
29
Sélé
12
0.63
0.61
10.9
-5.1
30
Pilatte
18
0.68
0.83
28.1
-13.1
Studied glaciers have been selected following four criteria related to the
availability of field data and remote sensing constraints, namely (i) the
annual glacier-wide SMB for the study period had to be available, (ii) the
glacier surface area had to be wide enough to allow robust multi-pixel
analysis, (iii) the glacier had to be predominantly free of debris to allow
remotely sensed observations of the albedo of snow and ice surfaces, and
(iv) summer SMB records had to be available to consider summer variability.
Finally, 11 glaciers have been selected in the Ecrins Range, 14 in Vanoise
and 5 in Mont Blanc (Fig. 1, and listed Table 1).
MODIS satellite images
The MODIS sensor, on board the TERRA–EOS/AM-1 satellite has been acquiring
near-daily images of the Earth since 25 February 2000. With 36 spectral bands
ranging from 0.459 to 14.385 µm, and spatial resolution ranging
from 0.25 to 1 km depending on the spectral band, MODIS is nowadays
one of the most used optical sensors for land surface observations. Because
of its short temporal revisit time, its long acquisition period and its
moderate resolution, images from MODIS are the most suitable for the present
work. We therefore rely on about 15 000 MODIS calibrated Level 1B (L1B)
swath images.
Surface mass balance data
In the French Alps, six glaciers allow both the summer and annual analyses to
be conducted, due to the availability of summer SMB data (bs)
obtained from in situ measurements with the glaciological method (unpublished
data, LGGE internal report, listed in Table 1). In addition, glacier-wide
annual SMB values of the 30 studied glaciers were computed by Rabatel et al. (2016)
using the end-of-summer snow line measured on optical remote-sensing images
and the glacier-wide mass change quantified from DEM differencing.
For the six glaciers where glacier-wide annual SMB is available from the two
methods, i.e. in situ and satellite measurements, the average of the two
estimates was used to calibrate and evaluate the albedo method, in order to
derive for each glacier a single relationship SMB vs. computed albedo. We do
not discuss here the differences between the considered datasets because
these differences have been investigated by Rabatel et al. (2016).
In situ albedo measurements
Albedo measurements acquired punctually using an AWS on Saint-Sorlin Glacier
have been used to evaluate the MODIS-retrieved albedo. In situ albedo
measurements were available for three periods in the ablation zone
(July–August 2006; June–August 2008; June–September 2009) and for one
period in the accumulation zone (June–September 2008). Albedo data from
these AWS have been calculated as the ratio of the reflected to incident
shortwave radiation (0.3–2.8 µm) using two Kipp and Zonen
pyranometers. With a potential tilt of the instrument with respect to surface
melting and the intrinsic sensor accuracy (±3 %, Six et al., 2009),
the calculated albedo at the AWS shows a ±10 % accuracy (Kipp and
Zonen, 2009; Dumont et al., 2012).
Methods
MODImLab products
MODIS L1B images were processed using the MODImLab toolbox (Sirguey, 2009).
Image fusion between MOD02QKM bands 1 and 2 at 250 m resolution and
MOD02HKM bands 3–7 at 500 m resolution allows seven spectral bands
at 250 m resolution to be produced (Sirguey et al., 2008). Then,
atmospheric and topographic corrections are applied that include multiple
reflections due to steep surrounding topography (Sirguey, 2009). Various
products are derived from the corrected ground reflectance including snow and
ice surface albedo (Dumont et al., 2012). As recommended by Dumont
et al. (2012), the white-sky albedo (estimated value of the surface albedo
under only diffuse illumination) is considered. The use of an anisotropic
reflection model for snow and ice has been preferred to the isotropic case,
due to its closer agreement with in situ measurements (Dumont et al., 2012).
The MODImLab toolbox also produces sensor geometrical characteristics at the
acquisition time such as the solar zenith angle (SZA) and the observation
zenith angle (OZA) used for post-processing the images (Sect. ).
The MODImLab cloud detection algorithm is more conservative than the original
MODIS product (MOD35), and has been preferred as recommended in Brun et al.
(2015).
According to Dumont et al. (2012) and further assessed by Sirguey et al. (2016) the overall accuracy of MODImLab albedo product under clear-sky
conditions is estimated at ±10 %.
To mitigate the impact of shadows over the glaciers, MODImLab uses a DEM from
the Shuttle Radar Topography Mission (SRTM – 90 m resolution –
acquired in 2000) to estimate the sky obstruction by the surrounding
topography and to correct the impact of shadows (see Sirguey et al., 2009).
The algorithm implemented in MODImLab is fully described by Sirguey
et al. (2009) and was inspired by Dozier et al. (1981) and Dozier and Frew
(1990) for the sky obstruction factor processing (Horizon and Vsky in Sirguey
et al., 2016), and Richter (1998) for the correction of shadows. It is first
computed at 125 m resolution, providing Boolean-type products of self
and cast shadows per pixel. Results are then averaged and aggregated to
250 m resolution, producing a sub-pixel fraction of shadow (further
detailed in Sirguey et al., 2009). Finally, MODIS data processed with
MODImLab provide, among others, near-daily maps of white-sky albedo at
250 m resolution together with cloud masks and cast and projected
shadows.
Albedo maps have been processed for 5068 images for the Ecrins range, 4973
for Mont Blanc and 5082 for Vanoise over the period 2000–2015. Only images
acquired between 09:50 and 11:10 UTC (+2 h in summer for local time
conversion) were selected to get minimum SZA and limit projected shadows of
surrounding reliefs.
Glacier masks
Following Dumont et al. (2012) and Brun et al. (2015), we manually created
raster masks of the 30 glaciers, based on the glaciers' outlines from the
1985–1987 (Rabatel et al., 2013) and high spatial resolution (6 m)
SPOT-6 images from 2014. All debris-covered areas, together with mixed pixels
(rock-snow/ice) have been removed to capture only the snow/ice albedo signal.
The resulting number of pixels per glacier is listed in Table 1.
Surface albedo and glacier-wide mass balance relationship
Basis of the method
For one glacier in the Alps (Dumont et al., 2012), two in the Himalayas (Brun
et al., 2015) and one in the Southern Alps of New Zealand (Sirguey et al.,
2016), the summer minimum glacier-wide averaged albedo
(α‾amin) has been significantly correlated
with the glacier-wide annual SMB. The relationship between
α‾amin and glacier-wide SMB results from the
fact that solar radiation is the main source of energy for melting snow and
ice, both at the surface and within the first centimetres below the surface
(Van As, 2011). But this is not sufficient to explain why averaged surface
albedo is suitable for monitoring glacier SMB.
If we consider a temperate glacier in the mid-latitudes, its surface is fully
covered by snow in winter, leading to high and uniform surface albedo
(α‾min ≈ 0.8 in Cuffey and Paterson, 2010).
During the ablation season, the accumulation area is still covered with snow
conversely to the ablation area where the ice is exposed and sometimes
covered by debris. The overall albedo of the glacier surface is therefore
decreasing over the course of the ablation season, providing information on
the ratio of these two areas. The ratio between the size of the accumulation
zone and the entire glacier, called the accumulation–area ratio (AAR) has
often been used as a predictor of SMB both qualitatively (LaChapelle, 1962;
Meier and Post, 1962; Mercer, 1961) or quantitatively (Dyurgerov et al.,
2009). Therefore, assessing α‾amin provides
insight into the relative share of the exposed ice and the snow-covered
areas at the end of the ablation season, also quantified by the AAR.
Schematic of a typical albedo cycle over one summer, displaying
parameters which have been linked to annual and summer (between 1 May and
30 September in the Northern Hemisphere) SMB.
α‾sint is retrieved using
Eq. (). The summer minimum value of albedo is represented by
α‾amin.
From annual to summer SMB
In this study, α‾amin has been computed for
the 30 glaciers in order to validate the method at a regional scale. Only the
α‾amin occurring in summer have been
considered because minimum values out of the summer period are artifacts.
Then, α‾amin has been directly correlated
with
available annual SMB data (listed in Table 1).
Following the work by Sirguey et al. (2016) on Brewster Glacier, a similar
approach has been used in order to validate the method at a summer scale but
only on six glaciers (within our sample of 30) for which the summer SMB are
available. Conversely to Sirguey et al. (2016), the summer
SMB bs has been compared to the integrated albedo signal
α‾sint during the entire ablation
season (1 May to 30 September) computed as follows and illustrated in Fig. 2:
α‾sint=∫05.0109.30α‾(t)⋅dt.
Integrated summer albedos enable us to account for snowfall events that can occur
during the ablation period (punctual high albedos). As an example, a strong
summer snowfall event leading to a rather persistent snow coverage of the
glacier will “feed” the integrated albedo, and physically reduces the
glacier melting, which has an impact on the SMB (Oerlemans and Klok, 2004).
The method therefore accounts for snowfall events to retrieve the glacier
summer SMB. To compare each year together and remove the impact of the
variable integration time period for each glacier,
α‾sint has been divided by the number
of integrated days.
Data filtering
MODIS offers the opportunity to get daily images, but retrieving daily maps
of Earth surface albedo remains challenging. Indeed, various sources of error
require filtering of the available images in order to only capture physical
changes of the observed surface and not artifacts. Clouds are known to be
a major problem in optical remote sensing of the Earth surface especially in
the case of ice- and snow-covered surfaces. Even though some algorithms exist to
differentiate clouds and snow-covered areas (e.g. Ackerman et al., 1998;
Sirguey et al., 2009), omission errors are difficult to avoid, leading to
erroneous albedo of the surface.
In this study, all images with a presence of cloud greater than 30 % of
the total glacier surface area have been discarded. This threshold is higher
than that chosen in Brun et al. (2015) on the Chhota Shigri Glacier
(20 %), and we thus discuss in Sect. the impact of the
computed cloud threshold on the derived albedo results. When determining
α‾amin, 0 % of cloud cover has been
imposed as a condition, and a visual check for each year and each glacier has
been performed. Snapshots from the fusion of MODIS bands 1–3 and from
bands 4–6 (Sirguey et al., 2009) have been used to visually check the
images, together with images from other satellites (mostly from the Landsat
archive) and pictures and comments from mountaineering forums. This last
step, although laborious when studying 30 glaciers, allowed the
identification of the summer minimum to be improved. A visual check of these
images also confirms that projected shadows of clouds are not affecting the
albedo maps of summer minimum. Another source of error is the impact of the
OZA. As mentioned in Sirguey et al. (2016), accuracy of the MODIS retrieved
albedo strongly decreases for viewing angles above 45∘ as pixel size
increases from 2- to 5-fold from OZA = 45∘ to 66∘ (Wolfe
et al., 1998). This phenomenon is accentuated when observing steep-sided
snow/ice surfaces, surrounded by contrasted surfaces (rocks, forests, lakes).
This distortion could lead to capturing the mean albedo of a glacier plus its
surroundings. As a result of this, we decided to filter the images according
to their OZA angle, as further described Sect. .
Results
Retrieved albedo assessment
A quantitative evaluation of the retrieved albedo has been performed with AWS
deployed on Saint-Sorlin Glacier. Measurements have been synchronized between
punctual albedo for MODIS and a 2 h averaged albedo around MODIS acquisition
time for the AWS. It is worth recalling some differences between the in situ
measured albedo data and the one retrieved using MODIS. The downward-facing
pyranometer stands at around 1 m above the surface, corresponding to
a monitored footprint of ca. 300 m2 (theoretical value for a flat
terrain) while the pixel area of MODImLab products matches
62 500 m2. Quantified albedos from each method are therefore not
representative of the same area. On the other hand, incoming radiation data
are extremely sensitive to a tilt of the sensor located on the AWS, and
maintaining a constant angle throughout the monitoring period remains
challenging, especially during the ablation season. For instance, a tilt of
5∘ of the pyranometer at the summer solstice can increase by 5 %
the error on the irradiance measurement (Bogren et al., 2016). No sensor tilt
was deployed on the AWS, thus preventing the application of tilt correction
methods (e.g. Wang et al., 2016). Nonetheless, regular visits allowed us to
maintain the sensor horizontal and to limit errors in the irradiance
measurements.
MODIS albedo and AWS albedo data for different OZA classes on
Saint-Sorlin Glacier. Years indicated in the caption correspond to the year
of acquisition while subscripts express the AWS location in the accumulation
or ablation areas. The mean discrepancy between MODIS and AWS albedo per OZA
is quantified by the RSS (residual sum of square). Correlation coefficient
per OZA classes are also provided, with r2, RMSE together with the
number of compared measurements (Nb), and coefficients of the equation:
MODISalbedo = P1MODISAWSalbedo + P2MODIS.
The continuous grey line illustrates the 1:1 relationship between AWS and
MODIS retrieved albedo. Thin and dotted lines represent the combined
uncertainties on both AWS- and MODIS-retrieved albedo (absolute value of
10 % for each), only accounting for intrinsic sensor accuracy and not for
errors related to the acquisition context, e.g. size of the footprint.
Figure 3 illustrates the comparison between the retrieved and measured
albedos at the AWS locations for various OZA classes. One can note minor
differences between the data plotted in Fig. 3 and those presented in Dumont
et al. (2012, Fig. 2). These differences are related to changes in the
MODImLab algorithm and different computation of the in situ albedo,
integrated over a 2 h period in the current study.
In Fig. 3, the spread between MODIS and AWS albedos is higher for low albedos
(i.e. ablation area). This is related to the footprint difference as
described earlier, accentuating the albedo differences when monitoring
heterogeneous surfaces (snow patches, melt pounds…), which are even more
pronounced in summer. One can also note that MODIS albedo often overestimates
the AWS albedo value. This overestimation could be explained by (1) the
MODImLab albedo retrieval algorithm. (Under-estimation of the incoming
radiation computed in the MODImLab algorithm would lead to overestimated
retrieved albedo values, and in addition the atmospheric corrections used to
compute the incident radiation could be hypothesized as source of error – e.g.
modelled transmittance through a simplified computed atmosphere; see
Sirguey et al. (2009) for further description), or (2) the AWS albedo
measurements. Indeed, view angles of AWS pyranometers (170∘) could
influence the retrieved albedo by monitoring out-of-glacier features (e.g.
moraines, rock walls,), resulting in underestimated albedo values. However,
it is worth noting that most of the points are within the combined
uncertainty of both sensors and these differences in albedo retrieved from
MODIS and the AWS are thus hard to interpret.
Filtering the images from OZA values.
Class
OZA (∘)
Criteria
I
OZA ≤ 10
All retained
II
10 < OZA ≤ 20
Retained if more than 7 days between consecutive images from class I
III
20 < OZA ≤ 30
Retained if more than 7 days between consecutive images from class I + II
IV
OZA > 30
Not retained
The ∼ 16-year albedo course for Saint-Sorlin Glacier.
Glacier-wide averaged albedo is represented with the continuous black line.
The green dots spot for each summer the minimum average albedo, and have been
manually checked for all years and glaciers. Dashed red and blue lines stand
for the beginning of the defined ablation and accumulation seasons (May and
1 October respectively).
Finally, Fig. 3 shows substantial differences between OZA < 10∘
and other OZA classes. For OZA < 10∘, MODIS albedos better agree
with AWS albedos than for the three other classes. Integrating MODIS images
with OZA > 10∘ substantially deteriorates the agreement with AWS
albedos (in term of r2, RMSE and the slope P1MODIS),
especially on “narrow” targets as alpine mountain glaciers. We therefore
chose to prioritize images acquired with low OZA to avoid detection of
non-glacierized surfaces. Therefore, four classes of images have been
selected following the criteria presented in Table 2.
For the rest of the computation, the absolute ±10 % accuracy per
pixel estimated in Dumont et al. (2012) has been considered. We determined
the uncertainty on α‾ by accounting for the spatial
variability of the albedo signal within the glacier and considering that our
sets of pixels are independent from each other (Eq. ):
σα‾=σN,
where σ stands for the standard deviation (SD) of the pixels albedo with N the number of pixels.
Temporal variability of the albedo signal
Using the “step-by-step” filtering procedure explained in Sect. ,
the ∼ 16-year albedo cycle of each of the 30 glaciers was obtained.
Figure 4 illustrates the entire albedo time series for Saint-Sorlin Glacier
over the period 2000–2015. We observed that the albedo decreases from the
beginning of summer (dashed red line), reaching
α‾amin in August/September and rising again
at the end of September. This cyclicality is a proxy of surface processes.
The snow cover decreases at the beginning of summer until reaching its lowest
extent, and finally increases again with the first snowfall in late summer to
reach its maximum extent in winter/spring.
Albedo cycle for Argentière Glacier as a function of the SZA.
Each point corresponds to glacier-wide averaged albedo for each available
image. The 16 years are displayed. Colour scale gives indication on the date
of the used image. The thick grey line describes the weekly albedo averaged
over the entire study period. For readability purpose, the averaged albedo
has been smoothed, using a seven-point running average.
The periodicity of the albedo signal is however not so well defined for some
of the studied glaciers. For instance, Argentière Glacier exhibits
a severe drop of α‾ in winter, reaching values as low as
summer minima (α‾ ∼ 0.4). The observed drop of albedo
in winter occurs during more than 1 month centred on the winter solstice
(21 December) and is observed for nine glaciers (Argentière, Baounet,
Casset, Blanc, Girose, Pilatte, Vallon Pilatte, Tour and Sélé
glaciers). These glaciers are located within the three studied mountain
ranges and have the common characteristic of being very incised, with steep
and high surrounding faces. We studied the albedo series as a function of the
SZA to reveal possible shadowing on the observed surfaces. Figure 5 displays
the same cycle as Fig. 4 for Argentière Glacier but providing information
about SZA. As a reminder, the MODImLab white-sky albedo is independent of the
illumination geometry but the computed albedo for each pixel can be subject
to shadowing from the surrounding topography.
Two main observations stand out from the winter part of the cycle in Fig. 5:
(i) most of MODIS α‾ severely decrease under
α‾ = 0.6 for SZA greater than 60∘ corresponding
to November to January images, and (ii) these drops are not systematic and we
rather observe a dispersion cone than a well-defined bias. As there are no
physical meanings to systematic change of the surface albedo during a part of
the winter period and owing to the fact that this dispersion is only observed
for topographically incised glaciers, these decreases in albedo have been
considered as artifacts. These observations led us to perform a sensitivity
study on the validity of the shadow mask produced by MODImLab, and to study
the impact of these shadows on the retrieved glacier-wide albedo (see
Sect. ).
Annual SMB as a function of the MODIS-retrieved summer minimum
glacier-wide average albedo for Blanc Glacier. Error bars show the
dispersion of the available annual SMB data and the quadratic sum of the
systematic errors made on each albedo measurement. The thin dashed grey line
illustrates the line of best fit, along with regression coefficients and
significance.
Albedo and glacier-wide SMB
α‾amin and annual SMB
The summer minimum average albedo for each year and each glacier has been
linearly correlated with the glacier-wide annual SMB. Figure 6 illustrates
the relationship between α‾amin and
ba for Blanc Glacier. Error bars show the dispersion of the SMB
dataset for each year, and from the glacier intrinsic variability of the
albedo signal on the day of α‾amin
acquisition. For the glaciers where the glacier-wide annual SMB is available
from the SLA method, the uncertainty is about ±0.22 mw.e. on
average (ranging from 0.19 to 0.40 mw.e. depending on the glacier;
Rabatel et al., 2016).
Twenty-seven glaciers show significant correlations (see Table 1 for
full results) if considering a risk of error of 5 % (according to
a Student's t test), which confirms the robust correlation between
α‾amin and ba. However, the
linear correlation has no statistical significance for three glaciers with
r2 < 0.25. A possible explanation is the high number of removed
images in summer due to manually checked thin overlying clouds not detected
by the MODImLab cloud algorithm.
Looking at the 27 glaciers for which significant relationships have been
found, 2001 is regularly identified as an outlier. According to existing SMB
datasets, 2001 is the only year of the period 2000–2015 for which the annual
SMB has been positive for all the studied glaciers
(+0.80 mw.e.yr-1 on average).
Summer SMB bs expressed as a function of the
integrated albedo over the entire ablation season for Saint-Sorlin Glacier.
Error bars result from the uncertainties related to the glaciological method
(measurements and interpolation at the glacier scale of the punctual
measurements, ±0.20 mw.e. in total), and on the quadratic sum
of the systematic errors made on each albedo measurement. The thin dashed grey
line represents the linear regression showing the best correlation between
the two variables, together with correlation coefficients.
To predict correctly the SMB values for the year 2001 using
the albedo method, monitored minimum glacier-wide average albedo would need
to be extremely high (often greater than 0.7, i.e. 0.83 and 0.95 for
Rochemelon and Vallonnet glaciers, respectively), to match the regression
line derived from other years of the time series (Table 1). Taking into
consideration snow metamorphism during the summer period, melting at the
surface and possible deposition of debris or dusts, monitoring such high
albedo values averaged at the glacier scale is unrealistic. As removing 2001
from the time series does not increase the number of glaciers for which the
correlation is significant, 2001 has been conserved in the time series.
However, this observation reveals a limitation of the albedo method by
underestimating the annual SMB value for years with very positive annual
SMB.
α‾sint and summer
SMB
Studying the integral of the albedo signal during the ablation season can
provide insight into the intensity of the ablation season and thus into the
summer SMB bs. As described in Sect. ,
α‾sint has been computed and connected
to the in situ bs. Figure 7 illustrates the results for
Saint-Sorlin Glacier.
Saint-Sorlin Glacier, together with the five other seasonally surveyed
glaciers, showed a significant correlation between the two observed variables
(from r2 = 0.46 to r2 = 0.94 with an error
risk < 5 %, all statistics detailed in Table 1). Conversely to
α‾amin, the α‾sint is slightly more robust to the presence of
undetected clouds as its value does not rely on a single image. The lowest
correlation has been found for Talèfre Glacier. The latter accounts for
a relatively large debris-covered tongue that has been excluded when
delineating the glacier mask (see Supplement). Consequently, the low
correlation could be partly explained by this missing area, considered in the
glaciological method but not remotely sensed. To conclude,
α‾sint has been significantly
correlated with bs and is therefore a reliable proxy to record
the ablation season.
Discussion
In this section, we first discuss the impact of the threshold applied to the
cloud cover fraction on the obtained results. Then, a sensitivity study
focused on the algorithm correcting the shadows is presented. We finally
express the main limitations and assessments of the albedo method.
The r2 for the six seasonally surveyed glaciers for the albedo
summer integral vs. summer SMB relationship against the cloud threshold above
which images have been discarded during the summer season. For the
computation, 100 thresholds have been tested between 0 and 100 %. The
inner histogram illustrates the number of considered images per summer and
averaged on the six glaciers.
Cloud coverage threshold
As stated in Sect. , a value of 30 % of cloud coverage over the
glacier mask has been defined as the acceptable maximum value for considering
the albedo map of the day. We computed a sensitivity study on the impact of
this threshold on the value of the obtained correlations between the
integrated summer albedo and the in situ summer SMB. The summer period has
been chosen as it represents the period when the albedo of the glacier is the
most contrasted, between bare ice and snow/firn. The glacier-wide average
albedo in this period is therefore more sensitive to possible shading of
a part of the glacier. Figure 8 illustrates the results for the six
seasonally surveyed glaciers. The used value of the allowed cloud coverage
appears not to have a substantial impact on the correlation. This observation
implies that the MODImLab cloud product is reliable enough to only
compute surface albedo and to avoid too frequent misclassification between
the clouds and the surface. It also suggests that removing too many images
because of partial cloud cover removes information about the glacier-wide
average albedo variability. However, allowing all images, even when the
glacier-wide average albedo is computed on only 10 % of the glacier
(90 % of detected cloud coverage), does not reduce significantly the
correlation for most of the six glaciers.
Nevertheless, hypothesizing that the glacier-wide average albedo of a small
fraction of the glacier (e.g. 10 %) is suitable to represent the entire
glacierized surface is questionable. It therefore depends on the size of the
observed glacier, where 10 % of a glacier of 3 and 30 km2 do
not have the same meaning, but also on the delineated mask (ablation area not
entirely considered because of debris coverage). The summer-integrated albedo
is also highly dependent on the time gap between valid seful images. In other
words, if an image has an “anomalous” glacier-wide average albedo because
of high cloud coverage, the impact on the integrated value will be smaller if
“normal condition” albedos are monitored at nearby dates.
The average number of available images per year does not largely differ
between the various computed cloud coverage thresholds. It varies on average
from 95 to 123 images per summer period for respectively 0 and 100 %
cloud coverage threshold. Intermediate values are 106, 111 and 116 images per
summer for 30, 50 and 75 % cloud coverage threshold, respectively. The
difference in significance of r2 (according to a Student's t test)
between opting for 0 and 100 % is almost negligible, and choosing the
best cloud threshold value is rather a compromise between the number of used
images and the resulting correlation with glacier-wide SMB. We finally
concluded that selecting a cloud coverage threshold of 30 % presents the
best determination coefficients between the integrated summer albedo and the
summer balance for most of the six glaciers without losing too much temporal
resolution.
Impact of the ratio of corrected pixels toward the difference
between non-corrected and glacier-wide albedo for Argentière Glacier.
Each point corresponds to one acquisition and the 16 years are therefore
displayed on this graph. Colour scale gives some indication of the date of the
acquired image. Grey shaded areas correspond to ratios of corrected pixels
for which α‾non-cor - α‾ has
low statistical robustness (refer to the main text). Thin grey lines
represent 1σ SD of α‾, averaged by classes of
5 % corrected pixels. The inner graph illustrates the amount of corrected
pixel, as function of the selected month.
Assessment of the impact of shadows on retrieved albedos
In light of the documented dispersion on α‾ during some of
the winter months on several studied glaciers (Sect. ), sensitivity
of the MODIS retrieved albedo against correction of shadows had been
assessed. This work has only been conducted on the 250 m resolution
raster products and specifically on the cast shadow product, because
self-shadow corrections can be considered as reliable enough as they are only
related to the DEM accuracy. We thus defined a pixel as “corrected” when at
least one of its sub-pixels was classified as shadowed. From then on, two
glacier-wide albedos α‾ have been defined:
(i) α‾non-cor computed on non-corrected pixels
only, classified as non-shadowed, and (ii) α‾ of both corrected
and non-corrected pixels, equal to the glacier-wide average albedo. Figure 9
illustrates the difference between α‾non-cor
and α‾ as a function of the percentage of corrected pixels
over the entire glacier. The study was performed on Argentière Glacier
(111 pixels) that exhibited large α‾ artifacts in winter
(Fig. 5). The inner diagram allows us to emphasize the annual “cycle” of
modelled shadows, contrasted between nearly no cast shadows in summer and an
almost fully shadowed surface in winter. We represent the 1 SD
of α‾, averaged by classes of 5 % corrected pixels. In
other words, it illustrates the mean variability of the glacier-wide surface
albedo. Therefore, for images with
α‾non-cor - α‾ within the
interval defined by 1 SD of α‾, errors resulting from the
correction algorithm are smaller than the spatial variability of the
glacier-wide albedo glacier. We also selected only significant values,
following a normal distribution of the averaged α‾.
Consequently, only values at ±1σ (68.2 %) in terms of
percentage of corrected pixels have been retained (i.e. when the relative
share of corrected pixels ranged from 15.9 to 84.1 %). Between 0 and
15.9 %, α‾non-cor and α‾ are
not sufficiently independent because of the low number of corrected pixels, and
beyond 84.1 %, α‾non-cor is computed over
a too small number of pixels. As a consequence, even if the albedo correction
in the shadowed parts of the glacier could be improved, most of the errors
related to this correction do not depreciate the results. Above 80 % of
corrected pixels (December to early February), differences between
α‾non-cor and α‾ exceed the
monitored spatial variability of α‾. These anomalies are at
the root of the observed artifacts in Fig. 5 caused by the severe drops of albedos and
described Sect. .
In addition, a seasonality in the albedo signal can be observed – with
α‾non-cor - α‾ > 0 in
early spring (February to April) and
α‾non-cor - α‾ < 0 in
summer and autumn (June to November). This could be explained by different
localizations of shadowed area for a given ratio of corrected pixel. As an
example, a glacier could have in October a snow- and shadow-free snout and
a fresh snow-covered and shadowed upper section. This configuration would
induce a negative difference, as we observe from June to November. Conversely,
this glacier could present in March (same ratio of corrected pixels as
October) a complete snow coverage, leading to a smaller difference between
α‾non-cor and α‾ (< 0.1), that
could even result in a positive difference, as we observe from February to
April.
Finally, observed albedo artifacts in winter are most likely due to the
correction of shadows. On the other hand, correcting shadows accurately and
consistently is extremely challenging. As illustrated by Fig. 9, a way to
confidently consider the albedo signal is to exclude values with too large a
share of corrected pixels. However, because of the inter-annual approach
carried out in this study, such a systematic artifact is not depreciating the
results but would be a major issue in studies focused on albedo values
themselves (e.g. maps of snow extent).
Limits of the albedo method
In agreement with Dumont et al. (2012) and Brun et al. (2015), retrieving the
glacier annual SMB from albedo summer minima proves to be an efficient
method. Low correlations often result from high and persistent cloud coverage
during summer, reducing the chance of spotting the albedo summer minimum. For
SMB reconstruction purpose, a future line of research could rest upon linking
morpho-topographic features of the glacier, such as glacier surface area, mean
altitude or slope, to the regression coefficients of both annual and seasonal
SMB vs. albedo relationships, giving the opportunity to establish analogy
between monitored and unmonitored glaciers. Tests have been carried out, but
no significant and satisfying results have been obtained, due to a presumably
too heterogeneous dataset, where large glaciers (> 10 km2)
and/or south-facing glaciers are largely under-represented. Larger-scale
studies and multi-variable correlations in between morpho-topographic
features could be for instance envisaged. Rabatel et al. (2017) recently
proposed an alternative approach to reconstruct the annual mass balance of
unmonitored glacier on the basis of the albedo method. This approach relies
on the ELA method (Rabatel et al., 2005), but using the remotely sensed
monitored α‾amin together with the
AAR, the glacier hypsometry, and the regional
SMB elevation gradient (which is the annual SMB gradient in the vicinity of
the glacier ELA). For an exhaustive description of this approach, see
Rabatel et al. (2017).
Using the albedo method for the summer period has shown promising results,
with significant correlations found for the six seasonally monitored
glaciers. There is still in this approach a step to retrieve the summer SMB
of an unmonitored glacier with high confidence.
The winter period has also been considered in the framework of this study,
but has not been presented in the main body of this publication because of
underwhelming results. The albedo signal between 1 October and 30 April has
been computed similarly to Sirguey et al. (2016) by integrating the winter
albedo signal, only when exceeding a certain threshold αT,
as described by
α‾wint=∫α‾(t)ifα‾(t)is found between 10.01 and 04.30Only
ifα‾(t)≥α‾T.
According to Sirguey et al. (2016), the use of
α‾T allows for detection of all snowfall events on the
glacier by monitoring abrupt rises of α‾. One of the main
conclusions of the above study was the ability of the computed
α‾wint to monitor the frequency of
snowfall events, themselves proxy of the accumulation of snow on the glacier,
known to be one of the main components of the winter SMB.
Coefficients of determination for the relationship between the
winter SMB bw and the integrated winter albedo, computed with
and without the albedo threshold α‾T.
Glacier
α‾T
r2 using α‾T
r2 without α‾T
Saint-Sorlin
0.76
0.75
0.21
Argentière
0.58
0.88
0.76
Talèfre
0.68
0.59
0.25
Mer de Glace
0.53
0.9
0.87
Gebroulaz
0.75
0.36
0.25
Blanc
0.7
0.33
0.21
α‾T has been chosen to maximize the correlation
between the retrieved cumulative winter albedo
α‾wint and the winter SMB. Threshold
values have been computed independently for each of the six seasonally
monitored glaciers. To evaluate the impact of this threshold,
α‾wint has also been computed without
threshold over winter months (equivalent to
α‾T = 0). Table 3 gathers all the
coefficients obtained from the relationship
α‾wint vs. bw, with and
without the use of an albedo threshold α‾T.
For Argentière and Mer de Glace glaciers, a significant correlation is
found whatever the value of the albedo
threshold α‾T. For the four other glaciers,
using α‾T largely improves the correlation.
However, α‾T is far from being uniform on the
six glaciers (0.53 ≥ α‾T ≥ 0.76). In
addition, for most of the considered glaciers, correlation coefficients
abruptly deteriorate when changing this threshold, which does not allow us to use
a “regional” threshold for all considered glaciers. On the other hand,
Argentière and Mer de Glace without the use
of α‾T provide the best correlation coefficients
compared to the other four glaciers; it is noteworthy that they are by far
the largest glaciers of our monitoring set (14.59 and 23.45 km2
for Argentière and Mer de Glace glaciers, respectively). With a glacier
snout reaching 1600 ma.s.l., the tongue of these glaciers can
experience melting events (resulting in contrasted pixels in terms of albedo
value), even during the winter season. Another difference between our study
and Sirguey et al. (2016) is that their work focused only on Brewster
Glacier, defined as a maritime glacier. These types of glaciers, even during
the accumulation period, can experience strongly varying albedos in their lower
reaches, which leads to similar behaviours in winter as for Argentière and
Mer de Glace glaciers. We therefore reconsider the idea of Sirguey
et al. (2016) to use a threshold as a representative value of fresh snowfall,
as there is no physical reason that this threshold varies, at least within
the same region. However, an interesting perspective would be to apply the
method without threshold, on a set of other maritime or large glaciers
(> 10 km2).
An additional approach has been carried out, aiming at
retrieving bw by deduction from the
reconstructed ba and bs from the albedo signal.
This approach, not using the winter albedo signal, is poorly correlated
(r2 < 0.16) with in situ bw for the six seasonally
monitored glaciers. Indeed, the result extremely depends on the quality of
the correlations between ba, bs and the albedo
signals. Saint-Sorlin Glacier is a good example, being one of the glaciers
with the highest correlations for the annual (r2 = 0.86) and summer
(r2 = 0.94) SMB. Subtracting bs from ba
to computed bw leads to an average difference between computed
and measured bw of ±0.41 mw.e. for the 10
simulated years. As a consequence, in the case of low correlations between SMB
and albedo, errors in the computed winter SMB become exacerbated.
Conclusion
In this study, we used the so-called albedo method to correlate annual and
summer SMB to glacier-wide average albedos obtained from MODIS images. This
method has been applied to 30 glaciers located in the French Alps, over the
period 2000–2015. Image processing has been performed using the MODImLab
algorithm, and filters on the images have been applied, removing images with
more than 30 % cloud coverage, and excluding images with satellite
observation angles greater than 30∘. Quality assessment has been
performed and close agreement has been found between albedos from AWS
installed on Saint-Sorlin Glacier and MODIS retrieved albedo values. Annual
SMB has been significantly correlated with the summer minimum albedo for 27 of
the 30 selected glaciers, confirming this variable as a good proxy of the
glacier-wide annual SMB. For the six seasonally monitored glaciers, summer
SMBs obtained from the glaciological method have been significantly linked to
the integral of the summer albedo. However, calculating the integral of the
winter albedo to quantify the winter SMB as done by Sirguey et al. (2016) has
shown underwhelming results. Monitoring winter glacier surface albedo may
provide good insight into the frequency of snow accumulation at the surface of
the glacier but is poor at quantifying the amount of accumulation. Glaciers
that experience complete snow coverage during most of the winter season
showed the lowest correlation (r2 ≤ 0.33) while the two glaciers
showing the best correlations are subject to some events of surface melting
in their lower reaches. This approach should not be definitively
forsaken, but it requires improvements in order to confidently retrieve winter SMB.
Sensitivity study on the impact of the considered cloud coverage has revealed
a high confidence in the MODImLab cloud algorithm, limiting pixel
misclassifications, and a rather high tolerance of the integrated signal to
the number of partly cloud-covered images. This confidence on cloud filters
is very promising to document unmonitored glaciers. Correction of shadows by
the MODImLab algorithm has however revealed some limitations when a large
share of the glacier is shadowed by the surrounding topography (around winter
solstice). Despite this, severe and artificial drops of albedo in winter have
not been identified as an obstacle for monitoring both summer and winter SMB.
Such systematic errors are not an issue for inter-annual studies, but would
be a serious issue on studies focused on albedo values themselves. For future
works, the MODIS archive together with albedo maps, cloud and shadow masks
processed with MODImLab, together with validation data from AWS, offer
a unique dataset to monitor the temporal and spatial evolution of the surface
albedo of glaciers at a regional scale. For instance, computing the absorbed
solar radiation (Bair et al., 2016) by date and for each glacier would
be an appropriate protocol to estimate the impact of a changing glacier
surface albedo in terms of snow or ice melt. Quantifying albedo changes and
resulting mass losses with such an approach would be of major interest to
better understand the potential effects of possibly increasing dust content,
glacier orientation or snow grain growth on glacier surface melt processes.
To conclude, the use of optical satellite images to estimate glacier surface
processes and quantify annual and summer SMB from the albedo cycle is very
promising and should be expanded to further regions. Using images from
different satellites, combining high spatial and temporal resolution
instruments, could substantially reduce uncertainties, especially for
spotting the albedo summer minimum with more confidence, but also to improve
the temporal resolution. This method could then in the short term become
reliable for retrieving SMB values of monitored and unmonitored glaciers.