1. Introduction

It is now widely agreed that glaciers constitute a very good indicator of climate variations (Reference OerlemansOerlemans and others, 1998; Reference HoughtonHoughton and others, 2001; Reference VincentVincent, 2002). Mass balance is directly dependent on climatic variables governing accumulation and ablation processes (Reference MartinMartin, 1974; Reference Vincent and VallonVincent and Vallon, 1997; Reference Braithwaite and ZhangBraithwaite and Zhang, 1999; Reference Oerlemans and ReichertOerlemans and Reichert, 2000; Reference KaserKaser, 2001). Thus, measurements of glacier mass balance and an understanding of its relationship with climatic variables can help improve knowledge of recent and past climate fluctuations (Reference Oerlemans and HoogendoornOerlemans and Hoogendoorn, 1989; Reference Vallon, Vincent and ReynaudVallon and others, 1998; Reference Vincent, Kappenberger, Valla, Bauder, Funk and Le MeurVincent and others, 2004). However, direct mass-balance measurements on the ground remain sparse due to the major logistical support required, and time series exceeding several decades are rare. In this context, many researchers have attempted to use information provided by remote sensing, based on the extensive image archives available for the past 30 years, to create databases and glaciological inventories (GLIMS (Global Land Ice Measurements from Space) program: Reference Raup, Kieffer, Hare and KargelRaup and others, 2000). Since the 1970s, attempts have been made to apply remote sensing to glaciological surveys (Reference MeierMeier, 1979). Reference ØstremØstrem (1975) and Reference BraithwaiteBraithwaite (1984) presented the first snowline altitude measurements using remotely sensed data and compared them to glacier mass balances without attempting their reconstruction. Since the 1990s, many studies have tested and discussed the different possibilities offered by optical or radar remote sensing (measurement of glacier surface areas, displacements and volume variations) (Reference Dedieu and ReynaudDedieu and Reynaud, 1990; Reference MassomMassom, 1995; Reference Adam, Pietroniro and BrugmanAdam and others, 1997; Reference BindschadlerBindschadler, 1998; Reference HubbardHubbard and others, 2000; Reference König, Winther and IsakssonKönig and others, 2001; Reference Kääb, Paul, Maisch, Hoelzle and HaeberliKääb and others, 2002; Reference Rabatel, Dedieu and ReynaudRabatel and others, 2002; Reference De Ruyter de Wildt and OerlemansDe Ruyter de Wildt and Oerlemans, 2003; Reference Berthier, Arnaud, Baratoux, Vincent and RémyBerthier and others, 2004; Reference Paul, Huggel and KääbPaul and others, 2004).

The equilibrium line divides the accumulation zone (where the mass balance is positive) from the ablation zone (where the mass balance is negative). Its fluctuation in terms of altitude results in a change in the proportion of each of these areas with respect to the whole glacier and therefore a variation of the glacier mass balance. Thus the equilibriumline altitude (ELA) is well correlated with and provides a very good indicator of the glacier mass balance (Reference BraithwaiteBraithwaite, 1984; Reference Kuhn and OerlemansKuhn, 1989; Reference PatersonPaterson, 1994; Reference Leonard and FountainLeonard and Fountain, 2003).

In the present paper, we use the late-summer position of the snowline, which is easy to discern in satellite imagery, to infer the location of the equilibrium line, from which we estimate glacier mass balance. At this period, i.e. the end of the ablation season (and therefore of the hydrological year), the snowline can be associated with the equilibrium line on mid-latitude glaciers (Reference LliboutryLliboutry, 1965). The method was applied to three glaciers in the French Alps where field measurements can be used to check results.

2. Data

Three glaciers included in a French glacier monitoring program (Laboratoire de Glaciologie et Géophysique de l’Environnement (LGGE)–Observatoire des Sciences de l’Univers de Grenoble (OSUG)) were selected for this study: Glacier ďArgentière in the Mont Blanc range, Glacier de Gébroulaz in the Vanoise range and Glacier de Saint-Sorlin in the Grandes Rousses range of the French Alps (Fig. 1; Table 1). On these glaciers, annual mass balance was measured using a stake network covering the whole ablation zone since 1957, 1975 and 1993 for Saint-Sorlin, Argentière and Gébroulaz glaciers respectively. Since 1994, systematic winter (May) and summer (September) mass- balance measurements have been carried out on these glaciers. In the accumulation zone, cores are drilled to measure winter mass balance from snow layering and density measurements. Stakes inserted in the boreholes allow measurement of the remaining winter snow at the end of summer, and determination of summer mass balance. In the ablation zone, winter mass balance is measured by drilling and measuring the snow thickness above the ice. At the end of summer, annual mass balance is determined from stakes inserted in ice the previous summer. The summer mass balance is the difference between these two balance terms. Thus specific glacier-wide mass-balance variations are obtained from these field measurements. Moreover, photogrammetric measurements have been performed using aerial photographs from 1949, 1970, 1980, 1994 and 1998 (Glacier d’Argentière), from 1953, 1967, 1986 and 1998 (Glacier de Gébroulaz) and from 1952, 1971, 1984, 1986, 1989 and 1998 (Glacier de Saint-Sorlin) to obtain the total cumulative mass balance of these glaciers. These data have been used to constrain mass-balance data obtained from the field measurements. The results have been analyzed and reported in previous studies (Reference Vincent, Vallon, Reynaud and MeurVincent and others, 2000; Reference VincentVincent 2002).

Fig. 1. Location map. Triangles represent the three French glaciers considered in this study.

Table 1. Topographical characteristics of the three French glaciers

For each hydrological year over the 1994–2002 period, several stakes were selected on both sides of the equilibrium line, along a central axis on each glacier. The linear regression of mass balance with stake altitude was used to calculate the ELA for each year and determine the yearly glacier mass-balance gradient ∂b/∂z across the equilibrium line. An example for Glacier d’Argentière is presented in Figure 2.

Fig. 2. Observed mass balance vs altitude close to the equilibriumline zone: example for Glacier d’Argentière, 1999–2002 (all observations were selected along the same longitudinal transect).

The satellite data used in this study come from several optical sensors: the Landsat Thematic Mapper, Système Probatoire pour l’Observation de la Terre (SPOT) 1–4 and the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER). Images were chosen depending on the quality of the archives available: recording date, absence of cloud cover, absence of recent snow cover, and pixel size. The image recording date must correspond to the end of the ablation season, i.e. late September to early October (Table 2). Figure 3 shows an example of image data used in the equilibrium-line assessment.

Table 2. Remote-sensing data description

Fig. 3. Glacier ďДrgentière (45º55′ N, 6º57′ E). SPOT image from 26 August 2000, P/R 051–257, pixel size 10m.

3. Method

Field measurements on each of the three glaciers show a good correlation between the ELA and the glacier-wide mass balance (Fig. 4). This has been shown in several studies (e.g. Reference BraithwaiteBraithwaite, 1984; Reference Kuhn and OerlemansKuhn, 1989). We propose to use the snowline obtained from the images to infer the ELA from which we reconstruct glacier mass-balance variations.

Fig. 4. ELA observed from field measurements vs glacier-wide mass balance (1994–2002). The uncertainty bars represent the confidence interval on the observed ELA obtained from the linear regression of the mass balance with stake altitude.

First, all images were geometrically and radiometrically corrected using a digital elevation model (DEM) grid of 10m. To facilitate locating the snowline, shadows were reduced by enhancing the brightness of shaded areas in comparison with lighted areas, and the contrast between snow and ice was amplified. After image correction, the snowline was located and its average altitude computed using the DEM. Considering that the snowline is representative of the glacier equilibrium line when measured at the end of the hydrological year (Reference LliboutryLliboutry, 1965; Reference BraithwaiteBraithwaite, 1984), we henceforth use the term ELA.

The annual average ELA was calculated on the central part of the glaciers to avoid border effects on the glacier banks (shadows from surrounding slopes, additional snow input by avalanches, over-accumulation due to wind) which could generate equilibrium-line position dependence on local conditions. With the ELA for each year determined by remote sensing, the mass-balance series can be reconstructed in two steps. First, we calculate for each year, i, the variation between ELA_j and an ELA representative of a steady state of the glacier, ELA_eq. ELA_eq represents the mean altitude that the equilibrium line would have had over the whole period if the glacier had been balanced (mass balance = 0), and is obtained by:

(1)

where is the mean glacier-wide mass balance over the period under consideration, computed from field measurements here but which can also be determined using photogrammetry (see section 4.5), and ∂b/∂z is the mass- balance gradient across the equilibrium line, fixed at 0.78 m (100 m)^–1 (see further below and section 4.4).

We multiply this variation of the ELA by the mass-balance gradient close to the ELA chosen for the period. The mass balance b(t) computed from remote-sensing data can then be expressed as:

(2)

To obtain the mass balance from the ELA variation, the mass- balance gradient across the ELA, ∂b/∂z, must be known. This gradient varies according to the altitude and local parameters. Mean values for the Alps are given by several authors (Reference LliboutryLliboutry, 1965; Reference Reynaud, Vallon and LetréguillyReynaud and others, 1986). For this study, the gradient was calculated on each glacier for each year with the measurements made on the selected stakes (Fig. 5). However, to reconstruct the mass balance over the 1994–2002 period, we used an average gradient of 0.78 m w.e. (100 m^–1 for all glaciers.

Fig. 5. Mass-balance gradient with altitude ∂b/∂z (mw.e. m ¹) close to the ELA (I994–2002). These data were obtained from field measurements. The uncertainty bars represent the standard error of the mass-balance gradient calculation obtained from the linear regression of the mass balance with stake altitude.

To validate our method, we proceeded in three steps. First, ELAs computed from remotely sensed data were compared with ELAs observed from field measurements. Next we calculated the mass balances from the remotely sensed ELAs using the procedure described above. For each glacier, the values obtained were compared with the mass balances calculated on the basis of field data measured from selected stakes located in a zone across the ELA_eq (2706 m for Glacier d’Argentière, 2829 m for Glacier de Saint-Sorlin and 2947 m for Glacier de Gébroulaz). Note that if ELA_eq is computed with field ELAs, the values obtained are 2750 m for Glacier d’Argentière, 2865 m for Glacier de Saint-Sorlin and 2979 m for Glacier de Gébroulaz (see Fig. 4). Finally, for each glacier, we compared the cumulative mass balance obtained from remotely sensed data with the cumulative glacier-wide mass balance obtained from the whole stake network and photogrammetric measurements (see section 2).

4. Results and Discussion

4.1. Validation of the method

Figure 6 shows an excellent correlation between the two series of ELA results (r ²>0.89, ρ<0.01) and demonstrates that satellite images can be used to determine the ELA accurately.

Fig. 6. Computed ELA obtained from remote sensing vs ELA observed from field measurements. Confidence intervals on the observed ELA are similar to those reported in Figure 4. Confidence intervals on the computed ELA depend on the pixel size of the images used (<30m in this study) and on the glacier slope across the ELA (<20% for the three glaciers). They do not exceed 6 m, and so are not shown.

Figure 7 shows good correlation between the series for yearly mass balance computed and measured at the remotely determined ELAs with r ²>0.90 (ρ<0.01). The average difference between the series for each glacier is low, between 0.24 and 0.51 m w.e. depending on the glacier. Nevertheless some years present differences of as much as 0.97 m.w.e. (Glacier d’Argentière 1997/98 and 2001/02). These are mainly due to the recording dates of the satellite images and to the choice of ∂b/∂z. The two dates should be as close as possible, but this can be difficult if, for instance, cloud cover or recent snowfall hides the snowline on the glacier at the end of the ablation season. Fortunately, the increase in the number of sensor-bearing satellites over recent years means images are now available over shorter intervals, which should make it easier to find usable images recorded at dates closer to the end of the hydrological year. In addition, if no optical image is available, it is possible to work with synthetic aperture radar (SAR) images. Geometrical processing of such images remains complex for mountainous areas but has proved successful in several studies (Reference Adam, Pietroniro and BrugmanAdam and others, 1997; Reference Engeset and R.S.Engeset and Ødegard, 1999).

Fig. 7. Surface mass balance in the area of the equilibrium line from remote sensing (computed b(t)) and from field measurements (ground mass balance) for the three glaciers, 1994–2002. These mass-balance data have been determined at an ELA corresponding to the steady state of the glacier (see text).

Figure 8 shows good correspondence between the series of cumulative mass balance obtained from remote-sensing and ground data. This indicates that the data obtained by remote sensing are representative of the glacier-wide mass balance. Note that both cumulative balances (remotesensing and field measurements) over the whole period are necessarily identical due to the method used (see Equations (1) and (2)). With this method, we determine the annual variation of the mass balance but do not attempt to assess the total volume variation over the period.

Fig. 8. Cumulative mass balance from remote sensing (Cum computed b(t)) and from field measurements (Cum glacier-wide ground B(t)) for the three glaciers, 1994–2002.

5. Conclusions

This study shows that remote sensing may be regarded as an adequate tool to reconstruct annual mass-balance series on glaciers where few or no direct field measurements are available. It can also be used to complete incomplete or interrupted series of field measurements. For glacier monitoring, photogrammetry and remote sensing appear to be complementary, i.e. photogrammetry can be used to calculate the total volume variation of a glacier over a given period, and remote sensing to reconstruct the annual mass- balance variation over this period.

Over the whole 1994–2002 period, results provided by our method of mass-balance calculation using optical remote-sensing data are satisfactory. Differences between the results obtained from remote-sensing data and field measurements remain on the whole quite small (on average, 0.24–0.51 mw.e. for the three glaciers). Thus, this method provides an effective way to reconstruct mass-balance series on the scale of a mountain range of moderate size, firstly because satellite images cover large areas and secondly because of the relative simplicity of the method.

However, it must be kept in mind that the results mainly depend on the recording date of the images which must correspond to the end of the hydrological year, and meteorological conditions may limit the use of optical data due to cloud or snow cover. In such a case, it is also possible to use SAR images. The main interest of radar sensors is to eliminate these restrictions related to meteorological conditions. However, improvements in the image-processing procedure are still necessary to reach the quality of the results obtained with optical images.