Change in geometry of a high Arctic glacier from 1948 to 2013 (Austre Lovénbreen, Svalbard)

ABSTRACT The change of Austre Lovénbreen, a 4.5 km2 land-based glacier along the west coast of Spitsbergen, is investigated using geodetic methods and mass balance measurements over 1948–2013. For 2008−2013, annual mass balances computed on 36-stake measurements were obtained, in addition to annual mass balances reconstructed from the neighbouring glaciers, Midtre Lovénbreen (1968−2007) and Austre Brøggerbreen (1963−1967). The mean rate of glacier retreat for 1948–2013 is −16.7 ± 0.3 m a−1. Fluctuations in area (1948–2013 mean, −0.027 ± 0.002 km2 a−1) showed a slowing as the glacier recedes within its valley from 1990 to 1995. For 1962–2013, the average volume loss calculated by digital elevation model subtraction of −0.441 ± 0.062 m w.e. a−1 (or −0.54 ± 0.07% a−1) is similar to the average annual mass balance (−0.451 ± 0.007 m w.e. a−1), demonstrating a good agreement between the loss rates computed by both methods over 1962−2013. When divided in two periods (1962−1995 and 1995−2013), an increase in the rate of ice mass loss is statistically significant for the glacier volume change. The 0°C isotherm elevation (based on mean May–September air temperatures) is estimated to have risen by about 250 m up to the upper parts of the glacier between 1948 and 2013. The glacier area exposed to melting during May to September almost increased by 1.8-fold while the area reduced by a third since 1948. Within a few years, the glacier area exposed to melting will decrease, leading the upper glacier parts under the 0°C isotherm while the snout will keep on retreating.


Introduction
As they are more sensitive to climate change, the small glaciers and ice caps currently contribute more to sea level rise than large ice sheets relative to their area (Paterson 1994;Meier et al. 2007;Gregory et al. 2013;Stocker et al. 2013). To estimate the glacier contribution to sea water level requires data of mass balance or glacier geometry change (Dyurgerov et al. 2010). In the Arctic, the dataset sources available to assess the long-term change of glaciers (in area and in volume) are quite rare, heterogeneous in nature and in accuracy and available for a period not exceeding a century (Stocker et al. 2013). Among the methods used to investigate glacier geometry change, remote sensing methods provide information from the Arctic scale (e.g. Rignot & Kanagaratnam 2006;Korona et al. 2009) to the local scale (e.g. Rees & Arnold 2007), with the largest sources of error at the largest scale.
With 33,837 km 2 of ice caps and glaciers, Svalbard is among the largest glaciated areas in the high Arctic (Radić et al. 2013). It has the largest density of glaciers monitored in the Arctic island zone defined by the World Glacier Monitoring Service (WGMS 2016). Along the west coast of Spitsbergen, the Brøgger Peninsula displays several small valley glaciers among which Midtre Lovénbreen (ML), Austre Lovénbreen (AL) and Austre Brøggerbreen (AB) have been studied since the 1960s (Corbel 1966;Corbel 1970;Hagen & Liestøl 1990;Liestøl 1993;WGMS 2016). Recently, the investigations on these valley glaciers have been intensified (e.g. Rippin et al. 2003;Kohler et al. 2007;Murray et al. 2007;Rees & Arnold 2007;Barrand et al. 2010;Mingxing et al. 2010;James et al. 2012). Most of these authors have shown a constant but irregular retreat of these glacier fronts since the end of the Little Ice Age (LIA).
The present paper investigates the changes in length, surface and volume of AL (78.87°N, 12.15°E) over a long period (1948−2013), using measurements of front position and annual mass balance combined to several dataset sources: a digitized contour map, aerial photographs, satellite images and digital elevation models (DEMs). In addition, the Ny-Ålesund station (6 km west of the study area) provides climate data from 1969. By taking into account a catchment area constant since the LIA, we discuss the potential relation between the glacier geometry change (area, volume) and air temperature (AT) data. The long-term evolution is discussed, combining our mass balances obtained on the AL with those extrapolated from ML and AB following the observed close correlations with these two neighbouring glaciers. The paper also provides a discussion about consistency of methods used for assessing volume change of AL over 1962−2013. Then, in order to understand the ongoing shrinking rates, the evolution of the average 0°C isotherm over May-September is proposed and examined for seven dates between 1948 and 2013.

General settings
Svalbard, an archipelago with 55.5% glacier cover, represents about 10% of the total Arctic small glaciers area (Liestøl 1993;Kohler et al. 2007;Radić et al. 2013). Similar to what is observed throughout the Arctic, this area is very reactive to climate change: Hagen et al. (2003) stated that all the small glaciers (area lower than 10 km 2 ) have been clearly retreating since the end of the LIA. Small valley glaciers of the Brøgger Peninsula have thus lost both in mass and in area (Lefauconnier & Hagen 1990;Hagen et al. 1993;Liestøl 1993;Lefauconnier et al. 1999;Kohler et al. 2007). In a recent study, Kohler et al. (2007) demonstrated that the average thinning rate of ML has increased steadily since 1936. They showed that the thinning rates from 2003 to 2005 were more than four times the average of the first period .
The AL glacier is a small land-based valley glacier, 4 km long from South to North along the Brøgger Peninsula (Figure 1). The glacier area was 4.48 km 2 in 2013 and its elevation ranges from 50 to 550 m a.s.l. Its catchment area spreads over 10.577 km 2 , taking into account an outlet where the main stream crosses a compact calcareous outcrop 400 m upstream from the coastline (Figure 1). The catchment is characterized by a proglacial area downstream and the glacier it-self upstream, surrounded by a series of rugged mountain peaks whose elevation reaches 880 m a.s.l. (Nobilefjellet). The first glaciological and hydrological investigations in the Brøgger Peninsula were conducted by French scientists during the early 1960s on the Lovén glaciers. In 1965, Geoffray (1968 implemented a network of 17 stakes on AL. Preliminary hydro-glaciological investigations conducted by Vivian (1964) were pursued by Vincent and Geoffray (1970). Two decades later, Griselin (1982Griselin ( , 1985 proposed the first hydrological balance of the AL catchment. More recently Mingxing et al. (2010) published annual mass balance data for 2005-2006.
In the present paper, the change in AL geometry over the 1948-2013 period is investigated using (i) geodetic methods (a topographic map, aerial photos, satellite images, GPS tracks, airborne light detection and ranging [LIDAR]) and (ii) annual mass balance (Ba after Cogley et al. [2011]) measured from 2008 to 2015. The source materials and data vary depending on whether the glacier change is studied in terms of length, area or volume change (Figure 2(a−f)).

Front position and area change
. 1962-1965 German topographic map: East German scientists produced a 1/25,000 map from 1962 to 1965 (Pillewizer 1967) that we georeferenced (Figure 2(a)). In this paper, this dataset will be referred to as the '1962-1965 map' since the AL snout (elevation lower than 300 m a.s.l.) was mapped in 1962 and the higher part of the glacier (above 300 m a.s.l.) was mapped in 1965. . Aerial photos: Six aerial stereographic photographs (Figure 2(b)) provided by the Norsk Polarinstitutt (NPI) were used to determine the glacier front position at different dates: 1948 (unknown scale), 1966 (scale of 1/50,000), 1971 (1/20,000 and 1/6,000), 1977 (1/50,000), 1990 (1/50,000 and 1/15,000) and 1995 (1/15,000). We georeferenced original aerial images with a GPS-referenced ground control points, at a density of approximately 1 point per km 2 using relevant ground features on the surrounding ridges and in the glacier forefield. . Airborne and satellite data: For the period 1995-2008, the only available, dataset at high resolution was a 2005 Scott Polar Institute Airborne LIDAR DEM (Rees & Arnold 2007). In this paper, it was only used to outline the front position in 2005 since the survey only covers AL glacier forefield and snout. A Formosat-2 image was used for 2009 (Friedt et al. 2012). Before 2006, multiple georeferenced Landsat7 images are available on the USGS website. Seven images (1985, 1989, 1990, 1998, 1999, 2002 and 2006) were analysed but rejected due to a poor pixel definition (30 m × 30 m). Additionally, on these Landsat7 images, we found the differentiation between the ice or snow-covered surfaces from rock or morainic material challenging, leading to an error of ±100 m on the glacier front positioning. . Front positioning by GPS: For the 2008-2013 period, the glacier front limit was surveyed every year at the end of September with a Coarse Acquisition GPS. When Formosat-2 images and GPS data were available for the same year, in situ GPS front positioning is considered more accurate.
Thus, a total of 14 AL front positions can be investigated over 1948-2013. The front positions were manually delineated for years between 1948 and 2005. After 2005, that is, for 2008-2013, the snout positions were determined by GPS. Since the margin is covered with rock debris and some residual ice may remain in the proglacial moraine, the actual glacier front is not always easy to delineate neither on images nor in the field. Even if the limit may also have changed in the upper part of the glacier, the available source materials are not precise enough to determine accurately any significant difference on the upper parts of the glacier (Bernard et al. 2014). This is due to (i) the steepness of surrounding slopes and/or (ii) the snow cover at the foot of slopes covering the rimaye . We therefore used a single image as the reference to delineate the glacier area behind the snout (Formosat-2 image of summer 2009). In a previous publication by our group, Friedt et al. (2012) analysed the error margin on the AL glacier limit position. Their results are consistent with the uncertainty analysis published by Rippin et al. (2003). As we used the same dataset sources as Friedt et al. (2012), the uncertainty analysis made in the paper remains valid here: . the contour map and all airborne/satellite images were re-sampled on a 5 m × 5 m grid; . the glacier boundary analysis using manual colour identification (upper limit of the glacier for all years and snout position before 2008) yields a 2 pixel uncertainty, that is, an uncertainty of ±10 m and . GPS delineation of the snout (2008-2013) yields a horizontal uncertainty of ±5 m.
Such boundary position uncertainties yield a variable uncertainty on the glacier area (Table 1): considering that the glacier limit is largely constant upstream (our reference for all years being the 2009 glacier ice-rock interface; see the thick line on Figure 3) and that only the snout position is significantly evolving (see the length of glacier front in Table 1 and Figure 3), the area uncertainty is given by the sum of (i) the uncertainty on the upper glacier limit (length of 12.29 km times 10 m for all years) and (ii) the uncertainty on the independently measured snout position (the length of the front times 10 m for 1948-2005 or times 5 m for 2008-2013).

Volume change
In order to assess the volume change of the glacier over 1962-2013 (51 years), we compared different dataset resources available for AL, all converted into DEMs: (i) the '1962-1965 map' (ii) the 1995 DEM (NPI) and (iii) 2 new DEMs produced from our GPS measurements in 2009 and 2013.
Other sources exist but, based on the elevation uncertainty analysis, only datasets exhibiting submeter standard deviation (SD) on the altitude were considered. Most significantly, we rejected:    1948, 1966, 1971, 1977, 1990 & 1995  Hence, the three periods investigated herein for assessing the volume change are 1962-1995, 1995-2009 and 2009-2013  When subtracting two DEMs, the uncertainty of elevation is assumed to be equal to the sum of elevation uncertainty of each image or map. It is therefore within ±4.5 m between the '1962-1965 map' and 1995 photogrammetry-derived DEM, within ±2.0 m uncertainty between the 1995 DEM and a GPS-derived DEM, within ±1.0 m uncertainty between two GPS-derived DEMs and within ±3.5 m uncertainty between the '1962-1965 map' and a GPS-derived DEM. The uncertainty on volume change is therefore the uncertainty of elevation times the mean glacier areas between two years.

Mass balance
Field measurements of ablation and accumulation have been made yearly using a 36-stake network that we set up in 2007 to cover the whole AL glacier surface (Figure 2(e)). Glacier-wide mass balance is computed from measurements conducted twice a year: at the end of winter (late April/early May) for winter mass balance (not used in this paper) and at the end of summer (late September/early October) for annual mass balance (Ba; after Cogley et al. 2011). The Ba were computed for eight years (from 2008 to 2015 meaning glaciological years 2007-2008 to [2014][2015]. The AL Ba was obtained by inverse distance weighting interpolation of 36-stake measurements (Bernard et al. 2010;Bernard 2011).
All height measurements at stakes are independent and the uncertainty on the height measurement is estimated to be ±0.05 m. Thus, the uncertainty on Ba derived from subtracting independently measured stake heights is ±0.10 or ±0.09 m w.e. (mean ice density of 0.9; e.g. Moholdt et al. 2010). This uncertainty considered on Ba is consistent with that given by Fountain and Vecchia (1999) for a glacier mass balance computed with about 30 stakes. The uncertainty of Ba averaged over a time period (year i-year j) is therefore the sum of the Ba uncertainty of each year (year i and year j) divided by the number of years separating the years i and j.
The longest Ba time series in the Brøgger peninsula concern two other glaciers: (i) ML, the neighbouring glacier of AL and (ii) AB, 6 km further West (Figure 1). In this paper, we use the Ba of ML between 1968 and 2007 provided by WGMS (2016). The ML Ba were computed by averaging 10stake measurements within 100 m elevation bins along the central line (Barrand et al. 2010). For 1963-1967, we used the AB Ba data given by Lefauconnier and Hagen (1990). Before 1967, these authors estimated AB Ba from positive AT of July-September recorded at Longyearbyen combined to winter precipitation for which coefficient correlation is 0.90.

Air temperature
AT time series are recorded since 1969 at the Ny-Ålesund station at 8 m a.s.l. (eKlima 2013). The AT over AL was deduced by applying an altitude, AT gradient to the Ny-Ålesund AT data. The gradient was established from daily AT obtained from two temperature loggers (Hobo pro V2 U23-004 Onset Hobo data loggers, Bourne, MA, U.S.A.; accuracy of ±0.2°C) installed on the AL: one downstream at 148 m a.s.l and the other upstream at 481 m a.s.l. The resulting average altitude, AT (−0.005°C m −1 for May-September) is consistent with the literature (e.g. Corbel 1966;Geoffray 1968;Corbel 1970;Griselin 1982;Griselin & Marlin 1999 for AL; Joly 1994 for ML). Additionally, a third similar temperature logger was set in the AL proglacial moraine at 25 m a.s.l.: the mean annual difference of 0.007°C lower than the accuracy on temperature measurement indicates that no significant longitudinal gradient exists between Ny-Ålesund and the AL catchment, 6 km further East.

AT data
In this paper, we consider hydro-glaciological years from October 1 to September 30 in order to compare AT data with Ba that is measured at the end of September/beginning of October each year. Over 1970Over -2013Over (meaning glaciological years from 1969Over -1970Over to 2012Over -2013, the MAAT in Ny-Ålesund was −5.22°C (SD of 1.27°C). Over the period, the MAAT displays a positive temporal trend of +0.57°C/decade (Figure 4). This is in agreement with the data analysed by Førland et al. (2011) for Svalbard. The segmented linear regression technique explained by Oosterbaan (1994) was applied to find potential breakpoints in the MAAT time series. The result is the following: the MAAT time series is statistically analysed as a period of constant temperature followed by a period of uniform temperature increase with a breakpoint between 1994 and 1995 (98% confidence interval): this temperature change occurring in the mid-1990s may be relevant to understand glacier volume evolution. During the first 25 years , there is no clear temporal trend (+0.04°C per decade) as opposed to the following 19 years (1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013) for which the MAAT significantly increases with a trend of +1.38°C/decade. This 1995-2013 gradient is 2.4 times the average gradient calculated over the whole period . The MAAT value is −4.45°C (SD of 1.12°C) over 1995-2013.
Mean summer air temperature (MSAT) was also calculated for May-September as an indicator of the melting period at Ny-Ålesund: it was +1.88°C (SD of 0.71°C) for 1970-2013. Using the segmented linear regression technique (Oosterbaan 1994), the MSAT may be also separated into two periods with a statistically significant breakpoint between 1996 and 1997: the trend over 1970-2013 was +0.34°C/decade (trends of +0.10°C/decade for 1970-1996 and +0.90°C/decade for 1997-2013; Figure 4). The mean MSAT value was +1.57°C (SD of 0.59°C) for 1970-1996 and increased to +2.37°C (SD of 0.59°C) for 1997-2013 (Figure 4).

AL length change
Between 1948 and 2013, AL front showed clear changes ( Figure 3). The recession was not however equally distributed over the front (Figure 3). A maximum retreat distance may be estimated along the central flow line with a total recession of 1247 ± 20 m between 1948 and 2013, that is, a mean retreat rate of −19.2 ± 0.3 m a −1 (Table 1). Seven fanned out profiles ( Figure 3) were arbitrarily yet regularly selected to assess the variability of the glacier retreat due to irregularities in the underlying bedrock. The results indicate a mean retreat rate of −16.7 ± 0.3 m a −1 between 1948 and 2013 with rate ranges from −12.8 ± 0.3 m a −1 on the western part to −19.2 ± 0.3 m a −1 in the central axis (Table 1; Figure 3). Figure 5 In details, the annual retreat rate displayed a wide range of values (Table 1) The important spatio-temporal variability is mostly linked to differences in ice thickness and in bedrock morphology. Moreover glacier length change is partly compensated for by glacier flow (Vincent et al. 2000). Mingxing et al. (2010) measured the surface ice flow velocity of AL using differential GPS, they obtained a mean velocity of 2.5 m a −1 along the central line of the AL snout, consistent with a velocity of 4 m a −1 given by Rees and Arnold (2007) for 2003−2005 for the ML also along the central line. The velocity is at least five times lower than the glacier margin retreat rate.

AL area change
In this paper, the change in area (Table 1 and Figure 5(b)) only shows the reduction of the snout area since the same upper limit of the glacier (measured in 2009) was considered constant for all years. Therefore, the glacier area is likely to be underestimated before 2009 and slightly overestimated after 2009. The results obtained for the area change of AL indicate that in 2013 the glacier covered 71% of its 1948 area. In other words, in 2013, the glacier covered only 42% of the total basin area (10.577 km 2 ), whereas it occupied 60% of the catchment in the late 1940s.
The glacier area data plotted over time in Figure 5(b) indicate a progressive temporal decrease (fit resulting from minimizing quadratic error) with an average reduction rate over 1948-2013, similarly to 1962-2013 (Table 2). An uncertainty of ±0.002 km 2 a −1 is obtained on the slope by computing the uncertainty on the slope of the regression 'glacier area upon time', which is the SD of the slope times a variable following Student's distribution for a 95% confidence interval (Oosterbaan 1994). The uncertainty is less than 10% of the observed temporal trend. Figure 5(b) shows that the area change with time has two periods of regular decrease separated by a perceptible breakpoint between 1990 and 1995: the gradient decreased from −0.033 ± 0.003 km 2 a −1 for 1948-1995 (similar to −0.032 ± 0.003 km 2 for 1962−1995) to −0.018 ± 0.005 km 2 a −1 for 1995-2013 (Table 2).

AL volume change determined by DEM differences
The AL change in volume was estimated by subtracting two by two 4 DEMs covering the 1962-2013 period that we can separate into three sub-periods: 1962-1995, 1995-2009 and 2009-2013 (Figure 6 and Table 2). For the whole 1962-2013 period, the total glacier ice volume loss was estimated at 129.1 ± 18.1 × 10 6 m 3 (Table 2). This corresponds to an average reduction rate of −2.5 ± 0.4 × 10 6 m 3 a −1 (the ratio of the volume divided by 51 years) or an average elevation difference of   1962-1995, 1995-2009, 2009-2013, 1995-2013 and 1962-2013. Change in glacier area DEM subtraction Annual mass balance Net loss in ice Net loss in water equivalent a Water equivalent a Period (km 2 a −1 ) (10 6 m 3 ) (10 6 m 3 a −1 ) −0.490 ± 0.069 m a −1 (ratio of −2.5 × 10 6 m 3 a −1 by the average glacier area between 1962 and 2013, i.e. 5.17 km 2 ). The annual volume change rate is not constant between the three investigated periods: . −2.3 ± 0.7 × 10 6 m 3 a −1 (1962−1995). The average elevation difference was −0.427 ± 0.136 m a −1 (based on the average 1962−1995 glacier area, 5.32 km 2 ); . −3.4 ± 0.7 × 10 6 m 3 a −1 (1995−2009). In terms of elevation difference, the rate was −0.720 ± 0.143 m a −1 based on an average 1995−2009 glacier area (4.67 km 2 ) and  1962-1995, 1995and 1962, the scale is different than that of the three other maps since the change of altitude for four years is very low.
For this last period, we see that the uncertainty accounts for two-third of the calculated net ice loss. As already shown by Friedt et al. (2012), a four-year interval is clearly too short to accurately determine the glacier volume change but only the DEMs of 2009 and 2013 were surveyed with the same instrument (GPS) and methods, in the frame of this study. To reduce the uncertainties, the two last periods (1995−2009 and 2009−2013) were gathered and gave a net ice loss of −3.0 ± 0.5 × 10 6 m 3 a −1 for the whole period. Expressed as elevation difference, the rate was −0.649 ± 0.111 m a −1 with respect to an average 1995−2013 glacier area (4.64 km 2 ). Using a mean ice density of 0.9 (e.g. Moholdt et al. 2010), AL lost −2.3 ± 0.3 × 10 6 m 3 a −1 w.e. during 1962-2013. The loss was −2.0 ± 0.7 and −2.7 ± 0.5 × 10 6 m 3 w.e. a −1 for 1962-1995 and 1995-2013, respectively (Table 2).

AL mass balance
The AL Ba was measured yearly for 2008-2015 ( Figure 7; Table 3 Earlier studies of the AL catchment (Geoffray 1968;Griselin 1982) did not provide data to establish past Ba since the seven available data were located in the ablation area only. Between 1965 and 1975 the point mass balance (ba) of the partial Geoffray's stake network spatially ranged from −1.05 m a −1 downstream to −0.24 m a −1 upstream (Table 4; Brossard & Joly 1986). They fall within the same range as the 1962−1995 DEM subtraction at these same seven points (from −0.17 to −1.09 m a −1 ; Table 4).
So, in order to estimate the past AL Ba for 1967−2007, we correlated AL versus ML Ba data, both series having eight years in common (2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015). We obtained a strong correlation between the Ba series for 2008−2015, with a linear fit yielding the following equation (Figure 8 where Ba were given in m w.e. By applying Equation (1) to the series of ML Ba, we obtained an AL Ba time series extrapolated for 1968−2007 (Figure 7). Since Ba were not available for ML prior to 1968, we used the estimated Ba values computed by Lefauconnier and Hagen (1990) for AB. Subsequently, the strong correlation between AB and ML (Equation (2) where Ba are given in m w.e. For extrapolated AL Ba, error bars are driven by the ML error bar (±0.25 m according to Kohler et al. 2007) times the regression coefficient, with uncertainty on each regression coefficient bringing a negligible contribution since r is close to 1 (see the equations in Oosterbaan 1994). Hence, we assessed uncertainties of ±0.26 m w.e. for each AL extrapolated Ba between 1968Ba between and 2007Ba between and ±0.28 m w.e. between 1963Ba between and 1967.

Discussion
During the 1948−2013 period, AL underwent changes of geometry (length, area and volume). The following discussion addresses (i) the change rates through time, (ii) the differences between the methods to estimate the change in volume (Ba versus DEM) and (iii) the relationship between geometry change and evolution of glacier areas exposed to melting.

Variations in rate of AL retreat (length, area) for 1948-2013
Whatever the resource type used to estimate the glacier retreat in length or in area through time ( Figure 5(a,b)), we observed a strong linear fit. However, it was not possible to assess the changes in glacier higher in the catchment for reasons explained in Section 3.1.
The mean retreat calculated by averaging the length along seven profiles was relatively constant in time (Figure 3). A straight line with a mean slope of −16.7 ± 0.3 m a −1 (n = 14 and r = 1.000) is representative of the average retreat rate of the glacier terminus. It is notable that the average AL velocity (2.5 m a −1 according to Mingxing et al. 2010) does not exceed the average front retreat rate along the main flow line which is quite homogeneous over 1948−2013 (−19.2 ± 0.3 m a −1 ; n = 14 and r = 0.997).
On the retreat rate versus time relationship determined for the central line ( Figure 5(a)), the breakpoint in 2005 is not the consequence of a climatic change but illustrates the local predominance of the surrounding terrain topography in the apparent acceleration of the axial retreat. Averaging over seven profiles smooths out bedrock topographic features and yields a homogeneous retreat rate rather constant in time.
Regarding the glacier area, the average change was −0.027 ± 0.002 km 2 a −1 over 1948-2013 (n = 14 and r = 0.993). A slowdown in the area reduction was observed between 1990 and 1995 ( Figure 5  (b)). This breakpoint may be surprising when considering the MAAT or MSAT series (Figure 4): the AT gradient increased after 1994, whereas the reduction rate of the glacier area slowed down. This apparent divergence may be partially explained by the reduction of the glacier terminus exposed to melting. We can observe that, in 1948, the glacier terminus was widely spread out in the glacier forefield uphill the LIA terminal moraine (Figure 3). Compared to 2013, the glacier terminus was less thick and the front itself was rather flat because it was not constrained by the surrounding terrain ( Figure 9). In the present-day configuration, the glacier snout clearly is constrained on its eastern and western sides by the steep slopes of the glacier basin valley. The glacier snout gradually became thicker and its front steeper over time (Figure 9). If we compare the ice thicknesses at the glacier snout at a same distance from the respective fronts of 1962, 1995, 2009 1962, 1995, 2009 and 2013, respectively. Further discussion about the glacier areas exposed to melting is given below inSection 5.5.
Even if the changes of snout length as well as glacier area are two convenient, visible proxies to study glacier dynamics, they may be delicate to interpret since they combine several processes that are not only dependent on climate conditions. Glacier shrinkage is also related to parameters including ice thickness, glacier velocity, basal thermal state of glacier, topography and roughness of underlying bedrock and geological structures (slope and fractures). Therefore, to assess glacier changes, glaciological investigations have to focus on volume in addition area or length of glaciers.

Variation in volume (reduction rate and percentage of total AL volume) for 1962-2013
Regarding the methods for assessing the volume change of the glacier, it could be hazardous to compare heterogeneous sources of dataset since investigating the long-term change of glacier often requires the use of various documents (maps, aerial photos, satellite and airborne images) with different accuracies and scales. In the case of AL, great care was applied to minimize data artefacts but oldest sources showed some discrepancies from expected trends. For the 2009 and 2013 datasets, the DEM difference produced by Rinex-post-processed GPS measurements is expected to lead to the best accuracy of our datasets but such a short time interval actually yields unacceptable signal to noise ratio (64%, i.e. an error of 0.25 m a −1 for a value of −0.39 m a −1 ). This short time interval will hence not be considered, in favour of the longer time interval 1995−2013 over which uncertainties are reduced to yield an acceptable signal to noise ratio of at least 10.
Like for the AL area change, the results undoubtedly indicate that AL reduced in volume over 1962−2013 with a rate of −2.5 ± 0.3 × 10 6 m 3 a −1 of ice for an average elevation difference of −0.490 ± 0.069 m a −1 (Table 2) Table 2). However, the acceleration is better demonstrated with Ba data because the error bars are lower than the ones on DEM differences. This acceleration is much lower than that given by Kohler et al. (2007) for ML (+245% between 1962−1969 and 2003−2005), which was computed on short time-spans instead of continuous, long time series to characterize the changes (1936−2005).
Expressed as change with respect to the whole glacier volume, the glacier lost 16 ± 5% of its 1962 volume at an average loss rate of −0.48 ± 0.15% a −1 during the first 33-year period while the glacier lost 14 ± 2% of its 1995 volume at a rate of −0.76 ± 0.13% a −1 during the following 18-year period.

AL volume change: DEM subtraction versus Ba
Since stake values of 1965−1975 are not usable for computing an AL Ba, (the retrieved stakes being only located in the ablation area), we used Ba reconstructed from long time series of ML Ba for 1968−2007 and AB Ba for 1963−1967 in addition to the eight years of in-situ measurements (2008−2015), in order to compare them to DEM differences (see the Sections 3.3 and 4.5).
Results showed that for the overall period (1962−2013), the average altitude difference between DEMs (−0.441 ± 0.062 m w.e. a −1 ) was similar to the average Ba (−0.451 ± 0.007 m w.e. a −1 ), indicating a good consistency between both methods to survey the glacier geometry change (Table 2). At shorter time scale, both methods also display similar rates except for the shortest period, 2009−2013 ( Figure 10 and Table 2): over 1962−1995, the average Ba (−0.422 ± 0.016 m w.e. a −1 ) is statistically Figure 10. Comparison of methods for estimating AL volume change (Ba and DEM subtraction) for four periods (1962-2013, 1962-1995, 1995-2013 and 2009-2013). similar to DEM subtraction values (−0.384 ± 0.123 m w.e. a −1 ) and for 1995−2013, the average Ba (−0.505 ± 0.020 m w.e. a −1 ) is also consistent with DEM subtraction values (−0.584 ± 0.100 m w.e. a −1 ). As already mentioned for DEM differencing (Section 5.2), the increase in the loss rate in time is more highlighted by Ba data due to low error bars ( Figure 10).
As no breakpoint was found in the whole time series of AL Ba (computed from our stake measurements or reconstructed from ML or AB Ba), the increase of loss rate is likely progressive through time.
All of this confirms that long-term data give accurate and similar results using Ba and DEM at the exception of short-term data that yield high error bars. The data presented in this paper reinforce the results obtained for AL by Friedt et al. (2012)

AL volume change (1962-2013) with respect to catchment area
To compare the ice volume loss between different periods during which the glacier area reduced, the glacier geometry change has to be given with respect to an area common and invariant over time. We expressed the volume change in water depth (w.e. in m) with respect to the catchment area which is considered unchanging in a glacier basin: in the case of AL, the outer edge was chosen where it crosses a stable, massive calcareous outcrop a few hundred metres upstream from the coastline ( Figure 1) and which is not affected by changes in coastline position.
The AL ice loss obtained for the whole period by DEM subtraction (Table 2) was −0.215 ± 0.030 m w.e. a −1 with respect to the catchment area (10.577 km 2 ). For the same period (1962−2013), the average Ba is −0.221 ± 0.003 m w.e. a −1 with respect to the catchment area, again emphasizing the consistency between the two methods.
Regarding the two periods mentioned above (1962−1995 and 1995−2013), the loss rates, normalized to the catchment area, are still consistent within each period (Table 2 Regarding the evolution of loss rates through time, both methods confirm an increase in the loss for the second period (Figure 7). Both proxies indicate increase of the melt rate in the second time interval even if the normalization to catchment area smooths the differences between the two considered periods.
5.5. AL change with respect to glacier surface exposed to melting  From 1962 to 2013, the AL regularly lost ice (−26% in volume and −23% in area). Under similar climatic conditions, we would expect that decreasing the glacier area would lead to a progressive decrease of melt rate, which is not the case for AL for which even though the area decreased, the rate of ice melt (in volume) increased. It is well known that the relationship between glacier size and change in ice volume is not straightforward, since a glacier response time must be considered: immediate for volume and delayed for length and area (Cuffey & Paterson 2010).
To discuss the apparent discrepancy between the overall area change and volume change, we may assess the glacier surface exposed to melting for 1948-2013 using AT data. For this purpose, we chose to compute the area of glacier surface exposed to melting by considering an average elevation of the 0°C isotherm based on the MSAT, that is, from May 1 to September 30. This particular time interval was selected as it covers most of the melting period. However, the choice of a constant period allows for the computing of an average 0°C isotherm elevation for each date, which has to be considered as relative values rather than absolute values.
For the estimate of the 0°C isotherm position, two climatic stations were used: Ny-Ålesund station  and Longyearbyen (1948Longyearbyen ( -1968. As no longitudinal gradient of AT exists between the lower part of the AL catchment and Ny-Ålesund station, the Ny-Ålesund MSAT time series corrected for altitude−AT gradient of −0.005°C m −1 was directly used to estimate yearly the elevation of the 0°C isotherm over the glacier from 1969 to 2013. To extend the time period before 1969, the Longyearbyen MSAT series was used since (i) this station started earlier than that of Ny-Ålesund and (ii) both monthly AT series (limited to May-September) are very well correlated. We established the relationship at T(Ny-Ålesund) = 0.82 × T(Longyearbyen) − 0.13 where T is the MSAT in°C (r = 0.95 and n = 175 months). These MSAT values was translated into values at AL and corrected for an altitude-AT gradient, then the yearly average elevation of the 0°C isotherm for May-September over AL was assessed for 1948−2013. Then, for seven dates for which the AL front position data are available, the area below the 0°C isotherm elevation, that is, the area with average positive MSAT was deduced to define a so-called 'glacier area exposed to melting' and reported in Figure 11.
From 1948 to 2013, we observe an upward shift in elevation of the 0°C isotherm, regularly from 1948 (209 m a.s.l.) to 2013 (454 m a.s.l.), except for 1962−1977 (0°C isotherm slightly decreased from 276 to 267 m a.s.l.). At the same time, the glacier area decreased (Figure 11). The AL area exposed to melting substantially increased from 1.9 km 2 in 1948 to 3.5 km 2 in 2013, that is, respectively, 30% and 78% of the whole area. In 65 years, the glacier area exposed to melting was multiplied by 1.8 while the total AL area reduced by almost a third (29%). This could be the main explanation of the fact that the change of AL volume increased while its area change decreased.
The evolution of AL areas, over and under the 0°C isotherm elevation, through time is shown in Figure 12. The total glacier area reduced while the area over the 0°C isotherm elevation decreased and the area below the 0°C isotherm line displayed a noticeable decreasing trend for 1948−1995 and then a strong increase between 1995 and 2013. The breakpoint in 1995 occurs due to the increase in MSAT observed at Ny-Ålesund at this time (cf. Section 4.1).
With such a change in the 0°C isotherm position towards higher elevation over the catchment, the average position of the 0°C isotherm will soon exceed the upper part of the glacier (550 m a.s.l.) during the May−September period and AAR will tend to zero at the end of the summer. Figure 11. Elevation of the average 0°C isotherm over AL for seven years (1948, 1962, 1977, 1995, 2005, 2009 and 2013). The position of the 0°C isotherm elevation was estimated from the Ny-Ålesund temperature data of summer months (May-September) corrected from an elevation gradient of −0.005°C m −1 . The values in km 2 refer to the glacier area under (light) or over (dark) the 0°C isotherm. The values in m are the elevation of the 0°C isotherm. Glacier elevation for 1948 and 1977 is that of 1962 and for 2005 it is that of 2009. Under such conditions, the glacier area will shrink and the output meltwater volume is then expected to decrease. This geometrical statement might be compensated for by climatic considerations. The melting period could extend in time, before May and/or after September, and MSAT may increase, countering once again the expected decreasing trend that should be seen in the melt rate. The whole glacier surface could be subject to only positive temperatures in the summer by ∼2020 (see regression line of area over 0°C extended to 0 km 2 in Figure 12). Such conditions might already be met: AAR data between 2008 and 2015 often showed values at or closed to 0%, in 2011, 2013 and 2015 (Table 3).

Conclusion
The changes in Austre Lovénbreen geometry were investigated using a set of data and documents whose source was heterogeneous in nature and scale (topographic map, aerial photos, satellite and airborne images). Recent annual mass balance measurements were also used based on a 36stake network established on the Austre Lovénbreen in 2007.
1. Austre Lovénbreen, like neighbouring glaciers of the Brøgger peninsula (e.g. ML), is shrinking. Its total retreat is 1064 ± 20 m in length (over seven profiles) over 1948−2013, 1.82 ± 0.28 km 2 in area over the same period. The loss in volume is −129.1 ± 18.1 × 10 6 m 3 over 1962−2013. In half a century, the glacier lost almost a third of its volume, from 471 ± 74 × 10 6 in 1962 to 342 ± 46 × 10 6 m 3 in 2013. 2. Austre Lovénbreen average annual rates were the following: −16.7 ± 0.3 m a −1 in length for 1948−2013, −0.027 ± 0.002 km 2 a −1 in area for 1948−2013 and −2.3 ± 0.3 × 10 6 m 3 w.e. a −1 for 1962−2013, that is, −0.54 ± 0.07% a −1 of the 1962 glacier volume. 3. The mean annual mass balance over 1962−2013 (−0.221 ± 0.003 m w.e. with respect to the Austre Lovénbreen catchment area) is comparable to the DEM subtraction values (−0.215 ± 0.030 m w.e. with respect to the catchment area). The good agreement between the two methods used to survey the annual glacier volume change demonstrates that the DEM difference is an efficient method if applied at dates separated by a time interval long enough for the altitude uncertainty to become negligible with respect to mass balance: in our case, such a condition is met for durations reaching a decade. 4. The perceptible breakpoint between 1990 and 1995 (decrease of area change rate from −0.032 ± 0.003 km 2 a −1 for 1948-1995 to −0.018 ± 0.005 km 2 a −1 for 1995-2013) is explained by the increased local influence of the topography of the surrounding terrain, inducing a thicker and less wide glacier terminus. 5. Regarding two periods (1962−1995 and 1995−2013), the increase in the loss rate in time is more highlighted by Ba data than DEM subtraction, due to low error bars: over 1962−1995, the average Ba was −0.422 ± 0.016 m w.e. a −1 whereas it was −0.505 ± 0.020 m w.e. a −1 or 1995−2013). Assuming the relative volume loss remains similar to that estimated from DEM difference for 1995-2013 (−0.76 ± 0.13% a −1 ), the glacier would have completely melted in 132 ± 27 years. 6. Between the periods used to study the glacier volume change (1962-1995 and 1995-2013), Austre Lovénbreen reduced its volume by 26% while its area dropped by 23%. AL area exposed to melting was modelled by assessing the 0°C isotherm elevation over the glacier by averaging May-September AT (from Ny-Ålesund station and extended to 1948 using the Longyearbyen AT) from 1948 to 2013 and applying an AT − altitude gradient of −0.005°C m −1 . The 0°C isotherm elevation rose over the glacier by 250 m on average in 65 years. The glacier area exposed to melting during the May-September period almost increased by 1.8-fold while the total Austre Lovénbreen area reduced by almost a third since 1948 (29%).
Austre Lovénbreen already experienced negative mass balance over the entire glacier surface (for instance in 2011 and 2013 when AAR was at or closed to 0%). In 2013, only 1.0 km 2 of the total glacier area (4.48 km 2 ) was over the 0°C isotherm. If this continues, within a few years, the glacier area exposed to melting will reduce as the entire present-day accumulation area will be under the 0°C isotherm while the snout will keep on retreating. This would then eventually imply a reduction of ice melt if ATs remain at least similar.