During the summer of 2006 and the springs of 2007 and 2009, we carried out radar profiles covering the entire surface of Ariebreen (Fig. 1). The total length of profiles was 6400 m (2200 m in 2006, 4000 m in 2007 and 200 m in 2009). The radar data were acquired using a Malå Ramac GPR system (Malå Geoscience, Malå, Sweden) with unshielded antennae of 200 MHz (2006) and of 25 MHz (2007 and 2009). The antennae configuration was collinear following the profile direction (parallel end-fire) in all cases. The 200-MHz antennae were chosen to obtain a higher resolution, in order to detect not only the glacier bed, but also the extent and thickness of the firn layer. The recommended equipment settings for working at 200 MHz limited the maximum depth sampled to about 40 m. Consequently, the bedrock was not reached in the areas of thickest ice. Using the 25-MHz antennae, the bedrock was detected in all cases.

There have not been radio-wave velocity (RWV) measurements on Ariebreen, but estimates from many common midpoint (CMP) measurements at the neighbouring Hansbreen glacier (Jania et al. 2005) are available, for both spring and summer periods, and both cold and temperate ice. From their results, we apply a RWV of 168 m µs⁻¹, typical of cold ice. At the frequencies of the GPR antennae used, this implies a theoretical range (vertical) resolution of the radar data of 1.68 m for the 25-MHz antennae, and 0.21 m for the 200-MHz antennae, considering the range resolution as one quarter of the wavelength in ice. The range resolution provides a lower bound of the error in thickness. The total error in thickness depends on many factors and will be larger, as explained later. The processing of radar data included band-pass filtering, amplitude scaling, deconvolution, migration where required and conversion to depth using the above RWV.

The DTMs of Ariebreen's surface elevation in different years have been constructed interpolating each year's elevation data at the nodes of a common grid. We used as the reference common grid that of the 1990 DTM, which was already available in gridded format (Jania et al. 2002; Kolondra 2002) and therefore did not require interpolation.

For estimating the error in elevation of any of our DTMs, ɛ _{z DTM}, we considered the contributions of both the error in the data points from which the DTM was constructed, ɛ _{z data}, and the surface interpolation error inherent to the generation of the DTM from such data points, ɛ _{z interp}. We assume that these errors are independent, so ɛ _{z DTM} can be estimated through the root of the squared summation of ɛ _{z data} and ɛ _{z interp}.

We used Surfer software (version 8) to calculate the planar area of Ariebreen in the different years from the corresponding DTMs, the volume in 2007 from the ice thickness map, and the volume change from the surface elevation changes between the different DTMs. For the volume change computation, we used Simpson's numerical integration method. These calculations involve both systematic errors (biases), which we corrected for, and various random errors, including the uncertainty on boundary delineation. The description of how all of these errors were estimated is given in the Supplementary File.

Using the geodetic approach, the mean mass balance rate (Cogley et al. 2011) during a period Δt (integer number of mass balance years) is given by 1 M ˙ ¯ = ρ Δ z ¯ Δ t , where ρ is the density of ice, Δ z ¯ = Δ V / A ¯ is the mean elevation change, ▵V is the volume change and A ¯ is the average glacier area (mean value between initial and final areas). Equation 1 assumes Sorge's Law (Bader 1954): that there is no changing firn thickness or density through time and that all volume changes are of glacier ice. This is a reasonable assumption in the case of Ariebreen, since most of the volume changes occur at lower elevations, below the equilibrium-line altitude, and therefore involve ice rather than firn. However, to account for a possible decrease in firn thickness, we took for the density a value of ρ=850 kg m⁻³, slightly biased towards lower values as compared to usual ice density, and assumed a value of ɛ _ρ =50 kg m⁻³ for its error (Huss et al. 2009).

The error in mean mass balance rate is estimated as 2 ε M ˙ ¯ = 1 Δ t ρ 2 ε Δ z ¯ 2 + Δ z ¯ 2 ε ρ 2 ,

where we computed the error in mean glacier elevation change ε Δ z ¯ as the error of the quotient Δ V / A ¯ .

The surface topography in 1936, 1990 and 2007, the ice thickness in 2006–07 and the subglacial relief maps are shown in Figs. 2 and 3. The average ice thickness in 2007 was very low at 27.2±1.6 m. The thickest ice in Ariebreen, 82.3±3.7 m, is found at its upper part. In the middle elevations it rarely exceeds 50 m, while the lower part of the glacier contains rather thin ice (<30 m).

The planar area and ice volume of Ariebreen in 1936, 1990 and 2007, together with their percent changes over the periods 1936–1990, 1990–2007 and 1936–2007, are shown in Table 1. Significant changes are observed for both area and volume. Figure 3c shows the surface elevation changes experienced by the glacier over the entire period 1936–2007. The glacier thinning is remarkable, reaching values up to 100 m (ca. 1.4 m y⁻¹) in the lower part of the glacier. To stress the different rates of mass loss over the periods 1936–1990 and 1990–2007, we present, in Fig. 4, the spatial distribution of the elevation change rates for both periods and, in Table 2, the corresponding mean mass balance rates. Note that the elevation change rates in Fig. 4a & b are given in metres of ice per year, while the mass balances in Table 2 are converted into metres in water equivalent (w.eq.) and computed over the average area for the period. Table 2 clearly shows that the mass loss has accelerated during the two last decades, while Fig. 4c shows the spatial distribution of this acceleration by displaying the elevation change acceleration between the centres of each of the two periods 1936–1990 and 1990–2007.

The analysis of the radar sections (two examples are provided in Fig. 5) shows two main features concerning the internal structure of Ariebreen: (1) the radar records of both high- (200 MHz) and low- (25 MHz) frequency radars do not show any englacial diffractors or scattering typical of temperate ice; (2) the firn layer observed in the field measurements, whose approximate extent is shown by the equilibrium line positions in Fig. 1, cannot be detected in our radar records because the 200-MHz profile on the upper glacier does not penetrate into the accumulation area (see Fig. 1), and the uppermost 6–8 m of the 25-MHz data are obscured by the direct waves.

The radar data suggest that Ariebreen is entirely cold. This is not surprising, given that the relatively thin ice is not sufficient to prevent conduction of geothermal and internal heat fluxes, that the slow dynamics implies little strain heating, and that the limited extent and thickness of the firn area implies a reduced penetration of percolating water and the release of latent heat upon refreezing. Nevertheless, Ariebreen was classified in the past as a polythermal glacier (Jania 1988), on the basis of occasional observations of water outflows during winter time and proglacial icings. This, however, is no longer so widely accepted as an indication that the glacier is polythermal (e.g., Hodgkins et al. 2004; Bælum & Benn 2011).

According to our results, during the period 1936–1990 the area of Ariebreen decreased by 26%, and the mean mass balance rate was −0.50±0.22 m y⁻¹ w.eq. For comparison, the results by Nuth et al. (2007) for Wedel Jarlsberg Land during the same period were a decrease of the glacierized area by 12%, and a mean mass balance rate of −0.39±0.02 m y⁻¹ w.eq. Ariebreen has therefore followed the regional pattern of changes, though at a larger rate. We attribute these enhanced losses to the small thickness of Ariebreen, which implies a short response time to changes in climate. The estimates of the mean mass balance rate of Svalbard by Hagen and co-workers (Hagen, Kohler et al. 2003; Hagen, Melvold et al. 2003) are even smaller in magnitude, −0.27 and −0.12 m y⁻¹ w.eq., obtained using two different methods and data from the late 1960s to about 2000. However, this discrepancy arises because the north and north-eastern regions of Svalbard studied by Hagen and co-workers are less negative than the southern and western regions.

During the second period analysed (1990–2007), our data show a mean mass balance rate of −0.95±0.17 m y⁻¹ w.eq., which can be compared to the −0.65±0.08 m y⁻¹ w.eq. estimated by Nuth et al. (2010) for Wedel Jarlsberg Land and a similar period (1990–2005). However, the mass losses experienced by Ariebreen are larger than the regional values.

The negative mean mass balance rate of Ariebreen has nearly doubled between the two periods analysed. This marked acceleration of the mass losses is consistent with the regional trend, but at a larger rate than the regional value. This acceleration is apparent comparing the maps of elevation change rates for the periods 1936–1990 and 1990–2007 (Fig. 4a, b), as well as in the map of elevation change acceleration (Fig. 4c).

Fig. 4a and b show the spatial distribution of the elevation change rates for the periods 1936–1990 and 1990–2007, respectively, where nearly ubiquitous thinning is observed. During the earlier period, the largest thinning is shown between 260 and 360 m of altitude, and approaches zero at ca. 420 m in the shadowed area of the cirque. Although at the upper elevations a limited zone shows a slight thickening (see Fig. 4a), this is not significant due to the rather large error of the map, stemming from the error of the 1936 DTM. This pattern of changes agrees with that observed in the regional study by Nuth et al. (2007), who pointed out that, during 1936–1990, the elevation losses were largest at the lower elevations, while the upper elevations slightly thickened, and is also consistent with other studies in the area (Bamber et al. 2004; Bamber et al. 2005). During 1990–2007, the thinning spanned the full altitude range of Ariebreen, though it was still more pronounced at the lower elevations. The changes at the upper elevations involve a switch from near-equilibrium conditions in 1936–1990 to clear thinning conditions in 1990–2007. Our elevation change rates for the latter period agree with the statement by Nuth et al. (2010) that, at higher elevations, Svalbard glaciers are generally thinning at rates from −0.1 to −1 m y⁻¹.

The likely reasons why the thinning rates of Ariebreen are largest at the lower elevations, and larger than the regional averages, are: (1) the morphology of Ariebreen, whose tongue is orientated towards the south and well exposed to solar radiation, while its upper part is largely shadowed, reducing melting by radiation; (2) the very low ice velocities of Ariebreen (maximum of ca. 1.6 m y⁻¹). On a more active glacier, the ice motion would replenish the ice lost by melting at the lower parts and the actual thinning would be less. However, on Ariebreen, with very low ice speeds, a large part of the melting would result in a surface lowering and the thinning rate would become higher.

As shown in Fig. 4c, the acceleration of elevation change has been largest in the mid-lower elevations, which differs from the observation by Kohler et al. (2007) and by James et al. (2012) that the thinning acceleration on the upper parts of their studied glaciers is larger or similar to that measured in the lower part. We first note that the glaciers that they studied are located in other Svalbard regions (northern and central Spitsbergen, and Edgeøya) and span elevation ranges different from that of Ariebreen. Second, both Kohler et al. (2007) and James et al. (2012) argue that changes in albedo will more strongly influence the response higher upglacier as surfaces there change from snow to bare ice, for instance as a consequence of a trend towards less winter accumulation. However, such a trend has not been reported for Ariebreen region. These arguments could explain the different behaviour of Ariebreen. Nevertheless, if we take into account the low quality of the 1936 map, based on oblique photography, the actual poor camera views towards Ariebreen when mapping its upper reaches, and the difficulties of mapping snow-covered areas, then our observation of higher accelerations at the upper reaches of Ariebreen cannot be established as a firm conclusion.