Introduction

Recent changes in atmospheric circulation have resulted in a 0.5˚C decade^–1 increase in the recorded annual mean air temperature at Longyearbyen on Spitsbergen, western Svalbard, and a precipitation increase of 1.7% decade^–1 since the late 1960s (Reference Førland and Hanssen-BauerFørland and Hanssen-Bauer, 2002). These data are supported by ice-core analyses from the ice cap Lomonosovfonna, the highest ice field on Spitsbergen, which indicated an accumulation rate increase of 25% over the latter half of the 20th century compared with the years 1715–1950 (Reference PohjolaPohjola and others, 2002).

Observations suggest that most low-altitude Arctic glaciers have been retreating since the 1920s, but with no significant increase in melting over the last 40 years (Reference McCarthy, Canziani, Leary, Dokken and WhiteMcCarthy and others, 2001). On Svalbard, ice masses are known to have generally retreated since the Holocene (Reference Hagen and LiestølHagen and Liestøl, 1990). However, the present-day mass balance of the majority of Svalbard’s ice caps and glaciers is poorly defined, so the contemporary response to recent climate change is difficult to assess. In situ mass-balance observations are mostly limited to a small number of more easily accessible glaciers in western Spitsbergen. However, the present climate on Svalbard is determined by a balance between two weather regimes: the first characterized by frequent passages of low-pressure systems from the southwest, and the second bringing the snow-bearing cold northeasterly polar winds from the Barents Sea. This zonal climate variation means that mass-balance measurements on Spitsbergen are probably not representative of the climate of ice masses to the east of Svalbard, such as Austfonna (8120 km²) and Vestfonna (2510km²), the two largest ice caps.

An estimate of the overall net balance of Svalbard ice masses of –4.5km³ a^–1 has been made by combining net balance altitude gradients for 13 different regions in Svalbard with a digital elevation model (DEM) (Reference Hagen, Melvold, Pinglot and DowdeswellHagen and others, 2003). Austfonna was included in this net balance estimate, and was determined to have a net balance close to zero using a balance ratio chosen to match that of other areas in Svalbard due to the lack of information on ablation rates.

In this study, we estimate the total mass balance for the accumulation zone of Austfonna by calculating the difference between measured and balance fluxes across the equilibrium line. The measured fluxes were the product of remotely sensed surface velocities and radio-echo sounded ice thicknesses. The balance fluxes were based on a specific mass-balance distribution, derived from ice-core data, integrated over the accumulation area. When referring to mass balance, the terminology of Reference Bamber and PayneBamber and Payne (2004) is used. This terminology defines specific mass balance to include only the sum of local accumulation and ablation; and local mass balance is used to describe the local mass change of the column. In order to obtain a picture of the spatial distribution of local mass balance, flux differences were apportioned according to drainage basin. Dividing each basin flux difference by the area of its accumulation zone gave a basin-mean local mass balance.

Methodology and Data

Calculation of balance fluxes

The balance flux is defined as the rate at which ice must be transported downstream in order for an ice mass to be in equilibrium with the accumulation and ablation rates and hence preserve a stable surface profile. The mean annual balance flux at the equilibrium-line altitude (ELA) for the whole ice cap and for individual drainage basin areas, S ^c, was calculated by integrating the distribution of mean annual specific mass balance B _n:

(1)

Drainage basin boundaries were geocoded and digitized from a glacier inventory of Svalbard (Reference Hagen, Liestøl, Roland and JørgensenHagen and others, 1993), and are referenced according to the World Glacier Inventory identification system.

The distribution of B _n was based on a set of transects of shallow ice cores drilled in 1998/99 in which the 1986 Chernobyl nuclear accident radioactive reference horizon could be detected (Reference Pinglot, Hagen, Melvold, Eiken and VincentPinglot and others, 2001). It has been shown that estimates of specific balance based on core data correlate well with direct measurements (Reference Lefauconnier, Hagen, Pinglot and PourchetLefauconnier and others, 1994). In order to calculate the B _n distribution, altitude gradients of B _n and estimates of the ELA based on the cores (Reference Pinglot, Hagen, Melvold, Eiken and VincentPinglot and others, 2001) were extrapolated over a 100m resolution grid using the Generic Mapping Tools minimum curvature spline interpolator with a tension of 0.65. The altitude gradients of B _n were then multiplied by the height above ELA, using elevations from the Norsk

Polarinstitutt 100m resolution DEM. This DEM was used rather than the interferometric heights calculated as part of the surface velocity method, in order to maintain independence between the two flux estimates.

Estimation of downslope velocity

The procedures for deriving glacier surface velocities using satellite radar interferometry (SRI) are well established (Reference Kwok and FahnestockKwok and Fahnestock, 1996). In this study, differential SRI was carried out on pairs of 3 day ERS-1 (European Remote-sensing Satellite) interferograms from 1994 and 1 day ERS-1/ERS-2 interferograms from 1996 (see Table 1; Fig. 1), using Gamma Remote Sensing software. In brief, pairs of interferograms were differenced to remove the effects of surface displacement on interferometric phase, leaving only topographic phase effects. After appropriate scaling, this topographic phase could be removed from one of the original interferograms. The resulting unwrapped interferograms then provided measurements of surface displacement in the line-of-sight (LOS) direction of the radar, over the period spanned by each interferogram.

Fig. 1. Airborne laser altimeter data points (personal communication from J. Bamber, 2005), and location of data frames listed in Table 1. Inset shows location of Nordaustlandet within Svalbard.

Table 1. Interferogram pairs (see Fig. 1 for locations) used for differential processing

Three-dimensional (3-D) surface velocities were derived from these LOS surface displacements by assuming that the ice flows parallel to the surface (Reference Kwok and FahnestockKwok and Fahnestock, 1996) and in the direction of maximum surface slope (Reference PatersonPaterson, 1994; Reference UnwinUnwin, 1998). The surface elevation used to compute flow directions was generated during the first part of the differential procedure by using a number of ground-control points (GCPs) to create a DEM from the topographic phase. Some GCPs were provided by assigning the coast, as identified on the multilooked synthetic aperture radar (SAR) intensity images, to a height of 0 ma.s.l. On the ice cap, 650 GCPs were taken from 1996 NASA airborne laser altimetry data (shown in Fig. 1; personal communication from J. Bamber, 2005). In order to determine flow directions, the DEM was not required to be of absolute accuracy. Differences between the effective heights of the scattering layers between lidar and the C-band radar, which may penetrate up to 9±2m in cold polar firn (Reference Rignot, Echelmeyer and KrabillRignot and others, 2001), are therefore not important.

In order to obtain as complete a coverage as possible over the ice cap, a composite of surface velocities was produced by infilling the 1996 results with measurements from 1994. Surface velocities were occasionally retrievable for the same area from more than one interferometric dataset. This overlap enabled us to ascertain that surface velocities had not changed significantly over this period, as changing the order of priority of datasets when producing the composite made no discernible difference to the resulting flux estimates.

The spatial resolution of the SAR data is ~4m in the azimuth direction and ~20m in the ground-range direction. After multilooking to reduce phase noise and conversion to a geographic coordinate system, the spatial resolution of the 3-D velocities was 50 m×50 m. A profile of annual surface displacements in the downslope direction was extracted along the equilibrium line at intervals of 50 m for use in the flux calculations.

Results

Balance fluxes

Based on the ice-core data, specific mass balances within the accumulation zone of Austfonna reach a maximum of 0.45 mw.e. a^–1 toward the summit of the ice cap at an altitude of ~800 m. Integrating the specific mass-balance distribution over the 5700 km² accumulation zone of Austfonna results in an estimated equilibrium-line balance flux of 10.5 ×10⁸m3w.e. a^–1. Basin equilibrium-line balance fluxes varied from 1.9×10⁸m3w.e. a^–1 for basin 21108, down to 8.0 ×104m3w.e. a^–1 for basin 25203, the variations being due to the altitude and areas of the different catchments (Fig. 2).

Fig. 2. Basin mean local mass balance. Shown in blue are those basins for which the mean local mass balance was positive, and in red those for which it was negative.

Measured velocities and fluxes

Downslope SRI velocities were obtained over almost all of Austfonna, Vestfonna and the two smaller ice caps to the southwest of Austfonna (Fig. 3). Outlet glaciers with maximum velocities of up to 100–150ma^–1 can be identified at various points around the ice cap. Ice divides are characterized by low velocities. Austfonna’s ELA as extrapolated from the ice-core estimates, and along which the measured velocities and ice thicknesses were extracted, varies from just over 100m in the southeast to over 460m in the northeast (black contour in Fig. 3). The ice thickness reaches a maximum of ~590m toward the centre of the ice cap, and for most of the north and east coasts the ice is grounded below sea level. Along the equilibrium line the ice thickness is 300–400m in the north and ~100m in the south.

Fig. 3. Composite of downslope interferometric velocities. In grey are regions for which it was not possible to retrieve velocities using the data selected for this study, due to either phase coherence losses or flow-direction restrictions. The black line marks the ELA.

The total measured ELA flux for Austfonna was (4.9± 1.0)×10^{8 m}3w.e. a^–1. Breaking the flux down into individual drainage basins, the largest contributions were 1.1× 10^{8 m}3w.e. a^–1 from basin 21106, and 0.7×10^{8 m}3w.e. a^–1 from basins 21108 and 25204, with estimated errors of about +0.3×10⁸m3w.e. a^–1.

Discussion

The total mass balance of the accumulation zone of Austfonna was found to be (5.6±2.0)×10⁸m3w.e. a^–1. This value represents just over half the annual accumulation of the ice cap and would seem to indicate that recent accumulation increases are leading to a steady gain in mass. However, when the spatial distribution of total mass balance over the ice cap is analyzed it becomes obvious that the imbalance between balance and measured fluxes is far from uniform. About 75% of the positive total mass balance comes from just three basins, 21108, 21110 and 22203, all of which are known to be surge-type glaciers in their quiescent phases.

Basin 21108 was shown to have been in surge in 1992, but to have slowed down by 1994 (Reference Dowdeswell, Unwin, Nuttall and WinghamDowdeswell and others, 1999). By 1996 it is shown here to have a mean local mass balance of 0.18mw.e. a^–1, and thus to be continuing to recover its pre-surge profile. Between 1936 and 1938, basin 21110, Bråsvellbreen, underwent the largest surge known for any ice mass (Reference Drewry and LiestølDrewry and Liestøl, 1985): the 30 km long ice edge advanced by 2 km; 60 years later it is still accumulating mass. Basin 22203, Etonbreen, also surged in 1938 (Reference Hagen, Liestøl, Roland and JørgensenHagen and others, 1993).

The local mass-balance distribution suggests that other basins, notably 22204 (Winsnesbreen) and 25105, may also be accumulating mass prior to a surge. Neither of these basins shows signs of ever having surged, nor have they been identified as surge-type glaciers on the basis of driving stresses (Reference DowdeswellDowdeswell, 1986) or glacier length and substrate (Reference Jiskoot, Murray and BoyleJiskoot and others, 2000). Basin 25204, Leighbreen, was identified by Reference DowdeswellDowdeswell (1986) as possibly being of surge type on the basis of its low driving stresses and surface profile. Measured velocities, deriving from 1994 data, were <40ma^–1 at all points on this glacier and showed no acceleration relative to 1992 velocities. Hence, although its local mass balance was negative in 1994, flow rates do not suggest that it was in surge.

In measuring the equilibrium fluxes, this study made two assumptions referred to, but not quantified, in the error analysis. The first was that all of the ice transport was achieved by basal sliding rather than by ice deformation, and the second was that the velocities measured are representative of annual velocities.

It is probable that for some sections of the equilibrium line the first assumption does not hold true, and that the sliding assumption causes the flux to be overestimated by up to 20% (Reference PatersonPaterson, 1994). This overestimate is only likely to be the case in areas of low flux, as it has been estimated that for much of Austfonna the maximum flow rate that can be achieved by deformation alone is 5 ma^–1 (Reference Dowdeswell, Unwin, Nuttall and WinghamDowdeswell and others, 1999), and it is apparent that at the ELA most surface velocities exceed this. In addition, plumes of sediment-laden basal meltwater have been identified in Landsat images for a number of tidewater-terminating glaciers along the eastern edge of Austfonna, indicating that their bases are at pressure-melting point and hence sliding is likely (Reference Dowdeswell and DrewryDowdeswell and Drewry, 1989). Of the individual basins where a negative total mass balance is indicated, only basin 21106 would be tipped into a positive balance by a basin-wide 20% decrease in flux.

If the second assumption of no seasonal variations in velocity does not hold true, it may be expected to have the opposite effect, i.e. the late-winter or early-spring flux rates measured here might underestimate mean annual flux rates and hence result in an overestimate of total mass balance. In order for the total mass balance for the ice cap to be zero, the mean annual velocities at all points around the equilibrium line would have to be double those measured. This ratio of mean annual to spring velocities would far exceed the seasonal variations generally observed on other polythermal Arctic glaciers, for example, on Hessbreen, Spitsbergen (Reference Sund and EikenSund and Eiken, 2004), Storglaciaren, Sweden (Reference Hooke, Brzozowski and BrongeHooke and others, 1983), or Jakobshavn Isbræ, Greenland (Reference Luckman and MurrayLuckman and Murray, 2005). Kongsvegen (Reference Melvold and HagenMelvold and Hagen, 1998) and Finsterwalderbreen (Reference Nuttall, Hagen and DowdeswellNuttall and others, 1997) on Spitsbergen have both been observed to have summer surface velocities double those of winter at upper levels. However, this seasonal velocity increase translates into a mean-annual to spring flux rate ratio of 1.5 because of the number of months over which the velocities were measured.

Evidence in support of continuing increases in total mass balance of the ice cap comes from repeat-pass airborne laser altimetry surveys in 1996 and 2002 (Reference Bamber, Krabill, Raper and DowdeswellBamber and others, 2004), the surface elevations acquired in 1996 being those used as ground control for the interferometry in this study and shown in Figure 1. The results of the surveys indicated that, from 1996 to 2002, ice-surface elevations over central regions of the ice cap increased by an average of 0.5 ma^–1. Even allowing for the conversion from ice to water equivalent, this value is twice as large as the largest mean local mass balance calculated here.

Reference Bamber, Krabill, Raper and DowdeswellBamber and others (2004) concluded that the elevation increases (dh/dt) detected by the laser altimetry surveys were not dynamic in origin but were due to increased accumulation rates. This conclusion was reached partly on the basis that the increases spanned several dynamically independent drainage basins. For example, there was no change in dh/dt crossing from basin 21108 to 22203 (referred to as basins 3 and 17, respectively, in Reference Bamber, Krabill, Raper and DowdeswellBamber and others (2004)). Our study indicates that although these two basins surged some 55 years apart, their accumulation zones exhibit very similar mean local mass balances. The elevation increase detected by the altimetry survey appears to decrease markedly from basin 21108 to basins 21106 and 25204, coinciding with the change from positive to negative mean local mass balances detected here. The measured dh/dt’s mostly post-date the ice-core accumulation rate estimates, which showed no signs of temporal trend between 1963–86 and 1986–98 (Reference Pinglot, Hagen, Melvold, Eiken and VincentPinglot and others, 2001). Therefore, we propose that the extensive elevation increases detected by the laser altimetry survey may be the result of both ongoing basin dynamics and a recent increase in accumulation rate.

In interpreting any imbalance between balance and measured fluxes in terms of mass gain of the ice cap, it is important to note that a comparison is being made here between quantities that are representative of different timescales. The balance fluxes, being based on ice cores, are averaged over more than a decade and hence can be taken to represent current climate. The measured fluxes are only a contemporary snapshot but, for steady-flow glaciers, are a reflection of past climatic conditions because of the long dynamic response time of Arctic ice masses. An order-of-magnitude estimate of the response time for Austfonna, given by the ratio of the maximum ice thickness to the ablation rate at the terminus (Reference PatersonPaterson, 1994), is 1000 years. Alternatively, relative response times of individual drainage basins can be inferred from the residence times, which were all in excess of 500 years.

It is also important to emphasize that this analysis deals only with the accumulation zone of Austfonna. In order for the mass balance of the ice cap to be interpreted in terms of its impact on global sea levels, ablation rates and calving fluxes must also be considered. It may be possible to use remote-sensing methods to estimate calving fluxes, but at present there is very little information available on ablation rates for Austfonna.

Conclusions

Although predictions and observations in the Arctic indicate that Svalbard’s ice caps will be important indicators of climate change, mass-balance assessments of glaciers in Svalbard are very limited. This study aimed to compare measured and balance fluxes at the ELA on Austfonna, and showed that during the period 1994–96 the accumulation zone was in a state of positive mass balance. Measured surface velocities obtained using SRI combined with RES ice thicknesses gave an equilibrium-line annual flux of (4.9 ±1.0)× 108^m3w.e. a^–1, equivalent to about half the total annual accumulation. The spatial distribution of local mass balance was revealed by separately analyzing each drainage basin. This analysis showed the positive mass balance to be contributed mainly by three glaciers known to be in surge recovery. The mean local mass balance within these basins is not inconsistent with elevation changes for 1996–2002 measured using repeat laser altimetry surveys, but indicates an underlying dynamic component to the changes.