3.1. GPR and GPS data

During the 2003/04 expedition, a 50 km long radar survey line was collected along the main flowline of Potsdam Glacier. Three cross-profiles were surveyed, each one being ˚ km long (Fig. 1b). We used a commercial RAMAC radar system (Malå Geoscience, Sweden) with a bistatic shielded 500 MHz antenna that was connected to the central unit via fibre optic cables. Data were stored on a Husky Px5 computer. The GPR antenna was mounted behind a Nansen sledge pulled by a snowmobile at an average speed of ~5kmh^–1. Traces were recorded every 0.5 m, triggered by a distance wheel. Each trace consisted of 2048 samples in a 400 ns time window, thus mapping the upper ~35–38m of the snowpack. Differential GPS data were collected simultaneously with GPR data. The roving station was mounted on the snowmobile, and two reference stations were situated at the field camp, i.e. about 1 km south of point F33 (see Fig. 1), and at the Schirmacheroase, respectively. The GPS data were collected every 1 s using a Trimble 4000SSi receiver and a choke-ring antenna. Processing of GPS data yields positions for the GPR profiles as well as surface elevation. The relative accuracy between the differential GPS points is generally in the range of several millimetres to a few centimetres for longitude and latitude, and of some centimetres to about one decimetre for the elevation. However, due to the movement of the roving station over severe sastrugi fields, we assume that actual accuracy declines to some centimetres for longitude and latitude and reaches a few decimetres for the elevation. The radar data were processed using Paradigm Geophysical FOCUS version 5.0 software by applying gain control, filtering using a bandpass Butterworth filter with cutoff frequencies of 350 and 850 MHz, and correction for the first arrival of the direct wave. From the processed radargrams, IRHs were tracked semi-automatically using Landmark OpenWorks release 2003.0 software. Within the depth section covered by the firn cores (given below), two internal horizons could be tracked throughout more than one GPR profile.

3.2. Firn cores and snow samples

At five locations (Fig. 1b; Table 1) along the radar profiles, shallow, 12.5–13.5m deep, firn cores were drilled. At the same sites 2 m deep snow pits were dug which were probed in intervals of 5 cm, giving 40 samples per pit. The density of the snow samples was determined in situ from the weight and the known volume of the probing cylinder.

Table 1. Location of firn cores

The firn cores and snow samples were transported to Germany and analyzed in the cold laboratory at the Alfred Wegener Institute, Bremerhaven, for physical and chemical properties. Snow-sample data were used to link firn-core data to the surface due to poor core quality in the upper 1–2m of drilling. The δ¹⁸O ratio was determined by mass spectrometry for both the firn cores as well as the snow samples. Firn-core analysis covered measurements of density using gamma-attenuation profiling (GAP) as well as dielectric profiling (DEP) that yield density, dielectric permittivity and electrical conductivity of the firn (Reference WilhelmsWilhelms, 1996, Reference Wilhelms2005).

3.3. Determination of accumulation rates

We derive distributions of electromagnetic wave speed and cumulative mass with depth from the firn-core data. The mean values of density, dielectric permittivity and conductivity of all five firn cores are used, since no further information about the lateral variations of those parameters between the firn-core drilling sites is available. Cumulative snow mass is obtained by integration of the mean density profile derived from the GAP measurements. Calculation of electromagnetic wave speed from DEP-derived parameters follows the procedure described by Reference Eisen, Nixdorf, Wilhelms and MillerEisen and others (2002). Error estimates are given below. Since the firn cores reach only a depth of about 12 m below the surface, the data of the two-way-travel-time (TWT)–depth and cumulative-mass– depth models were extrapolated down to 25 m depth. Extrapolation was done using the MATLABTM polyfit routine by fitting a third-order polynomial (Reference Richardson, Aarholt, Hamran, Holmlund and IsakssonRichardson and others, 1997; Reference FrezzottiFrezzotti and others, 2005) yielding a correlation coefficient of R = 0.90. Age–depth profiles are determined by counting the δ¹⁸O peaks which indicate summer maxima (Reference McMorrow, van Ommen, Morgan and CurranMcMorrow and others, 2004 and references therein).

Consistent dating of the different firn cores proved difficult due to local variations in the δ¹⁸O profiles which did not allow clear identification of maxima and minima for every firn core. However, firn core F39 shows a δ¹⁸O profile with pronounced maxima and minima (Fig. 3d), so it was used as a reference core for interpreting the radar data. F332 could likewise be dated sufficiently by its δ¹⁸O profile. However, since the tracked IRHs do not reach up to this core, F332 could not be used for dating the GPR layers. The two tracked horizons (IRH 1 and IRH 2; see Fig. 2b) are dated against F39 by comparing the depth of the respective IRH at the coring location with the depth–age scale of the firn core. The depth values for the IRHs at the drilling location are 8.65 m (IRH 1) and 11.55 m (IRH 2), and their estimated time of origin is 1970 and 1980, respectively, ±2 years for each dating. Three more IRHs (IRH Ia, Ib and Ic; see Fig. 2b) that could only be tracked throughout the uppermost ~20 km along the main flowline are also dated by the depth–age scale of F39: their estimated times of origin are 1995, 1992 and 1989 (±1 year for each dating).

Fig. 2. (a) Processed radargrams from profiles 041201 and 041202. The white arrows mark the IRHs chosen to determine the approximate beginning of the transition zone from accumulation to ablation. (b) Depth distribution of tracked and dated IRHs. Black solid line: IRH 1 (1980); black dashed line: IRH 2 (1970); grey dashed line: IRH Ia (1995); light grey line: IRH Ib (1992); dark grey line: IRH IC (1989).

Fig. 3. Data from firn core F39: (a) dielectric permittivity; (b) electrical conductivity; (c) density (from GAP); and (d) δ¹⁸O.

The accumulation rate along the GPR profiles can be calculated by dividing the cumulative mass difference of two selected IRHs by their respective age difference.

3.4. Estimation of errors

Errors in our density–depth distribution are assumed to be up to 14% at 12m depth, determined from the difference between the mean values (i.e. the model used) and F39 and F27, respectively (Fig. 4c). This includes errors from the density measurements using GAP which are up to 10 kgm^–3 (Reference WilhelmsWilhelms, 2005). Accuracy of DEP-derived parameters is within 1% (Reference WilhelmsWilhelms, 1996). Errors in TWT–depth conversion using DEP data are up to 1% as shown by Reference Eisen, Nixdorf, Wilhelms and MillerEisen and others (2002). Errors in calculations of the cumulative mass

Fig. 4. (a) Density distribution of all firn cores. Thick grey line: F33; solid black line: F332; light grey line: F39; dark grey line: F331; black dotted line: F27. The density plots are offset by intervals of 50 kgm^–3 in order to distinguish the individual cores. (b, c) Model for TWT–depth (b) and cumulative mass–depth (c). In each plot the solid line corresponds to the model derived from the mean values, the dashed line to the model derived from F39, and the dotted line to the model derived from F27. (d) Depth–age scale as derived from the dating of F39.

from the density profiles are likewise up to 1% due to error propagation. The dating uncertainty of the two IRHs used for determination of area-wide accumulation rates is ±2 years. Errors in tracking of IRHs are up to ±2 ns, which yields depth variations of up to ±0.2 m. However, for the two dated IRHs (IRH 1 and 2) this latter uncertainty does not affect the estimated age since 8.65 ±0.2m and 11.55±0.2m still correspond to the years 1980 and 1970, respectively (Fig. 4d). From analytic error propagation, the overall root-mean-square error in accumulation rates becomes 11.5% for profile 041201. The largest error was found to be 20%. We therefore assume that the accumulation values presented in this paper are accurate within about 12% on average. Errors from ray-path geometry due to the separation of transmitting and receiving antenna are neglected, since transmitter and receiver are separated by only 0.18 m. For the same reason, refraction within the snowpack can be neglected (Reference Sinisalo, Grinsted, Moore, Kärkäs and PetterssonSinisalo and others, 2003).

4.1. GPR profiles

In the processed radargrams the undulations of internal layers can clearly be seen (Fig. 2a). Internal layers show large slopes along profile 041201. At some locations the vertical distance between separate layers is very small (e.g. at –16 to –17 km), whereas a few kilometres away the same layers are spaced more widely (e.g. from about –10 to –15 km). Comparable undulating patterns have been reported before in DML, for example by Reference Richardson-NäslundRichardson-Näslund (2001). Closely spaced layers indicate areas with less accumulation, whereas more widely spaced layers are associated with regions of higher accumulation. Along profile 041202 (Fig. 2a), layers ascend in the direction of glacier flow (with the exception of the local undulations in the first 6–7 km). Such patterns are characteristic for ablation areas and the transition from an accumulation area to an ablation area, where internal horizons come to the surface due to surface erosion. However, it is not possible to resolve actual ablation from very low accumulation by GPR internal layering. A layer outcropping at the surface at a certain location along the GPR profile would only yield zero values for accumulation or ablation for this point. Besides, the isochronal layers cannot be traced up to the surface since they are lost within the time window of the direct wave (here the upper ~20 ns, equivalent to ~2m; Fig. 2a). Assuming zero advection, ascending layers with angles <90˚ relative to the surface would still provide accumulation, albeit low values (Fig. 2a, near x = 25 km). Without advection, therefore, only layers emerging perpendicularly at 90˚ indicate ablation. Yet in our case we can conclude from the ascending IRHs that the transition zone from accumulation to ablation is present and visible in the radargram. Since we do have advection effects here, we cannot clearly define the beginning of the ablation area. Thus, we do not address the actual ablation area, but rather the transition zone where very low accumulation and also local ablation might occur. We define the beginning of this zone by the point where the first IRH would reach the surface. Using two different IRHs marked by the white arrows in Figure 2a, and extrapolating from their respective slopes the points where they would reach the surface, results in x = 21.35 km and x = 23.84 km, respectively. Since these IRHs could not be dated, we are unable to apply a sufficient correction for glacier flow velocity. By choosing one very shallow and one rather deep IRH we can at least conclude that the transition zone from very low accumulation to ablation starts at this part of Potsdam Glacier between about 21 and 24 km downstream of F33. Thus, the actual ablation area is to be expected slightly farther down-glacier, which is in accordance with the description of Reference Bormann and FritzscheBormann and Fritzsche (1995) and Reference HorwathHorwath and others (2006).

4.2. Firn-core data and density distribution

The parameters derived from the firn-core analysis are depicted in Figure 3 for firn core F39. Dielectric permittivity as well as density increase with depth (Fig. 3a and c), but the parameters do not reach values of solid ice (ρ = 917 kgm^–3) within the depth section covered by the firn cores. Some of the peaks of the density coincide with observed ice lenses in the firn core.

Figure 3 shows the models for TWT–depth (Fig. 3b) and cumulative mass–depth (Fig. 3c) as derived from the mean values and from the ‘extreme’ cores, i.e. the core with the lowest mean density (F39) and the core with the highest mean density (F27). Down to about 5–6m depth, the density values of the different firn cores are very similar (Fig. 4a). Below this depth they start to differ slightly, up to ~100– 150 kgm^–3 at about 12 m depth. In the upper 6–7 m, density variations within one specific firn core are usually larger than the variations between the different cores at the same depth. Generally, F27 shows the largest density values. This core was drilled on the lower-elevation part of the glacier where the radar data indicate an ablation area nearby. Farther east a blue-ice area is found (Reference Bormann and FritzscheBormann and Fritzsche, 1995; Reference Korth and DietrichKorth and Dietrich, 1996; Reference Isaksson and KarlénHorwath and others, 2006) where the surface density should be higher than in the firn areas. Thus it can be assumed that density in the study area will increase in the direction of glacier flow, which is in accordance with our findings. However, density values of F27 are still in the range of firn density and do not reach the density of solid ice. Therefore we conclude that this part of the glacier is dominated by firn, at least in the uppermost 12 m.

4.3. Accumulation rates

The mean accumulation rate in the study area is derived for the periods 1970–80, 1970–2004 and 1980–2004, with 2004 corresponding to the surface at the time of data collection (Table 2). The depth distribution of the dated IRHs is depicted in Figure 2b. Taking into account a mean glacier flow velocity of 45 ma^–1 results in the accumulation distribution along the main flowline (Fig. 5c). Furthermore, annual accumulation rates are obtained from the two dated firn cores (Table 2; Fig. 5a).

Table 2. Accumulation values in the study area, given in kgm^–2 a^–1. Note that the top three rows (GPR-based accumulation rates) represent spatial means from the study area, whereas the bottom two rows (firn-core derived accumulation series) represent temporal accumulation means for the time period covered by the firn cores at the respective coring locations

Fig. 5. (a) Year-to-year accumulation values obtained from firn cores F39 (black solid line) and F332 (grey solid line); the respective core means are depicted by the black dashed line (F39) and the grey dashed line (F332). (b) Accumulation rates for a 10 year mean for F332 (grey dashed line) and F39 (black solid line). (c) Variability expressed as per cent difference of the respective core mean. Grey line/grey triangles: F332; black line/black squares: F39.

5.1. Temporal characteristics

Comparing the mean values of the GPR-derived accumulation rates from Table 2, we conclude that the spatial variability exceeds the mean temporal variability for the periods considered. This has been reported before at other places in East Antarctica, for example by Reference FrezzottiFrezzotti and others (2005). The temporal variations in accumulation rates derived from GPR measurements for the periods 1970–80 and 1980–2004 are about 1.5%, calculated from the mean values of the respective periods. However, interannual variability obtained from the two dated firn cores (Fig. 5a) is high, showing one-fold standard deviations of 30% and 39%, respectively (Table 2). Differences in per cent of the firn-core mean values range from –63% to +103% for F332 and from –46% to +65% for F39 (Fig. 5c). A mean over 10 years of the accumulation series obtained from the firn cores indicates a slight decrease at F332 and an even smaller increase at F39 for the period 1984–93 (Fig. 5b). Although the timescales are rather short, this suggests that the accumulation pattern comprising the last 30 years is quite stable on decadal scales in relation to the annual variability.

5.2. Spatial characteristics

Generally, our mean core-derived accumulation rates are about 12–23% higher than the average GPR-based accumulation rates in the investigation area. We therefore conclude that the spatial representativity of the firn cores is limited, as has been discussed before for West Antarctica (Reference Spikes, Hamilton, Arcone, Kaspari and MayewskiSpikes and others, 2004) and the western part of DML (Reference Richardson-NäslundRichardson-Näslund, 2001). The spatial variability of GPR-derived accumulation rates along the main flowline is very high (Fig. 6c). Differences in per cent of the mean range from –81% to +125% for the period 1980–2004, showing an undulating pattern. Accumulation rates show strong spatial gradients of up to 105 kgm^–2 a^–1 km^–1, with pronounced changes from increasing to decreasing accumulation in the direction of glacier flow, sometimes even within <1 km. For example, going 1 km upstream from near F33 yields a 10-fold increase in accumulation (from about 30 to 330 kgm^–2 a^–1) for the interval 1970–80. Average accumulation gradients are on the order of 23 kgm^–2 a^–1 km^–1. Generally, a decrease in accumulation in the direction of glacier flow is visible. The linear trend along profiles 041201/041202 amounts to –4.9 kgm^–2 a^–1km^–1. This is in accordance with the observation that IRHs tend to come to the surface at lower elevations on the main flowline (Fig. 2a).

Fig. 6. (a) Surface elevation; (b) linearly detrended surface elevation; (c) accumulation pattern; and (d) gradient of accumulation and surface slope on the main flowline. The solid curve in (c) corresponds to the period 1980–2004, the dashed curve to 1970– 2004 and the dotted curve to 1970–80. The solid line shows the linear trend fitted to the accumulation pattern. The solid line in (d) corresponds to the slope of surface elevation (vertically exaggerated by a factor of 5) in mm^–1, and the dashed line represents the slope of accumulation (1980–2004) in kgm^–2 a^–1m^–1.

Surface slope and slope of accumulation (Fig. 6d) show regular undulations similar to those in surface elevation (Fig. 6a and b) and in accumulation (Fig. 6c). Reference Anschütz, Eisen, Rack and ScheinertAnschütz and others (2006) show that these undulations are likely caused by a feedback system between atmosphere and cryosphere similar to the features ruling the genesis of megadunes on the polar plateau (Reference FrezzottiFrezzotti and others, 2002). Comparable association between surface slope and accumulation has been reported before in Antarctica (e.g. Reference Black and BuddBlack and Budd, 1964; Reference Pettré, Pinglot, Pourchet and ReynaudPettré and others, 1986; Reference GoodwinGoodwin, 1990; Reference Vaughan, Anderson, King, Mann, Mobbs and LadkinVaughan and others, 2004; Reference Eisen, Rack, Nixdorf and WilhelmsEisen and others, 2005) and is attributed to wind influence (Reference King, Anderson, Vaughan, Mann, Mobbs and VosperKing and others, 2004) where accumulation maxima are located within surface elevation troughs and on the windward slopes. Local deviations from this general pattern in our data are possibly due to different local-scale near-surface winds. Another reason probably arises from the correction for glacier flow where we used a measured mean flow speed of 45 ma^–1 to correct the GPR layer depths and thus the accumulation pattern. Flow speed is not constant along the main flowline but increases with decreasing elevation. Measurements of spatial variations of ice flow are too inaccurate to allow a more detailed correction of the isochronal layers. Thus, accumulation maxima can be slightly misplaced due to locally incorrect consideration of glacier flow speed. However, the spatial variability of the accumulation rate is not affected by these errors.

5.3. Comparison with other studies

Other ground-borne data in this region are sparse, but there are a few accumulation values available from pit studies and stake readings.

Reference Bormann and FritzscheBormann and Fritzsche (1995) report a mean accumulation value derived from pit studies in the vicinity of a drillhole at 70˚58′ S, 11˚22′ E, about 15km north of our radar profiles 041201/041202, that is about 130 kgm^–2 a^–1 (1950–84) which is in accordance with our mean values.

The mean annual accumulation from the stake readings presented by Reference Korth and DietrichKorth and Dietrich (1996) on the Insel traverse route (going from Novolazarevskaya station to Humboldt-fjella; see Fig. 1a) is 131 kgm^–2 a^–1, with a standard deviation of 140% because some of the stakes are located in an ablation area. This comparison should be viewed with caution since the stake readings cover the period 1988–93, so the time interval of the different accumulation values is not the same. Furthermore, Reference Korth and DietrichKorth and Dietrich (1996) do not state actual values for the densities used to calculate the accumulation. However, their mean value is in the range of our mean values, indicating that the overall distribution of accumulation is quite stable for the different time periods, although there are obvious small-scale differences. Their values obtained at stakes in the vicinity of our profiles, about 1 km away from the main flowline, are ~250 kgm^–2 a^–1 which is much larger than our nearby values of ~50 kgm^–2 a^–1. Yet accumulation rates for the intervals 1980–89, 1980–92 and 1980–95 along profile 041201 (calculated from IRH Ia, Ib and Ic; see Fig. 2b) are 18–35% higher than the other values in our study. Taking into account the report from Reference Korth and DietrichKorth and Dietrich (1996), this might indicate a higher accumulation at this part of the glacier during the 1980s and early 1990s of about 25% compared with the previous period (1970–80). Due to the dating uncertainty of F39, caution has to be used with these findings. However, dating uncertainty does not affect the accumulation pattern itself or the spatial variability which is clearly demonstrated by our study.

The accumulation values in the study area presented here are less than those reported by Reference Giovinetto and ZwallyGiovinetto and Zwally (2000) who derive values of ~200–250 kgm^–2 a^–1 for this region of Antarctica. Reference Vaughan, Bamber, Giovinetto, Russell and CooperVaughan and others (1999) report the same as Reference Giovinetto and ZwallyGiovinetto and Zwally (2000). Both studies are concerned with larger areas and neglect small-scale features. Our mean value of 141 kgm^–2 a^–1 (1970–2004) is less than these findings because there is an ablation area in the vicinity of our study area, which influences our results. Reference Van de Berg, van den Broeke, Reijmer and van MeijgaardVan de Berg and others (2006) derive specific surface mass balance (SSMB) from a regional atmospheric climate model, estimating precipitation, sublimation and melt. Snowdrift processes are not considered. The horizontal resolution is about 55 km. They derive values of ~200 kgm^–2 a^–1 for the vicinity of our study area, which is likewise larger than our mean accumulation values. Our study reveals a significant influence of blowing snow on the accumulation values in the area of investigation, so neglecting this process likely results in an overestimated SSMB for this area as given by Reference Van de Berg, van den Broeke, Reijmer and van MeijgaardVan de Berg and others (2006). Large-scale compilations like those cited above are usually based on a limited number of scattered observations. They do not take into account the spatial representativity of the respective point measurements which may be obscured by local-scale variability. Our study demonstrates a very high spatial variability in this area of coastal DML and indicates a limited representativity of firn-core derived accumulation data which are on average higher than the GPR-derived accumulation values. This might explain the higher accumulation rates in large-scale compilations of this area.

5.4. Implications for satellite-data interpretation

Satellite observations of surface elevation, for instance by European Remote-sensing Satellites-1 and -2 (ERS-1/-2) and the Ice, Cloud and land Elevation Satellite (ICESat), and gravity from the GRACE mission (Reference Tapley, Bettardpur, Watkins and ReigberTapley and others, 2004) can provide mass-distribution changes according to the mission-specific spatial and temporal resolutions. Combining GRACE data and altimetry data helps to discriminate ice-mass changes (Reference ZwallyZwally and others, 2005) from height changes induced by glacial isostatic adjustment or by changes in snow and firn density (Reference Wahr, Wingham and BentleyWahr and others, 2000). However, the effective spatial resolution of GRACE monthly solutions is only several hundred kilometres. To account for the GRACE error behavior and to separate mass signals from different geographic origins, adapted filter techniques have to be utilized (Reference Swenson and WahrSwenson and Wahr, 2002; Horwath and Dietrich, 2006b). Hence, GRACE provides only integrated mass-balance estimates over large areas.

Trends in ice-mass changes over a few years derived from satellite observations may be either due to interannual fluctuations in net ice surface mass balance or due to longterm ice dynamics. To distinguish between the two effects, information on the temporal and spatial covariance of the interannual surface mass-balance fluctuation is needed.

With regard to spatial covariance, Reference Anschütz, Eisen, Rack and ScheinertAnschütz and others (2006) report spatial autocorrelation lengths of only about 1 km for surface mass-balance fluctuations. For values averaged over ~100km the small-scale variations (deposition noise) are averaged out, so the standard deviation of temporal fluctuations will be smaller than the values of 30– 39% obtained from the firn-core time series (Table 2). Therefore, such small-scale fluctuations will not be resolved by GRACE. Concerning temporal covariance, there is, again, a large portion of small-scale deposition noise in the firn-core data: the autocorrelation length of the firn-core time series is only 0.6 years (Fig. 5a). However, the accumulation pattern seems fairly stable on decadal scales (Fig. 5b).

The GRACE mission, launched in 2002, is planned to cover ˚ years in total. Considering the discussion above, long-term surface mass-balance changes showing a considerably large spatial pattern would be sensed by GRACE. Hence, regional studies of mass fluctuations are very important to qualify the spatio-temporal behaviour of the ice surface mass balance in larger areas and to discriminate surface mass-balance fluctuations from long-term ice dynamics. In this context, the results presented by this study, combined with further estimates yielded by other authors for adjacent regions (e.g. Reference Richardson-NäslundRichardson-Näslund, 2001; Reference Rotschky, Eisen, Wilhelms, Nixdorf and OerterRotschky and others, 2004; Reference FrezzottiFrezzotti and others, 2005), provide valuable ground-based information to validate and interpret GRACE observations.