GPR and GPS

In the Antarctic summer season 2004/05, GPR measurements were carried out along an ice flowline and on cross-profiles (Fig. 1b) using a bistatic shielded 500 MHz antenna (RAMAC, Malå Geoscience, Sweden) which was pulled by a snow vehicle at an average speed of ∼5 km h⁻¹. Traces were recorded every 0.5 m in a time window of 400 ns, triggered by an odometer. Simultaneously, kinematic GPS data were collected at a sampling interval of 1 s using a Trimble 4000SSi receiver and a choke-ring antenna. The roving station was mounted on the snow vehicle, and the reference station was located on Weigel Nunatak, 10 km south of Kottas Camp (Fig. 1).

Global positioning system (GPS) data provided information about the surface elevation and horizontal positions along the GPR profiles. The offset between the GPS and GPR antennae was taken into account for the positioning of the GPR traces. GPR data were filtered using a bandpass Butterworth filter with cut-off frequencies of 350 and 850 MHz, automatic gain control (AGC) and correction for the first arrival of the direct wave. From the processed GPR data, IRHs were tracked throughout the GPR profiles where possible. Conversion of travel time to depth is given below. However, the uppermost layers (up to 1.5–2 m depth) are not visible in the radargram since they are lost within the time window of the direct wave. We restrict ourselves to the upper 12 m since this is the maximum depth of isochronous layers which can be dated using the firn cores (see below). On the profile 051202, four IRHs are tracked within this depth range (Fig. 2) against the ice-flow direction on a flowline (Fig. 1b).

Fig. 2. Depth distribution of the tracked IRHs for profile 051202. The solid horizons are used to calculate accumulation rate.

Firn cores

At four selected points (Fig. 1b; Table 2) of the GPR profiles, shallow firn cores were drilled to depths of 12.0–12.7 m.

Firn-core analyses included density measurements using, γ-attenuation profiling (GAP) over intervals of 2 mm and dielectric profiling (DEP) over 5 mm intervals (Reference WilhelmsWilhelms, 1996, Reference Wilhelms2005), yielding information about density, dielectric permittivity and the electrical conductivity of the firn. Chemical profiling was performed using a combination of continuous flow analyses (CFA) and ion chromatography (IC) (Reference RuthRuth and others, 2004). Mass spectrometry was used to derive a δ¹⁸O profile for each core with a sample size of 25–30 mm. Firn-core parameters from firn core FB0501 are exemplified in Figure 3.

Fig. 3. Firn-core parameters from FB0501: (a) dielectric permittivity (from DEP); (b) electrical conductivity (from DEP); (c) density (from GAP); (d) δ¹⁸O profile; (e) electrolytical conductivity (from CFA); and (f) sulphate (from IC).

Cumulative snow mass (i.e. the mass of overlying snow/firn up to a certain depth) was obtained by integrating GAP density profiles. Radar wave speed was calculated from the profiles of dielectric permittivity, to convert two-way travel time (TWTT) of tracked IRHs to depth and cumulative mass, following Reference Eisen, Nixdorf, Wilhelms and MillerEisen and others (2002) and Reference Anschütz, Eisen, Oerter, Steinhage and ScheinertAnschütz and others (2007), respectively. To establish models for TWTT–depth and cumulative mass–depth the mean profiles of density and dielectric permittivity for all four firn cores were used, since there is no further information about lateral variations of those variables between the drilling sites. However, profiles of density and dielectric permittivity show only small deviations between the four firn cores. In general, fluctuations within one specific core are higher than differences between the firn cores at the same depth (not shown).

Determination of accumulation rates

The δ¹⁸O profile and the chemical profiles of FB0501 (Fig. 3d–f) have been used to establish a depth–age scale as a dating reference for the tracked IRHs on profiles 051202 and 051203 (cross-profile; see Fig. 1b). However, unambiguous dating was not possible by the chemical profiles alone. The chemical profiles were therefore used to support the dating based on the δ¹⁸O profiles. Dating of the firn cores was carried out by annual-layer counting, with the δ¹⁸O peaks indicating summer maxima. The density profiles of the firn cores were used to calculate annual accumulation rates from the snow mass of the annual layers. Note that the firn cores do not reach up to the year 2005 (the age of the surface at the time of data collection) due to poor core quality in the upper 1–2 m. A mean accumulation rate was therefore used to estimate the age of the first datable layer, obtained from two nearby snow pits. Strain rates for this particular area are unknown, so they are not taken into account in our calculation of accumulation rates. As we are focusing on shallow depths, layer thinning can be assumed to be negligible.

Using the depth–age scale obtained from the dated firn cores, the IRHs were dated by comparing their depth values at the coring location with the age given by the depth–age scale. Accumulation rates along GPR profiles were calculated by dividing their cumulative mass difference by their age difference. Following the approach of earlier studies, the isochronous property of the IRHs on profile 051202 was tested by comparing the age of the two IRHs at the positions of FB0501, FB0502 and FB0503, yielding differences of up to ±1 year which is within the range of the dating uncertainties. We thus regard the IRHs as isochrones.

In order to account for temporal differences td of accumulation rates of IRH intervals along the GPR profiles, we define

where a denotes accumulation along the profile and t _i the respective time period.

Calculation of errors in accumulation rates follows the discussion of Reference Anschütz, Eisen, Oerter, Steinhage and ScheinertAnschütz and others (2007). Deviation of the density profiles from the different firn cores is as large as 7%, including measurement errors from GAP (up to 10 kg m⁻³; Reference WilhelmsWilhelms, 2005). This value represents the errors introduced by local density fluctuations with respect to the mean density profile used for the calculation of cumulative mass–depth. Errors from DEP measurements are 1% or less (Reference WilhelmsWilhelms, 1996), and conversion from TWTT to depth likewise yields errors of 1% (Reference Eisen, Nixdorf, Wilhelms and MillerEisen and others, 2002). Conversion of the tracked IRHs to cumulative mass results in errors of ∼1% (Reference Anschütz, Eisen, Oerter, Steinhage and ScheinertAnschütz and others, 2007). The dating uncertainty for the IRHs used here is ±1 year and the uncertainty in tracking the IRHs is up to ±2 ns, equivalent to a depth uncertainty of about ±0.2 m. The latter introduces an additional uncertainty of another ±1 year with respect to the depth–age scale of FB0501. Using the values given above, measurement and model errors result in a mean error of 10–15% for the accumulation data presented here, similar to that reported by Reference Anschütz, Eisen, Oerter, Steinhage and ScheinertAnschütz and others (2007) for a different area.

Comparison with nearby studies

Reference Oerter, Graf, Wilhelms, Minikin and MillerOerter and others (1999) report accumulation values at Kot-tas Camp of 129 kg m⁻² a⁻¹, with a standard deviation of 29%, obtained from a firn core (FB9802) drilled in December 1997 covering the time period 1881–1997. Similar to our firn cores, a 5 year running mean has also been applied to FB9802. To account for the timescales covered by our GPR data, we also apply a 25 year running mean to the accumulation series of FB9802 to enable a better comparison of temporal variations between GPR and firn-core data. The 5 year running mean and 25 year running mean of FB9802 show standard deviations of 14% and 6% of the core mean, respectively. Hence, firn core FB9802 reveals a rather smooth accumulation pattern on longer timescales and a high annual variability (Fig. 6c).

Together with our firn cores, this indicates that the temporal accumulation pattern on scales of 5–25 years is fairly stable, most probably because post-deposition noise and interannual fluctuations are averaged out. Using a mean standard deviation of 14%, as evident from the firn-core data, a surface density of 350 kg m⁻³ and a mean accumulation rate of 180 kg m⁻² a⁻¹ results in height fluctuations of ∼7 cm a⁻¹ that can be explained by temporal accumulation variations. The response of ice flow to temporal variations in accumulation is much longer than the 5 years used for averaging accumulation series. This suggests that height changes of up to ∼7 cm a⁻¹ may result from interannual variations of accumulation rates that are not instantaneously balanced by ice export. Accordingly, this result has implications for the correct interpretation of satellite-derived mass and elevation changes in this area.

Comparison of the standard deviation for the 25 year running mean of FB9802 with the spatial variability of our GPRderived accumulation rates shows that temporal variability on the scale of decades and spatial variability on the scale of 20 km are very similar (6% and 5%, respectively). In contrast, studies from the polar plateau report that spatial variability on the kilometre scale is one order of magnitude higher than temporal variability on multi-decadal scales (Reference FrezzottiFrezzotti and others, 2007). We suggest that these different characteristics are due to the different areas and timescales covered by our study, as the Heimefrontfjella forms a dominant topographic feature influencing wind regimes over a large area.

Considering the area-wide mean values (Table 3), our study reveals somewhat higher accumulation rates than those reported by Reference Oerter, Graf, Wilhelms, Minikin and MillerOerter and others (1999). The same holds for comparison of FB9802 with our firn-core data (Table 4). In order to take into account the different time periods covered by FB9802 and our firn cores, we calculate the mean accumulation of FB9802 over 1975–97 (i.e. the time period that overlaps with our firn cores) as 126 kg m⁻² a⁻¹. Hence, the time periods covered do not seem to be responsible for the different accumulation rates between FB9802 and our study. However, the spatial representativeness of firn cores is generally rather small (e.g. Reference Richardson-NäslundRichardson-Näslund, 2004; Reference Rotschky, Eisen, Wilhelms, Nixdorf and OerterRotschky and others, 2004; Reference Spikes, Hamilton, Arcone, Kaspari and MayewskiSpikes and others, 2004), and FB9802 is separated by 7–18 km from our firn-core locations and by about 3 km from the start of profile 051203. Comparing only accumulation rates from locations within our investigation that are nearest to FB9802, i.e. the start of profile 051203 (Fig. 1b), we derive annual accumulation rates of around 150 kg m⁻² a⁻¹ (Fig. 5b). These values are more in accordance with the value of 129 kg m⁻² a⁻¹ reported by Reference Oerter, Graf, Wilhelms, Minikin and MillerOerter and others (1999).

Reference Rotschky, Rack, Dierking and OerterRotschky and others (2006) present accumulation data obtained from stake readings along the transect from Neumayer station (70°39′ S, 08°15′ W) to Kottas Camp and farther on to the Kottasberge mountain range (Fig. 1a). Data obtained from stakes within 20–30 km of our GPR profiles range from 150 to 250 kg m⁻² a⁻¹ (Fig. 7a), with a high spatial variability. The transect up to Kottas Camp and the spatial variability of the accumulation data, complemented by GPR profiling, is further discussed by Reference Richardson-NäslundRichardson-Näslund (2004) with similar results. The stake-line data confirm the observation that in the immediate vicinity of Kottas Camp, accumulation values are slightly lower. Moreover, Reference RotschkyRotschky and others (2007) obtained an accumulation map of western DML by interpolation of all available firn-core data, reporting values of about 180 kg m⁻² a⁻¹ for our investigation area. Our study therefore provides values within the range of current observations, but contributes a variability of accumulation rates on smaller spatial and temporal scales than has been previously published.

Fig. 7. (a) Accumulation values from stakeline readings in the vicinity of Kottas Camp: 1998 (black solid curve), 1999 (black dashed curve), 2000 (grey solid curve), 2001 (grey dashed curve). (b) Temporal differences calculated as in Equation (1): 1998–99 (black solid curve), 1999–2000 (grey solid curve), 2000–01 (black dashed curve). Negative values on the abscissa correspond to stakes located north of Kottas Camp; positive values are stakes to the south.

Temporal variation of spatial characteristics

We consider the temporal difference td, as defined by Equation (1), of GPR-based accumulation rates on profile 051202 between the time intervals t ₁ = 1990–2005 and t ₂ = 1980–90. The result is a mean value of −16%, i.e. accumulation rates in the time period t ₁ are on average 16% lower than during t ₂. This value is not constant along the profile 051202, however. In fact, considering td pointwise along 051202 we see that temporal variations range from −1.3% to −23% (Fig. 4d). Comparing spatial and temporal differences along this profile, the variations seem to be linked, i.e. the largest temporal differences tend to occur at the places with largest relative spatial differences. Analysis of td on the cross-flow profile 051203 results in similar findings: the temporal differences likewise vary locally. Spatio-temporal characteristics of the stake-line data within 20–30 km around Kottas Camp (Fig. 7) confirm this observation, showing again a quite similar pattern of spatial and temporal accumulation, for instance between −15 and −10 km and ∼20 km.

Caution should be exercised with this comparison, however, as the stake-line data yield only annual variability whereas our GPR data consider decadal variability. In total, it seems that the spatial characteristics of accumulation are not constant in time in the considered region and timescales. Thus, it is important to derive the temporal differences point-wise along profiles and not only from the mean values. Small-scale features seem to affect both the temporal pattern and the spatial distribution.

Accumulation rates have been obtained likewise by combined analysis of GPR and firn-core studies on Potsdam Glacier, a near-coastal site in central Dronning Maud Land, in 2003/04. Similar to the area near Kottas Camp, the investigation area on Potsdam Glacier is characterized by the down-flow of ice from the polar plateau through mountain ranges. The spatial variability is discussed in detail by Reference Anschütz, Eisen, Oerter, Steinhage and ScheinertAnschütz and others (2007), reporting standard deviations of about 50% which is one order of magnitude higher than the standard deviations along the GPR profiles near Kottas Camp. On Potsdam Glacier, spatial differences from the respective mean value vary from −87 to +128% for the time period 1970–80 and from −79 to +130% for 1980–2004 (Fig. 8b). The temporal variation of accumulation rate of a few per cent as reported by Reference Anschütz, Eisen, Oerter, Steinhage and ScheinertAnschütz and others (2007) is obtained from the area-wide mean values of the time periods 1970–80 and 1980–2004, yet analysis of temporal variations along the profile on the main glacier flowline yields a varying pattern (Fig. 8c) as at Kottas Camp. The mean temporal difference of accumulation rates on Potsdam Glacier for the observed time periods t ₁ and t ₂ amounts to −3%, with values varying from −53% up to as much as +145%, as calculated from Equation (1) with t ₁ = 1980–2004 and t ₂ = 1970–80. Again, the largest temporal variations occur near maxima of spatial variability, indicating that temporal and spatial variations are not independent on these scales. The point-to-point variations of the temporal accumulation pattern near Kottas Camp (Figs 4e and 5e) exhibit less pronounced differences compared to those on Potsdam Glacier (Fig. 8c).

Fig. 8. (a) Main Potsdam Glacier flowline slope. (b) Potsdam Glacier accumulation spatial variation, expressed as differences from the mean, in per cent of the mean: 1980–2004 (solid curve) and 1970–80 (dashed curve). (c) Temporal variations between the time periods 1970–80 and 1980–2004 as calculated from Equation (1).

Reference Anschütz, Eisen, Rack and ScheinertAnschütz and others (2006) discuss the influence of the surface topography on the spatial accumulation pattern on Potsdam Glacier and find dune-like features of relatively short distance between troughs, comparable to the megadunes observed on the polar plateau (Reference Frezzotti, Gandolfi and UrbiniFrezzotti and others, 2002). Upstream migration of these dunes at an average rate of 45 m a⁻¹ (Reference Anschütz, Eisen, Rack and ScheinertAnschütz and others, 2006) as well as locally varying glacier flow speed might also influence the variations in temporal accumulation observed on Potsdam Glacier.

Comparing the spatial and the temporal variations on Potsdam Glacier (Fig. 8b and c) and near Kottas Camp (Figs 4d and e and 5d and e) with the respective surface slopes (Figs 8a, 4c and 5c), we suggest that in areas of strong interaction between surface elevation, slope and accumulation, temporally varying mean accumulation rates lead to changing spatial accumulation patterns.

In order to analyze a possible correlation between spatial and temporal variations, we calculate the correlation coefficients R for spatial differences, in per cent, of the respective mean and temporal differences td along the GPR profiles near Kottas Camp and on Potsdam Glacier. We obtain values of 0.24 (t ₁ = 1990–2005) and 0.69 (t ₂ = 1980–90) for profile 051202 and correlation coefficients of 0.66 (t ₁ = 1990–2005) and 0.55 (t ₂ = 1980–90) for profile 051203 near Kottas Camp. The profile on the glacier flowline of Potsdam Glacier reveals R = 0.48 for t ₁ = 1980–2004 and R = 0.28 for t ₂ = 1970–1980.

This indicates that spatial and temporal variations are at least weakly correlated in our investigation areas. However, inaccuracies of glacier flow velocity as well as dating uncertainties prevent a more detailed investigation. Influence of two-dimensional topography on accumulation rates might also be responsible for the observed spatio-temporal accumulation pattern. The topography in some of our investigation area can only be determined in high resolution along the GPR/GPS profiles, however. Due to the spacing between the profiles and the lack of a sufficient digital elevation model, we are unable to discuss possible small-scale topographical effects on our accumulation pattern.

Several other studies discussing temporal and spatial accumulation characteristics find different results. Reference Vaughan, Anderson, King, Mann, Mobbs and LadkinVaughan and others (2004) reported accumulation data from Lyddan Ice Rise where spatial and temporal variability can be separated. They found that the regional mean accumulation is modified locally by persistent spatial variation and a non-persistent residual variability which is most likely due to minor changes in wind regime. As we do not have wind data for our investigation areas, we cannot determine whether our profiles are aligned with the main wind direction.

The results of Reference Eisen, Rack, Nixdorf and WilhelmsEisen and others (2005) on the East Antarctic plateau and Reference Spikes, Hamilton, Arcone, Kaspari and MayewskiSpikes and others (2004) in West Antarctica also indicate that spatial and temporal variability are separable. At this point we are unable to determine whether our findings are representative for larger areas of the grounded coastal parts of the Antarctic ice sheet. We therefore suggest that in our investigation areas the influence of surface topography, wind field and glacier flow are responsible for the relation between spatial and temporal accumulation pattern.

Near-surface winds tend to be complicated in nunatak-dominated areas (Reference JonssonJonsson, 1995), as would be seen on Potsdam Glacier. Since spatial variability is usually implicated when considering accumulation rates obtained from GPR (e.g. Reference Richardson, Aarholt, Hamran, Holmlund and IsakssonRichardson and others, 1997; Reference Richardson-NäslundRichardson-Näslund, 2004; Reference Rotschky, Eisen, Wilhelms, Nixdorf and OerterRotschky and others, 2004), further research is necessary to reveal possible correlations between spatial and temporal variability. As temporal variability obtained from ice-core records can be influenced by spatial variability of accumulation rates upstream of the drilling site and glacier flow (e.g. Reference Spikes, Hamilton, Arcone, Kaspari and MayewskiSpikes and others, 2004; Reference Eisen, Rack, Nixdorf and WilhelmsEisen and others, 2005; Reference FrezzottiFrezzotti and others, 2007), detailed analysis of spatiotemporal characteristics is therefore important for the correct interpretation of climate signals obtained from ice cores.

Satellite observations such as those from GRACE allow the determination of ice-mass changes over several years with a spatial resolution of a few hundred kilometres. The spatial resolution of our ground-based observations on ice-mass changes is probably too low with too small a temporal overlap to validate the GRACE data. Our observations can contribute, however, to the assessment of statistical characteristics of the snow accumulation fluctuations which, in turn, is needed for the interpretation of satellite data. Ice-mass trends observed by satellite over a few years may be due either to interannual fluctuations in net ice surface mass balance or to long-term ice dynamics. In order to distinguish between these two effects, the temporal and spatial covariance of surface mass-balance fluctuation has to be known at least approximately.

Our GPR data analysis reveals the spatial behaviour of temporal changes in the investigation area. From Figures 4 and 5 it is evident that temporal variations can be spatially correlated over approximately 10 km. To determine the correlation length, and to draw conclusions about a comparison with GRACE data, it would be desirable to assess the correlation characteristics over larger distances. Clearly, for variations averaged over several hundred kilometres, the small-scale variations (deposition noise) are probably averaged out, therefore the standard deviation of temporal fluctuations will be smaller than the values of 28–33% obtained from the firn-core time series (Table 4). Such large fluctuations will therefore not be observed by GRACE.

Our observations and analyses help to qualify the spatiotemporal behaviour of the ice surface mass balance in larger areas and, together with studies from adjacent regions (e.g. Reference Oerter, Graf, Wilhelms, Minikin and MillerOerter and others, 1999; Reference Richardson-NäslundRichardson-Näslund, 2004; Reference RotschkyRotschky and others, 2007), will support the interpretation of GRACE (and other satellite) observations.