ERS-1 radar-altimeter data

ERS-1 radar-altimeter elevation data are available in two forms. The first is called fast-delivery (FD) data. This has reduced spatial resolution as the full surface-sampling rate of 20 Hz has been averaged to give a measurement of surface height every 6.7 km (1 Hz) along-track. The second form is known as low bit rate (LBR) data, in which the telemetered return-echo wave forms are available for analysis, and it provides the full 335 m (20 Hz) sampling along-track. An analysis of the echo wave forms permits a higher-precision surface height measurement than the FD data through a recalculation of the range estimate in a process known as retracking (Reference Martin, Zwally, Brenner and BindschadlerMartin and others, 1983). Only limited amounts of LBR data, from the 3 d repeat cycle of the ERS-1 mission, were available for this study.

Although the FD data used do not contain return-echo wave forms to allow for correction of tracking errors, it has been shown that ERS-1 tracks the surface well over the majority of the ice sheet (Reference ScottScott and others, 1992). However, careful data filtering is required to ensure that, as far as possible, range estimates obtained when the altimeter has lost track of the surface are excluded. Here, we use the pulse-peakiness parameter (provided in the data set) to reject faulty measurements (Reference ScottScott and others, 1992). Data points with a pulse-peakiness value of less than unity, which indicate that the altimeter is no longer tracking the first return from the surface, are rejected. This filter eliminates more than half of the poor tracking data, whilst retaining 99% of good tracking data. More stringent data filters can be placed on the data, but at the cost of losing further good, and potentially interesting, data. In this example it was decided to tolerate some anomalous data to allow the maximum information on ice-sheet features to be observed.

Only nominal values for the various altimeter corrections are provided in the FD data set. The dry, wet and ionospheric corrections are fixed at 2.32, 0.10 and 0.02 m, respectively, and there are no tidal corrections. However, the error introduced by using these values is likely to be no more than 0.2–0.3 m and this is small compared to the tracking and orbit errors (see below). Similarly, the slope-induced error (Reference Brenner, Bindschadler, Thomas and ZwallyBrenner and others, 1983) is <1 m in this region and so has been ignored. The effects of radar penetration into the surface (Reference Ridley and PartingtonRidley and Partington, 1988) have also not been accounted for, but this is expected to be fairly uniform over the region considered and so will affect only the overall bias in the map.

Data processing

FD data from May and June 1992, from a single 35 d repeat cycle, were used to produce the isometric view. The contour map of the vicinity of the Vostok lake was produced from three such 35 d cycles from April to September 1992, averaged to reduce the effects of orbit error. Extra coverage of the area was provided by a 3 d repeat and a number of tracks from the commissioning phase. The LBR data, from the 3 d repeat cycle, were used for the more detailed analysis of the profiles over the lake.

Over regions of Antarctica with low surface gradients, the accuracy of the data is principally determined by the knowledge of the satellite orbit. The FD data were processed using the ERS-1 restituted orbit available from ESA. This has a specification accuracy of ±25 m spatially, and 15 m radially (ERS-1 programme, 1991). To assess the error in our area of interest, a cross-over analysis was conducted over the region around the lake. A total of 1500 orbit cross-overs for the first 35 d repeat processed provided height differences with a r.m.s. of 3.5 m. Given that data from three 35 d repeats were averaged to generate the contour map, we can assume the relative error in the data points is of the order of 2 m r.m.s. As the area is contoured with 10 m contours, this error was deemed to be not sufficiently large to warrant carrying out a cross-over adjustment prior to contouring. The 2700 average surface elevations, from the FD data set, over the region of the lake were contoured using the method of Reference Franke and NielsonFranke and Nielson (1980). The absolute error in orbit data was not evaluated and so the height values shown on the contour map may be biased by up to 15 m.

A further parameter from the FD data set is the standard deviation of surface heights derived from the 20 individual samples which comprise the 1 Hz values. This is a measure of how flat and uniform the surface is over distances of 6.7 km. In order to extract that part of the data set for which the surface is considered topographically flat, the FD data were filtered using the criterion that the standard deviation of heights must be less than 0.5 m. In addition, regions of low overall surface gradient were determined by identifying data for which the gradient across three consecutive 1 Hz samples (20 km) was not greater than 0.5 m km⁻¹. This was the maximum gradient observed over the Terre Adélie lake (Reference Cudlip and McIntyreCudlip and MacIntyre, 1987). The results of this filtering are shown later.

Three satellite ground tracks crossed the area of the “lake” during the 3 d repeat cycle. The echo wave forms from LBR data available from this phase were retracked using a 10% threshold technique (Reference Guzkowska, Rapley, Ridley, Cudlip, Birkett and ScottGuzkowska and others, 1990), correcting the elevations for the on-board tracker lag. Comparison of repeated LBR tracks across the “lake” showed the retracked height precision of the measurements to be 0.11 m r.m.s. for 20 Hz data. To assess the error in the FD data due to these data not being retracked, the retracked heights from the LBR data were compared with the corresponding FD data. The r.m.s. height error was ~1.0 m, which is small compared to the orbit error.

Vostok lake

An LBR elevation profile of one of the tracks, track 1 in Figure 2, from the 3 d repeat cycle, which crosses the centre of the lake and the adjacent slopes is shown in Figure 3. This illustrates the sharp change in gradient between the surrounding ice sheet and the horizontal lake surface. The 3 d repeat LBR data are too sparse in coverage to provide a contour map of the region, so the FD data from the 35 d repeat were used (Fig. 4). The elevations used in the contour map are evaluated relative to the GRS-80 Earth reference ellipsoid. The ground tracks, and corresponding density of data points used in the contour map, are shown in Figure 5.

Fig. 3.

An elevation profile over the Vostok lake and its environs shown as track 1 in Figure 2. The elevation samples are at 0.35 km intervals and the profile runs from east to west.

Fig. 4.

Contour map (10 m intervals), compiled from ERS-1 fast-delivery data, of the ice surface over the large Vostok subglacial lake.

Fig. 5.

The location of data points used in the FD contour map in Figure 3.

Across the region of the lake, the ice-surface gradient is reduced from 0.08° (1.4 m km⁻¹) either side to < 0.002° (0.035 m km⁻¹) over the lake itself. However, there is a slight gradient, 0.006° (0.105 m km⁻¹) south to north, along the length of the lake, perpendicular to the gradient of the surrounding plateau. Other features evident in the contour map are a valley on the east side and a slight rise on the west (downstream) side of the flat region. The standard deviation of heights (SDH) over the flat region drops very rapidly from 2 m on the plateau to 0.2 m over the central part (Fig. 6), indicating that this central region is free from local grounding. On the northern part of the lake there is a small tongue about 20 km across which may be a slow ice stream entering from the northern end.

Fig. 6.

Map showing the region of the lake for which the surface standard deviation of heights for 20 consecutive samples is less than 1 m (shaded region). Overlaid on the map are the LBR tracks from the ERS-1 3 d repeal cycle, the track sections shown as dashed line correspond to the height profiles shown in Figure 7. Also shown are the RES flight paths and the locations of strong bottom echoes from radio-echo sounding (Reference Robin, Drewry and MeldrumRobin and others, 1977) which have been interpreted as the signature of basal water.

The altimetric surface-height contours are compared with the locations of bright bottom returns, from the Reference Robin, Drewry and MeldrumRobin and others (1977) airborne RES data, in Figure 6. Although there is general agreement with the location of the lake in both data sets, there are two areas where subglacial water is detected in the presence of a higher surface slope. At the south end of the lake, the disconnected subglacial water is probably a small adjacent lake, over which the altimeter FD sample spacing is too coarse to discriminate a distinct change in gradient. This hypothesis is supported by the RES data which show the detached lake to be ~30m lower in elevation than the main lake; the same elevation difference is seen in the surface contours. Overflow from the larger lake will likely be forced into this lake as a consequence of the north-south surface gradient. The other major discrepancy between the data sets is in the northwest of the map, where subglacial water was detected at a point where the surface gradient is relatively high. A lateral mislocation of the aircraft track of 5 km, due to navigation errors, is possible, but it is insufficient to place the aircraft ground tracks where the surface becomes flat.

The LBR elevation profiles across the flat region (Fig. 7a–c), whose locations are shown in Figure 6, provide detail of the general features seen in the contour map. These profiles all show an ice rise which bounds the lake to the east and a shallow depression on the western edge which is similar to that seen at grounding lines of ice shelves (Reference SmithSmith, 1991). Profiles A and C also show a surface hump of 1 m on the otherwise flat surface profile over the western half of the lake.

Fig. 7.

Details of the retracked height profiles across the lake for the three LBR tracks (A, Β and C locations shown in Figure 6) which crossed it during the 3 d ice phase. The suspected ice-grounding points and anomalous humps are shown. Ice flow is from west to east.

Interpretation

The dominant surface feature of the lake in Figure 4 is the 40 m drop in elevation over 220 km from north to south. The altimeter-derived heights have not been corrected for the local geoid, but inspection of the GEM-Τ1 model (Reference MarshMarsh and others, 1988) indicates a drop of only 5 m along the lake from north to south. The excess difference along the lake could be due to a local geoid not accounted for in the GEM-Τ1 model, but a 35 m geoid error is unlikely. The observed surface gradient follows the bend in the lake, remaining perpendicular to the ambient, grounded ice, suggesting that the ice is thicker at the northern end.

Since the ice on the lake must be in hydrostatic equilibrium with the basal water, the basal ice gradient must be 11 times the surface gradient (Reference Oswald and RobinOswald and Robin, 1973). A height change across the lake of 40 m would correspond to an effective depth of lake water of 440 m.

Search for other flat areas

We have identified that the surfaces of lakes are smooth from the standard deviation of surface heights (SDH) within the Vostok lake FD data. This criterion can be used to search for other lakes and flat areas within the complete FD data coverage of Antarctica. To do this, the data are filtered for SDH <0.5m, “smooth” and along-track gradient <0.3 m km⁻¹ over 20 km (three FD data points), “flat”.

The surface can only be considered to be smooth and flat in two dimensions if both the ascending and descending tracks show such characteristics. Tracks which run along linear features such as basins or ridges will satisfy the criterion in one direction only. The complete map of flat surfaces is compiled from segments of tracks at cross-over points where crossing tracks are both flat.

The main areas identified through this data filter are the Vostok lake and the ice shelves. Other continuous stretches of the sub-set are located on ridge lines where surface gradients are relatively low. All other points are located in small basins, between undulations, and large basins, such as that between Dome A and Dome G and between Dome C and Victoria Land. None of the locations for flat areas are coincident with lakes catalogued from the RES records by Reference MacIntyreMacIntyre (1983). The reasons for this are partially because the grounding-line undulation, observed in the LBR height profiles, increases the r.m.s. heights. The lake must then be up to 20 km wide along the ground track before it flattens out after the undulations. The lake must then be flat for another 20 km, the shortest length needed to measure the gradient from three samples. Most of the subglacial lakes, discovered through RES flights, have dimensions similar to the ice thickness, ~4km across, and so are not detectable by this method. The only other known lake with linear dimensions of ~40km, which should be detected, is the Terre Adélie lake (Reference Cudlip and McIntyreCudlip and MacIntyre, 1987). An examination of the data shows missing orbits across the area of the lake and so it is not detected.

Search for other lakes in the LBR data

We have shown that the FD data have an inadequate sample spacing to detect even intermediate-sized sub-glacial lakes, so a pilot study was undertaken to search for such lakes in the LBR data. The limited coverage of the 3 d repeat can be extended, if the technique proves successful, once the 35 d repeat LBR data are available.

The LBR data were examined to study the details of the “pock marks”, observed in Figure 1, which are suggestive of smaller subglacial lakes (Reference RobinsonRobinson, 1964). Small lakes will not be apparent in any search for flat areas, as they have linear dimensions on the order of the wavelength of the grounding-line undulations. The wavelength of the undulations at the grounding line, for the Vostok lake, are determined by the three LBR profiles in Figure 7, as ~20km. An examination of a track passing through an area of “pock marks”, track 2 in Figure 2, revealed that several short parts of the track had horizontal surfaces with sharp changes of gradient both upstream and downstream (Fig. 8). A close examination of these profiles reveals that they all have the form of a shallow undulation, similar to that which follows the Vostok lake upstream grounding line (Fig. 9). The undulation wavelengths on all three of the potential lakes on this single track are approximately the same but are shorter than that from the Vostok lake.

Fig. 8.

An LBR profile which crosses three flat areas that may be subglacial lakes too small to be detected in the coarser sampled FD data. This is shown as track 2 in Figure 2.

Fig. 9.

Detailed profiles of the three flat regions, shown in Figure 8, compared with the start of track Β across the Vostok lake. The low-amplitude undulations appear to be characteristic of a subglacial lake upstream of the grounding line.

The model of Reference SmithSmith (1991), referred to as Equation (1), is fitted by inspection to the first undulation of one of the “pock marks” and to the Vostok lake, and is found to provide a good description of part of the undulating surface (Fig. 10). A decrease in ice thickness, 3950 m at Vostok (Reference Robin, Drewry and MeldrumRobin and others, 1977) to ~2500 m along track 2 (Reference Drewry and DrewryDrewry, 1983) causes a decrease in undulation wavelength. The bending factor, β, is 3.8 × 10⁻⁴m⁻¹ for track 2 and 2.4 × 10⁻⁴ m⁻¹ for Vostok. The observation that the elastic bending model is applicable for part of the surface profile is indicative that the pock-mark features observed in Figure 1 may be intermediate-sized subglacial lakes.

Fig. 10.

The fit of the grounding-line model of Reference SmithSmith (1991) to the first undulation in the horizontal profile of subglacial lakes, a. Lake A from Figure 9; b. Track Β across the Vostok lake. Coarse estimates of the ice thickness and Young’s modulus of the ice may be determined from the fit.

However, as stated earlier, the double undulation observed is not permitted by the simple grounding-line model of elastic bending. If the first dip in the surface profile follows the grounding point, then a second dip should not be expected from floating ice. The model assumes a planar gentle gradient in the bedrock to the point of glacial lift-off, but in the case of subglacial lakes this may not be applicable. The bedrock geometry may include a step or series of steps into the subglacial water, and this would have a significant impact on the surface topog-raphy.

In order to search for flat lengths of LBR profile which have characteristics different from those exhibited in Figure 9, the same track was searched for 3.5 km segments with a standard deviation of less than 1 m in the intervening ten samples. Many small sections of track, of which Figure 11 is an example, did fulfill the requirement. They are different from the segments in Figure 9 in that the radius of surface curvature is greater immediately upstream and downstream of the horizontal section of profile, and they are shorter. They appear to be simply horizontal segments of the general ice-sheet undulations with wavelengths of 40 km or more. The segment in Figure 11 has similar gradients associated with it as the segments in Figure 9, and serves as a control to illustrate that the observed low-amplitude undulations are not of instrumental origin.

Fig. 11.

A control segment of the same LBR track shown in Figure 8, showing a flat section which does not have low-amplitude undulations. The length of the horizontal parts of such sections is generally less than 5 km.

One LBR track, track 3 in Figure 2, passes over two of the subglacial lakes located by Reference SteedSteed (1980), the altimeter-height profiles for which are shown in Figure 12. From the length of the horizontal surface, these lakes appear to be smaller than those in Figure 10. However, given positioning inaccuracies due to aircraft-navigation errors, we cannot be sure that the satellite track passes directly over the lakes. In both cases, the surface topography becomes flat for only ~5km and the upstream grounding-line undulation is absent. There is no apparent difference between the surface topography over the confirmed lake shown in Figure 12b from that over undulations such as that shown in Figure 11. Consequently, a greater horizontal surface, as determined by the altimeter, is required to detect the surface manifestation of subglacial lakes. The lower size limit for the detection of lakes within a single radar-altimeter profile is ~10km, approximately twice the length of normal undulation crests as seen in Figure 11.

Fig. 12.

a–b The elevation profiles across two small lakes previously identified from radio-echo sounding data ( Reference SteedSteed, 1980). These profiles are found on track 3 in Figure 2.

Ice-sheet reference surfaces

A surface that is flat in two dimensions is of value as a height-reference surface for radar altimeters (Reference Gorman, Drewry, Guyenne and HuntGorman and Drewry, 1984). The desirable criterion is that the cross-track slope is small, <0.05 m km⁻¹, or can be modelled accurately. This is needed because repeat tracks can vary in location in the cross-track direction by up to ± 1 km. Knowledge of the cross-track surface slope allows a correction for the cross-track vertical displacement to be applied, and the determination of the slope is the main source of error in the use of land-reference surfaces.

The Vostok lake is ideal for a reference surface, since the surface slopes are both low (0.1 m km⁻¹) and uniform. The retracked-height data can be averaged along-track to improve the precision, and so, given that the wet tropospheric correction is negligible in this region, precisions of a few centimetres should be achievable for relative radial-orbit error calculations. This is assuming, of course, that the surface properties of the snow do not change significantly. Detailed analysis of repeat waveform data will be required to establish the effect of, for example, fresh snowfall or possible seasonal variation in surface penetration.

The area also has the potential of an absolute orbit reference but this would require an independent estimate of the surface elevation (for example, using Global Positioning System) and a complete evaluation of all the biases involved in the altimeter observations. The deployment of a transponder could help in this regard.