Previous observations

The Amery Ice Shelf has been the subject of ground, aircraft and satellite survey. Early aerial exploration by Australian National Antarctic Research Expeditions (ANARE) provided information on ice-shelf surface features, including an approximate course for the grounding line (Reference Mellor and McKinnonMellor and McKinnon 1960). The course indicated in the vicinity of Lambert Glacier was oblique to the main direction of flow, and this has recently been confirmed with satellite observations by Reference SwithinbankSwithinbank (in press). Later, ground survey, airborne radio echo-sounding, and drilling were carried out by ANARE to measure ice movement, elevation, accumulation, and thickness in a comprehensive series of studies of the ice shelf in the 1960s and 1970s. These measurements were taken along traverse lines following the approximate centre line of flow, and across the ice shelf near the ice front and near the grounding line (Reference Budd, Smith, Wishart and OuraBudd and others 1967; Reference Morgan and BuddMorgan and Budd 1975; Reference Budd, Corry and JackaBudd and others 1982). The data produced from these surveys allowed re-assessment of the dynamics of the ice shelf (Reference BuddBudd 1966) and enabled new estimates of the mass balance of the drainage basin to be made (e.g. Reference Budd, Smith, Wishart and OuraBudd and others 1967; Reference AllisonAllison 1979). Importantly for this study, the position of a grounding point in the vicinity of Lambert Glacier was determined (Reference Budd, Corry and JackaBudd and others 1982).

Seasat, which flew in 1978, provided the first coverage by a satellite-borne altimeter, allowing Reference Brooks, Williams, Ferrigno, Krabil, Oliver, James and JagoBrooks and others (1983) to produce a topographic map of the ice shelf with a contour interval of 5 m and an accuracy of the order of I m. From the map, they compared corrected altimeter elevations with the centre-line profile obtained by Australian ground survey (Reference Budd, Corry and JackaBudd and others 1982). The two profiles agree well in shape from near the ice front to near the grounding zone. However, the apparent position of the grounding point, as observed in the altimeter profile, was displaced approximately 40 km up-stream from the true position, indicating a decrease in the reliability of the altimeter measurements in this region (discussed later). Elsewhere, the presence of crevasses in elevation profiles showed up as zones of rapid elevation fluctuations of amplitude ±(4–5) m and wavelength the order of a few kilometres. In addition, the presence of two grounded regions within the ice shelf was indicated by the presence of topographic highs.

Seasat altimeter-range measurements

The Seasat radar altimeter was designed for use over the open ocean, which can be assumed to be a planar, horizontal, and diffuse scatterer over the area sampled. For such surfaces, information on the surface dielectric and geometric properties within the pulse-limited footprint is contained in the leading edge of the echo wave form (Reference McGooganMcGoogan 1975). The instrument attempted to locate the centre of the digitizing window at the half-power point of the leading edge, and the range was estimated from the delay time associated with the centre of the sample. The on-board alignment of the digitizing window was carried out by prediction from previous estimates of range and range rate, and was modified by the generation of a height-error signal. As long as the centring was carried out successfully, the calculated range corresponded to the mean elevation within the pulse-limited footprint (Reference BrownBrown 1977). However, the instrument was not designed to track rough and rapidly varying ice-sheet surfaces (Reference Brenner, Bindschadler, Thomas and ZwallyBrenner and others 1983; Reference Partington and RapleyPartington and Rapley 1986).

Fig.1 shows four altimeter wave forms recorded over the Amery Ice Shelf, along with positions on each wave form associated with elevation calculated in four different ways, as discussed below. Wave form 1 is a typical signal received from a flatter part of the ice shelf. The on-board calculated elevation (method a) can be seen to align with the half-power position on the leading edge of the wave form, as a result of the low and slowly varying relief of the surface. The lengthened leading edge of wave form 2 suggests that it is from a rougher region of the ice shelf. The tracker again finds the half-power position because the surface elevation is varying slowly along track and the wave form similar in shape to rough ocean return. The complexity of wave forms 3 and 4 suggests that they are from geometrically more complex surfaces. Wave form 3 is double-ramped, suggesting the presence of two distinct reflecting regions in the sampled area. Wave form 4 is still more complex and difficult to interpret, with the leading edge hard to define. Areas contributing to the pulse-limited footprint in such cases may be spatially separated and variable in scattering properties and relief (Reference Griffiths, Guyenne and HuntGriffiths 1984), Wave forms 3 and 4 were given poor elevation estimates by the on-board tracker.

Fig. 1. Four ice-shelf wave forms with position ranged to by the on-board tracker (a), half-peak power retracked elevation (b), least-squares fitting of a model ocean return (c), and first-return retracked elevation (d).

Retracking methods

As the on-board tracker often failed to align the centre of the digitizing window with the half-power point of the leading edge, it is normally necessary to re-align these so that a more suitable position on the wave form is selected. Three methods have been reported in the literature to date.

Reference Brooks, Williams, Ferrigno, Krabil, Oliver, James and JagoBrooks and others (1983) retracked to the half-peak value in the wave form (Fig.1, method b) to produce their topographic map of the Amery Ice Shelf. For ocean return, this produces a range to the half-power position of the leading edge. Wave form 1 is successfully retracked using the half-peak method. The low slope of the leading edge of wave form 2, however, results in increased sensitivity to noise. Wave form 3 shows that the retracked elevation obtained from double-ramped wave forms is very sensitive to the relative amplitudes of the two ramps. In this case, it is the second ramp which is ranged to. A gradual increase in the amplitude of the first ramp relative to the second along a sequence of double-ramped wave forms would result in a spurious step in the elevation profile. The profiles of elevation produced by Reference Brooks, Williams, Ferrigno, Krabil, Oliver, James and JagoBrooks and others (1983) across crevassed zones may well suffer from this problem and therefore may not represent the true surface.

Reference Martin, Zwally, Brenner and BindschadlerMartin and others (1983) used a more sophisticated retracking technique (method c). The model ocean wave form assumed in design of the on-board tracking procedure (Reference BrownBrown 1977) was fitted to altimeter ice-sheet data by the method of least squares. They also used a “double-ramp” model to fit wave forms of type 3 (Fig.1), so that two range estimates could be made. Compared with the halfpeak method, this technique results in reduced sensitivity to noise. In addition, the method provides several parameters which may be used to describe wave-form shape, including leading-edge width, which have not been used to extract information on surface character to date. A similar version of the single-ramp model has been implemented for least-squares fitting in this study, for comparative purposes.

Methods a to c all assume that the return is ocean- .like, which is not necessarily appropriate for detection of subtle changes in wave-form shape associated with passage across surface features such as crevassed zones and the grounding line.

Reference Martin, Zwally, Brenner and BindschadlerMartin and others (1983) attempted to overcome this problem by fitting a double-ramp model wave form to return from more complex surfaces. Where the wave form exhibits a form which implies return from two distinct reflecting surfaces, then this method works well. However, visual inspection of returns from the Amery Ice Shelf indicates that many wave forms fail to fall into the “oceanlike” or “double-ramp” categories.

Reference Brenner, Bindschadler, Thomas and ZwallyThomas and others (1983) used a different retracking method to enable them to map the ice margin. They showed that the location of the ice margin could be determined from the position at which the return signal from sea ice begins a parabolic migration away from the satellite. In order to demonstrate this, they retracked the altimeter data to the first return associated with the sea ice, in a signal which contained returns from both sea ice and ice shelf. The retracked elevation then referred to the closest part of that surface to the satellite, and was a spot measurement rather than a mean over an area.

First-return retracking

A new method of retracking adopted here (d in Fig.1) is specially designed to provide meaningful elevation measurements over rougher ice-shelf topography, where the other methods, which assume an ocean return, produce highly ambiguous measurements. The method ranges to the first-return signal in the wave form, so providing a spot elevation measurement associated with the closest surface to the satellite.

The method used to retrack data employs a threshold retracker set at a value of ten “counts” (undimensionalized units of signal amplitude). Seasat used an on-board automatic gain control to attenuate the signal and keep it within the dynamic range of the instrument (Reference TownsendTownsend 1980). Counts are the signal-amplitude units after application of automatic gain control to the signal. Over the main body of the Amery Ice Shelf, the signal-amplitude value varied little, so noise was held at a fairly constant count level. This allowed the use of a signal-count value to detect the first return.

The first-return method results in a higher elevation value than other retracking methods, the difference being proportional to the width of the leading edge for an ocean return (Fig.1, wave forms 1 and 2). The method is particularly useful, however, for retracking of complex wave forms such as 3 and 4. Here, definition of the area of the surface contributing to the leading edge of the return is not required, so easing interpretation, though the closest surface to the satellite may not lie at nadir. Such cases may be flagged by the presence of parabolic sections in elevation profiles, suggesting that the retracking method is ranging to a single surface feature as the satellite approaches and recedes (Reference Gundestrup, Bindschadler and ZwallyGundestrup and others 1986).

Crevassed zones

Fig.3b shows a sequence of wave forms recorded during satellite passage across crevassed area B, which delimits flow originating from Charybdis and Lambert Glaciers. The crevassed area is clearly marked by an increase in the width of the leading edge of the wave forms, and by an increase in surface elevation indicated by the position of the first return. Over crevassed surfaces the precise nature of the relationship between surface roughness and leading edge is likely to be complex and therefore lead to difficulties in the interpretation of any elevation measurements which assume an ocean return (e.g. Reference Brooks, Williams, Ferrigno, Krabil, Oliver, James and JagoBrooks and others 1983).

Fig. 3. Two altimeter wave-form sequences shown crossing the Amery Ice Shelf from east to west (bottom to top of the plot). Each wave form is a histogram of received signal power (z-axis) against time/range (with non-absolute scale shown across base of plot). The wave forms overlap and are scaled to force the peak value of each wave form to be the same height. The high-amplitude parts of the wave forms are shaded to emphasize the passage of migrating features through the sequence.

The plot suggests that crevassed zones may be delimited by measurement of leading-edge width. One such measurement is provided as a by-product from least-squares fitting of a model ocean return to the data (Reference Martin, Zwally, Brenner and BindschadlerMartin and others 1983). However, the complex wave forms found in crevassed areas often defeat the fitting procedure, which either fails to converge iteratively or produces a poor fit. Another measure of leading-edge width is provided by significant wave height, which is automatically telemetered from the satellite. However, this measure is damped by a 0.8 s time constant, so tends to be insensitive. The most reliable method was found to be a difference between the first-return and the half-peak elevations. Fig.4 shows three transects across the Amery Ice Shelf, each containing the first-return and the half-peak elevations along with the difference between the two. Zones of crevassing are indicated by a large difference between the two values, with the contrast between crevassed and non-crevassed regions most clear in the lower regions of the ice shelf.

Fig. 4. Three transects of altimeter-derived surface elevation across the Amery Ice Shelf. Each transect contains two profiles obtained from first-return and half-peak retracked elevations.

This latter technique is sufficiently sensitive to detect regions of possible crevassing on the ice shelf which are not visible in digitally enhanced AVHRR and Landsat data. An example can be seen in Fig.3b, at the position of a marked change in surface gradient. The leading edge of the wave form increases in width, suggesting that a zone of crevasses may be located at this position. The possible shear zone can be detected intermittently along the western side of the ice shelf north of Charybdis Glacier in other sequences of altimeter data. Flow lines visible in AVHRR imagery show that its location is consistent with that of the edge of a relatively stagnant region determined from velocity measurements in the extreme north-west of the ice shelf (Reference Budd, Corry and JackaBudd and others 1982). Other possible crevassed zones are indicated by bold sections of ground tracks in Fig.2. The criterion for delimitation of crevassed zones for this map was a difference of 1.5 m in the elevations as determined by the first-return and half-peak methods, on purely empirical grounds.

Flow bands are delimited by shear zones. In Fig,4, two flow bands are visible, separated by crevassed zone B. Repeated measurements of the elevations and widths of flow bands delimited by shear zones can be used to infer mass-balance conditions within sub-catchments.

Measured widths of the leading edge cannot, however, be used indiscriminately to detect crevassed zones. There are a number of realistic surface geometries and scattering properties which can combine to produce similar wave forms and not all of these are crevassed surfaces. For example, the transect across the Amery Ice Shelf/Lambert Glacier transition region (Fig.4) shows a large and fluctuating difference between the first-return and half-peak elevations. The first-return elevation can be seen to follow a parabolic trajectory in two places, which indicates that a single surface feature, rather than the nadir surface, is being ranged to (Reference Gundestrup, Bindschadler and ZwallyGundestrup and others 1986). For this reason, initial detection of shear zones using altimetry requires validation from imagery, either from direct confirmation of the presence of crevasses or from the use of flow lines to indicate that a likely shear zone lies down-stream of a promontory or glacier confluence.

The grounding line

Fig.3 shows a sequence of wave forms over the grounding zone of Lambert Glacier. A grounding point (at station T4) identified by Reference Budd, Smith, Wishart and OuraBudd and others (1967) is located approximately 4 km to the north of the closest approach of the ground track at the position indicated. The closest approach of the satellite to the grounding point is marked by a sharp change in surface gradient indicated by the position of the first return. In addition, the wave forms in the vicinity of the grounding point show an evolution similar to those generated by simulation over a change in slope (Reference RapleyRapley and others 1985).

Fig.5 shows profiles of on-board height and three retracking heights along a track in the vicinity of the grounding point at T4. The first-return retracking method produces a profile of the nearest surface to the satellite as a series of spot measurements. With low surface slopes, this will be a good representation of the sub-satellite surface. The other profiles in Fig.5 show a decrease in surface elevation in the vicinity of the grounding line, which in each case is principally the result of assuming a model ocean return. As the return is focused by the surface geometry associated with the change in slope, these methods continue to produce range measurements to the grounding zone after passing over the grounded ice. This demonstrates that the first-return method is the only reliable method for ranging across the grounding line.

Fig. 5. Profiles of on-board tracking height and three types of retracked elevation in the region of the grounding point (T4) reported by Reference Budd, Corry and JackaBudd and others (1982) for Lambert Glacier.

Fig.4a shows a longer profile of the same track, with elevation associated with the first-return and half-peak methods. In addition to a grounding point, the first-return profile indicates the presence of two features sampled from off nadir, as discussed in the previous section. It is possible that these are grounded regions located to one side of the ground track, which would suggest that the grounding line is “wavy” in form.

Two methods are available for locating the position of the change in slope associated with the grounding line. The first utilizes the first-return method and applies a correction, The second employs the method of Reference Brenner, Bindschadler, Thomas and ZwallyThomas and others (1983) to locate the position at which return from the grounding zone begins a parabolic migration away from the satellite.

The grounded ice is detected prior to the satellite being positioned directly above it, and is detected by the first-return method as a “toe” moving out of the main ramp associated with the floating surface. Assuming the grounding line is a straight line separating two planar surfaces, the grounding line will be located by the first-return method a distance d before its true position on the satellite ground track where:

(1)

or

(2)

Here, h is the distance of the satellite from a floating surface, α is the slope of the grounded surface, (3 is the angle of incidence of the satellite with the grounding line, m is the elevation difference in metres between consecutive wave-form first returns, and n is the along-track distance between wave-form samples (662 m). For a horizontal floating ice surface, a grounded ice gradient of 0.29 (Table 1 and Fig.3a), a ß value of 90° and an h value of 800 km, d is 2025 m. The slopes associated with the floating ice in these areas will have a negligible effect on the magnitude of d. Where the satellite does not cross the grounding-line at right-angles, the estimated slope witl be lower than it actually is, leading to an underestimate of d. In the example given above, the value of d will increase to 2338 m for an approach angle of 60 to the grounding line, and to 4049 m for an approach angle of 30 . In principle, it is possible to gain a first-order estimate of the angle of incidence of the altimeter from the first-order estimate of the grounding-line position and iterate towards its true position where ground-track density is high enough.

Table I Gradients Either Side of Grounding Point (Mean Over 12 km)

In view of the limitations on accuracies achievable in positioning of the grounding point using this method alone, it is useful to employ an additional method analogous to that employed by Reference Brenner, Bindschadler, Thomas and ZwallyThomas and others (1983) in their mapping of the ice margin. They ranged to the earliest signal associated with the lower (sea-ice) surface on approach to the ice shelf. The point at which this began a parabolic trajectory away from the satellite marked the position of the ice margin. Although the grounding line in this case is a change in slope rather than a step, the same technique can be applied here to provide an additional measure of the grounding-point position. In the example given above (Fig.3a), the earliest signal associated with the grounding zone begins a parabolic trajectory away from the satellite at a distance of 2648 m beyond the uncorrected estimation of the grounding-line position obtained from the first-return method. The near-parabolic profile produced by two retracked elevations and on-board calculated elevation can be seen in Fig.5. All three methods continue to track to the grounding zone once the satellite has passed on to the grounded ice.

In the example above, the two techniques produce a discrepancy of 623 m, assuming the grounding line is at right-angles to the altimeter ground track. The accuracies achievable are limited by the along-track distance between wave-form samples and by the rough nature of the surface, which causes the assumptions behind the techniques to break down. The accuracies in positioning the beginning of the parabolic trajectory and positioning of the increase in surface gradient are each of the order of half the distance between wave-form samples along track (331 m). This places the discrepancy of 623 m within the maximum expected (662 m). The rough nature of the surface will cause additional errors in estimation of the beginning of the parabolic trajectory and in estimation of surface gradient, which may decrease accuracies substantially when the satellite crosses the grounding line obliquely. Along the track closest to T4, these methods produce a location for the grounding line approximately 2.8 km to the north-east, with an accuracy in location of the order of ±500 m.