Constraining ice dynamics at Dome C, Antarctica, using remotely sensed measurements

A first time description is given of the ice flow at Dome C, Antarctica, around the EPICA drilling site. We used satellite radar altimetry to obtain the precise ice surface topography, airborne radio echo sounding to obtain the ice thickness and satellite SAR interferometry to derive one component of the surface velocity field. The balance flux around the Dome C area is then accurately mapped and comparisons made between driving stress, surface and balance velocity to help us describe the ice flow in the region. As a by‐product of the study, we also recover anomalies in the ice flow conditions in sub‐glacial lake locations. These effects result from localy invalid shallow‐ice approximation. The results of this study form the basis for future investigations of the ice flow conditions at Dome C in relation to ice core interpretation.


Introduction
The EPICA (European Project on Ice Core drilling in Antarctica) chose Dome C as the site to perform the deepest drilling in Antarctica. The choice of this site was guided by the fact that around the summit of Dome C, the horizontal movement of the ice surface is negligible and thus the total ice column is formed by snowfall accumulation. Hence analysis of the ice cores gives a direct measure of the climate evolution at this place. The aim of this paper is to demonstrate how the use of remotely sensed data can help understand the ice movement around the EPICA drilling site. We map the balance, deformation and surface velocities using surface topography, thickness and interferometric synthetic aperture radar data. Finally, we compare all of these velocity fields and draw some conclusions about the ice movement around Dome C. The chosen grid spacing is a compromise between the radar footprint (2-3 km diameter) and the along and cross track resolution. The mapped spatial resolution is thus 1/30 degree (i.e., 3.7 km in a north-south direction and I km in east-west direction). All calculations presented in this paper refer to this grid unless otherwise indicated. The height precision of the mapped topography has been evaluated by comparison with a kinematic GPS survey [Ceffalo et al., 1996] and agreement is at an rms level of 20 cm. The ice thickness data are the result of an airborne radio echo sounding survey [Tabacco et al., 1998] collected over a 80'120 km rectangular grid with a 10 km across track grid spacing, refined to 5 km in the central region. These data have been interpolated [Remy and Tabacco, 2000] to the same 1/30 degree grid as the ice surface topography and the difference gives the bedrock topography. Finally, two ERS SAR acquisitions have been used to perform the interferometry.

Datasets. The ice surface topography has been
The SAR scene selection was difficult as there was no data available from ascending tracks over Dome C and only a few useful scenes on the descending tracks. At Dome C, the ice flow is slow ( 0-20 cm/a) and thus it is necessary to use a long temporal baseline (typically of the order of 70 days or more) to resolve a significant signal. It is also important to keep any radar coherence between the two acquisitions to form the interferogram. The coherence between scenes decreases with time separation (the surface state changes) and with orbital separation between the 2 acquisitions (if the ground target is not seen with the same incidence angle, the target response will differ). It is therefore important to have short orthogonal baselines. Many attempts at forming interferograms with long baselines lead to incoherence and no result. We only found one image pair (descending pass), centered at Dome C, with a 45 m orthogonal

UB(X) --• p
where H is the ice thickness, a½½ the accumulation rate and x the abscissa along the flow line from the top of the dome. The integration is performed along a flowline following the greatest slope. We computed the balance velocity on a 5 km grid using the method of Budd and Warner, [1996]. We experimented with many horizontal spatial scales to compute the slope, ranging from 10-30 km (3-10 times the ice thickness), but did not find any major differences, perhaps because the slopes were small. The value of 10 km (which corresponds to the resolution of our basic datasets) gave a more de- where A and n are ice constitutive law parameters (see [Glen, 1955;Paterson, 1994] for detailed description).
This deformation velocity only refers to local quantities (thickness and slope) and is not a priori dependent on the history of the flow from Dome C, in the same way as the balance velocity is. Thus this calculation provides an independent estimation of the way that the ice flows. SAR Interferometry.
We computed phase differences between the two SAR acquisitions using both NASA/JPL and CNES (DIAPASON) software. The coherence level between the images is of the order of 0.35.

4•r (Bcos(a + O) + 5tV. r) + •borb (4)
where A is the radar wavelength (5.6 cm), B the orbital separation between the two data acquisitions, c• the baseline angle with respect to the horizontal, r the unit range vector, t? the topography dependent angle of r, 5t the time separation between the two acquisitions, V the surface velocity vector, •borb is the residual phase signal linked to any data uncertainties in the area. The height of the phase ambiguity (topographic change necessary to produce one fringe) is of the order of 150 m and is computed at each point with the topographic correction applied using the surface elevation data. The topographic correction is however less than one fringe given the flatness of the area. The main signal present in the computed interferogram is composed of a constant slope, which is also the case for the balance and deformation velocities projected in the SAR line of sight. In such cases, it becomes diiFficult to sep-arate between velocity-induced fringes and residual orbital fringes, which usually appear as linear ramps. We computed the interferogram using both the ESA precise orbits and Delft orbits data [Scharoo and Visser, 1998].
The first set of orbits introduced many fringes and we separated the orbital fringes by least squares fitting of the interferometric fringe pattern to a simulated fringe pattern based on the balance velocities. The Delft orbits lead to the same result, but without the need for any fitting. We therefore assumed that the Delft orbits were precise enough and did not contain any residual orbit signal. The final interferogram consisted of 2 1/2 fringes. The phase was further unwrapped using the Goldstein et al., [1994] method. The error in the phase estimation is expected to be very small, since the troposphere is particularly dry at Dome C. Since the fringe pattern is simple, we estimated an error of 6 mm/a in the velocity based on the above phase noise. However, an absolute error from orbital uncertainties can still remain in the data at the same error level. We further assume a total error of I cm/a for the data in the following section. The resulting SAR velocities represent ice surface velocities, whilst the balance and deformation velocities refer to column-averaged velocities.

Comparison of the different velocity fields. Having only one direction of SAR acquisition, we cannot extend the SAR measurement into two directions.
We thus project all datasets in the horizontal plane and in the SAR line of sight direction. Figure 2 shows the maps of the projected driving stress, balance velocity and SAR velocity. We computed correlation coefficients to compare the different datasets. Comparing balance and SAR velocity (Figure 3a) leads to a 0.82 correlation, the scatter plot indicating a clear linear correspondence between both velocity estimations. (Standard theory for isothermal flow predicts a (n+l)/(n+2) factor between both, but the noise level prevents any conclusion between n=l, 2 or 3) A discrepancy arises, however, for high velocities (>0.12 m/a), and we can see from

Summary.
In this paper, we investigated the flow of ice at Dome C in the area surrounding the deep drilling site. We demonstrated that remotely sensed data may help describe the ice flow by mapping a number of physical parameters of concern for ice flow studies. Ice surface velocities are well recovered from a 69 day temporal baseline ERS interferogram, the balance velocity is accurately mapped using surface and bedrock topographies and the driving stress can also be well described. We found that the shalow-ice approximation is not valid over small sub-glacial lakes. It appears that a method to recover sub-glacial lakes can be achieved using precise topography and velocity. However, our analyses lack an ascending ERS track for a full INSAR description of the surface velocity and of an absolute velocity reference. This situation can be overcome easily with future acquisitions of ERS2 or ENVISAT data. In situ measurements of ice surface velocity will be beneficial to extend the analysis using in situ Doris and GPS surveys (C. Vincent and A. Cappra, personal comm.). The very slow movement (less than 1 cm/a) around the drilling site indicates that the ice present in the core may not have moved more than 1 km from that point, even for very old (deep) ice particles. Van der Veen and Whillans, [1992] showed that there can be discrepancy between the summit of the topography and the flow centre, but addressing this point will require additional and absolute measurements. Additionally, it would be of importance to have an improved measurement of this surface velocity and use modeling to constrain the flow divergence with depth, i.e., the longitudinal strain rate vertical profile [Bolzan, 1985].