Space and Time Topographic Signatures of Ice Sheet

Altimetry is probably one of the most powerful tools for the observation of ice sheets. The topography is one of the pertinent parameters related to the processes acting on ice sheets. Because it is a free surface, it description strongly helps in ice modelling. From the global scale to the km-scale, the topography hides the signature of the physical processes as well as the one of external forcing. With a careful analysis of the steady state topography one can detect the signature of the longitudinal stress, the boundary condition effects, the upslope anomaly of the outlet glaciers, the rheological properties ... One can also detect clear features that are not yet explained, such as the 250km undulations or double network of small-scale undulations. On the other hands, the altimetric series of ERS1, ERS2 and Envisat now provide 15 years of continuous and homogeneous observations. These long series allow noticing the shape and volume changes of both ice sheets, related to climate change. The methodology developed at the Legos by Benoît Legrésy (see this issue), based on the process of repeat tracks, provide maps of the temporal change with a very good space resolution. The temporal trend map exhibits coherent signals. The careful analysis of these maps allows also the detection of small-scale particular signatures. Some of these signatures are related to the steady features of the topography and point out some link between space and time topographic signatures. 1. ANTARCTIC ICE SHEET FEATURES The Antarctica ice sheet, with a surface of 15 million square kilometres covered by an average of 2000 m of ice, contains 90% of the Earth’s ice comprising a storage of 30 million cubic kilometers of ice. The behavior of this huge ice reservoir is one of the major unknown on future sea level rise. Nevertheless, the annual snow and ice fluxes of the Antarctica ice sheet are 6 mm/yr sea level equivalent, so that the slightest imbalance may contribute to sea level changes. Since few decades, remote sensing has offered a new vision of these elements of the cryosphere. Indeed, the size, the inaccessibility, the harsh climate conditions strongly limit in situ observations. Among the sensors flying over the polar regions, altimeter plays an important role. It is a unique mean to estimate sea ice thickness; it is one of the best tools for both ice sheet dynamics and ice sheet mass balance. 3.1 Topographic signatures Ice sheet surface topography plays an important role in ice sheet dynamics, flow and balance studies. This is due to the result of a balance between snow accumulation and ablation and ice flow above bedrock. Therefore it contains a signature of the main physical processes (climatic and dynamic) that act on an ice sheet. From the small scale to the large scale, topography contains important information on local anomalies or on general trend behaviours which can be inverted from precise topography [1]. It is also a present initial condition for the future evolution. The large scale topography controls flow direction and its mapping allows the derivation of the balance velocity. Moreover, the deformation and sliding velocities depend on the basal shear stress and thus on surface slopes. Accurate information about the topography is, then, crucial to the prediction of the future evolution and to knowledge of the ice dynamics, either by providing an empirical parameterization of the flow law or by pointing out unknown physical processes. From April 1994 to Marsh 1995, ERS-1 was placed on a geodetic orbit (two shifted cycles of 168-day repeat). Up to 30 million waveforms over Antarctica, and 3 million over Greenland, are available and were reprocessed [1]. The small-scale topography signal yields to a poor on-board tracking of the ground, that is corrected by using a dedicated retracking algorithm previously developed [2,3]. Data editing and _____________________________________________________ Proc. ‘Envisat Symposium 2007’, Montreux, Switzerland 23–27 April 2007 (ESA SP-636, July 2007) geophysical corrections are taken from [4]. The Delft Institute precise orbit is used and the altitude is given with respect to the WGS-84 ellipsoid with a grid size of 1/30°. This high-resolution topography reveals numerous details from the kilometric to the global scale. Figure 1. Curvature in the across-slope direction deduced from the high-resolution map of the Antarctic Ice Sheet topography from the ERS-1 mission [5] One of the most surprising features is the curvature of the surface in the across-slope direction. Fitting a biquadratic form at a given scale on the surface allows the estimation of the three curvatures of the surface. At the large scale, networks of anomalies of the surface topography perpendicularly to the great slope direction (with the help of the Y-curvature) can then be pointed out. They are due to boundary flow conditions of outlet glaciers that are propagated from the coast up to the dome [5]. This exhibits the drainage pattern, upstream glacier positions or the flowline directions, but also the role of the outlet flow conditions of the whole shape. At a smaller scale, this methodology allows to enhance subtle surface features observed in the ice sheet surface topography and to detect local anomalies. Several elongated features have been identified with this technique. They correspond to hydrological systems, which cross the continent over distances greater than a few hundred kilometres [6]. Some of these features are connected to the ice-sheet margin, although the low number of such features means that transportation of subglacial meltwater within these channels are not find to significantly contribute to mass loss for the ice sheet on the continental scale. So that the curvature of the topography in the acrossslope direction is a mean to both detect large scale flow anomaly due to outlet glacier and small scale anomalies related with subglacial lakes. 2 ICE SHEET MASS BALANCE Recently, three attempts to derive ice sheet mass balance with the help of the altimetric time series of ERS-1 and ERS-2 have been published [7, 8, 9]. The whole details of the data processes can be found in one of these papers. Some errors, such as atmospheric delay or orbit errors are now classical and commonly corrected with the same algorithms. Others, such as the slope error –the impact point being shifted in the upslope direction because of the ice sheet topographyare well understood and corrected with different techniques. Finally, the more critical one, due to the penetration of the radar wave within the snow-pack, are not really well understood but corrected with the same kinds of methodology, e.g. with the help of the waveform shape parameters. In order to derive the trend, most of the methodology focuses on the difference at cross-over points in order to minimize long-scale errors and the error due to the antenna polarization [10], only one [9] uses repeat tracks, leading to very larger data sets. Figure 2: Mass balance of the Antarctica ice sheet (in m/yr) from [9] A thinning of the West Antarctica at a rate of 47 Gt/yr and a thickening of the East part of 31 Gt/yr are found [7], correspond in average at an increase of sea level of 0.08 mm/yr. Another study detected dynamic responses of the west Antarctic ice sheet leading to either thickening or thinning [8]. On the contrary, they pointed out a local increase in accumulation rate in few areas, namely in the Peninsula, Dronning Maud land and East Wilkins part. In average, they found that the Antarctica is actually slightly increasing corresponding to a sea level decrease of 0.08 mm/yr. Finally, Legresy et al. [9] with a different methodology for extracting the temporal trend and the change in the snow-pack detected few areas of thickening, in East part of Wilkins land or in the Peninsula and few areas of thinning, near the Pine Island sector or near Law Dome. However, his methodology allows a greater space resolution so that very fine change in the topography shape can be performed. 3SMALL SCALE CHANGE We thus now look at these topographic signatures changes. Because the curvature of a surface is not linear, we add the elevation trend on the old topography and reprocess the fitting by a bi-quadratic form and the estimation of the Y-curvature. In order, to enhance the signal we add 100 times of annual trend. The change in Y-curvature exhibits a coherent signal with pattern elongated from the coast to the inside part of the ice sheet. Even in the interior of the ice sheet, such changes are clear and coherent. This suggests that the whole Antarctic ice sheet is put out of shape [11]. Figure 3: Temporal change in Y-curvature expressed in cm/km/100 yr [11]. These changes also exhibit a strong spatial signal with the same wavelength of the outlet anomalies, showing also their relation with outlet flow anomalies [11]. At the small scale, this methodology also allows to follow the inland signal of the outlet change. For instance, in the Admunsen sea sector, the signature of the three main glaciers (Pine Island, Thwaites and Smith, respectively from top to bottom in the Figure4) are very clear and can be followed over few hundred kilometres. The change of these signatures is very important for the Thwaites glacier, suggesting an acceleration that can be followed over 500 km inland. 0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700 800 900