Pine Island Glacier flow and dynamics Case for support 1. Introduction The aim of this project is to develop a threedimensional, first-order numerical model of ice flow and apply it to Pine Island Glacier, West Antarctica (PIG, WAIS). The two principal outcomes of the project will be an understanding of the relationship between basal traction and slip for the ice stream; and a predictive model of its future evolution. The project will also see the development of a generic ice-flow model suitable for the analysis of many of the ‘meso-scale’ problems of contemporary glaciology (e.g., the onset areas and margins of ice streams, and icedome flow). The WAIS contains enough water to raise global sea level by over 5 m [IPCC 1995]. PIG and its neighbour Thwaites Glacier (TG) drain 40% of the ice sheet. The marine termini of these glaciers have been highlighted as potential sources of rapid retreat because of their lack of significant ice shelves and a bedrock topography which deepens considerably inland [Hughes 1980; Bindschadler et al. 1998; Oppenheimer 1998]. The grounding line of PIG is known to have retreated between 1992 and 1994 at a rate of 1.2 km yr-1 [Rignot 1998]. There is therefore an urgent need to understand the causes of this retreat, as well as its future implications for the WAIS and global sea level. The project draws on several recent developments made by the glaciology groups at Southampton and University College London (UCL). These include: the mapping of PIG’s surface velocity using satellite radar interferometry (SRI); the mapping of a dramatic ice-surface lowering for PIG over the last seven years using repeat satellite altimetry (RA, see Figure 1); the development of a transect ice-flow model which fully incorporates longitudinal stresses (i.e., is a first-order approximation to ice flow). The project has four main objectives, which are: 1. Apply existing transect model to PIG. 2. Extend existing data coverage to cover the whole of the PIG drainage basin. 3. Develop three-dimensional (3-d) version of the first-order model. July 2000 Objective Two will be undertaken by a funded postdoctoral research associate (PDRA) at UCL (one year), while the remaining objectives will be undertaken by the principle investigator (PI), co-PI (SJC) and a second funded PDRA at Southampton (two years). Objectives One and Four both have two phases. The first is to apply the respective models in a diagnostic fashion with a fixed ice geometry and using SRI velocities to constrain the parameterization of basal slip in the model. The second phase is to allow ice geometry to evolve in response to the calculated ice-flow field using the basal parameterization determined in the first phase. Figure 1. Ice-surface elevation change (coloured dots in m yr-1) superimposed upon ice-surface velocity (greyscale in m yr-1) over the main trunk of PIG [Shepherd et al., submitted], showing the first-ever direct observation of imbalance in a WAIS ice stream. These new data indicate that the relatively unknown PIG basin is undergoing change, in contrast to the near stasis of the Siple coast and RonneFilchner regions. 4. Apply this model to PIG using additional data generated by the project. Pine Island Glacier 1 2. Scientific Background 2.1 The importance of WAIS ice streams The evolution of the WAIS has been identified by many authors as a key unknown in future sealevel change [Oppenheimer 1998; Bentley 1998; Bindschadler et al. 1998]. The vast majority (> 90%) of mass lost from the ice sheet flows through a relatively small number of ice streams [McIntyre 1985]. An understanding of the long-term behaviour of these ice streams is therefore vital if we are to predict future sea level accurately. PIG has the largest discharge (66 Gt yr-1) of all WAIS ice streams [Vaughan et al. submitted]. Despite its importance in draining large areas of the ice sheet (with TG 40%), relatively little is known about PIG in comparison to other WAIS ice streams. The exciting new findings summarized below suggest that PIG is changing rapidly. These changes may have far-reaching consequences for the future of the WAIS because of PIG’s role as the primary drainage portal of the ice sheet. 2.2 Previous PIG research Observations of PIG change by Rignot [1998] showed that the grounding line retreated 8 km inland between 1992 and 1994. This implies ice thinning at the grounding line of the order of 3.5 m yr-1. In addition to these measurements, the UCL group has recently shown [Shepherd et al. submitted], through the combination of SRI and RA data, that grounding-line retreat is due to a widespread pattern of ice thinning that extends up to 150 km inland, reaching the ice-stream head (Figure 1). This thinning cannot be explained by fluctuations in the surface mass budget, and is likely to have resulted from a change in the dynamics of the ice stream itself. However, the source of the disturbance still remains uncertain. One suggestion [Rignot 1998] is that the disequilibrium may have resulted from the disintegration of a large ice shelf in Pine Island Bay at some stage in the recent past. However, new thickness observations by British Antarctic Survey [Vaughan et al. submitted] cast doubt on this. PIG is shown to be lightly grounded for a short distance inland of its marine terminus. Immediately upstream of this area, there is a very deep subglacial trough. Given this configuration, it may be argued that the inland stream is insulated from changes at or downstream of the grounding line, and that the source of thinning must lie elsewhere. The grounding-line retreat observed by Rignot [1998] and the surface-lowering shown by Shepherd et al. [submitted] imply that PIG is changing rapidly. This may be a consequence of either external forcing or may be generated internally (possibly cyclic). The mechanisms driving this change will only be fully understood by modelling of PIG and its drainage area. In this way, internal variability within the ice-flow system can be quantified [e.g., Payne 1998] and the effects of external changes (for instance sea-level rise or ice-shelf removal) assessed. 2.3 Modelling Ice Flow Ice-sheet models can be divided into four coupled components: ice-thickness evolution; icetemperature evolution; ice flow and stress regime; and ancillary calculations (including isostasy and mass balance calculations). In this proposal, we are principally concerned with third component. The widely-accepted Shallow Ice Approximations (SIA) [Hutter 1983] are based on assumptions regarding the stress regime within ice masses, and relate this regime to ice velocities (or strain rates) using the non-linear flow law for ice proposed by Glen [1955]. Depending on the spatial scale of investigation (with respect to ice thickness) and the nature of ice flow, varying degrees of SIA are appropriate. Two sets of approximations are widely used within the glaciological literature. The first (the zero-order approximation) is the basis for virtually all models of grounded ice sheets [e.g., Huybrechts and de Wolde 1999; Payne 1999]. This assumption is strictly appropriate only at spatial scales 20 times ice thickness [Paterson 1994] (i.e. 20 to 50 km for the WAIS). It assumes that longitudinal stresses are minimal and flow is dominated by vertical shearing. This type of model is inappropriate for studying PIG because of this scale limitation, as well as the likelihood of high longitudinal stresses within the ice stream. The second commonly used model is specifically designed to study ice-stream and iceshelf flows. It replaces the assumptions mentioned above with an assumption that vertical shear is negligible [MacAyeal 1989]. These first-order models can be used down to spatial resolutions 4 times ice thickness [Paterson 1994] (5 to 10 km). However, their use is only justified in situations where basal traction is guaranteed to be low and vertical shear can therefore be ignored [MacAyeal 1989]. This type of model may not be applicable to PIG because it experiences high driving stresses [Bentley 1987] and flows over steeply inclined bedrock slopes [Vaughan et al. submitted]. Pine Island Glacier 2 Recently, significant progress has been made on a class of model that is first order (i.e., incorporates longitudinal stresses) but does not rely on the negligible vertical shear assumption [Blatter et al. 1998; Gudmundsson 1997]. The only assumptions made in these models are that acceleration can be ignored; that the momentum balance in the vertical is dominated by gravity; and that the vertical shearing is simple. These assumptions are all valid away from icefalls and at spatial scales similar to ice thickness. A secondorder model would avoid the latter two assumptions [Blatter 1995] but would necessarily be considerably more complex. It is believed that first-order models of this class represent a natural tool for the analysis of PIG flow. The PI has recently developed a first-order flowline model (FOFM, incorporating the vertical and one horizontal dimension) of the type described above. The numerical implementation is based around that proposed by Herterich [1987]. Several innovations have improved the numerical stability of the scheme in comparison with the original. These include the use of finite-volume discretizations [Patankar 1980]; a non-linear iteration technique [Hindmarsh and Payne 1996]; and a stretched vertical coordinate system [Jenssen 1977]. Figure 2 illustrates results from this model for the Arolla benchmark dataset [Blatter et al. 1998]. The scheme solves the momentum-balance and flow-law equations in the form of a highly non-linear elliptic equation. The required boundary conditions are discussed below. Figure 2 Results from a newly developed firstorder model applied to the Glacier d'Arolla, Switzerland. The variation of longditudinal stress (in kPa) throughout the ice mass is shown. Axes are in m. 3 Specific Objectives 3.1 Transect model of PIG The aim of this objective is to test and refine the methodology that will be used later in applying the 3-d first-order model to PIG. The FOFM was developed by the PI while on sabbatical at the University of British Columbia. Its immediate use is to study the flow of the Langjökull Ice Cap, Iceland under the NERC thematic programme Arctic Ice and Environmental Variability (ARCICE). This application is similar in many respects to the proposed PIG work, however Langjökull is isothermal so that thermally-induced variations in the viscosity of ice can be ignored. This is certainly not the case for PIG and Payne [1995; 1999] has shown that the coupling between temperature and flow may be crucial in the long-term evolution of ice streams. A certain amount of development work will therefore be necessary before the existing model can be applied to PIG. The use of an existing flowline model ensures that the proposed methodology can be tested rapidly and efficiently rather than waiting to a later, more critical stage of the project to discover potential flaws. A flowline representation of PIG is not ideal for two reasons. First, there are indications that PIG is fed by a number of tributaries [Stenoien 1998] and the geometry of its drainage basin is complex [Bamber and Bindschadler 1997]. Second, the incorporation of transverse shear at the ice-stream margins is problematic in flowline models. Nonetheless the FOFM should provide a useful test bed for the project. Table 1 shows the data that will used in this and the 3-d modelling. The FOFM’s velocity model requires boundary conditions at the upper and lower boundaries of the ice mass. On the former, a zero-traction boundary condition is appropriate. While the basal boundary condition depends on the nature of the ice/substrate interface. If ice is frozen to the substrate then a zero-velocity condition is appropriate. However, if basal meltwater is present a prescribed traction is most natural [Herterich 1987]. MacAyeal et al. [1995] parameterize this traction as a function of basal slip velocity. Alternatively, a basal slip velocity can be prescribed directly. Application to PIG is likely to use a horizontal grid of 5 km. The other components of the model (ice thickness and temperature evolution and ancillary calculations) already exist in a suitable form. The model application will be in two phases: prognostic and diagnostic. First, the model will be run in diagnostic mode with ice-mass geometry held fixed. The aim of this phase will be to use SRI-derived estimates of surface velocity to constrain the parameterization of basal slip. A Pine Island Glacier 3 number of alternative methods are available to do this. MacAyeal et al. [1995] use control methods to accomplish this task with a vertically-integrated ice-stream model. A naïve approach to this problem is as follows (we return in Objective Four to a more sophisticated approach based on control methods). 1. Determine velocity assuming a frozen bed. 2. Find anomaly between SRI and modelled upper-surface velocities. 3. Repeat the calculation using this anomaly as the prescribed slip velocity. 4. Iterate Steps 2 and 3 until anomaly between SRI and modelled velocities falls below a threshold value. The inclusion of temperature calculations and their coupling to ice flow will complicate this proceedure slightly. The scheme is analogous to the restoring boundary conditions used for seasurface temperatures and salinities in many general ocean circulation models. The resultant basal velocity and stress fields will be consistent with the SRI data and the model’s physics. The relationship between these two quantities can then be used to identify a realistic parameterization that can be used in the next, prognostic, stage of the objective. The precise details of this parameterization will depend on the results, however the separation of PIG into spatially distinct regimes is a likely approach. The robustness of these parameterizations to assumptions about ice viscosity, thermal regime etc will be investigated in a sensitivity analysis. The aim of the prognostic stage is to compare modelled changes in ice thickness to those available from RA assessments of surfaceelevation change [Shepherd et al. submitted] and grounding-line migration [Rignot 1998]. In particular, the modelling will attempt to determine whether the observed changes imply long-term collapse or internally-generated cyclic behaviour [Payne 1995; 1999]. This work will be complimented by a larger analysis of the effects of changes in sea level, sub-shelf melt rates, air temperatures, accumulation rates and basal traction on PIG. Objective One will therefore allow us to develop an effective research methodology using the computationally-efficient FOFM before moving to the more cumbersome 3-d model of Objectives Three and Four. In addition, it will generate publishable results in its own right. Table 1 Data required in the modelling. Likely data sources are indicated as well as data’s use in diagnostic (D), prognostic (P) or both (B). Data Surface topography and surface change Bed topography Surface velocities Air temperatures Geothermal flux Accumulation rates Sub-shelf melt rates Grounding line D Source RA B D B B P P B BAS’ BEDMAP SRI Giovinetto et al. 1990 Assumed Vaughan et al. 1999 Jenkins et al. 1997 Rignot 1998 3.2 Acquistion of new data This objective aims to extend the existing data coverage to include the majority of the Pine Island basin. This is needed so that the 3-d modelling is adequately contrained over the basin and can therefore be used to study long-term evolution. This objective will generate information of unprecedented detail for an area which includes all tributary flows to the PIG, as well as regions of slow-flowing ice in the basin interior. Two techniques will be used. First, the existing SRI coverage of ice-surface velocity (Figure 1) will be extended by a factor of four. Second, RA will be used to measure changes in ice-surface elevation over the same area. The spatial distribution and temporal variability of ice-surface velocity within the PIG drainage basin will be determined using SRI from the ERS satellites. The existing velocity mosaic will be extended to cover the remainder of the basin viewable by the synthetic aperture radar (SAR) sensor using existing ERS data (Figure 3). This task will lead to a fourfold increase in our existing ice-surface velocity map. The substantial ERS SAR data volumes that will be required are available to us through the VECTRA programme. In the slow-moving interior of the drainage basin, tandem and 3-day ERS SAR repeat passes may be insufficient to reveal the intricate nature of the ice flow patterns. Fortunately, snow accumulation is typically low in these regions, and 35-day repeat pass data, which is frequently available, can also be used to produce interferograms with good phase coherence. The temporal spread of the ERS SAR dataset, in conjunction with velocity estimates from other sources (e.g. feature tracking using historical satellite imagery), will be used to identify possible velocity variations within the PIG basin. Pine Island Glacier 4 Part of the southern lobe of the PIG drainage basin (Figure 3) falls beyond SAR coverage, and other methods of velocity estimation will be required to complete the velocity map. Interferometric data from the RADARSAT sensor (which covered this region during a dedicated Antarctic mapping mission in 1997) has been used to estimate the velocity of slow moving interior ice (<100 m yr-1) [Joughin et al. 1999]. We will endeavour to obtain similar data through existing collaborations, but in the event that RADARSAT data are unavailable to us, we will employ other remote sensing techniques, such as feature tracking using Landsat imagery, to obtain direct estimates of ice speed within the southern lobe. The RADARSAT data have been particularly useful in identifying regions of flow imbalance [Bamber et al., 2000] and, building upon these findings, we aim to characterise the nature of the ice-sheet flow within the southern lobe to determine any departure from equilibrium. As an alternative to the direct measurements of SRI, balance velocities [Budd and Warner 1996] may be sufficiently accurate in the slow-moving interior, and we will investigate the utility of this technique. Measurements of surface-elevation change will be extended through a succession of satellite altimeters (ERS, ENVISAT, and ICESAT). ENVISAT will provide a seamless continuation of the current ERS time series, and data from the ICESAT laser altimeter will offer increased spatial coverage over the Antarctic Ice Sheet. These extended time series will yield higher accuracy. An increasing amount of fine detail will therefore be revealed in the pattern of thinning across PIG and its drainage basin. 3.3 Development of 3-d model The aim of this objective is to develop a 3-d first-order model of ice flow suitable for application to PIG. The FOFM is not the perfect tool for the study of PIG. The main reasons for this are the tributary structure of the upper parts of the ice stream; the complex shape of the Pine Island drainage basin; and the incorporation of ice-stream shear margins. The development of a 3-d version of the model (3DFOM) is therefore necessary. Equivalent numerical models for the other components of a general 3-d ice-mass model already exist (thickness and temperature evolution, and ancillary calculations). They have been developed within the NERC non-thematic grants on ‘Coupling models of ice streams and ice sheets’ (GR3/11532) and ‘Stability of the Antarctic Ice Sheet: a numerical analysis’ (GR3/12917). The change in scale between those projects (20km grids) and the proposed project (5 km grid) does not affect the validity of these model components, although it may lead to numerical complications. The experience gained in developing the velocity/stress regime component of FOFM should prove very useful in developing 3DFOM. It is hoped that the same approach can be taken to the solution of the underlying non-linear elliptic equation. There are, however, two complicating factors. The first is that two coupled elliptic equations will have to be solved (one for each horizontal velocity component). Experience in solving these equations was gained in the completed GR3/11532. The main source of additional complexity is correcting for the stretched vertical coordinate system, which can often quadruple the number of terms involved. The second complicating factor is that the FOFM code uses a preconditioned conjugategradient method to solve the linear parts of the equation. This is acceptable in two dimensions with typically 20 vertical layers and 100 horizontal columns (2,000 points). However, it may become impractical over an equivalent 3-d domain (200,000 points). FOFM uses the sparse-array package SLAP [Seager 1988]. There are several ways of avoiding this problem. First, the larger capacity of parallel computers could be employed (as in the current GR3/12917). Second, FOFM could be used to explore the potential for dramatically reducing the number of layers (initial impressions are that the vertical structure of the stress fields is relatively simple). The development of a 3-d, first-order model which is fully coupled to both ice-thickness and ice- temperature evolution would represent a major methodological advance. The model would be the natural tool for the analysis ‘meso-scale’ problems in ice flow. Examples of this type of problem are the onset of ice streaming [Joughin et al. 1999]; the transmission of stress between ice streams and neighbouring sheet-flow areas [van der Veen and Whillans 1996]; and the long-term evolution of ice domes (with their potential as ice-coring locations). These types of problem are key to our understanding of the dynamics of large ice masses but are not readily amenable to analysis using existing classes of model. This is because their fine spatial scales violate the assumptions behind zero-order continental-scale models, while Pine Island Glacier 5 vertically-integrated ice-stream models may not be applicable because very low basal traction cannot always be assumed. The proposed methodology is equally applicable to vertical-shear dominated (sheet) flow and horizontal-stretching (stream/shelf) flow, as well as transitions between these types of flow. Its use therefore avoids the need for an a priori classification of flow before the appropriate model is applied. Another potential use of this type of model would be in studying ice caps and valley glaciers, which are simply to small for zero-order models to be applicable [Hubbard et al., 1998]. Objective Three will therefore develop 3DFOM using the experience gained in developing FOFM. The end result should be a very generic model, which would be appropriate to the study of the ‘meso-scale’ ice dynamics problems of PIG, as well as other glaciological features in Antarctica. More generally, it would also represent a better tool for the study of small ice caps and glaciers than currently exists. predicted to have beds at melting point. Areas predicted to be frozen to their beds should only have residual amounts of basal slip. 3.4 Application of 3-d model to PIG This objective aims to understand the flow dynamics of PIG and its long-term evolution by applying a 3-d first-order model of ice flow to the whole drainage basin. The strategy used in applying 3DFOM will be similar to that of Objective One. The computational domain will cover the entire Pine Island basin at 5 km resolution. The four glaciological regimes present in the area will therefore all be incorporated: slow-flowing inland ice; ice-stream tributaries; PIG itself; and the grounding-line and ice-shelf area. The physics of the model are appropriate to all four regimes, without a priori classification. It is essential that the whole drainage basin be modelled in this way rather than restricting the analysis to PIG itself. This is because the long-term evolution of the ice stream is likely to be controlled by ice drainage from the basin interior and its thermomechanics [Payne 1998]. The diagnostic phase of this objective will use the ice-surface velocities generated in Objective Two to constrain the unknown basal slip field (as explained in Objective One). The proceedure should be equally applicable in areas both with and without basal slip. A simple check on model consistency will be to compare the predicted basal slip and temperature fields. Areas predicted to experience large amounts of slip should also be Figure 3 Current (upper) and potential (lower) SRI coverage for Pine Island basin. Hatch orientation indicates ascending and descending (both are required to estimate the 3-d icesurface velocity vector), while hatch density indicates single and repeat pass coverage. A detailed analysis of the relationship between basal slip, basal traction and basal temperature will yield the parameterizations used in the prognostic phase of the objective. In this phase, ice thickness will be allowed to respond to the changing patterns of velocity predicted by the model. A series of experiments will be undertaken which gradually remove constraints on the ice mass. Examples include allowing the grounding line to migrate freely, and allowing the inland boundaries of the drainage basin to migrate. This later topic also addresses the influence of neighbouring ice streams on the drainage basin of PIG and will attempt to explain the latter’s peculiar shape (see Figure 3). The aims of these prognostic experiments are twofold. First, to determine whether the observed Pine Island Glacier 6 PIG changes are a consequence of external forcing or internal dynamics. Second, to assess the consequences of these changes for PIG’s long-term evolution and the likelihood of its collapse. In the event that the proceedure of Objective One proves inapplicable, we will follow the control method techniques proposed by MacAyeal [1993]. The key extension will be to apply these techniques to a model which allows for high driving stresses and vertical variability. The misfit between the observed velocity constraints and the output from the model is minimised using Lagrange multipliers and a gradient-descent algorithm. To ensure that the data is not overfitted, it is necessary that the minimisation incorporates a measure of the error in the data: random measurement error, interpolation error or mapdigitization error, and so we will minimise the chisquared between the data and the model. We have successfully applied this methodology in the context of electrical impedance tomography (EIT), which is a widely studied non-linear inverse problem in medical imaging [Blott et al., 2000]. There is also the potential, indeed likelihood, of multiple minima: an effective procedure to address this is outlined in MacAyeal [1993]. Furthermore, our experience from EIT work has demonstrated that the fully 3-d problem may be less susceptible to such problems when constraints are placed on its boundary, particularly if additional smoothness constraints are imposed on the final solution. 4 Timetable and Expertise The project will last for two years and will start on 1st February 2001. The grant is required principally to support two PDRAs. One PDRA will be based in Southampton and will work on the modelling objectives for the whole of the project. The second PDRA will work on the remotesensing objective at UCL for one year. The named reseacher for this post is Andrew Shepherd who has extensive experience in the application of SRI and RA in Antarctica. The four objectives will be subdivided between the PIs and PDRA as follows. 1. FOFM application during months 1 to 12 with AJP (support) and Southampton PDRA (main). 2. Data acquistion in months 1 to 12 with DJW (support) and UCL PDRA (main). 3. 3DFOM development in months 1 to 12 with AJP (main) and Southampton PDRA (support). 4. 3DFOM application in months 12 to 24 with AJP (support), SJC (support) and Southampton PDRA (main). The project is timetabled so that the data acquistion will be completed before the application of the 3-d model starts (Year Two). During this first year, the Southampton PDRA will gain training in the application of higher-order glaciological models and will help in the development of the 3-d model. Year Two will see the application of the 3-d model, however there is likely to be continued input from AJP and SJC on development and control methods, respectively. The three PIs have contrasting skills which are well suited to the proposed project. AJP has wide experience in the application of numerical models to ice-sheet and glacier flow. Southampton-based PDRAs D.J. Baldwin and A.L. Takeda will offer support, respectively, in the development of icestream models and the application of parallel computing. SJC has considerable expertise in the development of parallel algorithms and the solution of inverse problems. His work on nonlinear inverse problems in medical imaging will be particularly helpful in Objective Four. DJW and his group are world-leaders in the application of remote-sensing techniques to glaciology, with expertise in SRI and RA which is unparalleled in the UK. 5 Justification of Resources Previous awards to the Southampton group have led to the purchase of a Silicon Graphics Origin 200 server with associated workstations and peripherals. Other high-performance computing resources are available in Southampton through SJC. The group is therefore well resourced in terms of computational power. The purchase of a medium-specification personal computer is, however, requested to allow the Southampton PDRA unrestricted access to these resources. A compact-disk writer is also requested to facilitate the storage of the large volumes of data likely to be generated by the project. Funds to cover consumables such as software licences and magnetic tapes are also requested. The latter are needed because repeat-pass interferometric coverage of the PIG drainage basin will require around 400 further SAR scenes. To archive this data we will need a total of 27 35Gb DLT tapes (400×0.33Gb raw data, 400×1.1Gb SLC data, 200×1.1Gb interferograms, 100×1.1Gb differential Pine Island Glacier 7 interferograms). This is the only viable method of data storage for long strips of SAR data. Some travel funds have been requested to facilitate bi-monthly visits between UCL and Southampton. These will be essential in guiding model development and the acquistion of appropriate data to constrain the model. Regular visits to the British Antarctic Survey (Cambridge) are also anticipated for discussion on the bedrock topography and glaciology of PIG. Results from the project will be reported at the annual American Geophysical Union (AGU) meeting in 2002 (modelling results), and the International Symposium on Remote Sensing in Glaciology in 2001 (remote-sensing results). The latter meeting, in particular, will be useful in exposing the modelling methodology to criticism early in the project. The AGU meeting will be combined with a visit to Allied Researcher Rignot, who is a world-leader in the application of SRI to the WAIS. All data generated by the project will be submitted for archiving at the Antarctic Environmental Data Centre, Cambridge. 6 References Bamber, J.L., and R.A. Bindschadler, An improved elevation dataset for climate and ice-sheet modelling: validation with satellite imagery, Ann. Glaciol., 25, 1997. Bamber, J.L., et al.,Widespread complex flow in the interior of the Antarctic Ice Sheet, Science, 287, 1248-1250, 2000. Bentley, C.R., Rapid sea-level rise from a West Antarctic ice-sheet collapse: a short-term perspective, J. Glaciol., 44, 157-163, 1998. Bentley, C.R., Antarctic ice streams: a review, J. Geophys. Res., 92, 8843-8858, 1987. Bindschadler, R.A., et al., What is happening to the West Antarctic Ice Sheet?, EOS Trans., 79, 257-265, 1998. Blatter, H., Velocity and stress fields in grounded glaciers,: a simple algorithm for including deviatoric stress gradients, J. Glaciol., 41, 333-344, 1995. Blatter, H., et al., Stress and velocity fields in glaciers: Part II. Sliding and basal stress distribution, J. Glaciol., 44, 457-468, 1998. Blott, B.H., et al., High fidelity imaging and high performance computing in nonlinear EIT. Physiol. Meas., 21, 7-13, 2000. Budd, W.F., and R.C. Warner, A computer scheme for rapid calculations of balance-flux distributions, Ann. Glaciol., 23, 21-27, 1996. Giovinetto, M.B, et al., Dependence of Antarctic surface mass balance on temperature, elevation, and distance to the open ocean, J. Geophys. Res., 95, 3517-3531, 1990. Glen, J.W., The creep of polycrystalline ice, Proc. R. Soc. London, Ser. A, 228, 519-538, 1955. Herterich, K., On the flow within the transition zone between ice sheet and ice shelf}, in C. J. van der Veen and J. Oerlemans (eds.) Dynamics of the West Antarctic Ice Sheet, D. Reidel, Dordrecht, 185-202, 1987. Hindmarsh, R.C.A., and A.J. Payne, Time step limits for stable solutions of the ice sheet equation, Ann. Glaciol., 23, 74-85, 1996. Hubbard, A., et al., Comparison of a first-order approximation for ice flow with field data: Haut Glacier d’Arolla, Switzerland, J. Glaciol., 44, 368-378, 1998. Hughes, T.J., The weak underbelly of the West Antarctic Ice Sheet, J. Glaciol., 27, 518-525, 1980. Hutter, K., Theoretical glaciology, D. Reidel, Dordrecht, 1983. Huybrechts, P., and J. de Wolde, The dynamic response of the Greenland and Antarctic ice sheets to multiple-century climatic warming, J. Climate, 12, 2169-2188, 1999. Gudmundsson, G.H., 1997, Basal flow characteristics of a nonlinear flow sliding frictionless over strongly undulating bedrock, J. Glaciol., 43, 80-89, 1997. IPCC, Climate change: the science of climate change, Cambridge University Press, 1995. Jenkins, A., et al., Glaciological and oceanographic evidence of high melt rates beneath Pine Island Glacier, West, Antarctica, J. Glaciol., 43, 114-121, 1997. Jenssen, D., A three-dimensional polar ice-sheet model, J. Glaciol., 18, 373-389, 1977. Joughin, I., et al., Tributaries of West Antarctic ice streams revealed by RADARSAT interferometry, Science, 286, 283-286, 1999. MacAyeal, D.R., Large-scale flow over a viscous basal sediment: Theory and application to Ice Stream B, Antarctica, J. Geophys. Res., 94, 4071-4087, 1989. MacAyeal, D.R., A tutorial on the use of control methods in icesheet modeling, J. Glaciol., 39, 91-98, 1993. MacAyeal D.R., et al., Basal friction of Ice Stream E, West Antarctica, J. Glaciol., 41, 247-262, 1995. McIntyre, N.F., The dynamics of ice-sheet outlets, J. Glaciol., 31, 99-107, 1985. Oppenheimer, M., Global warming and the stability of the West Antarctic Ice Sheet, Nature, 393, 325-332, 1998. Patankar, S.V., Numerical heat transfer and fluid flow, Hemisphere Publishing, New York, 1980. Paterson, W.S.B., The physics of glaciers, Elsevier, Oxford, 1994. Payne, A.J., Limit cycles in the basal thermal regime of ice sheets, J. Geophys. Res., 100, 4249-4263, 1995. Payne, A.J., Dynamics of the Siple Coast ice streams, West Antarctica: results from a thermomechanical ice sheet model, Geophys. Res. Lett., 25, 3173-3176, 1998. Payne, A.J., A thermomechanical model of ice flow in West Antarctica, Clim. Dyn. 15, 115-125, 1999. Rignot, E.J., Fast recession of a West Antarctic glacier, Science, 281, 549-551, 1998. Seager, M., A SLAP for the masses, Lawrence Livermore Nat. Lab. Technical Report, 1988. Shepherd, A., et al., Inland thinning of Pine Island Glacier, Science, submitted Stenoien, M.D., Interferometric SAR observations of the Pine Island Glacier catchment area, Ph.D. Thesis, Univ. Wisconsin-Madison, 1998. van der Veen, C.J., and I.M. Whillans, Model experiments on the evolution and stability of ice-streams, Ann. Glaciol., 23, 129-137, 1996. Vaughan, D.G., et al., Reassessment of net surface mass balance in Antarctica, J. Climate, 12, 933-946, 1999. Vaughan, D.G., et al., A review of ice-sheet dynamics in the PIG basin, West Antarctica: hypothesis of instability versus observations of change, Ant. Res. Ser., submitted. Pine Island Glacier 8
© Copyright 2026 Paperzz