The majority of ice-sheet models have been developed by individual researchers or within small institution-based groups. This "do-it-yourself" history is in contrast to that of large community-based models, which dominate research in the fields of meteorology and oceanography. The resulting diversity of ice-sheet models is both a strength, in that specific models were honed to specific applications, and a weakness, in that no consensus on the basic behaviour of the models existed. The European Ice Sheet Modelling Initiative (EISMINT) was developed to address this diversity. Siegert and Payne (2001) provide details of how the EISMINT programme has assisted the development of ice sheet models. The following section is summarised from Siegert and Payne (2001) to illustrate the purpose of EISMINT and its achievements.
EISMINT had three main aims: first, to define and perform intercompar-ison exercises to help establish consensus on basic model prediction; second, to identify good practice in ice-sheet modelling; third, to develop the next generation of ice-sheet models. The EISMINT project was funded by the European Science Foundation in two phases, which ran from January 1993 to December 1995 and from January 1996 to December 1997. The funding allowed four major international meetings to concentrate on model intercomparison. It also allowed a series of smaller meetings on basal processes, ice rheology, ice-climate interactions, ice-oceanic interactions, ice-lithosphere interactions and former ice sheets.
The aims of model intercomparisons were threefold. The first was to test the effects of numerical implementation on model prediction. This required the physics incorporated into models to be tightly constrained, along with the values of model parameters and boundary conditions. A wide variety of numerical techniques has been employed by ice-sheet modellers. For example, several finite-element models existed, although the majority of ice-sheet models employed finite difference schemes. Within the latter class, a variety of methods were available to deal with the basic nonlinearity of ice flow. The EISMINT intercomparisons explained, for the first time, the effect of the type of numerical solution on model prediction. The second was to determine the effect which the many poorly constrained physical parameters had on the overall prediction of the models. The third was to model ice masses through a given time-dependent climate change scenario. Examples included the response of ice sheets to stepped changes in forcing, glacial-interglacial growth and decay, and the response to future, anthropogenic change. Particular attention was paid to how models replicated and forecasted Antarctic Ice Sheet dynamics.
Ice-sheet model intercomparison was designed to be as inclusive as possible, in order that results from models with one and two horizontal dimensions, which may or may not have included internal-temperature evolution, could be evaluated (Huybrechts et al., 1996, and papers within Annals of Glaciology, Vol. 23). Model boundary conditions and parameter values were prescribed as much as possible so that observed differences in output could be interpreted purely in terms of the numerics of the model.
The intercomparison exercise involved several iterations in which model results were submitted for analysis. A consensus set of results gradually emerged from this process. Many of the differences identified initially between models arose for non-scientific reasons (such as ambiguity in the experiment descriptions). One problem encountered was that results tended to converge towards median values as outlying models were modified. The modification process may have been genuine (for instance, in finding coding errors) but may also have been driven by a perceived need to conform with the bulk of models regardless of whether they were correct. In this way, genuine differences could have become obscured. This problem was offset somewhat by recognizing analytical solutions to ice flow equations, taken as ''truth''. While the number of analytical solutions available is quite limited for ice-sheet models, their use was an important feature of the intercomparison process.
In general, most models performed similarly in terms of their predictions of ice-thickness evolution, internal-temperature evolution and ice velocity patterns, but some differences were observed. Interpretation of these differences showed the effect of numerical solution on model predictions. Two groups of models were identified: those which employed a more stable scheme to solve the continuity equation were found to be less accurate in comparison to a more precise formulation which was, however, less stable numerically. In this way, the EISMINT programme was able to establish firm benchmarks for model types and their performance.
Simulations of the Antarctic Ice Sheet took place in the third level of the EISMINT exercise during 1997. The aim of this level was to compare model predictions of the past and future evolution of these ice masses with the minimum amount of constraint on the details of the individual models. Three experiments were undertaken. The first compared results from simulations of the present-day ice sheet. The second compared results from glacial-interglacial experiments. The third analysed differences between forecasts of future icesheet behaviour (over the next 500 years) (see http://homepages.vub.ac.be/ ~phuybrec/eismint.html for details).
Results for the first experiment were encouraging, as all four models revealed similar output. However, major differences were observed in the second and third experiments. Specifically, ice-sheet volumes predicted for both the Eemian interglacial (started at ca. 125 ka and ended at ca. 110 ka) and Last Glacial Maximum were noticeably different. Although only two of the four models yielded similar results, they were recommended as a benchmark for subsequent studies, presumably because other models had fatal flaws that became apparent in the experiment, allowing a level of ''verification'' for Antarctic Ice Sheet models.
There is no doubt that the EISMINT programme has led to agreement and commonality regarding ice-sheet modelling. One important outcome is the establishment of a community within the field of glaciology, which can develop ice-sheet modelling in future. Importantly, the EISMINT programme has led to the availability of free software, in the form of the GLIMMER model (http://forge.nesc.ac.uk/projects/glimmer/), based on the
''best practice'' elements established through model intercomparison exercises. The full development, documentation and release of GLIMMER was a consequence of the GENIE Earth System Model project (www. genie.ac.uk), which used an ice-sheet model built on the validated procedures established by EISMINT. It is very likely that this model will lead to an increase in ice-sheet modelling activity and, thus, its use in understanding past changes in Antarctica. The next phase of ice-sheet model intercompar-isons has recently been established in the ice sheet Model Intercomparison Programme (ISMIP). In ISMIP, the performance of next generation of icesheet models (accounting for the full three-dimensional flow of ice) will be analysed. It will also help to establish community agreement on how icesheet models predict the cryosphere to respond to future climate change scenarios (details of ISMIP can be found at the following website: homepages.vub.ac.be/~phuybrec/ismip.html).
6.6. Comparing Ice-Sheet Models with Antarctic Glaciological Data
Despite most ice-sheet models being based on well-established physical assumptions about the flow of ice, these assumptions, and the data used as input, may oversimplify the actual glaciological situation. The result is mismatch between model results and real glaciological measurements. When comparing model output with glaciological data, the scale of the datasets needs to be similar to the scale of the ice-sheet model output (e.g. averaged over 5-20 km) for the exercise to be meaningful. Real data at a finer resolution than this show how ice-sheet models simplify the actual flow of ice sheets. Determining the difference between model output and these real data represents an important way in which to assess the validity of ice-sheet models. As ice-sheet models become more sophisticated, it will be necessary to test their output against a variety of ice-sheet measurements for validation purposes. This section outlines datasets currently available in Antarctica that have yet to be compared fully with ice-sheet model output, but should be used for the future validation of ice-sheet models (Siegert and Payne, 2001).
6.6.1. Surface and Sub-Ice Morphology, and the Flow of Ice in Central Regions
The advent of satellite altimetry has resulted in the determination of the surface morphology of ice sheets to a high degree of accuracy. At present, most ice-sheet models of Antarctica work at a 5-20 km scale. These models replicate the broad shape of the ice sheet well. However, real morphology at this or a finer scale cannot be modelled at present. ERS-1 altimetry of the Antarctic Ice Sheets reveals that there is a complex morphology on the ice surface related to the flow of ice.
A good example of where ice-sheet model results (Huybrechts, 1990) match well with large-scale ice-sheet features, yet poorly with sub-grid cell morphology, is at Dome C, East Antarctica (Fig. 6.3). The ice surface around Dome C has a generalized surface slope of about 0.08°. However, there are a number of regions where the slope reduces to less than 0.01°. These ''flat'' surfaces are caused by ice flow over subglacial trenches and/or subglacial lakes (e.g. Lake Vostok). In either case, the flow of ice is altered from the base-parallel shearing that most ice-sheet models account for, by longitudinal extension. In order to solve this problem, an accurate representation of subglacial topography is required. Although there is a
Figure 6.3: The location of Antarctic subglacial lakes. Adapted from Siegert et al. (2005a).
Figure 6.3: The location of Antarctic subglacial lakes. Adapted from Siegert et al. (2005a).
major programme aimed at establishing an up to date bedrock elevation for Antarctica (e.g. BEDMAP), the resolution of these new data is not fine enough to solve the problem of complex flow of ice over subglacial topography highlighted here.
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