Response of the polar ice sheets to future climatic warming

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Three-dimensional ice-sheet modelling studies all indicate that on time-scales less than a century the direct effects of changes in the surface mass-balance dominate the response. This means that the response is largely static, and thus that the ice flow on this time-scale does not react much to changes in surface mass balance. Greenland studies by Van de Wal & Oerlemans (1997) and Huybrechts & de Wolde (1999) found that ice-dynamics counteract the direct effect of mass-balance changes by between 10 and 20%. The mechanism arises because surface slopes at the margin are steepened in response to the increased melting rates. This causes the ice to flow more rapidly from the accumu-laton to the ablation zone, leading to a dynamic thickening below the equilibrium line. The higher surface level of the ablation zone in turn leads to less melting than would be the case if ice dynamics were not included. Because of its longer response time-scales, the Antarctic ice sheet hardly exhibits any dynamic response on a century time-scale, except when melting rates below the ice shelves are prescribed to rise by in excess of

1myr-1 (O'Farrell et al, 1997; Warner & Budd, 1998; Huybrechts & de Wolde, 1999).

These responses should be considered in addition to the long-term background trend as a result of ongoing adjustment to past environmental changes as far back as the last glacial period. The IPCC Third Assessment Report estimates the latter contribution to be between 0 and 0.5 mmyr-1 of equivalent sea-level rise for both polar ice sheets combined (Church et al., 2001a). Three-dimensional modelling studies which analyse the imbalance pattern resulting for the present-day in glacial cycle simulations typically find a long-term sea-level evolution of between 1 and 4 cm per century for Antarctica but a negligible contribution of only a few millimetres per century for Greenland (Huybrechts & de Wolde, 1999; Huybrechts & Le Meur, 1999). Another component to the current and future evolution of ice sheets are the effects of'unexpected ice-dynamic responses' which may or may not be related to contemporary climate changes, and which find their origin in variations at the ice-sheet base or at the grounding line. Examples are the measured thinning of the Pine Island and Thwaites sectors of the West Antarctic ice sheet (Shepherd et al., 2002), the oscillatory behaviour of the Siple Coast ice streams (Joughin et al., 2002), or the surging behaviour of some Greenland outlet glaciers (Thomas et al., 2000a). Such mechanisms are hard to predict and currently are not incorporated in any large-scale model of the polar ice sheets.

Plate 80.6 shows an example of a series of ice-sheet simulations predicting 20th and 21st century volume changes. Boundary conditions of temperature and precipitation were in these experiments derived by perturbing present-day climatologies according to the geographically and spatially dependent patterns predicted by the T106 ECHAM4 model (Wild et al, 2003) for a doubling of CO2 under the IS92a scenario. To generate time-dependent boundary conditions, these patterns were scaled with the area-average changes over the ice sheets as a function of time for available AGCM results. Typically, mass-balance changes cause a Greenland contribution to global sea level rise of +2 to +7cm between 1975 and 2100, and an Antarctic contribution of between -2 and -14 cm. This differential response is because increased marginal melting on Greenland is predicted to outweigh the effect of increased precipitation, whereas a warmer atmosphere over Antarctica is expected to lead to more precipitation, but still negligible surface melting. For the majority of the driving AGCMs, the Antarctic response is larger than for Greenland, so that the combined sea-level contribution from mass-balance changes alone is negative. However, when the background trend is taken into account, the sea-level contribution from both polar ice sheets is not significantly different from zero (Huybrechts et al., 2004b), strengthening earlier conclusions that Antarctica and Greenland may well balance one another on a century time-scale.

The results shown in Plate 80.6 were used as the base for the IPCC TAR projections of sea-level rise from the polar ice sheets. To do that, they were regressed against global mean temperature to enable further scaling to take into account the complete range of IPCC temperature predictions for the most recent SRES emission scenarios. Taking into account the background evolution and various sources of uncertainties, this yielded a predicted Antarctic contribution to global sea-level change between 1990 and 2100 of between -19 and +5 cm, which range can be considered as a 95% confidence interval (Church et al., 2001). For Greenland, the range was -2 to +9 cm. Most of this spread came from the climate sensitivity of the forcing AGCMs, and less from the emission scenario or the uncertainty in the ice-sheet models. These numbers should be compared with the predicted contributions to 21st century sea level rise of between +11 and +43cm from thermal expansion of the sea water and of between +1 and +23 cm from melting of mountain glaciers and small ice caps, based on the same set of AGCMs. Taking into account all sources and uncertainties, the IPCC TAR predicts a sea-level rise from 1990 to 2100 of between 9 and 88 cm, with a central estimate of 48 cm (Church et al., 2001). Response during the third millennium and beyond

Beyond the 21st century, the approximate balance between both polar ice sheets is, however, unlikely to hold. If greenhouse warming conditions were to be sustained after the year 2100, the picture is expected to change drastically. In particular the Greenland ice sheet is very vulnerable to a climatic warming. For an annual average warming over Greenland of more than about 2.7°C, mass-balance models predict that ablation will exceed accumulation (Huybrechts et al., 1991; Janssens & Huybrechts, 2000). Under these circumstances, the ice sheet must contract, even if iceberg production is reduced to zero as it retreats from the coast. For a warming of 3°C, the ice sheet loses mass slowly and may be able to approach a new steady state with reduced extent and modified shape if this results in less ablation. For greater warming, mass is lost faster and the Greenland ice sheet eventually melts away, except for residual glaciers at high altitudes. Two powerful positive feedbacks may accelerate the melting process: lower ice-sheet elevations lead to higher surface temperatures, and land-surface changes from ice to tundra further increase summer temperatures (Toniazzo et al., 2004). Huybrechts & de Wolde (1999) find the Greenland ice sheet to contribute about 3 m of sea level rise by the year 3000 for a sustained warming of 5.5°C. For a warming of 8°C, they calculate a contribution of about 6 m. Greve (2000) reports that loss of mass would occur at a rate giving a sea-level rise of between 1mmyr-1 for a year-round temperature perturbation of 3°C to as much as 7mmyr-1 for a warming of 12°C. Gregory et al. (2004) have investigated the development of Greenland's temperature using IPCC scenarios in which atmospheric CO2 stabilizes at different levels over the next few centuries. They find that the 2.7°C threshold is passed in all but one of 35 combinations of AOGCM and stabilization level; the warming exceeds 8°C in many cases and continues to rise after 2350 for the higher concentrations. The conclusion is that the Greenland ice sheet is likely to be eliminated over the course of the next millennia, unless drastic measures are taken to curb the predicted warming. Even if atmospheric composition and the global climate were to return to pre-industrial conditions, the ice-sheet might not be regenerated, implying that the sea-level rise could be irreversible (Gregory et al., 2004; Toniazzo et al., 2004).

On centennial to millennial time-scales, Antarctic model predictions demonstrate how several mechanisms depending on the strength of the warming come into play. For warmings below about 5°C, runoff remains insignificant and there is hardly any change in the position of the grounding line (Huybrechts & de Wolde, 1999). For larger warmings, however, significant surface melting occurs around the ice-sheet edge and basal melting increases below the ice shelves, causing the ice shelves to thin. When rapid ice-shelf thinning occurs close to the grounding line, grounding-line retreat is induced. In large-scale ice-sheet models, this occurs in two ways: steeper gradients across the grounding zone cause larger driving stresses, and higher deviatoric stress gradients across the grounding zone lead to increased strain rates, and hence a speed-up of the grounded ice and subsequent thinning. In the model studies performed by the Australian group (Budd et al, 1994; O'Farrell et al, 1997; Warner & Budd, 1998), large increases in bottom melting are the dominant factor in the longer-term response of the Antarctic ice sheet, even for moderate climate warmings of a few degrees. Budd et al. (1994) found that without increased accumulation, the increased basal melt of 10myr-1 would greatly reduce ice shelves and contribute to a sea-level rise of over 0.6m by 500yr, but no drastic retreat of the grounding line. With a similar model but different climatic forcing, O'Farrell et al. (1997) find a sea-level rise of 0.21m after 500yr for a transient experiment with basal melt rates evolving up to 18.6myr-1. In the study by Warner & Budd (1998), a bottom melt rate of 5myr-1 causes the demise of WAIS ice shelves in a few hundred years and removal of the marine portions of the West Antarctic ice sheet and a retreat of coastal ice towards more firmly grounded regions elsewhere over a time period of about 1000 years. Predicted rates of sea-level rise in these studies are up to between 1.5 and 3.0mm yr-1 depending on whether accumulation rates increase together with the warming. Although these are large shrinking rates, obtained under severe conditions of climate change, they cannot be considered to support the concept of a catastrophic collapse or strongly unstable behaviour of the WAIS, which is usually defined to mean its demise within several centuries, implying sea-level rises in excess of 10 mmyr-1 (Oppenheimer, 1998; Vaughan & Spouge, 2002). It should, however, be noted that the mechanics of grounding-line migration are not fully understood, and that none of these three-dimensional models adequately includes ice streams, which may be instrumental in controlling the behaviour and future evolution of the ice sheet in West Antarctica.

80.5 Conclusions and future outlook

Three-dimensional ice-sheet modelling significantly contributes to a better understanding of the polar ice sheets and their interactions with the climate system. Current models available to the community are able to predict the spatial and temporal ice-sheet response to changes in environmental conditions with increasing confidence. Large-scale models perform best over interior portions of continentally-based ice sheets, where ice deformation is well understood, obeys a simple force balance, and can be reliably modelled taking into account the flow law of ice. In some instances, when the basal ice has developed a strong fabric, making the ice anisotropic, or when crystal properties have introduced gradients in hardness, the resulting effects usually can be handled satisfactorily by prescribing a (variable) enhancement factor in the flow law.

Shortcomings in these models require further investigation in two main fields: incorporation of more appropriate physics and incorporation of improved boundary data. In particular basal sliding, marine ice dynamics and iceberg calving remain problematic. These processes are not easily quantified and are typically highly parametrized. Fast glacier conditions at the base are poorly understood, and so is the development of ice streams in marine-based ice sheets. Processes related to bed roughness, till rheology, and basal water pressure are all thought to be important elements but a realistic basal boundary condition for use in numerical models has not yet been developed. A credible treatment will need to include subglacial hydrology and the geological controls on soft-sediment deformation. The physics of grounding-zone migration is subgrid scale and is also not yet portrayed reliably in current models. In the grounding zone, a change takes place between flow dominated by basal stress to a basal stress-free regime, with flow primarily driven by longitudinal extension rather than vertical shear deformation. The spatial scale over which this transition takes place is unclear, however, and is therefore included in current models in an ad hoc way, if at all. The classic example where many of these problems converge is the Siple Coast area of the West Antarctic ice sheet, which is characterized by extensive ice streaming, low surface slopes, and a seemingly smooth transition into a floating ice shelf. Iceberg calving may be an even greater challenge to model in large-scale treatments. Calving at marine margins is related to fracture dynamics and temperature and stress fields in the ice, but the process is not well understood and therefore impossible to model with confidence. A proper treatment of calving is nevertheless warranted because ice-front degradation into bordering marine waters is the dominant means of ablation in Greenland tidewater glaciers and Antarctic ice shelves.

Although ice-sheet evolution is sensitive to several glaciologi-cal controls, long-term variability is dictated by climate and mass-balance related boundary conditions. Uncertainties in parametrizations have a large impact, particularly with respect to ice-sheet ablation. The mass-balance calculation is also sensitive to model resolution, as topographic detail is important in high-

relief areas and ablation is typically concentrated in a narrow band at the ice-sheet margin. Present-day atmospheric boundary conditions such as mean annual air temperature and snow accumulation are known to a level of accuracy commensurate with that required by ice-sheet models but their patterns of change in past as well as future climates are poorly constrained. Even more troublesome is the melt rate from the underside of the ice shelves, which may affect grounding lines but for which we have very limited data. The same is also true of the geothermal heat warming at the ice-sheet base, which exerts a crucial control on the spatial extent of basal melting, but for which there are very few data.

Current developments in large-scale ice-sheet modelling mainly occur along two lines: incorporation of ice-sheet models in climate or earth system models of varying complexity, and refinements of the ice dynamics at the local scale using higherorder representations of the force balance. Interactive coupling of ice-sheet models with atmosphere and ocean models enables mass-balance changes over the ice sheets to be prescribed more directly and the effects of circulation changes to be dealt with more properly. If the coupling is two-way, the approach can additionally take into account the effect of ice-sheet changes on its own forcing. Such coupled experiments have only just begun but are likely to highlight interesting behaviour. Recent examples include the effects of freshwater fluxes on the circulation of the North Atlantic Ocean (Schmittner et al., 2002; Fichefet et al., 2003), the enhancing effect of ice-dammed lakes on ice-sheet growth (Krinner et al., 2004), or the climate feedbacks resulting from Greenland ice-sheet melting (Ridley et al., 2004). A second line of current research concerns the nesting of detailed higherorder flow models (e.g. Pattyn, 2003) into large-scale models to study the flow at high spatial resolution for which the usual assumptions made in zero-order models are known to break down. First attempts in this direction for limited inland areas near ice divides were presented in Greve et al. (1999) and further explored for the purpose of ice-core dating and interpretation in Huybrechts et al. (2004a).

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