## Modelling glacier response to climate change

Different approaches have been taken to estimate glacier, icefield and ice-sheet response to climate change. Haeberli (this volume, Chapter 84) summarizes present-day glacier and icesheet changes. I discuss the methods being used to estimate glacier sensitivity to climate change. A variety of techniques have been used to provide forecasts of glacier and ice-sheet response to the anticipated 21st century climate change, at both local and global scales.

where b is the ice-equivalent mass balance rate, as defined in section 32.2, and 3/ VjH) denotes the horizontal divergence of ice flux, where Vj is the vertically integrated horizontal velocity. The vertically integrated ice flux in Equation (13) is estimated as a function of ice-sheet geometry using a constitutive equation that relates strain rates (hence, velocity) to the stress field in the ice. Stresses that induce internal, creep deformation in ice masses are associated primarily with gravitational normal and shear stresses, and are a non-linear function of ice thickness and surface slope. Additional, generally second-order, stresses arise as a result of velocity gradients in the ice (compressive or extensional flow), topographic channelization (e.g. flow constrictions or convergence of tributary glaciers), or gradients in friction at the bed and the glacier margins (e.g. side drag from valley walls).

Glen's flow law (Glen, 1958; Paterson, 1994) is the prevailing ice rheology used in glacier flow modelling. Glen-flow-based icesheet models have had good success in simulating the internal shear deformation that dominates flux in ice sheets that are wellcoupled with their bed (e.g. East Antarctica, Greenland), but they are not adequate in ice masses where ice flux is dominated by basal flow. In the West Antarctic Ice Sheet, basal sliding and/or plastic failure in a thin layer of subglacial sediment are responsible for most of the motion in fast-flowing ice streams that drain over 90% of the ice sheet (Paterson, 1994; Tulaczyk et al., 2000a).

Modelling of basal flow remains a challenge, as the governing physics involve subglacial hydrology, roughness elements (basal pinning points or 'sticky spots'), and sediment dynamics (Alley et al., 1987a; MacAyeal et al., 1995; Tulaczyk et al., 2000a,b). These controls are complex, difficult to observe, and are subgrid-scale in most modelling studies. Even in West Antarctica, one of the

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