How (non)linear is the sliding law?

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One of the major shortcomings of past ice sheet models was their frequent assumption that basal sliding velocity is linearly dependent on driving stress/basal shear stress. Under such assumption doubling of ice flow velocity would require doubling of basal/driving stress. However, such fast recent changes in ice velocity appear to have been triggered by relatively small stress perturbations, implying non-linear dependence of sliding velocity on stress (e.g., Howat et. al. (2005)). The end result is that the relatively innocuous-looking assumption of linear sliding law has fundamental implications for model behavior because it forces the simulated velocity field to change relatively slowly since there are limits on how fast and large stress changes can be (e.g., driving stress changes substantially only when ice thickness and/or surface slope change substantially).

Studies of glacier sliding over bedrock typically indicate relatively non-linearity of the sliding law with the stress exponent n in the range of 2-4. With n=4 doubling of velocity can be accomplished with stress increase of about 20%. Moreover, motion of ice over weak sedimentary beds may be equivalent to a sliding law with stress exponent approaching infinity Tulaczyk et al. (2000) and Tulaczyk (2006). In the 'plastic bed' end-member, basal resistance to flow is velocity independent and changes in stress state trigger adjustments in longitudinal and transverse strain rates. Hence, the concept of a basal sliding law breaks down because the sliding velocity is not determined locally. The plastic bed concept has been explored in simple models examining recent changes in velocities of Siple coast ice streams Joughin et al. (2002), Bougamont et al. (2003a), Bougamont et al. (2003b).