Shallow shelf approximation as a "sliding law'' in a thermomechanically coupled ice sheet model

The shallow shelf approximation, a balance of membrane stresses for ice flow, is an effective "sliding law'' for ice sheet modeling. Our use of it as a sliding law becomes a standard model for ice stream flow when the sliding velocity is large (100 m a(-1) and faster). Following Schoof (2006a), we describe the basal resistance as plastic till for which the yield stress is given by a Mohr-Coulomb formula. Pore water pressure is related to basal melt rate. The velocity field used in the mass continuity and conservation of energy equations is an average of velocities from the shallow shelf approximation and the nonsliding shallow ice approximation. Using this scheme, our model has realistic, time-dependent ice streams which exhibit the range of surface velocities seen in actual ice streams. We demonstrate the model at high spatial resolution (5 km grid) over multiple millenia using its implementation in the Parallel Ice Sheet Model. Numerical experiments show that the entire scheme is stable with respect to many parameter changes. Some experiments reveal significant ice stream variability in a hypothetical steady climate, with characteristic cycles on the order of 1000 years. We believe this is the first practical whole ice sheet model with a unified treatment of vertical shear stresses and membrane stresses. It is capable of high-resolution, thermomechanically coupled, multimillenia simulations of ice sheets containing ice streams.