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Floating ice shelves can exert a retentive and hence stabilizing force onto the inland ice sheet of Antarctica. However, this effect has been observed to diminish by the dynamic effects of fracture processes within the protective ice shelves, leading to accelerated ice flow and hence to a sea-level contribution. In order to account for the macroscopic effect of fracture processes on large-scale viscous ice dynamics (i.e., ice-shelf scale) we apply a continuum representation of fractures and related fracture growth into the prognostic Parallel Ice Sheet Model (PISM) and compare the results to observations. To this end we introduce a higher order accuracy advection scheme for the transport of the two-dimensional fracture density across the regular computational grid. Dynamic coupling of fractures and ice flow is attained by a reduction of effective ice viscosity proportional to the inferred fracture density. This formulation implies the possibility of non-linear threshold behavior due to self-amplified fracturing in shear regions triggered by small variations in the fracture-initiation threshold. As a result of prognostic flow simulations, sharp across-flow velocity gradients appear in fracture-weakened regions. These modeled gradients compare well in magnitude and location with those in observed flow patterns. This model framework is in principle expandable to grounded ice streams and provides simple means of investigating climate-induced effects on fracturing (e. g., hydro fracturing) and hence on the ice flow. It further constitutes a physically sound basis for an enhanced fracture-based calving parameterization.
We present the Potsdam Parallel Ice Sheet Model (PISM-PIK), developed at the Potsdam Institute for Climate Impact Research to be used for simulations of large-scale ice sheet-shelf systems. It is derived from the Parallel Ice Sheet Model (Bueler and Brown, 2009). Velocities are calculated by superposition of two shallow stress balance approximations within the entire ice covered region: the shallow ice approximation (SIA) is dominant in grounded regions and accounts for shear deformation parallel to the geoid. The plug-flow type shallow shelf approximation (SSA) dominates the velocity field in ice shelf regions and serves as a basal sliding velocity in grounded regions. Ice streams can be identified diagnostically as regions with a significant contribution of membrane stresses to the local momentum balance. All lateral boundaries in PISM-PIK are free to evolve, including the grounding line and ice fronts. Ice shelf margins in particular are modeled using Neumann boundary conditions for the SSA equations, reflecting a hydrostatic stress imbalance along the vertical calving face. The ice front position is modeled using a subgrid-scale representation of calving front motion (Albrecht et al., 2011) and a physically-motivated calving law based on horizontal spreading rates. The model is tested in experiments from the Marine Ice Sheet Model Intercomparison Project (MISMIP). A dynamic equilibrium simulation of Antarctica under present-day conditions is presented in Martin et al. (2011).