Mass-conserving subglacial hydrology in the Parallel Ice Sheet Model

Abstract. We describe and test a distributed subglacial hydrology model which combines a pressurized, plastic till with a system of water-filled, linked cavities which open through sliding-generated cavitation and close through ice creep. The addition of this sub-model to the Parallel Ice Sheet Model accomplishes three specific goals: (1) conservation of the mass of two-phase (solid/liquid) water in the ice sheet, (2) simulation of spatially- and temporally-variable basal shear stress from physical mechanisms based on a minimal number of free parameters, and (3) convergence under two-horizontal-dimensional grid refinement of the subglacial water amount and pressure. The model is a common generalization of at least four others: (i) the undrained plastic bed model of Tulaczyk et al. (2000b), (ii) a standard "routing" model used for identifying locations of subglacial lakes, (iii) the lumped englacial/subglacial model of Bartholomaus et al. (2011), and (iv) the elliptic-pressure-equation model of Schoof et al. (2012). We use englacial porosity as a regularization, and we preserve physical bounds on the pressure. In steady state the model generates a local functional relationship between water amount and pressure. We construct an exact solution of the coupled, steady equations which is used for verification of our explicit time-stepping, parallel numerical implementation. We demonstrate the model at scale by five year simulations of the entire Greenland ice sheet at 2 km horizontal resolution, with one million nodes in the hydrology grid.