Abstract
Abstract. We describe and test a two-horizontal-dimension subglacial hydrology model which combines till with a distributed system of water-filled, linked cavities which open through sliding and close through ice creep. The addition of this sub-model to the Parallel Ice Sheet Model (PISM) accomplishes three specific goals: (a) conservation of the mass of water, (b) simulation of spatially and temporally variable basal shear stress from physical mechanisms based on a minimal number of free parameters, and (c) convergence under grid refinement. The model is a common generalization of 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 preserve physical bounds on the pressure. In steady state a functional relationship between water amount and pressure emerges. We construct an exact solution of the coupled, steady equations and use it for verification of our explicit time stepping, parallel numerical implementation. We demonstrate the model at scale by 5 year simulations of the entire Greenland ice sheet at 2 km horizontal resolution, with one million nodes in the hydrology grid.
Highlights
Any continuum-physics-based dynamical model of the liquid water underneath and within a glacier or ice sheet has at least these two elements: the mass of the water is conserved and the water flows from high to low values of the modeled hydraulic potential
Steady-state, nearly exact solution (Sect. 5.4) we verified most of the numerical schemes described above. (Verification is the process of measuring and analyzing the errors made by the numerical scheme, especially as the numerical grid is refined (Wesseling, 2001).) To do this we initialized our time-stepping numerical scheme with the nearly exact steady solution and we measured the error relative to the exact values after 1 model month
Only one-way coupling was tested: a steady ice dynamics model fed its fields to an evolving subglacial hydrology model
Summary
Any continuum-physics-based dynamical model of the liquid water underneath and within a glacier or ice sheet has at least these two elements: the mass of the water is conserved and the water flows from high to low values of the modeled hydraulic potential. Modeled aquifer geometry might be a system of linked cavities (Kamb, 1987), conduits (Nye, 1976), or a sheet (Creyts and Schoof, 2009). Geometry evolution processes might include the opening of cavities by sliding of the overlying ice past bedrock bumps (Schoof, 2005), the creation of cavities by interaction of the ice with deformable sediment (Schoof, 2007), closure of cavities and conduits by creep (Hewitt, 2011), or melt on the walls of cavities and conduits which causes them to open (Clarke, 2005). Models have combined subsets of these different morphologies and processes (Flowers and Clarke, 2002a; Hewitt, 2013; Hoffman and Price, 2014; Van der Wel et al, 2013; Werder et al, 2013; de Fleurian et al, 2014). The completeness of the modeled processes must be balanced against the number of uncertain model parameters and the ultimate availability of observations with which to constrain them
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