Choosing the stress balance

The basic stress balance used for all grounded ice in PISM is the non-sliding, thermomechanically-coupled SIA [16]. For the vast majority of most ice sheets, as measured by area or volume, this is an appropriate model, which is an \(O(\epsilon^2)\) approximation to the Stokes model if \(\epsilon\) is the depth-to-length ratio of the ice sheet [38].

The shallow shelf approximation (SSA) stress balance applies to floating ice. See the Ross ice shelf example in section An SSA flow model for the Ross Ice Shelf in Antarctica for an example in which the SSA is only applied to floating ice.

In PISM the SSA is also used to describe the sliding of grounded ice and the formation of ice streams [10]. Specifically for the SSA with “plastic” (Coulomb friction) basal resistance, the locations of ice streams are determined as part of a free boundary problem of Schoof [21], a model for emergent ice streams within a ice sheet and ice shelf system. This model explains ice streams through a combination of plastic till failure and SSA stress balance.

This SSA description of ice streams is the preferred “sliding law” for the SIA [10], [17]. The SSA should be combined with the SIA, in this way, in preference to classical SIA sliding laws which make the sliding velocity of ice a local function of the basal value of the driving stress. The resulting combination of SIA and SSA is a “hybrid” approximation of the Stokes model [17]. Option -stress_balance ssa+sia turns on this “hybrid” model. In this use of the SSA as a sliding law, floating ice is also subject to the SSA.

In addition to this, PISM includes an implementation of the first order approximation of Stokes equations due to Blatter (-stress_balance blatter, [41], [42]).

All stress balance options except for the first order approximation correspond to two basic choices:

  • modeling basal sliding, and

  • modeling of ice velocity within an ice column.

PISM supports the following stress balance choices, controlled using stress_balance­.model (option -stress_balance):

  1. none: no sliding, ice velocity is constant in each column. This equivalent to disabling ice flow completely.

  2. prescribed_sliding: Use the constant-in-time prescribed sliding velocity field read from a file set using stress_balance­.prescribed_sliding­.file, variables ubar and vbar. Horizontal ice velocity is constant throughout ice columns.

  3. ssa: Use the Shallow shelf approximation (SSA) model exclusively. Horizontal ice velocity is constant throughout ice columns.

  4. weertman_sliding: basal sliding is approximated using the Weertman-style sliding law, ice velocity is constant throughout ice columns.

  5. sia (default): no sliding; ice velocity within the column is approximated using the Shallow ice approximation (SIA). Floating ice does not flow, so this model is not recommended for marine ice sheets.

  6. prescribed_sliding+sia: basal ice velocity is read from an input file and held constant, ice velocity within the column is approximated using the Shallow ice approximation (SIA).

  7. ssa+sia: use Shallow shelf approximation (SSA) as a sliding law with a plastic or pseudo-plastic till, combining it with the Shallow ice approximation (SIA) according to the combination in [17]; similar to [10]. Floating ice uses SSA only. This “hybrid” stress balance is the recommended sliding law for the SIA.

  8. weertman_sliding+sia: basal sliding is approximated using the Weertman-style sliding law, ice velocity within the column is approximated using the Shallow ice approximation (SIA).

  9. blatter: use Blatter’s model.

Please see the following sections for details.

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