Evolutionary versus diagnostic modeling

The main goal of a numerical ice sheet model like PISM is to be a dynamical system which evolves as similarly as possible to the modeled ice sheet. Such a goal assumes one has the “right” climate inputs and parameter choices at each time step. It also assumes one has the “right” initial conditions, such as an adequate description of the present state of the ice sheet, but this assumption is rarely satisfied. Instead a variety of heuristics must be used to minimally-initialize an ice sheet model. For options associated to establishing mathematical initial conditions when first starting PISM, see section Initialization and bootstrapping.

Inside PISM are evolution-in-time partial differential equations which are solved by taking small time steps. “Small” may vary from thousandths to tens of model years, in practice, depending primarily on grid resolution, but also on modeled ice geometry and flow speed. Time steps are chosen adaptively in PISM, according to the stability criteria of the combined numerical methods [22], [23].

However, especially for ice streams and shelves, non-time-stepping “diagnostic” solution of the stress balance partial differential equations might be the desired computation, and PISM can also produce such “diagnostic” velocity fields. Such computations necessarily assume that the ice geometry, viscosity, and boundary stresses are known. Because of the slowness of the ice, in the sense that inertia can be neglected in the stress balance [24], such computations can determine the ice velocity.

Sections Getting started: a Greenland ice sheet example and An SSA flow model for the Ross Ice Shelf in Antarctica give examples illustrating evolutionary and diagnostic modes of PISM, respectively. The first describes time-stepping evolution models for the Greenland ice sheet, while the second describes a diagnostic SSA model for the Ross ice shelf.

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