A hierarchy of simplifying assumptions for grounded ice flow¶
Table 4 describes a hierarchy of models, listed roughly in order of increasing effectiveness in modeling grounded ice sheets with fast flow features. This is also the order of increasing need for data to serve as boundary and initial conditions, however, as also described in the Table.
Model 
Assumptions 
Required data 

perfectlyplastic ice 
steady state; ice has shear stresses below a predetermined ice “yield stress”; also needs predetermined location of ice sheet margin 

balance velocities 
steady state; ice flows down surface gradient [32] 
same as above, plus:

isothermal SIA 
same as above, but timedependence is allowed 

thermocoupled SIA 
nonsliding lubrication flow, temperaturedependent softness [30], [22] 
same as above, plus:

polythermal SIA 
allows liquid water fraction in temperate ice; conserves energy better [35], [36] 
same as above 
SIA + SSA hybrid 
SSA as a sliding law for thermocoupled SIA [29], [37]; polythermal by default 
same as above, plus:

First Order Approximation 
pressure within the ice is hydrostatic; \(x\) and \(y\) derivatives of the vertical velocity component are small compared to \(z\) derivatives of horizontal components [38], [39], [40] 
same as above 
It may also be helpful to view the implemented stress balances as PISM software components (C++ classes). Fig. 14 shows the sequences of actions taken by the SIAonly, SSAonly, and SIA+SSA hybrid model components. In each case a membrane stress solution is generated first, then a distribution of vertical shear in the column of ice is generated second, and finally a use of incompressibility computes the vertical component of the velocity. The nonsliding SIAonly model has a trivialized membrane stress solution. The SSAonly model has a trivialized computation of vertical shear.
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