Understanding adaptive timestepping¶
At each time step the PISM standard output includes “flags” and then a summary of the model state using a few numbers. A typical example is
v$Eh diffusivity (dt=0.83945 in 2 substeps; av dt_sub_mass_cont=0.41972)
S 124791.571: 3.11640 2.25720 3.62041 18099.93737
y SSA: 3 outer iterations, ~17.0 KSP iterations each
The characters “v$Eh
” at the beginning of the flags line, the first line in the above
example, give a very terse description of which physical processes were modeled in that
time step. Here “v
” means that a stress balance was solved to compute the velocity.
Then the enthalpy was updated (“E
”) and the ice thickness and surface elevation were
updated (“h
”). The rest of the flags line looks like
diffusivity (dt=0.83945 in 2 substeps; av dt_sub_mass_cont=0.41972)
Recall that the PISM time step is determined by an adaptive mechanism. Stable mass
conservation and conservation of energy solutions require such an adaptive timestepping
scheme [26]. The first character we see here, namely “diffusivity
”, is the
adaptivetimestepping “reason” flag. See Table 37. We also see
that there was a major time step of \(0.83945\) model years divided into \(2\)
substeps of about \(0.42\) years. The skip
option enables this mechanism,
while skip_max
sets the maximum number of such substeps. The adaptive mechanism
may choose to take fewer substeps than skip_max
so as to satisfy certain numerical
stability criteria, however.
The second line in the above, the line which starts with “S
”, is the summary. Its
format, and the units for these numbers, is simple and is given by a couple of lines
printed near the beginning of the standard output for the run:
P YEAR: ivol iarea max_diffusivity max_hor_vel
U years 10^6_km^3 10^6_km^2 m^2 s^1 m/year
That is, in each summary we have the total ice volume, total ice area, maximum diffusivity (of the SIA mass conservation equation), and maximum horizontal velocity (i.e. \(\max(\max(u), \max(v))\)).
The third line of the above example shows that the SSA stress balance was solved. Information on the number of nonlinear (outer) and linear (inner) iterations is provided [25].
PISM output 
Active adaptive constraint or PISM subsystem that limited timestep size 


threedimensional CFL for temperature/age advection [26] 



end of prescribed run time 

maximum allowed \(\Delta t\) applies; set with 

maximum \(\Delta t\) was temporarily set by a derived class 

2D CFL for mass conservation in SSA regions (upwinded; [25]) 

the 

the 

a surface or an atmosphere model 

an ocean model 

a hydrology model stability criterion, see section Subglacial hydrology 

timethe bedrock thermal layer model, see section Modeling conservation of energy 

the eigencalving model, see section Calving and front retreat 
Option 
Description 


Adaptive time stepping ratio for the explicit scheme for the mass balance equation. 

The maximum timestep in years. The adaptive timestepping scheme will make the timestep shorter than this as needed for stability, but not longer. 

Enables timestep skipping, see below. 

Number of massbalance steps, including SIA diffusivity updates, to perform before
temperature, age, and SSA stress balance computations are done. This is only
effective if the time step is being limited by the diffusivity time step
restriction associated to mass continuity using the SIA. The maximum recommended
value for 

Hit multiples of the number of model years specified. For example, if stability
criteria require a timestep of 11 years and the 
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