Regridding¶

It is common to want to interpolate a coarse grid model state onto a finer grid or vice versa. For example, one might want to do the EISMINT II experiment on the default grid, producing output foo.nc, but then interpolate both the ice thickness and the temperature onto a finer grid. The basic idea of “regridding” in PISM is that one starts over from the beginning on the finer grid, but one extracts the desired variables stored in the coarse grid file and interpolates these onto the finer grid before proceeding with the actual computation.

The transfer from grid to grid is reasonably general — one can go from coarse to fine or vice versa in each dimension \(x,y,z\) — but the transfer must always be done by interpolation and never extrapolation. (An attempt to do the latter will always produce a PISM error.)

Such “regridding” is done using the -regrid_file and -regrid_vars commands as in this example: }

pismr -eisII A -Mx 101 -My 101 -Mz 201 -y 1000 \
      -regrid_file foo.nc -regrid_vars thk,temp -o bar.nc

By specifying regridded variables “thk,temp”, the ice thickness and temperature values from the old grid are interpolated onto the new grid. Here one doesn’t need to regrid the bed elevation, which is set identically zero as part of the EISMINT II experiment A description, nor the ice surface elevation, which is computed as the bed elevation plus the ice thickness at each time step anyway.

A slightly different use of regridding occurs when “bootstrapping”, as described in section Initialization and bootstrapping and illustrated by example in section Getting started: a Greenland ice sheet example.

See Table 27 for the regriddable variables using -regrid_file. Only model state variables are regriddable, while climate and boundary data generally are not explicitly regriddable. (Bootstrapping, however, allows the same general interpolation as this explicit regrid.)

Table 27 Regriddable variables. Use `-regrid_vars` with these names.¶
Name	Description
`age`	age of ice
`bwat`	effective thickness of subglacial melt water
`bmelt`	basal melt rate
`dbdt`	bedrock uplift rate
`litho_temp`	lithosphere (bedrock) temperature
`mask`	grounded/dragging/floating integer mask, see section Flotation criterion, mask, and sea level
`temp`	ice temperature
`thk`	land ice thickness
`topg`	bedrock surface elevation
`enthalpy`	ice enthalpy

Here is another example: suppose you have an output of a PISM run on a fairly coarse grid (stored in foo.nc) and you want to continue this run on a finer grid. This can be done using -regrid_file along with -bootstrap:

pismr -i foo.nc -bootstrap -Mx 201 -My 201 -Mz 21 -Lz 4000 \
      -regrid_file foo.nc -regrid_vars litho_temp,enthalpy -y 100 -o bar.nc \
      -surface constant

In this case all the model-state 2D variables present in foo.nc will be interpolated onto the new grid during bootstrapping, which happens first, while three-dimensional variables are filled using heuristics mentioned in section Initialization and bootstrapping. Then temperature in bedrock (litho_temp) and ice enthalpy (enthalpy) will be interpolated from foo.nc onto the new grid during the regridding stage, overriding values set at the bootstrapping stage. All of this, bootstrapping and regridding, occurs before the first time step.

By default PISM checks the grid overlap and stops if the current computational domain is not a subset of the one in a -regrid_file. It is possible to disable this check and allow constant extrapolation: use the option -allow_extrapolation.

For example, in a PISM run the ice thickness has to be lower than the vertical extent of the computational domain. If the ice thickness exceeds Lz PISM saves the model state and stops with an error message.

pismr -i input.nc -bootstrap -Mz 11 -Lz 1000 -z_spacing equal \
      -y 3e3 \
      -o too-short.nc
PISM ERROR: Ice thickness exceeds the height of the computational box (1000.0000 m).
            The model state was saved to 'too-short_max_thickness.nc'.
            To continue this simulation, run with
            -i too-short_max_thickness.nc -bootstrap -regrid_file too-short_max_thickness.nc \
            -allow_extrapolation -Lz N [other options]
            where N > 1000.0000.

Regridding with extrapolation makes it possible to extend the vertical grid and continue a simulation like this one — just follow the instructions provided in the error message.