PISM supports spatially-variable bed topography but does not support spatially-variable sea level elevation. This is a problem, since GIA produces both the topography and sea level, and the sea level is not uniform in general.

Note, though, that all uses of the sea level elevation in PISM involve bed topography or the flotation criterion.

So, at flotation we want to have

bed(x,y) = sea_level(x,y) - rho_ice / rho_ocean * ice_thickness(x,y),

but PISM does not support sea_level(x,y).

Luckily this can be re-written as

bed(x,y) - sea_level(x,y) = 0 - rho_ice / rho_ocean * ice_thickness(x,y)

We define

bed_modified(x,y) = bed(x,y) - sea_level(x,y)

and use

bed_modified(x,y) = 0 - rho_ice / rho_ocean * ice_thickness(x,y),

which PISM can handle without issues.

Note also that the bed depth computed using bed_modified behaves the way we would expect: an increase in sea level corresponds to an increase of the water depth (0 - bed_modified).

We can track changes in the load used by the GIA model using modeled ice thickness reported by PISM at predefined intervals.

PISM reports ice thickness on an uniform cartesian grid, typically using the polar stereographic projection, so we need to transfer this thickness to the a longitude,latitude grid used by GIA.

We need to ensure that the total ice volume is conserved during when ice thickness is transferred from the PISM grid to the GIA grid, so we use conservative remapping (see CDO documentation for a reference).

To make sure that a PISM output file contains metadata defining the grid in the form recognized by CDO, run

nc2cdo.py pism_output.nc

Ths nc2cdo.py script is installed with PISM. (It requires Python modules numpy, pyproj, and netCDF.)

To create a netCDF file defining an GIA grid, run

ascii_to_nc.py gia_grid.xy gia_grid.nc

Both nc2cdo.py and ascii_to_nc.py compute latitude and longitude bounds (see below).

Computing weights is the most computationally expensive part of the interpolation process, but luckily we only need to do it once for each pair of grids and each interpolation direction.

CDO supports pre-computing weights using the genbil operator for bilinear interpolation and gencon for first order conservative interpolation.

To compute bilinear interpolation weights CDO needs a grid description. Conservative remapping methods also require latitude and longitude bounds.

We use bilinear interpolation to transfer data from the GIA grid to the PISM grid. To compute corresponding weights, run

cdo genbil,pism_output.nc gia_grid.nc gia_to_pism_weights.nc

Here pism_output.nc is a PISM output file processed using nc2cdo.py and gia_grid.nc is a NetCDF file produced by ascii_to_nc.py.

We use first-order conservative remapping to transfer data from the PISM grid to the GIA grid. To compute corresponding weights, run

cdo gencon,gia_grid.nc pism_output.nc pism_to_gia_weights.nc

Assume that pism_output.nc contains the PISM model state, running the following

 # extract ice thickness
 cdo selvar,thk pism_output.nc ice_thickness.nc
 # put it onto the GIA grid using pre-computed weights
 cdo remap,gia_grid.nc,pism_to_gia_weights.nc ice_thickness.nc ice_thickness_latlon.nc
 # replace missing values with zeros
 cdo setmisstoc,0 ice_thickness_latlon.nc ice_thickness_latlon_filled.nc
 nc_to_ascii.py ice_thickness_latlon_filled.nc ice_thickness.xyz

nc_to_ascii.py is not implemented yet.

Now we need to combine this field with thicknesses of other ice sheets, compute load changes, etc.

 ascii_to_nc.py bed_topography.xyz topg.nc
 cdo remap,pism_output.nc,gia_to_pism_weights.nc topg.nc topg_pism.nc
 # compute topography changes
 # apply them to the undeformed ("present-day") topography to recover
 # small features not resolved on the coarse GIA grid