Example: A regional model of the Jakobshavn outlet glacier in Greenland

Jakobshavn Isbrae is a fast-flowing outlet glacier in western Greenland that drains approximately 7% of the area of the Greenland ice sheet. It experienced a large acceleration following the loss of its floating tongue in the 1990s [51], an event which seems to have been driven by warmer ocean temperatures [52]. Because it is thick, has a steep surface slope, has a deep trough in its bedrock topography (Figure Fig. 33), and has a thick layer of low-viscosity temperate ice at its base [53], this ice flow is different from the ice streams in West Antarctica or Northeast Greenland [43].

This section describes how to build a PISM regional model of this outlet glacier [54] using scripts from examples/jako/. The same strategy should work for other outlet glaciers. We also demonstrate the PISM regional mode pismr -regional, and Python drainage-basin-delineation tools which can be downloaded from the PISM source code website. Such regional models allow modest-size computers to run high resolution models [1] and large ensembles. Regional analysis is justified if detailed data is available for the region.

The geometric data used here is the SeaRISE [55] 1 km dataset for the whole Greenland ice sheet. It contains bedrock topography from recent CReSIS radar in the Jakobshavn area. We also use the SeaRISE 5 km data set which has climatic mass balance from the Greenland-region climate model RACMO [56].

A regional ice flow model generally needs ice flow and stress boundary conditions. For this we use a 5 km grid, whole ice sheet, spun-up model state from PISM, described in Section Getting started: a Greenland ice sheet example of this Manual. You can download the large NetCDF result from the PISM website, or you can generate it by running a Section Getting started: a Greenland ice sheet example script.

../../_images/jako-mask-topg.png

Fig. 33 A regional-tools script computes a drainage basin mask from the surface DEM (left; Modis background) and from a user-identified terminus rectangle (blue). The regional model can exploit high-resolution bedrock elevations inland from Jakobshavn fjord (right; meters asl).

Get the drainage basin delineation tool

The drainage basin tool regional-tools is at https://github.com/pism/regional-tools. Get it using git and set it up as directed in its README.md. Then come back to the examples/jako/ directory and link the script. Here is the quick summary:

cd ~/usr/local/                                      # the location you want
git clone https://github.com/pism/regional-tools.git
cd regional-tools/
python setup.py install                              # may add "sudo" or "--user"
cd PISM/examples/jako/
ln -s ~/usr/local/regional-tools/pism_regional.py .  # symbolic link to tool

Preprocess the data and get the whole ice sheet model file

Script preprocess.sh downloads and cleans the 1 km SeaRISE data, an 80 Mb file called Greenland1km.nc. [2] The script also downloads the SeaRISE 5 km data set Greenland_5km_v1.1.nc, which contains the RACMO surface mass balance field (not present in the 1 km data set). If you have already run the example in Section Getting started: a Greenland ice sheet example then you already have this file and you can link to it to avoid downloading:

ln -s ../std-greenland/Greenland_5km_v1.1.nc

The same script also preprocesses a pre-computed 5 km grid PISM model result g5km_gridseq.nc for the whole ice sheet. This provides the boundary conditions, and the thermodynamical initial condition, for the regional flow model we are building. If you have already generated it by running the script in section Grid sequencing then link to it,

ln -s ../std-greenland/g5km_gridseq.nc

Otherwise running preprocess.sh will download it. Because it is about 0.6 Gb this may take some time.

So now let’s actual run the preprocessing script:

./preprocess.sh

Files gr1km.nc, g5km_climate.nc, and g5km_bc.nc will appear. These can be examined in the usual ways, for example:

ncdump -h gr1km.nc | less            # read metadata
ncview gr1km.nc                      # view fields

The boundary condition file g5km_bc.nc contains thermodynamical spun-up variables (enthalpy,bmelt,bwat) and boundary values for the sliding velocity (u_ssa_bc,v_ssa_bc); these have been extracted from g5km_gridseq.nc.

None of the above actions is specific to Jakobshavn, though all are specific to Greenland. If your goal is to build a regional model of another outlet glacier in Greenland, then you may be able to use preprocess.sh as is. The SeaRISE 1 km data set has recent CReSIS bed topography data only for the vicinity of the Jakobshavn outlet, however, and it is otherwise just BEDMAP. Because outlet glacier flows are bed-topography-dominated, additional bed elevation data should be sought.

Identify the drainage basin for the modeled outlet glacier

Here we are going to extract a “drainage basin mask” from the surface elevation data (DEM) in gr1km.nc. The goal is to determine, in part, the locations outside of the drainage basin where boundary conditions taken from the precomputed whole ice sheet run can be applied to modeling the outlet glacier flow itself.

The basin mask is determined by the gradient flow of the surface elevation. Thus generating the mask uses a highly-simplified ice dynamics model (namely: ice flows down the surface gradient). Once we have the mask, we will apply the full PISM model in the basin interior marked by the mask. Outside the basin mask we will apply simplified models or use the whole ice sheet results as boundary conditions.

The script pism_regional.py computes the drainage basin mask based on a user choice of a “terminus rectangle”; see Figure Fig. 33. There are two ways to use this script:

  • To use the graphical user interface (GUI) mode.

    Run

    python pism_regional.py
    

    Select gr1km.nc to open. Once the topographic map appears in the Figure window, you may zoom enough to see the general outlet glacier area. Then select the button “Select terminus rectangle”. Use the mouse to select a small rectangle around the Jakobshavn terminus (calving front), or around the terminus of another glacier if you want to model that. Once you have a highlighted rectangle, select a “border width” of at least 50 cells. [3] Then click “Compute the drainage basin mask.” Because this is a large data set there will be some delay. (Multi-core users will see that an automatic parallel computation is done.) Finally click “Save the drainage basin mask” and save with your preferred name; we will assume it is called jakomask.nc. Then quit.

  • To use the command-line interface.

    The command-line interface of pism_regional.py allows one to re-create the mask without changing the terminus rectangle choice. (It also avoids the slowness of the GUI mode for large data sets.) In fact, for repeatability, we will assume you have used this command to calculate the drainage basin:

    python pism_regional.py -i gr1km.nc -o jakomask.nc -x 360,382 -y 1135,1176 -b 50
    

    This call generates the red region in Fig. 33. Options -x A,B -y C,D identify the grid index ranges of the terminus rectangle, and option -b sets the border width. To see more script options, run with --help.

Cut out the computational domain for the regional model

We still need to “cut out” from the whole ice sheet geometry data gr1km.nc the computational domain for the regional model. The climate data file g5km_climate.nc and the boundary condition file g5km_bc.nc do not need this action because PISM’s coupling and SSA boundary condition codes already handle interpolation and/or subsampling for such data.

You may have noticed that the text output from running pism_regional.py included a cutout command which uses ncks from the NCO tools. This command also appears as a global attribute of jakomask.nc:

ncdump -h jakomask.nc | grep cutout

Copy and run the command that appears, something like

ncks -d x,299,918 -d y,970,1394 gr1km.nc jako.nc

This command is also applied to the mask file; note the option -A for “append”:

ncks -A -d x,299,918 -d y,970,1394 jakomask.nc jako.nc

Now look at jako.nc, for example with “ncview -minmax all jako.nc”. This file is the full geometry data ready for a regional model. The field ftt_mask identifies the drainage basin, outside of which we will use simplified time-independent boundary conditions. Specifically, outside of the ftt_mask area, but within the computational domain defined by the extent of jako.nc, we will essentially keep the initial thickness. Inside the ftt_mask area all fields will evolve normally.

Quick start

The previous steps starting with the command “./preprocess.sh” above, then using the command-line version of pism_regional.py, and then doing the ncks cut-out steps, are all accomplished in one script,

./quickjakosetup.sh

Running this takes about a minute on a fast laptop, assuming data files are already downloaded.

Spinning-up the regional model on a 5 km grid

To run the PISM regional model we will need to know the number of grid points in the 1 km grid in jako.nc. Do this:

ncdump -h jako.nc |head
    netcdf jako {
    dimensions:
      y = 425 ;
      x = 620 ;
    ...

The grid has spacing of 1 km, so our computational domain is a 620 km by 425 km rectangle. A 2 km resolution, century-scale model run is easily achievable on a desktop or laptop computer, and that is our goal below. A lower 5 km resolution spin-up run, matching the resolution of the 5 km whole ice sheet state computed earlier, is also achievable on a small computer; we do that first.

The boundary condition fields in g5km_bc.nc, from the whole ice sheet model result g5km_gridseq.nc, may or may not, depending on modeller intent, be spun-up adequately for the purposes of the regional model. For instance, the intention may be to study equilibrium states with model settings special to the region. Here, however we assume that some regional spin-up is needed, if for no other reason that the geometry used here (from the SeaRISE 1km data set) differs from that in the whole ice sheet model state.

We will get first an equilibrium 5 km regional model, and then do a century run of a 2 km model based on that. While determining “equilibrium” requires a decision, of course, a standard satisfied here is that the ice volume in the region changes by less than 0.1 percent in the final 100 model years. See ice_volume_glacierized in ts_spunjako_0.nc below.

The 5 km grid [4] uses -Mx 125 -My 86. So now we do a basic run using 4 MPI processes:

./spinup.sh 4 125 86 &> out.spin5km &

You can read the stdout log file while it runs: “less out.spin5km”. The run takes about 4.4 processor-hours on a 2016 laptop. It produces three files which can be viewed (e.g. with ncview): spunjako_0.nc, ts_spunjako_0.nc, and ex_spunjako_0.nc. Some more comments on this run are appropriate:

  • Generally the regridding techniques used at the start of this spin-up run are recommended for regional modeling. Read the actual run command by

    PISM_DO=echo ./spinup.sh 4 125 86 | less
    
  • We use -i jako.nc -bootstrap, so we get to choose our grid, and (as usual in PISM with -bootstrap) the fields are interpolated to our grid.

  • A modestly-fine vertical grid with 20 m spacing is chosen, but even finer is recommended, especially to resolve the temperate ice layer in these outlet glaciers.

  • There is an option -no_model_strip 10 asking pismr -regional to put a 10 km strip around edge of the computational domain. This strip is entirely outside of the drainage basin defined by ftt_mask. In this strip the thermodynamical spun-up variables bmelt,tillwat,enthalpy,litho_temp from g5km_bc.nc are held fixed and used as boundary conditions for the conservation of energy model. A key part of putting these boundary conditions into the model strip are the options

    -regrid_file g5km_bc.nc -regrid_vars bmelt,tillwat,enthalpy,litho_temp,vel_ssa_bc
    
  • Dirichlet boundary conditions u_ssa_bc,v_ssa_bc are also regridded from g5km_bc.nc for the sliding SSA stress balance, and the option -ssa_dirichlet_bc then uses them during the run. The SSA equations are solved as usual except in the no_model_strip where these Dirichlet boundary conditions are used. Note that the velocity tangent to the north and south edges of the computational domain is significantly nonzero, which motivates this usage.

  • The calving front of the glacier is handled by the following option combination:

    -calving ocean_kill -ocean_kill_file jako.nc -pik
    

    This choice uses the present-day ice extent, defined by SeaRISE data in Greenland1km.nc, to determine the location of the calving front. Recalling that -pik includes -cfbc, we are applying a PIK mechanism for the stress boundary condition at the calving front. The other PIK mechanisms are largely inactive because of -calving ocean_kill, but they should do no harm (see section PIK options for marine ice sheets).

../../_images/jako-csurf.png

Fig. 34 Left: modeled surface speed at the end of a 2 km grid, 100 model year, steady present-day climate run. Right: observed surface speed, an average of four winter velocity maps (2000,2006–2008) derived from RADARSAT data, as included in the SeaRISE 5 km data set [57], for the same region. Scales are in meters per year.

Century run on a 2 km grid

Now that we have a spun-up state, here is a 100 model year run on a 2 km grid with a 10 m grid in the vertical:

./century.sh 4 311 213 spunjako_0.nc &> out.2km_100a &

This run requires at least 6 GB of memory, and it takes about 16 processor-hours.

It produces a file jakofine_short.nc almost immediately and then restarts from it because we need to regrid fields from the end of the previous 5 km regional run (in spunjako_0.nc) and then to “go back” and regrid the SSA boundary conditions from the 5 km whole ice sheet results g5km_bc.nc. At the end of the run the final file jakofine.nc is produced. Also there is a time-series file ts_jakofine.nc with monthly scalar time-series and a spatial time-dependent file ex_jakofine.nc. The surface speed at the end of this run is shown in Fig. 34, with a comparison to observations.

Over this 100 year period the flow appears to be relatively steady state. Though this is not surprising because the climate forcing and boundary conditions are time-independent, a longer run reveals ongoing speed variability associated to subglacially-driven sliding cyclicity; compare [58].

The ice dynamics parameters chosen in spinup.sh and century.sh, especially the combination

-topg_to_phi 15.0,40.0,-300.0,700.0 -till_effective_fraction_overburden 0.02 \
   -pseudo_plastic -pseudo_plastic_q 0.25 -tauc_slippery_grounding_lines

are a topic for a parameter study (compare [59]) or a study of their relation to inverse modeling results (e.g. [60]).

Plotting results

Fig. 34 was generated using pypismtools, NCO and CDO. Do

ncpdq -a time,z,y,x spunjako_0.nc jako5km.nc
nc2cdo.py jako5km.nc
cdo remapbil,jako5km.nc Greenland_5km_v1.1.nc Greenland_5km_v1.1_jako.nc  # FIXME: if fails, proceed?
ncap2 -O -s "velsurf_mag=surfvelmag*1.;" Greenland_5km_v1.1_jako.nc \
    Greenland_5km_v1.1_jako.nc
basemap-plot.py -v velsurf_mag --singlerow -o jako-velsurf_mag.png jakofine.nc \
    Greenland_5km_v1.1_jako.nc

To choose a colormap foo.cpt add option --colormap foo.cpt in the last command. For this example PyPISMTools/colormaps/Full_saturation_spectrum_CCW.cpt was used.

Footnotes

[1]PISM can also do 1 km runs for the whole Greenland ice sheet; see this news item.
[2]If this file is already present then no actual download occurs, and preprocessing proceeds. Thus: Do not worry about download time if you need to preprocess again. The same comment applies to other downloaded files.
[3]This recommendation is somewhat Jakobshavn-specific. We want our model to have an ice-free down flow (western) boundary on the resulting computational domain for the modeled region.
[4]Calculate 620/5 + 1 and 425/5 + 1, for example.

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