ISMIP-HOM test suite exercise

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In this exercise, we will test out Glimmer/CISM's higher-order stress balance subroutines by running the model through a few of the ISMIP-HOM test suite problems. The tests we'll run are for 3d models, so the domain and boundary conditions vary in the x and y directions (i.e. in map plane). For test A, the topography varies periodically in x and y, and for test C, the basal traction varies periodically in x and y. While the amplitude of the variations is the same for all tests, the wavelength is decreased by a factor of two for each successive test. For λ=160 km, the velocities solutions essentially look like that from a shallow ice model. Halving λ to 80 km, then to 40, 20, 10, and finally 5 km, the higher-order components of the stress balance become successively more important to the velocity solution. Figures 1 and 2 below shows relevant input data for each of the two experiments for λ = 80km. Here, in the interest of time, we will only run tests for the first three wavelengths in the series (160, 80, and 40 km).

Figure 1: ISMIP-HOM test A input (periodic basal roughness with no sliding); ice thickness, basal topography, and surface elevation. The basal boundary condition is no slip and the lateral boundary conditions are periodic velocities in x and y.


Figure 2: ISMIP-HOM test C input (sliding according to periodic basal traction); ice thickness,bBetasquared, and surface elevation. Sliding takes place along the basal boundary according to a "betasquared" (traction) type sliding law. The lateral boundary conditions are periodic velocities in x and y (NOTE: In this experiment we have a slab of constant thickness on an inclined plane with only the sliding properties changing along/across the domain. Also, the surface slope is ~10x smaller than for experiment A).


Running the test cases

To set up the experiments, we will use some configuration files and python scripts developed by Tim Bocek and Jesse Johnson (also, see this link). These set the correct flags, so that Glimmer/CISM calls the necessary subroutines, and construct the necessary input netCDF files.

First, we need to change into the correct directory where the test scripts and configuration files live. Assuming that you are starting in the directory from the directory glimmer/src/fortran/, type

cd ../tests/ISMIP-HOM/; ls -l

to change into the appropriate directory and list its contents. The files with a .config extension are read by the appropriate python scripts to construct the appropriate fields for the input netCDF file. The .config files are also read by the model at run time, as they specify the values for various flags (including calls to the HO subroutines rather than the shallow ice dynamics routines). The files with a .py extension are the relevant python scripts.

Let's set up test cases A and C for a domain length of 160 km. First check the configuration file to make sure that the domain length, number of grid spaces, and the grid spacing give the correct input values.

vi ishom.a.config


upn = 11
ewn = 51
nsn = 51
dew = 3200
dns = 3200

for the grid variables. Note that 51 x 3200 = 16.32 km, so that our domain will actually have one 3.2 km grid space extra in each of the x and y directions. This is necessary in order to implement the periodic boundary conditions at the lateral domain boundaries. If we now type

python ishom.a.config

we will generate the necessary netCDF input file for the experiment. Using NCVIEW, you can look at the input data fields and make sure that they are the correct lateral dimensions. To run the model using these input data, we need to execute simple_glide. If that file is not in your path you can copy it into the test directory as follows

cp ../../src/fortran/simple_glide ./

and then execute it by typing


You will be prompted for the relevant configuration file, which is of course ishom.a.config. Another way to do this would have been to use the linux/unix pipe command

echo ishom.a.config | ./simple_glide     - or -    echo ishom.a.config | simple_glide          (the latter if "simple_glide" is already in your path)

Either way, after responding to the prompt, you should see some model output that looks something like this:

Running Payne/Price higher-order dynamics solver
iter #     uvel resid          vvel resid         target resid
 2         1.00000             1.00000            0.100000E-04
 3        0.143388            0.215689E-02        0.100000E-04
 4        0.392197E-01        0.902012E-03        0.100000E-04
 5        0.655156E-01        0.745786E-03        0.100000E-04
 6        0.503367E-01        0.465037E-03        0.100000E-04
 7        0.344782E-02        0.329053E-03        0.100000E-04
 8        0.100065E-01        0.256138E-03        0.100000E-04
 9        0.163779E-01        0.190435E-03        0.100000E-04
10        0.866196E-02        0.136968E-03        0.100000E-04
11        0.549490E-02        0.104118E-03        0.100000E-04
12        0.546429E-02        0.798739E-04        0.100000E-04

At this point, you know that the higher-order dynamics routine is working on a solution. The 1st column tells you which "outer loop" iteration you are on (that is, iteration on the effective viscosity - the "inner loop" iteration is the conjugate gradient iterative solution to the matrix inversion, and that output is normally suppressed). The 2nd and 3rd columns display the x (uvel) and y (vvel) residuals (the normalized, maximum change in the velocity field between the current and previous iterations) and the last column shows the target residual, at which point the solution is considered to be converged. When the model stops iterating it will create an output netCDF file that we can evaluate. In this case, the file name is


If you find that something weird is happening like your residuals are all over the place, the model just crashes, etc., trying replacing your configuration files with these default configuration files for ISMIP-HOM test.

Plotting model output

We can do a quick evaluation of using NCVIEW or some other netCDF file viewing utility. However, what we really want to do is compare our model solutions with the ISMIP-HOM benchmark solutions, so we can see how are model is doing relative to other models that took place in the benchmark exercise (see Pattyn et. al (2008) for a detailed discussion of the results). To do that, we'll use some of handy python test-suite scripts we mentioned above.

First, we need to generate a text file of output data, from our model result, which will be compared with other model results from the benchmarking study. To do that, we type

./ a glm1a160.txt

The script reads the netCDF output file and generates the text file glm1a160.txt (the "...a160..." denotes test A for a domain length of 160 km). We then type

./ --exp=a --size=160      -or-      ./ -ea -s160

which uses some python modules to make a nice Matlab style figure (see below). That figure will have a ".png" extension and can be found in


Now, do the same set of steps but decrease the domain wavelength to 80 and then 40 km. To make it easy for you, some grid parameters that work for this are

upn = 11
ewn = 51
nsn = 51
dew = 1600
dns = 1600 

for the 80 km test and

upn = 11
ewn = 51
nsn = 51
dew = 800
dns = 800

for the 40 km test. Output files for these tests will be generated in the same way as above,

 ./ a glm1a080.txt           - and -        ./ a glm1a040.txt

To plot all of the three ouputs for test A on one plot, use

./ --exp=a --size=40,80,160              - or -         ./ -ea -s40,80,160

which should give you something that looks similar to Figure 3.

Figure 3: Higher-order model output for ISMIP-HOM test A with domain lengths of 160, 80, and 40 km. Solid black line is output from the current model and the colored, shaded regions represent the standard deviation of other models participating in the benchmarking study (see HERE for a more detailed description of these plots).


Now go through the same set of steps for test case C (again, with wavelengths of 160, 80, and 40 km). You should get a figure that looks something like Figure 4.

Figure 4: Higher-order model output for ISMIP-HOM test C with domain lengths of 160, 80, and 40 km. Solid black line is output from the current model and the colored, shaded regions represent the standard deviation of other models participating in the benchmarking study (see HERE for a more detailed description of these plots).


Additional Exercises

  • Try adjusting the horizontal and vertical grid spacing to see how it affects the results and/or model performance. For example, for the 80km tests, decrease the number of horizontal grid cells by a factor of two and increase the grid spacing by a factor of two,
upn = 11
ewn = 26
nsn = 26
dew = 3200
dns = 3200 

How much faster does the model converge on a solution? Does the output still fall within the standard deviation given by the benchmarks? How What happens if the vertical resolution is doubled?

  • Compare higher-order and 0-order solutions for test A with the 80 km domain length. To do this, in ishom.a.config, set the diagnostic_run flag to 0 instead of 1, rebuild the file, and re-run the model. When the model has finished running, examine using NCVIEW. Click on the variable uvelhom to make a colormap of the higher-order x component of velocity at time 1 (as shown in figure below).

Figure 4: Using NCVIEW to plot output of "" to compare higher-order and SIA solutions. Note that the value of current time is 2001, not 2000.


Click somewhere on the image to get a 2d velocity profile (choose x0 under Xaxis). Next, pick the variable uvel (the velocity from the SIA model) and do the same thing. When comparing the two profiles you should see something like in Figure 5.

Figure 5: Comparison of higher-order (top) and SIA (bottom) velocity profiles. For the same model domain, the HO velocities are ~25% slower due to the influence of horizontal-stress gradients, which the SIA model does not "feel" at all.


  • Do the same for ISMIP-HOM test A for the 40 km domain. You should notice that, as the magnitude of the higher-order velocities continues to decrease with decreasing domain length, those for the SIA model do not. Why is this?