Temperate ice formation and vertical resolution

[talbrecht]

This issue is part of a discussion I started with @tkleiner on the question what vertical resolution would be required to see convergence in PISM simulations. I tested dz as parameter in transient glacial cycle simulations of Antarctica (16km horizontal resolution), in review in TCD.

I found for variation of dz at the base between 40m and 1m differences in sea-level equivalent ice volume of almost 18m SLE, which can be compared to the difference between glacial and modern state, see my jupyter notebook.
More ice volume for smaller dz seems do be related to the sum of temperate ice volume, which almost scales with vertical resolution, most of it from the outer sliding regions, where temperate ice layers can be 100-200m thick.

I have then also run nomass simulations, but with SSA and sliding applied (SSA velocity bounded by 5000m/yr), so see how temperate ice evolves in an equilibrium. In fact, the equilibrium volume of temperate ice seems to converge for dz finer than 1m at the base (see plots here). There is also much less of the relict temperate-ice chess-pattern in the inner ice sheet regions than in the glacial cycle simulations.

The experiments have been performed using a PISM version based on v1.0, but I have also tested v1.1 with similar results (see comparison here).

I assume that most Antarctic modelers use quadratically spaced vertical resolution of around 20-50m at the base, and we should emphasize in the manual, that this is really coarse and may affect the simulation results. How can we exclude that there might be a bug involved, any ideas for a simplified and quick test?!

I actually found an inconsistency in the linear interpolation of the CTS diagnostic, but this should not influence the results (see this artificial test case). I will write a pull request, if I am not wrong here?!

[aaschwanden]

@talbrecht Thanks for the detailed analysis. I have found differences in temperate ice thickness for Greenland too, though I never looked at it in such a systematic way. @ckhroulev and I will discuss this later today.

After some discussion with Mathieu Morlighem last year, @ckhroulev and I decided to overhaul the implementation of the conservation of energy. In short, we will change the vertical coordinate system. This will allow for concentrating layers near the base and the surface for improved accuracy while reducing the total number of layer, hopefully leading to a decrease RAM usage and significant performance boost. This effort will take some time and we don't have a clear timeline yet, but hope to complete it by the end of the year.

[talbrecht]

Great, let us know if we can help with it...

[talbrecht]

A reviewer ask about the influence of modeled ice sheet volume on vertical resolution: "Does the thermodynamic solver have a sub−iteration to ensure the CFL condition is not broken? What kind of switch is used to turn on basal sliding?"

Theres is no switch as SSA and hence basal sliding is calculated in the entire ice domain, right?

[tkleiner]

@talbrecht concerning the last part of your initial post:

I actually found an inconsistency in the linear interpolation of the CTS diagnostic, but this should not influence the results (see this artificial test case). I will write a pull request, if I am not wrong here?!

I did some experiments with the EISMINT II setup using PISM (stable v1.1.4 committed by Constantine Khrulev on 2019-06-17 10:14:35 -0800) and found no inconsistency in PISMs CTS diagnostic. All enthalpy versus depth profiles are crossing the enthalpy of the pressure melting point Epmp(z) = Es(p(z)) lines at the reported CTS positions. See figure.

Dotted lines are the enthalpy Epmp(z) and temperature Tpmp(z) at pressure melting point. Slight differences due to tue different ice thicknesses after 20ka.

low resolution (10km, nz=81):
pisms -eisII A -Mx 151 -My 151 -Mz 81 -Lz 4300 -verbose 2 -y 20000 -ts_file stable1.1_eisII_A1_dx10km_nz81_20ka_ts.nc -ts_times 10 -extra_file stable1.1_eisII_A1_dx10km_nz81_20ka_ex.nc -extra_times 1000 -extra_vars tempicethk_basal,temppabase,thk,velsurf_mag -energy enthalpy -stressbalance sia -o stable1.1_eisII_A1_dx10km_nz81_20ka.nc -o_size big -options_left

and high resolution run (10km, dz=1m):
pisms -eisII A -Mx 151 -My 151 -Mz 4301 -Lz 4300 -verbose 2 -z_spacing equal -y 20000 -ts_file stable1.1_eisII_A1_dx10km_dz1m_20ka_ts.nc -ts_times 10 -extra_file stable1.1_eisII_A1_dx10km_dz1m_20ka_ex.nc -extra_times 1000 -extra_vars tempicethk_basal,temppabase,thk,velsurf_mag -energy enthalpy -stressbalance sia -o stable1.1_eisII_A1_dx10km_dz1m_20ka.nc -o_size big -options_left

[talbrecht]

We had some discussions on vertical resolution and temperate ice in PISM recently. Is the update on the conservation of energy implementation still on the list?