additional testing of centered vs. upwided surface gradient calculations in Glissade dycore

[billsacks]

From @stephenprice on March 23, 2015 21:12

When using incremental remapping (or FO upwinding) for thickness evolution of idealized test cases (e.g. Halfar) checkerboard surface elevation patterns have been observed to develop when using a centered sfc elevation gradient calculation scheme. An "upwinding" sfc elev. gradient scheme was introduced and shown to alleviate the problem.

However, for realistic test cases (e.g. 4 km Greenland), exactly the opposite behavior has been observed; the centered gradient scheme results in smooth sfc elev (and velocity) fields and the upwinded gradient scheme introduces what appears to be a checkerboard mode after only a few years of fwd integration (see example figs below).

This behavior has been observed in multiple branches of the code (including devel), when using different dynamical cores, and when using either IR or FO upwinding for advection. A suggestion for further testing from W. Lipscomb is as follows:

"One test worth trying would be to set accuracy_flag_in = 1 in glissade_velo_higher.F90 in the call to the gradient routines. This would generate a 1st-order rather than 2nd -order accurate one-sided gradient, which might be less prone to checkerboard noise (or at any rate, the differences between 1st order and 2nd order might tell us something)."

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Image WITH checkerboarding in sfc speed field after ~20 years of integration (when using the upwinded elevation gradient scheme).

Image with NO checkerboarding in sfc speed field after ~20 years of integration (when using the centered elevation gradient scheme).

Copied from original issue: E3SM-Project/cism-piscees#25

[billsacks]

From @DanFMartin on March 23, 2015 21:27

For the idealized dome test case mentioned here, do you need to use
upwinded/one-sided gradients everywhere, or just at the ice margin?
(we've known for some time that we need to use one-sided differencing
for surface elevations at grounding lines, for example)

On 03/23/2015 02:12 PM, stephenprice wrote:

When using incremental remapping (or FO upwinding) for thickness
evolution of idealized test cases (e.g. Halfar) checkerboard surface
elevation patterns have been observed to develop when using a centered
sfc elevation gradient calculation scheme. An "upwinding" sfc elev.
gradient scheme was introduced and shown to alleviate the problem.

However, for realistic test cases (e.g. 4 km Greenland), exactly the
opposite behavior has been observed; the centered gradient scheme
results in smooth sfc elev (and velocity) fields and the upwinded
gradient scheme introduces what appears to be a checkerboard mode after
only a few years of fwd integration (see example figs below).

This behavior has been observed in multiple branches of the code
(including devel), when using different dynamical cores, and when using
either IR or FO upwinding for advection. A suggestion for further
testing from W. Lipscomb is as follows:

"One test worth trying would be to set accuracy_flag_in = 1 in
glissade_velo_higher.F90 in the call to the gradient routines. This
would generate a 1st-order rather than 2nd -order accurate one-sided
gradient, which might be less prone to checkerboard noise (or at any
rate, the differences between 1st order and 2nd order might tell us
something)."

---

Image WITH checkerboarding in sfc speed field after ~20 years of
integration (when using the upwinded elevation gradient scheme).
check
https://cloud.githubusercontent.com/assets/4983771/6790578/54fd143c-d16e-11e4-89a8-b1a8645b2338.png

Image with NO checkerboarding in sfc speed field after ~20 years of
integration (when using the centered elevation gradient scheme).
nocheck
https://cloud.githubusercontent.com/assets/4983771/6790610/870461f6-d16e-11e4-87ca-7c6cce9f1320.png

—
Reply to this email directly or view it on GitHub
https://github.com/ACME-Climate/cism-piscees/issues/25.

---

Dan Martin email: DFMartin@lbl.gov
Mail Stop 50A-1148 phone: (510) 495-2852
Lawrence Berkeley National Laboratory fax: (510) 486-6900
1 Cyclotron Rd.
Berkeley, CA 94720

[billsacks]

From @stephenprice on March 23, 2015 21:38

@DanFMartin, the relevant one-side gradients mentioned for the Halfar test case are applied in the interior. There's a range of options for how the gradients are calculated at the margins, but I'm not clear if those are relevant here or not.