[MITgcm-devel] lab_sea default adjoint verif. "broken" since April '11

[Patrick Heimbach]

Hi there,

recently, Jean-Michel added a test on the finite-difference gradient to the testreport. 
Since April we had a very good example why it would have been useful, 
but didn't notice (since the test existed yet):

Before a series of changes made to pkg/seaice
the adjoint vs. finite-difference gradient accuracy was about 10E-4
(revision 1.39 of output_adm.txt)
after those changes that accuracy deteriorated to 10E+7
(revision 1.43 of output_adm.txt)

Interestingly, what's changed was not really the adjoint,
but the finite difference, which increased by orders of magnitude.
Reducing epsilon, or the number of timesteps (from 4 to 2) seems to
reduce the problem somewhat, but points to an extremely sensitive
threshold behavior that kicks in quickly.
A tangent linear test still shows the problem.
Another way to remove this issue is to set new parameter SIsalFRAC = 0.

Also interesting is that output_adm.evp.txt does not show this problem.
But a direct implication of solvers as culprits is not obvious at all.
The results for output_adm.seaice.txt in global_ocean.cs32x15/
seem to be better-behaved as well.

One question is whether lab_sea is notoriously ill-designed
for the tests that we'd like to run (we've had problems in the past).
But it still doesn't explain
* why use of LSR vs. EVP show the drastically different behavior
  (EVP seemingly well behaved, and LSR also badly behaved in TLM mode);
  again, it's unlikely due to the solvers per se;
* why the large sensitivity to SIsalFRAC;

Looking at alternatives, the obvious choice seems to be 1D_ocean_ice_column/
But looking at output_adm.txt there shows adj. vs. f.d. gradient accuracies
of E+0 to E+4 i.e. those results can't be taken serious either.

-Patrick

---
Patrick Heimbach | heimbach at mit.edu | http://www.mit.edu/~heimbach
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