New test cases for TEOS/non-Boussinesq

[cbegeman]

Are there tests that we could design that would be specific to TEOS/non-Boussinesq features? One example would be a change in the volume of a water column following vertical displacement of a water parcel.

[xylar]

A single-column TEOS-10 test

I'm starting work on a single-column test for TEOS-10 and non-Boussinesq. This will first just verify that Omega's SpecVol and the same computed on the Polaris side agree with each other. Then, I will add a computation of the geopotential to Polaris and make sure it agrees with Omega's version.

[cbegeman]

If the purpose is making sure that the Omega implementation is correct, then it seems like a single-column vector of values is the right kind of thing to store as a ctest. And this verification activity doesn't seem to require solving the full model, just testing part of the code, right?

But now I'm understanding that the goal here is really to make sure that Polaris implementation of specvol and geopotential is correct. In that case, it seems like a one-off activity that could be a stepping stone to the test below but doesn't need to be retained as a polaris test. Am I off base here?

[xylar]

I guess I didn't see any harm in having it be a continual verification that Omega and Polaris are in sync. But I can understand not wanting to have a proliferation of trivial tests.

[cbegeman]

If you feel there's a danger of them going out of sync, I'm fine with including it. I appreciate you being thorough.

[xylar]

Well, we can always check all these things in each column of the two-column test. So no added value in a separate tests (other than as a stepping stone) now that you talk me through it.

[cbegeman]

I like that way forward. Thanks

[xylar]

A two-column HPGF test

I plan to follow up the single-column test with a two-column tests for verifying the horizontal pressure-gradient force (HPGF). This test will compute a series of reference pseudo-heights at layer midpoints and at the horizontal midpoint between the two columns (i.e. at locations corresponding to normal velocities in Omega). It will then use quadrature methods to compute the geopotential from each water column at each reference pseudo-height, and finally use finite difference to compute the horizontal gradient (at constant pseudo-height) to compute the HPGF. In the limit that the distance between the two columns is small, the HPGF computed by this method should have much smaller error than even higher-order methods in Omega.

Note: there may be ways to use partial derivatives to relate the HPGF to the horizontal gradients of CT and SA (which will be known by construction) but this may prove tricky because of the integral relationship between geopotential and specific volume.

[cbegeman]

How do you plan to impose the horizontal pressure gradient for this test?

[xylar]

One way is to have different CT and SA profiles in the 2 columns. But the other was to have just different pseudo-height levels but the same CT and SA profiles (maybe linear profiles), such that the exact solution is no pressure gradient.

[cbegeman]

Maybe the former is a more rigorous test since you can incorporate gradients of different magnitudes at different depths of the water column. The seamount test variant where the stratification is horizontally uniform and we have a sigma coordinate will have aspects of the latter test (no pressure gradient ideally, but horiz gradients in layer interfaces).

[xylar]

I think both are useful and are just different configurations of the same test in my view. But I agree that there will also be other tests that look at horizontally uniform CT and SA profiles so that configuration should not be the main focus. It's just widely viewed as the minimum hurdle that the HPGF has to clear so I think it would be good if we have a test focused entirely on the HPGF (not the other ensuing dynamics) that can verify how well it's clearing that particular bar. We could use the seamount configuration to do that verification as well if were to write out the HPGF before any time stepping occurs. But I think an isolated test is just going to be a lot easier to work with and configure.

[cbegeman]

Sounds good