Hi,
I wish to raise a few technical points about the computation of gravitational stability for use in computing Ri numbers. It turns out that this calculation is subtle. I spent some time writing up discussions for both the local gradient Ri number calculation (Section 2.2.3) and bulk Ri number calculation (Section 7.5.5). The following provides some highlights.
For KPP, we compute gravitational stability in MOM and POP by computing density with non-standard arguments, corresponding to adiabatic/isohaline parcel displacements starting from a reference point. I was originally bothered by this calculation, given that a similar approach proved very problematic for the neutral physics schemes. However, for KPP, I am now convinced that the original approach as implemented in POP and MOM are for the most part fine (but see next paragraph). The key point is that we must ensure that gravitational stability calculations, both for gradient and bulk Ri calculations, include the full effects of the nonlinear equation of state. When we instead linearize around a particular point, and introduce the thermal expansion and haline contraction coefficients, then we may miss some nonlinear EOS effects, particularly in the high latitudes where the EOS is very frisky.
On a related note, the calculation of vertical stability for the gradient Ri number calculation is in fact slightly flawed. This calculation should compute stability by referencing both the top and bottom point in any pair. Presently the reference is to only one of the pair in both MOM and POP's implementations. In contrast, for the bulk Ri calculation, reference should be made just to the value within the surface layer, with displacements only downward. The bulk Ri calculation appears fine in the present form in MOM and POP, but the gradient Ri number needs to be corrected.
Another concern originally was that by computing gravitational stability through accessing the equation of state, we may need to bring in the EOS to CVMix code. I no longer see the need. I believe we can merely send to CVMix the relevant stability arrays pre-computed using one's one equation of state. Perhaps I am missing something, but at this point I do not see a problem.
Steve
cvmix_09aug2012.pdf