bug in ENE and ENS vorticity schemes with partial steps?

[davestorkey]

In the ENE and ENS vorticity schemes (vor_ene and vor_ens) there are two formulations depending on ln_sco. If ln_sco is set to true then the fse3f, fse3u and fse3v scale factors are included, but if ln_sco is false then these terms are deemed to cancel and are excluded from the formulation. However the scale factors don't cancel for the partial steps case. I think the IF test on ln_sco should be instead: if( ln_sco .or. ln_zps ).

Can anyone confirm this?

[ducousso]

Replying to davestorkey:

In the ENE and ENS vorticity schemes (vor_ene and vor_ens) there are two formulations depending on ln_sco. If ln_sco is set to true then the fse3f, fse3u and fse3v scale factors are included, but if ln_sco is false then these terms are deemed to cancel and are excluded from the formulation. However the scale factors don't cancel for the partial steps case. I think the IF test on ln_sco should be instead: if( ln_sco .or. ln_zps ).

Can anyone confirm this?

I agree that the actual routines vor_ene and vor_ens are not correct when used with z partial steps. These routines are quite old, and they have been barely unchanged since when the only available vertical coordinate were z full steps and s.

The modification that you propose make use of fse3u and fse3v to compute volume transports, and fse3f to define the f-point thickness which enters in potential vorticity. I think it is indeed important to use fse3u and fse3v to maintain consistency with continuity, but the use of fse3f is more discutable...

For instance, in vor_een, it has been chosen not to use fse3f (which is the min over i an j of e3t in z partial steps) but to use a local variable ze3f which is the mask-weighted mean over i and j of e3t. I suggest to follow this idea for vor_ene and vor_ens.

It would be great to have a theoretical rationale to guide the way of defining the f-point thickness with z partial steps, but I think this rationale is still lacking. The main problem is that Sadourny and Arakawa have originally designed the ene, ens and een schemes for shallow water models, and that the definitions of vertical scale factors at u, v and f points in these models differ from the definitions in NEMO with z partial steps. By using the local variable ze3f rather than fse3f, one is closest from the development of Sadourny and Arakawa.

[clevy]

Suppressing tickets opened on the trunk since more than 2 years... cleaning started!