[MITgcm-devel] changes in tracer vertical implicit scheme

[Jean-Michel Campin]

Hi,

Some fix/changes related to tracer vertical direction implicit method:

1) implicit vertical advection conservation with Adams-Bashforth 
 and/or non-lin free-surf:
 the term Tr*d/dz(w) was not going through AB and neither was
 rescaled (NonLin-FreeSurf) and this was breaking tracer conservation.
 I remove Tr*d/dz(w) in gad_implicit_r.F and add it in gad_calc_rhs.F;
 this fix conservation in both cases.
2) implicit vertical diffusion or advection with non-lin free-surf:
 Was using current recip_hFacC instead of future recip_hFacC.
 This lead to small error when using NonLin-FreeSurf and also break 
 conservation with NonLin-FreeSurf in r-coordinate (but not with r*).
 The right recip_hFac is now computed in thermodynamics.F and passed
 to all vertical implicit S/R.

I also added diagnostics for gtNm1 & gsNm1, so that it's easier
to check tracer conservation with NonLin-FreeSurf + AB (the quantity
being conserved is Tr + (0.5+abEps)*deltaT*gtNm1).
And will add a secondary test to advect_xz to test implicit vertical
advection (+ NonLin-FreeSurf).

I don't know why those changes affect bottom_ctrl_5x5 (adjoint gradient)
and break agreement with forward gradient.
I removed all the implicit vertical code in thermodynamics.F (checked-in),
and it's better, but still not as good than what it used to be.
If someone has time to take a look at this experiment.

Cheers,
Jean-Michel