[MITgcm-support] T, S budget in the surafce layer

[Jean-Michel Campin]

Hi Ivana,

I don't remember if SOSE uses non-linear free-surface (with z* ?) or
if relies on the linear free-surface.

In the 1rst case, the conservation is exact (but you need to account 
for time variation of grid-cell volume), and you can find some
information in the 2004 Ocean Modelling paper (Vol 6, pp 221-244).

In the 2nd case, the volume of each grid-cell is kept constant
(despite the free-surface) and the global tracer content (or tracer 
integral) is not conserved. 
You can still diagnose the local tracer budget (as suggested by Dimitris
and reported here) but, since the integral of WTHMASS(k=1) is not zero,
the global tracer content will change (even without forcing).

The purpose of setting linFSConserveTr=.TRUE.,
is to correct (globally) for the integral of WTHMASS(k=1).
This correction (TsurfCor, SsurfCor) is applied uniformly to the 
surface level.

Cheers,
Jean-Michel

On Thu, Apr 24, 2014 at 09:07:44PM +0000, Cerovecki, Ivana wrote:
> Dear MITgcm world,
> 
> we would like to close temperature and salt budget with SOSE output. The SOSE uses implicit 
> free surface. What is the correct way to close the T/S budget in the surface layer to account for 
> heat/salt change at the surface. 
> 
> To follow up on Jean-Michel’s earlier comment (pasted below) – is the best way to
> set linFSConserveTr=.TRUE. In that case, is the correction that the model makes saved in 
> ADVr_TH output diagnostics, or in order to close the budget accurately in the top layer 
> do we need to use what Dimitris suggested in an earlier post:
> 
> For the surface surface level, can't the divergence term be computed 
> ADVx_TH(i,j,1) - ADVx_TH(i+1,j,1) + ...  
> ADVy_TH(i,j,1) - ADVy_TH(i,j+1,1) + ... 
> ADVr_TH(i,j,2) - WTHMASS(i,j,1) * RAC(i,j) 
> 
> which obviously implies we need to output WTHMASS and WSLTMASS fields.
> 
> We would very much like to close T/S budgets as accurately as possible, so I will be very grateful 
> if you could please let me know what needs to be done for the top layer,
> Ivana 
> 
> P.S. With all the work that ECCO and the other people have done diagnosing various budgets, is there 
> maybe a version of the scripts to diagnose T/S budgets available somewhere?
> 
> 
> Jean-Michel: 
> http://mitgcm.org/pipermail/mitgcm-support/2011-May/007205.html
> 
> “with Linear FreeSurf, there is a small loss of heat/salt/tracer  at the surface (d/dt(Eta) inconsistent with fixed surf grid cell thickness): 
> 
> a) if linFSConserveTr is set to true (file "data"), then the model    correct for this (see S/R calc_wsurf_tr.F). 
> 
> b) if linFSConserveTr=False (=the default), need to account for this term  in the budget, which can be obtain from the 1rst level of WTHMASS / WSLTMASS   diagnostics (diagnostics ADVr_TH / ADVr_SLT is not the right one for   this purpose, it's just zero at k=1).  “
> 
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