[MITgcm-support] Closing heat/salt/tracer budgets to machine precision

[Ruan Xiaozhou]

Dear MITgcm users,

I’m trying to close the point-wise heat/salt/tracer budget to machine precision in a regional model with RBCS, OBCS, KPP and EXF packages enabled. The model uses a linear free surface setup.

To give an example, I have examined a local point that is away from the surface and the RBCS sponge region (1300m deep). My heat budget calculation is as following (where all the fluxes are diagnosed as daily average):

The point is chosen at (i, j, k), and I start by calculating the local cell volume as:

CellVol = RAC(i,j) .* DRF(k) .* hFacC(i,j,k);

The diffusion tendency is as following where the KPP non-local flux is also added at the end:

Dif_tend_TH = -(  (DFrE_TH(i,j,k) - DFrE_TH(i,j,k+1))/CellVol + (DFrI_TH(i,j,k) - DFrI_TH(i,j,k+1))/CellVol  +  (DFx_TH(i+1,j,k) - DFx_TH(i,j,k))/CellVol + (DFy_TH(i,j+1,k) - DFy_TH(i,j,k))/CellVol + (KPPr_TH(i,j,k) - KPPr_TH(i,j,k+1))/CellVol    );

Here is the advection tendency:

Adv_tend_TH = -(  (ADVr_TH(i,j,k) - ADVr_TH(i,j,k+1))/CellVol + (ADVx_TH(i+1,j,k) - ADVx_TH(i,j,k))/CellVol + (ADVy_TH(i,j+1,k) - ADVy_TH(i,j,k))/CellVol  );

The time tendency term is

TOTTEND/86400 = 1.2712e-7 degC/s

And the sum of the advection and diffusion tendency is 1.2721e-7 degC/s, which is very close to the time tendency term but not quite the same. The same issue also happens with my salt and passive tracer budgets. The diagnosed forcing terms (gT_Forc and gS_Forc) are zero around this point. I cannot think of any other contribution in the model.. I was wondering if anyone has experienced this issue before? Thank you very much for your help!

Best,
Xiaozhou
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