[MITgcm-support] Mass balance

[Stefano Querin]

Dear MITgcmers,

we would like to compute the mass balance of a passive tracer for a  
single cell due to advection-diffusion (no source, no sink).
Is there any procedure to compute that?

We tried the following way.

For a given cell (i,j,k), for a given time period, we used:
- the values of ADVx_Tr01 and DFxETr01 at i and i+1 as zonal fluxes at  
the 2 cell boundaries;
- the values of ADVy_Tr01 and DFyETr01 at j and j+1 as meridional  
fluxes at the 2 cell boundaries;
- the values of ADVr_Tr01 and DFyITr01 at k and k+1 as vertical fluxes  
at the upper and lower cell boundary.

Then, we computed the sum of these six terms (changing the sign for i 
+1, j+1 and k fluxes). This value, multiplied by the time interval,  
should give the net variation of the tracer mass in the cell.
However, this result is not equal to the variation of tracer01, as  
computed by using the values of TRAC01 diagnostic at the beginning and  
at the end of the time period (multiplied by the cell volume).

Is there anything missing in such a procedure?

We are wondering if we are evaluating correctly the mass balance for a  
single cell since we would like to compute the overall mass balance in  
a specified basin.

Thank you in advance for your help!


Best regards,

Stefano and Gianpiero