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Dear Mr Ian，
Firstly, thanks for your patience and suggestion. Recently, I tried to close the salinity budget in a natural model grid at a deep layer without surface forcing but found that the result didn't close even in the magnitude. please let me introduce my works.
 First, i chose a tracer cell grid Ac(i,j,k) of salinity, which is bordered by the lengths  and  , and using the forced advection-diffusion equation. 
                                    
To calculate advection and diffusive terms, i chose 14 components in different direction around the center of Ac(i,j,k). 
For the tracer cell there are 6 advective terms, one for each face:(i,j,k denotes 'y','x','z' direction)
2 terms for the 'x' dimension lateral faces: ADVx_SLT, u(i,j,k) at the west grid and u(i,j+1,k) at the east grid
2 terms for the 'y' dimension lateral faces: ADVy_SLT, v(i-1,j,k) at the north grid and v(i,j,k) at the south grid
2 terms for the 'z' dimension bottom faces: ADVr_SLT, r(i-1,j,k-1) at the upper grid and r(i,j,k) at the deeper layer
and 8 diffusive terms,one for each face:(i,j,k denotes 'y','x','z' direction)

2 terms for the 'x' dimension lateral faces: DFx_SLT, u(i,j,k) at the west grid and u(i,j+1,k) at the east grid

2 terms for the 'y dimension lateral faces: DFy_SLT,  v(i-1,j,k) at the north grid and v(i,j,k) at the south grid

2 terms for the 'z' dimension bottom faces: DFrE_SLT, re(i-1,j,k-1) at the upper grid and re(i,j,k) at the deeper layer
2 terms for the 'z' dimension bottom faces: DFrI_SLT, ri(i-1,j,k-1) at the upper grid and ri(i,j,k) at the deeper layer
         In the west-east direction, i calculated the difference between u(i,j+1) and u(i,j)(the eastward direction is positive)as the U.comp of advection terms  across the salinity tracer cell grid. Similarly, the north components minus the south one(the northward direction is positive), the upper minus the deeper (the upward direction is positive). So, i could add 3 Advection terms (multiply by -1)and 4 Diffusive terms together as the right hand terms.
       Then, in order to fit with the unit of Salinity budget which are in "psi.m^3/month" , the salinity data(Ac(i,j,k)) was multiply by RAC(grid cell area, m^2) and DRC(vertical grid spacing, m), and used the "Diff" m.function to get the tendency of salinity term(ds/dt).Likewise, the right hand side was multiply by 3600*24*(28/29/30/31). As a result, the right hand is 10^2 times larger than the left.  
       Finally, i tried another way to calculate the right hand side , which is divide by the average lengths and their area
 of the face of the grid cell to be the unit of "psu/month", but it doesn't work!
I hope that you could point out my mistakes and give me some suggestion if you are convenient. Please forgive my poor work and my unprofessional questions.
Thank you for your patient reading! I really appreciate your help! 


Sincerely,
Guancheng








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