[MITgcm-support] On the calculation of the volume conservation from the output of a regional model

[whale]

Dear friends,
 
 
 
Recently, I was a little confused on the calculation of the volume budget. Let me explain what I want to calculate.
 
 
 
First, the grid in my model configuration is as simple as follows,
 
 
 
# Gridding parameters
 
 &PARM04
 
 usingSphericalPolarGrid=.TRUE.,
 
 delX=640*0.047,
 
 delY=640*0.0141,
 
 ygOrigin=-74,
 
 xgOrigin=60,
 
 delR = 10.0, 10.0, 10.0, 10.0, 15.0, 15.0, 15.0, 15.0, 15.0,
 
 20.0, 20.0, 20.0, 20.0, 20.0, 25.0, 25.0, 25.0, 25.0, 25.0,
 
 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0,
 
 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0,
 
 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 30.0, 35.0, 40.0, 45.0,
 
 50.0, 55.0, 60.0, 70.0, 80.0, 90.0, 100.0, 110.0, 120.0, 130.0,
 
 140.0, 155.0, 170.0, 185.0, 200.0, 215.0, 250.0, 250.0, 300.0, 450.0, 450.0,
 
 &
 
 
 
So, my grid resolution is 640*640*70, a simple cube.
 
 
 
What I am trying to do is to calculate the volume transport in a specified region or to check if the volume is conservative.
 
In order to understand how the model velocity fields control the volume balance, I have chosen a single water column (e.g., x=200, y=500, z=1:70) to make a preliminarily assessment. After several tests, I found an equation as follows,
 
 
 
volume_residual =
 
( u(x,y,:)*DRF(:)*DYG(x,y)*hFacW(x,y,:) - u(x+1,y,:) *DRF(:)*DYG(x+1,y)*hFacW(x+1,y,:) ) + 
 
( v(x,y,:)*DRF(k)*DXG(x,y)*hFacS(x,y,:) - v(x,y+1,:)* DRF(:)*DXG(x,y+1)*hFacS(x,y+1,:) )
 
 
 
Note that DRF, DXG, DYG, hFacW and hFacS are derived from the grid files.
 
If my understanding is right, in the equation, 
 
u(x,y,:)*DRF(:)*DYG(x,y)*hFacW(x,y,:) denotes the volume transport at the western face of the cell
 
u(x+1,y,:) *DRF(:)*DYG(x+1,y)*hFacW(x+1,y,:) denotes the volume transport at the eastern face of the cell
 
v(x,y,:)*DRF(k)*DXG(x,y)*hFacS(x,y,:) denotes the volume transport at the southern face of the cell, and 
 
v(x,y+1,:)* DRF(:)*DXG(x,y+1)*hFacS(x,y+1,:) denotes the volume transport at the northern face of the cell.
 
If the volume in this water column is conservative, the result of this equation should be 0. However, it is not. I always got a volume residual value at ~0.01. If I chose to calculate a relative larger region, the residual value will also increase and I will get a very large value at last.
 
 
 
So, my questions are 
 
Whether the equation of my calculation is right or wrong? 
 
If my equation is right, where will the residual volume goes? 
 
Will the residual volume contribute to the changes of ETAN or something else?
 
 
 
Any comments and suggestions are appreciated!
 
Cheers
 
Chengyan
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