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

[Jean-Michel Campin]

Hi Chengyan,

As I understand, you are trying to check the volume budget of a single
column, computing the convergence of the vertically integrated volume transport.

Your calculation seems good to me, and the results should match
the expected volume changes:
1) if using rigidLid=T, "volume_residual" is expected to be very small 
 (depending on how well the 2-D solver (cg2d) converges.
2) otherwise (implicitFreeSurface=T, i.e., the default)
  "volume_residual" should match the variation of SSH (ETAN*rAc).
  You can expect exact matching (down to machine precision) if you 
  use exactConserv=T ; otherwise the precision is again up to 
  the 2-D solver convergence.
3) the equation you wrote for volume_residual is the one that the model 
 uses (to get d/dt(eta)) but if you are using nonlinFreeSurf > 0, 
 hFacW and hFacS vary with time (as function of Eta) whereas the one that 
 are written as part of the grid files correspond to eta==0 everywhere
 (unperturbed resting state).
 In this case (nonlinFreeSurf > 0) it's easier to use diagnostics of
 the 2 product: uVel*hFacW and vVel*hFacS (diagnostics: UVELMASS & VVELMASS,
 pkg/timeave: hUtave, hVtave files) which are computed using the correct
 hFacW and hFacS.

Cheers,
Jean-Michel

On Wed, Jun 14, 2017 at 05:31:28AM +0800, whale wrote:
> 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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