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

Mon Jun 19 16:25:26 EDT 2017

Dear Jean-Michel and Michael

Thanks a lot for both your kind help and suggestions.

I have used these equation to calculate he volume budget and heat budget in a sub-ice-shelf cavity, and it works very well. 

By the way, I would like to remind others readers that the hFacW and hFacS need to one step inner ward when these equations are used on the open boundaries of a regional model, i.e., 

V*DRF*DXG(:,2)*hFacS (:,2,k)      --------------  for the western open boundary

U*DRF*DYG (2,:) *hFacW (2,:,k)  --------------  for the southern open boundary

Cheers

Chengyan

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  From:  "mitgcm-support-request";<mitgcm-support-request at mitgcm.org>;
 Date:  Wed, Jun 14, 2017 08:38 PM
 To:  "mitgcm-support"<mitgcm-support at mitgcm.org>; 

 Subject:  MITgcm-support Digest, Vol 168, Issue 12

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Today's Topics:

   1. On the calculation of the volume conservation from the output
      of a regional model (=?ISO-8859-1?B?d2hhbGU=?=)
   2. Re: On the calculation of the volume conservation from the
      output of a regional model (michael schaferkotter)

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Message: 1
Date: Wed, 14 Jun 2017 05:31:28 +0800
From: "=?ISO-8859-1?B?d2hhbGU=?=" <250107302 at qq.com>
To: "=?ISO-8859-1?B?bWl0Z2NtLXN1cHBvcnQ=?="
<mitgcm-support at mitgcm.org>
Subject: [MITgcm-support] On the calculation of the volume
conservation from the output of a regional model
Message-ID: <tencent_4DBACA560C5C101974FB5282 at qq.com>
Content-Type: text/plain; charset="iso-8859-1"

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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Message: 2
Date: Wed, 14 Jun 2017 07:54:08 -0500
From: michael schaferkotter <schaferk at bellsouth.net>
To: mitgcm-support at mitgcm.org
Subject: Re: [MITgcm-support] On the calculation of the volume
conservation from the output of a regional model
Message-ID: <648c8e4b-fea0-2129-ea72-0df0059a7045 at bellsouth.net>
Content-Type: text/plain; charset="windows-1252"; Format="flowed"

On 6/13/17 4:31 PM, whale wrote:
>
> 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.
>
there is no reason to assume that volume is conserved in the single cell 
for which the calculation is made.

the calculations are correct.

> 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.
>

Not necessarily. perhaps yes for your particular example.
>
> 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?
>

yes.

do the same calculation for the boundary of your domain and use the 
divergence theorem to calculate the expected sea surface height.

michael

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