question about the caculating of om_p, om_u, on_p, on_u

[xiaozhu557]

Hello everyone,
I am not understand the caculating of om_p, om_u, on_p, on_u, om_v, on_v. In the file mod_grid.F, they are discribed as

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!  om_p       PSI-grid spacing (meters) in the XI-direction.           !
!  om_r       RHO-grid spacing (meters) in the XI-direction.           !
!  om_u       U-grid spacing (meters) in the XI-direction.             !
!  om_v       V-grid spacing (meters) in the XI-direction.             !
!  on_p       PSI-grid spacing (meters) in the ETA-direction.          !
!  on_r       RHO-grid spacing (meters) in the ETA-direction.          !
!  on_u       U-grid spacing (meters) in the ETA-direction.            !
!  on_v       V-grid spacing (meters) in the ETA-direction.            !

and in the file metric.F, the om_r and on_r have been defined as

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om_r(i,j)=1.0_r8/pm(i,j)
on_r(i,j)=1.0_r8/pn(i,j)

It means that om_r=Δx, on_r=Δy. I can understand it. However, the om_u and on_u have been defined as

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om_u(i,j)=2.0_r8/(pm(i-1,j)+pm(i,j))
on_u(i,j)=2.0_r8/(pn(i-1,j)+pn(i,j))

They look like disagree with the defination of U-grid spacing (meters) in the XI/ETA-direction. In this case,

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on_u(i,j)=2*on_r(i,j)*on_r(i-1,j)/(on_r(i,j)+on_r(i-1,j))

.
In my opinion, it should be

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on_u(i,j)=(1/pn(i,j)+1/pn(i-1,j))/2=(on_r(i,j)+on_r(i-1,j))/2

This is the exactly U-grid spacing (meters) in the ETA-direction. Am I right? Or where am I wrong?

[jcwarner]

the metrics are computed in a way that is consistent in the code, and needs to be this way for mass conservation properties. Here is a post from 2003 on the similar issue:
viewtopic.php?f=19&t=150&view=next

[wilkin]

Those comments

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!  om_r   RHO-grid spacing (meters) in the XI-direction.                 !

should read

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!  om_r   reciprocal of RHO-grid spacing (meters^-1) in the XI-direction.!

The "o" is for "over" as in "one over m" (1/m). You will see this usage throughout the code.

The way these terms are computed at points other than the RHO cells where pm,pn are defined are as they are, as John Warner notes, for reasons of conservation in the discrete code.

The usage "pm" in place of "m" for 1/dx stems from historical predecessor codes to ROMS, where the FORTRAN implicit definition for all variables starting with characters I through N was type INTEGER, and all other variables was type REAL.

Safe FORTRAN practice is always to define IMPLICIT NONE, and declare all variables (as we do in ROMS).

[kate]

Those comments

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!  om_r   RHO-grid spacing (meters) in the XI-direction.                 !

should read

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!  om_r   reciprocal of RHO-grid spacing (meters^-1) in the XI-direction.!

The "o" is for "over" as in "one over m" (1/m). You will see this usage throughout the code.

Actually, "om" is one over m, where m is one over dx, so the original comment is correct.

It's true that these codes have a lot of baggage from the past.

[wilkin]

You are quite right Kate - my mistake. Two wrongs don't make a right, but three rights make a left. So one over one over DX is DX.

[xiaozhu557]

I have got it. Thanks all your replying.