[MITgcm-support] PH and PHRefC

[Jody Klymak]

Hi Ryan,

> On May 26, 2017, at  17:08 PM, Ryan Abernathey <ryan.abernathey at gmail.com> wrote:
> 
> Very useful! Thanks for sharing Jody!

Yes, well it took me a couple of hours, so I thought I could share, since others have asked over the years.  Its pretty hard to parse with all the IF statements, and calls to different routines.  I guess when something is as capable as the MITgcm it gets complicated!

> Once I figured this out and wrote it down so I would remember it:
> PHRefC = gravity * rhoref * RC[k]

I don’t think it has any rhoref in it.  Its just phiRef[k] = gravity* RC[k].  From `set_ref_state.F` I think its just:

```fortran
  	phiRef(1)   = top_Pres*recip_rhoConst
        pRefLocF(1) = top_Pres
        IF ( gravityFile.EQ.' ' ) THEN
         DO k=1,Nr
          phiRef(2*k)   = phiRef(1)
     &                  + (rC(k) - rF(1))*gravity*gravitySign
          phiRef(2*k+1) = phiRef(1)
     &                  + (rF(k+1)-rF(1))*gravity*gravitySign
```

…but maybe I misread one of the switches.  What mystifies me is the use of this variable, and why we’d want to write it to `PHRefC.data`, except maybe to tell us what `top_Pres` is?

Cheers,   Jody

> 
> On Fri, May 26, 2017 at 6:24 PM, Jody Klymak <jklymak at uvic.ca <mailto:jklymak at uvic.ca>> wrote:
> 
> Hi all,
> 
> OK, about once a year I get re-confused about the meaning of the data contained in `PH`, `PHL`, and `PHRefC`.  I use a linear equation of state in z-coordinates with an oceanic buoyancy relation, so it should be pretty simple.
> 
> One would think that to get the total pressure one would just add P = PH + PHRefC, but that is indeed not the case if tRef and/or sRef vary with depth (k).  PHRefC is simply g*Z (where Z is the z at the center of the cells).  PH is the dynamic pressure: (1/rho_0) \int (rho-rho_{Ref}(z)) g dz.  Nowhere, that I can tell, is the cumulative integral of rho_{Ref} stored (nor indeed tRef or sRef).
> 
> My sleuthing, mainly so I don’t do this again (ha), but perhaps is useful to others, is at
> 
> https://gist.github.com/jklymak/156c30b5344a9cf63e8aebc429fee1c6 <https://gist.github.com/jklymak/156c30b5344a9cf63e8aebc429fee1c6>
> 
> I do wonder why PHRefC doesn’t include the full reference pressure using tRef and sRef to calculate rhoRef: i.e. (1/rho_0) \int g rho_{Ref}(z) dz. I don’t need g*zc saved for any reason.  But maybe other co-ordinate systems or EOSs make sense of this variable?
> 
> Thanks,   Jody
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