[MITgcm-support] the implicit pressure components of PHIHYD?

[Jean-Michel Campin]

Hi CJ,

I think we are missing a little section in the manual to explain the
z* pressure diagnostics:
1) with z*, as described in the z* paper, when considering pressure gradient, 
  we have a second term due to the slope of the coordinate. And for this reason,
  we added 2 diagnostics for the 2 components of the pressure gradient:
    Um_dPhiX & Vm_dPhiY
  these could be used to close the momentum budget.
2) the diagnostics PHIHYD keeps the same meaning between z and z* coordianate,
  the pressure/rhoConst anomally (phiRef beeing removed) at the grid cell center.
  But with z*, the depth of the grid-cell center is no longer horizontally uniform,
  and this makes a difference that is not negligeable,
3) if I want, just for diagnostic purpose, to get a pressure field that I can easily
 compare with z coordinate, I will consider diagnostics "PHIHYDcR" of the z* run
 since this is the pressure/rhoConst evaluated at a fixed depth "rC", the same 
 depth as my z coordiante diagnostic PHIHYD.

Cheers,
Jean-Michel

On Thu, Oct 20, 2022 at 06:54:42PM +0800, ????????? wrote:
> Hi Martin,
> 
> Thanks for pointing out diags_phi_hyd.F for me to start.
> I believe I am still confused with the difference of totPhiHyd between r
> and r* coordinates.
> 
> With your kind comments and the help page (2.10.2.1. Pressure/geo-potential
> and free surface
> <https://mitgcm.readthedocs.io/en/latest/algorithm/nonlinear-freesurf.html>),
> I could understand the top part (line 62) of diags_phi_hyd.F.
> Could you please have a look at my interpretation? Is that correct?
> 
> (if only consider first grid,)
> help.page:
> PHI = PHI_reference.state [ g*rho_const*abs(z1) ]
>        + PHI' [ totPhiHyd ]
> & PHI' = PHI_s [ g*eta ]                   <--> could be considered as
> barotropic pressure/rho_const?
>            + PHI'_hyd [ g*(rho1-rho_const)*abs(z1)/rho_const ]  <-->
> baroclinic pressure/rho_const?
> 
> line 62:
> totPhiHyd(i,j,k,bi,bj)            <--> PHI'
>        = phiHydC(i,j)              <--> PHI'_hyd
>        + Bo_surf(i,j,bi,bj)*etaN(i,j,bi,bj)    <--> PHI_s
>        + phi0surf(i,j,bi,bj)          <--> EXFpress
> 
> that is,
> geo-potential f(x,y,z) = reference state f(z) + barotropic part f(x,y) +
> baroclinic part f(x,y,z) + other surface terms
> Now I guess the ECCO variable PHIHYD I plotted could probably be the
> baroclinic part only. (?)
> 
> 
> The next part, line 107, is it physically the same as totPhiHyd in line 62,
> but only in r* coordinate?
> The value of line 62 should be the same as line 107?
> Why does the reference state come into the equation?
> 
> dPhiRef =( Ro_surf(i,j,bi,bj)-rC(k) )*gravity            <-->
> PHI_reference.state
>  totPhiHyd(i,j,k,bi,bj)
>       = phiHydC(i,j)*rStarFacC(i,j,bi,bj)
>        + MAX( dPhiRef, 0. _d 0 ) *( rStarFacC(i,j,bi,bj) - 1. _d 0 )
>        + phi0surf(i,j,bi,bj)
> 
> Thank you for your time,
> Many thanks,
> 
> CJ

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