# [MITgcm-support] C grid and pressure

Jean-Michel Campin jmc at ocean.mit.edu
Wed Jul 11 21:24:34 EDT 2012

```Hi Nicolas,

On Tue, Jul 10, 2012 at 06:10:27PM -0400, Nicolas Grisouard wrote:
> Hi everyone,
>
> Allow me to follow up on a discussion I started 6 months ago.
>
> On 1/7/12 11:37 AM, Jean-Michel Campin wrote:
> >Hi Nicolas,
> >
> >[...] the pressure P can be obtained as:
> >P(i,j,k)/rhoConst = -g*rC(k) + PH(i,j,k) + PNH(i,j,k)
> >
> >And PHL would be the equivalent of PH (hydrostatic pressure potential anomaly)
> >but at the bottom, so that the hydrostatic pressure at the bottom Pb
> >would be: Pb(i,j)/rhoConst = g*Depth(i,j) + PHL(i,j)
>
> And what about the full bottom pressure? I am trying to compute the
> force acting on a topography, so I want to integrate something like
> P*h', where P is the pressure and h'is the topographic slope. The
> way I compute P is (following the previous notations):
>
> Pb(i,j)/rhoConst = g*Depth(i,j) + PHL(i,j) + PNHbott(i,j),
>
>
> where I created PNHbott by locating the lowermost cells with some
> water in them and picking up the value of PNH there. I guess my
> worry is that I am doing something with the PNH fields that was not
> supposed to be allowed with the PH fields. Am I?

I would have tried the same thing as you did. In fact the hydrostatic
bottom pressure does not enter the model formulation (in z coordinates);
it is just provided as a diagnostics (and computed from the
hydrostatic pressure at cell center plus a partial contribution
from the cell center down to the bottom); so I would extend the
same approach to the non-hydrostatic part (except that I don't know
precisely what non-hydrostatic partial contribution to add to go from the
cell center down to the bottom, so my first guess would be to add nothing,
like you did).

> The actual numbers tell that the g*Depth(i,j) term dwarfs the other
> ones, but not enough when integrated against h' to completely ignore
> the pressure anomalies.

I am not too much surprised regarding the magnitude of the 1rst term,
but does the final results (i.e, multiplied by h') prove to be usefull

Cheers,
Jean-Michel

>
> Thank you for your time and help,
> Nico.
>
> --
> Nicolas Grisouard -- Assistant Research Scientist
> Courant Institute of Mathematical Sciences
> 251 Mercer Street -- New York, NY 10012-1185
> tel: (+1) 212-992-9920 -- room 927
> Office Skype ID: nicolas.grisouard
> http://nicolas.grisouard.free.fr
> http://www.mendeley.com/profiles/nicolas-grisouard/
>
>
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```