[MITgcm-support] phiHydLow

[Martin Losch]

Hi,
because of the isomorphism implemented in the code, phiHyd is NOT 
pressure, but a potential function. In formulas (latex) it's:
\frac{\partial\phi}{\partial r} = b
where r is the vertical coordinate (height or pressure) and b is the 
"generalized buoyancy". If r=z (height coordinates, your case), b 
becomes the SCALED density g\rho/\rho_{0}. (In fact, it's the scaled 
density anomaly g(\rho-rho_{0})/\rho_{0}). The factor of \rho_{0} or 
reference density should not (and does not, I checked that once) change 
the result (except for numerical round off). So when you backout 
pressure from phiHyd, you have to multiply by \rho_{0}, which you have 
specified in your data file (rho_{0}=rhoConst) or use the default 
999.8. This will give you the pressure anomaly. For the full pressure 
(in which you are probably not really interested), you'll have to add 
the constant density contribution -g\rho_{0}z.

The same is true for phiHydLow, of course. So
P_{b} = phiHydLow*rhoConst + g*rhoConst*H
is the full bottom pressure, there first term is the contribution that 
you are most likely interested in.
And yes, I do recommend using the online formula, because it is 
correct. If your offline formula gives different results, it is most 
likely inconsistent with the model discretization/choice of parameters 
or whatever there is that can go wrong. Because we are dealing with 
large numbers, small change make a big difference.

Martin

On Aug 17, 2004, at 1:41 AM, Ichiro Fukumori wrote:

> Judging from the outputs, the phiHydLow calculation must have this 
> mask applied.
> Please check.
>
> -- I.
>
> At 04:29 PM 8/16/2004 -0700, Benny Cheng wrote:
>> Dimitri's formula doesn't have the hFacC masking the vertical integral
>> either. Isn't that important in your calculation ?
>>
>> - Benny
>>
>>
>> On Mon, 2004-08-16 at 16:26, Ichiro Fukumori wrote:
>> > Benny,
>> >
>> > This does seem to explain the difference between our formulation and
>> > the online phiHydLow.  I just recomputed pbot_1 using my routine but
>> > with Dimitris's formula below and the results seem to agree with 
>> each
>> > other (excpet for sea level contribution, pbot_2).
>> >
>> > The formula below has an extra factor of dividing by rhoconst.  PHL
>> > below does not have dimension of pressure because of this.  This
>> > additional factor explains the order 1000 difference we had.
>> >
>> > The use of constant density as reference is somewhat unconventional
>> > because water is compressible.  As a result, the range of values PHL
>> > takes is larger than what we get using water of (0C 35PSU) as a
>> > reference.  The consequence is a slight loss of precision (one 
>> order of
>> > magnitude).
>> >
>> > Given these facts, I suggest we do not use the on-line formula,
>> > but use our own off-line version instead.  What do you think?
>> >
>> > -- Ichiro
>> >
>> >
>> > At 03:14 PM 8/16/2004 -0700, Dimitris Menemenlis wrote:
>> > >On Monday 16 August 2004 02:03 pm, Ichiro Fukumori wrote:
>> > > > It appears that phiHydLow uses a different reference density
>> > > > from what we are using (0-deg C potential temperature, 35 PSU).
>> > >
>> > >reference density is rhoconst = 999.8
>> > >PHL is  | (rho(z) - rhoconst) * g / rhoconst dz
>> > >it is computed in model/src/calc_phi_hyd.F and diags_phi_rlow.F
>> > >
>> > >D.
>> > >
>> > >--
>> > >Dimitris Menemenlis <menemenlis at jpl.nasa.gov>
>> > >Jet Propulsion Lab, California Institute of Technology
>> > >MS 300-323, 4800 Oak Grove Dr, Pasadena CA 91109-8099
>> > >tel: 818-354-1656;  fax: 818-393-6720
>> >
>> > ===============================================================
>> > Ichiro Fukumori               | Jet Propulsion Laboratory
>> > e-mail: fukumori at jpl.nasa.gov | Mail Stop 300-323
>> > phone: +1 (818) 354-6965      | 4800 Oak Grove Drive
>> > fax: +1 (818) 393-6720        | Pasadena, California 91109, U.S.A.
>> > ===============================================================
>> >
>> >
>
> ===============================================================
> Ichiro Fukumori               | Jet Propulsion Laboratory
> e-mail: fukumori at jpl.nasa.gov | Mail Stop 300-323
> phone: +1 (818) 354-6965      | 4800 Oak Grove Drive
> fax: +1 (818) 393-6720        | Pasadena, California 91109, U.S.A.
> ===============================================================
>