[MITgcm-support] pressure from MITgcm

[Martin Losch]

Hi Sergey,

assuming that you include the surface elevation contribution 
rho0*g*eta, as Patrick suggested, I can think of another (maybe 
fundamental) difference in the computation of pressure, but I don't 
know if it can explain the differences you observe (which is which by 
the way? More variability in the model output = red?):

As you know, the hydrostatic equation is nonlinear: dp = - g*rho(p)*dz, 
because rho depends on p. You can linearize it by assuming some linear 
relationship between p and z, e.g. p approx.= p(z) = - g*rho*z. Then 
you can integrate to get p(z) = p0 - g*integral(rho(z)dz) from z0 to z. 
This is what is effectively done, if you use EOStype='JMD95Z', 
'LINEAR', or 'POLY3'. A better solution would be an iteration to solve 
dp = - g*rho(z)*dz. Doing so in a GCM, can change the circulation 
significantly (Dewar etal 1998, JPO), but is also expensive. We have 
adopted a different solution: If you use EOStype = 'JMD95P', or 
'MDJWF', pressure is lagged by one timestep, so that, effectively, 
pressure at timestep n is p(n) = p0 - g*integral(rho(p(n-1))dz). In 
these two EOS-cases the approximation of the nonlinear hydrostatic 
balance is better than in the former three. I don't know it that has an 
effect on the variability.
To check your computations, you have to compare model output with 
EOStype='JMD95Z', to your offline pressure calculations (where I assume 
that you always have rho=R(S,T,-g*rho*z) instead of R(S,T,p(z)), that 
is, a linearized hydrostatic balance in your offline computations).

Martin

PS: I attach two matlab files (densjmd95.m and denmdjwf.m) that use the 
same formulae as find_rho for eosTyp'es JMD95Z/P and MDJWF, but they do 
not include any nonlinear pressure computions (you have to provide 
pressure yourself, how ever you want to compute it). Maybe they are of 
use.
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On Nov 18, 2005, at 9:32 PM, Sergey Vinogradov wrote:

> Hi folks!
>
> Did anyone compare the pressure profiles computed from hydrostatic  
> anomaly ('PH' output) and from density?  I'm using atm. loading with  
> MITgcm. In order to compute the full pressure at the center of k-th  
> layer, I can either get it from T and S through density: p (rho) =  
> rho0*g*eta + g* J (rho*dz), or, use the PH output (phiHydC variable),  
> which, according to previous correspondence with Martin and Dimitris,  
> can also give me the full pressure (at k-th layer):
> p (PH) = rhoConst*PH(k) + g*rhoConst*D(k)
> Notations are: rho0 - surface density; g-gravity; eta-full sea-surface  
> elevation; dz-layer thicknesses; rhoConst - reference density; D -  
> central depths of layers; J - integral from cell center depth to the  
> surface.
> I get different variability from these two methods (see attached  
> fragment of timeseries sampled at some layer). Other than the  
> difference in eos that I use for density computations, what may be the  
> reason for discrepancy in the variability between these two pressure  
> computations? Am I missing something?
>
> Thanks,
>
> --  
> Sergey Vinogradov, Ph.D.
> Oceanography Group
> Atmospheric and Environmental Research, Inc.
> 131 Hartwell Ave., Lexington, MA 02421, USA
> Phone:  1-781-761-2256       sergey at aer.com
> Fax:    1-781-761-2299   http://www.aer.com
>
> <series-pressures 
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