[MITgcm-support] phihydlow without topography signal

[Martin Losch]

Hi Katy,

you are absolutely right. Apparently I wrote this email too late at night and did not pay attention. rho' is a function of position (i,j,k) and thus the third term has to be an integral from R_low (-D) to eta as you say. Sorry for the confusion.

Martin

On Sep 16, 2011, at 8:30 PM, Katherine Quinn wrote:

> Hi Martin,
> This was very helpful.  I can see now that if rho_0 isn't a good approximation of the mean density then there will still be quite a large imprint of topography on the instantaneous phihydlow.
> One more question - is the density anomaly, rho', a 3D variable?  I am assuming yes, which means the third term in your bottom pressure equation will actually be an integral w.r.t depth from R_low to eta. That is:
> bottom pressure = p_atmosphere + g*rho_0*(D+eta) + int(from R_low to eta){g*rho'*dz}
> thanks, Katy
> 
> ------------------------------
> 
> Message: 2
> Date: Fri, 16 Sep 2011 00:20:04 +0200
> From: Martin Losch <Martin.Losch at awi.de>
> To: mitgcm-support at mitgcm.org
> Subject: Re: [MITgcm-support] phihydlow without topography signal
> Message-ID: <08D4E79B-E5FE-4BEC-96BF-F98EC9B1D022 at awi.de>
> Content-Type: text/plain; CHARSET=US-ASCII
> 
> Hi Katy,
> 
> not sure if I completely understand your question. But maybe this helps:
> 
> bottom pressure = p_atmosphere + g*rho_0*(D+eta) + g*rho'*(D+eta)
> D=Water depth (=-R_low)
> eta=sea surface height/"dynamic topography"
> rho_0=reference density (=rhoConst)
> rho'= rho-rho_0 = density anomaly
> 
> phiHydLow = [p_atmosphere + g*rho_0*eta + g*rho'*(D+eta)]/rho_0
> phiHydLow = (bottom pressure)/rho_0 - g*D
> 
> From this, you can see that  phiHydLow is the hydrostatic potential
> anomaly at the depths in R_low with the constant depth-term (g*D)
> removed. Add it back in, and you'll have your nearly linear fit to
> R_low. There will probably always (except for special cases) be an
> imprint of topography on an instantaneous phiHydLow because of
> g*rho'*D/rho_0. You can remove that part, too, but that means that
> you'll have to save rho' (diagnostics: RHOAnoma (?)) to remove any
> terms involving D.
> Does that make sense?
> 
> Martin
> 
> -- 
> Katherine J. Quinn
> Atmospheric and Environmental Research, Inc.   voice: 781-761-2234
> 131 Hartwell Avenue                              fax: 781-761-2299
> Lexington, MA  02421-3126                     e-mail: kquinn at aer.com
> 
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