[MITgcm-support] phihydlow formula

[Martin Losch]

Benny,

in an older version of the code (somewhere around checkpoint46m), I 
coded the computation of phiHydLow using the hFacC's, but (I think) 
Jean-Michel moved this part out of calc_phi_hyd to diag_phi_rlow. The 
"problem" (maybe JMC can confirm) is that phiHyd is integrated  in two 
steps from the kth cell face (phiHydF, only an intermediate value) to 
the kth cell center  (phiHydC) (where it's value is needed for 
dynamics) and in second step to the k+1th cell  face, for the next 
cycle in the k-loop, this way only values from the k-th level are used 
and no reference to k+1,k-1 is necessary. diag_phi_rlow uses the 
dynamically relevant value phiHydC at the cell center and integrates 
further to the bottom, which is deltaZ=ddRloc=rC-R_low "meters" away. 
If the bottom is ABOVE the cell center (hFacC<0.5), then ddRloc<0 and 
we are integrating backwards a little. With hFacC's you'd need to 
integrate from phiHydF at level k which at this point no longer exists. 
I guess that's the whole secret (true, Jean-Michel?).

so the answer is: the same informations that's used to compute the 
hFacC's (rC-R_low, see ini_masks_etc.F) is used here, therefore the 
masks are properly applied.

Martin

On Aug 17, 2004, at 6:37 PM, Benny Cheng wrote:

> Thanks Martin. I'm more interested in whether some land masking is
> applied to the integral or not, since Ichiro thinks it's a "bug" 
> without
> it. Dimitri already replied that it was masked. The way it's done in 
> the
> code is rather complicated (min ,max , ddrloc ,rec_drm, drlocm), and if
> it is equivalent to hfacc, why not just use it? perhaps not...
> - Benny
>
> On Tue, 2004-08-17 at 00:01, Martin Losch wrote:
>> Benny,
>> the formulae are all in the documentation, so equation 1.32 on that
>> page is it. As I wrote in my previous email to the other thread, for
>> height coordinates, b in 1.32 is the scaled density g\rho/\rho_{0}. In
>> the code it's actually the scale density anomaly, as Dimitris pointed
>> out: g(\rho-\rho_{0})/\rho_{0}, so the phiHyd and phiHydLow is the
>> corresponding pressure anomaly scaled by \rho_{0}. If you compute the
>> full bottom pressure (including the g\rho_{0}H contribution), then you
>> won't see much except topography. Because topography (=depth) 
>> dominates
>> the bottom pressure, it really only makes sense to look at 
>> fluctuations
>> of bottom pressure. and for those the choice of \rho_{0} (=rhoConst in
>> data) is irrelevant.
>>
>> There is a paper by John Marshall which also should have all the
>> formulae:
>> Marshall, J. A. Adcroft, J-M Campin and  C. Hill (2004)
>>   Atmosphere-ocean modeling exploiting fluid isomorphisms. submitted 
>> to
>> Monthly Weather Review. You can download a preprint from
>> http://paoc.mit.edu/paoc/marshall/latest_papers.htm
>> Also in Losch etal 2004 JPO 34(1), pp 306-319, we describe the
>> ismorphism and all equations in detail in the appendix (in particulare
>> Eq A23 and the following text). Appendix C describes the 
>> discretization
>> issue I was alluding to earlier. If you don't have access to JPO, you
>> can download a preprint from
>> http://mitgcm.org/~mlosch/nonbouss_pp.pdf
>>
>> Good luck,
>> Martin
>>
>> On Aug 16, 2004, at 11:54 PM, Benny Cheng wrote:
>>
>>> Could someone show me or email me the exact phihydlow computation ( 
>>> in
>>> mathematical notation , not code) used in the MITgcm. It looks rather
>>> murky to tread through the code... is it close to what is described 
>>> in
>>> http://mitgcm.org/sealion/online_documents/node20.html ? thanks.
>>>
>>> - Benny
>>>
>>>
>>>
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>> Martin Losch // mailto:mlosch at awi-bremerhaven.de
>> Alfred-Wegener-Institut für Polar- und Meeresforschung
>> Postfach 120161, 27515 Bremerhaven, Germany
>> Tel./Fax: ++49(471)4831-1872/1797
>> http://www.awi-bremerhaven.de/People/show?mlosch
>>
>>
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>
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