[MITgcm-support] Calculation of eta

[Martin Losch]

Thanks Matt, that's actually much clearer than my explanation. 

Jonathan: I forgot to mention, that it may be useful to read Greatbatch (1994), JGR about this subject. He also states that the global steric expansion/contraction can be parameterized in a Boussinesq model by adding a global constant as Matt suggested. That can also be done after the simulation (because it does not change the flow). I have done something like that in a paper in in Losch et al. 2004, JPO, 34(1). In that paper there are references about Boussinesq/non-Boussinesq modelling that you may want to have a look at.

Martin

On Apr 19, 2013, at 8:31 PM, Matthew Mazloff <mmazloff at ucsd.edu> wrote:

> To elaborate...what Martin says will, in practice, result in an ETAN field that shows steric height gradients but not the overall offset. 
> 
> So if you heat your whole ocean equally ETAN will not change. 
> 
> If you heat the south and cool the north you will get the appropriate ETAN induced from the steric gradient.
> 
> But, if you only heat the north you will see that the south will actually change -- you will get the correct gradient, but the whole average ETAN may not change. The north will rise, but not as much as it should and instead the south will drop.
> 
> So in summary, ETAN shows steric height gradients, but there is a net offset that is missing. This missing constant of integration can readily be calculated and added in, but that is not done so at this time
> 
> -Matt
> 
> 
> 
> 
> 
> On Apr 19, 2013, at 12:33 AM, Martin Losch <Martin.Losch at awi.de> wrote:
> 
>> I am no specialist, but the steric height causes a lot of confusion.
>> 
>> A Boussinesq model neglects the contribution of variations in density to the continuity equation, that's why we talk about incompressilbe fluids. 
>> Still the geostrophic balance that evolves in any Boussinesq model leads to a surface elevation that you would also get from steric height computations. That is kind of obvious, because the geostrophic currents do include the density variations (thermal wind). Does that make it clearer?
>> 
>> Martin
>> 
>> On Apr 18, 2013, at 8:18 PM, Jonathan Whitefield <jwhitefield at alaska.edu> wrote:
>> 
>>> Hi all.
>>> 
>>> I was just wondering whether the calculation of the ETAN field (sea
>>> surface height anomaly) includes variations in steric height (i.e.
>>> density driven changes) or not. I did have a look in the handbook, but
>>> couldn't see a reference to steric height in there. Apologies if I
>>> missed an obvious answer!
>>> 
>>> --
>>> Jonathan Whitefield, M.Sc.
>>> Ph.D. Student, Physical Oceanography
>>> 
>>> 110 O'Neill Building,
>>> P.O. Box 757220
>>> University of Alaska Fairbanks
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>>> 
>>> Phone: (907) 474-5184
>>> Fax: (907) 474-5863
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>> 
>> 
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