[MITgcm-support] Nonlinear equations of state

[Martin Losch]

Hi all,

I don’t seem to be on top of things here, so thanks to Paola for the clarification.

But the MITgcm can do more (o:

there’s the parameter `selectP_inEOS_Zc` that can be set in data&PARM01. Otherwise it defaults to the historical settings associated with the eosType. From `PARAMS.h`:
C     selectP_inEOS_Zc    :: select which pressure to use in EOS (for z-coords)
C                           =0: simply: -g*rhoConst*z
C                           =1: use pRef = integral{-g*rho(Tref,Sref,pRef)*dz}
C                           =2: use hydrostatic dynamical pressure
C                           =3: use full (Hyd+NH) dynamical pressure

So using eosType=‘MDJWF’ together with selectP_inEOS_Zc = 0 should also work and not violate the energy budget.

Martin

> On 12. Mar 2024, at 16:49, Paola Cessi <pcessi at ucsd.edu> wrote:
> 
> Hi Dave,
> 
> another issue of using a complex EoS such as TEOS-10 in a model which makes the Boussinesq approximation is that proper conservation of total energy (including internal energy) is lost unless some care is taken. For example, with the Boussinesq approximation the dependence of the EoS on the pressure, p, must be through the term  p = -rhoConst*gravity*z, not the in situ pressure. If the actual in situ pressure  is used in a Boussinesq model, then there is an inconsistent energy budget. 
> 
> This is explained in detail in the attached paper. If you are using an incompressible, Boussinesq model use JMD95Z, not JMD95P.
> 
> Cheers,
> Paola
> 
> 
>> On Mar 12, 2024, at 4:44 AM, Dave Munday - BAS <danday at bas.ac.uk <mailto:danday at bas.ac.uk>> wrote:
>> 
>> Thanks Martin. That’s quite reassuring that I haven’t made a daft choice with at least trying out MDJWF. TEOS-10 would have been nice, but I’m quite happy to do without for now.
>> 
>> D
>> 
>>> On 12 Mar 2024, at 09:16, Martin Losch <Martin.Losch at awi.de <mailto:Martin.Losch at awi.de>> wrote:
>>> 
>>> Hi Dave,
>>> 
>>> JMD95Z (based on Jackett and McDougall 1995) is basically a “re-tuned” UNESCO formula (UNESCO for in-situ temperature and JMD95Z for potential temperature), both use p = -rhoConst*gravity*z as an approximation for pressure.
>>> JMD95Z uses the actual hydrostatic pressure (lagged by one timestep), and hence requires a little more computation
>>> MDJWF implements McDougall, et al (2003). The EOS is based on a different fromula and principles and contains fewer terms, so that the authors (?) claim that there fewer computations involved, hence it should be faster. This EOS also uses the hydrostatic pressure of the previous time step
>>> 
>>> In practice, the EOS is not the bottleneck of any simulation, so that I would not expect any significant speed differences. For potential temperature I wouild use MDJWF, just because it is “newer”. 
>>> 
>>> There’s also TEOS10, which requires that “THETA” and “SALT” are interpreted as conservative temperature and absolute salinity. This implementation is not quite complete yet, see PR #812: https://github.com/MITgcm/MITgcm/pull/812 <https://urldefense.com/v3/__https://github.com/MITgcm/MITgcm/pull/812__;!!Mih3wA!DjhCnEwPZhyprmcYr_89m6KqNgmJNB21EC-PMgNe0EpUy6Vm-BFs2jS5snW4uYL1HBOPG_wQVFB303U$>
>>> 
>>> Martin
>>> 
>>>> On 11. Mar 2024, at 18:35, Dave Munday - BAS <danday at bas.ac.uk <mailto:danday at bas.ac.uk>> wrote:
>>>> 
>>>> Dear MITgcm-ers,
>>>> 
>>>> I’ve just been trying to make a decision about which particular nonlinear EOS to use for a very long-running two basin sector model with biogeochemistry. In reading the docs the MDJWF EOS is described as “more accurate and less expensive”, which is appealing when running models for 10-20 000 years. A lot of the verification experiments are set to use JMD95Z or JMD95P. Is there a reason to prefer them over MDJWF?
>>>> 
>>>> Many thanks,
>>>> 
>>>> Dave
>>>> 
>>>> 
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> 
> <SeawaterBoussinesq.pdf>

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