[MITgcm-support] Potential temperature

[Sergio Jaramillo]

Martin,

That is exactly what I have, then:

tRef(z)=(rho_reference-rhoNil)/(tAlpha*rhoNil)

where, with 32 levels, if I use (from measurements in a rotating tank):
rho_reference (kg/m^3)= [1004.3,    1008.7,    1012.8,    1016.3,    
1019.2,    1021.3, ...
      1022.8,    1024.0,    1025.2,    1026.6,    1028.0,    1029.1, ...
      1030.3,    1031.7,    1032.9,    1033.8,    1034.8,    1036.1, ...
      1037.4,    1038.4,    1039.3,    1040.1,    1041.1,    1042.1, ...
      1043.1,    1043.9,    1044.7,    1045.3,    1046.1,    1047.1, ...
      1048.6,    1050.6];

rhoNil =mean(rho);
tAlpha=2e-4;

I get :

tRef = [-142.678, -121.397, -101.567, -84.6392, -70.6133, ...
        -60.4566, -53.2018, -47.3979, -41.5941,  -34.823, ...
        -28.0518, -22.7317, -16.9278, -10.1567, -4.35287, ...      
         0,  4.83653,   11.124,  17.4115,   22.248,       ...
         26.6009,  30.4701,  35.3066,  40.1432,  44.9797, ...
         48.8489,  52.7181,    55.62,  59.4893,  64.3258, ...
         71.5806,  81.2536];

with these values for tRef(z), the model breaks, so what I am doing is 
increasing arbitrarily tAlpha to 2e-3, and then the model runs fine. But 
I was wondering if there was a way of doing it without increasing 
tAlpha. Is the measured density (rho_reference above) ok for this 
calculation? should I change something in it?

Thanks again,

Sergio


>Message: 3
>Date: Thu, 3 Jun 2004 09:26:06 +0200
>From: Martin Losch <mlosch at awi-bremerhaven.de>
>Subject: Re: [MITgcm-support] Potential temperature
>To: mitgcm-support at mitgcm.org
>Message-ID: <46A87684-B52F-11D8-8770-000A9591B488 at awi-bremerhaven.de>
>Content-Type: text/plain; charset=US-ASCII; format=flowed
>
>Not quite sure, what you mean, but
>rho=rhoNil*(1-tAlpha*(theta(z)-tRef(z)) + sBeta*(salt(z)-sRef(z)))
>is the linear eos. rhoNil is a constant. So if sBeta=0 then 
>rhoNil*(1+tAlpha*tRef(z)) is your reference density.
>
>Martin
>
>On Wednesday, June 2, 2004, at 07:48 PM, Sergio Jaramillo wrote:
>
>  
>
>>Dear MITgcm support,
>>
>>I have what may be a dumb question but it is one of the few things 
>>that I want to verify before send it to Martin Losch who kindly 
>>offered a detailed check.
>>
>>Question: If I have a density profile, constant salinity, and I want 
>>to use a linear equation of state, how can I get the potential 
>>temperature profile (tRef in data file) that matches the density to 
>>use it as an input for the model?
>>
>>I am not confident with the way I am doing this now, and I appreciate 
>>any help.
>>
>>Many thanks,
>>
>>Sergio Jaramillo
>>UBC
>>
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>>MITgcm-support at mitgcm.org
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>>    
>>