potential temperature to temperature

[ccsmwrf@gmail_com]

To whom it may concern:

The POP monthly output contains potential temperature in different depths. I am wondering how I can calculate the in-situ temperature from the potential temperature.

Thanks

Yang

 

[bates]

Hi Yang,

We convert everything to potential temperature for comparison purposes because of the compressibility effect. The formula to convert back to in situ temperature is very complicated (See the book titled "Atmospheric-Ocean Dynamics" by Adrian Gill, p. 602 for the formula. You would have to solve for t.). If you are trying to make this conversion so you can compare to some other data, it would be easier to convert the other data into potential temperature.

Susan
Ocean Model Science Liaison

 

[bates]

Hi Yang,

We have found code that will convert potential temperature to temperature that you can use with CCSM model output. There is a fortran script found here, http://www.ncl.ucar.edu/Support/talk_archives/2011/att-1609/potmp.f, and a ferret script called THETA_FO that you can find documented here, http://ferret.pmel.noaa.gov/Ferret/documentation/users-guide/variables-xpressions/XPRESSIONS. Both of these functions are written to convert temperature to potential temperature, but to do the reverse calculation, all you have to do is reverse reference and in situ pressure in the function call. For example, for the ferret function

THETA_FO(SALT, TEMP, P, REF)

you would perform this calculation

THETA_FO(SALT, TEMP, REF, P).

Note that in the model we defined reference pressure as 0, so that is what you would want to use in your reverse calculation as well. We are unable to view the Ferret scirpt, but the fortran script is based on the following reference.
N.P. FOFONOFF
DEEP SEA RESEARCH
1977

We use a different equation than this within the POP2 model (the equation from Gill cited in the previous post) to calculate potential temperature, so the conversion back to in situ temperature may not be exact.

Susan