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Polynomial versions of TEOS-10 seawater equation of state (Fortran, Matlab and Python)


A new set of approximations to the standard TEOS-10 equation of state has recently been proposed. These follow a polynomial form, making it computationally efficient for use in numerical ocean models. Two versions are provided, the first polyTEOS10_bsq being a fit of density for Boussinesq ocean models, and the second polyTEOS10_55t fitting specific volume which is more suitable for compressible models.

Both versions are given as the sum of a vertical reference profile (6th-order polynomial) and an anomaly (52-term polynomial, cubic in pressure), with relative errors of 0.1% on the thermal expansion coefficients.

A 75-term polynomial expression polyTEOS10_75t is also presented for computing specific volume, with a better accuracy than the existing TEOS-10 48-term rational approximation, especially regarding the sound speed. This version is now used (since 2015) as the standard approximation of the TEOS-10 equation of state.

Finally, a stiffened version polyTEOS10_stif of the equation of state is also proposed.

More details on these approximations of the TEOS-10 equation of state are available in Roquet et al. (2016).

Reference: Roquet, F., Madec, G., McDougall, T. J., and Barker, P. M., 2015. Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard. Ocean Modelling, 90:29-43.

Fortran code

The file polyTEOS10_bsq.F90 includes fortran procedures to compute in-situ density, thermal expansion and haline contraction coefficients. It also provides an approximation to convert conservative temperature into potential temperature, useful in ocean models to compute air-sea fluxes.

We propose only the polyTEOS10_bsq approximation in Fortran, as this is the one that is generally most well suited for most ocean models. Note that the ocean model NEMO uses this equation of state as the standard since version 3.6.

A fortran version of polyTEOS10_75t is also available as part of the standard TEOS-10 package.

Python code

The four versions of polyTEOS10 are coded in the python script

Matlab code

Each version of polyTEOS10 is also distributed for Matlab:

  • polyTEOS10_bsq.m
  • polyTEOS10_55t.m
  • polyTEOS10_75t.m
  • polyTEOS10_stif.m


Fabien Roquet (Department of Meteorology at Stockholm University). More information on the author on his personal webpage


This software is distributed under the terms of the GNU GENERAL PUBLIC LICENSE v3. The GNU General Public License is a free, copyleft license for software and other kinds of works.


polynomial versions of TEOS-10 seawater equation of state




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