## Contents

## USAGE:

t_freezing = gsw_t_freezing(SA,p,saturation_fraction)

## DESCRIPTION:

Calculates the in-situ temperature at which seawater freezes. The
in-situ temperature freezing point is calculated from the exact
in-situ freezing temperature which is found by a modified Newton-Raphson
iteration (McDougall and Wotherspoon, 2013) of the equality of the
chemical potentials of water in seawater and in ice.

An alternative GSW function, gsw_t_freezing_poly, it is based on a
computationally-efficient polynomial, and is accurate to within -5e-4 K
and 6e-4 K, when compared with this function.

## INPUT:

SA = Absolute Salinity [ g/kg ]
p = sea pressure [ dbar ]
( i.e. absolute pressure - 10.1325 dbar )
OPTIONAL:
saturation_fraction = the saturation fraction of dissolved air
in seawater
(i.e., saturation_fraction must be between 0 and 1, and the
default is 0, air free)
p & saturation_fraction (if provided) may have dimensions 1x1 or Mx1
or 1xN or MxN, where SA is MxN.

## OUTPUT:

t_freezing = in-situ temperature at which seawater freezes. [ deg C ]
(ITS-90)

## EXAMPLE:

SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
p = [ 10; 50; 125; 250; 600; 1000;]
saturation_fraction = 1;

t_freezing = gsw_t_freezing(SA,p,saturation_fraction)

t_freezing =

-1.902730710149803
-1.942908619287183
-2.006861069199743
-2.090985086875259
-2.351293130342102
-2.660498762776720

## AUTHOR:

Paul Barker, Trevor McDougall and Rainer Feistal [ help@teos-10.org ]

## VERSION NUMBER:

3.05 (16th February, 2015)

## REFERENCES:

IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. Available from the TEOS-10 web site.
See section 3.3 of this TEOS-10 Manual.

McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014:
Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation.
Journal of Physical Oceanography, 44, 1751-1775.

McDougall, T.J. and S.J. Wotherspoon, 2013: A simple modification of
Newtonâ€™s method to achieve convergence of order "1 + sqrt(2)". *Applied
Mathematics Letters*, **29**, 20-25.
http://dx.doi.org/10.1016/j.aml.2013.10.008

The software is available from http://www.TEOS-10.org