# gsw_rho_alpha_beta

in-situ density, thermal expansion & saline contraction coefficient (75-term equation)

## Contents

## USAGE:

[rho, alpha, beta] = gsw_rho_alpha_beta(SA,CT,p)

## DESCRIPTION:

Calculates in-situ density, the appropiate thermal expansion coefficient and the appropriate saline contraction coefficient of seawater from Absolute Salinity and Conservative Temperature. This function uses the computationally-efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

Note that the 75-term equation has been fitted in a restricted range of parameter space, and is most accurate inside the "oceanographic funnel" described in McDougall et al. (2003). The GSW library function "gsw_infunnel(SA,CT,p)" is avaialble to be used if one wants to test if some of one's data lies outside this "funnel".

Click for a more detailed description of rho, alpha and beta. |

## INPUT:

SA = Absolute Salinity [ g/kg ] CT = Conservative Temperature [ deg C ] p = sea pressure [ dbar ] (ie. absolute pressure - 10.1325 dbar)

SA & CT need to have the same dimensions. p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT are MxN.

## OUTPUT:

rho = in-situ density [ kg/m^3 ] alpha = thermal expansion coefficient [ 1/K ] with respect to Conservative Temperature beta = saline contraction coefficient [ kg/g ] at constant Conservative Temperature

## EXAMPLE:

SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;] CT = [28.8099; 28.4392; 22.7862; 10.2262; 6.8272; 4.3236;] p = [ 10; 50; 125; 250; 600; 1000;]

[rho, alpha, beta] = gsw_rho_alpha_beta(SA,CT,p)

rho =

1.0e+003 *

1.021839935738108 1.022262457966867 1.024427195413316 1.027790152759127 1.029837779000189 1.032002453224572

alpha =

1.0e-003 *

0.324638934509245 0.322655537959731 0.281145723210171 0.173199716344780 0.146289673594824 0.129414845334599

beta =

1.0e-003 *

0.717483987596135 0.717647512290095 0.726211643644768 0.750500751749777 0.755052064788492 0.757050813384370

## AUTHOR:

Paul Barker and Trevor McDougall [ 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 appendix A.20 and appendix K of this TEOS-10 Manual.

McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003: Accurate and computationally efficient algorithms for potential temperature and density of seawater. J. Atmosph. Ocean. Tech., 20, pp. 730-741.

Roquet, F., G. Madec, T.J. McDougall and P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard.Ocean Modelling,90, pp. 29-43. http://dx.doi.org/10.1016/j.ocemod.2015.04.002

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