# gsw_alpha_on_beta

thermal expansion divided by the saline contraction coefficient (75-term equation)

## Contents

## USAGE:

alpha_on_beta = gsw_alpha_on_beta(SA,CT,p)

## DESCRIPTION:

Calculates alpha divided by beta, where alpha is the thermal expansion coefficient and beta is the 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 alpha on 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:

alpha_on_beta = thermal expansion coefficient with respect to Conservative Temperature divided by the saline contraction coefficient at constant Conservative Temperature. [ g kg^-1 K^-1 ]

## 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;]

alpha_on_beta = gsw_alpha_on_beta(SA,CT,p)

alpha_on_beta =

0.452468543022009 0.449601695030057 0.387140203094424 0.230778871228268 0.193747796234162 0.170946048860385

## AUTHOR:

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

## VERSION NUMBER:

3.06.15 (1st June, 2022)

## 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.

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, P.M. Barker, 2015: Accurate polynomial expressions for the density and specifc volume of seawater using the TEOS-10 standard. Ocean Modelling.

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