# gsw_specvol_alpha_beta_CT_exact

    specific volume, thermal expansion & saline
    contraction coefficients from CT

## Contents

- USAGE:
- DESCRIPTION:
- INPUT:
- OUTPUT:
- EXAMPLE:
- AUTHOR:
- VERSION NUMBER:
- REFERENCES:

## USAGE:

    [specvol, alpha_CT, beta_CT] = gsw_specvol_alpha_beta_CT_exact(SA,CT,p)

## DESCRIPTION:

    Calculates specific volume, the appropiate thermal expansion coefficient
    and the appropriate saline contraction coefficient of seawater from
    Absolute Salinity and Conservative Temperature.

    Note that this function uses the full Gibbs function.  There is an
    alternative to calling this function, namely gsw_specvol_alpha_beta(SA,CT,p),
    which uses the computationally-efficient 75-term expression for specific
    volume in terms of SA, CT and p (Roquet et al., 2015).

## INPUT:

    SA  =  Absolute Salinity                                        [ g/kg ]
    CT  =  Conservative Temperature                                [ deg C ]
    p   =  sea pressure                                             [ dbar ]
           ( i.e. 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:

    specvol   =  specific volume                                  [ m^3/kg ]
    alpha_CT  =  thermal expansion coefficient                       [ 1/K ]
                 with respect to Conservative Temperature
    beta_CT   =  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;]

    [specvol, alpha_CT, beta_CT] = gsw_specvol_alpha_beta_CT_exact(SA,CT,p)

    specvol =

     1.0e-003 *

       0.978626618725186
       0.978222134953103
       0.976154774939840
       0.972961213383549
       0.971026778012244
       0.968989993773259

    alpha_CT =

     1.0e-003 *

       0.324707799687110
       0.322723974596565
       0.281179083137791
       0.173138326981408
       0.146269069937061
       0.129427106726016

    beta_CT =

     1.0e-003 *

       0.717486805409467
       0.717647610706394
       0.726219007035780
       0.750509225553259
       0.755062996958255
       0.757065832066916

## AUTHOR:

    Trevor McDougall and Paul Barker             [ 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 sections (2.8), (2.18) and (2.19) of this TEOS-10 Manual.

    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