# gsw_rho_alpha_beta

    in-situ density, thermal expansion & saline
    contraction coefficient (48-term equation)

## Contents

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

## 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 48-term expression for density in terms of
    SA, CT and p (McDougall et al., 2011).

    Note that potential density (pot_rho) with respect to reference pressure
    p_ref is obtained by calling this function with the pressure argument being
    p_ref as in [pot_rho, ~, ~] = gsw_rho_alpha_beta(SA,CT,p_ref).

    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 *

       1.021840446566116
       1.022262985174925
       1.024427770449335
       1.027790499661129
       1.029837753532120
       1.032002083264508

    alpha =

    1.0e-003 *

       0.324655171916243
       0.322668478458351
       0.281151938214040
       0.173151289088423
       0.146219836227099
       0.129341856239010

    beta =

    1.0e-003 *

       0.717542079424497
       0.717702525468585
       0.726263506499359
       0.750590941859954
       0.755150882623787
       0.757150836844134

## AUTHOR:

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

## VERSION NUMBER:

    3.01 (23rd May, 2011)

## 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., P.M. Barker, R. Feistel and D.R. Jackett, 2011:  A
     computationally efficient 48-term expression for the density of
     seawater in terms of Conservative Temperature, and related properties
     of seawater.  To be submitted to Ocean Science Discussions.

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