# gsw_steric_height

    steric height anomaly

## Contents

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

## USAGE:

    steric_height = gsw_steric_height(SA,CT,p,p_ref)

## DESCRIPTION:

    Calculates steric height anomaly as the pressure integral of specific
    volume anomaly from the pressure p of the "bottle" to the reference
    pressure p_ref, divided by the constant value of the gravitational
    acceleration, 9.7963 m s^-2.  That is, this function returns the dynamic
    height anomaly divided by 9.7963 m s^-2; this being the gravitational
    acceleration averaged over the surface of the global ocean (see page 46
    of Griffies, 2004).  Hence, steric_height is the steric height anomaly
    with respect to a given reference pressure p_ref.

    Dynamic height anomaly is the geostrophic streamfunction for the
    difference between the horizontal velocity at the pressure concerned, p,
    and the horizontal velocity at p_ref.  Dynamic height anomaly is the
    exact geostrophic streamfunction in isobaric surfaces even though the
    gravitational acceleration varies with latitude and pressure.  Steric
    height anomaly, being simply proportional to dynamic height anomaly, is
    also an exact geostrophic streamfunction in an isobaric surface (up to
    the constant of proportionality, 9.7963 m s^-2).

    Note however that steric_height is not exactly the height (in metres)
    of an isobaric surface above a geopotential surface.  It is tempting to
    divide  dynamic height anomaly by the local value of the gravitational
    acceleration, but doing so robs the resulting quantity of either being
       (i)  an exact geostrophic streamfunction, or
       (ii) exactly the height of an isobaric surface above a geopotential
            surface.
    By using a constant value of the gravitational acceleration, we have
    retained the first of these two properties.  So it should be noted that
    becasue of the variation of the gravitational acceleration with
    latitude, steric_height does not exactly represent the height of an
    isobaric surface above a geopotential surface under the assumption of
    geostropy.

    The reference values used for the specific volume anomaly are
    SSO = 35.16504 g/kg and CT = 0 deg C.  This function calculates
    specific volume anomaly using the computationally efficient 48-term
    expression for specific volume of McDougall et al. (2013). Note that the
    48-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. (2013) and IOC et al. (2010).  For dynamical
    oceanography we may take the 48-term rational function expression for
    density as essentially reflecting the full accuracy of TEOS-10.  The GSW
    internal 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 steric
    height anomaly.

## INPUT:

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

    SA & CT need to have the same dimensions.
    p may have dimensions Mx1 or 1xN or MxN, where SA & CT are MxN.
    p_ref needs to be a single value, it can have dimensions 1x1 or Mx1 or
    1xN or MxN.

## OUTPUT:

    steric_height = steric height anomaly                             [ m ]

## 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;]
    p_ref = 1000

    steric_height = gsw_steric_height(SA,CT,p,p_ref)

    steric_height =

       1.765180536020077
       1.524364510386766
       1.142048352223201
       0.806540901776844
       0.368221554068097
                       0

## AUTHOR:

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

## VERSION NUMBER:

    3.02 (17th November, 2012)

## 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 Eqn. (3.7.3) and section 3.27 of this TEOS-10 Manual.

    McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2013:  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 J. Atm. Ocean. Technol., xx, yyy-zzz.

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