# gsw_steric_height

    steric height anomaly (75-term equation)

## Contents

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

## USAGE:

    steric_height = gsw_geo_strf_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
    because 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 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). For dynamical oceanography we may
    take the 75-term  expression for specific volume 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_geo_strf_steric_height(SA,CT,p,p_ref)

    steric_height =

       1.739351036388176
       1.497080916746352
       1.113977842340865
       0.772529305837402
       0.346408751831337
                       0

## 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 Eqn. (3.7.3) and section 3.27 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, 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