# gsw_geo_strf_PISH

    Pressure intergrated steric height PISH (75-term equation)

## Contents

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

## USAGE:

    geo_strf_PISH = gsw_geo_strf_PISH(SA,CT,p,p_ref)

## DESCRIPTION:

    Calculates pressure-integrated steric height PISH as the integral of
    pressure multiplied by 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, this being the
    gravitational acceleration averaged over the surface of the global ocean
    (see page 46 of Griffies, 2004).

    This function evaluates the pressure integral of specific volume using
    SA and CT interpolated with respect to the intergral of bouyancy
    frequency N2 using the method of Barker et al. (2017).  This "curve
    fitting" method uses a Piecewise Cubic Hermite Interpolating Polynomial
    to produce a smooth curve with minimal artificial watermasses  between
    the observed data points.

    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
    expression for specific volume of 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 rational function expression for specific volume as
    essentially reflecting the full accuracy of TEOS-10.  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 PISH.

## 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:

    geo_strf_PISH = Pressure intergrated steric height           [ kg s^2 ]
     The output geo_strf_PISH has dimensions 1xN, where N is the number of
     profiles in the input data.
     Note. If p_ref exceeds the pressure of the deepest “bottle” on a
       vertical profile, then the pressure-integrated steric height is
       returned as NaN.

## EXAMPLE 1:

    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

    geo_strf_PISH = gsw_geo_strf_PISH(SA,CT,p,p_ref)

    geo_strf_PISH =

      5.766680282284854e+06

## AUTHOR:

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

## VERSION NUMBER:

    3.06 (15th May, 2017)

## REFERENCES:

    Barker, P.M., T.J. McDougall and S.J. Wotherspoon, 2017: An
     interpolation method for oceanographic data. J. Atmosph. Ocean. Tech.
      (To be submitted).

    Griffies, S. M., 2004: Fundamentals of Ocean Climate Models. Princeton,
    NJ: Princeton University Press, 518 pp + xxxiv.

    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. (3.31.4) and section 3.31 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 and P.M. Barker, 2015: Accurate
     polynomial expressions for the density and specific volume of seawater
     using the TEOS-10 standard.  Ocean Modelling, 90, pp. 29-43.
     http://dx.doi.org/10.1016/j.ocemod.2015.04.002

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