# gsw_geo_strf_dyn_height_pc

    dynamic height anomaly for piecewise
    constant profiles

## Contents

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

## USAGE:

    [geo_strf_dyn_height_pc, p_mid, in_funnel] = gsw_geo_strf_dyn_height_pc(SA,CT,delta_p)

## DESCRIPTION:

    Calculates dynamic height anomaly as the integral of specific volume
    anomaly from the the sea surface pressure (0 Pa) to the pressure p.
    This function, gsw_geo_strf_dyn_height_pc.m, is to used when the Absolute
    Salinity and Conservative Temperature are piecewise constant in the
    vertical over sucessive pressure intervals of delta_p (such as in
    a forward "z-coordinate" ocean model).  "geo_strf_dyn_height_pc" is the
    dynamic height anomaly with respect to the sea surface.  That is,
    "geo_strf_dyn_height_pc" is the geostrophic streamfunction for the
    difference between the horizontal velocity at the pressure concerned, p,
    and the horizontal velocity at the sea surface.  Dynamic height anomaly
    is the geostrophic streamfunction in an isobaric surface.  The reference
    values used for the specific volume anomaly are SA = SSO = 35.16504 g/kg
    and CT = 0 deg C.  The output values of geo_strf_dyn_height_pc are given
    at the mid-point pressures, p_mid, of each layer in which SA and CT are
    vertically piecewice constant(pc).  This function calculates specific
    volume anomaly using the computationally efficient 25-term expression
    for specific volume of McDougall et al. (2010).

    Click for a more detailed description of dynamic
    height anomaly for piecewise constant profiles.

## INPUT:

    SA       =  Absolute Salinity                                   [ g/kg ]
    CT       =  Conservative Temperature                           [ deg C ]
    delta_p  =  difference in sea pressure between the deep and     [ dbar ]
                shallow  extents of each layer in which SA and CT
                are vertically constant delta_p must be positive.

    Note. Sea pressure is absolute pressure minus 10.1325 dbar.

    SA & CT need to have the same dimensions.
    delta_p may have dimensions Mx1 or 1xN or MxN, where SA & CT are MxN.

## OUTPUT:

    geo_strf_dyn_height_pc  =  dynamic height anomaly            [ m^2/s^2 ]
    p_mid                   =  mid-point pressure in each layer     [ dbar ]

    in_funnel               =  0, if SA, CT and p are outside the "funnel"
                            =  1, if SA, CT and p are inside the "funnel"
    Note. The term "funnel" describes the range of SA, CT and p over which
      the error in the fit of the computationally-efficient 25-term
      expression for density was calculated (McDougall et al., 2010).

## 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;]
    delta_p = [     10;      40;      75;     125;     350;     400;]

    [geo_strf_dyn_height_pc, p_mid, in_funnel] = ...
                                gsw_geo_strf_dyn_height_pc(SA,CT,delta_p)

    geo_strf_dyn_height_pc =

       -0.3003
       -1.7548
       -4.4227
       -6.8133
       -9.4431
      -12.7042

    p_mid =

        5.0000
       30.0000
       87.5000
      187.5000
      425.0000
      800.0000

    in_funnel =

         1
         1
         1
         1
         1
         1

## AUTHOR:

    Trevor McDougall & Claire Roberts-Thomson.       [ help_gsw@csiro.au ]

## VERSION NUMBER:

    2.0 (28th August, 2010)

## 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 Eqns. (3.32.2) and (A.30.6) of this TEOS-10 Manual.

    McDougall T. J., D. R. Jackett, P. M. Barker, C. Roberts-Thomson, R.
     Feistel and R. W. Hallberg, 2010:  A computationally efficient 25-term
     expression for the density of seawater in terms of Conservative
     Temperature, and related properties of seawater.  To be submitted
     to Ocean Science Discussions.

    McDougall, T. J. and A. Klocker, 2010: An approximate geostrophic
     streamfunction for use in density surfaces. Ocean Modelling, 32,
     105-117.
      See section 8 of this paper.

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