# 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] = 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, 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 48-term
    expression for specific volume of McDougall et al. (2011).

    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. (2011).  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 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 ]

## 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] = ...
                                gsw_geo_strf_dyn_height_pc(SA,CT,delta_p)

    geo_strf_dyn_height_pc =

      -0.300323385462846
      -1.755023270288433
      -4.423073310767904
      -6.815705622756923
      -9.451462627823275
     -12.718482463704731

    p_mid =

    1.0e+002 *

       0.050000000000000
       0.300000000000000
       0.875000000000000
       1.875000000000000
       4.250000000000000
       8.000000000000000

## AUTHOR:

    Trevor McDougall & Claire Roberts-Thomson.         [ help@teos-10.org ]

## VERSION NUMBER:

    3.01 (18th 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 Eqns. (3.32.2) and (A.30.6) 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.

    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