approximate isopycnal geostrophic streamfunction 
for piecewise constant profiles (75-term equation)



[geo_strf_McD_Klocker_pc, p_mid] = gsw_geo_strf_isopycnal_pc(SA,CT,delta_p,gamma_n,layer_indx,A)


Calculates the McDougall-Klocker geostrophic streamfunction (see Eqn.
(3.30.1) of IOC et al. (2010).  This function 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, and in isopycnal layered ocean 
models).  The McDougall-Klocker geostrophic streamfunction is designed 
to be used as the geostrophic streamfunction in an approximately neutral
surface (such as a Neutral Density surface, a potential density surface 
or an omega surface (Klocker et al. (2009)).  Reference values of 
Absolute Salinity, Conservative Temperature and pressure are found by 
interpolation of a one-dimensional look-up table, with the interpolating
variable being Neutral Density (gamma_n) or sigma_2.  This function 
calculates specific volume anomaly using the computationally efficient 
76-term expression for specific volume (Roquet et al., 2015).
Click for a more detailed description of the
isopycnal geostrophic streamfunction
for piecewise constant profiles


SA         =  Absolute Salinity                                 [ g/kg ]
CT         =  Conservative Temperature                         [ deg C ]
delta_p    =  difference in sea pressure between the deep and shallow
              extents of each layer in which SA and CT are vertically
              constant.  delta_p must be positive.              [ dbar ]
Note. Sea pressure is absolute pressure minus 10.1325 dbar.
gamma_n    =  Neutral Density anomaly                         [ kg/m^3 ]
              ( i.e. Neutral Density minus 1000 kg/m^3 )
layer_indx =  Index of the layers of the gamma_n surfaces
A          =  if nothing is entered the programme defaults to "Neutral
              Density" as the vertical interpolating variable. 
           =  's2' or 'sigma2', for sigma_2 as the vertical interpolating
SA, CT & delta_p need to have the same dimensions.
gamma_n & layer_indx need to have the same dimensions, there should be 
only one "gamma_n" or "sigma_2" value per level of interest.
A needs to be 1x1.


geo_strf_isopycnal_pc =  isopycnal geostrophic               [ m^2/s^2 ]
                         streamfunction as defined by 
                         McDougall & Klocker (2010)
p_mid                 =  mid-point pressure in each layer       [ dbar ]


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;]
gamma_n     = [26.7; 27.8;]
layer_indx  = [   3;    5;]
[geo_strf_isopycnal_pc, p_mid] = ...
geo_strf_isopycnal_pc =
p_mid =
  1.0e+002 *


Trevor McDougall and Paul Barker                    [ ]


3.06 (15th May, 2017)


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 section 3.30 of this TEOS-10 Manual.
Jackett, D. R. and T. J. McDougall, 1997: A neutral density variable
 for the world’s oceans. Journal of Physical Oceanography, 27, 237-263.
Klocker, A., T. J. McDougall and D. R. Jackett, 2009: A new method
 for forming approximately neutral surfaces.  Ocean Sci., 5, 155-172.
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.
McDougall, T. J. and A. Klocker, 2010: An approximate geostrophic
 streamfunction for use in density surfaces.  Ocean Modelling, 32,
  The McDougall-Klocker geostrophic streamfunction is defined in
 Eqn. (62) of this paper.
  See section 8 of this paper for a discussion of this piecewise-
 constant version of the McDougall-Klocker geostrophic streamfunction.
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