[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).
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] = ...
Trevor McDougall and Paul Barker [ email@example.com ]
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,
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 http://www.TEOS-10.org