# gsw_geo_strf_isopycnal_pc

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

## Contents

## USAGE:

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

## DESCRIPTION:

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 |

## INPUT:

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

OPTIONAL:

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 variable.

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.

## OUTPUT:

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 ]

## 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;]

gamma_n = [26.7; 27.8;] layer_indx = [ 3; 5;]

[geo_strf_isopycnal_pc, p_mid] = ... gsw_geo_strf_isopycnal_pc(SA,CT,delta_p,gamma_n,layer_indx)

geo_strf_isopycnal_pc =

-5.270417210618314 -10.380530051934258

p_mid =

1.0e+002 *

0.875000000000000 4.250000000000000

## AUTHOR:

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

## VERSION NUMBER:

3.06 (15th May, 2017)

## 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 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, 105-117. 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