Ratio of the gradient of Conservative 
Temperature in a potential density
surface to that in the neutral tangent 
plane (75-term equation)



[G_CT, p_mid] = gsw_isopycnal_vs_ntp_CT_ratio(SA,CT,p,p_ref)


Calculates the ratio of the two-dimensional gradient of Conservative
Temperature in a potential density surface (with reference sea pressure
(p_ref)) versus that in the neutral tangent plane (ntp) (see Eqns. (3.17.3)
and (3.17.4) of IOC et al. (2010)).  This ratio has been called the
"isopycnal Conservative Temperature gradient ratio".  This ratio is
evaluated at the mid pressure between the individual data points in the
vertical.  The reference sea pressure of the potential density surface
must have a constant value.  This function uses from the computationally
efficient 75-term expression for specific volume in terms of SA, CT and 
p (Roquet et al., 2015).
Note that the 75-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. (2003).  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 the
isopycnal versus ntp CT ratio.


SA    =  Absolute Salinity                                      [ g/kg ]
CT    =  Conservative Temperature                              [ deg C ]
p     =  sea pressure                                           [ dbar ]
         ( i.e. absolute pressure - 10.1325 dbar )
p_ref =  reference sea pressure of the potential density surface
         ( i.e. reference absolute pressure - 10.1325 dbar )    [ dbar ]
SA & CT need to have the same dimensions.
p & pr may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT
are MxN


G_CT  =  The ratio of the gradient of CT in a potential density surface
         to that in a neutral tangent plane.  G_CT is output on the 
         same vertical (M-1)xN grid as p_mid, where M & N are the 
         dimensions of SA.  G_CT is dimensionless.          [ unitless ]
p_mid =  mid pressure between the individual points of the p grid.
         That is, p_mid is on a (M-1)xN grid.                   [ 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;]
p =  [     10;      50;     125;     250;     600;    1000;]
p_ref = 0
[G_CT, p_mid] = gsw_isopycnal_vs_ntp_CT_ratio(SA,CT,p,p_ref)
G_CT =
p_mid =
1.0e+002 *


Trevor McDougall, Paul Barker & David Jackett   [ ]


3.05 (16th February, 2015)


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. (3.17.3) and (3.17.4) of this TEOS-10 Manual.
McDougall, T. J., 1987: Neutral surfaces. Journal of Physical
 Oceanography, 17, 1950-1964.  See Eqn. (29) of this paper.
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.
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