# gsw_isopycnal_vs_ntp_CT_ratio

    Ratio of the gradient of Conservative
    Temperature in a potential density
    surface to that in the neutral tangent
    plane (48-term equation)

## Contents

- USAGE:
- DESCRIPTION:
- INPUT:
- OUTPUT:
- EXAMPLE:
- AUTHOR:
- VERSION NUMBER:
- REFERENCES:

## USAGE:

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

## DESCRIPTION:

    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 48-term expression for density in terms of SA, CT and p
    (McDougall et al., 2013).

    Click for a more detailed description of the
    isopycnal versus ntp CT ratio.

## INPUT:

    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

## OUTPUT:

    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 ]

## 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;]
    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 =

       1.000630863388660
       1.004179196949259
       1.016635934710221
       1.080042249305421
       1.174924051056580

    p_mid =

    1.0e+002 *

       0.300000000000000
       0.875000000000000
       1.875000000000000
       4.250000000000000
       8.000000000000000

## AUTHOR:

    Trevor McDougall, Paul Barker & David Jackett   [ help@teos-10.org ]

## VERSION NUMBER:

    3.02 (17th November, 2012)

## 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. (3.17.3) 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., P.M. Barker, R. Feistel and D.R. Jackett, 2013:  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 J. Atm. Ocean. Technol., xx, yyy-zzz.

     The software is available from http://www.TEOS-10.org