gsw_IPV_vs_fNsquared_ratio

Ratio of the vertical gradient of potential
density (with reference pressure, p_ref), to 
the vertical gradient of locally-referenced 
potential density (48-term equation)

Contents

USAGE:

[IPV_vs_fNsquared_ratio, p_mid] =
                             gsw_IPV_vs_fNsquared_ratio(SA,CT,p,p_ref)

DESCRIPTION:

Calculates the ratio of the vertical gradient of potential density to
the vertical gradient of locally-referenced potential density.  This
ratio is also the ratio of the planetary Isopycnal Potential
Vorticity (IPV) to f times N^2, hence the name for this variable,
IPV_vs_fNsquared_ratio (see Eqn. (3.20.5) of IOC et al. (2010)).
The reference sea pressure of the potential density surface must have
a constant value.
IPV_vs_fNsquared_ratio is evaluated at the mid pressure between 
the individual data points in the vertical. This function uses the
computationally-efficient 48-term expression for density in terms of
SA, CT and p (McDougall et al., 2011).
TEOS-10 
Click for a more detailed description of the
IPV vs fNsquared 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
                                                                [ dbar ]
SA & CT need to have the same dimensions.
p & p_ref may have dimensions 1x1 or 1xN or MxN, where SA & CT are MxN.

OUTPUT:

IPV_vs_fNsquared_ratio
                   =  The ratio of the vertical gradient of potential
                      density referenced to pr, to the vertical gradient
                      of locally-referenced potential density.
                      IPV_vs_fNsquared_ratio is ouput on the same
                      vertical (M-1)xN grid as p_mid.
                      IPV_vs_fNsquared_ratio 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.
                      p_mid has units of dbar.                  [ 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
[IPV_vs_fNsquared_ratio, p_mid] = ... 
                              gsw_IPV_vs_fNsquared_ratio(SA,CT,p,p_ref)
IPV_vs_fNsquared_ratio =
   0.999745283730840
   0.996950635279959
   0.986153962640181
   0.931618955820649
   0.861271753240207
p_mid =
1.0e+002 *
   0.300000000000000
   0.875000000000000
   1.875000000000000
   4.250000000000000
   8.000000000000000

AUTHOR:

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

VERSION NUMBER:

3.01 (23rd May, 2011)

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 Eqn. (3.20.5) of this TEOS-10 Manual.
McDougall T.J., P.M. Barker, R. Feistel and D.R. Jackett, 2011:  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 Ocean Science Discussions. 
 The software is available from http://www.TEOS-10.org