# 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 (75-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. (3.20.17) 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 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 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 =

0.999742244888022 0.996939883468178 0.986141997098021 0.931595598713477 0.861224354872028

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:

3.05 (3rd June, 2016)

## 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., 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 http://www.TEOS-10.org