# gsw_isopycnal_slope_ratio

ratio of the slopes of isopycnals on the SA-CT diagram for p and p_ref (75-term equation)

## Contents

## USAGE:

isopycnal_slope_ratio = gsw_isopycnal_slope_ratio(SA,CT,p,p_ref)

## DESCRIPTION:

Calculates the ratio of alpha_CT/beta_CT at pressure p to that at pressure p_ref. 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 isopycnal slope 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 pressure [ dbar ] ( i.e. absolute reference pressure - 10.1325 dbar )

SA & CT need to have the same dimensions. p & p_ref may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT are MxN

## OUTPUT:

isopycnal_slope_ratio = The ratio of alpha_CT/beta_CT evaluated at pressure p to that at pressure p_ref. [ unitless ]

## 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

isopycnal_slope_ratio = gsw_isopycnal_slope_ratio(SA,CT,p,p_ref)

isopycnal_slope_ratio =

1.000435598406882 1.002211450149232 1.007313601141281 1.033747554906412 1.112513649348894 1.254180124792826

## AUTHOR:

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

## VERSION NUMBER:

3.05 (16th February, 2015)

## 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. (3.17.2) 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.

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