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

## 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