# gsw_isopycnal_slope_ratio

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

## 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`