# gsw_specvol_second_derivatives

`second derivatives of specific volume (75-term equation)`

## USAGE:

`[v_SA_SA, v_SA_CT, v_CT_CT, v_SA_P, v_CT_P] = gsw_specvol_second_derivatives(SA,CT,p)`

## DESCRIPTION:

```Calculates the following three second-order derivatives of specific
volume (v),
(1) v_SA_SA, second order derivative with respect to Absolute Salinity
at constant CT & p.
(2) v_SA_CT, second order derivative with respect to SA & CT at
constant p.
(3) v_CT_CT, second order derivative with respect to CT at constant
SA & p.
(4) v_SA_P, second-order derivative with respect to SA & P at
constant CT.
(5) v_CT_P, second-order derivative with respect to CT & P at
constant SA```
```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". ```

## INPUT:

```SA  =  Absolute Salinity                                        [ g/kg ]
CT  =  Conservative Temperature                                [ deg C ]
p   =  sea pressure                                             [ dbar ]
(i.e. absolute pressure - 10.1325 dbar)```
```SA & CT need to have the same dimensions.
p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT are MxN.```

## OUTPUT:

```v_SA_SA  =  The second derivative of specific volume with respect to
Absolute Salinity at constant CT & p.  [ (m^3/kg)(g/kg)^-2 ]
v_SA_CT  =  The second derivative of specific volume with respect to
SA & CT at constant p.             [ (m^3/kg)(g/kg)^-1 K^-1]
v_CT_CT  =  The second derivative of specific volume with respect to
CT at constant SA and p.                  [ (m^3/kg) K^-2) ]
v_SA_P  =  The second derivative of specific volume with respect to
SA & P at constant CT.           [ (m^3/kg)(g/kg)^-1 Pa^-1 ]
v_CT_P  =  The second derivative of specific volume with respect to
CT & P at constant SA.               [ (m^3/kg) K^-1 Pa^-1 ]```

## EXAMPLE:

```SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
CT = [28.7856; 28.4329; 22.8103; 10.2600;  6.8863;  4.4036;]
p =  [     10;      50;     125;     250;     600;    1000;]```
`[v_SA_SA, v_SA_CT, v_CT_CT, v_SA_P, v_CT_P] = gsw_specvol_second_derivatives(SA,CT,p)`
`v_SA_SA =`
`   1.0e-08 *`
```   0.080906777599140
0.080915086639384
0.084568844270812
0.096725108896007
0.099111765836648
0.100302277946072```
`v_SA_CT =`
`   1.0e-08 *`
```   0.129965332117084
0.130523053162130
0.149555815430615
0.217023290441810
0.233892039070486
0.243659989480325```
`v_CT_CT =`
`   1.0e-07 *`
```  0.071409582006642
0.071582962051991
0.077436153664104
0.095329736274850
0.100105336953738
0.103044572835472```
`v_SA_P =`
`   1.0e-14 *`
```   0.116889015000936
0.116897424150385
0.121500614193893
0.136008673596132
0.139023051292893
0.140581903529772```
`v_CT_P =`
`   1.0e-14 *`
```   0.085542828707964
0.086723632576213
0.112156562396990
0.188269893599500
0.211615556759369
0.228609575049911```

## AUTHOR:

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

## VERSION NUMBER:

`3.06.16 (28th September, 2022)`

## 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.
```
```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 and P.M. Barker, 2015: Accurate
polynomial expressions for the density and specific volume of seawater
using the TEOS-10 standard.  Ocean Modelling, 90, pp. 29-43.
http://dx.doi.org/10.1016/j.ocemod.2015.04.002```
`This software is available from http://www.TEOS-10.org`