# gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact

```second derivatives of specific volume
with respect to enthalpy```

## USAGE:

```[v_SA_SA_wrt_h, v_SA_h, v_h_h] = ...
gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)```

## DESCRIPTION:

```Calculates the following three second-order derivatives of specific
volume (v),
(1) v_SA_SA_wrt_h, second-order derivative with respect to Absolute
Salinity at constant h & p.
(2) v_SA_h, second-order derivative with respect to SA & h at
constant p.
(3) v_h_h, second-order derivative with respect to h at
constant SA & p.```
```Note that this function uses the full Gibbs function.  There is an
alternative to calling this function, namely
gsw_specvol_second_derivatives_wrt_enthalpy(SA,CT,p), which uses the
computationally efficient 75-term expression for specific volume in
terms of SA, CT and p (Roquet et al., 2015).```

## INPUT:

```SA  =  Absolute Salinity                                        [ g/kg ]
CT  =  Conservative Temperature                                [ deg C ]
p   =  sea pressure                                             [ dbar ]
(ie. 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_wrt_h = The second-order derivative of specific volume with
respect to Absolute Salinity at constant h & p.
[ (m^3/kg)(g/kg)^-2 (J/kg)^-1 ]
v_SA_h  = The second-order derivative of specific volume with respect to
SA and h at constant p.        [ (m^3/kg)(g/kg)^-1 (J/kg)^-1 ]
v_h_h   = The second-order derivative with respect to h at
constant SA & p.                         [ (m^3/kg)(J/kg)^-2 ]```

## 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;]```
```[v_SA_SA_wrt_h, v_SA_h, v_h_h] = ...
gsw_specvol_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)```
`v_SA_SA_wrt_h =`
`   1.0e-08 *`
```   0.082738436622270
0.082820472626935
0.087012384310439
0.098568931415547
0.100885432010628
0.102276246439309```
`v_SA_h =`
`   1.0e-12 *`
```  0.326217843241685
0.327716371538871
0.375607041087142
0.545165574576489
0.589676769358126
0.616103304530989```
`v_h_h =`
`   1.0e-15 *`
```   0.447981834829075
0.449172935265639
0.486697221526866
0.598047368579426
0.627835291967017
0.646576186556108```

## AUTHOR:

`Paul Barker and Trevor McDougall          [ 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.```
```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`