# gsw_specvol_first_derivatives_wrt_enthalpy_CT_exact

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

## USAGE:

`[v_SA_wrt_h, v_h] = gsw_specvol_first_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)`

## DESCRIPTION:

```Calculates the following two first-order derivatives of specific
volume (v),
(1) v_SA_wrt_h, first-order derivative with respect to Absolute Salinity
at constant h & p.
(2) v_h, first-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_first_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_wrt_h  =  The first derivative of specific volume with respect to
Absolute Salinity at constant CT & p.
[ (m^3/kg)(g/kg)^-1 ]
v_h  =  The first derivative of specific volume with respect to
SA and CT at constant p.               [ (m^3/kg)(J/kg)^-1 ]```

## 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_wrt_h, v_h] = gsw_specvol_first_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)`
`v_SA_wrt_h =`
`   1.0e-06 *`
```  -0.702146096545289
-0.701991007935082
-0.708841162302751
-0.730139156726518
-0.733029001570477
-0.733356567333861```
`v_h =`
`   1.0e-10 *`
```   0.796031257306406
0.790815890007698
0.687524686991260
0.421956231960832
0.355728796960838
0.314083120405946```

## AUTHOR:

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

## VERSION NUMBER:

`3.06.15 (1st June, 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.```
```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```
`The software is available from http://www.TEOS-10.org`