# gsw_specvol_second_derivatives_wrt_enthalpy

```second derivatives of specific volume
with respect to enthalpy (75-term equation)```

## USAGE:

```[v_SA_SA_wrt_h, v_SA_h, v_h_h] = ...
gsw_specvol_second_derivatives_wrt_enthalpy(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.```
```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". ```

## 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 ]
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(SA,CT,p)```
`v_SA_SA_wrt_h =`
`   1.0e-08 *`
```   0.080898741086877
0.080931595349498
0.084648485333225
0.096952812049233
0.099684475381589
0.101288447077547```
`v_SA_h =`
`   1.0e-12 *`
```  0.325437133570796
0.327060462851431
0.375273569184178
0.545188833073084
0.589424881889351
0.616101548209175```
`v_h_h =`
`   1.0e-15 *`
```   0.447949998681476
0.449121446914278
0.485998151346315
0.598480711660961
0.628708349875318
0.647433212216398```

## AUTHOR:

`Paul Barker and Trevor McDougall          [ 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```
`The software is available from http://www.TEOS-10.org`