# gsw_rho_second_derivatives_wrt_enthalpy_CT_exact

```second derivatives of density
with respect to enthalpy```

## USAGE:

```[rho_SA_SA_wrt_h, rho_SA_h, rho_h_h] = ...
gsw_rho_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)```

## DESCRIPTION:

```Calculates the following three second-order derivatives of density
(rho),
(1) rho_SA_SA_wrt_h, second-order derivative with respect to Absolute
Salinity at constant h & p.
(2) rho_SA_h, second-order derivative with respect to SA & h at
constant p.
(3) rho_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_rho_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:

```rho_SA_SA_wrt_h = The second-order derivative of density with
respect to Absolute Salinity at constant h & p.
[ (kg/m^3)(g/kg)^-2 (J/kg)^-1 ]
rho_SA_h  = The second-order derivative of density with respect to
SA and h at constant p.        [ (kg/m^3)(g/kg)^-1 (J/kg)^-1 ]
rho_h_h   = The second-order derivative of density with respect to
h at constant SA & p.                    [ (kg/m^3)(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;]```
```[rho_SA_SA_wrt_h, rho_SA_h, rho_h_h] = ...
gsw_rho_second_derivatives_wrt_enthalpy_CT_exact(SA,CT,p)```
`rho_SA_SA_wrt_h =`
`   1.0e-03 *`
```   0.188124506388597
0.187392915799686
0.167214908475657
0.116354239332502
0.103802027436498
0.092959759919644```
`rho_SA_h =`
`   1.0e-06 *`
```  -0.459894218037865
-0.461081364269496
-0.498969518512561
-0.642785635927268
-0.682351831685558
-0.706800653783123```
`rho_h_h =`
`   1.0e-09 *`
```  -0.454241581845215
-0.456033258712955
-0.500601766903036
-0.627882803785457
-0.663096358715998
-0.686453851147432```

## 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.```
```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`