# gsw_enthalpy_second_derivatives

`second derivatives of enthalpy (75-term equation)`

## USAGE:

`[h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives(SA,CT,p)`

## DESCRIPTION:

```Calculates the following three second-order derivatives of specific
enthalpy (h),
(1) h_SA_SA, second order derivative with respect to Absolute Salinity
at constant CT & p.
(2) h_SA_CT, second order derivative with respect to SA & CT at
constant p.
(3) h_CT_CT, second order derivative with respect to CT at constant
SA & p.```
```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". ``` ```Click for a more detailed description of the second derivatives of specific enthalpy.```

## 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:

```h_SA_SA  =  The second derivative of specific enthalpy with respect to
Absolute Salinity at constant CT & p.
[ (J/kg)(g/kg)^-2) ] i.e. [ (J kg/g^2) ]
h_SA_CT  =  The second derivative of specific enthalpy with respect to
SA and CT at constant p.                  [ J/(kg K(g/kg)) ]
h_CT_CT  =  The second derivative of specific enthalpy with respect to
CT at constant SA and p.                      [ J/(kg K^2) ]```

## 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;]```
`[h_SA_SA, h_SA_CT, h_CT_CT] = gsw_enthalpy_second_derivatives(SA,CT,p)`
`h_SA_SA =`
```   0.000080922482023
0.000404963500641
0.001059800046742
0.002431088963823
0.006019611828423
0.010225411250217

h_SA_CT =

0.000130004715129
0.000653614489248
0.001877220817849
0.005470392103793
0.014314756132297
0.025195603327700

h_CT_CT =

0.000714303909834
0.003584401249266
0.009718730753139
0.024064471995224
0.061547884081343
0.107493969308119```

## AUTHOR:

`Trevor McDougall and Paul Barker.          [ 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.
See Notes on the first and second order isobaric derivatives of
specific enthalpy.```
```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.```
`This software is available from http://www.TEOS-10.org`