# gsw_enthalpy_first_derivatives

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

## USAGE:

`[h_SA, h_CT] = gsw_enthalpy_first_derivatives(SA,CT,p)`

## DESCRIPTION:

```Calculates the following two derivatives of specific enthalpy (h),
of seawater using the computationally-efficient 75-term expression
for specific volume in terms of SA, CT and p (Roquet et al., 2015).
(1) h_SA, the derivative with respect to Absolute Salinity at
constant CT and p, and
(2) h_CT, derivative with respect to CT at constant SA and 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 first 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   =  The first derivative of specific enthalpy with respect to
Absolute Salinity at constant CT and p.
[ J/(kg (g/kg))]  i.e. [ J/g ]
h_CT   =  The first derivative of specific enthalpy with respect to
CT at constant SA and p.                          [ J/(kg K) ]```

## 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, h_CT] = gsw_enthalpy_first_derivatives(SA,CT,p)`
`h_SA =`
```  -0.070223912348929
-0.351159768365102
-0.887025065692568
-1.829602387915694
-4.423463748270238
-7.405100077558673```
`h_CT =`
`1.0e+003 *`
```   3.991899705530481
3.992025640520101
3.992210365030743
3.992284150250490
3.992685389122658
3.993014168534175```

## AUTHOR:

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

## VERSION NUMBER:

`3.05.6 (20th March, 2017)`

## 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 Eqns. (A.11.18), (A.11.15) and (A.11.12) of this TEOS-10 Manual.```
```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```
`This software is available from http://www.TEOS-10.org`