# gsw_internal_energy_first_derivatives

```SA, CT and p partial derivatives of internal_energy
(75-term equation)```

## USAGE:

`[u_SA, u_CT, u_P] = gsw_internal_energy_first_derivatives(SA,CT,p)`

## DESCRIPTION:

```Calculates the three (3) partial derivatives of internal energy with
respect to Absolute Salinity, Conservative Temperature and pressure.
Note that the pressure derivative is done with respect to pressure in
Pa, not dbar.  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:

```u_SA  =  partial derivative of internal_energy with respect to
Absolute Salinity          [ (J/kg)(g/kg)^-1 ] i.e. [ J/g ]
u_CT  =  partial derivative of internal_energy with respect to
Conservative Temperature                    [ (J/kg) K^-1 ]
u_P   =  partial derivative of internal energy with respect to
pressure in Pa                             [ (J/kg) Pa^-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;]```
`[u_SA, u_CT, u_P] = gsw_internal_energy_first_derivatives(SA,CT,p)`
`u_SA =`
```   0.071187610402307
0.071215557423953
0.071105286125378
0.069730589312430
0.049035910573059
0.002958348659863```
`u_CT =`
`   1.0e+03 *`
```   3.991835761856051
3.991835867574300
3.991839270596763
3.991844970098064
3.991815048606444
3.991738836685656```
`u_P =`
`   1.0e-03 *`
```   0.978707891379082
0.978464186284615
0.976704798645003
0.974063899959057
0.973627094487500
0.973297052143081```

## 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.```
```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.```
`The software is available from http://www.TEOS-10.org`