# gsw_rho_second_derivatives_CT_exact

`second derivatives of rho`

## USAGE:

```[rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = ...
gsw_rho_second_derivatives_CT_exact(SA,CT,p)```

## DESCRIPTION:

```Calculates the following three second-order derivatives of rho,
(1) rho_SA_SA, second order derivative with respect to Absolute Salinity
at constant CT & p.
(2) rho_SA_CT, second order derivative with respect to SA & CT at
constant p.
(3) rho_CT_CT, second order derivative with respect to CT at constant
SA & p.
(4) rho_SA_P, second-order derivative with respect to SA & P at
constant CT.
(5) rho_CT_P, second-order derivative with respect to CT & P at
constant SA```
```Note that this function uses the full Gibbs function.  There is an
alternative to calling this function, namely
gsw_rho_second_derivatives(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 ]
(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:

```rho_SA_SA = The second derivative of rho with respect to
Absolute Salinity at constant CT & p.  [ (kg/m^3)(g/kg)^-2 ]
rho_SA_CT = The second derivative of rho with respect to
SA & CT at constant p.             [ (kg/m^3)(g/kg)^-1 K^-1]
rho_CT_CT = The second derivative of rho with respect to
CT at constant SA and p.                   [ (kg/m^3) K^-2 ]
rho_SA_P  = The second derivative of rho with respect to
SA & P at constant CT.           [ (kg/m^3)(g/kg)^-1 Pa^-1 ]
rho_CT_P  = The second derivative of rho with respect to
CT & P at constant SA.               [ (kg/m^3) K^-1 Pa^-1 ]```

## 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;]```
```[rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = ...
gsw_rho_second_derivatives_CT_exact(SA,CT,p)```
`rho_SA_SA =`
`   1.0e-03 *`
```    0.188147803529947
0.187736836321965
0.168284283716908
0.118937108838259
0.110314719705899
0.104201573868626```
`rho_SA_CT =`
```  -0.001836215029399
-0.001840192571434
-0.001989522503234
-0.002559991033648
-0.002710008063805
-0.002798643987570```
`rho_CT_CT =`
```  -0.007241739106885
-0.007268592861024
-0.007975897762363
-0.010001038700960
-0.010557570576970
-0.010924662024630```
`rho_SA_P =`
`   1.0e-09 *`
```  -0.618450119516638
-0.619495810826076
-0.659236700264537
-0.765879906314218
-0.791905157633432
-0.809440672756091```
`rho_CT_P =`
`   1.0e-08 *`
```  -0.116411869394607
-0.117562611767344
-0.142111284622683
-0.214682405591971
-0.237654164605583
-0.255182895824723```

## 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.```
```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`