# gsw_rho_second_derivatives

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

## USAGE:

`[rho_SA_SA, rho_SA_CT, rho_CT_CT, rho_SA_P, rho_CT_P] = gsw_rho_second_derivatives(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 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 ]
(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(SA,CT,p)```
`rho_SA_SA =`
`   1.0e-03 *`
```   0.207364734477357
0.207415414547223
0.192903197286004
0.135809142211237
0.122627562106076
0.114042431905783```
`rho_SA_CT =`
```  -0.001832856561477
-0.001837354806146
-0.001988065808078
-0.002560181494807
-0.002708939446458
-0.002798484050141```
`rho_CT_CT =`
```  -0.007241243828334
-0.007267807914635
-0.007964270843331
-0.010008164822017
-0.010572200761984
-0.010939294762200```
`rho_SA_P =`
`   1.0e-09 *`
```  -0.617330965378778
-0.618403843947729
-0.655302447133274
-0.764800777480716
-0.792168044875350
-0.810125648949170```
`rho_CT_P =`
`   1.0e-08 *`
```  -0.116597992537549
-0.117744271236102
-0.141712549466964
-0.214414626736539
-0.237704139801551
-0.255296606034074```

## AUTHOR:

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

## VERSION NUMBER:

`3.06.16 (28th September, 2022)`

## 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 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`