# gsw_CT_second_derivatives

`second derivatives of Conservative Temperature`

## USAGE:

`[CT_SA_SA, CT_SA_pt, CT_pt_pt] = gsw_CT_second_derivatives(SA,pt)`

## DESCRIPTION:

```Calculates the following three, second-order derivatives of Conservative
Temperature
(1) CT_SA_SA, the second derivative with respect to Absolute Salinity
at constant potential temperature (with pr = 0 dbar),
(2) CT_SA_pt, the derivative with respect to potential temperature
(the regular potential temperature which is referenced to 0 dbar)
and Absolute Salinity, and
(3) CT_pt_pt, the second derivative with respect to potential
temperature (the regular potential temperature which is referenced
to 0 dbar) at constant Absolute Salinity.``` ```Click for a more detailed description of the second derivatives of Conservative Temperature.```

## INPUT:

```SA  =  Absolute Salinity                                        [ g/kg ]
pt  =  potential temperature (ITS-90)                          [ deg C ]```
`SA & pt need to have the same dimensions.`

## OUTPUT:

```CT_SA_SA  =  The second derivative of Conservative Temperature with
respect to Absolute Salinity at constant potential
temperature (the regular potential temperature which
has reference sea pressure of 0 dbar).
The CT_SA_SA output has units of:          [ K/((g/kg)^2) ]
CT_SA_pt  =  The derivative of Conservative Temperature with
respect to potential temperature (the regular one with
pr = 0 dbar) and Absolute Salinity.
CT_SA_pt has units of:                         [ 1/(g/kg) ]
CT_pt_pt  =  The second derivative of Conservative Temperature with
respect to potential temperature (the regular one with
pr = 0 dbar) at constant SA.
CT_pt_pt has units of:                              [ 1/K ]```

## EXAMPLE:

```SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
pt = [28.7832; 28.4209; 22.7850; 10.2305;  6.8292;  4.3245;]```
`[CT_SA_SA, CT_SA_pt, CT_pt_pt] = gsw_CT_second_derivatives(SA,pt)`
`CT_SA_SA =`
`1.0e-003 *`
```  -0.060718502077064
-0.062065324400873
-0.084017055354742
-0.148436050120131
-0.171270386500246
-0.189920754900116```
`CT_SA_pt =`
```  -0.001197415000869
-0.001198309530139
-0.001226523296082
-0.001335896286481
-0.001380492698572
-0.001417751669135```
`CT_pt_pt =`
`1.0e-003 *`
```   0.123012754427165
0.124662008871290
0.140829458783465
0.140646803448163
0.113684095615074
0.082286843477997```

## AUTHOR:

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

## VERSION NUMBER:

`3.06.12 (1st September, 2020)`

## 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 appendix A.12 of this TEOS-10 Manual.```
`This software is available from http://www.TEOS-10.org`