# gsw_pt_second_derivatives

`second derivatives of potential temperature`

## USAGE:

`[pt_SA_SA, pt_SA_CT, pt_CT_CT] = gsw_pt_second_derivatives(SA,CT)`

## DESCRIPTION:

```Calculates the following three second-order derivatives of potential
temperature (the regular potential temperature which has a reference
sea pressure of 0 dbar),
(1) pt_SA_SA, the second derivative with respect to Absolute Salinity
at constant Conservative Temperature,
(2) pt_SA_CT, the derivative with respect to Conservative Temperature
and Absolute Salinity, and
(3) pt_CT_CT, the second derivative with respect to Conservative
Temperature at constant Absolute Salinity.``` ```Click for a more detailed description of the second derivatives of potential temperature.```

## INPUT:

```SA  =  Absolute Salinity                                        [ g/kg ]
CT  =  Conservative Temperature                                [ deg C ]```
`SA & CT need to have the same dimensions.`

## OUTPUT:

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

## 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;]```
`[pt_SA_SA, pt_SA_CT, pt_CT_CT] = gsw_pt_second_derivatives(SA,CT)`
`pt_SA_SA =`
`1.0e-003 *`
```   0.160307058371208
0.160785497957769
0.168647220588324
0.198377949876584
0.210181899321236
0.220018966513329```
`pt_SA_CT =`
```   0.001185581323691
0.001187068518686
0.001217629686266
0.001333254154015
0.001379674342678
0.001418371539325```
`pt_CT_CT =`
`1.0e-003 *`
```  -0.121979811279463
-0.123711264754503
-0.140136818504977
-0.140645384127949
-0.113781055410824
-0.082417269009484```

## 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.
See Eqns. (A.12.9) and (A.12.10) of this TEOS-10 Manual.```
`This software is available from http://www.TEOS-10.org`