# gsw_CT_first_derivatives_wrt_t_exact

```first derivatives of Conservative Temperature with
respect to (or at constant) in-situ temperature```

## USAGE:

`[CT_SA_wrt_t, CT_T_wrt_t, CT_P_wrt_t] = gsw_CT_first_derivatives_wrt_t_exact(SA,t,p)`

## DESCRIPTION:

```Calculates the following three derivatives of Conservative Temperature.
These derivatives are done with respect to in-situ temperature t (in the
case of CT_T_wrt_t) or at constant in-situ tempertature (in the cases of
CT_SA_wrt_t and CT_P_wrt_t).
(1) CT_SA_wrt_t, the derivative of CT with respect to Absolute Salinity
at constant t and p, and
(2) CT_T_wrt_t, derivative of CT with respect to in-situ temperature t
at constant SA and p.
(3) CT_P_wrt_t, derivative of CT with respect to pressure P (in Pa) at
constant SA and t.
This function uses the full Gibbs function. Note that this function
avoids the NaN that would exist in CT_SA_wrt_t at SA = 0 if it were
evaluated in the straightforward way from the derivatives of the Gibbs
function function.```

## INPUT:

```SA  =  Absolute Salinity                                        [ g/kg ]
t    =   in-situ temperature (ITS-90)                          [ deg C ]
p    =   sea pressure                                           [ dbar ]
( ie. absolute pressure - 10.1325 dbar )```
```SA & t need to have the same dimensions.
p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & t are MxN.```

## OUTPUT:

```CT_SA_wrt_t  =  The first derivative of Conservative Temperature with
respect to Absolute Salinity at constant t and p.
[ K/(g/kg)]  i.e. [ K kg/g ]
CT_T_wrt_t  =   The first derivative of Conservative Temperature with
respect to in-situ temperature, t, at constant SA and p.
[ unitless ]
CT_P_wrt_t  =   The first derivative of Conservative Temperature with
respect to pressure P (in Pa) at constant SA and t.
[ K/Pa ]```

## EXAMPLE:

```SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
t =  [28.7856; 28.4329; 22.8103; 10.2600;  6.8863;  4.4036;]
p =  [     10;      50;     125;     250;     600;    1000;]```
```[CT_SA_wrt_t, CT_T_wrt_t, CT_P_wrt_t] = ...
gsw_CT_first_derivatives_wrt_t_exact(SA,t,p)```
`CT_SA_wrt_t =`
```  -0.041988694538987
-0.041596549088952
-0.034853545749326
-0.019067140454607
-0.015016439826591
-0.012233725491373```
`CT_T_wrt_t =`
```   1.002752642867571
1.002243118597902
1.000835702767227
0.998194915250648
0.995219303532390
0.991780205482695```
`CT_P_wrt_t =`
`  1.0e-007 * `
```  -0.241011880838437
-0.239031676279078
-0.203649928441505
-0.119370679226136
-0.099140832825342
-0.086458168643579```

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