# gsw_rho_first_derivatives_CT_exact

    SA, CT and p partial derivatives of density

## Contents

- USAGE:
- DESCRIPTION:
- INPUT:
- OUTPUT:
- EXAMPLE:
- AUTHOR:
- VERSION NUMBER:
- REFERENCES:

## USAGE:

    [rho_SA, rho_CT, drho_P] = gsw_rho_first_derivatives_CT_exact(SA,CT,p)

## DESCRIPTION:

    Calculates the three (3) partial derivatives of in situ density with
    respect to Absolute Salinity, Conservative Temperature and pressure.
    Note that the pressure derivative is done with respect to pressure in
    Pa, not dbar.

    Note that this function uses the full Gibbs function.  There is an
    alternative to calling this function, namely
    gsw_rho_first_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).

    Click for a more detailed description of three (3)
    partial derivatives of in situ density with respect
    to Absolute Salinity, Conservative Temperature and
    pressure.

## INPUT:

    SA  =  Absolute Salinity                                        [ g/kg ]
    CT  =  Conservative Temperature                                [ deg C ]
    p   =  sea pressure                                             [ dbar ]
           (ie. 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  =  partial derivatives of density with respect to
                  Absolute Salinity                  [ (kg/m^3)(g/kg)^-1 ]
    rho_CT  =  partial derivatives of density with respect to
                  Conservative Temperature                  [ kg/(m^3 K) ]
    rho_P   =  partial derivatives of density with respect to
                  pressure in Pa                           [ kg/(m^3 Pa) ]

## 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;]
    p =  [     10;      50;     125;     250;     600;    1000;]

    [rho_SA, rho_CT, rho_P] = gsw_rho_first_derivatives_CT_exact(SA,CT,p)

    rho_SA =

       0.733156846217923
       0.733624383525935
       0.743958873817461
       0.771366026959394
       0.777592352812266
       0.781293756315164

    rho_CT =

      -0.331799476403056
      -0.329908681336511
      -0.288047644037924
      -0.177949875698853
      -0.150633405019462
      -0.133569084879840

    rho_P =

      1.0e-006 *

       0.420227501717672
       0.420179717709499
       0.426714635192923
       0.447775625648340
       0.452020205408281
       0.454119774041303

## AUTHOR:

    Paul Barker and Trevor McDougall          [ 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 appendix A.20 and appendix K of this TEOS-10 Manual.

    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.

    The software is available from http://www.TEOS-10.org