# gsw_rho_first_derivatives

SA, CT and p partial derivatives of density (75-term equation)

## Contents

## USAGE:

[rho_SA, rho_CT, rho_P] = gsw_rho_first_derivatives(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. This function uses the computationally-efficient 75-term expression for specific volume in terms of SA, CT and p (Roquet et al., 2015).

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".

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(SA,CT,p)

rho_SA =

0.733153791778356 0.733624109867480 0.743950957375504 0.771357282286743 0.777581141431288 0.781278296628328

rho_CT =

-0.331729027977015 -0.329838643311336 -0.288013324730644 -0.178012962919839 -0.150654632545556 -0.133556437868984

rho_P =

1.0e-006 *

0.420302360738476 0.420251070273888 0.426773054953941 0.447763615252861 0.452011501791479 0.454118117103094

## 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.

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, 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