# gsw_stabilise_SA_CT

minimally adjusts both Absolute Salinity and Conservative Temperature to produce a stable water column (75-term equation)

## Contents

## USAGE:

[SA_out, CT_out] = gsw_stabilise_SA_CT(SA_in,CT_in,p,{opt_1,opt_2})

## DESCRIPTION:

This function stabilises a water column, this is achieved by minimally adjusting both the Absolute Salinity SA and Conservative Temperature CT values such that the minimum stability is adjusted to be atleast 1/5th of the square of earth's rotation rate.

This programme requires either Tomlab CPLEX or IBM CPLEX or the Optimization toolbox. Note that if there are a up to several hundred data points in the cast then Matlab's Optimization toolbox produces reasonable results, but if there are thousands of bottles in the cast or the best possible output is wanted then the CPLEX solver is required. This programme will determine if a slover is available to the user, if there is more than one it will use first in the following order Tomlab, IBM, then Matlab.

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 adjusting salinities to produce a stablised water column |

## INPUT:

SA_in = uncorrected Absolute Salinity [ g kg^{-1}] CT_in = uncorrected Conservative Temperature (ITS-90) [ deg C ] p = sea pressure [ dbar ] (ie. absolute pressure - 10.1325 dbar)

OPTIONAL: opt_1 = Nsquared_lowerlimit [ s^{-2}] Note. If Nsquared_lowerlimit is not supplied, a default minimum stability of 1 x 10^-9 s^-2 will be applied. or, opt_1 = longitude in decimal degrees [ 0 ... +360 ] or [ -180 ... +180 ] opt_2 = latitude in decimal degrees north [ -90 ... +90 ]

SA & t need to have the same dimensions. p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT_in are MxN. opt_1 equal to Nsquared_lowerlimit, if provided, may have dimensions 1x1 or (M-1)x1 or 1xN or (M-1)xN, where SA_in & CT_in are MxN. opt_1 equal to long & opt_2 equal to lat, if provided, may have Sdimensions 1x1 or (M-1)x1 or 1xN or (M-1)xN, where SA_in & CT_in are MxN.

## OUTPUT:

SA_out = corrected stabilised Absolute Salinity [ g kg^{-1}] CT_out = corrected Conservative Temperature (ITS-90) [ deg C ]

## EXAMPLES

Note that the availibilty of the licence will choose which solver is used, it is not controllable by the calling command line.

## EXAMPLE 1 (using Tomlab CPLEX):

SA = [34.7118; 34.8915; 35.0256; 31.0472; 34.7366; 34.7324;] CT = [28.7856; 28.4329; 22.8103; 10.2600; 6.8863; 4.4036;] p = [ 10; 50; 125; 250; 600; 1000;]

[SA_out, CT_out] = gsw_stabilise_SA_CT(SA,CT,p)

SA_out =

34.7118 34.8915 34.6116 31.4612 34.7366 34.7324

CT_out =

28.7856 28.4329 24.7758 7.9461 6.8863 4.4036

## EXAMPLE 2 (using IBM CPLEX):

SA = [34.7118; 34.8915; 35.0256; 31.0472; 34.7366; 34.7324;] CT = [28.7856; 28.4329; 22.8103; 10.2600; 6.8863; 4.4036;] p = [ 10; 50; 125; 250; 600; 1000;] N2_lowerlimit = 7.5e-8;

[SA_out, CT_out] = gsw_stabilise_SA_CT(SA,CT,p,N2_lowerlimit)

SA_out =

34.7118 34.8915 34.4909 31.5819 34.7366 34.7324

CT_out =

28.7856 28.4329 23.5097 7.7167 6.8863 4.4036

## EXAMPLE 3 (using Matlab Optimization Toolbox):

SA = [34.7118; 34.8915; 35.0256; 32.0472; 34.7366; 34.7324;] CT = [28.7856; 28.4329; 22.8103; 10.2600; 6.8863; 4.4036;] p = [ 10; 50; 125; 250; 600; 1000;] long = 180; lat = 10;

[SA_out, CT_out] = gsw_stabilise_SA_CT(SA,CT,p,long,lat)

SA_out =

34.7118 34.8915 34.9499 32.1229 34.7366 34.7324

CT_out =

28.7856 28.4329 22.9218 9.9176 6.8863 4.4036

## AUTHOR:

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

## VERSION NUMBER:

3.06.12 (15th June, 2020)

## REFERENCES:

Barker, P.M., and T.J. McDougall, 2017: Stabilizing hydrographic profiles with minimal change to the water masses.J. Atmosph. Ocean. Tech.,34, pp. 1935 - 1945. http://dx.doi.org/10.1175/JTECH-D-16-0111.1

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.

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 and P.M. Barker, 2015: Accurate polynomial expressions for the density and specific volume of seawater using the TEOS-10 standard.Ocean Modelling,90, pp. 29-43. http://dx.doi.org/10.1016/j.ocemod.2015.04.002

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