# 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 the Optimization toolbox or Tomlab CPLEX. 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 Tomlab or the Optimization toolbox is available to the user, if both are available it will use Tomlab.

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 ]

## EXAMPLE 1:

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:

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 34.6116 31.4612 34.7366 34.7324

CT_out =

28.7856 28.4329 24.7758 7.9461 6.8863 4.4036

## EXAMPLE 3:

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 34.9670 32.1058 34.7366 34.7324

CT_out =

28.7856 28.4329 23.0755 9.9176 6.8863 4.4036

## AUTHOR:

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

## VERSION NUMBER:

3.05.5 (16th June, 2016)

## REFERENCES:

Barker, P.M., and T.J. McDougall, 2016: Stabilisation of hydrographic profiles.J. Atmosph. Ocean. Tech., submitted.

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