# gsw_SA_CT_interp

SA and CT interpolation to p_i on a cast

## Contents

## USAGE:

[SA_i, CT_i] = gsw_SA_CT_interp(SA,CT,p,p_i)

## DESCRIPTION:

This function interpolates vertical casts of values of Absolute Salinity and Conservative Temperature to the arbitrary pressures p_i. The interpolation method is designed to respect the shape of the SA-CT diagram. That is, the interpolated SA_i and CT_i values look realistic when plotted on the SA-CT diagram. The interpolation method uses sixteen PCHIPs (Piecewise Cubic Hermite Interpolating Polynomials), one for each of sixteen different linear combinations of the SA and CT input data. Each of these sixteen PCHIPs use the "bottle number" as the independent variable. A final seventeenth PCHIP is used to relate the interpolated data back to pressure space (rather than "botttle number" space). The interpolation method is described as method MRST-PCHIP in Barker and McDougall (2020).

This function requires scaling the temperature and salinity data so that the SA-CT diagram reflects the relative variation of temperature and salinity in the world ocean. A suitable value of the this scaling parameter, factor, was found to be 9. This scaling factor was chosen to reflect the ratio of the global ranges of temperature and salinity in the world ocean. The interpolation technique performs well when this scaling factor is between 3 to 25 with only small changes in the resulting interpolated data, so the method is not particularly sensitive to the value of "factor".

Any interpolated bottles that have pressures shallower than the shallowest observed bottle are set equal to the shallowest observed bottle.

Note that this interpolation scheme requires at least four observed bottles on the cast.

## INPUT:

SA = Absolute Salinity [ g/kg ] CT = Conservative Temperature [ deg C ] p = sea pressure [ dbar ] ( i.e. absolute pressure - 10.1325 dbar ) p_i = specific query points at which the interpolated SA_i and CT_i are required [ dbar ]

SA & CT need to have the same dimensions. p may have dimensions Mx1 or 1xN or MxN, where SA & CT are MxN. p_i needs to be either a vector or a matrix and have dimensions M_ix1 or M_ixN.

## OUTPUT:

SA_i = interpolated SA values at pressures p_i [ g/kg ] CT_i = interpolated CT values at pressures p_i [ deg C ]

## EXAMPLE:

SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;] CT = [28.7856; 28.4329; 22.8103; 10.2600; 6.8863; 4.4036;] p = [ 10; 50; 125; 250; 600; 1000;] p_i = [ 10; 50; 200; 500; 750; 1000;]

[SA_i, CT_i] = gsw_SA_CT_interp(SA,CT,p,p_i)

SA_i =

34.7118 34.8915 34.9151 34.7520 34.7253 34.7324

CT_i =

28.7856 28.4329 13.4287 7.5381 5.8243 4.4036

## AUTHOR:

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

## VERSION NUMBER:

3.06.12 (25th June, 2020)

## REFERENCES:

Barker, P.M., and T.J. McDougall, 2020: Two interpolation methods using multiply-rotated piecewise cubic hermite interpolating polynomials. J. Atmosph. Ocean. Tech., 37, pp. 605-619. doi: 10.1175/JTECH-D-19-0211.1.

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