# gsw_tracer_CT_interp

tracer and CT interpolation to p_i on a cast

## Contents

## USAGE:

[tracer_i, CT_i] = gsw_tracer_CT_interp(tracer,CT,p,p_i,factor)

## DESCRIPTION:

This function interpolates vertical casts of values of a tracer and Conservative Temperature to the arbitrary pressures p_i. The interpolation method is designed to respect the shape of the tracer-CT diagram. That is, the interpolated tracer_i and CT_i values look realistic when plotted on the tracer-CT diagram. The interpolation method uses sixteen PCHIPs (Piecewise Cubic Hermite Interpolating Polynomials), one for each of sixteen different linear combinations of the tracer 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 is the MRST-PCHIP method described in Barker and McDougall (2020), with the tracer data being used in place of Absoluate Salinity data.

This function requires scaling the tracer and temperature data so that the tracer-CT diagram reflects the relative variation of the tracer and temperature in the world ocean. Specifically, "factor" should be chosen to be the ratio of the global range of CT to that of the tracer variable in the world ocean. A list of suitable values of "factor" for various tracers is given here.

TRACER UNITS FACTOR Absolute Salinity g/kg 9 dissolved oxygen ? ? AOU ? ? silicic acid ? ? nitrate ? ? phosphate ? ? carbon 14 ? ? tritium ? ? eastward velocity m/s 100 westward velocity m/s 100

If an input value of "factor" is not given in the function call, it is set equal to 9.

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:

tracer = tracer [ ? ] 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 [ dbar ] tracer_i and CT_i are required

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

## OUTPUT:

tracer_i = interpolated tracer values at pressures p_i [ ? ] CT_i = interpolated CT values at pressures p_i [ deg C ]

## EXAMPLE:

tracer = [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;] factor = 9;

[tracer_i, CT_i] = gsw_tracer_CT_interp(tracer,CT,p,p_i,factor)

tracer_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