# gsw_t_interp

interpolation of in-situ temperature to p_i on a cast

## Contents

## USAGE:

t_i = gsw_t_interp(t,p,p_i)

## DESCRIPTION:

This function interpolates vertical casts of values of in-situ temperature to the arbitrary pressures p_i.

The interpolation method uses sixteen PCHIPs (Piecewise Cubic Hermite Interpolating Polynomials), one for each of sixteen different linear combinations of the tracer data and a scaled version of the independent variable. Each of these sixteen PCHIPs use a scaled version of 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 the MR-PCHIP method in Barker and McDougall (2020).

The scaling factor that we use for the independent variable is 0.33 times the maximum magnitude (over all data pairs) of the slope on the [CT - bottle_number] diagram. With the oceanographic data that we have tested we have found that using multiplying factors between 0.1 and 1 (instead of 0.33) also gave good interpolants, so the method is not sensitive to this choice of "scale_factor".

The code uses Conservative Temperature (of TEOS-10) as the temperature variable in the interpolation procedure. The output of the code is converted back to in-situ temperature. The conversions between in-situ and Conservative Temperatures are done using the constant value of Absolute Salinity equal to the Standard Ocean Reference Salinity (35.16504 g/kg) which is found by calling gsw_SSO. We have found that the use of this salinity rather than the estimate salinity from MRST-PCHIP method in Barker and McDougall (2020) results in an temperature error less than 1 mK.

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:

t = in-situ temperature (ITS-90) [ 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 ]

p may have dimensions Mx1 or 1xN or MxN, where t is MxN. p_i needs to be either a vector or a matrix and have dimensions M_ix1 or M_ixN.

## OUTPUT:

t_i = interpolated in-situ temperature values at [ deg C ] pressures p_i

## EXAMPLE:

t = [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;]

t_i = gsw_t_interp(t,p,p_i)

t_i =

28.7856 28.4329 13.4427 7.5396 5.8155 4.4036

## AUTHOR:

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

## VERSION NUMBER:

3.06.12 (15th July, 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