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