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= 2-dimensional interpolation and gridding =

2-dimensional interpolation and gridding is a common problem for the representation of measurements on a map. Usually measurements are taken at irregular sample points and not in a regular grid. There are various approaches for the problem and the best solution depends on the data.

In the following we will look at oceanographic parameters that have been measured with the Argo system.

= Example data from Argo system =

[[http://en.wikipedia.org/wiki/Argo_%28oceanography%29|Argo observation system]]

Data are provided at, i.e. ftp://ftp.ifremer.fr//ifremer/argo/

First we have to download the data. Here is a [[/download script]] that can be used to retrieve one month of Argo data.

We extract only the surface temperature to reduce the large amount of data. This [[/extract script]] generates an overview of the data and writes the surface temperature in a file [[attachment:lat_lon_T.tab]]  which contains latitude, longitude and surface temperature.  We can use this file in the following.


{{attachment:argo_position.png}}

Argo positions of measurements

{{attachment:Argo_plot.png}}

Measured temperature profiles (unfiltered data).

= Tools for 2-dimensional interpolation and gridding =

== Python ==

{{{
Help on function griddata in module matplotlib.mlab:

griddata(x, y, z, xi, yi)
    ``zi = griddata(x,y,z,xi,yi)`` fits a surface of the form *z* =
    *f*(*x*, *y*) to the data in the (usually) nonuniformly spaced
    vectors (*x*, *y*, *z*).  :func:`griddata` interpolates this
    surface at the points specified by (*xi*, *yi*) to produce
    *zi*. *xi* and *yi* must describe a regular grid, can be either 1D
    or 2D, but must be monotonically increasing.

    A masked array is returned if any grid points are outside convex
    hull defined by input data (no extrapolation is done).

    Uses natural neighbor interpolation based on Delaunay
    triangulation...
}}}

== GMT ==

[[http://gmt.soest.hawaii.edu/|GMT]]


[[http://gmt.soest.hawaii.edu/gmt/doc/gmt/html/GMT_Tutorial/node44.html|Nearest neighbor gridding]] with 5 degree grid cell size
{{{
nearneighbor lat_lon_T.tab -Rd -I300m -S300m -N1 -Ggrid.nc
}}}

Generate color table:
{{{
makecpt -Crainbow -T-2/30/1 > g.cpt
}}}

Plot grid files in 2-D
{{{
grdimage grid.nc -Rd -JG-45/0/4i -Cg.cpt -K  > out.ps
}}}

Plot continents on map
{{{
pscoast -Rd -JG-45/0/4i -B15g15 -Dc  -Gblack -O >> out.ps
}}}

Common options:
{{{
-G name of output grid.
-R specifies the min/max coordinates of data region in user units.
-J Selects map projection.
-K Means allow for more plot code to be appended later.
-O means Overlay plot mode.
}}}


Show resulting postscript map
{{{
gv out.ps
}}}

Convert to png format for this Wiki page
{{{
convert -trim out.ps out.png
}}}

Convert postscript to pdf format (you can zoom in the map with acroread)
{{{
ps2pdf out.ps
acroread out.pdf
}}}




{{attachment:out.png}}

=== Exercises ===

Read the GMT manual:
 * Find out the meaning of the options I, S, N of the nearest neighbor gridding
 * What does -Rd mean? 
 * What does -Dc mean?
 * What projection was chosen? 

Produce new plots:
 * Select a sub region of the data, i.e. only the North Atlantic.
 * Select a different projection
 * Plot the data with this projection

Use new interpolation parameters:
 * Modify grid cell size (increment) to obtain a finer grid
 * Modify search radius

Interaction with Python:
 * Read the GMT-netcdf file into Python with {{{scipy.io.netcdf_file}}}, (variable z)
 * Write a Python  script that does the interpolation with GMT by using {{{os.system()}}}


Use different interpolation technique:
 * {{{surface}}}, adjustable tension continuous curvature surface gridding algorithm