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

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 lat_lon_T.tab which contains latitude, longitude and surface temperature. We can use this file in the following.

Argo positions of measurements

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

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 -P -O >> out.ps

Show resulting postscript map

gv out.ps

Convert to png format for this Wiki page

convert -trim out.ps out.png

Common options:

-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.

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 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

LehreWiki: OpenSource2010/Lesson12 (last edited 2011-01-17 13:34:14 by anonymous)

-  ⇤ ← Revision 10 as of 2011-01-17 11:57:45 → 
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  Comment:
+   ← Revision 13 as of 2011-01-17 12:22:14 → ⇥
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-Deletions are marked like this.
+Additions are marked like this.
 Line 36:
+{{{
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...
}}}
-Line 41:
+Line 59:
-Nearest neighbor gridding with 5 degree grid cell size

{{{nearneighbor lat_lon_T.tab -Rd -I300m -S300m -N1 -Ggrid.nc}}}
+[[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
}}}
-Line 50:
+Line 69:
+Plot grid files in 2-D
-Line 51:
+Line 71:
-grdimage grid.nc -Rg -JG-45/0/4i -Cg.cpt -K  > out.ps
+grdimage grid.nc -Rd -JG-45/0/4i -Cg.cpt -K  > out.ps
-Line 54:
+Line 74:
+Plot continents on map
-Line 58:
+Line 79:
+Show resulting postscript map
-Line 62:
+Line 84:
+Convert to png format for this Wiki page
{{{
convert -trim out.ps out.png
}}}


Common options:
{{{
-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.
}}}
-Line 63:
+Line 100:
+=== 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 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