DESCRIPTION

v.krige allows to perform kriging operations in GRASS environment, using R software functions in background.

NOTES

v.krige is just a front-end to R. The options and parameters are the same offered by packages automap and gstat.

Kriging, like other interpolation methods, is fully dependent on input data features. Exploratory analysis of data is encouraged to find out outliers, trends, anisotropies, uneven distributions and consequently choose the kriging algorithm that will give the most acceptable result. Good knowledge of the dataset is more valuable than hundreds of parameters or powerful hardware. See Isaaks and Srivastava's book, exhaustive and clear even if a bit outdated.

Dependencies

R software >= 2.x
rpy2: Python binding to R. Note! rpy version 1 is not supported.
R packages automap and gstat.: automap is optional (provides automatic variogram fit).

Notes for Debian GNU/Linux

Install the dependiencies. Attention! python-rpy IS NOT SUITABLE.:

  aptitude install R python-rpy2

To install R packages, use either R's function (as root):

  install.packages("gstat", dep=T)
  install.packages("spgrass6", dep=T)

either the brand new Debian packages [5], add to repositories' list for 32bit or 64bit (pick up the suitable line):

  deb http://debian.cran.r-project.org/cran2deb/debian-i386 testing/
  deb http://debian.cran.r-project.org/cran2deb/debian-amd64 testing/

and get the packages via aptitude:

  aptitude install r-cran-gstat r-cran-spgrass6

Notes for Windows

Compile GRASS following this guide. You could also use Linux in a virtual machine. Or install Linux in a separate partition of the HD. This is not as painful as it appears, there are lots of guides over the Internet to help you.

Computation time issues

Please note that kriging calculation is slown down both by high number of input data points and/or high region resolution, even if they both contribute to a better output.

EXAMPLES

Kriging example based on elevation map (Spearfish data set).

Part 1: random sampling of 2000 vector points from known elevation map. Each point will receive the elevation value from the elevation raster, as if it came from a point survey.

 g.region rast=elevation.10m -p
 v.random output=rand2k_elev n=2000
 v.db.addtable map=rand2k_elev column="elevation double precision"
 v.what.rast vect=rand2k_elev rast=elevation.10m column=elevation

Part 2: remove points lacking elevation attributes. Points sampled at the border of the elevation map didn't receive any value. v.krige has no preferred action to cope with no data values, so the user must check for them and decide what to do (remove points, fill with the value of the nearest point, fill with the global/local mean...). In the following line of code, points with no data are removed from the map.

 v.extract rand2k_elev output=rand2k_elev_filt where="elevation not NULL"

Check the result of previous line ("number of NULL attributes" must be 0):

 v.univar rand2k_elev_filt type=point column=elevation

Part 3: reconstruct DEM through kriging. Using automatic variogram fit is the simplest way to run v.krige from CLI (note: requires R's automap package). Output map name is optional, the modules creates it automatically appending "_kriging" the the input map name and also checks for overwrite. If output_var is specified, the variance map is also created. Automatic variogram fit is provided by R package automap, the variogram models tested by the fitting functions are: exponential, spherical, Gaussian, Matern, M.Stein's parametrisation. A wider range of models is available from gstat package and can be tested on the GUI via the variogram plotting. If model is specified in the CLI, also sill, nugget and range values are to be provided, otherwise an error is raised (see second example of v.krige command).

 v.krige input=rand2k_elev_filt column=elevation output=rand2k_elev_kriging \
         output_var=rand2k_elev_kriging_var
 v.krige input=rand2k_elev_filt column=elevation output=rand2k_elev_kriging \
         output_var=rand2k_elev_kriging_var model=Lin sill=2500 nugget=0 range=1000 \
         --overwrite

Or run wxGUI, to interactively fit the variogram and explore options:

  v.krige

Calculate prediction error:

 r.mapcalc "rand2k_elev_kriging_pe = sqrt(rand2k_elev_kriging_var)"
 r.univar elevation.10m
 r.univar rand2k_elev_kriging
 r.univar rand2k_elev_kriging_pe

The results show high errors, as the kriging techniques (ordinary and block kriging) are unable to handle a dataset with a trend, like the one used in this example: elevation is higher in the southwest corner and lower on northeast corner. Universal kriging can give far better results in these cases as it can handle the trend. It is available in R package gstat and will be part of a future v.krige release.

REFERENCES

Isaaks and Srivastava, 1989: "An Introduction to Applied Geostatistics" (ISBN 0-19-505013-4)

AUTHOR

Anne Ghisla, Google Summer of Code 2009

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