## DESCRIPTION

v.krige allows performing Kriging operations in GRASS GIS 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 See Isaaks and Srivastava's book, exhaustive and clear even if a bit outdated.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, gstat, rgrass7 and rgeos.
  automap is optional (provides automatic variogram fit).

Install the packages via R command line (or your preferred GUI):

      install.packages("rgeos", dep=T)
      install.packages("gstat", dep=T)
      install.packages("rgrass7", dep=T)
      install.packages("automap", dep=T)

#### 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 functions listed above (as root or as user), either the 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-rgrass7

#### Notes for Windows

Compile GRASS GIS 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 although high number of input data points and/or high region resolution contribute to a better output, both will also slow down the kriging calculation.

## 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.

    # reduce resolution for this example
    g.region raster=elevation -p res=100
    v.random output=rand2k_elev npoints=2000
    v.db.addtable map=rand2k_elev columns="elevation double precision"
    v.what.rast map=rand2k_elev raster=elevation 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 input=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 map=rand2k_elev_filt type=point column=elevation

Part 3: reconstruct DEM through kriging. The simplest way to run v.krige from CLI is using automatic variogram fit (note: requires R's automap package). Output map name is optional, the modules creates it automatically appending "_kriging" to 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 a 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).

    # automatic variogram fit
    v.krige input=rand2k_elev_filt column=elevation \
            output=rand2k_elev_kriging output_var=rand2k_elev_kriging_var

    # define variogram model, create variance map as well
    v.krige input=rand2k_elev_filt column=elevation \
            output=rand2k_elev_filt_kriging output_var=rand2k_elev_filt_kriging_var \
            model=Mat sill=2500 nugget=0 range=1000

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 map=elevation
    r.univar map=rand2k_elev_kriging
    r.univar map=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 in a future v.krige release.

## SEE ALSO

R package gstat, maintained by Edzer J. Pebesma and others
R package rgrass7, maintained by Roger Bivand
The Short Introduction to Geostatistical and Spatial Data Analysis with GRASS GIS and R statistical data language at the GRASS Wiki (includes installation tips). It contains a subsection about rgrass7.
v.krige's wiki page

## REFERENCES

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

## AUTHOR

Anne Ghisla, Google Summer of Code 2009

Last changed: $Date: 2015-10-01 12:26:43 +0200 (Thu, 01 Oct 2015) $