Kriging standard errors as function of grid spacing and block size

Calculate, for a given variogram model, ordinary block kriging standard errors as a function of sampling spaces and block sizes

Usage

ossfim(spacings = 1:5, block.sizes = 1:5, model, nmax = 25, debug = 0)

Arguments

spacings: range of grid (data) spacings to be used
block.sizes: range of block sizes to be used
model: variogram model, output of vgm
nmax: set the kriging neighbourhood size
debug: debug level; set to 32 to see a lot of output

Value

data frame with columns spacing (the grid spacing), block.size (the block size), and kriging.se (block kriging standard error)

References

Burrough, P.A., R.A. McDonnell (1999) Principles of Geographical Information Systems. Oxford University Press (e.g., figure 10.11 on page 261)

Burgess, T.M., R. Webster, A.B. McBratney (1981) Optimal interpolation and isarithmic mapping of soil properties. IV Sampling strategy. The journal of soil science 32(4), 643-660.

McBratney, A.B., R. Webster (1981) The design of optimal sampling schemes for local estimation and mapping of regionalized variables: 2 program and examples. Computers and Geosciences 7: 335-365.

Author

Edzer Pebesma

Note

The idea is old, simple, but still of value. If you want to map a variable with a given accuracy, you will have to sample it. Suppose the variogram of the variable is known. Given a regular sampling scheme, the kriging standard error decreases when either (i) the data spacing is smaller, or (ii) predictions are made for larger blocks. This function helps quantifying this relationship. Ossfim probably refers to “optimal sampling scheme for isarithmic mapping”.

Examples

if (FALSE) { # \dontrun{
x <- ossfim(1:15,1:15, model = vgm(1,"Exp",15))
library(lattice)
levelplot(kriging.se~spacing+block.size, x, 
  main = "Ossfim results, variogram 1 Exp(15)")
} # }
# if you wonder about the decrease in the upper left corner of the graph,
# try the above with nmax set to 100, or perhaps 200.