R: Kriging methods

Kriging {RandomFields}

R Documentation

Kriging methods

Description

The function allows for different methods of kriging.

Usage

Kriging(krige.method, x, y=NULL, z=NULL, T=NULL, grid,
        gridtriple=FALSE, model, param, given, data, trend=NULL, pch=".",
        return.variance=FALSE, allowdistanceZero = FALSE, cholesky=FALSE)

Arguments

`krige.method`	kriging method; currently only 'S' (simple kriging), 'O' (ordinary kriging), 'U' (universal kriging) and 'I' (intrinsic kriging) implemented.
`x`	(n x d) matrix or vector of `x` coordinates; coordinates of n points to be kriged
`y`	vector of `y` coordinates.
`z`	vector of `z` coordinates.
`T`	vector in grid triple form for the time coordinates.
`grid`	logical; determines whether the vectors `x`, `y`, and `z` should be interpreted as a grid definition, see Details.
`gridtriple`	logical. Only relevant if `grid=TRUE`. If `gridtriple=TRUE` then `x`, `y`, and `z` are of the form `c(start,end,step)`; if `gridtriple=FALSE` then `x`, `y`, and `z` must be vectors of ascending values.
`model`	string; covariance model, see `CovarianceFct`, or type `PrintModelList()` to get all options.
`param`	parameter vector: `param=c(mean, variance, nugget, scale,...)`; the parameters must be given in this order. Further parameters are to be added in case of a parametrised class of covariance functions, see CovarianceFct. The value of `mean` must be finite in the case of simple kriging, and is ignored otherwise.
`given`	matrix or vector of points where data are available.
`data`	the data values given at `given`; it might be a vector or a matrix. If a matrix is given multivariate data are assumed which are kriged separately.
`trend`	only used for universal and intrinsic kriging. In case of universal kriging `trend` is a non-negative integer (monomials up to order k as trend functions), a list of functions or a formula (the summands are the trend functions); you have the choice of using either x, y, z or X1, X2, X3,... as spatial variables; in case of intrinsic kriging trend should be a nonnegative integer which is the order of the underlying model.
`pch`	Kriging procedures are quite time consuming in general. The character `pch` is printed after roughly each 80th part of calculation.
`return.variance`	logical. If `FALSE` the kriged field is returned. If `TRUE` a list of two elements, `estim` and `var`, i.e. the kriged field and the kriging variances, is returned.
`allowdistanceZero`	if `TRUE` then identical locations are slightly scattered
`cholesky`	if `TRUE` cholesky decomposition is used instead of LU.

Details

grid=FALSE : the vectors x, y, and z are interpreted as vectors of coordinates
(grid=TRUE) && (gridtriple=FALSE) : the vectors x, y, and z are increasing sequences with identical lags for each sequence. A corresponding grid is created (as given by expand.grid).
(grid=TRUE) && (gridtriple=TRUE) : the vectors x, y, and z are triples of the form (start,end,step) defining a grid (as given by expand.grid(seq(x$start,x$end,x$step), seq(y$start,y$end,y$step), seq(z$start,z$end,z$step)))

Value

If variance.return=FALSE Kriging returns a vector or matrix of kriged values corresponding to the specification of x, y, z, and grid, and data.

data: a vector or matrix with one column
* grid=FALSE. A vector of simulated values is returned (independent of the dimension of the random field)
* grid=TRUE. An array of the dimension of the random field is returned (according to the specification of x, y, and z).

data: a matrix with at least two columns
* grid=FALSE. A matrix with the ncol(data) columns is returned.
* grid=TRUE. An array of dimension d+1, where d is the dimension of the random field, is returned (according to the specification of x, y, and z). The last dimension contains the realisations.

If variance.return=TRUE a list of two elements, estim and var, i.e. the kriged field and the kriging variances, is returned. The format of estim is the same as described above. The format of var is accordingly.

Author(s)

Martin Schlather, martin.schlather@math.uni-goettingen.de http://www.stochastik.math.uni-goettingen.de/~schlather

References

Chiles, J.-P. and Delfiner, P. (1999) Geostatistics. Modeling Spatial Uncertainty. New York: Wiley.

Cressie, N.A.C. (1993) Statistics for Spatial Data. New York: Wiley.

Goovaerts, P. (1997) Geostatistics for Natural Resources Evaluation. New York: Oxford University Press.

Wackernagel, H. (1998) Multivariate Geostatistics. Berlin: Springer, 2nd edition.

Examples

###Example 1: Ordinary Kriging
## creating random variables first
## here, a grid is chosen, but does not matter
step <- 0.25 
x <-  seq(0,7,step)
param <- c(0,1,0,1)
model <- "exponential"
RFparameters(PracticalRange=FALSE)
p <- 1:7
points <- as.matrix(expand.grid(p,p))
data <- GaussRF(points, grid=FALSE, model=model, param=param)

## visualise generated spatial data
zlim <- c(-2.6,2.6)
colour <- rainbow(100)
image(p, p, xlim=range(x), ylim=range(x),
      matrix(data,ncol=length(p)),
      col=colour,zlim=zlim)

## now: kriging
krige.method <- "O" ## ordinary kriging
z <-  Kriging(krige.method=krige.method,
              x=x, y=x, grid=TRUE,
              model=model, param=param,
              given=points, data=data)
image(x,x,z,col=colour,zlim=zlim)

[Package RandomFields version 2.0.54 Index]