Kriging {RandomFields} | R Documentation |
The function allows for different methods of kriging.
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)
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 |
y |
vector of |
z |
vector of |
T |
vector in grid triple form for the time coordinates. |
grid |
logical; determines whether the vectors |
gridtriple |
logical. Only relevant if |
model |
string; covariance model, see |
param |
parameter vector:
|
given |
matrix or vector of points where data are available. |
data |
the data values given at |
trend |
only used for universal and intrinsic kriging. In case of
universal kriging |
pch |
Kriging procedures are quite time consuming in general.
The character |
return.variance |
logical. If |
allowdistanceZero |
if |
cholesky |
if |
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))
)
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.
Martin Schlather, martin.schlather@math.uni-goettingen.de http://www.stochastik.math.uni-goettingen.de/~schlather
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.
CondSimu
,
Covariance
,
CovarianceFct
,
EmpiricalVariogram
,
RandomFields
,
###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)