gstat (version 0.9-11)

predict.gstat: Multivariable Geostatistical Prediction and Simulation

Description

The function provides the following prediction methods: simple, ordinary, and universal kriging, simple, ordinary, and universal cokriging, point- or block-kriging, and conditional simulation equivalents for each of the kriging methods.

Usage

predict.gstat(object, newdata, block = numeric(0), nsim = 0, 
	indicators = FALSE, BLUE = FALSE, debug.level = 1, mask, 
	na.action = na.pass, ...)

Arguments

object

object of class gstat, see gstat and krige

newdata

data frame with prediction/simulation locations; should contain columns with the independent variables (if present) and the coordinates with names as defined in locations

block

block size; a vector with 1, 2 or 3 values containing the size of a rectangular in x-, y- and z-dimension respectively (0 if not set), or a data frame with 1, 2 or 3 columns, containing the points that discretize the block in the x-, y- and z-dimens

nsim

integer; if set to a non-zero value, conditional simulation is used instead of kriging interpolation. For this, sequential Gaussian or indicator simulation is used (depending on the value of indicators), following a single random path

indicators

logical; only relevant if nsim is non-zero; if TRUE, use indicator simulation, else use Gaussian simulation

BLUE

logical; if TRUE return the BLUE trend estimates only, if FALSE return the BLUP predictions (kriging)

debug.level

integer; set gstat internal debug level

mask

not supported anymore -- use na.action; logical or numerical vector; pattern with valid values in newdata (marked as TRUE, non-zero, or non-NA); if mask is specified, the returned data frame will have the same number and order of rows in newdata, and ma

na.action

function determining what should be done with missing values in 'newdata'. The default is to predict 'NA'. Missing values in coordinates and predictors are both dealt with.

...

ignored (but necessary for the S3 generic/method consistency)

Value

• a data frame containing the coordinates of newdata, and columns of prediction and prediction variance (in case of kriging) or the columns of the conditional Gaussian or indicator simulations

Details

When a non-stationary (i.e., non-constant) mean is used, both for simulation and prediction purposes the variogram model defined should be that of the residual process, and not that of the raw observations.

The algorithm used by gstat for simulation random fields is the sequential simulation algorithm. This algorithm scales well to large or very large fields (e.g., more than $10^6$ nodes). Its power lies in using only data and simulated values in a local neighbourhood to approximate the conditional distribution at that location, see nmax in krige and gstat. The larger nmax, the better the approximation, the smaller nmax, the faster the simulation process. For selecting the nearest nmax data or previously simulated points, gstat uses a bucket PR quadtree neighbourhood search algorithm; see the reference below.

For sequential Gaussian or indicator simulations, a random path through the simulation locations is taken, which is usually done for sequential simulations. The reason for this is that the local approximation of the conditional distribution, using only the nmax neareast observed (or simulated) values may cause spurious correlations when a regular path would be followed. Following a single path through the locations, gstat reuses the expensive results (neighbourhood selection and solution to the kriging equations) for each of the subsequent simulations when multiple realisations are requested. You may expect a considerable speed gain in simulating 1000 fields in a single call to predict.gstat, compared to 1000 calls, each for simulating a single field.

The random number generator used for generating simulations is the native random number generator of the environment (R, S); fixing randomness by setting seeds with set.seed() therefore works.

When mean coefficient are not supplied, they are generated as well from their conditional distribution (MVN, BLUE estimate and covariance); for a reference to the algorithm used see Abrahamsen and Benth, Math. Geol. 33(6), page 742 and leave out all constraints.

Memory requirements for sequential simulation: let n be the product of the number of variables, the number of simulation locations, and the number of simulations required in a single call. the gstat C function gstat_predict requires a table of size n * 12 bytes to pass the simulations back to R, before it can free n * 4 bytes. Hopefully, R does not have to duplicate the remaining n * 8 bytes when the coordinates are added as columns, and when the resulting matrix is coerced to a data.frame.

References

N.A.C. Cressie, 1993, Statistics for Spatial Data, Wiley.

http://www.gstat.org/

For bucket PR quadtrees, excellent demos are found at http://www.cs.umd.edu/~brabec/quadtree/index.html

See Also

gstat, krige

Examples

# generate 5 conditional simulations
data(meuse)
data(meuse.grid)
v <- variogram(log(zinc)~1,~x+y, meuse)
m <- fit.variogram(v, vgm(1, "Sph", 300, 1))
plot(v, model = m)
set.seed(131)
sim <- krige(formula = log(zinc)~1, locations = ~x+y, model = m, data 
	= meuse, newdata = meuse.grid, nmax = 15, beta = 5.9, nsim = 5)
# show all 5 simulation, using map.to.lev to rearrange sim:
levelplot(z~x+y|name, map.to.lev(sim, z=c(3:7)), aspect = mapasp(sim))

# calculate generalised least squares residuals w.r.t. constant trend:
g <- gstat(id = "log.zinc", formula = log(zinc)~1, locations = ~x+y, 
     model = m, data = meuse)
blue0 <- predict(g, newdata = meuse, BLUE = TRUE)
blue0$blue.res <- log(meuse$zinc) - blue0$log.zinc.pred
bubble(blue0, zcol = "blue.res", main = "GLS residuals w.r.t. constant")

# calculate generalised least squares residuals w.r.t. linear trend:
m <- fit.variogram(variogram(log(zinc)~sqrt(dist.m),~x+y, meuse), 
	vgm(1, "Sph", 300, 1))
g <- gstat(id = "log.zinc", formula = log(zinc)~sqrt(dist.m), 
	locations = ~x+y, model = m, data = meuse)
blue1 <- predict(g, newdata = meuse, BLUE = TRUE)
blue1$blue.res <- log(meuse$zinc) - blue1$log.zinc.pred
bubble(blue1, zcol = "blue.res", 
	main = "GLS residuals w.r.t. linear trend")

# unconditional simulation on a 100 x 100 grid
xy <- expand.grid(1:100, 1:100)
names(xy) <- c("x","y")
g.dummy <- gstat(formula = z~1, locations = ~x+y, dummy = TRUE, beta = 0,
	model = vgm(1,"Exp",15), nmax = 20)
yy <- predict(g.dummy, newdata = xy, nsim = 4)
# show one realisation:
levelplot(sim1~x+y, yy, aspect = mapasp(yy))
# show all four:
levelplot(z~x+y|name, map.to.lev(yy, z=c(3:6)), aspect = mapasp(yy))