Ordinary global Spatio-Temporal Kriging

Function for ordinary global and local and trans Gaussian spatio-temporal kriging on point support

Usage

krigeST(formula, data, newdata, modelList, beta, y, ...,
        nmax = Inf, stAni = NULL,
        computeVar = FALSE,  fullCovariance = FALSE,
        bufferNmax=2, progress=TRUE)
krigeSTTg(formula, data, newdata, modelList, y, nmax=Inf, stAni=NULL,
                      bufferNmax=2, progress=TRUE, lambda = 0)

Arguments

formula: formula that defines the dependent variable as a linear model of independent variables; suppose the dependent variable has name z, for ordinary and simple kriging use the formula z~1; for simple kriging also define beta (see below); for universal kriging, suppose z is linearly dependent on x and y, use the formula z~x+y
data: ST object: should contain the dependent variable and independent variables.
newdata: ST object with prediction/simulation locations in space and time; should contain attribute columns with the independent variables (if present).
modelList: object of class StVariogramModel, created by vgmST - see below or the function vgmAreaST for area-to-point kriging. For the general kriging case: a list with named elements: space, time and/or joint depending on the spatio-temporal covariance family, and an entry stModel. Currently implemented families that may be used for stModel are separable, productSum, metric, sumMetric and simpleSumMetric. See the examples section in fit.StVariogram or variogramSurface for details on how to define spatio-temporal covariance models. krigeST will look for a "temporal unit" attribute in the provided modelList in order to adjust the temporal scales.
y: matrix; to krige multiple fields in a single step, pass data as columns of matrix y. This will ignore the value of the response in formula.
beta: The (known) mean for simple kriging.
nmax: The maximum number of neighbouring locations for a spatio-temporal local neighbourhood
stAni: a spatio-temporal anisotropy scaling assuming a metric spatio-temporal space. Used only for the selection of the closest neighbours. This scaling needs only to be provided in case the model does not have a stAni parameter, or if a different one should be used for the neighbourhood selection. Mind the correct spatial unit. Currently, no coordinate conversion is made for the neighbourhood selection (i.e. Lat and Lon require a spatio-temporal anisotropy scaling in degrees per second).
...: further arguments used for instance to pass the model into vgmAreaST for area-to-point kriging
computeVar: logical; if TRUE, prediction variances will be returned
fullCovariance: logical; if FALSE a vector with prediction variances will be returned, if TRUE the full covariance matrix of all predictions will be returned
bufferNmax: factor with which nmax is multiplied for an extended search radius (default=2). Set to 1 for no extension of the search radius.
progress: whether a progress bar shall be printed for local spatio-temporal kriging; default=TRUE
lambda: The value of lambda used in the box-cox transformation.

Details

Function krigeST is a R implementation of the kriging function from gstat using spatio-temporal covariance models following the implementation of krige0. Function krigeST offers some particular methods for ordinary spatio-temporal (ST) kriging. In particular, it does not support block kriging or kriging in a distance-based neighbourhood, and does not provide simulation.

If data is of class sftime, then newdata MUST be of class stars or sftime, i.e. mixing form old-style classes (package spacetime) and new-style classes (sf, stars, sftime) is not supported.

Value

An object of the same class as newdata (deriving from ST). Attributes columns contain prediction and prediction variance.

References

Benedikt Graeler, Edzer Pebesma, Gerard Heuvelink. Spatio-Temporal Geostatistics using gstat. The R Journal 8(1), 204–218. https://journal.r-project.org/archive/2016/RJ-2016-014/index.html

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

http://www.gstat.org/

Pebesma, E.J., 2004. Multivariable geostatistics in S: the gstat package. Computers and Geosciences, 30: 683-691.

Author

Edzer Pebesma, Benedikt Graeler

Examples

library(sp)
library(spacetime)
sumMetricVgm <- vgmST("sumMetric",
                      space = vgm( 4.4, "Lin", 196.6,  3),
                      time  = vgm( 2.2, "Lin",   1.1,  2),
                      joint = vgm(34.6, "Exp", 136.6, 12),
                      stAni = 51.7)

data(air)
suppressWarnings(proj4string(stations) <- CRS(proj4string(stations)))
rural = STFDF(stations, dates, data.frame(PM10 = as.vector(air)))

rr <- rural[,"2005-06-01/2005-06-03"]
rr <- as(rr,"STSDF")

x1 <- seq(from=6,to=15,by=1)
x2 <- seq(from=48,to=55,by=1)

DE_gridded <- SpatialPoints(cbind(rep(x1,length(x2)), rep(x2,each=length(x1))), 
                            proj4string=CRS(proj4string(rr@sp)))
gridded(DE_gridded) <- TRUE
DE_pred <- STF(sp=as(DE_gridded,"SpatialPoints"), time=rr@time)
DE_kriged <- krigeST(PM10~1, data=rr, newdata=DE_pred,
                     modelList=sumMetricVgm)
#> Warning: The spatio-temporal variogram model does not carry the strongly recommended attribute 'temporal unit'.
#>  The unit 'days' has been assumed. krigeST could not check whether the temporal distances between locations and in the variogram coincide.
gridded(DE_kriged@sp) <- TRUE
stplot(DE_kriged)