# krigeST: Ordinary global Spatio-Temporal Kriging In gstat: Spatial and Spatio-Temporal Geostatistical Modelling, Prediction and Simulation

 krigeST R Documentation

## Ordinary global Spatio-Temporal Kriging

### Description

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.

### Author(s)

Edzer Pebesma, Benedikt Graeler

### 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.

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

`krige0`, `gstat`, `predict`, `krigeTg`

### 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)
gridded(DE_kriged@sp) <- TRUE
stplot(DE_kriged)
``````

gstat documentation built on April 6, 2023, 5:21 p.m.