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

## Description

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

## Usage

 ```1 2 3 4 5 6``` ```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.

## 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

Spatio-Temporal Geostatistics using gstat. Benedikt Graeler, Edzer Pebesma, Gerard Heuvelink. The R Journal, accepted.

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

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

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```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) ```

### Example output ```[Using the following time unit: days]
[Using the following time unit: days]
[Using the following time unit: days]
Warning message:
In krigeST(PM10 ~ 1, data = rr, newdata = DE_pred, modelList = sumMetricVgm) :
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.
```

gstat documentation built on March 19, 2021, 9:06 a.m.