gstat (version 2.1-1)

vgmST: Constructing a spatio-temporal variogram

Description

Constructs a spatio-temporal variogram of a given type checking for a minimal set of parameters.

Usage

vgmST(stModel, ..., space, time, joint, sill, k, nugget, stAni, temporalUnit)

Value

Returns an S3 object of class StVariogramModel.

Arguments

stModel

A string identifying the spatio-temporal variogram model (see details below). Only the string before an optional "_" is used to identify the model. This mechanism can be used to identify different fits of the same model (separable_A and separable_B will be interpreted as separable models, but carry different names).

...

unused, but ensure an exact match of the following parameters.

space

A spatial variogram.

time

A temporal variogram.

joint

A joint spatio-temporal variogram.

sill

A joint spatio-temporal sill.

k

The weighting of the product in the product-sum model.

nugget

A joint spatio-temporal nugget.

stAni

A spatio-temporal anisotropy; the number of space units equivalent to one time unit.

temporalUnit

length one character vector, indicating the temporal unit (like secs)

Author

Benedikt Graeler

Details

The different implemented spatio-temporal variogram models have the following required parameters (see as well the example section)

separable:

A variogram for space and time each and a joint spatio-temporal sill (variograms may have a separate nugget effect, but their joint sill will be 1) generating the call

vgmST("separable", space, time, sill)

productSum:

A variogram for space and time each, and the weighting of product k generating the call

vgmST("productSum", space, time, k)

sumMetric:

A variogram (potentially including a nugget effect) for space, time and joint each and a spatio-temporal anisotropy ratio stAni generating the call

vgmST("sumMetric", space, time, joint, stAni)

simpleSumMetric:

A variogram (without nugget effect) for space, time and joint each, a joint spatio-temporal nugget effect and a spatio-temporal anisotropy ratio stAni generating the call

vgmST("simpleSumMetric", space, time, joint, nugget, stAni)

metric:

A spatio-temporal joint variogram (potentially including a nugget effect) and stAni generating the call

vgmST("metric", joint, stAni)

See Also

fit.StVariogram for fitting, variogramSurface to plot the variogram and extractParNames to better understand the parameter structure of spatio-temporal variogram models.

Examples

# separable model: spatial and temporal sill will be ignored
# and kept constant at 1-nugget respectively. A joint sill is used.
separableModel <- vgmST("separable", 
                        space=vgm(0.9,"Exp", 147, 0.1),
                        time =vgm(0.9,"Exp", 3.5, 0.1),
                        sill=40)

# product sum model: spatial and temporal nugget will be ignored and kept
# constant at 0. Only a joint nugget is used.
prodSumModel <- vgmST("productSum",
                      space=vgm(39, "Sph", 343, 0),
                      time= vgm(36, "Exp",   3, 0), 
                      k=15)

# sum metric model: spatial, temporal and joint nugget will be estimated
sumMetricModel <- vgmST("sumMetric",
                        space=vgm( 6.9, "Lin", 200, 3.0),
                        time =vgm(10.3, "Lin",  15, 3.6),
                        joint=vgm(37.2, "Exp",  84,11.7),
                        stAni=77.7)
                       
# simplified sumMetric model, only a overall nugget is fitted. The spatial, 
# temporal and jont nuggets are set to 0.
simpleSumMetricModel <- vgmST("simpleSumMetric",
                              space=vgm(20,"Lin", 150, 0),
                              time =vgm(20,"Lin", 10,  0),
                              joint=vgm(20,"Exp", 150, 0),
                              nugget=1, stAni=15)

# metric model
metricModel <- vgmST("metric",
                     joint=vgm(60, "Exp", 150, 10),
                     stAni=60)