vgmST: Constructing a spatio-temporal variogram

In gstat: Spatial and Spatio-Temporal Geostatistical Modelling, Prediction and Simulation

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)

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)

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)

Value

Returns an S3 object of class StVariogramModel.

Author(s)

Benedikt Graeler

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)

gstat documentation built on Sept. 11, 2024, 7:46 p.m.