R: Constructing a spatio-temporal variogram

vgmST {gstat} | R Documentation

## 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)

[Package gstat version 2.0-3 Index]