R: Turning Bands Method

RMtbm {RandomFields} | R Documentation

## Turning Bands Method

### Description

`RMtbm` is a univariate stationary isotropic covariance model in dimension `reduceddim` which depends on a univariate stationary isotropic covariance phi in a bigger dimension `fulldim`. For formulas for the covariance function see details.

### Usage

    RMtbm(phi, fulldim, reduceddim, layers, var, scale, Aniso, proj)

### Arguments

`phi, fulldim, reduceddim, layers` | see `RPtbm`.
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

The turning bands method stems from the 1:1 correspondence between the isotropic covariance functions of different dimensions. See Gneiting (1999) and Strokorb and Schlather (2014).

The standard case `reduceddim=1` and `fulldim=3`. If only one of the arguments are given, then the difference of the two arguments equals 2.

For `d == n + 2`, where `n=reduceddim` and `d==fulldim` the original dimension, we have

C(r) = phi(r) + r phi'(r) / n

which, for `n=1` reduced to the standard TBM operator

C(r) = d/dr [ r phi(r) ]

For `d == 2 && n == 1` we have

C(r) = d/dr int_0^r [ r phi(r) ] / [ sqrt{r^2 - u^2} ] d u

‘Turning layers’ is a generalization of the turning bands method, see Schlather (2011).

### Value

`RMtbm` returns an object of class `RMmodel`

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### References

Turning bands

- Gneiting, T. (1999) On the derivatives of radial positive definite function. J. Math. Anal. Appl, 236, 86-99

- Matheron, G. (1973). The intrinsic random functions and their applications. Adv . Appl. Probab., 5, 439-468.

- Strokorb, K., Ballani, F., and Schlather, M. (2014) Tail correlation functions of max-stable processes: Construction principles, recovery and diversity of some mixing max-stable processes with identical TCF. Extremes, Submitted.

Turning layers

- Schlather, M. (2011) Construction of covariance functions and unconditional simulation of random fields. In Porcu, E., Montero, J.M. and Schlather, M., Space-Time Processes and Challenges Related to Environmental Problems. New York: Springer.

### See Also

`RPtbm`, `RFsimulate`.

### Examples

    RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
    ##                   RFoptions(seed=NA) to make them all random again

    x <- seq(0, 10, 0.02)
    model <- RMspheric()
    plot(model, model.on.the.line=RMtbm(RMspheric()), xlim=c(-1.5, 1.5))

    z <- RFsimulate(RPtbm(model), x, x)
    plot(z)

[Package RandomFields version 3.1.50 Index]