# RMvector: Vector Covariance Model In RandomFields: Simulation and Analysis of Random Fields

## Description

`RMvector` is a multivariate covariance model which depends on a univariate covariance model that is stationary in the first Dspace coordinates h and where the covariance function phi(h,t) is twice differentiable in the first component h.

The corresponding matrix-valued covariance function C of the model only depends on the difference h between two points in the first component. It is given by

C(h,t)=( -0.5 * (a + 1) Δ + a \nabla \nabla^T ) C_0(h, t)

where the operator is applied to the first component h only.

## Usage

 `1` ```RMvector(phi, a, Dspace, var, scale, Aniso, proj) ```

## Arguments

 `phi` an `RMmodel`; has two components h (2 or 3 dimensional and stationary) and t (arbitrary dimension) `a` a numerical value; should be in the interval [-1,1]. `Dspace` an integer; either 2 or 3; the first Dspace coordinates give the first component h `var,scale,Aniso,proj` optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

## Details

C_0 is either a spatiotemporal model (then t is the time component) or it is an isotropic model. Then, the first Dspace coordinates are considered as h coordinates and the remaining ones as t coordinates. By default, Dspace equals the dimension of the field (and there is no t component). If a=-1 then the field is curl free; if a=1 then the field is divergence free.

## Value

`RMvector` returns an object of class `RMmodel`

## Author(s)

Martin Schlather, [email protected]

## References

• Scheuerer, M. and Schlather, M. (2012) Covariance Models for Divergence-Free and Curl-Free Random Vector Fields. Stochastic Models 28:3.

`RMcurlfree`, `RMdivfree`, `RMmodel`, `RFsimulate`, `RFfit`.
 ```1 2 3 4 5 6``` ```RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again model <- RMvector(RMgauss(), scale=0.3) x <- seq(0, 10, 0.4) plot(RFsimulate(model, x=x, y=x, z=0), select.variables=list(1:2)) ```