R: Covariance models valid on a sphere

Spherical models {RandomFields} | R Documentation

## Covariance models valid on a sphere

### Description

This page summarizes the covariance models that can be used for spherical coordinates (and earth coordinates)

### Details

The following models are available

Completely monotone function allowing for arbitray scale

`RMbcw` | Model bridging stationary and intrinsically stationary processes for `alpha <= 1` and `beta < 0`
`RMcubic` | cubic model
`RMdagum` | Dagum model with β < γ and γ ≤ 1
`RMexp` | exponential model
`RMgencauchy` | generalized Cauchy family with α ≤ 1 (and arbitrary β> 0)
`RMmatern` | Whittle-Matern model with ν ≤ 1/2
`RMstable` | symmetric stable family or powered exponential model with α ≤ 1
`RMwhittle` | Whittle-Matern model, alternative parametrization with ν ≤ 1/2

Other isotropic models with arbitray scale

`RMconstant` | spatially constant model
`RMnugget` | nugget effect model

Compactly supported covariance functions allowing for scales up π (or 180 degree)

`RMaskey` | Askey's model
`RMcircular` | circular model
`RMgengneiting` | Wendland-Gneiting model; differentiable models with compact support
`RMgneiting` | differentiable model with compact support
`RMspheric` | spherical model

Anisotropic models

none up to now.

Basic Operators

`RMmult`, `*` | product of covariance models
`RMplus`, `+` | sum of covariance models or variograms

See RMmodels for cartesian models.

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software

### See Also

coordinate systems, `RMmodels`, `RMtrafo`

### Examples

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

    RFgetModelNames(isotropy=c("spherical isotropic"))

    ## an example of a simple model valid on a sphere
    model <- RMexp(var=1.6, scale=0.5) + RMnugget(var=0) #exponential + nugget
    plot(model)

    ## a simple simulation
    l <- seq(0, 85, 1.2)
    coord <- cbind(lon=l, lat=l)

    z <- RFsimulate(RMwhittle(s=30, nu=0.45), coord, grid=TRUE) # takes 1 min
    plot(z)

    z <- RFsimulate(RMwhittle(s=500, nu=0.5), coord, grid=TRUE,
                    new_coord_sys="orthographic", zenit=c(25, 25))
    plot(z)

    z <- RFsimulate(RMwhittle(s=500, nu=0.5), coord, grid=TRUE,
                    new_coord_sys="gnomonic", zenit=c(25, 25))
    plot(z)

    ## space-time modelling on the sphere
    sigma <- 5 * sqrt((R.lat()-30)^2 + (R.lon()-20)^2)
    model <- RMprod(sigma) * RMtrafo(RMexp(s=500, proj="space"), "cartesian") *
      RMspheric(proj="time")

    z <- RFsimulate(model, 0:10, 10:20, T=seq(0, 1, 0.1),
                    coord_system="earth", new_coordunits="km")
    plot(z, MARGIN.slices=3)

[Package RandomFields version 3.1.50 Index]