RandomFields (version 3.1.12)

Spherical models: 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 ll{ RMbcw Model bridging stationary and intrinsically stationary processes for alpha <= 1<="" code=""> and beta < 0 RMcubic cubic model RMdagum Dagum model with $\beta < \gamma$ and $\gamma \le 1$ RMexp exponential model RMgencauchy generalized Cauchy family with $\alpha \le 1$ (and arbitrary $\beta> 0$) RMmatern Whittle-Matern model with $\nu \le 1/2$ RMstable symmetric stable family or powered exponential model with $\alpha \le 1$ RMwhittle Whittle-Matern model, alternative parametrization with $\nu \le 1/2$ } Other isotropic models with arbitray scale ll{ RMconstant spatially constant model RMnugget nugget effect model } Compactly supported covariance functions allowing for scales up $\pi$ (or $180$ degree) ll{ 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 ll{ none up to now. } Basic Operators ll{ RMmult, * product of covariance models RMplus, + sum of covariance models or variograms }

See RMmodels for cartesian models.

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
StartExample()
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)

FinalizeExample();