RMmodelsSphere: Covariance models valid on a sphere

In RandomFields: Simulation and Analysis of Random Fields

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 functions allowing for arbitrary scale

RMbcw	Model bridging stationary and intrinsically stationary processes for α ≤ 1 and β < 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 arbitrary scale

RMconstant	spatially constant model
RMnugget	nugget effect model

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

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.

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)

RandomFields documentation built on Jan. 19, 2022, 1:06 a.m.