\name{Spherical models}
\alias{sphere}
\alias{spherical models}
\alias{Spherical models}
\alias{earth models}
\alias{Earth models}
\title{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
\bold{Completely monotone function allowing for arbitray scale}
\tabular{ll}{
\command{\link{RMbcw}} \tab Model bridging stationary and
intrinsically stationary processes for \code{alpha <= 1}
and \code{beta < 0}\cr
\command{\link{RMcubic}} \tab cubic model\cr
\command{\link{RMdagum}} \tab Dagum model with \eqn{\beta < \gamma}
and \eqn{\gamma \le 1}\cr
\command{\link{RMexp}} \tab exponential model \cr
\command{\link{RMgencauchy}} \tab generalized Cauchy family with
\eqn{\alpha \le 1} (and arbitrary \eqn{\beta> 0})\cr
\command{\link{RMmatern}} \tab Whittle-Matern model with
\eqn{\nu \le 1/2}\cr
%multiquadric todo
%sine power todo
\command{\link{RMstable}} \tab symmetric stable family or powered
exponential model with \eqn{\alpha \le 1}\cr
\command{\link{RMwhittle}} \tab Whittle-Matern model, alternative
parametrization with \eqn{\nu \le 1/2}\cr
}
\bold{Other isotropic models with arbitray scale}
\tabular{ll}{
\command{\link{RMconstant}} \tab spatially constant model \cr
\command{\link{RMnugget}} \tab nugget effect model \cr
}
\bold{Compactly supported covariance functions allowing for scales up
\eqn{\pi} (or \eqn{180} degree)}
\tabular{ll}{
\command{\link{RMaskey}} \tab Askey's model\cr
\command{\link{RMcircular}} \tab circular model\cr
\command{\link{RMgengneiting}} \tab Wendland-Gneiting model;
differentiable models with compact support \cr
\command{\link{RMgneiting}} \tab differentiable model with compact
support \cr
\command{\link{RMspheric}} \tab spherical model \cr
}
\bold{Anisotropic models}
\tabular{ll}{
none up to now.
}
\bold{Basic Operators}
\tabular{ll}{
\command{\link{RMmult}}, \code{*} \tab product of covariance models \cr
\command{\link{RMplus}}, \code{+} \tab sum of covariance models or variograms\cr
}
\bold{See \link{RMmodels} for cartesian models.}
}
\author{
Martin Schlather, \email{schlather@math.uni-mannheim.de}
\url{http://ms.math.uni-mannheim.de/de/publications/software}
}
\seealso{
\link{coordinate systems},
\command{\link{RMmodels}},
\command{\link{RMtrafo}}
}
\keyword{spatial}
\keyword{models}
\examples{
% library(RandomFields, lib="~/TMP")
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
\dontshow{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)
\dontshow{FinalizeExample(); }
}