| Spherical models {RandomFields} | R Documentation |
This page summarizes the covariance models that can be used for spherical coordinates (and earth coordinates)
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.
Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software
coordinate systems,
RMmodels,
RMtrafo
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)