- Cartesian coordinate system
- Earth coordinate systems The earth is considered as an ellipsoid; The first angle takes values in $[0, 360)$, the second angle takes values in $[-90, 90]$.
- Spherical coordinate systems The earth is considered as an ellipsoid; The first angle takes values in $[0, 2\pi)$, the second angle takes values in $[-\pi/2, \pi/2]$.

- Earth to cartesian The 3-dimensional resulting coordinates are either given in ‘km’ or in ‘miles’.
- Gnomonic an orthographic projections
The 2-dimensional resulting coordinates
are either given in ‘km’ or in ‘miles’.
The projection direction is given by the
`zenit`

. - Earth to spherical In this case the Earth is considered as a ball.

- Schlather, M. (2011) Construction of covariance functions and
unconditional simulation of random fields. In Porcu, E., Montero, J.M.
and Schlather, M.,
*Space-Time Processes and Challenges Related to Environmental Problems.*New York: Springer.

Covariance models on a sphere

- Gneiting, T. (2013) Strictly and non-strictly positive definite
functions on spheres.
*Bernoulli*,**19**, 1327-1349.

Tail correlation function

- Strokorb, K., Ballani, F., and Schlather, M. (2014)
Tail correlation functions of max-stable processes: Construction
principles, recovery and diversity of some mixing max-stable
processes with identical TCF.
*Extremes*, Submitted.

`RMtrafo`

,
`RFearth2cartesian`

,
`RPdirect`

,
`models valid on a sphere`

,
`RFoptions`

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again z <- 1:4 x <- cbind(z, 0) y <- cbind(0, z) model <- RMwhittle(nu=0.5) RFcov(model, x, y, grid=FALSE)## standard is (cartesian) models ## same as above, but explicite: RFcov(model, x, y, grid=FALSE, coord_sys="cartesian") ## model is valid not on a sphere; x,y coordinates are ## transformed from earth coordinates to sphereical coordinates RFcov(model, x, y, grid=FALSE, coord_sys="earth") ## now comparable the scale chosen sucht that the covariance ## values are comparable to those int the cartesian case RFcov(RMS(model, s= 1 / 180 * pi), x, y, grid=FALSE, coord_sys="earth") ## projection onto a plane first. Then the scale is interpreted ## in the usual, i.e. cartesian, sense: RFoptions(zenit = c(2.5, 2.5)) RFcov(model, x, y, grid=FALSE, coord_sys="earth", new_coord_sys="orthographic") ## again, here the scale is chosen to comparable to cartesian case ## here the (standard) units are [km] RFcov(RMS(model, s= 6350 / 180 * pi), x, y, grid=FALSE, coord_sys="earth", new_coord_sys="orthographic") ## as above, but in miles RFcov(RMS(model, s= 3750 / 180 * pi), x, y, grid=FALSE, coord_sys="earth", new_coord_sys="orthographic", new_coordunits="miles")