RandomFields (version 3.0.5)

Coordinate systems: Coordinate systems

Description

Implemened Coordinate Systems

Implemented coordinate systems

• 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$[-\pi/2, \pi/2]$.

Transformations between the system

• Earth to cartesian The 3-dimensional resulting coordinates are either given inkmor inmiles.
• Gnomonic an orthographic projections The 2-dimensional resulting coordinates are either given inkmor inmiles. The projection direction is given by thezenit.
• Earth to spherical In this case the Earth is considered as a ball.

Cartesian systems cannot be transformed to earth or spherical coordinate systems, nor a spherical system to earth coordinates.

References

Covariance models in a cartesian system

• 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.

See Also

RMtrafo, RFearth2cartesian, RPdirect, models valid on a sphere, RFoptions

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

x <- seq(0, 10, 0.01)
z <- RFsimulate(RMexp(), x)
RFgetModelInfo(RFsimulate, level=0, which="internal")
# i.e., circulant embedding has been chosen



x <- 1:4
s <- 2
RFcov(model=RMexp(s=s), x, x, coord_sys="cartesian") ## scale interpreted as
##                                     for standard (cartesian) models
RFcov(model=RMexp(s=s), x, x, coord_sys="earth") ## scale measured in degree 
RFcov(model=RMexp(s=s / 180 * pi), x, x, coord_sys="earth") # now comparable to
##                                     the cartesian case
RFcov(model=RMexp(s=s), x, x, coord_sys="earth", zenit=c(2.5, 2.4),
      new_coord_sys="gnomonic") # projection onto a plane first. Then the
##                   scale is interpreted in the usual, i.e. cartesian, sense
RFcov(model=RMexp(s=s * 6350 / 180 * pi), x, x, coord_sys="earth",
      zenit=c(2.5, 2.5), new_coord_sys="gnomonic") # projection onto a plane
##      first. Then the scale is interpreted in usual, i.e. cartesian, sense



FinalizeExample()