RandomFields (version 3.1.36)

# 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 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.
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.

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

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")