fields (version 6.7.5)

poisson.cov: Poisson spherical covariance function

Description

Given two sets of locations in lon/lat computes the cross covariance matrix for the Poisson covariance among all pairings.

Usage

poisson.cov(x1, x2, eta = .2)

Arguments

x1

Matrix of first set of locations where each row gives the coordinates of a particular point. First column is longitudes and the second column is latitudes.

x2

Matrix of second set of locations where each row gives the coordinates of a particular point. If this is missing x1 is used.

eta

Range (or scale) parameter. Should be in the interval [0,1]

Value

• If nrow(x1)=m and nrow(x2)=n then the returned cross covariance matrix, will be mXn.

Details

This covariance is one of the few closed form covariances for the sphere and also know as the Poisson kernel. If x1 and x2 are matrices where nrow(x1)=m and nrow(x2)=n then this function should return a mXn matrix where the (i,j) element is the covariance between the locations x1[i,] and x2[j,]. The covariance is found as (1-eta**2)/(1 - 2 * eta * D.ij + eta**2)**(1.5)

where D.ij is the great circle distance between x1[i,] and x2[j,].

See Also

Krig, rdist.earth

Examples

# plot of covariance

x<- make.surface.grid( list( x=seq( -180,180,,40), y= seq( -85,85,,40)))
x0<- matrix( c(0,0), ncol=2)
look<- poisson.cov( x,x0, eta=.5)
image.plot(as.surface(x,look))