EmpiricalVariogram {RandomFields}R Documentation

Empirical (Semi-)Variogram

Description

EmpiricalVariogram calculates the empirical (semi-)variogram of a random field realisation

Usage

EmpiricalVariogram(x, y=NULL, z=NULL, T=NULL, data, grid, bin,
                   gridtriple=FALSE, phi, theta, deltaT)

Arguments

x

vector of x-coordinates, or matrix

y

vector of y-coordinates

z

vector of z-coordinates

T

vector of time components; here T is given in grid format, see GaussRF.

data

vector or matrix of data; if data has a multiple number of components as expected by the definition of the coordinates then it is assumed that the data stem from repeated, independent measurements at the given locations; the empirical variogram is calculated for the repeated data.

grid

logical; if TRUE then x, y, and z define a grid; otherwise x, y, and z are interpreted as points

bin

vector of ascending values giving the bin boundaries

gridtriple

logical. Only relevant if grid=TRUE. If gridtriple=TRUE then x, y, and z are of the form c(start,end,step); if gridtriple=FALSE then x, y, and z must be vectors of ascending values

phi

vector of two components. First component gives the angle for the first line of midpoints of an angular variogram. The second component gives the number of directions (on the half circle). The spatial dimension must be at least 2.

theta

vector of two components. First component gives the angle for the first line of midpoints of an angular variogram (angle is zero for the xy-plane). The second component gives the number of directions (on the half circle). The spatial dimension must be at least 3.

deltaT

vector of two components. First component gives the largest temporal distance; the second component the grid length, that must be a multiple of T[3].

Details

Comments on specific parameters:

Value

The function returns a list:

centers

central points of the bins

emp.vario

empirical variogram; vector or matrix or array, depending on the anisotropy definitions. The sequence is distances, phi, theta, Tbins. If phi, theta, or Tbins below are not given, the respective dimensions are missing.

sd

sd of the variogram cloud within each bin

n.bin

number of points within a bin

phi

vector of angles in xy plane

theta

vector of angles in the third dimensions

Tbins

vector of temporal distances

The first four elements are vectors of length (length(bin)-1).

Author(s)

Martin Schlather, martin.schlather@math.uni-goettingen.de http://www.stochastik.math.uni-goettingen.de/~schlather

See Also

GaussRF, fitvario, and

RandomFields

Examples





  #############################################################
  ## this example checks whether a certain simulation method ##
  ## works well for a specified covariance model and         ##
  ## a configuration of points                               ##
  #############################################################
  x <- seq(0, 10, 0.5)
  y <- seq(0, 10, 0.5)
  gridtriple <- FALSE      ## see help("GaussRF")
  model <- "whittle"       ## whittlematern
  bins <- seq(0, 5, 0.001)
  realisations <- 5 ## by far too small to get reliable results!!
                   ## It should be of order 500, but then it will
                   ## take some time to do the simulations
  param <- c(mean=1, variance=10, nugget=5, scale=2, alpha=2)
  f <- GaussRF(x=x, y=y, grid=TRUE, gridtriple=gridtriple,
               model=model, param=param, method="TBM3",
               n=realisations)
  binned <- EmpiricalVariogram(x=x, y=y, data=f, grid=TRUE,
                               gridtriple=gridtriple, bin=bins)
  truevariogram  <- Variogram(binned$c, model, param)
  matplot(binned$c, cbind(truevariogram,binned$e), pch=c("*","e"))
  ##black curve gives the theoretical values
























[Package RandomFields version 2.0.54 Index]