GeoVariogramDir: Empirical directional semivariogram

Description

Computes empirical semivariograms in multiple directions (e.g., 0, 45, 90, 135 degrees) to assess spatial anisotropy.

Usage

GeoVariogramDir(data, coordx, coordy = NULL, coordz = NULL,
                directions = c(0, 45, 90, 135), tolerance = 22.5, numbins = 13,
                maxdist = NULL, neighb = NULL, distance = "Eucl",
                subsample = 1)

Value

A list of class "GeoVariogramDir" with one element for each direction. Each element is a list with components:

centers: Centers of the distance bins.
gamma: Empirical semivariogram values for each bin.
npairs: Number of point pairs in each bin.

Arguments

data: A numeric vector containing the observed values at each location.
coordx: Spatial coordinates. Either a numeric vector giving the first coordinate, or a matrix with 2 (or 3) columns. If a matrix is provided, coordy and coordz are ignored.
coordy: A numeric vector of the second coordinate. Optional; defaults to NULL.
coordz: A numeric vector of the third coordinate (if needed). Optional; defaults to NULL.
directions: Numeric vector giving the principal directions (in degrees) for which the semivariogram is computed (default: c(0, 45, 90, 135)).
tolerance: Angular tolerance (in degrees) around each direction (default: 22.5).
numbins: Number of distance bins for the empirical semivariogram (default: 13).
maxdist: Maximum spatial distance to consider between pairs. If NULL, an internal default is used.
neighb: Number of nearest neighbors to use for each location. If NULL, an internal default is used.
distance: Type of distance metric to use (default: "Eucl"). See GeoFit for options.
subsample: Numeric in \((0,1]\). Proportion of spatial locations used to compute the directional semivariograms (useful for large datasets). Default is 1 (use all locations).

Details

The function computes empirical semivariograms for several directions by:

Selecting pairs of points within maxdist and among the neighb nearest neighbors using GeoNeighIndex.
Computing squared differences for each selected pair.
Assigning each pair to a directional class if the vector connecting the pair falls within the specified angular tolerance around a given direction.
Binning pairs by distance and computing the average squared difference (semivariogram) within each bin.

The direction is defined in the xy-plane even in 3D. For 2D data, set coordz = NULL.

The subsample argument can be used to reduce computational cost by randomly selecting a subset of spatial locations prior to pair construction. This is particularly useful for large datasets.

Examples

Run this code

require(GeoModels)
set.seed(960)
NN <- 2500
coords <- cbind(runif(NN), runif(NN))
scale <- 0.5/3
param <- list(mean = 0, sill = 1, nugget = 0, scale = scale, smooth = 0.5)
corrmodel <- "Matern"

set.seed(951)
data <- GeoSim(coordx = coords, corrmodel = corrmodel,
               model = "Gaussian", param = param)$data

vario_dir <- GeoVariogramDir(data = data, coordx = coords, maxdist = 0.4,
                             subsample = 0.5)

plot(vario_dir, ylim = c(0,1))