network.design: Generating `AKSE` associated with a conditioned network design

Description

Generates a sampling network for a given sampling distance or type (configuration), and calculates the average kriging standard error (AKSE) associated with the spatial configuration for a given predefined variogram

Usage

network.design(formula, vgm.model, xmin, xmax, ymin, ymax, npoint.x, npoint.y,
npoints, boundary=NULL, type, ...)

Value

returns the AKSE value associated with the spatial distribution of points and the kriging method used.

Arguments

formula: formula that defines the dependent variable as a linear model of independent variables; suppose the dependent variable has name z, for ordinary and simple kriging use the formula z~1; for simple kriging also define beta (see below); for universal kriging, suppose z is linearly dependent on x and y, use the formula z~x+y
vgm.model: variogram model of dependent variable (or its residuals), defined by a call to vgm or fit.variogram
npoint.x: number of points to generate on the x-axis
npoint.y: number of points to generate on the y-axis
npoints: (approximate) sample size inside (shapefile) border
xmin: minimum x-coordinate of the study area.
ymin: minimum y-coordinate of the study area.
xmax: maximum x-coordinate of the study area.
ymax: maximum y-coordinate of the study area.
boundary: SpatialPolygons or SpatialPolygonsDataFrame object
type: character; "random" for completely spatial random; "regular" for regular (systematically aligned) sampling; "stratified" for stratified random (one single random location in each "cell"); "nonaligned" for nonaligned systematic sampling (nx random y coordinates, ny random x coordinates); "hexagonal" for sampling on a hexagonal lattice; "clustered" for clustered sampling; "Fibonacci" for Fibonacci sampling on the sphere (see references). By default type ="regular".
...: further arguments will be passed of the krige and spsample functions.

References

Fibonacci sampling: Alvaro Gonzalez, 2010. Measurement of Areas on a Sphere Using Fibonacci and Latitude-Longitude Lattices. Mathematical Geosciences 42(1), p. 49-64

Examples

Run this code

if (FALSE) {
### regular grid 10x10
vgmok <- vgm(112.33, "Sph", 4.3441,0)
vgmsk <- vgm(74.703, "Sph", 3.573,0)
vgmuk <- vgm(53.064, "Sph", 2.8858,0)
vgmuk2 <- vgm(19.201, "Sph", 1.5823,0)
# network: ordinary kriging (without boundary)
net1.ok <- network.design(z~1,vgmok, xmin=0,xmax=10, ymin=0, ymax=10, npoint.x=10,
    npoint.y=10, nmax=6)
net2.ok <- network.design(z~1,vgmok, xmin=0,xmax=10, ymin=0, ymax=10, npoint.x=20,
    npoint.y=20, nmax=6)
# it's worth noting that the variograms are different in each kriging

# network: simple kriging (without boundary)

net1.sk <- network.design(z~1,vgmsk, xmin=0,xmax=10, ymin=0, ymax=10, npoint.x=10,
    npoint.y=10, nmax=6, beta=2)
net2.sk <- network.design(z~1,vgmsk, xmin=0,xmax=10, ymin=0, ymax=10, npoint.x=20,
    npoint.y=20, nmax=6, beta=2)
# network: universal kriging, second order trend (without boundary)
net1.uk <- network.design(z~x + y + x*y + I(x^2)+I(y^2),vgmuk, xmin=0,xmax=10, ymin=0,
    ymax=10, npoint.x=10, npoint.y=10, nmax=8)
net2.uk <- network.design(z~x + y + x*y + I(x^2)+I(y^2),vgmuk2, xmin=0,xmax=10, ymin=0,
    ymax=10, npoint.x=20, npoint.y=20, nmax=8)


# Creating the grid with the prediction and plotting points
library(geoR)
data(ca20)
Sr1 <- Polygon(ca20$borders)
Srs1 = Polygons(list(Sr1), "s1")
Polygon = SpatialPolygons(list(Srs1))
vgmok.ca <- vgm(112.33, "Sph", 244.9,0)
vgmsk.ca <- vgm(100, "Sph", 150.2,0)
vgmuk.ca <- vgm(85.57, "Sph", 110.5,0)
vgmuk2.ca <- vgm(62.14, "Sph", 89.7,0)

# network: ordinary kriging (with boundary)
netb1.ok<- network.design(z~1, vgmok.ca, npoints=50, boundary=Polygon, nmax=6)
netb2.ok<- network.design(z~1, vgmok.ca, npoints=100, boundary=Polygon, nmax=6)
# network: simple kriging (with boundary)
netb1.sk <- network.design(z~1, vgmsk.ca, npoints=50, boundary=Polygon, nmax=6, beta=2)
netb2.sk <- network.design(z~1, vgmsk.ca, npoints=100, boundary=Polygon, nmax=6, beta=2)
# network: universal kriging, second order trend (with boundary)
netb1.uk <- network.design(z~x + y + x*y + I(x^2)+I(y^2), vgmuk.ca, npoints=50,
    boundary=Polygon, nmax=8)
netb2.uk <- network.design(z~x + y + x*y + I(x^2)+I(y^2), vgmuk2.ca, npoints=100,
    boundary=Polygon, nmax=8)
}