network.design {geospt}

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, ...)

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.

Value

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

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

See Also

krige, krige.cv, spsample, point.in.polygon, sample

Examples

## Not run: 
### 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)

## End(Not run)