Kriging with gstat

You can use the krige (or krige.cv) utilities in gstat package together with as.vgm for (global or local) kriging…

Wolfcamp aquifer data:

library(npsp)
# ?aquifer; str(aquifer); summary(aquifer)
# Scatter plot with a color scale
with(aquifer, spoints(lon, lat, head, main = "Wolfcamp aquifer data"))

Kriging

Trend estimation

lp <- locpol(aquifer[,1:2], aquifer$head, h = diag(75, 2), 
             hat.bin = TRUE)  
            # np.svariso.corr: 'lp' must have a '$locpol$hat' component

# Mask grid nodes far from data
mask <- log(np.den(lp, h = diag(c(55,55)), degree = 0)$est) > -15
lp <- mask(lp, mask = mask)

spersp(lp, main = 'Trend estimates', 
       zlab = 'piezometric-head levels', theta = 120)

cpu.time(total = FALSE)

## Time of last operation: 
##    user  system elapsed 
##  25.597   4.381  23.361

Variogram estimation

lp.resid <- residuals(lp)
esvar <- np.svariso(aquifer[,1:2], lp.resid, maxlag = 150, nlags = 60, h = 60)
svm <- fitsvar.sb.iso(esvar)  # dk = 2
esvar2 <- np.svariso.corr(lp, maxlag = 150, nlags = 60, h = 60)
svm2 <- fitsvar.sb.iso(esvar2, dk = 0)  # dk = Inf
plot(svm2, main = "Nonparametric bias-corrected semivariogram and fitted models", 
     lwd = 2) 
with(svm$fit, lines(u, fitted.sv, lty = 2))

cpu.time(total = FALSE)

## Time of last operation: 
##    user  system elapsed 
##   0.189   0.083   0.180

Residual Kriging

library(sp)
library(gstat)
spdf <- SpatialPointsDataFrame(aquifer[,1:2], 
            data.frame(y = aquifer$head, r = lp.resid))
newdata <- SpatialPoints(coords(lp))
krig <- krige(r ~ 1, locations = spdf, newdata = newdata, 
              model = as.vgm(svm), beta = 0)

## [using simple kriging]

krig.grid <- data.grid(kpred = lp$est + krig@data$var1.pred, 
                       ksd = sqrt(krig@data$var1.var), 
        grid = lp$grid)
krig2 <- krige(r ~ 1, locations = spdf, newdata = newdata, 
               model = as.vgm(svm2), beta = 0)

## [using simple kriging]

krig2.grid <- data.grid(kpred = lp$est + krig2@data$var1.pred, 
                        ksd = sqrt(krig2@data$var1.var), 
        grid = lp$grid)
scale.color <- jet.colors(64)
scale.range <- c(1100, 4100)
# 1x2 plot with some room for the legend...
old.par <- par(mfrow = c(1,2), omd = c(0.01, 0.9, 0.05, 0.95),
               plt= c(0.08, 0.94, 0.1, 0.8))
spersp(krig.grid, main = 'Kriging predictions', col = scale.color, 
       legend = FALSE, theta = 120, reset = FALSE)
spersp(krig2.grid, main = 'Kriging predictions \n (bias-corrected)', 
       col = scale.color, legend = FALSE, theta = 120, reset = FALSE)
par(old.par)
splot(slim = scale.range, col = scale.color, legend.shrink = 0.6, add = TRUE)

old.par <- par(mfrow = c(1,2), omd = c(0.05, 0.85, 0.05, 0.95))
scale.range <- c(125, 200)
scale.range <- range(krig.grid$ksd, krig2.grid$ksd, finite = TRUE)
image( krig.grid, 'ksd', zlim = scale.range, # asp = 1, 
       main = 'Kriging sd', col = scale.color)
with(aquifer, points(lon, lat, cex = 0.75))
image( krig2.grid, 'ksd', zlim = scale.range, # asp = 1, 
       main = 'Kriging sd (bias-corrected)', col = scale.color)
with(aquifer, points(lon, lat, cex = 0.75))
par(old.par)
splot(slim = scale.range, col = scale.color, add = TRUE)

cpu.time()

## Time of last operation: 
##    user  system elapsed 
##   1.105   0.645   0.966 
## Total time:
##    user  system elapsed 
##  26.891   5.109  24.507

Notes:

To reproduce results in SERRA paper use data(wolfcamp) in package geoR.
Results obtained with aquifer data set are comparable with those in Cressie (1993, section 4.1).

- Kriging with gstat