Variogram

Empirical Variogram

library(sp)
library(gstat)

data("meuse")
head(meuse)

##        x      y cadmium copper lead zinc  elev       dist   om ffreq soil
## 1 181072 333611    11.7     85  299 1022 7.909 0.00135803 13.6     1    1
## 2 181025 333558     8.6     81  277 1141 6.983 0.01222430 14.0     1    1
## 3 181165 333537     6.5     68  199  640 7.800 0.10302900 13.0     1    1
## 4 181298 333484     2.6     81  116  257 7.655 0.19009400  8.0     1    2
## 5 181307 333330     2.8     48  117  269 7.480 0.27709000  8.7     1    2
## 6 181390 333260     3.0     61  137  281 7.791 0.36406700  7.8     1    2
##   lime landuse dist.m
## 1    1      Ah     50
## 2    1      Ah     30
## 3    1      Ah    150
## 4    0      Ga    270
## 5    0      Ah    380
## 6    0      Ga    470

coordinates(meuse) <- ~x+y

v <- variogram(log(zinc)~1, meuse, 
               cutoff=2000, width=80)
plot(v)

Fit a variogram model

Models:

vgm()

##    short                                      long
## 1    Nug                              Nug (nugget)
## 2    Exp                         Exp (exponential)
## 3    Sph                           Sph (spherical)
## 4    Gau                            Gau (gaussian)
## 5    Exc        Exclass (Exponential class/stable)
## 6    Mat                              Mat (Matern)
## 7    Ste Mat (Matern, M. Stein's parameterization)
## 8    Cir                            Cir (circular)
## 9    Lin                              Lin (linear)
## 10   Bes                              Bes (bessel)
## 11   Pen                      Pen (pentaspherical)
## 12   Per                            Per (periodic)
## 13   Wav                                Wav (wave)
## 14   Hol                                Hol (hole)
## 15   Log                         Log (logarithmic)
## 16   Pow                               Pow (power)
## 17   Spl                              Spl (spline)
## 18   Leg                            Leg (Legendre)
## 19   Err                   Err (Measurement error)
## 20   Int                           Int (Intercept)

Exponential

gstExp <- fit.variogram(v, vgm("Exp"), fit.method=1)
plot(v, model = gstExp)

Spherical

gstSph <- fit.variogram(v, vgm("Sph"), fit.method=1)
plot(v, model = gstSph)