Covariance Parameters for Krig in geoR ksline

Question

I have a small data set of locations and benzene concentrations in mg/kg

    WELL.ID   X           Y     BENZENE
1   MW-02   268.8155    282.83  0.00150
2   IW-06   271.6961    377.01  0.00050
3   IW-07   251.0236    300.41  0.01040
4   IW-08   278.9238    300.37  0.03190
5   MW-10   281.4008    414.15  2.04000
6   MW-12   391.3973    449.40  0.01350
7   MW-13   309.5307    335.55  0.01940
8   MW-15   372.8967    370.04  0.01620
9   MW-17   250.0000    428.04  0.01900
10  MW-24   424.4025    295.69  0.00780
11  MW-28   419.3205    250.00  0.00100
12  MW-29   352.9197    277.27  0.00031
13  MW-31   309.3174    370.92  0.17900

and I am trying to krig the values in a grid (the property these wells reside on) like so

setwd("C:/.....")
getwd()

require(geoR)
require(ggplot2)


a <- read.table("krigbenz_loc.csv", sep = ",", header = TRUE)
b <- data.matrix(a)
c <- as.geodata(b)

x.range <- as.integer(range(a[,2]))
y.range <- as.integer(range(a[,3]))
x = seq(from=x.range[1], to=x.range[2], by=1)
y = seq(from=y.range[1], to=y.range[2], by=1)
length(x)
length(y)
xv <- rep(x,length(y))
yv <- rep(y, each=length(x))
in_mat <- as.matrix(cbind(xv, yv))

this is when I start the Krig with

q <- ksline(c, cov.model="exp", cov.pars=c(10,3.33), nugget=0, locations=in_mat)

however, when looking at the output of this with

cbind(q$predict[1:10], q$krige.var[1:10])

i see

         [,1]     [,2]
 [1,] 343.8958 10.91698
 [2,] 343.8958 10.91698
 [3,] 343.8958 10.91698
 [4,] 343.8958 10.91698
 [5,] 343.8958 10.91698
 [6,] 343.8958 10.91698
 [7,] 343.8958 10.91698
 [8,] 343.8958 10.91698
 [9,] 343.8958 10.91698
[10,] 343.8958 10.91698

these values do not change for the first 5000 rows... (cant view more because max.print = 5000... not sure how to change this either but that is a tangent..)

I am realizing that my

cov.pars = c(10,3.33)

being range and sill, are probably the issue.

the geoR.pdf, pg 19 describes what is expected from cov.pars however I am not sure how I should decide what these covariance parameters need to be.

Is there a method to find the appropriate values from my existing data or can I set these to generic values where my output will be similar to a kriging performed in the spatial analyst package of ESRI's ArcGIS?

ZR

::::EDIT:::

my geodata object was improperly converted... here is the correct way to do this

c <- as.geodata(b, coords.col = 2:3, data.col = 4, )

also...for the variogram,

v1 <- variog(c)
length(v1$n)
v1.summary <- cbind(c(1:11), v1$v, v1$n)
colnames(v1.summary) <- c("lag", "semi-variance", "# of pairs")
v1.summary

Answer 1

One way to do this is to use the variofit function (also in the geoR package) to estimate the covariance parameters. For example, using your data and initial values:

vario <- variog(c)  # See other options here for binning, etc
# Note that the order of the cov.pars is variance, then range, (see your question)
fitted_model <- variofit(vario=vario, ini.cov.pars=c(10, 3.33), cov.model='exp')
q <- ksline(c, cov.model=fitted_model$cov.model, cov.pars=fitted_model$cov.pars,
            nugget=fitted_model$nugget, locations=in_mat)

It is worth your time to look at the variogram, by the way.