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odei_james_project2.R
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##################################################################################################################
### ###
### The following code is written to illustrate Variogram and its model fitting as well ###
### Spatial Predictions using Ordinary, Simple and Universal Kriging. ###
### ###
### Author: JAMES B. ODEI ###
### ###
### Date: April 10, 2009 ###
### ###
##################################################################################################################
################################## EXAMPLE #1 (VARIOGRAM) #############################################
data_url<-"http://www.math.usu.edu/~symanzik/teaching/2009_stat6560/RDataAndScripts/odei_james_project2_ozone.txt"
ozonedata<-read.table(url(data_url), header=FALSE)
names(ozonedata)=c("Longitude", "Latitude", "Ozone.Conc")
#ozonedata=read.table("odei_james_project2_ozone.txt")
#names(ozonedata)=c("Longitude", "Latitude", "Ozone.Conc")
########## Spatial Plot for Ozone Conc. #####################
pdf(file = "odei_james_project2_fig2.pdf",width=8, height=8, pointsize = 12, bg = "white")
plot(ozonedata[,1],ozonedata[,2],type="n",xlab="Longitude",ylab="Latitude",xlim=c(-88.35, -87), ylim=c(41.4, 42.5),
main="Spatial Process Field of Ozone Conc. in Chicago (Summer 1987)")
symbols(ozonedata[,1],ozonedata[,2],circles=(ozonedata[,3]-min(ozonedata[,3]))/600,bg=2,inches=FALSE,add=TRUE)
dev.off()
############# Variogram (as well as Cloud) ##########
library(gstat)
coordinates(ozonedata)=c("Longitude", "Latitude")
plot(variogram(log(Ozone.Conc) ~ 1, ozonedata), col=2, main="Variogram of Ozone Conc. in Chicago (Summer 1987)")
plot(variogram(log(Ozone.Conc) ~ 1,ozonedata, cloud=TRUE), col=4, main="Variogram Cloud of Ozone Conc. in Chicago (Summer 1987)")
#################### Variogram Modeling ########################
show.vgms() # An Overview of the basic variogram models available in gstat package
show.vgms(model="Mat", kappa.range=c(0.1,0.2,0.5,1,2,5,10), max=10) # An overview of various models in the Matern Class
#### Variogram models are buit as follows: #######
vgm() ### Gives list of model types
vgm(1, "Sph", 300)
vgm(1, "Sph", 300, 0.5)
v1=vgm(1, "Sph", 300, 0.5)
v2=vgm(0.8, "Sph", 300, add.to=v1)
v2
vgm(0.5, "Nug", 0) ## and so on
## NOTE: Not all of these models are equally useful, in practice. Most practical studies have so used Exponential, Spherical, Gaussian, Matern,
## or Power models with or without a nugget or a combination of those.
vm=variogram(log(Ozone.Conc) ~ 1, ozonedata)
plot(vm, col=2, main="Variogram of Ozone Concentration in Chicago (Summer 1987)")
#par(mfrow=c(2,2))
vm.fit1= fit.variogram(vm, vgm(0.08, "Sph", 0.3, 0))
plot(vm, vm.fit1, col=4, main="Variogram of Ozone Conc. in Chicago (Summer 1987)
and Shperical Fitted Model" )
vm.fit2= fit.variogram(vm, vgm(0.08, "Exp", 0.2, 0))
plot(vm, vm.fit2, col=4, main="Variogram of Ozone Conc. in Chicago (Summer 1987)
and Exponential Fitted Model")
vm.fit3= fit.variogram(vm, vgm(0.15, "Gau", 0.5, 0))
plot(vm, vm.fit3, col=4, main="Variogram of Ozone Conc. in Chicago (Summer 1987)
and Gaussian Fitted Model" )
vm.fit4= fit.variogram(vm, vgm(1, "Mat", 1, kappa=5))
plot(vm, vm.fit4, col=4, main="Variogram of Ozone Conc. in Chicago (Summer 1987)
and Matern Fitted Model" )
################################## EXAMPLE #2 (SPATIAL PREDICTIONS) #######################################
data_url<-"http://www.math.usu.edu/~symanzik/teaching/2009_stat6560/RDataAndScripts/odei_james_project2_rabbit.txt"
rabbitdata<-read.table(url(data_url), header=TRUE)
data_url<-"http://www.math.usu.edu/~symanzik/teaching/2009_stat6560/RDataAndScripts/odei_james_project2_rabbit.grid.txt"
rabbit.grid<-read.table(url(data_url), header=TRUE)
library(gstat)
#rabbitdata=read.table("odei_james_project2_rabbit.txt", header=TRUE)
coordinates(rabbitdata)=c("UTMX", "UTMY")
#rabbit.grid=read.table("odei_james_project2_rabbit.grid.txt", header=TRUE)
gridded(rabbit.grid) = c("UTMX", "UTMY")
rt1=variogram(log(Sign/Obs+0.001) ~ 1, rabbitdata)
plot(rt1, vgm(3.5, "Exp",2000,0))
rabbit.lm1=krige(log(Sign/Obs+0.001) ~ 1, rabbitdata, rabbit.grid)
rt2=variogram(log(Sign/Obs+0.001) ~ sqrt(Slope_mean), rabbitdata)
plot(rt2, vgm(3.5, "Exp",2000,0))
rabbit.lm2=krige(log(Sign/Obs+0.001)~ sqrt(Slope_mean), rabbitdata, rabbit.grid)
m=vgm(3.5, "Exp",2000,0)
######## Ordinary Kriging: ########
x <- krige(log(Sign/Obs+0.001) ~ 1, rabbitdata, rabbit.grid, model = m)
spplot(x["var1.pred"], main = "Ordinary kriging predictions for Rabbit Burrow Occupancy")
spplot(x["var1.var"], main = "Ordinary kriging variance for Rabbit Burrow Occupancy")
####### Simple Kriging: ########
y <- krige(log(Sign/Obs+0.001) ~ 1, rabbitdata, rabbit.grid, model = m, beta = 2)
spplot(y["var1.pred"], main = "Simple kriging predictions for Rabbit Burrow Occupancy")
spplot(y["var1.var"], main = "Simple kriging variance for Rabbit Burrow Occupancy")
####### Universal Block Kriging: ######
z <- krige(log(Sign/Obs+0.001) ~ sqrt(Slope_mean), rabbitdata, rabbit.grid, model = m, block = c(0,0))
spplot(z["var1.pred"], main = "Universal kriging predictions for Rabbit Burrow Occupancy")