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# Display a Taylor diagram
# Taylor K.E. (2001)
# Summarizing multiple aspects of model performance in a single diagram
# Journal of Geophysical Research, 106: 7183-7192.
# version 1.0
# progr. Olivier.Eterradossi, 12/2007
# 2007-01-12 - modifications and Anglicizing - Jim Lemon
# version 2.0
# progr. initiale OLE, 8/01/2007
# rev. OLE 3/09/2008 : remove samples with NA's from mean, sd and cor calculations
# 2008-09-04 - integration and more anglicizing - Jim Lemon
# 2008-12-09 - added correlation radii, sd arcs to the pos.cor=FALSE routine
# and stopped the pos.cor=FALSE routine from calculating arcs for zero radius
# Jim Lemon
# 2010-4-30 - added the gamma.col argument for pos.cor=TRUE plots - Jim Lemon
# 2010-6-24 - added mar argument to pos.cor=TRUE plots - Jim Lemon
taylor.diagram<-function(ref,model,add=FALSE,col="red",pch=19,pos.cor=TRUE,
xlab="",ylab="",main="Taylor Diagram",show.gamma=TRUE,ngamma=3,gamma.col=8,
sd.arcs=0,ref.sd=FALSE,grad.corr.lines=c(0.2,0.4,0.6,0.8,0.9),pcex=1,
normalize=FALSE,mar=c(5,4,6,6),...) {
grad.corr.full<-c(0,0.2,0.4,0.6,0.8,0.9,0.95,0.99,1)
R<-cor(ref,model,use="pairwise")
sd.r<-sd(ref)
sd.f<-sd(model)
if(normalize) {
sd.f<-sd.f/sd.r
sd.r<-1
}
maxsd<-1.5*max(sd.f,sd.r)
oldpar<-par("mar","xpd","xaxs","yaxs")
if(!add) {
# display the diagram
if(pos.cor) {
if(nchar(ylab) == 0) ylab="Standard deviation"
par(mar=mar)
plot(0,xlim=c(0,maxsd),ylim=c(0,maxsd),xaxs="i",yaxs="i",axes=FALSE,
main=main,xlab=xlab,ylab=ylab,type="n",...)
if(grad.corr.lines[1]) {
for(gcl in grad.corr.lines)
lines(c(0,maxsd*gcl),c(0,maxsd*sqrt(1-gcl^2)),lty=3)
}
# add the axes
segments(c(0,0),c(0,0),c(0,maxsd),c(maxsd,0))
axis.ticks<-pretty(c(0,maxsd))
axis.ticks<-axis.ticks[axis.ticks<=maxsd]
axis(1,at=axis.ticks)
axis(2,at=axis.ticks)
if(sd.arcs[1]) {
if(length(sd.arcs) == 1) sd.arcs<-axis.ticks
for(sdarc in sd.arcs) {
xcurve<-cos(seq(0,pi/2,by=0.03))*sdarc
ycurve<-sin(seq(0,pi/2,by=0.03))*sdarc
lines(xcurve,ycurve,col="blue",lty=3)
}
}
if(show.gamma[1]) {
# if the user has passed a set of gamma values, use that
if(length(show.gamma) > 1) gamma<-show.gamma
# otherwise make up a set
else gamma<-pretty(c(0,maxsd),n=ngamma)[-1]
if(gamma[length(gamma)] > maxsd) gamma<-gamma[-length(gamma)]
labelpos<-seq(45,70,length.out=length(gamma))
# do the gamma curves
for(gindex in 1:length(gamma)) {
xcurve<-cos(seq(0,pi,by=0.03))*gamma[gindex]+sd.r
# find where to clip the curves
endcurve<-which(xcurve<0)
endcurve<-ifelse(length(endcurve),min(endcurve)-1,105)
ycurve<-sin(seq(0,pi,by=0.03))*gamma[gindex]
maxcurve<-xcurve*xcurve+ycurve*ycurve
startcurve<-which(maxcurve>maxsd*maxsd)
startcurve<-ifelse(length(startcurve),max(startcurve)+1,0)
lines(xcurve[startcurve:endcurve],ycurve[startcurve:endcurve],
col=gamma.col)
boxed.labels(xcurve[labelpos[gindex]],ycurve[labelpos[gindex]],
gamma[gindex],border=FALSE)
}
}
# the outer curve for correlation
xcurve<-cos(seq(0,pi/2,by=0.01))*maxsd
ycurve<-sin(seq(0,pi/2,by=0.01))*maxsd
lines(xcurve,ycurve)
bigtickangles<-acos(seq(0.1,0.9,by=0.1))
medtickangles<-acos(seq(0.05,0.95,by=0.1))
smltickangles<-acos(seq(0.91,0.99,by=0.01))
segments(cos(bigtickangles)*maxsd,sin(bigtickangles)*maxsd,
cos(bigtickangles)*0.97*maxsd,sin(bigtickangles)*0.97*maxsd)
par(xpd=TRUE)
if(ref.sd) {
# the inner curve for reference SD
xcurve<-cos(seq(0,pi/2,by=0.01))*sd.r
ycurve<-sin(seq(0,pi/2,by=0.01))*sd.r
lines(xcurve,ycurve)
}
points(sd.r,0)
text(cos(c(bigtickangles,acos(c(0.95,0.99))))*1.05*maxsd,
sin(c(bigtickangles,acos(c(0.95,0.99))))*1.05*maxsd,
c(seq(0.1,0.9,by=0.1),0.95,0.99))
text(maxsd*0.75,maxsd*0.8,"Correlation")
segments(cos(medtickangles)*maxsd,sin(medtickangles)*maxsd,
cos(medtickangles)*0.98*maxsd,sin(medtickangles)*0.98*maxsd)
segments(cos(smltickangles)*maxsd,sin(smltickangles)*maxsd,
cos(smltickangles)*0.99*maxsd,sin(smltickangles)*0.99*maxsd)
}
else {
x<- ref
y<- model
R<-cor(x,y,use="pairwise.complete.obs")
E<-mean(x,na.rm=TRUE)-mean(y,na.rm=TRUE) # overall bias
xprime<-x-mean(x,na.rm=TRUE)
yprime<-y-mean(y,na.rm=TRUE)
sumofsquares<-(xprime-yprime)^2
Eprime<-sqrt(sum(sumofsquares)/length(complete.cases(x))) # centered pattern RMS
E2<-E^2+Eprime^2
if (add==FALSE) {
# pourtour du diagramme (display the diagram)
maxray<-1.5*max(sd.f,sd.r)
plot(c(-maxray,maxray),c(0,maxray),type="n",asp=1,bty="n",xaxt="n",yaxt="n",
xlab=xlab,ylab=ylab,main=main)
discrete<-seq(180,0,by=-1)
listepoints<-NULL
for (i in discrete){
listepoints<-cbind(listepoints,maxray*cos(i*pi/180),maxray*sin(i*pi/180))
}
listepoints<-matrix(listepoints,2,length(listepoints)/2)
listepoints<-t(listepoints)
lines(listepoints[,1],listepoints[,2])
# axes x,y
lines(c(-maxray,maxray),c(0,0))
lines(c(0,0),c(0,maxray))
# lignes radiales jusqu'� R = +/- 0.8
for (i in grad.corr.lines){
lines(c(0,maxray*i),c(0,maxray*sqrt(1-i^2)),lty=3)
lines(c(0,-maxray*i),c(0,maxray*sqrt(1-i^2)),lty=3)
}
# texte radial
for (i in grad.corr.full){
text(1.05*maxray*i,1.05*maxray*sqrt(1-i^2),i,cex=0.6)
text(-1.05*maxray*i,1.05*maxray*sqrt(1-i^2),-i,cex=0.6)
}
# sd concentriques autour de la reference
seq.sd<-seq.int(0,2*maxray,by=(maxray/10))[-1]
for (i in seq.sd){
xcircle<-sd.r+(cos(discrete*pi/180)*i)
ycircle<-sin(discrete*pi/180)*i
for (j in 1:length(xcircle)){
if ((xcircle[j]^2+ycircle[j]^2)<(maxray^2)){
points(xcircle[j],ycircle[j], col="darkgreen",pch=".")
if(j==10)
text(xcircle[j],ycircle[j],signif(i,2),cex=0.5,col="darkgreen")
}
}
}
# sd concentriques autour de l'origine
seq.sd<-seq.int(0,maxray,length.out=5)
for (i in seq.sd){
xcircle<-(cos(discrete*pi/180)*i)
ycircle<-sin(discrete*pi/180)*i
if(i) lines(xcircle,ycircle,lty=3,col="blue")
text(min(xcircle),-0.03*maxray,signif(i,2),cex=0.5,col="blue")
text(max(xcircle),-0.03*maxray,signif(i,2),cex=0.5,col="blue")
}
text(0,-0.08*maxray,"Standard Deviation",cex=0.7,col="blue")
text(0,-0.12*maxray,"Centered RMS Difference",cex=0.7,col="darkgreen")
points(sd.r,0,pch=22,bg="darkgreen",cex=1.1)
text(0,1.1*maxray,"Correlation Coefficient",cex=0.7)
}
S<-(2*(1+R))/(sd.f+(1/sd.f))^2
# Taylor<-S
}
}
# display the points
points(sd.f*R,sd.f*sin(acos(R)),pch=pch,col=col,cex=pcex)
invisible(oldpar)
}
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