R help - May 2013 - Help on sound identification of "distance between lines"

Dear List

I would like to ask for some input on the following (here is a simplified
version of the code):

t <-t(seq(0,120,by=120/48))
d <-500
k <-0.1
x <-matrix((d/20)*exp(-k*0.9*t))
y <-matrix((d/15)*exp(-k*0.7*t))
z<-matrix((d/22)*exp(-k*1.1*t))
w<-matrix((d/17)*exp(-k*0.2*t))
t <-matrix(seq(0,120,by=120/48))
plot(t,x,type="l",ylab="Response",xlab="Time (h)")
lines(t,y,col="green")
lines(t,z,col="blue")
lines(t,w,col="yellow")
sim <-t(cbind(x,y,z,w))
true <-t((d/19)*exp(-k*0.35*t))
lines(t,true,col="red")

#find closest line
M <- rbind(sim, true) 
D <- as.matrix(dist(M)) 
diag(D) <- NA 
which.min(tail(D, 1))

In reality sim will consist of 5000 rows. My goal here is to use a sound method
to find the row in sim that is most identical or closest to true (represented by
the red line in the plot) taking into consideration the whole time interval
evaluated.

as always, thanks for the input...

Andras