There are at least two reasons why the reduction in data might lead to spurious oscillations. One is simple averaging - fewer sites means greater variance in the mean. The other is geographical spread. I might be able to say something later about spread, but for this post I'm looking at the averaging effect.

I simulated with some artificial data on the actual site histories (from Briffa's 1998 paper). I took a 40-year sinusoid and added AR1 noise (with a 5-year time constant). And I plotted the results below the jump.

Update - I should add that another effect, maybe as important, is the loss of replication within sites. This analysis only covers reduction in sites.

The sinusoid had unit amplitude. On each site I convolved a unit uniform variate (default rnorm) with the function 3*exp(-0.2*i). In choosing these numbers I was trying to best illustrate the effect. I did this 383 times, assigning to each sequence the starting point of one of the Briffa sites (in sequence). The first run produced this plot:

The site starting years are shown in red, and the true sinusoid in green. The common signal, the sinusoid, is coming through fairly well above 1600, but gets ragged earlier on from there. But the raggedness is random - doing it again gives

and again

So that is what is bad about drawing plots when the data runs low. You produce spurious deviations which are not reproducible in artificial data, and are misleading. That's why Briffa didn't do it, as most scientists wouldn't.

Update. RuhRoh in comments has suggested that I should have shown smoothed noise comparable to that in the Briffa/Steve plots. I think that is a good idea. I originally used AR1 noise as a well-recognised kind of red noise, but I'll now use the same filter that Steve did. The formula is

e1=truncated.gauss.weights(50)*20

The 20 is the factor that regulates the size of the noise relative to the sinusoid. Here are the corresponding 3 plots (random repeats):

Appendix.

Here is my R code. yy is the vector of starting years (minus 1400) (see prev post) and u1 is the ordered version (I could have used u1-1400 instead of yy). Here is the code:

# Add AR1 noise to a sinusoid

i1=1:550; h=pi/40; s1=sin(i1*h);

e1=3*exp(-i1*0.2);

for (k in 1:3){ # Do it 3 times

M=z=i1*0; N=383;

for(i in 1:N){ # Looping over sites

z1=rnorm(600);

z2=filter(z1,e1,method="conv",sides=1,circular=T)

# z2 is the AR1 noise

j1=max(yy[i],1):550;

K=M[j1]=M[j1]+1;

z[j1]=z[j1]+(z2[j1]-z[j1])/K; # Averaging

}

jpeg(paste(c("sinew",k,".jpg"),collapse=""));

plot(1400+i1,z+s1,type="l"); # Output

lines(u1,1:383/100-2,col="red"); # Site numbers

lines(c(1400,1950),c(-2,-2),col="red");

lines(1400+i1,s1,col="green"); # Sinusoid

dev.off();

}