o Signal and noise are uncorrelated.
o Signal strength is constant in the replicate measurements.
o Noise is random, with a mean of zero and constant variance in the replicate measurements.
http://en.wikipedia.org/wiki/Signal_averaging

Do you know that the above is true for treemometers?

By the way, in the imaging world, challenging low-signal images are made by characterizing the noise of the imager (make a suitably long exposure with no signal ie. with the lens cap on) and subtracting that noise from a suitably long real exposure.

In brief, I propose that Milankovitch not be tained by association with this amazing trick.

Instead, I suggest that it be called the Mannkovitch CO2 Bodge.

If I did that to bring station data in line with Oke’s theory about the relationship between population and UHI, you would scream bloody murder.
Don’t pretend you wouldn’t. Don’t pretend that you would let Willis or Anthony get away with this kind of bodge. Now, I don’t want to get into a debate about whether this is ethical or unethical. It’s not best practice and we deserve better science.

a) Did Briffa use his knowledge of the divergence between actual and reconstructed temperatures to develop an ad hoc correction factor for the MXD reconstruction? If so, Briffa is guilty of artificially manipulating the data to obtain a desired result. Everyone that has used his reconstruction has somewhat better validation statistics because of Briffa’s manipulations.

b) Did Briffa use the divergence between the TRW data and the MXD data to determine that a correction to the MXD data was necessary? In that case, Briffa has developed a legitimate improved method for reconstructing temperature using a combination of MXD and TRW data.

How can we tell which is the correct interpretation? That’s easy: what would you do if you thought you had invented an improved method? First, you’d certainly mention your improved methodology in the abstract and Briffa did not. Second, you’d try your new method on other data sets to see if it improved other reconstructions. By his own actions, Briffa tells us that the bodge was a one-time trick to reduce the divergence at one site, not a legitimate technique for improving reconstructions.

If Briffa had looked at both CE and RE, he might have found that TRW were inferior to MXD at reproducing annual temperature changes but superior for reproducing low frequency temperature change. If that were the case, he would have had a good reason for choosing the TRW data

TFP, your mistake is assuming you know the meaning of the buried signal. You say that if you take enough trees, the water and nutrient levels will “get reduced” but the temperature will not. Yet you provide no proof the remaining signal is temperature. And now we see that the supposedly “non temperature” data was simply removed.

Why is that a problem?

Let’s use your experiment as an example. You averaged a bunch of noisy photos and got a reasonably clear picture of one dimension (looks like Y in Y/Cr/Cb terms) of the potential signal. That assumes Y is the desired result, not Cr or Cb — presumably what we see of your final result is woefully lacking in chroma “signal.” It ALSO assumes you know what the “Y” picture should look like!

You were able to cheat: you knew to remove photos of spouse, kids, dog/cat etc. You knew what the final picture “should” look like. So, by manipulating the source, data, you were able to reproduce the result you desired.

What if you didn’t know the desired final result? You couldn’t remove those extra photos.

Even worse:
* what if the desired result was not in the Y dimension but rather in the chroma?
* what if what we are seeing is not Y but Cr or Cb — randomly? Your method doesn’t resolve this question.
* what if what we are seeing is something else altogether, perhaps an infrared image? Again, we can’t answer.

Bottom line: unless you know in advance the type of signal you seek, your method doesn’t work well.

[BTW, your method IS very powerful when the signal being sought is known. This is how cell phone GPS works -- it takes about a thousand very-noisy samples, merges them, and finds the faint GPS signal pattern in the mix. Far more sensitive than older GPS receiver technologies.]

thefordprefect
Posted Mar 31, 2011 at 8:40 PM |
….
Reports generated a decade ago are not necessarily fixed in stone more recent ideas/data can displace such ancient documents. Why are these constantly paraded before us?

Right on! Once these two reports, in Science and Reviews of Geophysics, have been retracted, we will no longer have to see them constantly paraded before us.