Ah, those at least three fundamental assumptions ..

But you need to be careful, MBH98:

(1) The indicators in our multiproxy trainee network are linearly related to one or more of the instrumental training patterns.

Maybe one or more are exclusive, IOW maybe the model assumes there is a linear dependence in the composite, not in the individual proxies.

This point cannot be emphasized strongly enough.

It’s also a point that folks like Schmidt and Mann seem to gloss over. Oddly, the tree-ring/temperature “linear relationship” is mentioned in MBH98, with a notation that “absent such a relationship, these results are meaningless” (paraphrased), yet nobody seems to care.

However, the signal to noise problem I was referring to was extracting the long term temperature change from the instrumental temperature record. While in theory it should be possible to correct the readings at each station for systematic errors, remove the high frequency noise by low pass filtering and increase the precision from +/- 0.5 degrees to a few millidegrees by averaging over a large number of stations, in practice it is not possible to achieve the necessary precision because the information to correct all the errors just isn’t available.

It’s not even +/- 0.5. According to GISS, it’s +/- 1. I think the problem is not one of “information just isn’t available,” it’s one of “we don’t know how much is available.” This a direct result of the unwillingness of interested parties to release their coveted data and methods.

Mark

The problem with the tree-rings, however, is not necessarily one of noise. It is actually one of attribution: nobody has ever definitively determined what each signal actually represents. PCA, ICA, MCA, regEM, etc., do not identify signals… a-priori knowledge must exist to assign the results to known signals. Said knowledge does not exist. In fact, recent studies (the only I’ve ever heard of) seem to indicate that temperature is not even one of the signals (in the case of the BCPs).

This point cannot be emphasized strongly enough. However, the signal to noise problem I was referring to was extracting the long term temperature change from the instrumental temperature record. While in theory it should be possible to correct the readings at each station for systematic errors, remove the high frequency noise by low pass filtering and increase the precision from +/- 0.5 degrees to a few millidegrees by averaging over a large number of stations, in practice it is not possible to achieve the necessary precision because the information to correct all the errors just isn’t available.

Mark, There is a limit to what you can accomplish with signal processing because any processing introduces new errors. At some point, it is not possible to recover even a known signal from the noise. I think this is basic conclusion of information theory.

There is always error associated with signal processing. Information theory simply puts a bound on the amount of information vs. amount of noise (ala Nyquist, for example). In the context we’re discussing, the “signals” are very slowly changing compared to the inherent noise, i.e. they have a much narrower bandwdith. Each additional observation (proxies), coupled with filtering (and decimation) serves to decrease the noise bandwidth to that of the signal, making detection more probable (note that there is always a probability of a false detection, as well as a probability of no detection).

The problem with the tree-rings, however, is not necessarily one of noise. It is actually one of attribution: nobody has ever definitively determined what each signal actually represents. PCA, ICA, MCA, regEM, etc., do not identify signals… a-priori knowledge must exist to assign the results to known signals. Said knowledge does not exist. In fact, recent studies (the only I’ve ever heard of) seem to indicate that temperature is not even one of the signals (in the case of the BCPs).

Mark

Mark, it depends on how you are thinking of the “signal”. It seems to me, you are suggesting the “signal” is the “growth rate” or some such of the tree. However, people who are using proxies in multi-proxy studies are treating the proxies as if there is a “temperature” signal in there somewhere (presumably along with a precipitation signal, a CO2 signal, a fertilizer signal, an insect strike signal, etc. etc.).

Actually, the growth rate is the “observation.” The “signal” would be temperature.

Mark

So my point is, given that they are trying to extract one of what is surely many signals in the proxy, how do they know they got the right one? Even worse, if they are making assumptions about the shape of the signal (e.g. that it’s a rising trend), then the proxies can no longer tell them whether temperature is rising or not – they’ve already assumed that as part of their signal search.

So, your point confirms mine. The GPS signal has *known* properties. Not guessed, not assumed, known. The “temperature” signal, from a proper neutral point of scientific interest, has no known properties. It’s those very properties that we’re trying to *determine* from the proxy. Going in there with a predetermined idea of what the signal is that we’re trying to extract, is not going to help us discover the properties of the signal. Now, there ARE some things we know about the temperature signal that we can use – such as its autocorrelation parameters, standard deviation, etc. – from what I can gather, those things tend to be fairly similar in temperature series. But the trend itself is what we’re trying to determine so we can’t start with any assumption about that.

So, to sum up, you can think of there being one signal, or many signals. If you think of there being one signal, then successfully extracting it does not necessarily give you temperature, as temperature is only one component of the total signal. If you think of there being multiple signals, how do you know which one you are extracting? And again, it comes back to the point that with GPS etc. despite the fact it may look like noise, we still know a lot about its properties, so that we can distinguish it from noise. We know far less about temperature signals – especially if we’re not going to even bother correlating the proxy to local temperature records.