Comments on: Moberg #4: Lake Tsuolbmajavri

By: TCO

TCO — Sun, 11 Sep 2005 15:23:03 +0000

so what’s the implication of low frequency? Is it low noise? Why mention the term or reven move to the frequency domain at all. I mean it’s all data for a regression versus time, no? Do they actually think that there are periodic effects (waves) that are different from the noise?

By: Steve McIntyre

Steve McIntyre — Sun, 11 Sep 2005 15:04:14 +0000

These guys import signal-processing terms. High-frequency is rapid up and down fluctuations; low-frequency is long fluctuations. Whether these are “frequencies” in a Fourier sense or simply red noise is, as far as I’m concerned, an open question. If you have fractional processes, you get “power” at all frequencies.

You’re being energetic in browsing through these old posts. It’s nice to see that they’re not lost, since some of these older posts stand up pretty well.

By: TCO

TCO — Sun, 11 Sep 2005 14:54:44 +0000

What is a “low frequency” proxy?

By: Louis Hissink

Louis Hissink — Fri, 25 Feb 2005 11:21:43 +0000

Looking at the above graph and the comments “above average warming” when we are dealing variations of mean temperature within 0.5 Degree Celsius, is not what I would interpret as “warming” or “cooling” in a practical sense. We need to relate these data to human experierence, and temperature fluctuations of +/- 0.5 Deg. Celsius are imperceptible to the senses.

If we restrict the analysis to the data in hand, sure, there seems to be obvious trends but all within the resolution of a standard mercury thermometer?

I suspect our researchers have become lost in the forrest of data, forgetting that all science ultimately is used to explain human experience of reality. We cannot experience such thermal subtleties.

By: Michael Mayson

Michael Mayson — Mon, 21 Feb 2005 04:56:02 +0000

You are right about the Nyquist criterion. Perhaps by “only information at frequencies lower than the Nyquist frequency” they mean band limited? Is there anywhere I can view this paper?

By: Greg F

Greg F — Sat, 19 Feb 2005 15:56:19 +0000

From a sampled data point of view I see a number of potential problems with this paper. The following statement under the heading, "Averaging of calibrated low-resolution temperature indicators", is especially striking (NATURE - VOL 43 pg. 617). "Timescales of > 340 yr are long enough to ensure that only information at frequencies lower than the Nyquist frequency for the most poorly resolved proxy series are used." This statement is at odds with sampling theorem. The Nyquist criterion requires that signal of interest be band limited to less than half the sample rate. If the signal of interest is not band limited, and there are frequencies greater then or equal to the sampling rate, then aliasing occurs. For example, assume we are taking samples once every second (sample frequency 1Hz). Let us also assume the signal has not been band limited and we have a frequency of .9Hz present. This .9Hz component will result in an alias which will appear in the frequency spectrum between 0 and .5Hz, as a 0.1Hz signal. Also, a frequency of 0.6 Hz would result in a alias of 0.4 Hz. In other words, any frequencies component between .5 to 1 times the sample rate would be mirrored into the 0Hz to .5Hz frequency spectra. From 1 to 1.5 times the sample rate the frequency components would create aliases but would not be mirrored. A 1.1Hz component would appear as a 0.1Hz component. Frequencies from 1.5Hz to 2Hz would again mirror as did the frequencies in .5Hz to 1Hz band and so on. The key here, and the reason for the Nyquist limit, is that when aliasing occurs there is no way to distinguish an alias from a real signal. The simple fact is there is no way to remove the aliases, the signal is irreversibly corrupted. Their claim that they "ensure that only information at frequencies lower than the Nyquist frequency" is at odds with the sampling theorem and provably wrong.