Science Heresy - December 2010

Huybers and Curry (2006)

Reid (unpublished)

How Peer Review Fails

by John Reid

A detailed analysis of one reviewer's comments

My paper on Ice Ages was rejected by Journal of Climate. The original reviews can be downloaded here (A) and here (B). Below are my comments on Reviewer B’s review of my paper. My comments are in italics.

Review of "A re-examination of Ice Age Time Series" by J.S. Reid

In this manuscript, the author attempts to provide some new interpretation of ice ages using some basic time series techniques (FFT). The author's knowledge on climate as well as on time series analysis appear to be limited and sometimes flawed. The number of misconceptions that are present in this manuscript is quite remarkable. This manuscript has probably no scientific value and should not be published.

The author has a very strange point of view on deterministic, vs stochastic processes.

My “strange” point of view is described in more detail here

In contrast to the author's claim, it is simply not possible, in physics, to define a sharp distinction between the two, in particular from data analysis.


Mandic, D.P., M. Chen. T. Gautama, M.M. Van Hulle and A. Costantinides. (2008). “On the characterization of the deterministic / stochastic and linear / non-linear nature of time series”. Proc. R. Soc. 464, 1141 -1160. doi:10.1098/rspa.2007.0154 (

Any physical realisation of a stochastic process is actually a deterministic chaotic process.

Is this an a priori philosophical statement, part of the Reviewer’s belief system or is it founded in observation? If the latter I would appreciate a reference.

"Stochastic processes" are a mathematical notion, not a physical one. For instance, the random number generator of any computer is a deterministic algorithm very sensitive to initial condition (this is called chaos).

What a strange interpretation of the term “stochastic” which actually means “governed by the laws of probability”. Are we to believe that the equations of statistical physics, e.g. the Fokker-Planck equation, are purely mathematical?

A contrario, it is very easy to design mathematical stochastic processes with very nice spectral peaks (for instance, AR(n) processes when n>1).

Agreed. It is impossible, experimentally, to detect the difference between a narrow band AR(2) process and a sine wave plus added noise. Mathematically the difference is that in the first case the auto-covariance function tends to zero at infinite lag and this is not something that can always be decided experimentally from a time series of finite length.

So any attempt to discuss "stochasticity vs. determinism" by simply looking at the spectrum is completely meaningless. The distinction between the two is always a matter of taste, and not a fundamental one.

So does God play dice with the Universe? Einstein seemed to think it was fairly fundamental.

I believe the author should read some textbook on this subject before writing a scientific paper.

See below.

Furthermore, in practice, the "continuous or discrete" nature of a spectrum is linked to the hypothesis made on the time series at infinity (is it a finite time series or a periodic one). This is always an assumption, not a result. So it is not possible to distinguish a "continuous spectrum" from a "discontinuous" one from data analysis. This is of course particularly true when the data series is short, as often in paleoclimatic situations (we are dealing here with a 100 kyr periodicity on a 400 kyr time series ! There is no chance to find out if this is "periodic" or "pure chance").

Perhaps the Reviewer could propose an alternative, deterministic model which leads to the observed n=-2 power law spectrum.

The whole discussion pages 6 to 8 is completely meaningless.

If the Reviewer cannot understand the arguments presented he should not have agreed to review the paper in the first place.

A list of several other MAJOR flaws of this manuscript: - FFT (or any fourier transform algorithm) is not a suitable algorithm for spectral analysis. This problem is actually THE central problem of spectral analysis (again, please look at a basic textbook on this subject) since it is too unstable... Statistically significant spectra require some "spectral smoothing" using one or another technique. Blackman-Tukey is one of them.

This is the most revealing statement in this review. Blackman and Tukey (1959) “The Measurement of Power Spectra from the point of view of Communications Engineering.”(B&T) is an early text book in the field of signal processing. It predates the computer age and describes a crude but computationally efficient method for computing power spectra with a hand calculator. The resulting spectral estimates are highly distorted by the process.

Signal processing engineers are concerned largely with the suppression of side-lobes in antennas and electronic circuitry and this book goes to great lengths in describing how to do this. Since that time ever more sophisticated techniques have been developed for this purpose, most recently the computationally intensive multi-taper method (MTM).

However signal processing and time series analysis are not the same thing. In signal processing, ample data are available and the objective is usually to filter these data as cleanly as possible. In time series analysis, the objective is to test a relatively small amount of data against a null hypothesis.

In this case, it is vital that data processing be kept as simple as possible so that assumptions made about the distribution of variables can be justified. While it was good enough for signal processing in its earliest days, the intentional blurring or smoothing of data by the B&T process has never been good statistical practice for time series analysis.

It is more than a bit awkward to state that FFT (Cooley et al. 1965) is a recent technique of spectral analysis (which is actually not the case), when many recent papers have proposed new (true spectral analysis) ones (MTM, SSA, ...). Spectral analysis is a bit more than a Fourier transform.

Well at least the FFT is slightly more recent than B&T. The idea that the FFT “is not a suitable tool for spectral analysis .. because it is too unstable” has also been around since the 1960’s. I cannot find an original reference to this idea. Perhaps it is a tea-room myth rather than a peer-reviewed hypothesis. In any case it is incorrect. The term “unstable” comes from signal processing.

Presumably what is meant is that a spectral estimate derived from the FFT is not a consistent estimator of the population value. A consistent estimator is one which converges, i.e. one which gets less and less noisy as the sample size increases. The mean of a sample is an example of a consistent estimator because it gets closer and closer to the "true" mean as the sample size increases.

This argument goes as follows: a white noise process, one in which all terms are statistically independent, has a Fourier transform in which all the real and imaginary parts of all the positive frequency components are also independent and can be assumed to be Gaussian. So when we square and add the real and imaginary parts of each ordinate to form the spectral estimate, the latter has a chi-squared distribution with 2 degrees of freedom. Hence as we increase N, the length of the time series sample, the spectral estimate at any given frequency still has 2 degrees of freedom and so does not converge. The spectral estimate remains very noisy as N increases. Therefore the FFT spectral estimator is not consistent; it is "unstable".

This argument is incorrect for the following reason:

The length, N, of a sample time series is the dimension.

It is not the sample size.

The sample size is one.

An ensemble of M independent sample time series, all of the same length and all from the same population, can be envisaged. Now estimate the FFT spectrum for each time series and take the mean of the M values at each frequency. These mean values will each have a chi squared distribution with 2M degrees of freedom and so will converge as M increases.

Therefore the FFT spectral estimate is a consistent estimator.

Typically we assume the original time series to be white, as the null hypothesis. Then any peak whose chi-squared probability exceeds some predetermined value can be judged as significant under the null hypothesis. We can also test the spectral estimate as a whole using the Kolmogorov-Smirnov test.

Reviewer B does not appear to understand these basic concepts of statistical inference.

- Any "whitening" technique is usually strongly discouraged in textbooks, because it lowers considerably the signal to noise ratio when applied to "red type" spectra. In other terms, the author assumes that the "redness" of the spectrum is of a noisy nature and should be removed.

An inverse square law red spectrum is the outcome of integrating a white noise process. If the original process includes a cyclic component which was added prior to integration then whitening by taking first differences is a sensible thing to do. If, on the other hand, the cyclic components were added after the integration then it would be incorrect to attenuate these components by differencing.

The appearance of the original spectral estimates indicate that the former was most likely the case; the cyclic components, if any, are so immersed in the red spectrum it seems unlikely they were added after integration. Furthermore the role of ice sheet dynamics in the Milankovic theory implies that orbital forcing would occur prior to integration.

Most geophysical time series analysis are envisioned the opposite way: the signal is in the red part of the spectrum, because we are not dealing with perfectly periodic signals.

- This leads to another major misconception of the author that climate should be a perfect periodic oscillator (the author is looking for spectral sharp features). There is no reason that it should be so. In physics, spectral lines are coming naturally out of linear systems (where periodicities are the eigenvalues of the dynamical matrix) but not necessarily out of non linear systems.

Yes, the thrust of the paper is to place an upper limit on periodic signals which should be evident in the spectra if the Milankovic hypothesis is correct.

All current models of glacial-interglacial cycles are non linear (and even strongly non-linear). Their spectral response is usually not "sharp" but is often quite "redish", in particular when the time window is as short as 400 kyr which is not sufficient to resolve potential fine structures in the spectrum. In practice, fine structures are meaningless for non-stationary signals.

So Reviewer B is saying that even if orbital forcing were true, we would not expect to find evidence for it in the data because of the non-stationarity of the process and the non-linearity of proposed mechanisms.

A cyclical signal forcing a non-linear system does not give rise to a background continuum as the Reviewer appears to believe. Spectral lines due to the original signal would continue to be present in the output along with new spectral lines at harmonics of the original frequency. The mixer of a super heterodyne receiver is a good example.

I therefore do not understand the author's desire to isolate these spectral lines, that are probably non existent and certainly not relevant.

The absence of spectral lines representing cyclical forcing of climate is highly relevant. It is called "hypothesis testing". It is an important aspect of the scientific method.

Again, an AR(2) process can also be described as a "deterministic" oscillator in some circumstances since there is already some physics into it (two time constants).

What on earth is he talking about? An autoregressive process is a stochastic process by definition.

In contrast to the author's view, Physics does extend beyond linear systems and simple linear techniques can be misleading. - there is a clear misunderstanding of the paleoclimatic records as highlighted by the 10Be discussion.

The fact that the 10Be record has some similarities with the temperature record is most likely due to the recording process itself. If the zeroth order "correction" to obtain a flux from a concentration measurement is indeed to divide by the accumulation (this is actually not a correction but just a requirement from physical dimensionality), this does not garantee that there is no other climatic influence on the resulting 10Be flux record. There are many reasons for that. For instance, the Beryllium deposition is influenced by atmospheric circulation, by stratosphere-troposphere exchanges, by the water cycle and many other processes linked to climate. Assuming that the 10Be flux record is a pure extraterrestrial signal is likely to appear a bit naïve in the paleoclimatic community. A similar comment could be made on the time scales of the records, or more generally on their physical interpretation. These signals are noisy and not dated with perfect accuracy.

Granted 10Be flux can be influenced by climate, and perhaps I should have made mention of that, but that does not explain why the 10Be flux is well correlated with Dansgaard-Oeschger events between 20 and 40 ky BP, but not with the most recent termination and the Younger Dryas between 10 and 15 ky BP as seen in my Figure 7 (below)

- it is quite well known within the climate community that there is no simple relationship between the insolation forcing and the glacial-interglacial cycles. This "finding" of the author is not really a news. The litterature on the subject is vast. It strikes me that, except for the data sources, the references given by the author are quite old (about 10 to 20 years old). Apparently, the author is not up to date on the litterature on the subject. The most recent cited paper concerning the dynamics of glacial cycles is Milankovitch (1941)...

I thought it appropriate to reference the scientist who first proposed the theory. This was the earliest reference I could find although I believe Milankovic thought of it as early as 1912.

My failure to cite more recent references is easily remedied. A useful list was proposed by Reviewer A. Of interest are the papers by Wunsch (2003, 2004) whose views on the insignificance of orbital forcing are similar to those presented here. Wunsch's ideas are not widely known outside the "climate community". Had I heard of them earlier I may not have proceeded with this paper. As it is, my paper augments the work of Wunsch, particularly with regard to the 10Be flux.

- it seems very strange that the slope of the red spectrum is "exactly" -2.

According to other authors who have performed similar analysis (eg. Huybers and Curry, Nature, 2006, cf Fig.2), it should be about -1.64±0.04. This is significantly different from a red noise slope of -2, and this points to the fact that it is likely to be a non linear signal, ie. something significantly different from a noise that should be remove in the analysis...

The -2 slope is a theoretical preconception of the author that the data is a red noise..

The -2 slope is an experimental result, not a preconception. It can clearly be seen in the spectral estimate in Figure 2 of my paper (top of page, right).

It is very strong evidence that ice age climate variations are a random walk stochastic process.

Huybers and Curry fitted straight lines to their log spectra only for periods shorter than 15,000 years, “to minimize the influence of the Milankovic bands” (top of page,left). In doing so, they intentionally avoided the frequency range in which orbital forcing is supposed to occur. Their spectra in the Milankovic range in their diagram are similar to my own. All they had to do was look and they would have arrived at the same conclusion as I did.

It was staring them in the face! Why did THEY choose not to examine the Milankovic bands? Whose preconceptions are we talking about here?

The -1.64 slope is a result that points to non-linear dynamics.

How exactly? Has anyone proposed a non-linear model which predicts such a power law? If so there is no reference to it in Huybers and Curry’s paper.

I could add many more points that indicate why this manuscript is not suitable for a publication in Journal of Climate, but I will stop here. In summary, there is no new scientific content in this manuscript, the authors is not mastering the question he is trying to address, and the conclusions are either obvious or wrong.

"And he is not one of us."

A pdf version of this page can be found here.

December 2010