# Riding a Pseudocycle

Guest Post by Willis Eschenbach

Loehle and Scafetta recently posted a piece on decomposing the HadCRUT3 temperature record into a couple of component cycles plus a trend. I disagreed with their analysis on a variety of grounds. In the process, I was reminded of work I had done a few years ago using what is called “Periodicity Analysis” (PDF).

A couple of centuries ago, a gentleman named Fourier showed that any signal could be uniquely decomposed into a number of sine waves with different periods. Fourier analysis has been a mainstay analytical tool since that time. It allows us to detect any underlying regular sinusoidal cycles in a chaotic signal.

Figure 1. Joseph Fourier, looking like the world’s happiest mathematician

While Fourier analysis is very useful, it has a few shortcomings. First, it can only extract sinusoidal signals. Second, although it has good resolution as short timescales, it has poor resolution at the longer timescales. For many kinds of cyclical analysis, I prefer periodicity analysis.

So how does periodicity analysis work? The citation above gives a very technical description of the process, and it’s where I learned how to do periodicity analysis. Let me attempt to give a simpler description, although I recommend the citation for mathematicians.

Periodicity analysis breaks down a signal into cycles, but not sinusoidal cycles. It does so by directly averaging the data itself, so that it shows the actual cycles rather than theoretical cycles.

For example, suppose that we want to find the actual cycle of length two in a given dataset. We can do it by numbering the data points in order, and then dividing them into odd- and even-numbered data points. If we average all of the odd data points, and we average all of the even data, it will give us the average cycle of length two in the data. Here is what we get when we apply that procedure to the HadCRUT3 dataset:

Figure 2. Periodicity in the HadCRUT3 global surface temperature dataset, with a cycle length of 2. The cycle has been extended to be as long as the original dataset.

As you might imagine for a cycle of length 2, it is a simple zigzag. The amplitude is quite small, only plus/minus a hundredth of a degree. So we can conclude that there is only a tiny cycle of length two in the HadCRUT3.

Next, here is the same analysis, but with a cycle length of four. To do the analysis, we number the dataset in order with a cycle of four, i.e. “1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4 …”

Then we average all the “ones” together, and all of the twos and the threes and the fours. When we plot these out, we see the following pattern:

Figure 3. Periodicity in the HadCRUT3 global surface temperature dataset, with a cycle length of 4. The cycle has been extended to be as long as the original dataset.

As I mentioned above, we are not reducing the dataset to sinusoidal (sine wave shaped) cycles. Instead, we are determining the actual cycles in the dataset. This becomes more evident when we look at say the twenty year cycle:

Figure 4. Periodicity in the HadCRUT3 dataset, with a cycle length of 20. The cycle has been extended to be as long as the original dataset.

Note that the actual 20 year cycle is not sinusoidal. Instead, it rises quite sharply, and then decays slowly.

Now, as you can see from the three examples above, the amplitudes of the various length cycles are quite different. If we set the mean (average) of the original data to zero, we can measure the power in the cyclical underlying signals as the sum of the absolute values of the signal data. It is useful to compare this power value to the total power in the original signal. If we do this at all possible frequencies, we get a graph of the strength of each of the underlying cycles.

For example, suppose we are looking at a simple sine wave with a period of 24 years. Figure 5 shows the sine wave, along with periodicity analysis in blue showing the power in each of the various length cycles:

Figure 5. A sine wave, along with the periodicity analysis of all cycles up to half the length of the dataset.

Looking at Figure 5, we can see one clear difference between Fourier analysis and periodicity analysis — the periodicity analysis shows peaks at 24, 48, and 72 years, while a Fourier analysis of the same data would only show the 24-year cycle. Of course, the apparent 48 and 72 year peaks are merely a result of the 24 year cycle. Note also that the shortest length peak (24 years) is sharper than the longest length (72-year) peak. This is because there are fewer data points to measure and average when we are dealing with longer time spans, so the sharp peaks tend to broaden with increasing cycle length.

To move to a more interesting example relevant to the Loehle/Scafetta paper, consider the barycentric cycle of the sun. The sun rotates around the center of mass of the solar system. As it rotates, it speeds up and slows down because of the varying pull of the planets. What are the underlying cycles?

We can use periodicity analysis to find the cycles that have the most effect on the barycentric velocity. Figure 6 shows the process, step by step:

Figure 6. Periodicity analysis of the annual barycentric velocity data.

The top row shows the barycentric data on the left, along with the amount of power in cycles of various lengths on the right in blue. The periodicity diagram at the top right shows that the overwhelming majority of the power in the barycentric data comes from a ~20 year cycle. It also demonstrates what we saw above, the spreading of the peaks of the signal at longer time periods because of the decreasing amount of data.

The second row left panel shows the signal that is left once we subtract out the 20-year cycle from the barycentric data. The periodicity diagram on the second row right shows that after we remove the 20-year cycle, the maximum amount of power is in the 83 year cycle. So as before, we remove that 83-year cycle.

Once that is done, the third row right panel shows that there is a clear 19-year cycle (visible as peaks at 19, 38, 57, and 76 years. This cycle may be a result of the fact that the “20-year cycle” is actually slightly less than 20 years). When that 19-year cycle is removed, there is a 13-year cycle visible at 13, 26, 39 years etc. And once that 13-year cycle is removed … well, there’s not much left at all.

The bottom left panel shows the original barycentric data in black, and the reconstruction made by adding just these four cycles of different lengths is shown in blue. As you can see, these four cycles are sufficient to reconstruct the barycentric data quite closely. This shows that we’ve done a valid deconstruction of the original data.

Now, what does all of this have to do with the Loehle/Scafetta paper? Well, two things. First, in the discussion on that thread I had said that I thought that the 60 year cycle that Loehle/Scafetta said was in the barycentric data was very weak. As the analysis above shows, the barycentric data does not have any kind of strong 60-year underlying cycle. Loehle/Scafetta claimed that there were ~ 20-year and ~ 60-year cycles in both the solar barycentric data and the surface temperature data. I find no such 60-year cycle in the barycentric data.

However, that’s not what I set out to investigate. I started all of this because I thought that the analysis of random red-noise datasets might show spurious cycles. So I made up some random red-noise datasets the same length as the HadCRUT3 annual temperature records (158 years), and I checked to see if they contained what look like cycles.

A “red-noise” dataset is one which is “auto-correlated”. In a temperature dataset, auto-correlated means that todays temperature depends in part on yesterday’s temperature. One kind of red-noise data is created by what are called “ARMA” processes. “AR” stands for “auto-regressive”, and “MA” stands for “moving average”. This kind of random noise is very similar observational datasets such as the HadCRUT3 dataset.

So, I made up a couple dozen random ARMA “pseudo-temperature” datasets using the AR and MA values calculated from the HadCRUT3 dataset, and I ran a periodicity analysis on each of the pseudo-temperature datasets to see what kinds of cycles they contained. Figure 6 shows eight of the two dozen random pseudo-temperature datasets in black, along with the corresponding periodicity analysis of the power in various cycles in blue to the right of the graph of the dataset:

Figure 6. Pseudo-temperature datasets (black lines) and their associated periodicity (blue circles). All pseudo-temperature datasets have been detrended.

Note that all of these pseudo-temperature datasets have some kind of apparent underlying cycles, as shown by the peaks in the periodicity analyses in blue on the right. But because they are purely random data, these are only pseudo-cycles, not real underlying cycles. Despite being clearly visible in the data and in the periodicity analyses, the cycles are an artifact of the auto-correlation of the datasets.

So for example random set 1 shows a strong cycle of about 42 years. Random set 6 shows two strong cycles, of about 38 and 65 years. Random set 17 shows a strong ~ 45-year cycle, and a weaker cycle around 20 years or so. We see this same pattern in all eight of the pseudo-temperature datasets, with random set 20 having cycles at 22 and 44 years, and random set 21 having a 60-year cycle and weak smaller cycles.

That is the main problem with the Loehle/Scafetta paper. While they do in fact find cycles in the HadCRUT3 data, the cycles are neither stronger nor more apparent than the cycles in the random datasets above. In other words, there is no indication at all that the HadCRUT3 dataset has any kind of significant multi-decadal cycles.

How do I know that?

Well, one of the datasets shown in Figure 6 above is actually not a random dataset. It is the HadCRUT3 surface temperature dataset itself … and it is indistinguishable from the truly random datasets in terms of its underlying cycles. All of them have visible cycles, it’s true, in some cases strong cycles … but they don’t mean anything.

w.

APPENDIX:

I did the work in the R computer language. Here’s the code, giving the “periods” function which does the periodicity function calculations. I’m not that fluent in R, it’s about the eighth computer language I’ve learned, so it might be kinda klutzy.

#FUNCTIONS

PI=4*atan(1) # value of pi

dsin=function(x) sin(PI*x/180) # sine function for degrees

regb =function(x) {lm(x~c(1:length(x)))[[1]][[1]]} #gives the intercept of the trend line

regm =function(x) {lm(x~c(1:length(x)))[[1]][[2]]} #gives the slope of the trend line

detrend = function(x){ #detrends a line

x-(regm(x)*c(1:length(x))+regb(x))

}

meanbyrow=function(modline,x){ #returns a full length repetition of the underlying cycle means

rep(tapply(x,modline,mean),length.out=length(x))

}

countbyrow=function(modline,x){ #returns a full length repetition of the underlying cycle number of datapoints N

rep(tapply(x,modline,length),length.out=length(x))

}

sdbyrow=function(modline,x){ #returns a full length repetition of the underlying cycle standard deviations

rep(tapply(x,modline,sd),length.out=length(x))

}

normmatrix=function(x) sum(abs(x)) #returns the norm of the dataset, which is proportional to the power in the signal

# Function “periods” (below) is the main function that calculates the percentage of power in each of the cycles. It takes as input the data being analyzed (inputx). It displays the strength of each cycle. It returns a list of the power of the cycles (vals), along with the means (means), numner of datapoints N (count), and standard deviations (sds).

# There’s probably an easier way to do this, I’ve used a brute force method. It’s slow on big datasets

periods=function(inputx,detrendit=TRUE,doplot=TRUE,val_lim=1/2) {

x=inputx

if (detrendit==TRUE) x=detrend(as.vector(inputx))

xlen=length(x)

modmatrix=matrix(NA, xlen,xlen)

modmatrix=matrix(mod((col(modmatrix)-1),row(modmatrix)),xlen,xlen)

countmatrix=aperm(apply(modmatrix,1,countbyrow,x))

meanmatrix=aperm(apply(modmatrix,1,meanbyrow,x))

sdmatrix=aperm(apply(modmatrix,1,sdbyrow,x))

xpower=normmatrix(x)

powerlist=apply(meanmatrix,1,normmatrix)/xpower

plotlist=powerlist[1:(length(powerlist)*val_lim)]

if (doplot) plot(plotlist,ylim=c(0,1),ylab=”% of total power”,xlab=”Cycle Length (yrs)”,col=”blue”)

invisible(list(vals=powerlist,means=meanmatrix,count=countmatrix,sds=sdmatrix))

}

# /////////////////////////// END OF FUNCTIONS

# TEST

# each row in the values returned represents a different period length.

myreturn=periods(c(1,2,1,4,1,2,1,8,1,2,2,4,1,2,1,8,6,5))

myreturn\$vals

myreturn\$means

myreturn\$sds

myreturn\$count

#ARIMA pseudotemps

# note that they are standardized to a mean of zero and a standard deviation of 0.2546, which is the standard deviation of the HadCRUT3 dataset.

# each row is a pseudotemperature record

instances=24 # number of records

instlength=158 # length of each record

rand1=matrix(arima.sim(list(order=c(1,0,1), ar=.9673,ma=-.4591),

n=instances*instlength),instlength,instances) #create pseudotemps

pseudotemps =(rand1-mean(rand1))*.2546/sd(rand1)

# Periodicity analysis of simple sine wave

par(mfrow=c(1,2),mai=c(.8,.8,.2,.2)*.8,mgp=c(2,1,0)) # split window

sintest=dsin((0:157)*15)# sine function

plotx=sintest

plot(detrend(plotx)~c(1850:2007),type=”l”,ylab= “24 year sine wave”,xlab=”Year”)

myperiod=periods(plotx)

Article Rating
Inline Feedbacks
Andrew Marvell
July 30, 2011 2:01 am
Ed Zuiderwijk
July 30, 2011 2:05 am

Have a look into wavelet analysis.

stephen richards
July 30, 2011 2:26 am

Good stuff Willis. I did fourier and laplasse functions many years ago. You have explained this particular use as well as anyone I remember.

Katherine
July 30, 2011 2:40 am

Willis, thanks for making this easy for a layperson to follow. Food for thought, indeed.
Just one thing. You wrote: Note also that the shortest length peak (24 years) is sharper than the longest length (72-year) peak. This is because there are fewer data points to measure and average when we are dealing with longer time spans, so the sharp peaks tend to broaden with increasing cycle length.
But later you wrote: It also demonstrates what we saw above, the spreading of the peaks of the signal at longer time periods because of the decreasing amount of data.
Based on the former, I think the latter should be “It also demonstrates what we saw above, the spreading of the peaks of the signal at longer time periods because of the increasing amount of data.”

Sean Houlihane
July 30, 2011 2:40 am

Numerology? Why? – your graphs of cycles have ZERO basis to have the original time scale applied under them. Sorry, but it appears that you don’t understand the analysis you are doing here and that doesn’t inspire to try and work out what your point is.

oMan
July 30, 2011 3:00 am

Very clear and informative. Thanks much. As a layman, I appreciate this mini-tutorial, which shows a powerful analytic tool and a reminder of how easily our eyes and mind find patterns, only some of which are really there.

July 30, 2011 3:12 am

You appear to have used a mathematical algorithm to generate the random data. Is it not possible that there is an element of non-randomness here, which is why you see the periods you do?
I’d be more likely to be convinced if you had used truly random data. Why not grab some datasets here and run the tests again: http://www.random.org/

Editor
July 30, 2011 3:25 am

Willis – do you have anything in your toolbox that would handle cycles of varying length, such as the solar cycle or the PDO?

commieBob
July 30, 2011 3:30 am

The practical use of Fourier Analysis has a really nasty problem that most people aren’t aware of. It is called spectral leakage and it isn’t dealt with in many/most digital signal processing texts. The fact that the dataset is necessarily truncated produces spurious frequencies and the result is that the analysis can be complete garbage. A time series of fewer that 200 data points (one for each year) is a problem. You will see frequencies that aren’t there and may miss important frequencies because of spectral leakage. A good reference is The Scientist and Engineer’s Guide to Digital Signal Processing By Steven W. Smith, Ph.D. http://www.dspguide.com/pdfbook.htm It is written with the idea that you might actually want to do some digital signal processing and deals with the gotchas that will probably bite you if you don’t know about them.
The fact that Fourier Analysis finds sine waves isn’t a problem. A sine wave is is the basic unit of oscillation. It isn’t theoretical, it is really there. Any other repeating waveform can be broken down to its component sine waves. If my spectrometer tells me that a frequency exists, I can tune into that frequency with a radio and find that it does indeed exist.

Stephen Wilde
July 30, 2011 3:53 am

That seems to be a mathematical way of showing that the cycles we think we see in the historical records and the proxies are not ‘significant’.
But does that matter?
On human timescales the changes that appear to arise from apparent climate cycling are real and in the past have led to the rise and fall of civilisations.
From our perspective there is enough ‘significance’ in those allegedly spurious cycles to give us a degree of predictive ability albeit within a wide range and albeit not guaranteed.
Thus if the sun gets a bit less active the vertical temperature profile of the atmosphere changes with effects on surface pressure distribution and likewise but from the bottom up when ocean surfaces are in heat releasing mode.
So who cares about statistical exercises when the linkages are so apparent?

Richard Saumarez
July 30, 2011 3:54 am

The peak at 60+ period is almost certainly a function of record length,which appears to be 130 years from your plots. This is a well known problem in any orthogonal, or non-orthogal transform and there are well-known ways of eliminating it.
Since the periodic transform uses a non-orthogonal basis set, the physical interpretation of the periodicities is difficult. To decompose a signal into a limited set of non-orthogonal basis functions and then reconstruct it (with some error presumably) tells us nothing about the signal. The PT is closely related to frequency domain template matching, where phase dependence can be specified, appears to give better understanding to structure of the signal.
Your thesis is that a 60 year periodicity in the HADCRUT data is an artefact of the processing methods. I am not convinced that you have done this correctly and I would be interested to see the results of more established methods, applied correctly, to your data set. If there is a 60 year periodity in the data, it should be possible to establish this, although the statistical significance is likely to be low as it is only twice the fundamental frequency of the data. Since you have appeared to use an ensemble of the HADCRUT data, a stratified approach may yield more information.

Robert of Ottawa
July 30, 2011 3:59 am

Willis Eschenbach says:
July 30, 2011 at 3:24 am
It looks like cycles … but it’s not.
Which was the whole point of the article I believe. The human mind looks for patterns where there are not necessailry any – both a gift and curse.

July 30, 2011 4:02 am

Willis Eschenbach says:
July 30, 2011 at 3:24 am

Fair enough, and thanks for the explanation.

Henry
July 30, 2011 4:18 am

Willis. You seem to be use “mod”, possibly from the matlab package. You might find “%/%” does integer division.

Kasuha
July 30, 2011 4:21 am

This is very impressive analysis and explanation, many thanks for it.
I wonder what fits would it make if the periodicity analysis was extended into non-integer domain (i.e. to cover also periods like 19.7 etc)

R. de Haan
July 30, 2011 4:22 am

Great article.
Looking forward to a response from Loehle and Scafetta here at WUWT.

Nick Stokes
July 30, 2011 4:26 am

Willis,
I think the problem here is that you are dealing with non-orthogonal functions, and seeking to partition the power between them. In Fourier analysis you can do that, because of orthogonality, but without, you can’t.
The power of the sum of two frequencies, v1 and v2, say, is (v1+v2)^2. And this adds as v1^2 and v2^2 only if the average power in the product v1*v2 is zero – orthogonality.
You might like to check Ed Z’s comment. I think what you are describing is a fast wavelet transform, which works by repeated doubling of the interval length.
What’s in a name? Just that wavelet transforms are very popular, and there is a stack of R packages to help. Eg wavelets.
I note that your IEEE paper anticipates that and points out that their version doubles the period rather than the frequency. But with the fast transform based on doubling, this is just looking at the same sequence in reverse.

July 30, 2011 4:33 am

Willis, my (limited) understanding of the limitations of average global atmospheric temperature data sets seems that they might not be very representative of real natural processes. I wonder what might happen if you apply the same technique to say the CET data set? I would attempt it myself, however, I suspect it would take me much longer than you… you seem to have the tools at your fingertips and neurons to spare :-).

David
July 30, 2011 4:43 am

The ‘drunkards walk’ is Brownian motion isn’t it? Or a random walk. A stock price can be said to follow such a motion (chartists may disagree – not too may wealthy chartists).

Katherine
July 30, 2011 5:01 am

As you can see, increasing the cycle length decreases the amount of data available to average for each point in the cycle.
I see. Thanks for the clarification.

polistra
July 30, 2011 5:15 am

When I worked in speech research I used a similar brute force method in analyzing voice waves to locate glottal jitter. Fourier doesn’t work well on these waves because the basic pulse is NOT sinusoidal. Contrary to an earlier comment, the sine wave is not “always there”, it’s always an artifact of Fourier. In a semi-coupled system like the glottis and articulators, Fourier generates a lot of ‘frequencies’ that simply aren’t part of the real process. They only get in the way of a meaningful analysis.
As I recall (25 years later), my algorithm was fairly close to an LPC method, though I didn’t start out trying to implement LPC. Most good speech analysis uses LPC in one way or another.

Jeff L
July 30, 2011 5:20 am

Willis,
Could you post a picture of the auto correlation of your random data sets & the real data set & use those plots to show the difference between a “real” signal & an artifact? TIA

Steve McIntyre
July 30, 2011 5:28 am

Willis, I also dislike attempts to find wave patterns in series that are almost certainly red noise. Your reference to Sethares and Staley looks interesting. Since Sethares and Staley refer to wavelet transforms, I presume that (contra Nick Stokes) their methodology has considered wavelet methods, though I am not in a position right now to comment on whether Sethares and Staley’s method is a useful improvement on wavelets or not.

Jeff L
July 30, 2011 5:35 am

Another thing for readers to understand is that a Fourier transform is a technique to visualize data in a different domain – there is nothing inherently wrong with it, regardless of the nature of the signal that is being transformed. It is a fully reversible process (ie you can transform any time domain dataset into the frequency domain & take any frequency domain dataset back to the time domain without losing any information). The real issue here is how you interpret the results of that transformation / analysis.

Don K
July 30, 2011 5:52 am

1. As I understand it, Any “waveform” including digitized random pencil squiggles has a Fourier transform into the frequency domain that exactly reproduces the waveform. Therefore the fact that cycles appear when the data is subjected to Fourier analysis really doesn’t prove anything. I’m not 100% sure of that, and the underlying math is pretty intimidating to those of us to whom equations do not speak with a loud, clear voice. But I think that one really needs to show physical phenomena with appropriate phase and amplitude to back up Fourier decomposition. The same probably holds true for Periodocity analysis?
2. commieBob on spectral leakage. I was aware that spurious cycles appear due to data set truncation. But I thought they were mostly high frequency cycles and could be removed by low pass filtering or simply ignored in most cases. Am I wrong about that also?
3. CommieBob on whether Fourier’s dependence on sine(/cosine) waves is a problem. Well, yes, you’ll see the components if you do a spectral scan so they are sort of “real”. But it’s not so clear that someone looking for a physical cause for a periodic phenomenon is going to get all that much information from the sine waves if the actual waveform is a square wave or sawtooth or some other arbitrary shape.
4. Derek Sorenson and Willis on randomness. Both right but talking past each other? Willis almost certainly correct that you need to mimic autocorrelation by using red noise. But Derek is probably correct that — at least in concept — the red noise needs to be based on truly random values — white noise — not computer generated pseudo-random numbers. In practice, I think that pseudo-random numbers might be good enough. And all that assumes that red noise is generated by some sort of transformation on an input purportedly random data set. I don’t have the slightest idea how it is actually generated.

Ninderthana
July 30, 2011 5:57 am

Willis Eschenbach,
A very impressive technique but I must take you up on one point. There is a very strong underlying physical reason for a 60 year cycle in the Barycentre motion.
If you were considering speed and not velocity then I would not dispute your identification of a 20 year cycle but NO 60 year cycle. The speed of the Sun about the centre-of- mass of the Solar System is primarily modulated by the alignments of Jupiter and Saturn every 19.858 years. However, if you are considering the Sun’s velocity (i.e. the Sun’s speed and velocity of the Sun about the centre-of-mass of the Solar System) then this roughly repeats every 59.574 (= 19.858 x 3) years.
This is caused by the fact that the Sun completes one loop around the barycentre roughly once every every 20 years, However, the axis of alignment of the orbital loop (about the barycentre) advances by 120 degrees with each completed orbit. This means that the Sun must complete three twenty year orbits for it to return to roughly same position with respect to the distant stars.
Given that Loehle and Scafetta are claiming that planetary forces are somehow playing an indirect role in influencing the Earth’s climate, this influence would have to synchronized with the forces involved. This means that they would have to search for both the 20 year periodicity related to the Sun barycentric speed, and the 60 year periodicity associated with the Sun’s barycentric velocity.
This shows that it is important to consider the underlying physical principles when you are using periodicity analysis otherwise you might come to the wrong conclusion.
I agree that Loehle and Scafetta should have given the statistical significance of the periodicities that they found in the HADCRUT data compared to AR(1) red-noise. They should have used Singular Spectral Analysis with Monte Carlo trials to test the statistical significance of their results.

A physicist
July 30, 2011 6:13 am

Anthony,
As a professional scientist I have to correct this statement you make:
“First, it can only extract sinusoidal signals. Second, although it has good resolution as short timescales, it has poor resolution at the longer timescales. ”
This statement is, unfortunately, incorrect. Mathematically, Fourier expansion/analysis has shown to be complete expansion: Any function can be expanded in an infinite series of sinusoidal functions. If the periodic function of period T is NOT sinusoidal, then this periodicity can be seen in the Fourier expansion coefficient of terms which has period T. T/2, T/3, T/4, ….. . All those terms have a period of T after 1,2,3,4, … repetitions. Resolution wise – it depends on HOW many terms included in the expansion. You can include as far as T/100 or T/1000 to get bettter resolution. Of course, computation wise this is costly. Of course, it is DIFFICULT / IMPOSSIBLE to find a periodic signal in the data with period longer than the total duration of the recorded data/signal (If the data is only recorded for 1000 years, there is no way to find a periodic behavior with period longer than 1000 years, even larger than 500 years).
[You are mistaken about the author of the statement you quoted. ~dbs, mod.]

John Day
July 30, 2011 6:24 am

Hi Willis,
A very interesting presentation, applying an idea that was originally intended for another domain (music, Sethares, the inventor of this technique is a music theory expert). This kind of ‘idea recycling’ is often very rewarding, especially older ideas that initially failed, maybe due to lack of computation resources, and blossom when reexamined when more powerful research tools bcome available.
However, I’ll have to pick a few nits with you on this:
“While Fourier analysis is very useful, it has a few shortcomings. First, it can only extract sinusoidal signals. Second, although it has good resolution as short timescales, it has poor resolution at the longer timescales.”
‘First’) This is not a shortcoming, it’s incredibly useful for analysis. Fourier’s theorem makes an amazing, higly non-inutitive claim: any bounded signal (i.e. ‘real world’) can be decomposed into a set of weighted sinusoids. Guaranteed! How do we prove that? Simple, just add the sinusoids together and you reconstruct the original signal assuming the signal was sampled at least twice per period for each time step (Nyquist).
This also proves that there are no other ‘missing’ waveforms in the analysis, because we can reconstruct the original signal _entirely_ from sinusoids. Any other ‘waveforms’ observed in the signal will also be reduced to sinusoids.
It can also be shown that the resulting sets of sinuoids are unique (independent of the ordering of the calculation steps) and preserve the conservation of energy (Parseval Theorem). I.e. the sum of the energy in each sinuoid is equal to the total energy in the time envelope.
‘Second’) Perhaps you misstated this. Frequency resolution improves as the length of the time samples increase. It’s a Heisenberg tradeoff: we become more certain about frequency resolutions as we lose time resolution, and vice versa.
One of the problems with Periodicity Analysis (as Sethares and Stacey point out in their original paper) is that the resulting patterns are not unique, depending on how you order the steps of your calculation. This is due to the fact that the underlying subspaces of the decomposition are not orthognal. Whereas in Fourier (and Wavelet) decomposition the subspaces are othognal, and so the transforms produce unique pattern features.
So you can’t reconstruct the original signal by simply adding the spectral components, at least not without a lot of complicated bookkeeping to account for interactions between components.
I’m not saying this kind of analysis is useless, but you have to be careful about making claims of ‘reality’ concerning the output products, because they might disappear if you perform the transform in a diferent order. (Fourier outputs are real in the sense of uniqueness and energy convervation. If it says there is a spectral component at 60, then it’s there, up to Nyquist aliasing and noise issues.)
So, if you’re careful about how the compoents are produced, then this kind of analysis might be useful for classfication and discrimative modeling purposes, and might provide insights into data that other techniques don’t provide.
Can you provide a pointer to the HADCRUT3 datasets you used above. I’d like to do my spectral analysis on this data.
Thank again for a thought-provoking article!

David L. Hagen
July 30, 2011 6:29 am

Willis
Interesting analysis for “cycles” – however “nature” may have regular “oscillations” that are not exact “cycles”. e.g. the Pacific Decadal Oscillation (PDO) has been tracked across may centuries, but may not have exactly the same length. There are multiple lines of supporting data supporting the ~ 20 and 60 year oscillations that provide further support for Loehle & Scafetta. e.g. see Easterbrook
Stockwell at Niche Modeling lists some of PDO analysis papers: Natural Variation – 60 year cycle e.g.

The reconstruction indicates that the PDO is a robust feature of North Pacific climate variability throughout the study period, however, the major modes of oscillation providing the basic PDO regime timescale have not been persistent over the last 530 years. The quasi-centennial (75–115-yr) and pentadecadal (50–70-yr) oscillations dominated the periods before and after 1850, respectively. Our analysis suggest that solar forcing fluctuation on quasi-centennial time scale (Gleissberg cycle) could be the pace-maker of the PDO before 1850, and the PDO behavior after 1850 could be due, in part, to the global warming.

e.g. Shen et al. A Pacific Decadal Oscillation record since 1470 AD reconstructed from proxy data of summer rainfall over eastern China, GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L03702, 4 PP., 2006 doi:10.1029/2005GL024804
Stocker & Mysak “Climatic Fluctuations on the Century Time Scale: A Review of High-Resolution Proxy Data and Possible Mechanisms.” Climatic Change 20:227-250, (1992) 227-250.

The results indicate that this oceanic circulation exhibits natural variability on the century time scale which produces oscillations in the ocean-to-atmosphere heat flux. Although global in extent, these fluctuations are largest in the Atlantic Ocean.

Ed Fix’s Solar activity simulation model seems to capture well the major solar variations which have varying amplitude and length. These could well be the primary cause for the ocean oscillations – even if they are not precise “cycles”. (Shown by David Archibald) See
Ed Fix The Relationship of Sunspot Cycles to Gravitational Stresses on the Sun: Results of a Proof-of-Concept Simulation”. Ch 14 p 335 of Dr. Donald Easterbrook, ed. (Elsevier, 2011) e-book (Search the book for “355″ or “barycenter” or “sunspot cycles”)

See also the major variations in the Length of Day (LOD), including reviews by Paul L. Vaughan

chrism
July 30, 2011 6:53 am

good to see,
did you ever see Shaw and Tigg, Applied Mathematica ? It has some absolutely neat Time series evaluation and a maximum entropy data reconstruction,
I would imagine either of the authors would be interested in lending advice from what I remember of their writing,
anyone know them ??

July 30, 2011 6:57 am

In calculating a global average temperature, the strongest known physical cycles (diuranal and seasonal at each site) are “averaged out”. I would expect that red noise becomes a stronger signal in the process. I suggest that because radiative energy transfer is “line of site and fast as light” that the relationship between atmospheric CO2 concentrations and energy lost to space is best determined on a site by site and hourly time frame.

July 30, 2011 7:09 am

Willis!
You are a fantastic pedagog. And the knowledge and aplication of statistics in science in general and in climate science especially is weak or bad. The ower interpritations are more a rule than an exception.
Often when I hear that they found “signals” as well now as “cycles” the red flagg hoists!

paulID
July 30, 2011 7:13 am

Thank you Willis for 2 things first for writing these things in a manner that those of us without a “tidy mind” can understand and second for keeping up the search for the truth in “climate science” you are helping the common man understand that there is an unethical agenda in “climate science” and as with all things the truth will out.

Michael Larkin
July 30, 2011 7:30 am

“The bottom left panel shows the original barycentric data in black, and the reconstruction made by adding just these four cycles of different lengths is shown in blue. As you can see, these four cycles are sufficient to reconstruct the barycentric data quite closely. This shows that we’ve done a valid deconstruction of the original data.”
Willis, at the magnification of that bottom left curve, it’s hard to make out the fact that there might be a black curve and a blue curve.I kept staring at it until I noticed what I assumed were tiny gaps.The black and the blue are so near in tone, and it might have worked better with black and red, for example.
Maths has always been my Achilles’ heel. Whilst I get the gist of what you are saying, I had trouble with the following, from which I didn’t recover:
“For example, suppose that we want to find the actual cycle of length two in a given dataset. We can do it by numbering the data points in order, and then dividing them into odd- and even-numbered data points. If we average all of the odd data points, and we average all of the even data, it will give us the average cycle of length two in the data. Here is what we get when we apply that procedure to the HadCRUT3 dataset:”
You speak of data points, but you do not speak of the values of data points. I can see an amplitude arises of about 0.01, and that seems to be dimensionless; it’s not degrees centrigrade, for example. Because you don’t give a worked numeric example, I’m struggling to understand how that amplitude arises and what it means, here and in the elaborated examples for periods 4 and 20.
What I’m failing to grasp may be very simple for you, so simple that you didn’t think to spell it out. If I could grasp it, I think pretty much anyone could.

Michael Larkin
July 30, 2011 7:38 am

I suppose I should have said an amplitude of 0.02 peak-to-peak.

PiperPaul
July 30, 2011 7:50 am

Robert of Ottawa wrote:
The human mind looks for patterns where there are not necessailry any – both a gift and curse.
Great observation. And people that don’t understand confirmation bias are doomed to continue misinterpreting things due to mental myopia.

charlesH
July 30, 2011 7:52 am

Assuming my understanding is correct, I think you have it backwards Willis.
The Loehle and Scafetta paper isn’t significant because 60 and 20 yr cycles have been PROVEN to exist in the temperature record, rather they have been shown to replicate the temperature record quite well when a rather small co2 climate sensitivity is added.
This result is consistent with the recent paper of Spencer and Braswell regarding climate sensitivity.
Both paper support the idea that the IPCC overestimates climate sensitivity.
Am I missing something?

Darren Parker
July 30, 2011 8:00 am

What about the Great Year Cycle of approx 26,000 years? And you could also possibly consider the 70,000 year cycle , the precession of the ecliptic

ChE
July 30, 2011 8:07 am

AP –
The low-frequency resolution problem that Willis (not Anthony) talks about is no less fundemental than the Heisenberg Uncertainty Principal. In fact, it really is the basis of it.

July 30, 2011 8:13 am

Fourier analysis of the distance [in AU] between the sun and the barycenter [inversely related to the speed; doesn’t matter which one is used] http://www.leif.org/research/FFT-Barycenter-Distance.png covering 6000 [3000 BC to 3000 AD] years with a datapoint every 100 days shows the following periods [above 9 years]
9.92
11.87 Jupiter
12.78 second largest
13.8
19.85 largest peak
29.42 Saturn
35.89
45.31
61.03 very tiny (about 30 times smaller than the 19.85 yr peak)
83.85 Uranus
169.28 Neptune
There is thus no significant 60 yr period as is also evident by simple inspection of any section of the data, e.g. http://www.leif.org/research/Barycenter-Distance-2500BC-2000BC.
The spectral lines are very sharp, because there is no noise and the number of data points is very large ~22,000 and the cycles are actually there and nearly sinusoidal.

ChE
July 30, 2011 8:14 am

Oh, and Willis, kudos for publishing your code. If only this were standard practice.

July 30, 2011 8:16 am

Leif Svalgaard says:
July 30, 2011 at 8:13 am
http://www.leif.org/research/Barycenter-Distance-2500BC-2000BC.png is better

Surse
July 30, 2011 8:29 am

Truly fascinating post and comments. I am not a scientist but in following WUWT for years, I think i’m catching the drift!
Willis: “…what does all of this have to do with the Loehle/Scafetta paper? Well, two things. First, in the discussion on that thread I had said that I thought that the 60 year cycle that Loehle/Scafetta said was in the barycentric data was very weak. As the analysis above shows, the barycentric data does not have any kind of strong 60-year underlying cycle. Loehle/Scafetta claimed that there were ~ 20-year and ~ 60-year cycles in both the solar barycentric data and the surface temperature data. I find no such 60-year cycle in the barycentric data.”
Ninderthana: “A very impressive technique but I must take you up on one point. There is a very strong underlying physical reason for a 60 year cycle in the Barycentre motion.”
“If you were considering speed and not velocity then I would not dispute your identification of a 20 year cycle but NO 60 year cycle. The speed of the Sun about the centre-of- mass of the Solar System is primarily modulated by the alignments of Jupiter and Saturn every 19.858 years. However, if you are considering the Sun’s velocity (i.e. the Sun’s speed and velocity of the Sun about the centre-of-mass of the Solar System) then this roughly repeats every 59.574 (= 19.858 x 3) years.”
“This is caused by the fact that the Sun completes one loop around the barycentre roughly once every every 20 years, However, the axis of alignment of the orbital loop (about the barycentre) advances by 120 degrees with each completed orbit. This means that the Sun must complete three twenty year orbits for it to return to roughly same position with respect to the distant stars.”
Me: So is there a 60 year cycle or not?

Ric Locke
July 30, 2011 8:30 am

::sigh:: Mathematicians and non-mathematicians talking past one another. Nothing to see here…
First off, there’s nothing in Fourier analysis that prevents it from analyzing odd-shaped waveforms; in fact, that’s the point. A square wave is almost the trivial case — it’s the sum of an infinite number of odd harmonics (“multiples”) of the square wave’s frequency.
Any form of frequency analysis, regardless of method, when applied to a real (limited) data set, will show erroneous frequencies. This is a consequence of the fact that the data set can be thought of as a pulse: (no data)(dataset)(no data). The transition from no data -> data and the one from data -> no data constituted the edges of one cycle of a square wave, so the results will show frequencies at odd harmonics of twice the period of the data. One of the reasons for using wavelet analysis is that it tends to suppress this effect.
Regards,
Ric

July 30, 2011 8:33 am

Critically challenging published articles here with new analysis, explaining it in a way the layman reader can understand, plus publishing complete code….whaddya think this is, Real Climate?
Oh, wait.

Brian Macker
July 30, 2011 8:34 am

Derek Sorensen,
“Numerology? Why? – your graphs of cycles have ZERO basis to have the original time scale applied under them.”
If the assumption is that we start a particular time and that temperature changes behave as red noise from that time with the same magnitude as real temperature changes then the time frames make sense. Just as placing time frames on other models make sense. It just so happens that this model is timeless in that you can start with any date you want. It would only need be fixed if you chose a real temperature from a real date to start the process, or a particular temperature range within a particular time period. Since the claim wasn’t that this is a predictive model, but a non-predictive one, none of that matters.
So apparently it is you who doesn’t understand, and that includes some quite obvious if implicit assumptions.

KR
July 30, 2011 8:41 am

Excellent analysis, Willis.
I would note that Fourier analysis can uniquely decompose any signal up to the sampling/Nyquist limits. What it does do is simply identify internal patterns in the data that are not sinusoids, as the spectral data of (for example) a sawtooth pattern is spread between multiple sinusoids. However, since the majority of the energy is in those first few low frequency components and harmonics, you can usually identify those major cyclic behaviors.
I’m going to look into the Periodicity Transforms – they might be useful for some of the things I work on. I will echo the concern of others, though, that a non-orthogonal basis function such as that will be operation order dependent, meaning that each implementation of PT will potentially provide different answers even if using the same basis functions.
Robert of Ottowa“The human mind looks for patterns where there are not necessarily any – both a gift and curse.”
Absolutely right.
It’s worth keeping in mind that cyclic behavior is seen when there is a physical basis behind it, such as a pendulum. But it can also be an artifact of a short data set, which _looks_ cyclic even if it isn’t. For example, the velocity of my car may appear cyclic while trying to get out of a parking space, but that’s a poor prediction of my velocity once I’m on the road. Cyclic analysis not tied to the physical system exhibiting that behavior may well be an artifact of the analysis or the time frame examined – it really lacks explanatory power. And if there’s not a pendulum behind the curtain, predicting future behavior on purely output data analysis will be a serious c***shoot. That’s my major issue with Loehle and Scafetta – they identify nothing in the physics of the climate system that could show such behaviors.

c1ue
July 30, 2011 8:43 am

So what you’re saying is possibly, if you’re a hammer, everything looks like a nail.
Fair enough.

DirkH
July 30, 2011 8:48 am

“Spectral leakage” of Fourier transforms in real life data analysis can and should be reduced by using a good window function, for instance a Hamming window. Just cutting out a slice out of a time series implicitly uses a rectangular window function, leading to lots of spurious frequencies in the transform.
http://en.wikipedia.org/wiki/Window_function

DirkH
July 30, 2011 8:52 am

Periodicity analysis reminds me a little of the Hough transform.
http://en.wikipedia.org/wiki/Hough_transform

July 30, 2011 8:52 am

Ninderthana says:
July 30, 2011 at 5:57 am
This is caused by the fact that the Sun completes one loop around the barycentre roughly once every every 20 years, However, the axis of alignment of the orbital loop (about the barycentre) advances by 120 degrees with each completed orbit. This means that the Sun must complete three twenty year orbits for it to return to roughly same position with respect to the distant stars.
If you assume that the cause is astrological [‘distant stars’ – e.g. whether the Sun is in Leo or some other sign] you may have a point, but if you assume that the actual, local, configuration of the planets [via physical cause, such as tides] is the cause, then the orientation of the axis of the loop with respect to the distant stars doesn’t matter. Which is it?

wsbriggs
July 30, 2011 9:00 am

For those who believe that a square wave is actually the sum of the odd numbered components of the square wave frequency, I would like to point out that Fourier was analyzing waveforms. They can be represented as the sum of the frequencies, however, the assumption of infinite cycles, is what makes the whole thing problematic when single pulses are involved. The Gibbs Phenomenon is another clue that this is a tool (map) not the territory.
I agree with several posters, that wavelet transforms will probably bring interesting results.
Thanks a lot Willis, I always learn, and sometimes have to rethink what I thought I knew, when you write.

Paul Vaughan
July 30, 2011 9:08 am

Willis Eschenbach linked to the following article:
Sethares, W.A.; & Staley, T.W. (1999). Periodicity Transforms. IEEE Transactions of Signal Processing 47(11), 2953-2964.
From it’s abstract:
“The algorithm ﬁnds its own set of nonorthogonal basis elements (based on the data), rather than assuming a ﬁxed predetermined basis as in the Fourier, Gabor, and wavelet transforms.”
The authors have a very narrow view (or at least had a very narrow view in 1999) of what can be done with wavelet methods. Wavelet methods are incredibly flexible and ABSOLUTELY DO NOT demand assumption of a predetermined dyadic basis. I NEVER assume a predetermined basis when applying exploratory wavelet methods. Untenable assumptions are NOT the course to enlightenment.
Regards.

July 30, 2011 9:21 am

There are very good reasons why Fourier analysis doesn’t always pick up certain cycles that are apparent through other methods. The quasi 60 year cycle is a 2nd level harmonic that is not present in the first level, ie the quasi 60 year cycle is a modulation of the quasi 20 year cycle. This modulation to the velocity curve (highs and lows) at the higher level is a direct result of Uranus and Neptune.
Also when looking at the 172 year cycle in the temperature or solar proxy record is not supremely evident because the cycle has multiple prongs. It travels in a cluster (usually 3) or multiple components that occur each 172 years. Think of it as a hand on a clock that ends in a trident, every time it goes past midnight the amount of prongs varies, sometimes it has the last prong missing or the first prong could be missing or all three are present. Add to that a variable “strength” to each prong and you see why a regular pattern cannot be teased out, but the underlying force is still there. This is how grand minima works, another example of Uranus and Neptune at work.
If we only relied on Fourier analysis the world would be a poorer place. Nature does not always conform.

Hoser
July 30, 2011 9:32 am

While Fourier analysis is very useful, it has a few shortcomings. First, it can only extract sinusoidal signals.
A physicist says:
July 30, 2011 at 6:13 am
John Day says:
July 30, 2011 at 6:24 am

Good answers to the issue mentioned above.
However, let’s turn the argument around. What you need to perform a Fourier type analysis is a set of orthnormal functions. They don’t have to be sines.
http://75.24.127.133/Courses/tutorials/Generalized_Fourier_Series.htm
Maybe this makes sense: Any function can be described by a linear combination of sine functions. That’s the standard Fourier approach most people use. Then a linear combination of functions composed of linear combinations of sines can also serve in Fourier analysis.
For example, square waves can be constructed from sines. Square pulses can be used instead of sines in a generalized Fourier analysis.
http://www.icrepq.com/icrepq-08/365-iwaszkiewicz.pdf
Sines are just convenient.

July 30, 2011 9:37 am

The observation of patterns or associations is the first step towards knowledge. After that comes hypothesis as to causation. The hypothesis is rarely unique, but the observation is or should be.
Regardless of the Fourier vs periodicity analysis argument, is it true that a 60/120 year cycle of some regularity can be found in the global temperature record of the last 200 years? As a non-mathematician I do not understand whether this disagreement on analysis style says the “observation” is an artefact or a reality.

commieBob
July 30, 2011 9:37 am

Ric Locke says:
July 30, 2011 at 8:30 am
::sigh:: Mathematicians and non-mathematicians talking past one another. Nothing to see here…
First off, there’s nothing in Fourier analysis that prevents it from analyzing odd-shaped waveforms; in fact, that’s the point. A square wave is almost the trivial case — it’s the sum of an infinite number of odd harmonics (“multiples”) of the square wave’s frequency.
Any form of frequency analysis, regardless of method, when applied to a real (limited) data set, will show erroneous frequencies.

Amen brother. The naive application of Fourier Analysis can produce results that are somewhere between being valid and being complete garbage. The difference usually depends on luck. 😉

July 30, 2011 9:42 am

Here is the barycentre velocity graph from Willis with the quasi 60 year cycle annotated.
http://tinyurl.com/2dg9u22/images/willis.png

NikFromNYC
July 30, 2011 9:52 am

I have added the parable of the blind men and the elephant to my poster graphic about myopic lack of practical intelligence on both sides of the silly climate war:
http://i.minus.com/ijfwX2.jpg
A single underwater volcano can suddenly becomes active for a century or two in a critical location where an ocean current initiates a thousand mile wide twisty path to the surface, tickling the whole system away from its current state, enough to alter all the but the very longest cycles, which themselves are unpredictable due to three body problem orbital chaos. On both century and millennial time scales, simple fluid dynamic chaos of ocean currents are reasonably expected to dominate sea surface and atmospheric temperature due to the massive heat content of the oceans, this despite any minor changes in external forcings and feedbacks that involve the sun and atmosphere. You also have non-volcanic shifts in crust thickness of the ocean floor such as seems to be occurring around the Antarctic peninsula, and a sudden 20th century loosening of the location of the magnetic poles due to chaotic shirts in magna currents. A tiny angular shift in the North Pole extended out into space represents a shift of hundreds of miles of magnetic influence on cosmic ray shielding over Greenland.
“No, so holp me Petault, it is not a miseffectual whyancinthinous riot of blots and blurs and bars and balls and hoops and wriggles and juxtaposed jottings linked by spurts of speed: it only looks as like is as damn it; and, sure, we ought really to rest thankful that at this deleteful hour of dungflies dawning we have even a written on with dried ink scrap of paper at all to show for ourselves, tare it or leaf it, (and we are lufted to ourselves as the soulfisher when he led the cat out of the bout) after all that we lost and plundered of it even to the hidmost coignings of the earth and all it has gone through and by all means, after a good ground kiss to Terracussa and for wars luck our lefftoff’s flung over our home homeplate, cling to it as with drowning hands, hoping against all hope all the while that, by the light of philosophy, (and may she never folsage us!) things will begain to clear up a bit one way or another within the next quarrel of an hour and be hanged to them as ten to one they will too, please the pigs, as they ought to categorically, as, strickly between ourselves, there is a limit to all things so this will never do.” -James Joyce (Finnegans Wake 1939)

tallbloke
July 30, 2011 9:58 am

Leif Svalgaard says:
July 30, 2011 at 8:52 am
Ninderthana says:
July 30, 2011 at 5:57 am
This is caused by the fact that the Sun completes one loop around the barycentre roughly once every every 20 years, However, the axis of alignment of the orbital loop (about the barycentre) advances by 120 degrees with each completed orbit. This means that the Sun must complete three twenty year orbits for it to return to roughly same position with respect to the distant stars.
If you assume that the cause is astrological [‘distant stars’ – e.g. whether the Sun is in Leo or some other sign] you may have a point, but if you assume that the actual, local, configuration of the planets [via physical cause, such as tides] is the cause, then the orientation of the axis of the loop with respect to the distant stars doesn’t matter. Which is it?

It’s possible that there is more than one type of physical cause. So there could be a tidal effect and an electromagnetic effect of planetary alignments. Rather than astrology “Sun is in Leo”, it may be significant for the apparent 60 year signal that every third Jupiter-Saturn conjunction takes place between the Sun and the centre of our galaxy, and/or that every third conjunction takes place towards the bowshock of the heliosphere. We don’t know yet, but it seems reasonable to me to investigate these possibilities.
I commend Willis for doing the analysis, it adds to our knowledge. I don’t think it provides a basis for dismissing Loehle and Scafetta’s paper, or other efforts to discover the linkage between solar system dynamics and climate, but it should galvanise efforts to improve on their ‘first foray’ into this area.
Whilst this type of study proves that apparent cycles in climate might just be random walk chance, it doesn’t rule out the possibility that they might not be. The apparent 60 year signal in climate may be the result of the terrestrial amplification of a small astronomical signal because the planets also directly affect the Earth Moon system, as well as indirectly affecting Earth’s climate via an effect on solar activity levels. I’m not saying this is necessarily so, but it’s a possibility.

Paul Vaughan
July 30, 2011 9:59 am

John Day wrote (July 30, 2011 at 6:24 am) wrote:
“Whereas in […] Wavelet […] decomposition the subspaces are othognal, and so the transforms produce unique pattern features.”
Not necessarily, nor necessarily even desirable. Wavelet methods are far more flexible & adaptable than many seem to conceive. Some of the misunderstandings might be arising out of an assumption that the goal is to model the signal (&/or perform statistical inference). For those of us who stick to data exploration, this is not the goal. Some of the communication divides frequently arising in these discussions are fundamentally paradigmatic. We need to get past untenable assumptions that have taken DEEP cultural root (some might say rot).
Best Regards.

Ron Cram
July 30, 2011 10:05 am

Willis and Anthony,
Thank you. Anthony, I love that you will host a blog post by the authors of a newly published peer reviewed paper and within days host a second blog post criticizing the paper. This is the way science should work.
Willis, thank you for your writing. Very interesting, as always (almost always – your blog post criticizing mine was slightly less interesting ) The way I see it you have clearly expressed why you are not persuaded by the Loehle and Scafetta paper, but have not refuted the paper. It will be interesting to see the response by Loehle and Scafetta.

Stephen Wilde
July 30, 2011 10:10 am

Willis said:
“Well, if like Loehle and Scafetta you think that you can find out fundamental climate truths by analyzing the “cycles”, yes, the fact that they are artifacts does indeed matter”
There is the nub. Loehle and Scafetta (and me) are noting fundamental climate truths from observations of solar and oceanic variability and their recorded effects on climate and seeking to interpret their nature and significance.
Whether those real natural fundamental climate truths fail to come through mathematical analysis after applying various sorts of filtering and processing which obscure the difference between artifacts and real cycles is rather beside the point.
So I think what you have shown us is simply the wrong way around. By all means use those methods to tease out cycles or other forms of relationship that are not otherwise apparent but it’s not useful to use those techniques to support an assertion that cycles that exist out in the real world (as evidenced by lots of other sources of data) are mere artifacts just because they don’t survive the processing of the limited data that you use.

July 30, 2011 10:10 am

“But because they are purely random data, these are only pseudo-cycles, not real underlying cycles.
You can only say that because you know the means by which the data were generated. In the case of observations of real-world data, we don’t know, so we have to analyze the data and try to find out whether any of the apparent cycles are real.
One technique I’d like to try is to look at smaller chunks of the time series, analyze each of them separately, and see if there are any signals that appear strongly across them all. Unfortunately, with 150 years of data, if we split it into three parts, we wouldn’t even have a full 60-year cycle to look at. It would be impossible to give an estimate of the confidence level on a 60-year component when our data only span 2.5 such cycles. Maybe if we had six centuries of solid data, we could find a statistically-significant signal at the 60 y level.
Another obvious problem is the arbitrary assignment of cycles in full years. As the known cycles for Jupiter and Saturn don’t work out to an exact number of years, the 19.85y signal is mis-analyzed as two separate 19- and 20- year cycles.

Ninderthana
July 30, 2011 10:18 am

Leif Svalgaard ,
One circuit with respect to the stars means that what ever mechanism is involved, it is aligned/synchronized with the seasons here on the Earth.
It is neither astrological nor is it planetary tidal forces directly acting on the atmosphere, since, as you and I both know, they are either totally insignificant or delusional.
The only reason/hypothesis that I can [logically] come up with is a long-term synchronization between factors that are know to influence the Earth’s atmosphere (i.e. lunar tides and/or the level of solar activity), and the planetary configuration. I agree with you that this has still yet to be proven. However, I disagree with your contention that it is not worth looking for a possible connection.
The hypothesis that I have presented here would be possible if the rate of procession the lunar line-of-apse and line-of-nodes were set by periodic resonances between the lunar orbit and weak gravitational perturbations of Venus and Jupiter over the last few billion years.
None of these ideas are so far fetched as to beyond the borders of reasonable scientific research.
Some times the answer is right in front our nose but very often we are either too silly or too blind to see it.

RACookPE1978
Editor
July 30, 2011 10:24 am

Geoff Sharp says:
July 30, 2011 at 9:42 am

Here is the barycentre velocity graph from Willis with the quasi 60 year cycle annotated.
http://tinyurl.com/2dg9u22/images/willis.png

Thank you. But, you need to add the “minus” points as well: 3 of the 4 minimums between each red dot maximum) are “lowest minimums” as well. Thus, you are seeing a (strong) 20 year cyclle – that Lief found in his analysis of the solar-planet movements! – and a much weaker 60 year cycle – that you plotted only the four “red dot” high points.
Now, go look at the sunspot (22 year) cycles of positive to positive (or negative to negative) sunspot count peaks. There also, the peaks tend to be grouped in sets of high, medium, and low counts.

Ninderthana
July 30, 2011 10:26 am

Willis Eschenbach,
You won’t see a 60 year signal because you are doing your periodic analysis on the Sun’s speed about the Barycentre. The periodicity does not exist in that data set.
You will see a 60 year periodicity if you do you periodic analysis of the Sun’s velocity about the Barycentre. Speed only deals with the magnitude of the rate of motion, while velocity deals with both the magnitude and direction of the rate of motion. The 60 year signal is
buried in the direction part of the rate-of motion of the Sun about the Barycentre.

July 30, 2011 10:30 am

Ninderthana says:
July 30, 2011 at 10:18 am
One circuit with respect to the stars means that what ever mechanism is involved, it is aligned/synchronized with the seasons here on the Earth.
The seasons are synchronized with the sun [the tropical year], not with the distant stars.

July 30, 2011 10:34 am

Geoff Sharp says:
July 30, 2011 at 9:42 am
Here is the barycentre velocity graph from Willis with the quasi 60 year cycle annotated.
http://tinyurl.com/2dg9u22/images/willis.png

Which clearly shows how insignificant the 60-yr modulation is. Thanks for pointing that out so succinctly.

Wayne
July 30, 2011 10:35 am

Here’s what I did to get a nice wavelet display in R:
library (dplR)
# –> Time-Series [1:1944] from 1850 to 2012: -1.757 -0.267 -0.409 -0.779 -0.552 …
The resulting graph is very pretty and shows a roughly 20-year frequency across the timeframe. It's statistically significant, though it may simply be an artifact of red noise, as you note. The dplR package makes it quite easy to make this nice graph, and interestingly it is a package meant for working with tree rings.

Geoff Sharp
July 30, 2011 10:36 am

RACookPE1978 says:
July 30, 2011 at 10:24 am
If you look at the original Scafetta graph you will see the low points are taken into consideration. He uses spectral analysis to create his quasi 60 year trend.

dp
July 30, 2011 10:37 am

Leif beat me to the send button with

If you assume that the cause is astrological [‘distant stars’ – e.g. whether the Sun is in Leo or some other sign] you may have a point, …

Unless someone has shown a short term (60 year) galactic influence on the local climate this is an insignificant factoid. I think that changes if we consider what happens when the local system ascends out of the galactic plane and becomes exposed to the full brunt of the disk of the Milky Way. Our current orientation in our galaxy is such that we are shielded by dust from the vast majority of our neighboring stars. What might the night sky temperature be if we were not in the shadow of the Milky Way?

July 30, 2011 10:40 am

The Monster says:
July 30, 2011 at 10:10 am
Unfortunately, with 150 years of data, if we split it into three parts, we wouldn’t even have a full 60-year cycle to look at.
Since L&S [or at least S] claims that the cause of the temperature variations is solar and related to its barycentric motions [or tides] we can investigate the source. Here is the power spectrum of 6000 years of barycentric distance [~22,000 data points]: http://www.leif.org/research/FFT-Barycenter-Distance.png There is no prominent 60-year cycle.

Paul Vaughan
July 30, 2011 10:40 am

Steve McIntyre (July 30, 2011 at 5:28 am) wrote:
“Since Sethares and Staley refer to wavelet transforms, I presume that (contra Nick Stokes) their methodology has considered wavelet methods, though I am not in a position right now to comment on whether Sethares and Staley’s method is a useful improvement on wavelets or not.”
Wavelet methods were in relative infancy in 1999. Their application has risen exponentially and with this rise has come adaptive radiation (in the sense used in evolutionary biology). I would caution against cookbook implementation of the more dull conceptions of “what wavelet methods do”. Wavelet methods are extraordinarily flexible and limited only by shortcomings of practitioners’ imaginations. Many theoreticians are HOPELESSLY blinded in practice by algebraic abstractions underpinned by untenable assumptions. And many practitioners just parrot the widely-available NARROW-SCOPE wavelet algorithms of others before hastily drawing premature (& inaccurate) conclusions about utility, rather than operating intuitively & adeptly from a base in deep conceptual understanding.
Regards.

Geoff Sharp
July 30, 2011 10:46 am

Willis Eschenbach says:
July 30, 2011 at 10:36 am
Geoff Sharp says:
July 30, 2011 at 9:42 am
Here is the barycentre velocity graph from Willis with the quasi 60 year cycle annotated.
http://tinyurl.com/2dg9u22/images/willis.png
Not sure what your point is here, Geoff. Both periodicity and Fourier analysis show that the ~60-year cycle is very tiny, an order of magnitude or more smaller than the 20-year cycle. Yes, it exists, but it’s hardly significant.

Willis I am afraid you keep missing the point. Think of the 20 year cycle as a background engine, the power of that engine is controlled by another force or modulator. The engine is slowing for 30 years then speeding up for 30 years….this is the same as the PDO cycle. To ignore it would be foolish.

July 30, 2011 11:06 am

To Willis Eschenbach,
I am sorry that I need to contradict Willis, his analysis is very poor.
Our analysis is based on the correct thecniques, that is “multiple” power spectrum analisis agaist red noise background. I would like to insist on the word “multiple” because I used three alternative methods. The quasi 20 and 60 year cycles are quite evident in the data. This tests are done in Scafetta 2010. In L&S 2011 we simply references those results
Moreover similar cycles have been found by numerous other people in numerous climatic data and published in numerous data. So, ther is very little to question.
Moreover the curves shown in figure 1,2,3,4 show equal cycles which are not sinusoisal, but are clearly equal.
See for example the above 20-year modulation shown in figure 4. The cycles are not sinusoidal, but they are still perfectly “equal”.
It is very unlikely that the temperature present such a perfect repetition of cycles that would be possible only is the temperature were made of cycles with perfect period 20, 10, 5, 4, 2.
What Willis did is simply to calculate a single average cycle and then he plotted this same cycle many times in a consecutive way.
Try to use a sequence made of two cycles with period 20 and 15, then use your 20 period and you will see that your thecnique fails to properly reproduce the modulation of the curve.

July 30, 2011 11:28 am

Geoff Sharp says:
July 30, 2011 at 9:21 am
Also when looking at the 172 year cycle in the temperature or solar proxy record is not supremely evident because the cycle has multiple prongs.[…]
If we only relied on Fourier analysis the world would be a poorer place.

Sometimes just looking at the data works too [although Fourier analysis would also pick up any cycles, even if the period is not strictly constant]. There is no correlation between your U/N 172 stuff and solar activity. Here are a direct comparison for the past 6000 years. The solar activity is the ‘latest and greatest’ from Steinhilber et al. combining both 10Be and 14C. The activity data are 25-year means so wont show the solar cycle:
http://www.leif.org/research/Solar-Activity-vs.Barycenter-Distance-BC.png
As you and everybody can clearly see there is no consistent correlation between your U/N influences [denoted by circles] and Grand Minima, or anything else for that matter.

commieBob
July 30, 2011 11:46 am

nicola scafetta says:
My assumption is that you are working with a data set consisting of average annual temperatures. You have fewer than 200 data points. Although I have zero experience with geophysical data my experience with electronic signals tells me that you should not defend your results too tenaciously. 😉

Steve from Rockwood
July 30, 2011 11:46 am

Joseph Fourier looks a little bit like my girlfriend’s hairdresser, who also by coincidence is a Ph.D mathematician who never made it to the AGW trough. /s
But I always thought Fourier transforms didn’t like non-periodic trends in the data due to the assumption of a periodic function. We always removed the trend or applied a tapering filter at either ends to force periodicity.
Willis, all your graphs seem to represent data sets that more or less start and end at the same value (of the y-axis). In the example of temperature curves, today’s temperature “background” is a positive value higher than the trough-to-peak values of the so-called periodic trends that return to the baseline. I think Fourier Analysis wouldn’t like such a data set.
Periodicity analysis would be even worse for long term trends (features of the time series that have a period much longer than the sampling period). In your Figure 6 none of the data sets shows a long term positive trend so I’m not sure you’ve proven anything. You seem to have used periodic data as input and proved periodicity analysis works.
Plus I thought Loehle and Scafetta produced a very good piece. Their numbers make sense when I eyeball the measured temperature graphs.
But I always enjoy your articles Willis – I haven’t frequency filtered anything in years.

July 30, 2011 11:56 am

I think the randomization test you’re showing is great if Loehle and Scafetta were just looking to see if any sort of periodicities existed, but they weren’t – they were fitting models on the 20- and 60-year cycles that were already known to exist. So that means that it isn’t really a multiple comparison problem, which is what your randomization approach seems to be testing (if I’m understanding the situation – a dubious assumption at best).

BarryW
July 30, 2011 12:38 pm

Ah Willis, I don’t think your red noise test really shows that their fourier analysis fails on red noise. It just shows that your periodicity test fails on it by finding a pseudo-cycle. You would have to show that a fourier analysis also produced the same results on the red noise data sets.

NikFromNYC
July 30, 2011 12:39 pm

Adding a tear to the debased nun rounds out my take on this issue by better expressing the sadness I attach to over-specialized and myopic analysis paralysis and it’s corrupting influence upon contemporary affairs, as does the addition of a photo of my green bile drooling dead cat Freddy in ’05, back when I started wasting my life on weather worry, long after I had exited science due to the victory of hype, political correctness and corporatism over substance, bravado and curiosity within academia. The time I wasted online that afternoon meant Fred died alone in the other room, for what I thought was a half hour online had turned to six so he was now stiff as a board. A section from S. Dali’s last painting covers both the last and next century to mark the end of a muddled era as illuminated by the glistening and terrible Beauty of pure mathematics.
http://i.minus.com/ijkhds.jpg
“The individual sciences of our epoch have become specialized in these three eternal vital constants the sexual instinct, the sense of death, and the space-time anguish. After their analysis, after the experimental speculation, it again becomes necessary to sublimate them. The sexual instinct must be sublimated in esthetics; the sense of death in love; and the space-time anguish in metaphysics and religion. Enough of denying; one must affirm. Enough of trying to cure; one must sublimate! Enough of disintegration; one must integrate, integrate, integrate. Instead of automatism, style; instead of nihilism, technique; instead of skepticism, faith; instead of promiscuity, rigor; instead of collectivism and uniformization individualism, differentiation, and hierarchization; instead of experimentation, tradition. Instead of Reaction or Revolution, RENAISSANCE!” – Salvador Dali (The Secret Life of Salvador Dali 1942)

William
July 30, 2011 12:52 pm

It seems the orbital position of the planets is affecting the sun, however, the analysis of the problem/observations will be difficult if there are multiple changes occurring which interact with each other. It seems based on the reasons and observations noted below the mechanism may not necessary be just gravitational effects of one body on another.
There is unequivocal paleoclimatic evidence that the earth’s climate changes on a pseudo cycle on a centennial and millennial basis (Medieval warm period, Little Ice Age, and so on), with a strong change with a period of 1470 years (plus or minus a beat frequency), and with very, very strong changes (abrupt climate events such as the Younger Dryas event or the 8200 BP abrupt cooling event, or the termination event of the last 22 interglacial periods) with a period of roughly 8000 to 10,000 years.
Paleoclimatic researchers have known for years that there is concurrent with these pseudo cycles of warming and cooling and abrupt climate changes events, cosmogenic isotope changes. What was not known is what is causing the cosmogenic isotope changes and how what was causing the cosmogenic isotope changes, could cause the planet to cool or warm. It is now apparent the cooling or warming is caused by changes that affect the amount of planetary cloud cover, the albedo of planetary clouds, and regionally the amount and albedo of the clouds that form. (The mechanism can cause some regions to have less clouds and warm and other regions to have more clouds and cool which complicates the paleoclimatic analysis.)
As I have noted, geomagnetic field specialists in the last 10 years have found that the tilt of the geomagnetic field is abruptly changing with a pseudo cycle and related to the geomagnetic field axis change that there are pseudo cyclic intensity changes to the geomagnetic field (sometimes the event reinforces the field and other times it apposes the field). The axis orientation change of the geomagnetic field, changes the poles location relative the earth’s rotational axis which changes the relative distance from the geomagnetic pole to different locations on the continents. The geomagnetic field change, in turn changes GCR intensity and magnitude at lower latitudes and at higher latitudes (Svensmark’s book explains the mechanism and how it is affected by distance from the geomagnetic pole.). i.e. The geomagnetic pole no longer aligns with the rotational axis of the planet. After the event the geomagnetic field integrates the change causing the geomagnetic field intensity to increase or decrease. There are unexplained cycles of geomagnetic field intensity.
The geomagnetic field change has a long term affect on the planet’s climate. That explains how a short term solar event can have a long term affect on the planet’s climate. (i.e. 70% of the Younger Dryas cooling occurred in roughly 10 years with almost of 100% the cooling in 100 years and the cooling lasted for around 1200 years. The solar magnetic field cycle or TSI does not reduce for 1400 years.)
Further complicating the after the fact analysis of the cycles and abrupt changes – based on an assumed mechanism where the sun is the cause of the observed change – how much the solar event changes the geomagnetic field depends on the eccentricity of the earth’s orbit, the tilt of the earth at the time of the event, the timing of perihelion at the time of event, and whether there are insulating ice sheets on the planet. (Think of a large solar event -there are also smaller more frequent solar events – that occurs roughly at a frequency of 8000 to 10,000 years now see how the tilt of the planet and timing of perihelion has changed between events to change the effect of the event on the geomagnetic field.) There are also smaller geomagnetic field tilt changes with a periodicity of roughly 400 years.
There must be a physical reason, a cause as to what is changing the geomagnetic field. The fact that there are roughly a hundred papers noting cosmogenic isotopes changes correlate with climate changes is smoking gun evidence that the sun is the serial climate changer. There appears to be no earth mechanism that can change the geomagnetic field as rapidly and with observed cyclic timing (there are physical limits as to how fast a core based change can affect the total geomagnetic field due to counter acting EMF fields that are generated in the liquid core and there is no physical event that abruptly cause core base changes which in turn could cause the geomagnetic field to change, core based changes are orders of magnitude slower.) If the assertion that a core based change is physically capable of causing the geomagnetic field observations then it seems there must be some pseudo cyclical solar event that is causing the geomagnetic field to change. There appears to be no other logical possible cause. There must be a physical cause to what is observed.
There are a whole suite of astrophysical anomalies that could possibly be explained by the fundamental reason why the sun is changing and how it could affect the geomagnetic field and the magnetic field of the other planets (For example a cyclic abrupt solar event could possibly explain the anomalous orientation of the Uranus and Neptune magnetic field where the field does not align with the planet’s rotational axis and is further more off set from the center of the planet’s core.).
A possible methodology to develop the mechanism is to start with a strawman of the fundamental mechanism then to look for anomalies to outline and define the fundamental mechanism. For example, I found an interesting series of papers written to explain very strong magnetic fields associated with quasars and cyclic monotonically increasing long scale changes of quasar spectrum, and so forth, which indicate the collapse of a large object does not form a black hole. The object formed is not stable and gradually breaks up with an electromagnetic mechanism which explains the very strong magnetic field, jets, and ejected material. Perhaps the object formed for the collapse of large objects could be similar for the collapse of a super nova.
There are at least a dozen different groups/individuals from four or five different specialties that have published papers concerning observations and anomalies that appear to be related to this mechanism. Observational data concerning the astrophysical anomalies is improving. Perhaps an answer will come out of that work.
http://www.sciencedirect.com/science/article/pii/S1364682610004074
Sun–earth relationship inferred by tree growth rings in conifers from Severiano De Almeida, Southern Brazil
This study of Sun–Earth relationships is based on tree growth rings analysis of araucarias (Araucaria angustifolia) collected at Severiano de Almeida (RS) Brazil. A chronology of 359 years was obtained, … periods of solar activity of 11 (Schwabe cycle), 22 (Hale cycle), and 80 (Gleissberg cycle) years. The result shows the possible influence of the solar activity on tree growth in the last 350 years. Periods of 2–7 years were also found and could represent a response of the trees to local climatic conditions. Good agreement between the time series of tree growth rings and the 11 year solar cycle was found during the maximum solar activity periods.
http://ruby.fgcu.edu/courses/twimberley/EnviroPhilo/LongPeriod.pdf
LONG-PERIOD CYCLES OF THE SUN’S ACTIVITY RECORDED IN DIRECT SOLAR DATA AND PROXIES
Abstract. Different records of solar activity (Wolf and group sunspot number, data on cosmogenic isotopes, historic data) were analyzed by …. It was confirmed that two long-term variations in solar activity …. of 50–80 years and 90–140 year periodicities. The structure of the Suess cycle is less complex showing a variation with a period of 170–260 years. Strong variability in Gleissberg and Suess frequency bands was found in northern hemisphere temperature multiproxy that confirms the existence of a long-term relationship between solar activity and terrestial climate.
Stuiver and Braziunas (1993) analyzed the long decadal 14C series and found significant 89 and 148 year periodicities for 6000–2000 B.C. and a 126-year variation for 2000 B.C.–1840 A.D. Existence of two kinds of century-long solar variability – 115 year and 95 year cycles – was claimed by Chistyakov (1986). …variations in the Gleissberg and Suess frequency range, using all the complexity of direct and indirect solar data and applying modern statistical methods. The link between solar activity and terrestrial climate is also considered.
The following is a link to Bond’s paper “Persistent Solar influence on the North Atlantic Climate during the Holocene”
http://www.essc.psu.edu/essc_web/seminars/spring2006/Mar1/Bond%20et%20al%202001.pdf

July 30, 2011 1:04 pm

Steve from Rockwood says:
July 30, 2011 at 11:46 am
Willis, all your graphs seem to represent data sets that more or less start and end at the same value (of the y-axis). In the example of temperature curves, today’s temperature “background” is a positive value higher than the trough-to-peak values of the so-called periodic trends that return to the baseline. I think Fourier Analysis wouldn’t like such a data set.
It actually works quite well. Here are four cases of the function a*t+sin(t), where the sine curve will have a period of 2pi=6.3: http://www.leif.org/research/FFT-Periods-with-Trends.png where a varies from 0 [no trend] to a rather extreme a = 0.1 where the trend over the ~40 cycles is about 12 times larger than the amplitude of the sine-curve [peak to valley]. In all cases the FFT picks up a clear peak at 6.3.

July 30, 2011 1:14 pm

I disagreed with the L & S 60 year analysis, for reason I could not see it in the 350 year old CET record.
Only place where there is a sort of longish quasi 60 year cycle is in the secular variation of the geomagnetic field in the Hudson Bay magnetic pole. Even so it is only ‘around 60ish’, detected as a negative forcing (falling GMF) – troughs at: ~1750, ~1810, ~ 1870s, ~1930s and late 1990s
I think it is due to the Earth’s passage trough so called ‘magnetic clouds’ (CMEs) connecting the sun to the two largest magnetospheres (Jupiter & Saturn). More (speculative) details at
http://www.vukcevic.talktalk.net/LFC5.htm
also see Fig. 8 in the ‘Earth bound effects’ chapter, not all graphs are numbered.

jorgekafkazar
July 30, 2011 1:15 pm

Robert of Ottawa wrote:
The human mind looks for patterns where there are not necessailry any – both a gift and curse.
PiperPaul says:
Great observation. And people that don’t understand confirmation bias are doomed to continue misinterpreting things due to mental myopia.
Both comments are core to the understanding of both paranoia (not involved here!) and “wiggle-matching.” Humans (and others) detect potential threats by isolating a dim image from surrounding noise, as, for example, discerning a tiger amongst foliage. This capability is “designed” (ha-ha, just kidding!) to err on the consrvative side, giving a TIGER! EEK! signal when there is no tiger a lot more often than vice versa. It’s safer to see imaginary tigers and reach for your spear 100 times than to NOT see a real tiger once and get eaten. Cost-to-risk ratio very reasonable.
So L&S’s “tiger” may be imaginary. But, if so, they are not the only ones seeing tigers in the data, and at least L&S are not demanding we reach for our wallets to drive phantom beasts away.

July 30, 2011 1:16 pm

Leif Svalgaard says:
July 30, 2011 at 1:04 pm
http://www.leif.org/research/FFT-Periods-with-Trends.png

J_Bob
July 30, 2011 1:38 pm

Great post.
A couple of years ago I posted a comment,using Fourier Analysis, or Spectral Analysis, showing a recent leveling off of the NOAA global temperature. It did raise a hornet’s nest of comments, at RC, including from one “Tamino” who dismissed it as bungled. Although in mean time, he seems to have discovered as variation, called “wavelets”. The graph I posted back then is referenced below:
http://www.4shared.com/photo/uv-Q2YoJ/NOAA_yr_001.html
I also compared a Fourier and Empirical Mode Decomposition (EMD) analysis of HadCrut global temperature result, and would have posted it here. However the site with my graphs, seems to have been removed and will take a little while to get my graphs back on line.
The IEEE paper you referenced is vary interesting, and will merit some study. An additional note was that mentioning the IEEE at RC, seemed to be like referencing a cultist belief in their minds. While Dr. Norbert Wiener was some unknown, who knew nothing of mathematical perdition methods. Which said a lot.

phlogiston
July 30, 2011 1:42 pm

The search for wave signatures in the climate record identifying direct astrophysical forcings of climate, makes a major assumption that has not been spelled out here; namely, that the climate system responds in a passive, linear manner. The climate record is noisy, and Willis’ study here is an important critical shot across the bows for such an approach, demonstrating the prevalence of spurious underlying wave signals in noisy wavetrains, arising from autocorrelation.
However climate exhibits nonlinear, chaotic characteristics, as has been explained by several here on WUWT, notably Willis himself. A nonlinear-chaotic climate may not respond passively and linearly to forcings, astrophysical or otherwise. In a periodically forced nonlinear oscillator the forcing can either be strong – in which case the periodicity of the forcer is clearly evident in the forced system, or it can be weak. In a weakly periodically forced nonlinear oscillator, the relationship between the forcing and responsive frequencies can be very complex, such as to defeat analytical attempts to find simple underlying forcing wave frequencies.
In this case one has to look for a very different type of diagnostic pattern to analyse the system as a nonlinear oscillator, such as log-log and fractal character.

July 30, 2011 1:45 pm

Geoff & Willis
Graph shown at http://www.landscheidt.info/images/willis.png
has peaks very close to the Hudson bay magnetic pole’s secular variation troughs (forcing) at
~1750, ~1810, ~ 1870s, ~1930s and late 1990s
as calculated from the ETH Zurich data.
http://www.vukcevic.talktalk.net/LFC5.htm
graph at Fig. 8.

tallbloke
July 30, 2011 1:53 pm

Willis Eschenbach says:
July 30, 2011 at 10:42 am
tallbloke says:
July 30, 2011 at 9:58 am
I commend Willis for doing the analysis, it adds to our knowledge. I don’t think it provides a basis for dismissing Loehle and Scafetta’s paper, or other efforts to discover the linkage between solar system dynamics and climate, but it should galvanise efforts to improve on their ‘first foray’ into this area.
For the Loehle/Scafetta paper to be valid, the cycles need to be valid. The actual 20 year cycle in the temperature data is extremely weak. Their claimed 60 year cycle in the temperature data cannot be determined to be real. The relative sizes are reversed between the barycentric cycles and the temperature cycles. I’ve shown that we can reconstruct the data (using their method) with a 40 and 60 year cycle.
If that together doesn’t provide “a basis for dismissing Loehle and Scafetta’s paper”, what more do you want?

Hi Willis,
It’s great that you can also get a good fit to the temperature data with 40 and 60 year cycles (I think you’d find it work even better with 60 and 37.6 years – your old pal Ted L liked 37.6, he found it was the best natural subdivision of the 179 year cycle of the outer planets). There are lots of cycles buried in the temperature data. But this doesn’t mean L & S are wrong to use 60 and 20 years, it just means there are several ways of going about doing a study similar to theirs which will produce similarly good looking results.
The question is, how good is the predictive power? It would take a long time to test if we sat and waited for 90 years to see if they’re right, so you have used stats techniques to determine the matter. However, while you show that 60 years is not strong in the solar speed relative to barycentre data, you haven’t done a velocity study, as Nindathana points out. It may be that direction of the vector is unimportant, but given the historical evidence for 60 year cycles, it may be.
Also, the Gnevyshev and Ohl rule tells us that odd numbered solar cycles are usually stronger than even numbered cycles. In a 60 year period, you get ~30 years of two odds and one even, followed by another ~30 year period where you get two even’s and one odd. This rule gets violated in a way we have found is predictable, and the next solar cycle 25 is one of those times. This means the L&S temperature projection is like to get a fairly early falsification in phenomenological terms, regardless of the stats tests.
You probably think I’m rambling by now, but what I’m trying to point out is that we are actually making some good progress with the planetary theory in terms of predicting solar activity. I successfully predicted a solar cycle 24 amplitude of 35-50 SSN in 2008 on CA using Ted L’s methods. L&S have tried to go a step further and predict temperatures and deduce co2 contribution. I personally think they’ve overstretched, but it’s great to see the pioneering spirit alive and well. Scafetta agreed with me that this is a first foray in to the modern climate literature for the planetary theory, and will need to be followed up with more and better developed studies.
Scafetta has complained that you haven’t analysed his preparatory work in Scafetta 2010, so take a look at that, and see if it makes a difference to your view. It would be a shame to see the development of our understanding of the relationships between solar system dynamics and climate killed off before it has a chance to get into a stronger stride.
Best to you.
tb

July 30, 2011 2:11 pm

tallbloke says:
July 30, 2011 at 1:53 pm
I successfully predicted a solar cycle 24 amplitude of 35-50 SSN in 2008 on CA using Ted L’s methods.
First, SC24 has not peaked yet, so your ‘prediction’ cannot be said to be ‘successful’. Second, other people predict a smallish cycle as well, so that you also do that, does not show that your ‘prediction’ stand out as decisive.

July 30, 2011 2:56 pm

Sunspot FFT power spectrum shows large trough at 20 (19.8) years and also smaller one at 60 years.
See http://www.vukcevic.talktalk.net/LFC5.htm Fig.9. However the gmf secular change shows negative imprint of relatively strong 60ish year cycle.
p.s. there is a nice sunspot line-up at the moment, 4-5 groups all in strait line (SDO 30/07/2011) http://sdo.gsfc.nasa.gov/assets/img/latest/latest_1024_4500.jpg

dp
July 30, 2011 3:07 pm

This caught my attention:

There are also smaller geomagnetic field tilt changes with a periodicity of roughly 400 years.

That is the period of time required for the Earth’s core to advance one full rotation relative to the Earth’s surface. The core has a day length that is about 2/3 seconds shorter than the surface. The magnetic field is tied to the core and the magnetic poles are not symmetrical which suggests the core is not the smooth ball of iron shown in the classroom science books. The core and the surface also do not share a common equator.
So if the core has a ragged irregular shape and it is churning in the soup between the core and the surface, there should also be a some kind of bow wave at any significant irregularity on the core. That should be revealed in the regional sea level and in undulations of the Earth’s surface over the 400 year cycle. Perhaps even in the global earthquake and volcanism record.
But if there is a direct climate impact that is driven by cosmic rays whose path is influenced by the variations in the position of the magnetic pole (among other things), that should be stand out from the noise with a period of 400 years.

Richard S Courtney
July 30, 2011 4:06 pm

Willis:
The L&S paper attempted to estimate climate sensitivity (to atmospheric CO2 concentration), but the focus here – and on the other thread – seems to be about astronomical effects on climate.
The important point is whether or not the assumptions that L&S used to derive climate sensitivity are a valid method to determine climate sensitivity. And the astronomical debate is irrelevant to that consideration.
The L&S estimate assumed there are only two cycles (of 20-year and 60-year lengths) which are significant in the climate data, and it assumed those cycles are constant over the analysis and prediction period.
Those assumptions are problematic for several reasons only one of which you are discussing here. As Mike Jonas and I discussed on the earlier thread, the issues are:
Are there ‘real’ (not merely apparent) cycles in climate data?
If there are real cycles, then do they have a cause other than being an indication of resonant frequencies in the climate system?
Are all cycles significant or only some?
Do individual cycles vary in amplitude and frequency?
In my opinion, the significant point of your analysis in this thread is stated by you when (at July 30, 2011 at 2:21 pm ) you say;
“My point is simple. I have shown that the appearance of the 60-year cycle in the temperature data is extremely likely to be an artifact of the length of the record and its autocorrelated nature. In addition, there is no strong 20-year cycle in the temperature data either.”
But that is only a part of the problem. I spelled out the entire issue in my post (July 30, 2011 at 1:02 am ) in the other thread where I wrote:
“[snip]
The issue is that apparent cycles vary but the L&S method assumes they don’t.
The amplitude of cycles varies and not all cycles continue without interruption. The L&S method assesses only two cycles 20-year and 60-year cycle length. Either or both could have increased or reduced its amplitude. And there are other cycles that could have varied, too.
For example, there is another cycle of ~900-year duration that provides the Roman, Medieaval and Present warm periods seperated by the cool periods of the Dark Age and Little Ice Age. This ~900-year cycle is certainly not sinusoidal (warming from the LIA has been approximately linear), and if it continues then it will soon enter (or has started to enter) a cooling phase. The slope of this cycle may have increased or reduced as part of its transition to cooling.
So,
variations in natural cycles could be entirely responsible for the difference between adjacent cycles which the L&S method ascribes to ‘climate sensitivity’.
or, alternatively,
variations in natural cycles may have masked almost all the difference between adjacent cycles which the L&S method ascribes to ‘climate sensitivity’.
It is not possible to determine which of these alternative possiblities is true because
(a) we lack detailed knowledge of the cycles and their causes
and
(b) there is no possibility of deconvoluting the cycles if we had detailed knowledge of the cycles and their causes.
[snip]
In this case, it is not possible to demonstrate the L&S determination of climate sensitivity is ‘good’ because we lack detailed knowledge of the cycles and their causes.
[snip]”
In summation, the climate sensitivity indicated by the L&S method is not justified by the method. The value of climate sensitivity obtained by the L&S method may be near its ‘true’ value (and I think it is) but – if so – then that could be a mere coincidence. In the absence of other information, the possible errors of the method are so great that – according to the L&S method – the ‘true’ climate sensitivity could be larger than the largest used by the IPCC or negative, or anything in between.
Richard

July 30, 2011 4:28 pm

Leif Svalgaard says:
July 30, 2011 at 11:28 am
Geoff Sharp says:
July 30, 2011 at 9:21 am
Also when looking at the 172 year cycle in the temperature or solar proxy record is not supremely evident because the cycle has multiple prongs.[…]
If we only relied on Fourier analysis the world would be a poorer place.
——————————
Sometimes just looking at the data works too [although Fourier analysis would also pick up any cycles, even if the period is not strictly constant]. There is no correlation between your U/N 172 stuff and solar activity. Here are a direct comparison for the past 6000 years
.
Wow, Leif contemplating the Wolff & Patrone paper and now analyzing JPL barycentric data, the world is a changing place. While the JPL distance values are of some use the velocity figures are quite different, you still probably wont see the 60 year signal for the good reasons outlined but you should be working with the right dataset.
But back to your comment…You must have missed my earlier post regarding how the 172 year quasi cycle is hidden from Fourier type analysis so I will repeat, it also applies to the JPL AM data.
———————-
“Also when looking at the 172 year cycle in the temperature or solar proxy record is not supremely evident because the cycle has multiple prongs. It travels in a cluster (usually 3) or multiple components that occur each 172 years. Think of it as a hand on a clock that ends in a trident, every time it goes past midnight the amount of prongs varies, sometimes it has the last prong missing or the first prong could be missing or all three are present. Add to that a variable “strength” to each prong and you see why a regular pattern cannot be teased out, but the underlying force is still there. This is how grand minima works, another example of Uranus and Neptune at work.
If we only relied on Fourier analysis the world would be a poorer place. Nature does not always conform.”
I am trying to make it as simple as possible, if you can see any problem with my reasoning I will step through it slowly if required.

Paul Vaughan
July 30, 2011 5:08 pm

In recent related threads (at WUWT & Climate Etc.) someone linked to this:
Vincze, M.; & Janosi, I.M. (2011). Is the Atlantic Multidecadal Oscillation (AMO) a statistical phantom? Nonlinear Processes in Geophysics 18, 469-475. doi:10.5194/npg-18-469-2011.
http://www.nonlin-processes-geophys.net/18/469/2011/npg-18-469-2011.pdf
Found time to look it over. 3 comments:
1. Erroneously conflates AMO with AMOC.
2. Uses 10-year-smoothed AMO definition without even mentioning more-commonly-encountered AMO definitions.
3. Based on garbage “Gaussian IID” assumption. (For a good laugh, see figure 7. Hopelessly blinded by patently untenable abstraction.)
HOWEVER, they got one very important thing right:
There’s no stationary 60 year cycle.
Regards.

Paul Vaughan
July 30, 2011 5:37 pm

Confounding once again very wisely pointed out by Ninderthana (July 30, 2011 at 10:18 am) [accepting refinement/clarification by Leif Svalgaard (July 30, 2011 at 10:30 am)] sounds sensible. Piers Corbyn appears to be on the same page and I thank him for very efficiently straightening me out (via one very concise e-mail) where I had either misunderstood &/or been misdirected by past comments of Leif Svalgaard. Regards.

July 30, 2011 5:52 pm

Geoff Sharp says:
July 30, 2011 at 4:28 pm
Wow, Leif contemplating the Wolff & Patrone paper and now analyzing JPL barycentric data, the world is a changing place.
In stark contrast to you, I actually examine other possibilities, instaed of being stuck on one worldview.
While the JPL distance values are of some use the velocity figures are quite different, you still probably wont see the 60 year signal for the good reasons outlined but you should be working with the right dataset.
It makes no difference with dataset you are working as they all are just variations on the same reality.
But back to your comment…You must have missed my earlier post regarding how the 172 year quasi cycle is hidden from Fourier type analysis so I will repeat, it also applies to the JPL AM data.
I showed the actual data in an easy to compare format. No Fourier analysis needed.
possible, if you can see any problem with my reasoning I will step through it slowly if required.
You can begin by
1) showing that the speed or AM data are different from the distance data.
2) annotating [with circles or red dots] how the U/N perturbations align with the grand minima on the plots I provided.
Paul Vaughan says:
July 30, 2011 at 5:08 pm
HOWEVER, they got one very important thing right:
There’s no stationary 60 year cycle.

Agree, Geoff?
Regards.
Paul Vaughan says:
July 30, 2011 at 5:37 pm
Confounding once again very wisely pointed out by Ninderthana (July 30, 2011 at 10:18 am) [accepting refinement/clarification by Leif Svalgaard (July 30, 2011 at 10:30 am)] sounds sensible.
Obscure as always. If you have something to say, say it in plain English.

John Day
July 30, 2011 6:20 pm

Day
So you can’t reconstruct the original signal by simply adding the spectral components, at least not without a lot of complicated bookkeeping to account for interactions between components.
@Willis
Well … since I reconstructed the signal in Figure 6 without any “complicated bookkeeping”, I’m not sure what you mean by this objection. I just calculated the individual cycles and added them together … what am I missing?
Sorry, I didn’t make myself clear. What I meant was (if the projection space axes are not orthogonal) that you get a different decomposition depending on the order in which you pick the projections to subtract for calculating residuals. The ‘bookkeeping’ would be the calculation of the interactions between the non-orthogonal components, to reconcile the variance caused by ordering.
Quoting Sephares and Staley from their original paper on periodicty analysis:
“… a projection onto one sinusoidal basis function (in the Fourier transform)
is independent of the projections onto others, and the Fourier
decomposition can proceed by projecting onto one subspace,
subtracting out the projection, and repeating. Orthogonality
guarantees that the order of projection is irrelevant. This is
not true for projection onto nonorthogonal subspaces such as
the periodic subspaces [for Periodicity Analysis] … ”
Consider the simple example of a 2-D orthogonal system eg. X-Y axes for plotting 2-D points. If I change the X coordinate of a point, it will move in the X direction, but the Y value of the point will remain the same. Now what happens if the X-Y axes are not orthogonal, i.e. some other angle than ninety degrees (say 45 degrees). Now the Y values are dependent on the X values. If I change the X value and replot the new point will have a different Y value, dependent on the amount of non-orthogonality.
The authors go on to say that this is not always bad. It creates a kind of non-unique redundacy that they found useful. But I think it’s bad if you’re depending on the spectral analysis to create unique signatures which are invariant to spatial shifting (which Fourier (and Gabor) components offer).
There is a similar concept in wavelet analysis (that Paul Vaughan mentioned) called ‘wavelet frames’, which are wavelet bases which have a certain amount of redundant non-orthognality (with a frame parameter which allows you to adjust this redundacy from ‘loose’ (highly redundant) to ‘tight’ (almost orthogonal): http://inst.eecs.berkeley.edu/~ee225b/sp11/handouts/wavelet-vetterli-1991.pdf [see page 23]
I’m still not clear on the HADCRUT3 spectra above. Could you provide a pointer to the data you analyzed so I can do my own spectral analysis?
Thanks.

July 30, 2011 6:55 pm

Willis
Does not the global mean temperature anomaly show a 60 years cycle as shown below?
http://bit.ly/ePQnJj

July 30, 2011 8:59 pm

Leif Svalgaard says:
July 30, 2011 at 5:52 pm
You can begin by
1) showing that the speed or AM data are different from the distance data.
2) annotating [with circles or red dots] how the U/N perturbations align with the grand minima on the plots I provided.

1. You are not keeping up Leif. I produced this graph in May 2009, it is on my website, in my paper and produced here at least 5 times in the past few days.
http://tinyurl.com/2dg9u22/images/vel_am.jpg
Please take the time to study it properly. While AM and solar velocity are related you will notice there are times when there is some divergence in the peaks and troughs. This happens mainly near the yellow dots which is the U/N conjunction. The AM data is more closely related to the distance data but still not the same.
2. It is far better to plot the AM when looking for U/N perturbations, once again the detail you require has been published since 2008. My paper has the annotations back to 1200BC. These perturbations relate to grand minima triggers, they have nothing to do with the 60 year cycle.
http://arxiv.org/ftp/arxiv/papers/1005/1005.5303.pdf
Both yourself and Willis have refused to look at the data via other methods and rely solely on a one pass method of analysis. I have shown why the cycles are not apparent in the Fourier analysis but to no avail. Are you guys talking past me?
When it comes to solar velocity and the solar powerwave the background trend is what is important. I cant see why you fail to see this. Once again look at the powerwave diagram, see the AM wave that modulates solar cycle output, it is a 172 year modulation of the solar dynamo which is a second level background trend that will never show via your methods.
http://tinyurl.com/2dg9u22/images/Powerwave.png
A guide to understanding the powerwave below…read it.
http://tinyurl.com/2dg9u22/?q=node/218

July 30, 2011 9:41 pm

Geoff Sharp says:
July 30, 2011 at 8:59 pm
Please take the time to study it properly. While AM and solar velocity are related you will notice there are times when there is some divergence in the peaks and troughs. This happens mainly near the yellow dots which is the U/N conjunction. The AM data is more closely related to the distance data but still not the same.
Granted that the solar velocity is a crappy fit to AM. However the distance shows the influence of U/N even more clearly, while otherwise agreeing closely with AM:
http://www.leif.org/research/Comparison-AM-Barycenter-Distance.png
Because 1) the Steinhilber solar activity curve is the best we have for the moment [based both on 10Be and 14C], and 2) we need to see the result on a bigger scale, please annotate with red dots the graphs I provided:
http://www.leif.org/research/Solar-Activity-vs.Barycenter-Distance-BC.png
Failure to do so is a clear indication thet the curves don’t correlate, right?
Are you guys talking past me?
No, i’m showing you the raw data, no FFT, so please annotate the graphs and show us.
When it comes to solar velocity and the solar powerwave the background trend is what is important. I cant see why you fail to see this.
If the comparison fails or you fail to make it, there is no need to look at the rest.

July 30, 2011 10:02 pm

Geoff Sharp says:
July 30, 2011 at 8:59 pm
Once again look at the powerwave diagram, see the AM wave that modulates solar cycle output
It is clear by inspection that what you label ‘Angular Momentum’ and call ‘the AM Wave on
http://www.landscheidt.info/images/Powerwave.png
is not what you show as labelled ‘Angular Momentum’ ob this graph
http://tinyurl.com/2dg9u22/images/vel_am.jpg
Perhaps you could explain that. It seems that on the first graph the AM wave have 11-yr cycles to match[?] the solar cycles, but on the second graph you show the real AM with its 20-yr period.

July 30, 2011 10:10 pm

Geoff Sharp says:
July 30, 2011 at 8:59 pm
When it comes to solar velocity and the solar powerwave the background trend is what is important. I cant see why you fail to see this.
If the comparison fails or you fail to make it, there is no need to look at the rest.
But it is also clear that what you label ‘Angular Momentum’ on the ‘powerwave plot’
http://tinyurl.com/2dg9u22/images/Powerwave.png [seems to have ~11-yr period]
is not what you [correctly] label ‘Angular Momentum’ on this plot:
http://tinyurl.com/2dg9u22/images/vel_am.jpg [seems to have ~20-yr period, as it should]
This is perhaps one reason that we don’t see it…

July 30, 2011 11:11 pm

Leif Svalgaard says:
July 30, 2011 at 10:02 pm
Perhaps you could explain that. It seems that on the first graph the AM wave have 11-yr cycles to match[?] the solar cycles, but on the second graph you show the real AM with its 20-yr period.
There is an explanation on my website and in my paper but happy to repeat here. The AM graph is a sine wave, but the high and low values have equal value. Think of linear acceleration/deceleration where each is just as important. Another method would be to invert every second sunspot cycle but I chose to invert the bottom half of the AM graph to show the wave. The objective is to show the power function that might be difficult to visualize using other methods.
It is important to compare the solar AM values with the Holocene record. The U/N perturbations come in different forms that need to be understood, using a different format will cause confusion. It is a big job to produce the AM charts, 3000 years should be enough data (1200BC) to do an initial check. If need be I can go back further at a later date or you could try yourself using Carl’s data, the important issue is to understand how to quantify the U/N perturbation, there are at least 2 types that vary in intensity. There are other factors that need to be known before comparison and I suggest you read my paper thoroughly. You will also see I have already done the comparison you are attempting in my paper using the Solanki data.
I will await your questions on perturbation quantification.

July 30, 2011 11:32 pm

Geoff Sharp says:
July 30, 2011 at 11:11 pm
The AM graph is a sine wave, but the high and low values have equal value.
If they have equal value they cannot be high and low. In any event, the graph is the misleadingly mislabeled. Both the text and the left-hand scale.
Think of linear acceleration/deceleration where each is just as important.
This does not make sense. What you are doing is to invert half of the down slope and half of the up slope. There is no justification for this as the deceleration covers the whole of the down slope and the acceleration covers the whole of the up slope, not just half.
The objective is to show the power function that might be difficult to visualize using other methods.
It seems to me that the objective is to cope with the fact that the AM shows a 20-yr cycle and not a 10-yr cycle, and thus is just a misleading sleight of hand. Not science.
It is important to compare the solar AM values with the Holocene record.
This is what I do, 5000 years of it.
It is a big job to produce the AM charts
It took me all of 10 minutes.
I will await your questions on perturbation quantification.
Naw, not needed as the correlation you claim has already been shown to be non-existing. I have carefully prepared corresponding AM and solar activity records for you to put dots on. To regain a little credibility you should annotate the graphs I [with minimal effort] have prepared for you. This is like dividing a cake. One person does the slicing, the other person chooses which slice he wants. In this way, a fair division is assured. So, annotate!

July 31, 2011 12:56 am

Leif Svalgaard says:
July 30, 2011 at 11:32 pm
Geoff Sharp says:
July 30, 2011 at 11:11 pm
The AM graph is a sine wave, but the high and low values have equal value.
If they have equal value they cannot be high and low. In any event, the graph is the misleadingly mislabeled. Both the text and the left-hand scale.

The left hand scale is a calculated value for all values under 2E+47, so maybe a bit confusing.
Think of linear acceleration/deceleration where each is just as important.
This does not make sense. What you are doing is to invert half of the down slope and half of the up slope. There is no justification for this as the deceleration covers the whole of the down slope and the acceleration covers the whole of the up slope, not just half.

Yes, your right a bad analogy, the second half of the cycle would be more appropriate. Observations show that solar cycles are higher the further the AM chart gets away from the centre line. When you get into perturbation quantification this will become clear. Your analysis could also be useful.
The objective is to show the power function that might be difficult to visualize using other methods.
It seems to me that the objective is to cope with the fact that the AM shows a 20-yr cycle and not a 10-yr cycle, and thus is just a misleading sleight of hand. Not science.

Not at all. I can tell you have not read the paper, otherwise you would realize I am NOT trying to line up the AM cycles with the solar cycles. The AM curve is purely a background engine and not responsible for cycle length, it doesn’t matter how long the cycle is. This is the mistake that Ed Fix is making. To make it clearer, each AM cycle represents the outer and inner loop of the solar path which is around 10 years each. A large outer loop usually corresponds with a high solar cycle, a tight inner loop close to the SSB corresponds with a higher solar cycle. This is the modulating force, but there are times when the disruptive force (grand minima) over rides. The timing of the U/N perturbation should also start to become clear. This diagram will help. (you should have studied it already)
http://tinyurl.com/2dg9u22/images/carsten.jpg
It is important to compare the solar AM values with the Holocene record.
——————-
This is what I do, 5000 years of it.
It is a big job to produce the AM charts
It took me all of 10 minutes.

This exercise cannot be done with the solar distance values, you need to either plot Carl’s AM values or pull out all the JPL vector data and apply a formula.
I will await your questions on perturbation quantification.
Naw, not needed as the correlation you claim has already been shown to be non-existing. I have carefully prepared corresponding AM and solar activity records for you to put dots on. To regain a little credibility you should annotate the graphs I [with minimal effort] have prepared for you. This is like dividing a cake. One person does the slicing, the other person chooses which slice he wants. In this way, a fair division is assured. So, annotate!

No, you have prepared solar distance graphs. I have already annotated the AM graphs back to 1200BC. If they are not sufficient we will have to start again. You are not in a position yet to determine correlation.

July 31, 2011 1:39 am

Drs. Svalgaard & Eschenbach
Here is 4 centuries long data file.
http://www.vukcevic.talktalk.net/4C-data.txt
To resolve the dilemma of a natural ~60 year component ‘operating’ in the geo-sphere could you please do independently spectral analysis and provide links to the output data in numerical (and graphic, if you whish to do so) form.

July 31, 2011 1:52 am

Geoff Sharp says:
July 31, 2011 at 12:56 am
Not at all. I can tell you have not read the paper
Yes I have, but doesn’t make sense.
This exercise cannot be done with the solar distance values, you need to either plot Carl’s AM values or pull out all the JPL vector data and apply a formula.
No, as I show here http://www.leif.org/Comparison-AM-Barycentric-Distance, the two curves agree very well.
No, you have prepared solar distance graphs. I have already annotated the AM graphs back to 1200BC. If they are not sufficient we will have to start again. You are not in a position yet to determine correlation.
Solar distance and AM show the same variations, so either can be used. Once can even argue that the distance is the better one [c.f. the Wolf-Patrone paper]. And the better solar curve to use is Steinhilber’s. I have annotated already: http://www.leif.org/research/Solar-Activity-vs.Barycenter-Distance-Annotated.png but probably too crudely, so you should annotate using your view on things on
http://www.leif.org/research/Solar-Activity-vs.Barycenter-Distance-BC.png
Maybe use different colored dots for the many different types of variations you claim to see. So far, I see no correlation.

July 31, 2011 1:54 am

Leif Svalgaard says:
July 31, 2011 at 1:53 am
It is getting late:
No, as I show here http://www.leif.org/Comparison-AM-Barycenter-Distance.png , the two curves agree very well.

July 31, 2011 1:55 am

Leif Svalgaard says:
July 31, 2011 at 1:54 am
When it rains, it pours:
It is getting late:
No, as I show here http://www.leif.org/research/Comparison-AM-Barycenter-Distance.png , the two curves agree very well.

July 31, 2011 4:23 am

Leif Svalgaard says:
July 31, 2011 at 1:55 am
Leif Svalgaard says:
July 31, 2011 at 1:54 am
When it rains, it pours:
It is getting late:
No, as I show here http://www.leif.org/research/Comparison-AM-Barycenter-Distance.png , the two curves agree very well.

The shape of the perturbation curves is instrumental in determining the timing and strength of the perturbation. The distant graph has the perturbations in the same place but they are different. For the sake of the exercise I will transpose the perturbation values from the AM graph (1 to 5) on your graph back to 1200BC. I would normally also expand out the graph to define the detail. Another method is to compare planet angles.
I will update tomorrow, meanwhile we still have the argument to address that is the centrepoint of this thread. My powerwave diagram shows an AM modulating cycle over 172 years that is not available through Willis’s analysis. It doesn’t matter how it is displayed orbital physics dictates solar AM must be greatest (and lowest as per Landsch***t zero crossing) at the U/N conjunction. The background trend being important, the 20 year cycle is irrelevant. That is just the modulating force, if looking at the disruptive force there would be no way of recognizing a background cycle.
The same logic is applicable to the quasi 60 year cycle ala Scafetta.

Ninderthana
July 31, 2011 6:16 am

Leif Svalgaard says: July 30, 2011 at 10:30 am
LS: The seasons are synchronized with the sun [the tropical year], not with the distant stars.
This shows me that you are totally clueless about the basic physics involved.
LS: Fourier analysis of the distance [in AU] between the sun and the barycenter [inversely related to the speed; doesn’t matter which one is used]
This confirms it.
I made the mistake of assuming that you have completed a basic high school physics course. If you had you would understand the difference between magnitude and direction, between a vector and a scaler, and between the magnitude of a force and the direction of a force. Clearly you don’t.
An object will react differently depending on both the magnitude and the direction of the force that is applied to it.
Since you clearly haven’t a clue about these basic definitions there is no point going any further.
You make original Sophists look good!

Ninderthana
July 31, 2011 6:30 am

Oh and if you are wondering why I am calling Leif a sophist? The following statement by him says it all.
LS said: The seasons are synchronized with the sun [the tropical year], not with the distant stars.
If a external force plays a role in the Earth’s climate (either directly or indirectly) it most likely will be one where is applied at the same point in the seasonal (i.e. tropical year). This occurs at roughly the same point in the Earth’s orbit compared to the fixed stars (e.g. perihelion occurs on January 3rd).
Leif is trying to quibble over the slow drift the Earth’s orbit and Earth’s tilt with respect to the stars that take place over tens of thousands of years. Of course he thinks that people will be impressed by the fact that he brought up this shiny little piece of minutia, since he sees the world through the eye’s of a Sophist.

Paul Vaughan
July 31, 2011 7:19 am

Ninderthana, surely there are publications on the confounding? Do you have any references? Or perhaps the names of experts who specialize in coupling and the evolving balance of competing astrophysical synchronizations?

tallbloke
July 31, 2011 7:34 am

Willis, the strong sixty year modulation in the barycentre data is in the z axis. The Sun is tilted wrt the plane of invariance and so when the conjunction between Jupiter and Saturn takes place near the nodes of the solar equatorial plane and the plane of invariance there is less ‘pull’ on the Solar core in the up or down direction. Because the three conjunctions over the sixty year period take place almost exactly 240 degrees apart (the precession period is 934 years for a 120 degree displacement), the power of this effect will be modulated over 934/2=467 year period (because there are two nodes), but since there seems to be a ~934 year analog in Earth’s climate, (MWP-LIA-Now) it seems likely that another factor comes into play, such as the orientation of the conjunctions to the bowshock of the heliosphere (Vuk’s idea) or the orientation wrt the galactic centre.
The 467 year period is near a cyclic frequency we found to be important in this study:
http://tallbloke.wordpress.com/2011/02/21/tallbloke-and-tim-channon-a-cycles-analysis-approach-to-predicting-solar-activity/

Steve from Rockwood
July 31, 2011 7:59 am

Leif Svalgaard says:
July 30, 2011 at 1:04 pm
Steve from Rockwood says:
July 30, 2011 at 11:46 am
@Leif,
It looks to me as though your data set is heavily over-sampled with one single – very well represented sine wave of very high frequency (best case scenario) – superimposed on a linear trend – yes that has a higher amplitude than the sine wave.
I may be missing something but isn’t the temperature record good only for about 150 years and the cycles you are examining are are 20 to 60 years in period. Try creating a data set with 150 points that shows two 20 year cycles superimposed on what looks like a liner trend having an amplitude greater than that of the cycles. That would convince me.
If you selected a 128 point data set (one for each year) I don’t see how you have the resolution to ignore large trends in the data. A 60 year cycle represents half your time series.
If someone can point me to the raw temperature time series from 1850 to present (one that’s not fudged) I’ll dust off my FFT program and run it through.
Leif you have 45 cycles or so in your time series. Assuming a 150 year period to your data set and 4 points per cycle, you used a frequency of under 4 years equivalent. No wonder it works.
Steve

dp
July 31, 2011 9:15 am

Ninderthana says:

This occurs at roughly the same point in the Earth’s orbit compared to the fixed stars (e.g. perihelion occurs on January 3rd).

You are using spatial orientation based on star locations to describe what Leif is saying using only the local system for orientation. Both yours and Leif’s orientations land us at the same place relative to the sun in the short term, but Leif’s point remains clearer – it is only the local system and not the rest of the universe that influences with any degree of significance, our weather. That slow drift you’re kicking to the curb does in fact affect climate.

July 31, 2011 10:04 am

Ninderthana says:
July 31, 2011 at 6:16 am
An object will react differently depending on both the magnitude and the direction of the force that is applied to it.
Gravity [hence tides] between two always works along the line connecting the centers of the bodies.
The influence of the Sun on the Earth follows the tropical year [not with respect to the stars]. A simple example: the day-night cycles. There are 365 such in the course of a year, but the Earth rotates 366 times a year with respect to the distant stars.
tallbloke says:
July 31, 2011 at 7:34 am
Willis, the strong sixty year modulation in the barycentre data is in the z axis.
The sun is in free fall and feels to forces so has no modulation from that source.
Steve from Rockwood says:
July 31, 2011 at 7:59 am
I may be missing something but isn’t the temperature record good only for about 150 years and the cycles you are examining are are 20 to 60 years in period.
I’m not concerned with the temperature record [and have not commented on it]. I’m looking at ten thousand years of solar cycles which people claim are responsible for the temperature changes [at least until the last half century where they claim the changes are man-made].

July 31, 2011 10:06 am

Geoff Sharp says:
July 31, 2011 at 4:23 am
I will update tomorrow, meanwhile we still have the argument to address that is the centrepoint of this thread.
Please update the graphs I gave you, so we know the data is good.

July 31, 2011 10:07 am

Ninderthana says:
July 31, 2011 at 6:16 am
An object will react differently depending on both the magnitude and the direction of the force that is applied to it.
Gravity [hence tides] between two always works along the line connecting the centers of the bodies.
The influence of the Sun on the Earth follows the tropical year [not with respect to the stars]. A simple example: the day-night cycles. There are 365 such in the course of a year, but the Earth rotates 366 times a year with respect to the distant stars.

Paul Vaughan
July 31, 2011 10:50 am

tallbloke (July 31, 2011 at 7:34 am) wrote:
“Willis, the strong sixty year modulation in the barycentre data is in the z axis.”
The dominant z-axis terms are J, S, U, & N
(none of which has a period of 60 years
and no pair of which produce 60 year beats).

July 31, 2011 11:28 am

Riding a Pseudocycle
Posted on July 30, 2011 by Willis Eschenbach
Guest Post by Willis Eschenbach
“… I started all of this because I thought that the analysis of random red-noise datasets might show spurious cycles. So I made up some random red-noise datasets the same length as the HadCRUT3 annual temperature records (158 years), and I checked to see if they contained what look like cycles.”
Hi Willis,
I am sorry, but your investigation is a fallacy called Ignoratio elenchi. Nicola Scafetta has argued a ~60 year cycle from empirical evidence for a celestial origin of the climate oscillations. In his paper in 2010 on Fig. 2 a ~ 60 year cycle is possible, and because it is not out of the question that there is a real basis from celestial body frequencies, this period can have a real basis in the solar system.
Your investigation is a demonstration using irrelevant material, which you call random, (random is not an object of science, because it cannot be proofed. It is like the demonstration 3/0 = infinite, 4/0 = infinite, conclusion 3 = 4.)
‘The fallacy of Irrelevant Conclusion consists of claiming that an argument supports a particular conclusion when it is actually logically nothing to do with that conclusion.’
That indeed there is some celestial substance behind a ~60 year cycle one can find if he sum up some synodic tide couples using of empirical magnitudes:
http://volker-doormann.org/gif/bulloides_1650_a.gif
OK, there are some more tunes as the ~60 year sound, but as the possible simulation shows, there IS a connection.
The point of critique was taking the cycle as cycle without any phase or coherence in time
Like darkness, or cold, also pseudo is not to be grasp, always only intensity or heat or that what IS (real) (Parmenides).
Volker

old engineer
July 31, 2011 11:39 am

Willis-
Thanks for another thought provoking post. You always make me think and stretch my math knowledge and understanding.
I am not at all qualified to comment on the discussion of Fourier Analysis versus Periodicity Analysis. But there something in the logic of your discussion that I don’t understand.
You take a number of red noise cycles (and one real world cycle- HadCRUT3) and apply Periodicity Analysis to them. You get cycles for each case. Doesn’t that discredit the idea of using Periodicity, since it shows cycles where there were none? And as you point out, you can’t tell the HadCRUT3 data from the red noise.
If I understand Fourier Analysis correctly, if you did a Fourier Analysis on your red noise cycles you would get a whole bunch of sine waves for each case that would add up to the actual data over the year range considered (So you get cycles here too, where there are none). Of course, these sine waves are just mathematical entities that happen add up to the data over the range considered. So I really don’t see the difference between using Periodicity Analysis and Fourier Analysis.
I remember when I first started looking at temperature data several years ago, The thing that jumped out at me was the eyeballed 60 year cycle of the data (of course the data coverage is only for two 2 cycles). Your random 21 looks most like the HadCRUT3 data (although you don’t say you included it the graphs). Its shows a strong 60 year cycle.
I understand (I think) that with Periodicity Analysis the component cycles don’t have to be sine waves, which may help in understanding the physical causes of the temperature variation. But my question is: If with periodicity Analysis you can’t distinguish between red noise and a real cycle how is it better than Fourier Analysis?
Thanks again for making me think and expanding my understanding.

tallbloke
July 31, 2011 1:16 pm

Paul Vaughan says:
July 31, 2011 at 10:50 am
tallbloke (July 31, 2011 at 7:34 am) wrote:
“Willis, the strong sixty year modulation in the barycentre data is in the z axis.”
The dominant z-axis terms are J, S, U, & N
(none of which has a period of 60 years
and no pair of which produce 60 year beats).

Clearly you didn’t understand what I wrote, assuming you bothered to read it.

tallbloke
July 31, 2011 1:25 pm

Leif Svalgaard says:
July 31, 2011 at 10:04 am
tallbloke says:
July 31, 2011 at 7:34 am
Willis, the strong sixty year modulation in the barycentre data is in the z axis.
The sun is in free fall and feels to forces so has no modulation from that source.

There is a relativistic effect proposed by Ray Tomes which could account for motion of the solar core relative to the surface caused by the passage of the outer planets above and below the solar equatorial plane which would cause significant meridional flows at the solar surface. The resultant amplitude of motion of the core would not introduce a detectable libration in Mercury’s orbit however, so that previous objection of yours is ruled out.

July 31, 2011 1:38 pm

tallbloke says:
July 31, 2011 at 1:25 pm
There is a relativistic effect proposed by Ray Tomes
Sorry, Ray’s ‘harmonic theories’ [ http://ray.tomes.biz//maths.html ] are pseudo-science, worthy of a place on your blog. His ‘relativistic effect’ http://ray.tomes.biz/rt106.htm is gibberish.

tallbloke
July 31, 2011 2:50 pm

Leif Svalgaard says:
July 31, 2011 at 1:38 pm
Ray’s ‘harmonic theories’ [ http://ray.tomes.biz//maths.html ] are pseudo-science, worthy of a place on your blog. His ‘relativistic effect’ http://ray.tomes.biz/rt106.htm is gibberish.
You are entitled to your opinions, poorly informed and boorish though they are.

Paul Vaughan
July 31, 2011 2:57 pm

tallbloke (July 31, 2011 at 1:16 pm) “Clearly you didn’t understand what I wrote, assuming you bothered to read it.”
There’s no stationary 60 year cycle in terrestrial climate.

tallbloke
July 31, 2011 3:09 pm

Paul Vaughan says:
July 31, 2011 at 2:57 pm
tallbloke (July 31, 2011 at 1:16 pm) “Clearly you didn’t understand what I wrote, assuming you bothered to read it.”
There’s no stationary 60 year cycle in terrestrial climate.

The 60 year J-S signal in the z-axis barycentre data is modulated by U & N, which shifts things around quite a lot.

Paul Vaughan
July 31, 2011 3:59 pm

tallbloke (July 31, 2011 at 3:09 pm)
“The 60 year J-S signal in the z-axis barycentre data is modulated by U & N, which shifts things around quite a lot.”
Uh, yeah, ok. Be sure & show us your methods…

July 31, 2011 4:15 pm

tallbloke says:
July 31, 2011 at 2:50 pm
You are entitled to your opinions, poorly informed and boorish though they are.
hitting a new low point, eh?

July 31, 2011 4:19 pm

tallbloke says:
July 31, 2011 at 3:09 pm
The 60 year J-S signal in the z-axis barycentre data is modulated by U & N, which shifts things around quite a lot.
How far back have you gone with the “z” data. I have only seen graphs over a short timeframe from you. I would have thought the “z” axis movements would be highly affected by orbit precession?

tallbloke
July 31, 2011 4:27 pm

Leif Svalgaard says:
July 31, 2011 at 4:15 pm
tallbloke says:
July 31, 2011 at 2:50 pm
You are entitled to your opinions, poorly informed and boorish though they are.
hitting a new low point, eh?

With such an ad hom attack on Ray Tomes who isn’t here to speak for himself I’d agree you did, yes.

tallbloke
July 31, 2011 4:29 pm

Geoff Sharp says:
July 31, 2011 at 4:19 pm
How far back have you gone with the “z” data. I have only seen graphs over a short timeframe from you. I would have thought the “z” axis movements would be highly affected by orbit precession?

I ran it back 3000 years.
The precession of which orbit or orbits?

July 31, 2011 4:35 pm

tallbloke says:
July 31, 2011 at 4:27 pm
With such an ad hom attack on Ray Tomes who isn’t here to speak for himself I’d agree you did, yes.
You need to make a distinction between talking about someones ideas and the person. I was referring to his ideas. You were ad-homing a person [me]. Do you understand the difference?

tallbloke
July 31, 2011 4:45 pm

You didn’t talk about his ideas, you arrogantly and rudely dismissed them without any supporting argument.
Goodnight.

July 31, 2011 5:22 pm

tallbloke says:
July 31, 2011 at 4:45 pm
You didn’t talk about his ideas, you arrogantly and rudely dismissed them without any supporting argument.
I referred yo his theories:
“Ray’s ‘harmonic theories’ [ http://ray.tomes.biz//maths.html ] are pseudo-science, worthy of a place on your blog. His ‘relativistic effect’ http://ray.tomes.biz/rt106.htm is gibberish.”
There are things that are so wrong [or not even wrong] that no supporting argument is needed to debunk them. For starters, he begins:
“Einstein showed that gravity has an effect on horizontal light which is to bend it by twice as much as would be expected by Newtonian physics. That is, horizontal light is accelerated by gravity twice as much as other matter! Because vertical light is affected only the same as other matter, the average effect on randomly moving light is 5/3 times.”
Horizontal light? Vertical light? Accelerated twice as much as other matter? Vertical light affected the same as other matter? Already there he is off the rail.
Light moving out from the core of the Sun moves on average radially out and the sun is a symmetric sphere, so there is no ‘horizontal/vertical’ light. It is all ‘vertical’, and so on. As I said: gibberish.

Geoff Sharp
July 31, 2011 5:25 pm

tallbloke says:
July 31, 2011 at 4:29 pm
Geoff Sharp says:
July 31, 2011 at 4:19 pm
How far back have you gone with the “z” data. I have only seen graphs over a short timeframe from you. I would have thought the “z” axis movements would be highly affected by orbit precession?
______________________
I ran it back 3000 years.
The precession of which orbit or orbits?

Can we see the results over 3000 years to see if there is a regular cycle. I was thinking all planetary orbits with their differing precessions would vary the z axis values over time allowing no repeatable pattern.

J. Bob
July 31, 2011 7:30 pm

Girma,
Enclosed is a comparison between the Fourier (cutoff freq. 0.025 cycles/yr) & the EMD method as proposed by Wu, etc., “On the Trend, De-trending and Variability of Nonlinear and Non-stationary Time Series” by Wu, Huang, Long and Peng.
http://www.4shared.com/photo/2foIw4k7/CRU-Fig-6a.html
While there may be some differences, the EMD & Fourier Filtered results are about the same, as well as a fairly well defined ~60-65 year wave.

July 31, 2011 10:22 pm

Leif Svalgaard says:
July 31, 2011 at 1:52 am
First stage of perturbation annotation complete.
I have labelled two areas where the Solanki data diverges from the Steinhilber. The scaling method is .5, 1,2,3,4 with 4 being the strongest. I have used the visual method of quantification as per fig. 10 in paper. Future calibration could be improved with planet angles of perhaps by Wolff and Patrone. I have spoken to Dr. Wolff who thinks the grand minima perturbations also fit in with their theory.
Tip. Read up on Wilson’s Law (fig. 11 in paper) as per 1830. AM is a background engine and can depend on timing of the solar cycle as to if a disruption occurs ie, if perturbation happens just before cycle max it may be wasted and not allow conditions for “phase catastrophe” (following solar cycle is affected also).
It is quite possible that the dynamo theory can work with AM theory, all the dynamo principles stay intact except for the origin of the dynamo (no more crap shoot) and the poles would not be a driver but more an indicator.

tallbloke
July 31, 2011 11:50 pm

Leif Svalgaard says:
July 31, 2011 at 5:22 pm
Horizontal light? Vertical light? Accelerated twice as much as other matter? ….Gibberish…pseudoscience.

Ray knows the difference between orthogonal and radial Leif. He is addressing a lay audience.
This is Willis’ thread about cycles and we’re not discussing physical causation of solar variation here. I’ll set up a discussion on my blog where Ray can answer your (politely put) questions if he wishes. Impolitely put questions will be deleted.
He told me he consulted with more than one recognised expert on relativity while formulating his hypothesis, and they couldn’t agree with each other, so he gave calcs for both scenarios in a later formulation than the one you linked. Given your demonstrated inability to understand the Newtonian property dynamics of bulk gases as opposed to their constituent atoms or molecules I very much doubt you were one of those experts. I recognise your expertise in stats and programming, but I think you are a bit of a duffer in some other areas. In fact, after reading your long argument with Bart on Pat Franks’ thread I’m not too sure about your knowledge or ability around spectral analysis any more either.
Good day.

tallbloke
August 1, 2011 12:06 am

Geoff Sharp says:
July 31, 2011 at 5:25 pm
Can we see the results over 3000 years to see if there is a regular cycle. I was thinking all planetary orbits with their differing precessions would vary the z axis values over time allowing no repeatable pattern.

I’ll have to dig the graph off my backup disc, when I’ve found it’s power cable…It might be quicker to download it.
In the meantime, take it from me that with about the same amount of variation as the X-Y data, the pattern regularly repeats on the same timescales.
Do you mean the precession of the nodes of the orbits? If so, do you have a table of these?
Judging by the regularity of the pattern the nodes of the gas giant’s orbits change very slowly, and a couple of them to and fro rather than continuing around solar system reference frame relative to ‘fixed stars’. E.g. there’s an angular momentum exchange between J and N at the frequency of the Hallstadt cycle. The inner planets don’t affect the curve much.

August 1, 2011 12:41 am

tallbloke says:
August 1, 2011 at 12:06 am
Geoff Sharp says:
July 31, 2011 at 5:25 pm
Can we see the results over 3000 years to see if there is a regular cycle. I was thinking all planetary orbits with their differing precessions would vary the z axis values over time allowing no repeatable pattern.
—————————–
I’ll have to dig the graph off my backup disc, when I’ve found it’s power cable…It might be quicker to download it.

Thanks I would be interested to see. In relation to the precession, looking at the solar system from the side in line with the solar equator let’s say the Jupiter Z axis is at its highest point right now. In 55,000 years it will be at its lowest point (at the same timing point of the orbit) if my figures are correct. The other planets would be precessing at different rates on their inclined orbits which should mean the total Z axis data will be shifting on a constant basis. I am not sure if the plane of the planet inclined orbit shifts with the precession, but either way the total mass must change over time?
Precession in the XY plane along with the differing orbit speeds produce different planet positions every 172 years (this is the shape of the solar proxy holocene record) but this is quite different to the mass changes experienced in the Z axis.

August 1, 2011 4:28 am

Geoff Sharp says:
July 31, 2011 at 5:25 pm
“Can we see the results over 3000 years to see if there is a regular cycle. I was thinking all planetary orbits with their differing precessions would vary the z axis values over time allowing no repeatable pattern.”
Things are simple.
A cycle related to the Earth says nothing. The common dimension is the frequency [year^ -1].
I propos the unit Kepler [Kp] with 1 Kp = 1/y.
Things then are more simple and can easy related to an energy or an angular momentum
[kg m^2 sec^-1] or [V A s^2]. Same unit as Planck’s constant h (This means that an angular momentum multiplied with a frequency is an energy [J] (!) ).
Using the unit [Kp] it is easy to find synodic frequencies of couples.
The dimension year is good for counting celebrations of human couples.
But also synodic frequencies tell not much, because of the nonregular movement of the synodic function. But is very simple to calculate the absolute angles measured on the ecliptic and moreover to calculate the >9 main body synodic functions.
Doing this, one can get a function, which include all real syndic function, and can compared it with what you like, 14C, gletcher retreats, sea level, CO2, global temperatures, a.s.o.
This graph is an example that compares your plot with the AM and Landscheidt’s calculation:
http://volker-doormann.org/images/ghi4n_vs_land_1.jpg
You can see that the frequency resolution of the GHI4n is better as the resolution from Landscheidt. This can be understood, because he was dealing with cycles, not with real celestial functions of synodic couples.
Most of the same synodic couples are used to sum up the GHI6, which can compared to the sample of G. Bulloides Nicola Scafetta has used in hie 2010 paper.
http://volker-doormann.org/gif/bulloides_1650_a.gif
In general the strength of the couple’s amplitude could be found by an automatic fitting starting with this empiric data using the high frequency proxies from A. Moberg et. al or global temperatures like Hadcrut or other. I have done this GHI amplitudes by hand using table calculation on my old 486 CPU PC.
Volker

August 1, 2011 6:43 am

Geoff Sharp says:
July 31, 2011 at 10:22 pm
First stage of perturbation annotation complete.
I have spoken to Dr. Wolff who thinks the grand minima perturbations also fit in with their theory.

So far the agreement does not look so good. I presume you also do the the BC part. Wolff does not believe in AM having any influence.

August 1, 2011 6:50 am

tallbloke says:
July 31, 2011 at 11:50 pm
Ray knows the difference between orthogonal and radial Leif. He is addressing a lay audience.
That still does not make it any better. On the contrary, it means that he should try even harder to make it make sense.
Given your demonstrated inability to understand the Newtonian property dynamics of bulk gases as opposed to their constituent atoms or molecules
Newton’s laws are universal, it doesn’t matter if the stuff is in bulk or is just an atom. To obtain the gravity from a piece [or effect] of bulk matter you just sum over the constituents.

August 1, 2011 7:55 am

Leif Svalgaard says:
August 1, 2011 at 6:43 am
So far the agreement does not look so good. I presume you also do the the BC part. Wolff does not believe in AM having any influence.
You are a hard man to please, I think at this point you are in denial.
Wolff is more concerned about the solar path changes that are a result of AM. He suggests (via email) the altered path during grand minima would have a downward effect on solar output.

August 1, 2011 8:04 am

Geoff Sharp says:
August 1, 2011 at 7:55 am
You are a hard man to please, I think at this point you are in denial.
A standard practice is to show all the data, not just a section that you like.
Wolff is more concerned about the solar path changes that are a result of AM. He suggests (via email) the altered path during grand minima would have a downward effect on solar output.
You have this backwards. AM is a consequence of changes in the orbit, not the cause.

August 1, 2011 8:15 am

Talbloke
“Impolitely put questions will be deleted.”
……. Given your demonstrated inability to understand the Newtonian property dynamics of bulk gases as opposed to their constituent atoms or molecules I very much doubt you were one of those experts. I recognise your expertise in stats and programming, but I think you are a bit of a duffer in some other areas. In fact, after reading your long argument with Bart on Pat Franks’ thread I’m not too sure about your knowledge or ability around spectral analysis any more either”
Thats nice. Invite someone to ask questions if they are polite and then insult them.

August 1, 2011 8:42 am

Leif Svalgaard says:
August 1, 2011 at 8:04 am
A standard practice is to show all the data, not just a section that you like.
You have 2000 years to play with, not exactly chicken feed. Detail your objections so far.
You have this backwards. AM is a consequence of changes in the orbit, not the cause.
Can’t argue with that….a supreme marker. But that takes nothing away from Wolff’s analysis.

August 1, 2011 9:09 am

Geoff Sharp says:
August 1, 2011 at 8:42 am
A standard practice is to show all the data, not just a section that you like.
You have 2000 years to play with, not exactly chicken feed. Detail your objections so far.

So far, there does not seem to be any significant correlation between the 172-year ‘anomalies’ you have marked with grand minima. One could hope that if you plotted all of the data, that correlations might improve. At least, it becomes possible to compare coincidences with twice as much data. This seems a reasonable thing to do. So, do it. I may not have been specific enough. I also wanted you to mark on the Steinhilber curves which dips you would consider grand minima, then one can see the covariance by eye.
But that takes nothing away from Wolff’s analysis.
But everything from yours, it would seem.

August 1, 2011 9:35 am

Leif Svalgaard says:
August 1, 2011 at 9:09 am
Geoff Sharp says:
August 1, 2011 at 8:42 am
“But that takes nothing away from Wolff’s analysis.”
But everything from yours, it would seem.

Let me elaborate a bit on that. The AM curve is almost identical to the barycenter distance curve, so if it could be shown that the distance is the determining factor, then the AM would just – as you say – be a marker and not a cause as such, i.e. no spin-orbit coupling. In this sense Wolff removes your argument than spin-orbit coupling [whatever that impossibility is] is the cause. So, perhaps you should jump on the other bandwagon [tidal forces] that tallbloke and others are pushing. At least, then there would be some commonality as tallbloke might even refer to your work in more detail.

August 1, 2011 10:05 am

Leif Svalgaard says:
August 1, 2011 at 9:09 am
So much ramble. I repeat, show me your objections to the correlations so far.

August 1, 2011 10:44 am

Willis Eschenbach says:
August 1, 2011 at 10:02
I don’t know where to start Willis, or even if I should bother. Try to keep up and follow what Leif and I are discussing.

August 1, 2011 11:15 am

Willis is losing a lot of creditability here. So many ill founded attacks on those that disagree with the basic fabric of this thread. There seems to be a trend lately that WUWT is promoting Luke Warmer resident guest authors on a permanent basis.
Maybe I am just being paranoid?

August 1, 2011 11:19 am

tallbloke says:
July 31, 2011 at 7:34 am
there is less ‘pull’ on the Solar core in the up or down direction.
Apart from the free fall condition, the forces on the solar ‘core’ also work on the rest of the sun. The core is not special.

August 1, 2011 11:23 am

Geoff Sharp says:
August 1, 2011 at 10:44 am
I don’t know where to start Willis, or even if I should bother. Try to keep up and follow what Leif and I are discussing.
Well, it is Willis’ post… And he is quite correct. His comment is very pertinent to your claims. Perhaps your Uranus+Neptune cycles don’t show up because they aren’t there with enough amplitude to begin with.

August 1, 2011 11:25 am

Geoff Sharp says:
August 1, 2011 at 10:05 am
show me your objections to the correlations so far.
Short and sweet: there are none.

August 1, 2011 11:28 am

Geoff Sharp says:
August 1, 2011 at 11:15 am
So many ill founded attacks on those that disagree with the basic fabric of this thread.
Those are not ‘attacks’, just pointing out the weakness of your argument. And he is quite correct. You tend to see everything as attacks and credibility issues. Try to contemplate that perhaps you are just wrong, but can’t take well-founded criticism.

tallbloke
August 1, 2011 11:29 am

Leif Svalgaard says:
August 1, 2011 at 6:50 am
Newton’s laws are universal, it doesn’t matter if the stuff is in bulk or is just an atom. To obtain the gravity from a piece [or effect] of bulk matter you just sum over the constituents.

You still don’t get it. When we consider the effects of one body exerting gravitation on another, we need to consider not only the “bulk of the constituents” in mass terms defining how much gravitational pull it exerts but also the Newtonian properties of the material. I pointed out on the Loehle and Scafetta thread That:
“Newton knew his equations of motion and kinematics applied to idealised bodies with perfect elasticity. The Sun is not a perfectly elastic body, the layer which we see has differential speeds of rotation which vary both from each other and with respect to time. There are peer reviewed papers in the literature which empirically derive a linkage between the variations in the speed of rotation of various latitudinal bands and the motion of the Sun with respect to the SSB. These observations are indicative of a spin-orbit coupling caused by planetary motion.”
You responded with this:
“The Sun is a gas and Newton’s law apply to every atom of the gas.” and this:
“BTW, I don’t think you know what ‘elastic’ means.
http://en.wikipedia.org/wiki/Elasticity_(physics)
“In physics, elasticity is the physical property of a material that returns to its original shape after the stress (e.g. external forces) that made it deform or distort is removed.”
Since the Sun is a gas, when you remove any stress it will revert to its original spherical shape, so it is perfectly elastic.
“Newton’s laws are universal and work on gases, fluids, solid bodies, anything. The ‘elastic’ bit is just nonsense. And we should really works with Einstein’s General Relativity, except for the kind of stuff we are discussing here, Newton is good enough [if you only understood it].
To which I responded:
“Keep going Leif. Tell us how the smoke you’re blowing reacts to an impacting object. By magically reforming into the perfect sphere it was originally to demonstrate its elasticity no doubt. 🙂
Try it on a snooker table with some nice hard elastic balls and a lump of warm putty. See how well the kinetics of energy transfer are maintained as motion vectors. Clue, the putty might get a bit warmer, but it won’t magically regain its shape as it is inelastic, just as the Sun’s gases are. The only reason the Sun’s gases would reform a sphere after an impact (though with many non-reverting internal redistributions) is because they form around their own centre of gravity.
You’ve clearly proved to me, and anyone else who understands Newtonian kinematics (hands up engineers) that you don’t understand how a spin-orbit coupling can arise in an inelastic body due to gravitational interaction. The Sun as a bulk gas does not behave with the elasticity of a molecule of it’s constituent material. An orbiting planet will set up eddy currents in the Sun which will dissipate energy, or assist in the release of potential energy in a preferential location (facing the barycentre) a la Wolff and Patrone.
The Earth Moon system exhibits spin orbit coupling due to the drag caused by the Moon’s gravitational action on the inelastic oceans. I originally said that the differential motion of the various latitudinal bands on the Sun’s observable surface were indicative of a spin orbit coupling. It remains to be discovered whether that arises through the possibility proposed by Ted L, the Wolff and Patrone mechanism, tidal action or something else not yet considered, The point is that the observations stand. Your arguments about the newtonian properties of the bulk gases of the Sun don’t.

August 1, 2011 11:38 am

tallbloke says:
August 1, 2011 at 11:29 am
“Newton knew his equations of motion and kinematics applied to idealised bodies with perfect elasticity.
Complete nonsense. Newton’s laws are universal and apply to all bodies, whatsoever.
An orbiting planet will set up eddy currents in the Sun
No, as both are in free fall.
The point is that the observations stand
The observations are marginal, at best.

August 1, 2011 11:38 am

Leif Svalgaard says:
August 1, 2011 at 11:23 am
Well, it is Willis’ post… And he is quite correct. His comment is very pertinent to your claims. Perhaps your Uranus+Neptune cycles don’t show up because they aren’t there with enough amplitude to begin with.
No, I have shown that fourier type analysis can miss the important detail. But that seems to be overridden by ego driven rant.

August 1, 2011 11:42 am

tallbloke says:
August 1, 2011 at 11:29 am
“Newton knew his equations of motion and kinematics applied to idealised bodies with perfect elasticity.
Complete nonsense. Newton’s laws are universal and apply to all bodies, whatsoever.
A planet consisting of a gas, like Jupiter, orbits exactly the same that it would do if it consisted of steel.

August 1, 2011 11:45 am

tallbloke says:
August 1, 2011 at 11:29 am
“Newton knew his equations of motion and kinematics applied to idealised bodies with perfect elasticity.
Complete nonsense. Newton’s laws are universal and apply to all bodies, whatsoever.
A binary star system with two gaseous stars obey Newton’s equations of motion quite well. Now, what does that say about your understanding of Newtonian mechanics?

August 1, 2011 11:46 am

Leif Svalgaard says:
August 1, 2011 at 11:23 am
But I am still waiting for your comprehensive analysis on the pie we are sharing. Perhaps Willis will take notice of the detail and finally understand the Hydra headed wave….we can only hope.

August 1, 2011 12:16 pm

Geoff Sharp says:
August 1, 2011 at 11:46 am
But I am still waiting for your comprehensive analysis on the pie we are sharing
Bake the pie first: annotate the BC part, mark grand minima, so we don’t have to haggle over those. Then I’ll be happy to look at the pie.

August 1, 2011 12:28 pm

Willis Eschenbach says:
August 1, 2011 at 10:06 am
Nothing sinister, link I posted contained 2 sets of data which I omitted to subtract, that has been now corrected. My old DOS prog came up with graph with the peak period of about 65 years, but the spectral resolution isn’t very good, a bit on the high side, but it does sort of agree with AMO. I needed a crosscheck with a more advanced spectral analysis.
http://www.vukcevic.talktalk.net/dGMF.htm
Thank you.

August 1, 2011 12:51 pm

Geoff Sharp says:
August 1, 2011 at 11:38 am
No, I have shown that fourier type analysis can miss the important detail. But that seems to be overridden by ego driven rant.
You have shown nothing like that. Even if the bumps move around a bit they will show up in Fourier analysis, just with a broader peak. http://www.leif.org/research/FFT-Barycenter-Distance-170.png The red circle shows you the power near 170 years. It is tiny as is the 60-yr peak.
I’m not so sure who is doing the ego driven rant here. You really should tone down those personal barbs. Keep them over on your own blog, if you must.

Richard S Courtney
August 1, 2011 1:04 pm

Geoff Sharp:
At August 1, 2011 at 11:15 am you say:
“Willis is losing a lot of creditability here. So many ill founded attacks on those that disagree with the basic fabric of this thread. There seems to be a trend lately that WUWT is promoting Luke Warmer resident guest authors on a permanent basis.
Maybe I am just being paranoid?”
I do not think you are being “paranoid” but I do think you are mistaken. And I strongly disagree that Willis is “losing credibility here”.
Firstly, if you look at the previous thread then you will see that several people – I was the first – objected to the tone Willis used in his intial objections to the paper. Clearly, he felt strongly about it.
But his reaction to that strong feeling was to formulate the essay at the top of this thread and then to engage with those who questioned his essay in the thread. Such is very proper scientific behaviour. Everybody can judge his arguments for themselves.
And it is obvious to all who have followed WUWT that Willis has become a “resident guest author” because his essays have received such strong support – indeed, admiration – from many readers of WUWT.
I have been a guest author on WUWT but only once because my contribution did not obtain the clear good response that the articles from Willis usually do. I am not offended at this because I see no reason for jealousy at the success of Willis or anybody else.
Willis is clearly not a “Luke Warmer”. He is what ‘warmers’ call a ‘denier’: read his series of guest articles on WUWT if you doubt this.
I, too, am a ‘denier’ of the AGW-scare (indeed, I am probably the original ‘denier’ because I predicted the scare before it first arose – my prediction was then rejected as being “implausible” – and I have opposed it continuously since then). But if you read my post at July 30, 2011 at 4:06 pm in this thread then you will see my disagreement with the Lohele & Scaffetta paper is stronger than that presented by Willis: his disagreement is only one part of my disagreement with the L&S analysis.
Science progresses by honest disagreements openly debated. Those of us who dispute the AGW-hypothesis do not have to agree with everything from every person who shares our skepticism of AGW. We seek to gain proximity to the truth of the matter and we can expect a variety of opinions as to what is – and is not – correct interpretation of available empirical data.
Richard

tallbloke
August 1, 2011 1:19 pm

Willis Eschenbach says:
August 1, 2011 at 1:04 pm
Heck, there’s not even an apparent connection between barycentric cycles (the main one being at ~19.86 years) and sunspot cycles (~ 22 years).

Ah, yes there is. 19.86 years (Jupiter – Saturn synodic cycle) is one of the periods involved in the solar cycle period. the other is 2x the Jupiter orbital period.
http://tallbloke.wordpress.com/2011/07/31/bart-modeling-the-historical-sunspot-record-from-planetary-periods/
there is no significant 20 year cycle in the temperature data,
It has been known since 1989 (GRL Vol 16 p311) that southern hemisphere night-time marine air temperatures follow the Hale cycle of ~22 years.
http://tallbloke.wordpress.com/2011/08/01/newell-climate-follows-hale-solar-sunspot-cycle/
Best to you
tb

tallbloke
August 1, 2011 1:31 pm

Leif Svalgaard says:
August 1, 2011 at 11:45 am
Newton’s laws are universal and apply to all bodies, whatsoever.
A binary star system with two gaseous stars obey Newton’s equations of motion quite well. Now, what does that say about your understanding of Newtonian mechanics?

My statement as you well know was in the context of your claim that a spin orbit coupling is not possible because the sun is in freefall and feels no forces. Binary stars will orbit their common barycentre as Newton predicts. There will however be considerable churn within the gaseous envelopes of the stars because they are inelastic bodies and the tides raised will slow them down prematurely compared to hard solid elastic bodies because of lost ‘innate motion’ due to friction generated in tides. Just as the earth has slowed and the Moon receded because of the friction of the inelastic oceans affected by Lunar tides.
Are you still going to stand by this statement?:
Leif svalgaard said:
Since the Sun is a gas, when you remove any stress it will revert to its original spherical shape, so it is perfectly elastic.
A simple “yes” or “no” is sufficient.

tallbloke
August 1, 2011 1:40 pm

Leif Svalgaard says:
August 1, 2011 at 11:42 am
tallbloke says:
August 1, 2011 at 11:29 am
“Newton knew his equations of motion and kinematics applied to idealised bodies with perfect elasticity.
Complete nonsense. Newton’s laws are universal and apply to all bodies, whatsoever.

See my previous reply. Yes Newtons laws apply to all bodies, but they result in different outcomes for elastic and inelastic bodies. This is easily proved with the ball of putty on the pool table experiment.
A planet consisting of a gas, like Jupiter, orbits exactly the same that it would do if it consisted of steel.
Excellent, another proof you don’t understand Newtonian dynamics for my next blog post. Thanks.
Now, this thread is about timing of cycles in relation to climate changes, not causation of cycles, so if you want to argue further. come on over to the talkshop again and let’s have a polite debate there. Give me half an hour to finalise the post.

August 1, 2011 1:45 pm

tallbloke says:
August 1, 2011 at 1:19 pm
Ah, yes there is. 19.86 years (Jupiter – Saturn synodic cycle) is one of the periods involved in the solar cycle period. the other is 2x the Jupiter orbital period.
No, the sunspot cycles have an average period of 10.81 years, but the amplitude varies with a ~120 year period, giving rise to peaks that are in the neighborhood of half the synodic cycle and the Jupiter period.
tallbloke says:
August 1, 2011 at 1:31 pm
There will however be considerable churn within the gaseous envelopes of the stars because they are inelastic bodies and the tides raised will slow them down prematurely compared to hard solid elastic bodies because of lost ‘innate motion’ due to friction generated in tides. Just as the earth has slowed and the Moon receded because of the friction of the inelastic oceans affected by Lunar tides.
Tides also kneed solid bodies, the moon Io comes to mind. And no need to bring up tides and everyone agrees that the only effects on bodies in free fall are tidal. You are denying the universality of Newton’s laws.
Are you still going to stand by this statement?:
Since the Sun is a gas, when you remove any stress it will revert to its original spherical shape, so it is perfectly elastic.
A simple “yes” or “no” is sufficient.

Absolutely yes as the sun’s own gravity is the restoring force, so the Sun answers to the definition of ‘elastic’. The only issue could one of time scale, but the Sun’s gravity is strong.

August 1, 2011 1:58 pm

tallbloke says:
August 1, 2011 at 1:40 pm
Now, this thread is about timing of cycles in relation to climate changes, not causation of cycles, so if you want to argue further
The thread is about the past 150 years, which is so short that any cycles seen could well be [and probably are] spurious, so not worth discussing per se. What makes the thread potentially interesting is the question of causation, because only then could the cycles have real predictive power [they would not have if there is no causal relationship]. No need to argue further as the solar cycles have been argued over and over again with no progress in sight.

tallbloke
August 1, 2011 2:01 pm

Leif Svalgaard says:
August 1, 2011 at 11:19 am
tallbloke says:
July 31, 2011 at 7:34 am
there is less ‘pull’ on the Solar core in the up or down direction.
Apart from the free fall condition, the forces on the solar ‘core’ also work on the rest of the sun. The core is not special.

We’re not talking about a special core. We’re talking about a gradient of density with transitions from densities where energy moves by radiation only to densities where energy moves by radiation and convection.

tallbloke
August 1, 2011 2:09 pm

Willis Eschenbach says:
August 1, 2011 at 10:54 am
tallbloke says:
July 31, 2011 at 7:34 am
Willis, the strong sixty year modulation in the barycentre data is in the z axis. The Sun is tilted wrt the plane of invariance and so when the conjunction between Jupiter and Saturn takes place near the nodes of the solar equatorial plane and the plane of invariance there is less ‘pull’ on the Solar core in the up or down direction.
Thanks, Tallbloke. The motion in the Z axis is only 2.6% of the motion in either the X or Y axes, so your claim that the modulation in that axis is ‘strong’ doesn’t mean much. It’s like saying “that’s a really big ant”, it isn’t too relevant in the larger scale of things. The effect of variations in the z direction on either total distance, velocity, or angular momentum is trivial.

Hi Willis, thanks for your reply. The thing is, whereas barycentric effects in the x-y plane will get cancelled in 13 days or so over half a solar rotation, the effects in the z-axis range from 44 days for Mercury, to 86 years for Neptune. The range of motion of the sun’s equatorial plane wrt barycentre is around 100,000km, or about 14 times less than the relative motion in the x-y plane, but the longevity of the effects we hypothesise will be so much greater that this deficiency in scale is more than made up for.

tallbloke
August 1, 2011 2:13 pm

Leif Svalgaard says:
August 1, 2011 at 1:58 pm
No need to argue further as the solar cycles have been argued over and over again with no progress in sight.

Well you are well qualified to judge the progress of the Babcock Leighton dynamo theory I grant you. 🙂
New post is up here:
http://tallbloke.wordpress.com/2011/08/01/spin-orbit-coupling-between-newton-and-his-grave/

August 1, 2011 2:14 pm

Leif Svalgaard says:
August 1, 2011 at 1:58 pm
………..
Hi doc
Perhaps you would like to have a go at the 390 year long dataset:
http://www.vukcevic.talktalk.net/dGMF.htm
see the post
http://wattsupwiththat.com/2011/07/30/riding-a-pseudocycle/#comment-710221

August 1, 2011 2:16 pm

tallbloke says:
August 1, 2011 at 2:01 pm
“The core is not special”
We’re not talking about a special core.

There must be some difference or distinguishing characteristic since you mentioned ‘solar core’ specifically, that makes it special with respect to what is not ‘solar core’.
We’re talking about a gradient of density with transitions from densities where energy moves by radiation only to densities where energy moves by radiation and convection.
Somewhat gibberish. Within a radius of 0.713 from the center, energy flows by radiation, taking about a quarter million years to make the journey to the outer layer, where energy travels by convection, taking about a month to make the final stretch to the surface. Are you talking about, say halfway from the center the place in the radiative solar core from where it will still take a hundred thousand years for the energy to get out? Or what is your point?

tallbloke
August 1, 2011 2:19 pm

Leif Svalgaard says:
August 1, 2011 at 1:45 pm
the sunspot cycles have an average period of 10.81 years, but the amplitude varies with a ~120 year period, giving rise to peaks that are in the neighborhood of half the synodic cycle and the Jupiter period.

Well, that’s another way of looking at it, but I think you’re wrong for several reasons.
1) The average solar cycle is 11.07 years not 10.81 as you claim.
2)You have no firm theory or observation for the cause of a ~120 year cycle in the Sun.
3)The biggest and second biggest planets in the solar system have the right frequency of interaction and period to explain the solar cycle. There are several possible mechanisms, and we are much closer to nailing this than the dynamo theorists are.

August 1, 2011 2:22 pm

M.A.Vukcevic says:
August 1, 2011 at 2:14 pm
Perhaps you would like to have a go at the 390 year long dataset:
http://www.vukcevic.talktalk.net/dGMF.htm

It shows a 60-yr cycle and the expected harmonics of that [the peaks on the left] so does not show anything special and is furthermore not related physically to either the sun or the climate as the Earth’s magnetic field [which I presume this is] is not influenced by either, or vice versa. If you look around here, there, and everywhere, you are bound to find something that correlates with anything you imagine.

tallbloke
August 1, 2011 2:22 pm

Leif Svalgaard says:
August 1, 2011 at 2:16 pm
Somewhat gibberish.

Whatever. We have a well formulated hypothesis which has been discussed with people who understand relativity better then you do. I don’t feel the need to discuss it with someone throwing words like “Gibberish” around.

August 1, 2011 2:30 pm

tallbloke says:
August 1, 2011 at 2:22 pm
I don’t feel the need to discuss it with someone throwing words like “Gibberish” around.
Is “boorish” better, then.

August 1, 2011 2:54 pm

tallbloke says:
August 1, 2011 at 2:19 pm
1) The average solar cycle is 11.07 years not 10.81 as you claim.
The average length is 11.02 [132.3 months] with a standard deviation of +/-1.28 years and a standard error of the mean [‘error bar’] of +/-0.27 years, so my figure of 10.81 is within the error bar. BTW that figure 10.81 was illustrative only, and picked to mimic the astronomical values. Any figure within the error bar would do.
2)You have no firm theory or observation for the cause of a ~120 year cycle in the Sun.
The length of the good record is too short to nail down that period [Bart found 131 years]. The power spectrum of actual observed daily sunspot numbers since 1820 [from when we have good data] shows the strongest power north of 100 years: http://www.leif.org/research/FFT-Daily-Sunspot-Number.png so this is an observational fact.
3)The biggest and second biggest planets in the solar system have the right frequency of interaction and period to explain the solar cycle. There are several possible mechanisms, and we are much closer to nailing this than the dynamo theorists are.
The mechanisms are generally not physically plausible, and your assessment is just that of an enthusiast.
But it is simpler than that, the sunspot numbers really don’t cluster about a single average length. A good test is to run the analysis separately on the first half and the second half of the series, this is what you get: http://www.leif.org/research/FFT-Daily-Sunspot-Number-1st-2nd-halves.png
For the interval 1820-1916 the length was 10.6 years, while for the 1st half, 1820-2011, the period was 11.3 years. The astronomical cycles would not give this, but the dynamo theory has a natural explanation, namely a variation of the speed of the meridional circulation. Lots of stars have variation of the properties and it is no surprise that the sun has too.

August 1, 2011 3:03 pm

One statement was typed too quickly. Should have been:
For the interval 1820-1916 the length was 11.3 years, while for the 2nd half, 1917-2011, the period was 10.6 years.

August 1, 2011 3:28 pm

tallbloke says:
August 1, 2011 at 2:13 pm
Well you are well qualified to judge the progress of the Babcock Leighton dynamo theory I grant you.
That is not argued over and over, it stands firm.

tallbloke
August 1, 2011 3:52 pm

Leif Svalgaard says:
August 1, 2011 at 3:28 pm
tallbloke says:
August 1, 2011 at 2:13 pm
Leif says: No progress in sight
Well you are well qualified to judge the progress of the Babcock Leighton dynamo theory I grant you. 🙂
That is not argued over and over, it stands firm.

With you around to sandbag it Leif, I’d expect nothing less. 😉
The mechanisms are generally not physically plausible, and your assessment is just that of an enthusiast.
I’m a qualified mechanical engineer with a better understanding of Newtonian mechanics than you.
Hows the refutation of Wolff and Patrone coming along Leif? Any progress with equations 2a, 2b and 4 yet?

August 1, 2011 4:17 pm

tallbloke says:
August 1, 2011 at 3:52 pm
I’m a qualified mechanical engineer with a better understanding of Newtonian mechanics than you.
It doesn’t show. You hide it well.
Hows the refutation of Wolff and Patrone coming along Leif? Any progress with equations 2a, 2b and 4 yet?
Still where I left it. The problem is with equation (2) as your experts in relativity will tell you. Einstein’s equivalence principle tells you “No experiment, no clever exploitation of the laws of physics can tell us whether we are in free space or in a gravitational field. One of the consequences: In a reference frame that is in free fall, the laws of physics are the same as if there were no gravity at all”
If W&P are correct, then the sun can tell that it is in a gravitational field [that of the planets] which would violate the principle.

RACookPE1978
Editor
August 1, 2011 4:37 pm

Leif Svalgaard says:
August 1, 2011 at 2:54 pm
(Responding to various comments/rejonders from tallbloke…)
tallbloke says:
August 1, 2011 at 2:19 pm
1) The average solar cycle is 11.07 years not 10.81 as you claim.
The average length is 11.02 [132.3 months] with a standard deviation of +/-1.28 years and a standard error of the mean [‘error bar’] of +/-0.27 years, so my figure of 10.81 is within the error bar. BTW that figure 10.81 was illustrative only, and picked to mimic the astronomical values. Any figure within the error bar would do.
2)You have no firm theory or observation for the cause of a ~120 year cycle in the Sun.
The length of the good record is too short to nail down that period [Bart found 131 years]. The power spectrum of actual observed daily sunspot numbers since 1820 [from when we have good data] shows the strongest power north of 100 years: http://www.leif.org/research/FFT-Daily-Sunspot-Number.png so this is an observational fact.
3)The biggest and second biggest planets in the solar system have the right frequency of interaction and period to explain the solar cycle. There are several possible mechanisms, and we are much closer to nailing this than the dynamo theorists are.
The mechanisms are generally not physically plausible, and your assessment is just that of an enthusiast.
But it is simpler than that, the sunspot numbers really don’t cluster about a single average length. A good test is to run the analysis separately on the first half and the second half of the series, this is what you get: http://www.leif.org/research/FFT-Daily-Sunspot-Number-1st-2nd-halves.png
For the interval 1820-1916 the length was 10.6 years, while for the 1st half, 1820-2011, the period was 11.3 years. The astronomical cycles would not give this, but the dynamo theory has a natural explanation, namely a variation of the speed of the meridional circulation. Lots of stars have variation of the properties and it is no surprise that the sun has too.

OK. So, then would not the best test of any barycentric theory be just that: Rather than try to match a single “perfect” sunspot cycle (that is (falsely) assumed to be fixed during the record), do any barycentric-inspired indices vary with (either in synchronous periods with, or in synchronous periods opposite to) the known varying lengths and intensities of the sunspot cycles, or in any synchronous or resonance pattern with the observed trends in the actual sunspot cycles?

August 1, 2011 6:58 pm

RACookPE1978 says:
August 1, 2011 at 4:37 pm
OK. So, then would not the best test of any barycentric theory be just that […] with the observed trends in the actual sunspot cycles?
The problem is that the actual sunspot cycle is noisy enough and the record short enough that if the test fails, people will just blame it on the noise. I did give an example of a mismatch. A better test is to look at other star systems that have large planets in close-in orbits so their periods are shorter [we don’t need to wait decades] and the effects should be much larger. If these stars do not show synchronizations with their large planets we might assume that the barycentric theories have been refuted. Two such stars come to mind: HD 168443 and HD 74156. See e.g. http://www.leif.org/EOS/1010-0966v1-Exoplanets-Barycenter-Tests.pdf

August 1, 2011 8:03 pm

Leif Svalgaard says:
August 1, 2011 at 6:58 pm
If these stars do not show synchronizations with their large planets we might assume that the barycentric theories have been refuted.
That being said, it is clear that if the exoplanet is VERY close-in, say less than 0.1 AU there will be very strong tidal effects as those increase by a factor of a thousand if the distance decreases from 1 AU to 0.1 AU. We are not really looking for tidal effects as these are undisputed if the distance is small enough. The[] issue is if there are other mechanisms.

August 1, 2011 9:33 pm

Leif Svalgaard says:
August 1, 2011 at 6:58 pm
If these stars do not show synchronizations with their large planets we might assume that the barycentric theories have been refuted.
An interesting case is that of tau Bootis where a gas planet with something like at least four times the mass of Jupiter orbits at a distance of 0.05 AU in 3.3 days. The star has a magnetic field that reversed polarity in ~2006.5 and again in ~2007.5, suggesting a stellar cycle of about 1 year, much different from the 3.3 days orbital period of its planet. tau Bootis may have synchronized its rotation with the period of the planet by tidal action. This whole field of research in still in its infancy so one cannot draw too wide-ranging conclusions, yet.

Septic Matthew
August 1, 2011 9:55 pm

Despite being clearly visible in the data and in the periodicity analyses, the cycles are an artifact of the auto-correlation of the datasets.
You decline to come to terms with the fact that Fourier and AR representations of stationary time series are interconvertible. Consult the time series text that I referenced earlier. The cycles are not an “artifact” of the autocorrelation, they are a mathematical consequence of the autocorrelations.