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)

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416 thoughts on “Riding a Pseudocycle

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

  2. 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.”

  3. 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.

  4. 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.

  5. Katherine says:
    July 30, 2011 at 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.”

    Thanks, Katherine. Actually, the amount of data decreases as the cycle length increases. Consider a cycle of length two. Each one is the average of half the data.

    Now consider a cycle length of three. Each one is the average of a third of the data.

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

    w.

  6. Sean Houlihane says:
    July 30, 2011 at 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.

    Sean, it sounds like you didn’t understand the analysis I am doing here. If you have questions, I’m happy to answer them.

    w.

  7. 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/

  8. Derek Sorensen says:
    July 30, 2011 at 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/

    Derek, I have used datasets which are not simple random normal datasets. Those kinds of random datasets are called “white noise”. However, they do not resemble observational datasets of things like temperature.

    This is because temperature datasets are “autocorrelated”, meaning that today’s temperature depends in part on yesterday’s temperature. Datasets composed of autocorrelated noise are called “red noise” datasets.

    Note that the quality of these datasets is that they don’t take huge jumps, say from way up high to way down low and back again. Instead, they follow something like a “drunkard’s walk”, a random trail that, although not taking large jumps, wanders widely. Because today’s temperature depends in part on yesterday’s temperature, the list of temperatures forms a trail, not just random white noise.

    It is entirely possible to generate random “red noise” datasets. They do not, as you suggest, contain the periods. Instead, because they are a trail and they wander up and down, pseudo-cycles are quite common. It looks like cycles … but it’s not.

    w.

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

  10. 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.

  11. 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?

  12. 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.

  13. 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.

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

  15. 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)

  16. 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.

  17. 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 :-).

  18. 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).

  19. 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.

  20. 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.

  21. 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

  22. 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.

  23. 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.

  24. Some comments on various things:

    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.

  25. 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.

  26. 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.]

  27. 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!

  28. 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”)

    Powered by Ingram Digital

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

  29. 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 ??

  30. 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.

  31. 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!

  32. 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.

  33. “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.

  34. 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.

  35. 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?

  36. 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

  37. 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.

  38. 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.

  39. 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?

  40. ::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

  41. 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.

  42. 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.

  43. 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.

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

    Fair enough.

  45. “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

  46. 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?

  47. 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.

  48. 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.

  49. 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.

  50. 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.

  51. 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.

  52. 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. ;-)

  53. Mike Jonas says:
    July 30, 2011 at 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?

    Sorry, nothing for that. Doesn’t mean it doesn’t exist, however.

    w.

  54. 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:

    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)

  55. Stephen Wilde says:
    July 30, 2011 at 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?

    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.

    w.

  56. Henry says:
    July 30, 2011 at 4:18 am

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

    Thanks, Henry, nice. As I said, I’m not that well versed in R.

    w.

  57. 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.

  58. 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.

  59. Nick Stokes says:
    July 30, 2011 at 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.

    Thanks, Nick. I’m not sure what you mean when you say you can’t “partition the power between them”. I’m not doing that. I’m directly calculating the power each individual cycle has. That’s why they all together sum up to much more than 100%.

    I have partitioned the barycentric data into 20, 83, 19, and 13 year cycles. I have then combined the cycles to closely reconstitute the original data.

    So what is the problem? I mean, the method finds the cycles. It doesn’t find a significant 60-year cycle in the barycentric data, mostly a large 20 year cycle. It doesn’t find a large 20-year cycle in the temperature data.

    As a result, I believe I’ve shown that the Loehle/Scafetta analysis is fatally flawed. Do you disagree with that conclusion?

    w.

  60. James Reid says:
    July 30, 2011 at 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 :-).

    Excellent question, James. I’ll take a look when I find the time.

    w.

  61. 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.

  62. Ninderthana says:
    July 30, 2011 at 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.

    This may be all correct … but where is the signal? Take another look at my analysis of the barycentric signal in Figure 6. If there were a 60 year cycle, we’d see evidence of it once we remove the 20 year cycle. But it’s not there.

    So you may be right, but if so, such a 60 year cycle is quite small.

    w.

  63. 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.

  64. “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.

  65. A physicist says:
    July 30, 2011 at 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,

    First, I wrote the piece, not Anthony, please don’t blame him for my errors.

    Second, let me quote for you from the Sethares document cited above:

    Because the Fourier transform is linear-in-frequency, the values are less accurate at long periods (low frequencies).

    If we have a dataset of 158 datapoints, the Fourier transform returns values at cycle lengths of 158 years, 158/2 years, 158/3 years, 158/4 years, etc. This means we get answers at 158, 79, 52.33 years, 39.5 years, etc. … but not in between.

    That is what I meant by reduced resolution at longer timescales. Sorry for my lack of clarity.

    w.

  66. 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.

  67. John Day says:
    July 30, 2011 at 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.

    Well, yes, it is “incredibly useful for analysis” … but it can also be a shortcoming. Consider, for example, the 20 year cycle shown in the HadCRUT3 data. It is very irregular. Now, you could reduce that to a sum of shorter cycles using Fourier analysis … but I do not think that provides us with more information that the 20 year cycle I found.

    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.

    True.

    ‘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.

    See my previous comment to “A Physicist” above. You are correct that my statement was misunderstood.

    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.

    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?

    w.

  68. 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.


    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.

  69. 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.

  70. charlesH says:
    July 30, 2011 at 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?

    Yes. At a minimum you are missing my comment in the Loehle/Scafetta thread where I showed that you can replicate the temperature record “quite well” using 40 and 60 year cycles … which means that their results are not significant.

    I addition, you’re missing the fact that the cycles, although they can replicate the temperature, appear to be artifacts rather than real cycles.

    w.

  71. 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.

  72. Leif Svalgaard says:
    July 30, 2011 at 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.

    Thanks, Leif. As I pointed out, the 60-year cycle in the barycentric data is very small. This makes the claimed 60-year cycle in the temperature even more unlikely to be solar-related.

    w.

  73. Here’s what I did to get a nice wavelet display in R:

    library (dplR)

    str (hadcrut3)
    # –> Time-Series [1:1944] from 1850 to 2012: -1.757 -0.267 -0.409 -0.779 -0.552 …

    hadcrut3.s <- smooth.spline (hadcrut3, spar=0.9)
    hadcrut3.r <- hadcrut3 – hadcrut3.s$y # Detrending, may or may not pass muster
    hadcrut3.wave <- morlet (y1=hadcrut3.r, x1=seq (from=1850, by=1/12, length.out=1944), p2=10, dj=0.1)
    wavelet.plot (hadcrut3.wave2)

    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.

  74. 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.

    w.

  75. 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.

  76. 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?

  77. 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.

  78. 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.

  79. 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?

    w.

  80. 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.

    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.

  81. Geoff Sharp says:
    July 30, 2011 at 10:36 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.

    Again, Geoff, I’m not sure what your point is here. Yes, there is a tiny 60 year cycle in the barycentric data. Leif has shown that it is a thirtieth of the 20 year cycle. So we can hardly assume that it makes more difference to the temperature than the 20 year cycle … but that is what L/S claims.

    w.

  82. 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.

  83. 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:

    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.

  84. 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. ;-)

  85. 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.

  86. 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).

  87. 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.

  88. 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.

    “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)

  89. 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

  90. 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.

  91. 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.

  92. 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.

  93. 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.

  94. 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.

  95. 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

  96. 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.

  97. Tad says:
    July 30, 2011 at 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).

    20- and 60-year cycles that were already known to exist? Known from where? Cycles in what? L/S claimed that they were present in the barycentric velocity data. And they are … but the 60 year cycle is tiny compared to other cycles.

    And why choose those two cycle lengths, rather than say the 13 year cycle that is also “already known to exist”?

    Tad, there’s an infinity of cycles that “are already known to exist.” However, the fact that there is a tiny sixty year cycle in the barycentric velocity data hardly justifies using it as the largest cycle in the temperature data.

    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.

    w.

  98. 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.

  99. 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

  100. 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.

  101. 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.

  102. 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.

  103. 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.

  104. @John 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:

    http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1.8853&rep=rep1&type=pdf

    “… 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.

  105. 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.

    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.

    A guide to understanding the powerwave below…read it.

    http://tinyurl.com/2dg9u22/?q=node/218

  106. 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:

    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:

    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.

  107. 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

    is not what you show as labelled ‘Angular Momentum’ ob this graph

    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.

  108. 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…

  109. 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.

  110. 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!

  111. 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)

    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.

  112. 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

    Maybe use different colored dots for the many different types of variations you claim to see. So far, I see no correlation.

  113. 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.

  114. 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!

  115. 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.

  116. 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?

  117. 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/

  118. 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

  119. 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.

  120. 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].

  121. 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.

  122. 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.

  123. 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).

  124. 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:

    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

  125. 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.

  126. 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.

  127. 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.

  128. 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.

  129. 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.

  130. 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…

  131. 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?

  132. 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.

  133. 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?

  134. 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?

  135. 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.

  136. 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.

  137. 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.

  138. 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.

  139. 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.

  140. 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.

  141. 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.

  142. 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:

    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.

    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

  143. 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.

  144. 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.

  145. 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.

  146. 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.

  147. 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.

  148. 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.

  149. 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.

  150. Girma says:
    July 30, 2011 at 6:55 pm

    Willis

    Does not the global mean temperature anomaly show a 60 years cycle as shown below?

    http://bit.ly/ePQnJj

    The cycle certainly appears to exist, but that’s not the question. The question is whether that cycle is apparent or real. The data is too short to answer that, so I attempted to throw some light on it by a Monte Carlo analysis. That analysis, shown in Figure 6 above, shows conclusively that such “pseudocycles” are quite common in random datasets. I found no less than eight of them in the first 20 datasets I looked at.

    So the cycle is there, but it is very likely that it is just a spurious artifact of the shortness of the record.

    w.

  151. 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.

  152. Geoff Sharp says:
    July 30, 2011 at 8:59 pm

    … 2. It is far better to plot the AM [angular momentum] when looking for U/N [Uranus/Neptune] 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?

    “One pass method”? I showed the multipass nature of my analysis in Fig. 5 above, and you accuse me of not reading what you wrote?

    And if you showed how cycles were hiding from Fourier analysis, I certainly missed it.

    If you wish to make such claims, PUT IN A LINK, because there’s no way I’m going searching for someone’s claims. In either case, I didn’t “refuse” to look at your methods, I didn’t understand them. And now that I’ve looked more closely at some of them, I find them totally missing in information necessary to replicate them.

    For example, you did say this:

    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.

    Now, that may be the “explanation” you speak of above as to how the Hydra-headed waves escape Fourier analysis, but if so, it did not clarify anything. It reminds me a lot of the stuff Ted Landscheidt used to tell me, and I couldn’t understand it either. It seems like industrial-strength hand-waving to me.

    Now Geoff, if you have a) a reliable mathematical way to tell “trident” shaped cycles from other cycles, and b) a mathematical way to count the number of prongs on the “trident”, c) a way to mathematically determine how long a cycle with a “trident” actually lasts, and d) a demonstration of how such a wave escapes Fourier analysis, then you might have something here.

    Heck, you could start by providing us with a mathematical function that actually generates waves with “multiple prongs”, so we could be sure what you’re talking about.

    But since you haven’t revealed any of those necessary parts to your “trident-shaped wave” theory, sorry, it doesn’t pass the transparency test.

    Finally, given that your arguments are missing and your claims don’t pass the transparency test, you should cut back on the accusations of bad faith regarding folks who don’t read what you write. We may have read it and merely laughed, or we may just be inutterably bored with unsubstantiated claims.

    w.

  153. M.A.Vukcevic says:
    July 31, 2011 at 1:39 am

    Drs. Svalgaard & Eschenbach
    Here is 4 centuries long data file.

    http://www.vukcevic.talktalk.net/4C-data.txt

    Umm … err … here’s what I find.

    Not Found
    The requested URL /4C-data.txt was not found on this server.
    Apache/2.2.3 (CentOS) Server at http://www.vukcevic.talktalk.net Port 80

    I can understand a dead link to someone else’s web site. But a dead link to your own web site? Doesn’t inspire confidence.

    w.

  154. 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.

  155. 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.

    This is because distance (or velocity or momentum) is figured generally as the square root of (X^2 + Y^2 + Z^2). So at the extremes (when X and Y = 100, and Z = 2.6), the distance neglecting the Z component is SQRT(X^2+Y^2) = SQRT(20,000) = 141.4213.

    Including the Z component the distance is 141.4452, a trivial difference of two hundredths of one percent … and the same is true for the velocity calculations. Velocity is SQRT(∆X^2 + ∆Y^2 + ∆Z^2), so the same proportions apply.

    Ah, you say, but the X and Y aren’t always at the extremes at the same time. OK, suppose X=0. The distance neglecting the Z axis is SQRT(Y^2) = 100. Including the Z axis, at a maximum it is SQRT(Y^2 + Z^2) = 100.034, about three hundredths of one percent.

    My point, which keeps getting lost in the glare of competing solar claims, is twofold:

    1. 60 year cycles in solar barycentric data are tiny, orders of magnitude smaller than the dominant cycles, and

    2. Long-period (e.g. 60 year) pseudo-cycles are common in datasets the length of the temperature data.

    w.

  156. 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?

  157. 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.

  158. 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.

  159. 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.

  160. old engineer says:
    July 31, 2011 at 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.

    The appearance of the pseudo-cycles is nothing but a function of the short length of the data and the fact that “red-noise” makes a “trail” rather than a totally random bunch of jumps. It is a kind of one-dimensional drunkards walk, which is totally random but which nonetheless forms a trail. As such, it naturally goes up and down. In a short dataset, these give the appearance of cycles. If the dataset were longer, they would be seen to be spurious.

    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.

    You are right that Fourier and Periodicity Analysis are similar, and I use both. There’s a couple of things I prefer periodicity analysis for.

    One is that it can distinguish between actual and spurious cycles. In periodicity analysis, a real cycle is shown at twice the cycle length, and three times the cycle length, as I illustrate in Figure 5. This doesn’t happen for a spurious cycle.

    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.

    Yes, and a number of the others also show strong long-period cycles. My point is that the rough appearance of such a cycle means nothing. It turns up all the time in random pseudo-data of that length. Eight of the first 20 pseudo-temperature datasets contain spurious indications of cycles.

    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?

    The problem is not with either fourier or periodicity analysis. It is the short length of the observational dataset, combined with the “red-noise” nature of that same dataset, that creates the illusion of cycles where none exist. Those pseudo-cycles will be be shown by either Fourier or Periodicity analysis, but they are very common in random datasets, so we can place absolutely no reliance on them at all.

    Thanks again for making me think and expanding my understanding.

    My pleasure,

    w.

  161. 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.

  162. 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.

  163. 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.

  164. 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.

  165. 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?

  166. 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.

  167. 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.

  168. Willis Eschenbach says:
    August 1, 2011 at 10:06 am
    I can understand a dead link to someone else’s web site. But a dead link to your own web site? Doesn’t inspire confidence.

    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

    Hope link works.
    Thank you.

  169. 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.

  170. Geoff Sharp says:
    August 1, 2011 at 10:44 am

    I don’t know where to start Willis, or even if I should bother.

    I’ve raised valid and cogent objections to your claims. I’ve asked you for citations for identified claims. I’ve asked specific questions about what you have done and what you mean.

    In response, you say that you don’t know where to begin, and follow that up with an insult.

    That’s your answer? That you don’t know where to begin? Do you get away with that at work? Because you won’t get away with it here.

    How about you begin by answering my specific questions, like, what kind of an equation makes a “trident” headed wave? Or why don’t you begin by demonstrating exactly how such a wave might escape Fourier analysis? Or you could show the mathematical methods that you use to isolate trident headed waves from normal waves, as I requested.

    I don’t care where you start, Geoff. But to say you don’t know where to start, and then follow that with an insult?

    Sorry, my friend, but when you do that I just point and laugh.

    w.

  171. Geoff Sharp says:
    August 1, 2011 at 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.

    Geoff, the basic fabric of this thread is that a) there is no significant 20 year cycle in the temperature data, b) there is no significant 60 year cycle in the solar data, and c) the 60-year cycle in the temperature data stands a very good chance of being an artifact.

    Now, does that make me a Luke Warmer? I don’t understand what that has to do with anything.

    And as to whether my objections to your claims are “ill founded”, well, time will tell. But I doubt that I lose credibility by making what I see as honest scientific objections. Someone is losing credibility here, but it’s not me.

    Maybe I am just being paranoid?

    !’d say 100% that you are, but YMMV.

    The part you don’t seem to get is that I’m on your side. I’d love to establish a connection between the climate and the barycentric cycles of the sun. It’s just that I’ve tried and failed at that task, and near as I can tell, so has everyone else. Heck, there’s not even an apparent connection between barycentric cycles (the main one being at ~19.86 years) and sunspot cycles (~ 22 years).

    So you’re attacking a straw man. I agree that there could easily be something to barycentric analysis … I just haven’t found anyone yet who could demonstrate such a connection, myself included.

    And if that causes me to lose credibility, then so be it.

    w.

  172. 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

  173. 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

  174. 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.

  175. 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.

  176. 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.

  177. 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.

  178. 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.

  179. 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.

  180. 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?

  181. 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.

  182. 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.

  183. 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.

  184. 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.

  185. 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.

  186. 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.

  187. 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.

  188. 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?

  189. 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.

  190. 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?

  191. 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

  192. 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.

  193. 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.

  194. 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.

  195. tallbloke says:
    August 1, 2011 at 1:19 pm (Edit)

    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/

    Not sure what to say about that, since Bart doesn’t seem to have put his results online. What do his results say about the size of the current cycle? How well do they fit past cycles?

    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

    It has also been known since 1989 that a cycle of 20 years != a cycle of 22 years …

    w.

  196. Septic Matthew says:
    August 1, 2011 at 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.

    I “decline to come to terms” with something? Please, leave your speculations about my motives and mental state at home. I’m doing what I can, and I’m doing my best.

    If cycles are a consequence of the autocorrelation, then all AR datasets should show cycles. A simple Monte Carlo exploration of the AR dataspace shows that many AR datasets show no particular cyclical behavior.

    In addition, if you examine longer AR datasets you’ll see that the “cycles” come and go. Again, if the cycles were a result of the autocorrelation, wouldn’t they be constant, or at least generally visible?

    In fact, if you look at the code above you’ll see I generated the sequence of ARMA random datasets as one long string, and then chopped it into 158 “year” lengths. So if you look at the cycles in Figure 6, they are all from the same ARMA random dataset, just starting at different points.

    So no, the apparent cycles you see are only an artifact of data length and data type. If they weren’t we’d see the same cycle in all of the datasets, because they are just subsets of one long dataset.

    Septic, I strongly recommend that you actually play with the data. Generate some high AR negative MA pseudo-temperature datasets and look at them one by one, the code is in the head post. Do Fourier analyses on them. Graph them and consider the graphs.

    My conclusion from doing that is that autoregressive datasets are extremely likely to contain spurious “cycles”. Think of it as a drunkard walking down a long road. He wanders to the right of the dotted line, he wanders to the left of the dotted line, he weaves back across to the other lane, and then drifts back over to the left again …

    Now, you’d have to say that would be a common kind of drunkard’s walk. But notice that he’s done two complete cycles … so if you did a Fourier or a Periodicity analysis of his walk, it would definitely show cycles … but are those cycles something deeply fundamental to the system?

    Well … no. If we watch him for a while longer, he drifts to the right, and sort of wanders back and forth over there for a while, then he fixates on a streetlamp and crosses to the other side of the road and stays there for a while. The apparent cycles from before disappear, and a new, much slower and longer term apparent cycle takes its place.

    But none of these are real cycles. They are a result of 1) the shortness of the record combined with 2) the fact that a random path will cross and recross its trend line, giving the appearance of cycles.

    Thanks for your interest,

    w.

  197. Willis Eschenbach says:
    August 1, 2011 at 1:04 pm

    Geoff Sharp says:
    August 1, 2011 at 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.
    ——————————-
    Geoff, the basic fabric of this thread is that a) there is no significant 20 year cycle in the temperature data, b) there is no significant 60 year cycle in the solar data, and c) the 60-year cycle in the temperature data stands a very good chance of being an artifact.

    Willis, I have clearly shown the 60 year cycle in the velocity record. I have given examples of how a background trend can be the cornerstone of a particular line of research, I have clearly shown why the 60 year cycle doesn’t show up in Fourier type analysis but you insist on only using the Fourier method to push “what looks like an agenda” against the Loehle and Scafetta paper. If evidence is presented and then ignored the question is asked why. For me that is a loss of credibility.

    A horse can be led to water but you can’t make it drink.

    <i<How about you begin by answering my specific questions, like, what kind of an equation makes a “trident” headed wave? Or why don’t you begin by demonstrating exactly how such a wave might escape Fourier analysis? Or you could show the mathematical methods that you use to isolate trident headed waves from normal waves, as I requested.

    It would be very difficult to write an equation that would capture the variability of the trident head phenomenon. It is visible via my annotations on Leifs solar distance charts but the outcome is reliant on planet positions that vary every time. Not everything in science fits into an equation or is visible via Fourier analysis. Have a good look at my annotations and it should become clear. The annotations are the forks in the trident example.

    Leif Svalgaard says:
    August 1, 2011 at 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.

    I dont know why you are playing these funny games but I can see that I will ultimately be wasting my time. I don’t think it would matter what evidence I provide you, the end result would be the same.

    You did not stipulate that you wanted the grand minima marked, but in essence it is not required. This is the part you are missing, the sun slows down on a quasi 172 year period almost every time, the only difference is the magnitude of that slowdown. This is determined by the planet angles which I have annotated via color coded dots on your plot.

    I will get around to the BC record in time, but I have had several nights with little sleep so you will have to wait.

  198. RACookPE1978 says:
    August 1, 2011 at 4:37 pm
    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?

    Yes. Charvatova’s observations on the synchronisation of ‘harmonious and disharmoniuous’ periods of solar -barycenrtric motion WRT cold and warm phases in climate and periods of generally low and high solar cycles for example.

    http://tallbloke.wordpress.com/2011/06/10/interview-with-ivanka-charvatova-is-climate-change-caused-by-solar-inertial-motion/

  199. Willis Eschenbach says:
    August 1, 2011 at 10:51 pm
    tallbloke says:
    August 1, 2011 at 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/

    Not sure what to say about that, since Bart doesn’t seem to have put his results online. What do his results say about the size of the current cycle? How well do they fit past cycles?

    The result is published in the article I linked at figure 3. Current solar cycle looks very low, as do the next two. However, it is a work in progress with a planned path of improvement.

    It has also been known since 1989 that a cycle of 20 years != a cycle of 22 years …

    Well for a first approximation you should average the two periods involved: 19.86 years and 23.72 years. This gives the average Hale cycle length pretty closely.The Hale cycle varies between ~18-~27 years. As Leif is fond of saying, the sun is a messy place. So is Earth’s climate, so I wouldn’t expect to see nice neat matches. However, because the orbital interactions of most of the planets in the solar system are synchronised one way and another, we can also use another cycles analysis method to predict solar cycle length.

    The conjunction cycle of Jupiter, Earth and Venus also works out on average to be the average solar cycle length. I discovered that by constructing a simple index of the alignment strengths along the Parker spiral, (I modified Roy Martin’s index) and modulating the result with Leif’s reconstruction of solar windspeed, I got a very good match between the JEV cycle and solar cycle length. You can see the result here:

    (ignore the sc24 ‘prediction’ on that plot, it’s Roy’s from his earlier effort)

    We think it likely more than one of the fundamental forces is involved, so we are testing both gravitational and electromagnetic possibilities.

    So JEV considered electromagnetically (Parker spiral alignment, solar windspeed adjusted) gives close timing predictions, and the Jupiter-Saturn model gives good solar cycle amplitude prediction (to be improved with further modulating algorithms related to Uranus and (particularly) Neptune).

    I understand your desire to see everything about methods published online, but as this is still under development, and we have a lot of time and effort invested, we’re being a little coy at the moment. Once we are happy with what we’ve achieved, we’ll publish, and issue all necessary info for replication in the SI.

    Best to you

    tb

  200. Leif Svalgaard says:
    August 1, 2011 at 2:54 pm
    tallbloke says:
    August 1, 2011 at 2:19 pm

    2)You have no firm theory or observation for the cause of a ~120 year cycle in the Sun.

    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.

    You would expect the amplitude of the cycle representing the beat interaction period of the principal periods (19.86 and 23.72 years) to be larger than the signals from the principals, which are 19.86 and 23.72 years, since at the peak they are additive and at the base they cancel. So this is likely where the long period cycle seen in the obs comes from. We get 131 years, you get 121. Both are within the error bounds.

    And you still don’t have any firm theory or observation on the cause of your proposed 121 year principal solar cycle either. We have two thunking great big planets (Jupiter and Saturn) exhibiting just the right frequencies to explain observations (peaks in the spectral analysis at 9.93 years(j-S synodic/2) and 11.86 years (J orbital) and 10.8 (sideband you claim as principal) and ~121 years (beat frequency you claim as other principal) . We also have two viable mechanisms, one of them published in the peer reviewed literature. And it’s a prestigious journal:

    Solar Phys (2010) 266: 227–246
    DOI 10.1007/s11207-010-9628-y

    A New Way that Planets Can Affect the Sun
    Charles L. Wolff · Paul N. Patrone
    Received: 5 May 2010 / Accepted: 16 August 2010 / Published online: 18 September 2010

  201. Willis Eschenbach says:
    August 1, 2011 at 1:04 pm

    I agree that there could easily be something to barycentric analysis … I just haven’t found anyone yet who could demonstrate such a connection, myself included.

    Have you read my paper?

  202. Two rather boring points that have been alluded to by various posters, which are important:
    1) The length of the record fixes to fundamental period for a Discrete Fourier series and the sampling frequency fixes the frequency resolution.
    Is the data aliased? This could produce spurious low frequency cycles and is a problem that has bitten many people (who should know better) in the hindquarters.

    2) A Fourier TRANSFORM cannot be made on a real signal. It is an analytical concept that requires knowledge of the existance of the signal between +- infinity and in continuous in frequency. It can be approximated for a time windowed signal using a Discrete Fourier transform, in which many of the manipulations between the time and frequency domains that apply to the FT are still valid, but must be carefully interpreted in signals in which there are components that have an infinite bandwandwidth (i.e.: impulses, a square wave). Please note that a step function, i.e.: a sudden change in base line, is not a Fourier Transformable function.
    The failure to distinguish between an FT and a Fouriers series, which can be computed on a real signal, is a major source of confusion.

  203. Leif Svalgaard says:
    August 1, 2011 at 2:22 pm
    ……………
    Absolutely agree (as you did not read my post).
    As my late grandfather use to say:
    “Every nature’s puzzle has a hidden treasure far greater than the puzzle itself.”
    I have removed data file portion from the link

    http://www.vukcevic.talktalk.net/dGMF.htm

    since there is no interest from the other contributors.

  204. @Richard Saumarez
    A Fourier TRANSFORM cannot be made on a real signal. It is an analytical concept that requires knowledge of the existance of the signal between +- infinity and in continuous in frequency. It can be approximated for a time windowed signal using a Discrete Fourier transform, in which many of the manipulations between the time and frequency domains that apply to the FT are still valid, but must be carefully interpreted in signals in which there are components that have an infinite bandwandwidth (i.e.: impulses, a square wave).

    Actually, that’s not correct. Have you not heard of the Shannon sampling theorem?

    http://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem

    “If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.”

    I.e. a band-limited analog signal can be perfectly reconstructed from its samples, provided the highest frequency is sampled at least twice per period.

    In the real world, “real signals” (as you say) tend to be automatically band-limited, due to constraining, filtering effects of electronic devices and channels. (Show me a signal with infinite frequency). So, as long as you have filtered the data somehow (or let it filter itself) observing the Nyquist limits in your sampling, the resulting reconstructions are not approximations, but “perfect”, in the same sense that a line may be “perfectly” reconstructed from two samples of the line, taken in two different locations.

    Now, you may quibble that, in a practical sense, it’s not possible to sample a line perfectly, because it must be rendered with some thickness, so there’s always some uncertainty about the two samples.

    Yes, agreed. That’s why draftsmen and carpenters typically make three or more samples when sampling lines, even though the mathematical theory clearly shows you only need two samples.

    Same problem happens in sampling signals. Sampling can’t be done without some measurement errors, which you might decide are ‘neglible’. Also, oversampling tends to reduce the uncertainty by averaging out random measurement errors.

    But do you agree with Shannon’s postulate that band-limited sampling is _not_ an approximation and mathematically captures _all_ the information in the signal? Most people, even some engineers and scientists don’t understand this at all. It is a highly non-intuitive notion that is difficult to grasp at first glance.

  205. Leif Svalgaard says:
    August 1, 2011 at 4:17 pm

    tallbloke says:
    August 1, 2011 at 3:52 pm
    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.

    I think you’ll find when you’ve studied a bit harder that no equation in the paper demands that the sun is not in freefall.

    By the way, Wolff and Patrone have replied to my email. They confirm what I’ve been saying about your misinterpretation of the ‘potential energy PE’ they posit as being ‘gravitational potential energy’. It is as I’ve been saying to you for more than two years now, energy from fusion radiating and convecting from solar core simultaneaously with barycentric motion which makes possible the barycentric effect on solar activity. Their paper confirms what I intuited from my understanding of Newtonian dynamics in 2008.

    Over on the Loehle and Scafetta thread, you make this claim:

    http://wattsupwiththat.com/2011/07/25/loehle-and-scafetta-calculate-0-66%c2%b0ccentury-for-agw/#comment-709669

    In dynamo models of the solar cycle we actually solve the MHD equations derived from Newton’s and Maxwell’s laws. That is, we do not ‘model’ anything by curve fitting. The equations are solved by integration in time and space and result in a single cycle. The average length of that cycle is 10.8 years, depending a bit on the meridional circulation, which serves as input to the solution. Since we have not observed the latter for more than a couple of cycles, we don’t know how it varies over the longer term, except that the solar cycles vary, so we conclude that what controls the cycles will also vary.

    Please could you give a link to where this derivation is demonstrated, along with links to the supporting empirical observational evidence for the validity of any parameterisations used to obtain the result.

    Please could you also supply a link to a helioseismology result which shows a solar cycle length oscillation in the sun which I requested in the linked comment but never got a reply to.

    Thanks.

  206. 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.

  207. Geoff Sharp says:
    August 2, 2011 at 6:20 am
    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?

    Hi Geoff, sorry I haven’t found the cable yet, I’ll have a look tonight. Your 110k year cycle for Jupiter sounds very interesting, and I’d like more info on that in return for digging out the plots. Over the 6000 years I looked at (annual datapoints), the 172 year signal was evident throughout, but was modulated on longer cycles too, just like the x-y data. Given the A/M exchange between (IIRC) Jupiter and Neptune at the Hallstadt cycle length, I think the precessions might be tied together, certainly for those planets, and quite likely for the others too, if perturbation theory is anywhere like right. But over the long term (millions of years) the solar system is chaotic, and some big events will occur which will change things drastically. However, the degree of order and synchronisation we see currently must come about somehow. It could be that there is a self organising principle at work which actively causes the planets to adopt as stable a pattern as possible after a disruptive event. I suspect it’s tied to, is influenced by and influences solar activity levels in a true cybernetic system of feedbacks.

    Tying that down is much further down the line however.

  208. As with any math tool, understanding on how it works is a prerequisite on it value. In evaluating date to acquire information, the Fourier Transform allow some interesting views of the data, including methods of filtering data. The following figure, shows how the oldest temperature station in Europe, was filtered using Fourier methods. In this case, frequencies greater then 0.02 cycles/yr were cut off. On the lower part of the figure, the Power Density per frequency was shown, indicating the power or energy at each frequency. The greater the magnitude the greater the energy.

    http://www.4shared.com/photo/7rxAWINH/Ave1_2010_FF_50yr.html

    It shows considerable energy in the 0.015-0.02 cycle/yr area, as well in the 0.04-0.05 and 0.07 areas. However these latter frequencies were cut off, in the filtering process.

    A more interesting set of plots, using anomaly data from14 European stations. These stations have records prior to 1800. There include the CEL, as well as Debilt, Berlin, Basel, etc.

    http://www.4shared.com/photo/I04JY2jI/Ave14_2010_FF_20yr.html

    http://www.4shared.com/photo/cjSOIdlU/Ave14_2010_FF_25yr.html

    http://www.4shared.com/photo/4FKXcwnw/Ave14_2010_FF_50yr.html

    In this case, three different filters were used, 20 yr. (0.05 c/y), 25 yr. (0.04 c/y) and 50 yr. (0.02 cy/y). Here one can see the various cycles ( or clumps of cycles indicating almost periodic) emerge from the raw data.

  209. Geoff Sharp says:
    August 2, 2011 at 12:16 am
    Willis, I have clearly shown the 60 year cycle in the velocity record.
    Both the 60-yr and 170-y cycles are present in the Fourier analysis, but both with minuscule and insignificant amplitude.

    Geoff Sharp says:
    August 1, 2011 at 11:46 am
    I dont know why you are playing these funny games but I can see that I will ultimately be wasting my time.
    I’m giving you a chance to redeem yourself and present your case. If you consider that a waste of time [some might] that is your choice.

    You did not stipulate that you wanted the grand minima marked, but in essence it is not required.
    You often make completely unfounded statements like this one. I even gave you an example of what I wanted http://www.leif.org/research/Solar-Activity-vs.Barycenter-Distance-Annotated.png where I tried to mark the ‘strongest’ U/N cycle on both plots, but seeing that you marked just about half of all the cycles it would be better for you to simply mark the strongest [in each triple] on the distance plot and what you think are grand minima on the solar activity plots.

    so you will have to wait.
    Have waited a long time already, so a few more weeks won’t make any difference.

    tallbloke says:
    August 2, 2011 at 1:01 am
    Well for a first approximation you should average the two periods involved: 19.86 years and 23.72 years. This gives the average Hale cycle length pretty closely.
    There is no Hale activity cycle. Each 11-yr cycle is an entity in itself. That the polarities flip is incidental to and a consequence of how the 11-yr cycle works.

    I understand your desire to see everything about methods published online, but as this is still under development,
    If you can’t show it, don’t hype it.

    tallbloke says:
    August 2, 2011 at 1:43 am
    You would expect the amplitude of the cycle representing the beat interaction period of the principal periods (19.86 and 23.72 years) to be larger than the signals from the principals, which are 19.86 and 23.72 years, since at the peak they are additive and at the base they cancel.
    Physically there are no two cycles beating, and even if there were they would never cancel each other [where is the cancellation of energy (which is always positive) in the purported W&P mechanism?]

    And you still don’t have any firm theory or observation on the cause of your proposed 121 year principal solar cycle either.
    As I pointed out the speed of the meridonal circulation sets the solar cycle and we do observe that circulation to vary. There can be many reasons for such variation [stellar variations are commonplace]. At this point we do not need to know precisely which one, it suffices to admit observed variability.

    We have two thunking great big planets (Jupiter and Saturn) exhibiting just the right frequencies to explain observations (peaks in the spectral analysis at 9.93 years(j-S synodic/2) and 11.86 years (J orbital) and 10.8 (sideband you claim as principal) and ~121 years (beat frequency you claim as other principal)
    Perhaps I didn’t stress strongly enough that my example was a toy-example to demonstrate how the three peaks can be explained by amplitude modulation and not only by adding two cycles. The peaks in the actual sunspot data 1820-2011 are at 10.04, 10.92, and 11.92 yrs, but those are mainly artifacts from mixing two populations: the actual data has a varying fundamental period [from 11.3 in the first half to 10.6 in the 2nd half] likely reflecting a changing speed of the circulation.

    We also have two viable mechanisms
    Both of which violate physical law [which doesn't seem to bother you - hey, perhaps new physics is in the offing]

    M.A.Vukcevic says:
    August 2, 2011 at 4:21 am
    “Every nature’s puzzle has a hidden treasure far greater than the puzzle itself.”
    “For every complex phenomenon there is a simple explanation, which is wrong.”

    tallbloke says:
    August 1, 2011 at 3:52 pm
    It is as I’ve been saying to you for more than two years now, energy from fusion radiating and convecting from solar core simultaneously with barycentric motion which makes possible the barycentric effect on solar activity. Their paper confirms what I intuited from my understanding of Newtonian dynamics in 2008.
    You try to infuse some ‘high-value’ words to lend legitimacy to your ‘intuition’. Fusion is irrelevant [it doesn't matter how the energy is produce] and it takes hundreds of thousands of years for the energy from the solar core to reach the convection zone. Your ‘understanding’ of Newtonian dynamics suffers from your denial of its universality.

    Please could you give a link to where this derivation is demonstrated, along with links to the supporting empirical observational evidence for the validity of any parameterisations used to obtain the result.
    Accessible explanations may be found here:

    http://www.leif.org/EOS/Sunspot-Predictions-Dynamo-India.pdf

    http://www.leif.org/EOS/SunMagneticCycle.pdf

    http://solarphysics.livingreviews.org/Articles/lrsp-2010-3/download/lrsp-2010-3Color.pdf [see section 4.9]

    http://solarphysics.livingreviews.org/Articles/lrsp-2005-1/download/lrsp-2005-1Color.pdf

    http://solarphysics.livingreviews.org/Articles/lrsp-2010-6/download/lrsp-2010-6Color.pdf

    These papers have references to the [much harder] technical papers describing the calculations.
    Please could you also supply a link to a helioseismology result which shows a solar cycle length oscillation in the sun which I requested in the linked comment but never got a reply to.
    Second time: E.g. Figure 1 of http://arxiv.org/abs/1004.2869v1
    But note that helioseismology uses sound waves with travel times of a few minutes so naturally will not show longer oscillations. What it does show is solar cycle variation of the frequency of those waves. So, the interior of the sun has [ever so slightly] different characteristics as a function of phase through the 11-yr cycle.

  210. Leif Svalgaard says:
    August 2, 2011 at 9:51 am
    ………….
    My granddad (life long optimist)
    “Every nature’s puzzle has a hidden treasure far greater than the puzzle itself.”
    Dr. S’s (life long ? ) cyclopedia of wisdom:
    “For every complex phenomenon there is a simple explanation, which is wrong.”
    e.g. E=mc^2, F=ma, P=VI, PV=const end so on & on & on … all wrong !
    Bye bye.

  211. M.A.Vukcevic says:
    August 2, 2011 at 10:29 am
    E=mc^2, F=ma, P=VI, PV=const end so on & on & on … all wrong !
    If you believe that, then:
    Bye bye.
    good riddance.

  212. @Dr. S.
    “For every complex phenomenon there is a simple explanation, which is wrong.”
    @Vuk
    “… all wrong

    Logical fallacy. You are conflating ‘existential’ vs ‘universal’ quantification.

    Leif didn’t say ‘all simple explanations are wrong’, merely that ‘at least one wrong simple explanation exists’ for each complex phenomenon.

    http://en.wikipedia.org/wiki/Existential_quantification

    http://en.wikipedia.org/wiki/Universal_quantification

  213. Geoff Sharp commented on Riding a Pseudocycle.

    in response to a comment by Willis Eschenbach:

    ….

    Willis, I have clearly shown the 60 year cycle in the velocity record.

    Yes, you have, and I have not denied it, so I’m not sure what you’re on about. The 60-year cycle is miniscule, smaller by orders of magnitude than the 20 year cycle. You could find a tiny cycle like that in most datasets. So what?

    I have given examples of how a background trend can be the cornerstone of a particular line of research,

    I haven’t a clue what you are referring to here.

    I have clearly shown why the 60 year cycle doesn’t show up in Fourier type analysis …

    Not that I’ve seen, not in any sense. You have claimed in a very unclear fashion that a wave with three heads like a trident can avoid detection by Fourier analysis. Despite being asked for clarification on this particular subject, you have not shown how or why this might occur. So no, you have NOT shown why the cycle doesn’t show up.

    … but you insist on only using the Fourier method to push “what looks like an agenda” against the Loehle and Scafetta paper.

    Say what? I used Periodicity analysis, not Fourier analysis, is your reading ability really that poor? However, you can use either one to show what I showed.

    And why is “what looks like an agenda” in quotes, when you are the only one to say that in this thread? I have no “agenda” against the L/S paper. I just thought it was extremely bad science. Do you think it is valid to use the trend in the first 2/3s of the data as the null hypothesis? Really? Do you think they have established that, as they claim, humans caused no warming up until 1950, and then a huge amount since then? Really? Because if so, you’ll have to explain how that works. L/S didn’t explain it, they just threw a could cycles and a trend at the data and claimed that it has meaning. I say it has no meaning. If you think it does have meaning, then you can explain how.

    If evidence is presented and then ignored the question is asked why. For me that is a loss of credibility.

    Huh? What evidence have I ignored?

    You, on the other hand, have ignored the following request, more than once, which is eroding away your credibility as we speak. Here’s the request:

    How about you begin by answering my specific questions, like, what kind of an equation makes a “trident” headed wave? Or why don’t you begin by demonstrating exactly how such a wave might escape Fourier analysis? Or you could show the mathematical methods that you use to isolate trident headed waves from normal waves, as I requested.

    I don’t care where you start, Geoff. But to say you don’t know where to start, and then follow that with an insult?

    I gave you your choice of issues with your claims that you could address. You have ignored them all, and instead choose to call me names and claim that I’m ignoring evidence … right, like you’ve provided any evidence for three headed trident waves.

    And like I said, Geoff, when you do that folks just point and laugh at you. DO THE MATH and come back and tell us how the trident shaped waves are generated. Because the only waves you’ve demonstrated so far involve your hands, which are definitely waving like crazy …

    w.

  214. tallbloke says:
    August 2, 2011 at 1:01 am

    So JEV considered electromagnetically (Parker spiral alignment, solar windspeed adjusted) gives close timing predictions, and the Jupiter-Saturn model gives good solar cycle amplitude prediction (to be improved with further modulating algorithms related to Uranus and (particularly) Neptune).

    Parker spiral alignment? Solar windspeed adjusted? I thought we were discussing the barycentric cycles … in any case, you say:

    I understand your desire to see everything about methods published online, but as this is still under development, and we have a lot of time and effort invested, we’re being a little coy at the moment.

    Hey, that’s great, Tallbloke. Please come back when you’re cured of being coy, because I have no interest in half-revealed ideas, or claims where you’re sorry but you can’t supply the underlying stuff.

    In short, if you want to wait until publication before dazzling us with your ideas, please go be coy somewheres else. I’m not going to play that game.

    w.

  215. Geoff Sharp says:
    August 2, 2011 at 2:33 am

    Willis Eschenbach says:
    August 1, 2011 at 1:04 pm

    I agree that there could easily be something to barycentric analysis … I just haven’t found anyone yet who could demonstrate such a connection, myself included.

    Have you read my paper?

    Why on Earth would I read the paper of someone who claims there are trident-headed waves that escape Fourier analysis, but who won’t give us the math for either how the trident-headed waves are formed or how they evade analysis? Sorry, I prefer to read science.

    w.

  216. Willis Eschenbach says:
    August 2, 2011 at 11:22 am

    Parker spiral alignment? Solar windspeed adjusted? I thought we were discussing the barycentric cycles …

    Nature isn’t neatly compartmentalised to suit your thread topics.

    I have no interest in half-revealed ideas,
    In short, if you want to wait until publication before dazzling us with your ideas, please go be coy somewheres else.

    Fair enough.

    Bye for now.

  217. John Day says:
    August 2, 2011 at 11:04 am
    “@Vuk “… all wrong”
    Logical fallacy. You are conflating ‘existential’ vs ‘universal’ quantification.

    He is committing another fallacy: because E=mc^2 is right, therefore his ideas must be right.

  218. John Day says:
    August 2, 2011 at 11:04 am
    …..
    Thank you Mr. Day.
    If statement is true, then it is the explanation of phenomenon.
    If assertion is wrong then it is not the explanation it is a guess, whereby: explanation = the statement describing a set of facts which clarifies the cause.
    For a complex problem there may be more than one explanation (e.g. light = wave & light = particle, Newtonian and Einstein’s gravity, etc), but they all must be true.

  219. @Vuk
    > For a complex problem there may be more than one explanation …

    True. But you seem to be denying that there could be multiple, simple wrong answers too. That was the gist of Leif’s aphorism.

    In fact there can be an infinite number of simple answers, all of which are wrong. For example, ‘What is the meaning of Life, the Universe and Everything?’ (which I assume you’ll accept as a ‘complex’ issue)

    Here is an infinite set of simple answers, all wrong:
    ans={1..Inf} – {42}

    Note how I cleverly excluded the right answer.
    :-]

  220. Well-founded signal analysis distinguishes categorically between strictly
    periodic and aperiodic or random oscillations. It is only the former that
    can be exactly decomposed by the harmonic Fourier series (provided that we
    have at least one complete cycle of non-aliased data). Although the
    decomposition is entirely in terms of sinusoids, the shape or complexity of
    the waveform doesn’t impact the exactitude at all.

    Random signals, on the other hand, are NEVER the superposition of discrete
    sinusoids. They are represented not by line spectra in a series summation,
    but by a spectral continuum in a Fourier-Stieljes integral, with random
    phases for the infintesimal sinusoids that synthesize the signal. The
    Wiener-Kintchine Theorem rigorously defines their power density spectrum as
    the Fourier transform of the autocovariance function of the signal.
    Applying FFT analysis to such signals tacitly imposes the PRESUMPTION of
    periodicity corresponding to the available length of record. That is what
    leads to various short-record artifacts in the raw periodogram obtained by
    squaring the magnitude of the FFT coefficents, which novices commonly
    mistake for the power spectrum.

    While “periodicity analysis” appeals strongly to primitive intuition and may
    be useful in distinguishing strictly periodic signals from those that are
    not, it provides no new analytic insight into the stochastic structure of
    random signals. The decomposition obtained is likewise mistakenly
    periodic–and lacks orthogonality to boot, as the authors of the method
    admit. And as others have pointed out here, its goals are readily achieved
    by less quaint means, such as wavelet analysis. Fourier’s place in the
    pantheon of science remains secure.

    I wholeheartedly agreed with Willis on the original thread that L&S made a
    basic conceptual mistake by positing strictly periodic multidecadal
    oscillations in their model of GST. Unfortunately, Willis now makes the
    opposite-pole mistake of claiming, largely on the basis of the qualitative
    features of red-noise modeling, that such oscillations are
    “pseudo-cycles”–mere artifacts of faulty analysis.

    But red noise is not at all evident in long records of yearly temperature
    averages, instrumental or proxy. Properly estimated power spectra of such
    records (some hundreds to thousands years long) almost invariably show
    statistically significant spectral peaks and valleys, instead of a power
    density monotonically rising with decreasing frequency, as with red noise.
    In fact, in some regions (e.g., northeast Europe) the spectral density of
    vetted records consistently FALLS at the lowest frequencies. And what
    makes the contrary evidence even more convincing is the high cross-spectral
    coherence at widely separated stations.

    There is an extremely wide range of stochastic signal structures in the real
    world that result in aperiodic, but coherent, oscillations that do not
    resemble any academic noise models. This is the case because real-world
    signals are invariably band-limited by physics. In narrow-band situations,
    there’s even some useful predictability of amplitude and phase (but never
    perfect predictability, as the prognosticators of SC24 must acknowledge).
    In wide-band situations, even optimal prediction filters produce no
    practically useful results.

    Instead of jumping from one conceptual extreme to the other on the basis of
    inapropriate models, we should pay more attention to what the entire body
    of geophysical data is showing. It is showing that multidecadal and longer
    natural cycles may not be predictable and the mechanisms uncertain, but they are real signals rather than
    noise.

  221. The new system of posting comments on WUWT is queer. It attached a link to a website with which I have no affiliation.

  222. @John Day
    I beg to disagree.
    This is one of the most fundamental ideas in signal processing, I agree that if you compute a DFT of a time windowed signal, it can be inverted. This does not detract from the analytical concept that a signal that can be measured from +- infinfibity has infinestimal frequency resolution.Your comments about the Nyquist theorem (=the Shannon theoem? ) are wrong. If you have a system in which the sampling is not dictated by the Nyquist theorem, i.e.: the samples are not adequately prefillered, you will end up with an aliased signal, which cannot be reconstructed form the aliased data.
    As I have pointed out, this is one of the most elemtary pitfalls in signal processing. For example, consider daily records that are averaged into monthy records. The averaging process is a filter that has zeros at n/(30 days) The first zero is at 1/month. This is decimated ated 1/month, giving a Nyquist frequency at 1/(2months). Since this is aliased, the monthly record is corrupt.
    As I pointed out, this is a problem that occurs with monotonous regularity.

  223. Willis Eschenbach says:
    August 2, 2011 at 11:29 am

    Why on Earth would I read the paper of someone who claims there are trident-headed waves that escape Fourier analysis, but who won’t give us the math for either how the trident-headed waves are formed or how they evade analysis? Sorry, I prefer to read science.

    Ok Willis I am beginning to understand your brand of science, basically if the data doesn’t suit your agenda you will refuse to look at it. I will call this “3 monkey science”.

    You say you have seen nothing in the barycentre data but refuse to look at the latest research that has been developing over the last 3 years….where have you been?

    I provided a clock face with variable trident arm as an analogy to demonstrate how cycles can go undetected using your method. I then provided the actual graphs created by Leif showing the occurrence and strength of the so called prongs on the clock arm. You once again ignored the data.

    This is not good enough from a frequent author on a science blog, you are doing this blog a disservice and in my mind have zero credibility. I will not waste any more time on you.

  224. PS: @John Day,
    I did my PhD in a World class signal processing laboratory and I am familiar with the concepts that you claim to understand.

  225. Geoff Sharp says:
    August 2, 2011 at 3:29 pm
    I provided a clock face with variable trident arm as an analogy to demonstrate how cycles can go undetected using your method.
    I don’t understand why you make this strident claim as those cycles are not undetected at all. Here they are [in red circle]: http://www.leif.org/research/FFT-Barycenter-Distance-170.png
    They are [like the 60-yr cycles] completely insignificant, but they are there, as they should be.

  226. Richard Saumarez says:
    August 2, 2011 at 3:28 pm

    “This is decimated ated 1/month, giving a Nyquist frequency at 1/(2months). Since this is aliased, the monthly record is corrupt.”

    You’re absolutely correct. I’ve long been an advocate of SEMI-decimation, but very few understand the issue.

  227. 1sky1 says:
    August 2, 2011 at 3:06 pm


    While “periodicity analysis” appeals strongly to primitive intuition and may be useful in distinguishing strictly periodic signals from those that are not, it provides no new analytic insight into the stochastic structure of random signals.

    You can’t have it both ways. Either it is useful in detecting strictly periodic signals from those that are not (it is, as you say), or, it provides no new analytic insight.

    As to whether it “appeals strongly to primitive intuition”, I love the underlying mathematical class-based claim that some kinds of intuition are “primitive”. It also neglects the fact that we have “primitive intuitions” because historically they’ve worked …

    The decomposition obtained is likewise mistakenly periodic–

    I’m not sure what you mean by “mistakenly periodic”.

    and lacks orthogonality to boot, as the authors of the method admit.

    I find the lack of orthogonality to be a great advantage at times. Periodicity analysis shows me the actual shape and size of the real 20-year signal in the data. As far as I know it is the only method of its type that can do this. For example, as Figure 4 above shows, the 20 year cycle in the data consists of a slow decline in temperature, followed by a very quick warming. I find this quite interesting, as there are enough 20 year cycles in the data to give 8 data points each. That’s miles from ideal … but it gives the best idea available of the actual 20 cycle as opposed to some theoretical sine wave.

    It is also capable of finding a simplified solution which is not apparent in Fourier analysis. For example, if we add a square wave and and triangle wave with periods of say 7 and 11, Fourier analysis will show the insanely complex pattern of sine waves that you’d need to add together to get that square plus triangle wave.

    Periodicity analysis, on the other hand, reveals the exact shape (square, triangular, or whatever) of the underlying dominant patterns. Specifically because it is not orthogonal, it can reveal the shape and period of the square and triangle waves that make up the final result. This ability to examine and recognize patterns adds to our understanding of what we are discussing.

    At least that’s my primitive intuition, your intuition may vary …

    And as others have pointed out here, its goals are readily achieved
    by less quaint means, such as wavelet analysis.

    I’m not down on any of the methods, Fourier or wavelet or others. I’m pointing out that there is an additional method, periodicity analysis, which (like all methods) has its advantages and disadvantages. Unlike all the rest, it can reveal the actual shape of the intermediate repeating patterns that exist in the dataset. Among other things, it reinforces the idea that there are cycles at all frequencies, the only question is their strength.

    Fourier’s place in the pantheon of science remains secure.

    I’m sorry if my writing is that unclear. I’m not dissing Joe Fourier, he’s one of my personal heros, his was a stupendous insight. I started this with a picture of Fourier, in homage to the man.

    I wholeheartedly agreed with Willis on the original thread that L&S made a basic conceptual mistake by positing strictly periodic multidecadal
    oscillations in their model of GST. Unfortunately, Willis now makes the opposite-pole mistake of claiming, largely on the basis of the qualitative features of red-noise modeling, that such oscillations are “pseudo-cycles”–mere artifacts of faulty analysis.

    1sky1, you may have noted before I respond to someone, I post their exact words to which I am responding. This avoids misunderstandings on either side – if I am mistaken in what I understand from your words, we both have your original words to refer to. That way, my misunderstanding can be cleared up.

    In this case you make a statement that I am “claiming” something, which you say is largely on the basis of some other thing, and that I’m concluding something else … my friend, I’ve written thousands of words on various subjects, including almost two thousand in the head post on this thread alone, never mind what I’ve written in the comments. What exactly did I say that you are responding to?

    Without knowing exactly what I said, I don’t even know what you are objecting to. Without that, I don’t know where our mutual areas of understanding (which are great) began to diverge.

    So everyone, please. QUOTE MY EXACT WORDS so we can all know what it is you are talking about.

    Thanks,

    w.

  228. Willis,

    The claim of pseudocycles is in the title of your post. Then in your comments

    Willis Eschenbach says:
    July 30, 2011 at 10:42 am

    “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. ”

    I have an upcoming appointment this evening, but I’ll find time tomorrow to locate your comment on how red noise explains multidecadal cycles and then discuss the attendant technical issues.

  229. Geoff Sharp says: “Willis is losing a lot of creditability here.”

    I don’t believe Willis’s credit score has been impacted by anything he’s written on this thread.

    Geoff Sharp says: “So many ill founded attacks on those that disagree with the basic fabric of this thread.”

    You are the only blogger I know who considers questions posed to you and requests of you to be attacks.

    Geoff Sharp says: “There seems to be a trend lately that WUWT is promoting Luke Warmer resident guest authors on a permanent basis.”

    I would have avoided commenting on this thread, but I accept this part of your comment to be directed at me as well. Here’s a suggestion, Geoff. Maybe you should create your own website and blog where you can have the guest authors of your choice.

  230. I second Bob Tisdale’s post above. Willis is one of only a handful of people that I find 100% credible.

  231. Leif Svalgaard says:
    August 2, 2011 at 4:52 pm

    Geoff Sharp says:
    August 2, 2011 at 3:29 pm
    I provided a clock face with variable trident arm as an analogy to demonstrate how cycles can go undetected using your method.
    I don’t understand why you make this strident claim as those cycles are not undetected at all. Here they are [in red circle]: http://www.leif.org/research/FFT-Barycenter-Distance-170.png
    They are [like the 60-yr cycles] completely insignificant, but they are there, as they should be.

    This is the exact point I am trying to make Leif. Your analysis shows the 172 cycle as insignificant. But what does the actual data tell us? It tells us without any doubt there is a 172 year fluctuation (cycle) in distance (AM) that is far from insignificant. If the theory is correct is means the 172 year wave is responsible or at least correlates with solar cycle modulation, the same logic is being used by Scafetta and his 60 year cycle. I am saying undetected is basically the same as insignificant.

    Willis says “I find no such 60-year cycle in the barycentric data.”

    I and Scafetta have shown there is a clear 60 cycle in the solar velocity record. We use different scientific methods to isolate that cycle.

    One method of analysis shows little or no significance of a cycle and another method shows a very clear cycle that is fundamental to a scientific theory. Willis has put all his eggs in one basket without taking into consideration other methods. This is his decision, but it is also very bad science. I object to the title of this thread based on these reasons.

  232. @Richard Saumarez:
    > I did my PhD in a World class signal processing laboratory …

    Hmm, you claim to have a PhD in signal processing, yet you seem to be ignorant of Shannon’s sampling theorem. How can that be? In what area is your PhD?

    Your objections were somewhat incoherent and in no way refute Shannon’s theorem. For example, I specifically stated the theorem only holds for band limited signals, where the Nyquist limit is observed. And of course signal averaging acts like a low-pass filter, so how does that refute Shannon’s theorem?

    If you really had doctoral-level knowledge of signal processing you would certainly understand this notion of ‘perfect reconstruction’ of analog signals from their digitized samples.

  233. Bob Tisdale and Smokey:

    Above (at August 1, 2011 at 1:04 pm) I have already supported your position but I write to iterate my view by citing that post because I think it needs repeating here.

    Richard

  234. tallbloke says:
    August 2, 2011 at 8:17 am

    Hi Geoff, sorry I haven’t found the cable yet, I’ll have a look tonight. Your 110k year cycle for Jupiter sounds very interesting, and I’d like more info on that in return for digging out the plots. Over the 6000 years I looked at (annual datapoints), the 172 year signal was evident throughout, but was modulated on longer cycles too, just like the x-y data. Given the A/M exchange between (IIRC) Jupiter and Neptune at the Hallstadt cycle length, I think the precessions might be tied together, certainly for those planets, and quite likely for the others too, if perturbation theory is anywhere like right. But over the long term (millions of years) the solar system is chaotic, and some big events will occur which will change things drastically. However, the degree of order and synchronisation we see currently must come about somehow. It could be that there is a self organising principle at work which actively causes the planets to adopt as stable a pattern as possible after a disruptive event. I suspect it’s tied to, is influenced by and influences solar activity levels in a true cybernetic system of feedbacks.

    Tying that down is much further down the line however.

    Hi Rog, I am a bit confused with your response, it doesnt really answer my question. The precession issue with z axis mass above and below the solar equator that changes that mass over time is what i am trying to resolve. I did some work this morning using JPL, Semi’s Ephemerides Viewer and the Sky View Cafe website, and if my research is correct it shows precession of the planets moves the mass in the z axis over time.

    It appears the actual orbit incline of the planets does not move over time (6000 years). The perihelion point moves with the precession along with the mass. I looked at Jupiter and it showed a movement of about 2 deg in the z axis per 6000 years which is significant. The planets all have their own inclination angle which can be in opposition to each other. If my figures are correct it means the z axis mass totals would not follow a repeatable pattern, especially when looking at longer timeframes. Your graph showing the correlation of z axis and SSN may just be a coincidence or it could also mean the solar cycle modulation does not follow a regular cycle, this is a fairly large difference between our two theory’s.

    I would be interested to see if you come up with the same results.

  235. Geoff Sharp says:
    August 2, 2011 at 8:47 pm
    This is the exact point I am trying to make Leif. Your analysis shows the 172 cycle as insignificant. But what does the actual data tell us? It tells us without any doubt there is a 172 year fluctuation (cycle) in distance (AM) that is far from insignificant.
    It is just a minor perturbation and is indeed insignificant. That you attach significance to it is another matter.

    If the theory is correct is means the 172 year wave is responsible or at least correlates with solar cycle modulation, the same logic is being used by Scafetta and his 60 year cycle. I am saying undetected is basically the same as insignificant.
    But most likely theory is not correct as it is physically impossible.

    Willis says “I find no such 60-year cycle in the barycentric data.”
    I and Scafetta have shown there is a clear 60 cycle in the solar velocity record. We use different scientific methods to isolate that cycle.

    There is a tiny cycle not a dominant one as in the very short temperature record

    One method of analysis shows little or no significance of a cycle and another method shows a very clear cycle that is fundamental to a scientific theory.
    There is no clear cycle, just a minor perturbation, and there is no scientific theory, just hand waving. Your perturbations are not even correlated with solar activity. The power spectrum of Steinhilber’s solar activity data http://www.leif.org/research/FFT-Steinhilber.png shows no prominent peak at 172 years, but lack of power at 170 and a peak at 177 years. The dominant cycle is the Hallstatt cycle at 2343 yrs and the Suess cycle at 208 yrs. The 86 yr peak is half of your 172 yrs. There is broad power around 120-130 yrs. It is clear that your 172 yr perturbation is not a major influence.

    I object to the title of this thread based on these reasons.
    so you disagree, but that is hardly grounds for rejection of his opinion.

  236. Geoff Sharp says:
    August 2, 2011 at 3:29 pm

    Ok Willis I am beginning to understand your brand of science, basically if the data doesn’t suit your agenda you will refuse to look at it. I will call this “3 monkey science”.

    You say you have seen nothing in the barycentre data but refuse to look at the latest research that has been developing over the last 3 years….where have you been?

    I provided a clock face with variable trident arm as an analogy to demonstrate how cycles can go undetected using your method. I then provided the actual graphs created by Leif showing the occurrence and strength of the so called prongs on the clock arm. You once again ignored the data.

    Since you haven’t provided any citation for that claim, I assume you are referring to this:

    It would be very difficult to write an equation that would capture the variability of the trident head phenomenon. It is visible via my annotations on Leifs solar distance charts but the outcome is reliant on planet positions that vary every time. Not everything in science fits into an equation or is visible via Fourier analysis. Have a good look at my annotations and it should become clear. The annotations are the forks in the trident example.

    http://tinyurl.com/2dg9u22/images/Solar-Activity-vs.Barycenter-Distance-AD.png

    So in short, you don’t have a clue what kind of equation would “capture the variability of the trident head phenomenon”. You don’t know how it is created. You don’t know how it escapes Fourier analysis as you claimed.

    You have also provided a link to a chart of Ted Landscheidts … I discussed this stuff with Ted himself, Geoff. Unfortunately, he did what you are doing. You are noticing a phenomenon, that sometimes a combination of cycles ends up looking like a trident. You yourself admit you have no explanation for this supposed entity.

    You say that the trident-head wave can go undetected because one or more of the three prongs of the trident may not show up. You don’t have a theory of how or when that might happen.

    So no, I’m not “ignoring” the data as you claim. I find the data totally unexceptional. Sure, when you have varying waves you can easily get a beat frequency that looks like a trident. I could make you some if you like. Then you could play with them, and notice that the appearance of such a pattern is very common. You could also understand why under some circumstances such a beat frequency may not appear as a fundamental frequency in fourier analysis … because it’s not a fundamental frequency,

    However, such a beat frequency will appear in periodicity analysis … just sayin …

    This is not good enough from a frequent author on a science blog, you are doing this blog a disservice and in my mind have zero credibility. I will not waste any more time on you.

    You keep coming back to credibility. You are making some kind of claim that a phenomenon called a “trident headed wave” exists as a separate category of wave. You are unable to provide any theoretical or mathematical understanding beyond saying well, there really are trident headed waves, and your evidence is that you you can point to them.

    I, on the other hand, have provided full accountability for the mathematical methods I used, including the code.

    I’ll let the reader decide whose ideas are more credible here.

    w.

  237. nicola scafetta says:
    July 30, 2011 at 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 [would] present such a perfect repetition of cycles that would be possible only if the temperature were made of cycles with perfect periods of: 20, 10, 5, 4, 2.[years]

    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.

    I hope Willis is taking his time to consider Nicola Scafetta’s response, and is carefully formulating a well considered reply. Because if not he is just ignoring Scafetta’s criticism, having written a post which purports to rebut Loehle and Scafetta’s paper.

    That Scafetta took the time to answer Willis should be regarded as a compliment, even though he is critical of the analysis technique employed to rebut the L & S 2011 paper.

    Hack and run tactics will not enhance the reputation of open peer review. I think Willis owes it to the open science community as well as to Craig Loehle and Nicola Scafetta to respond to the criticism.

  238. @John Day,
    Yes, I did do a PhD in Electrical/Biomedical engineering in a signal processing laboratory. I am familiar with the Nyquist theorem that relates the sampling frequency necessary to define a signal and I am also familiar with Shannon’s theorem which relates signal entropy and spectral charateristics. (See Papoulis, Bendat & Piersol, Oppenheim & Schaeffer).

    I agree that a signal, when filtered with anti-aliasing filtered and then sampled at, or above, the Nyquist frequency can be reconstructed with tolerable accuracy, although to do so one, theoretically, needs an infinite length of of samples obtained at infinitesimal resolution to do so. (Why? Because construction of a continuous signal from samples is simply convolution with a sin(x)/x waveform that is not bounded in time and has an asymptotic amplitude).

    However, you have missed a very fundamental point. Many variables that are treated as signals in climatology cannot be treated with an anti-aliasing filter and so may be aliased. You clearly haven’t thought about my example: The CRUTEMP data, which is presented as monthly samples, is severely aliased, simply because the daily samples are effectively filtered by averaging with a frequency response that is the form of sin(w)/w (w=complex frequency) and this filter has its first zero at 1/month. The signal is then decimated at 1/month, giving a Nyquist frequency of 1/2months. Therefore the signal is aliased and the daily data cannot be reconstructed from the monthly data.,

    I suggest that you take the CRUTEMP data, segment it into, say, 10 year records and compute the ensemble amplitude spectrum ( having applied a cosine bell window and detrended the record). You will see immediately that the data is aliased. You might also like to take a well-sampled signal, obtain averages samples, and decimate the signal at a period equal to the length of the averaging window.

    Does this matter? It depends on what you want to do with the data. As you must be aware, the effect of aliasing in the frequency domain is to fold the spectrum, which is the true spectrum convolved with sampling process, an infinite sequence of impulses speced at the sampling frequency. Therefore, the high frequency components in the signal appear as spurious lower frequency signals in the aliased spectrum, leading to trends in the time-domain signal. If this is used as an input, say, to a model, it will produce spurious results.

    I stand by my comment that ignoring the Nyquist theorem, or at least not being aware of its finer points, is depressingly common and, in my view, stems from a mindless application of DSP techniques without sufficient analysis.

  239. As a follow-up to my last remark, the thesis presented in this post has been constructed using aliased data and therefore the results are simply wrong.

    One advantage of spectral analysis is that it is relatively easy to determine if data is aliased and this is a good first step to apply to data before applying further signal processing techniques.

  240. Willis Eschenbach says:
    August 2, 2011 at 11:01 pm

    So in short, you don’t have a clue what kind of equation would “capture the variability of the trident head phenomenon”. You don’t know how it is created. You don’t know how it escapes Fourier analysis as you claimed.

    Incorrect. An equation cant capture the variability, its like saying how powerful will the swell of the ocean be in 1001 days. The infinite variability of the planet positions govern the strength of the prong and how many. If you can write an equation for that I will be impressed. I know exactly how it is created and have provided the data to back it up, you simply dont understand it. The trident example was meant to convey to you how I do understand why the process of Fourier analysis are not picking up a regular signal, that is because it is not regular. Leif points out the De Vries or Suess cycle, that is a product of the trident. One of the prongs is weak so the gap increases. Look at the Dalton minimum and now, 210 years between grand minima, the last prong of the Dalton didnt fire and the first prong (SC20) of the current cycle was the same. One day you guys will get it.

    You have also provided a link to a chart of Ted Landsc***ts … I discussed this stuff with Ted himself, Geoff. Unfortunately, he did what you are doing. You are noticing a phenomenon, that sometimes a combination of cycles ends up looking like a trident. You yourself admit you have no explanation for this supposed entity.

    Incorrect again, the charts I have linked to have nothing to do with Landsch**dt, you have no idea of what you are discussing. The chart mentioned (which chart?) was probably related to the famous chart created by the now deceased Carl Smith who we are indebted to. The new work that has sprung from his graph I think is ground braking, you have absolutely no knowledge on this topic. You need to bring yourself up to speed before you can criticize. My research has very little to do with the Landsche*** method.

    You say that the trident-head wave can go undetected because one or more of the three prongs of the trident may not show up. You don’t have a theory of how or when that might happen.

    Incorrect again. Read my paper, everything is answered if you bother to read.

    So no, I’m not “ignoring” the data as you claim. I find the data totally unexceptional. Sure, when you have varying waves you can easily get a beat frequency that looks like a trident. I could make you some if you like. Then you could play with them, and notice that the appearance of such a pattern is very common. You could also understand why under some circumstances such a beat frequency may not appear as a fundamental frequency in fourier analysis … because it’s not a fundamental frequency,

    However, such a beat frequency will appear in periodicity analysis … just sayin …

    You havent even looked at the data…this is the problem. Read the paper.

    This is not good enough from a frequent author on a science blog, you are doing this blog a disservice and in my mind have zero credibility. I will not waste any more time on you.
    ———————
    You keep coming back to credibility. You are making some kind of claim that a phenomenon called a “trident headed wave” exists as a separate category of wave. You are unable to provide any theoretical or mathematical understanding beyond saying well, there really are trident headed waves, and your evidence is that you you can point to them.

    Incorrect again (this is getting boring) The planet angles create the perturbations that cause solar slowdown that usually travel in threes. They are different everytime, this is how nature works and it is normal orbital physics, the data used is from JPL and beyond question. You have absolutely no understanding of the process and refuse to look at it. I will leave people to judge your credibility.

  241. Richard Saumarez and John Day,
    Please would you take a look at the DSP techniques employed in this post and leave some comment.

    http://tallbloke.wordpress.com/2011/07/31/bart-modeling-the-historical-sunspot-record-from-planetary-periods/

    I’d also appreciate any input you can give to the discussion about sampling rates for barycentric data towards the bottom of the comments in this thread too if you can spare the time

    http://tallbloke.wordpress.com/2011/07/25/ed-fix-solar-activity-simulation-model-revealed/

    Many thanks

  242. Bob Tisdale says:
    August 2, 2011 at 7:02 pm

    I would have avoided commenting on this thread, but I accept this part of your comment to be directed at me as well. Here’s a suggestion, Geoff. Maybe you should create your own website and blog where you can have the guest authors of your choice.

    I have two blogs Bob, this goes to show how incredibly out of touch you are…click on my name.

  243. Leif Svalgaard says:
    August 2, 2011 at 10:07 pm

    I object to the title of this thread based on these reasons.
    ———————————————-
    so you disagree, but that is hardly grounds for rejection of his opinion.

    The title of this “story” is offensive and very clearly suggests that the work of Loehle and Scafetta is pseudo-science. All based on very weak science by the author. I would not be proud to have this story on my blogs, but do understand Anthony is a busy man and respect the work that he does.

  244. tallbloke says:
    August 3, 2011 at 12:15 am

    nicola scafetta says:
    July 30, 2011 at 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 [would] present such a perfect repetition of cycles that would be possible only if the temperature were made of cycles with perfect periods of: 20, 10, 5, 4, 2.[years]

    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.

    I hope Willis is taking his time to consider Nicola Scafetta’s response, and is carefully formulating a well considered reply. Because if not he is just ignoring Scafetta’s criticism, having written a post which purports to rebut Loehle and Scafetta’s paper.

    That Scafetta took the time to answer Willis should be regarded as a compliment, even though he is critical of the analysis technique employed to rebut the L & S 2011 paper.

    Hack and run tactics will not enhance the reputation of open peer review. I think Willis owes it to the open science community as well as to Craig Loehle and Nicola Scafetta to respond to the criticism.

    Oh, please, tallbloke, enough with the veiled insults. If I had seen Scafetta’s response, I would have answered it. I have a lot on my plate, it’s four AM and I’m leaving for Alaska. I’ll get back to Nicola as soon as I can.

    But for you to put out all that ‘Is Willis hiding from Nicola’ kind of innuendo is just nasty, tallbloke. A simple “did you see this” without spilling the ugly contents of your mental suspicion machine would have been sufficient, I could have said ‘no I missed it’ and gone on.

    That kind of thing is far beneath you, tallbloke. I’m surprised, usually you use your indoor voice and play well with the other kids.

    Back in a bit,

    w.

  245. Geoff Sharp:

    As I have repeatedly said, I think the Lohle &Scaffetta method is flawed. But I do NOT consider it to be pseudo-science.

    However, at August 3, 2011 at 3:39 am you say to Willis:

    “The title of this “story” is offensive and very clearly suggests that the work of Loehle and Scafetta is pseudo-science.”

    Hmmm. I had not thought the title made that suggestion, and I still don’t. Just saying.

    I wonder if emotions are getting a little high in this discussion.

    Richard

  246. @Richard Saumarez
    I agree that a signal, when filtered with anti-aliasing filtered and then sampled at, or above, the Nyquist frequency can be reconstructed with tolerable accuracy,…

    Apparently you do not know the sampling theorem.

    But you’re making progress. You started with
    ‘A Fourier TRANSFORM cannot be made on a real signal.’
    then
    ‘It can be approximated for a time windowed signal using a Discrete Fourier transform’

    Now you allow reconstruction with ‘tolerable accuracy’.

    When will you admit that the Shannon sampling theorem shows us, mathematically, that analog band-limited signals can be perfectly from digitized specimens of that signal? In the same sense, mathematically, that a continuous straight line may be reconstructed perfectly from only two samples.

    Here are Claude Shannon’s own words [1] on this subject:
    “Theorem 1: If a function f(t) contains no frequencies
    higher than W cps, it is completely determined by giving
    its ordinates at a series of points spaced 1/2W seconds
    apart.
    This is a fact which is common knowledge in the
    communication art. The intuitive justification is that, if f(t)
    contains no frequencies higher than W, it cannot change to
    a substantially new value in a time less than one-half cycle
    of the highest frequency, that is, 1/2 . A mathematical
    proof showing that this is not only approximately, but
    exactly, true
    can be given as follows. [snip]”

    Your homework tonight is to read and understand this proof.
    :-|

    [1] Claude Shannon, “Communication in the Presence of Noise”, Proc. Institute of Radio Engineers vol. 37 (1): 10–21, 1949.( http://www.stanford.edu/class/ee104/shannonpaper.pdf )

  247. Willis Eschenbach says:
    August 3, 2011 at 4:32 am
    But for you to put out all that ‘Is Willis hiding from Nicola’ kind of innuendo is just nasty, tallbloke. A simple “did you see this” without spilling the ugly contents of your mental suspicion machine would have been sufficient, I could have said ‘no I missed it’ and gone on.

    The lady doth protest too much. I referred to Scafetta’s reply to you in an answer to you three days ago. Mind you, checking back, you never replied to that either. It might explain why you know squat about solar system dynamics though, your arithmomania leads you to ignore responses which don’t contain numerical information couched in terms which can be handled by the technique you think is best.

  248. Geoff Sharp says: “I have two blogs Bob, this goes to show how incredibly out of touch you are…click on my name.”

    I’m aware of your website and blogs, Geoff. I visited your website twice–once a couple of years ago when I was researching the works of Theodor Landscheidt, and once within the past few months when I was trying to determine if you personally presented anything of value at your website.

    With respect to my earlier comment, apparently I have to be more specific with you. The topic of discussion was authors of guest posts at WUWT. As you might recall, the basis of my earlier statement was your reply to Willis, “There seems to be a trend lately that WUWT is promoting Luke Warmer resident guest authors on a permanent basis.”

    I’ll clarify my reply. Here’s a suggestion, Geoff. Maybe you should attempt to create and maintain a website and blog comparable to WUWT where you can have the guest authors of your choice and where those guest authors would want to have their posts presented.

    It is interesting to see that you use the same debate tactics with Willis that you do with me (and continue to use with Leif). When you are presented with data-based reality, you offer conjecture in an attempt to redirect the discussion. When you are incapable of responding to a question or request for information, you misdirect and you attack the person asking the question or making the request. You’re predictable. Any reader can scroll through the recent threads where you’ve argued and see how you repeat the same tiresome and time-wasting tactics.

    Willis has not lost any credibility on this thread, Geoff, but you are incapable of restoring yours.

  249. Geoff Sharp says:
    August 3, 2011 at 1:17 am
    the process of Fourier analysis are not picking up a regular signal, that is because it is not regular. Leif points out the De Vries or Suess cycle, that is a product of the trident. One of the prongs is weak so the gap increases.
    The Fourier analysis of the barycenter data does pick up the 172 yr wave and no 208 yr wave. The solar data does not have any 172 yr signal, but a strong 208 yr signal. And there is no correlation between the tridents and grand minima.

  250. So, just to be clear – this (below) is what Willis and his sagacious companions are describing as noise or an instrumental artefact:

  251. Leif Svalgaard says:
    August 3, 2011 at 6:11 am
    The solar data does not have any 172 yr signal, but a strong 208 yr signal.

    Or to be more precise, the spectra of proxy datasets from 10Be and 14C believed to be representative of solar activity contain a strong 208 year signal. The directly observed sunspot record isn’t long enough to tell if this really is a solar signal or a terrestrial artifact.

  252. phlogiston says:
    August 3, 2011 at 6:41 am

    So, just to be clear – this (below) is what Willis and his sagacious companions are describing as noise or an instrumental artefact:

    http://i53.tinypic.com/2s0g5te.jpg

    To be fair, I think what is being said is that it could be an autocorrelated random walk (red noise).

  253. Geoff Sharp says:
    August 3, 2011 at 1:17 am
    the process of Fourier analysis are not picking up a regular signal, that is because it is not regular. Leif points out the De Vries or Suess cycle, that is a product of the trident. One of the prongs is weak so the gap increases. Look at the Dalton minimum and now, 210 years between grand minima, the last prong of the Dalton didnt fire and the first prong (SC20) of the current cycle was the same.

    There is no 210 year gap in the recent barycenter distance: http://www.leif.org/research/Barycenter-Distance-1600AD-2100AD.png Your ‘signal’ has been marked with arrows. There are arrows precisely 179 years later. In fact, if you shift the curve 179 years you get an almost perfect match [the pink curve is 1929 plotted at 1750, etc]. Presumably the ‘last prong’ of the Dalton [which was not really a Grand Minimum, BTW] is what I have marked with a red arrow. The whole situation today is just what it was 179 years ago as far as the barycenter distance is concerned.

  254. tallbloke says:
    August 3, 2011 at 7:18 am
    Or to be more precise, the spectra of proxy datasets from 10Be and 14C believed to be representative of solar activity contain a strong 208 year signal. The directly observed sunspot record isn’t long enough to tell if this really is a solar signal or a terrestrial artifact.
    You can always blame the data if they don’t fit…
    Or use them if they do fit. This is the noble art of cherry picking.

  255. Leif Svalgaard says:
    August 3, 2011 at 7:36 am
    You can always blame the data if they don’t fit…
    Or use them if they do fit. This is the noble art of cherry picking.

    I think you’ve got sour grapes.

  256. What the S&L paper does do:
    It derives the residual of an observed 20 and 60 year temperature cycle plus an underlying trend, and shows that if this residual is attributed to CO2, the sensitivity to doubling is considerably less than imputed by IPCC.

    What the S&L paper does not do:
    Prove that the residual has anything to do with CO2.

  257. Pochas – spot on.

    The argument here is how good their evidence is that the observed cycle really is a cycle, and whether such supporting evidence as they do have from the paleo record is bolstered or not by cycles in planetary motions which may be affecting the Sun and Earth.

  258. Leif Svalgaard says:
    August 3, 2011 at 7:42 am
    And what do base that unfounded assertion on? and what is it to you?

    Easy now Leif, I should have added a Brit humour alert.

  259. pochas says:
    August 3, 2011 at 7:53 am
    What the S&L paper does not do:
    Prove that the residual has anything to do with CO2.

    S&L claim that their paper shows ['prove' is inappropriate] a “Warming due to anthropogenic GHG+Aerosol of 0.66 oC/Century”. If not due to CO2, what do you think S&L would ascribe it to? What do you think their ‘GHG’ refers to?

  260. tallbloke says:
    August 3, 2011 at 8:06 am
    “And what do base that unfounded assertion on? and what is it to you?”
    Easy now Leif, I should have added a Brit humour alert.

    You did not answer my questions. What you should have done is to not have said anything at all if you cannot substantiate it. Capice?

  261. tallbloke says:
    August 3, 2011 at 8:02 am
    The argument here is how good their evidence is that the observed cycle really is a cycle, and whether such supporting evidence as they do have from the paleo record is bolstered or not by cycles in planetary motions which may be affecting the Sun and Earth.

    What S&L claims is that “The fitted components match solar model forcings within their uncertainty” and that therefore the excess is anthropogenic. So their claimed planetary effect in central to their argument.

  262. @John Day.
    I really do not see the point in continuing this conversation. I am well aware that one can generate a filtered analogue waveform from a correctly digitised signal that approximates to the original waveform, provided one uses a linear phase shift filter.

    However, mathematically, it is not possible to interpolate a general signal digitised in accordance with the Sampling Theorem (Nyquist theorem, Shannon-Nyquist theorem, WKS .. etc) completely accurately without knowledge of the signal at +- infinity. This is because the interpolating function, Sinc(t), is not bounded, as clearly is shown, and dicussed, in the Whittaker-Shannon theorem. If one samples a periodic signal interpolation can be performed by computation of the Fourier series obtained by a DFT at any particular instance within the cycle but the assumption under this condition is that the signal has existed as periodic signal from -+ infinity. However, this is not the perfect reconstruction you appear to believe beause a) adc samples are not Dirac functions , b) the samples involve a phase shift, and c) you cannot be certain what happened before and after the sampling period. What I think you mean is that a signal can be reconstructed with tolerable engineering accuracy, which is a very different issue. If one is to reproduce a signal “perfectly”, it is best to be aware of the limitations of perfection in the real world.

    My general point is very simple – if a signal is not digitised with a sampling frequency greater than twice its bandwidth, it cannot be interpolated correctly. Many time series, such as temperature records, have either not been collected, or have been processed, without consideration of the Sampling theorem.

  263. tallbloke says:
    August 3, 2011 at 5:13 am

    Willis Eschenbach says:
    August 3, 2011 at 4:32 am

    But for you to put out all that ‘Is Willis hiding from Nicola’ kind of innuendo is just nasty, tallbloke. Asimple “did you see this” without spilling the ugly contents of your mental suspicion machine would have been sufficient, I could have said ‘no I missed it’ and gone on.

    The lady doth protest too much. I referred to Scafetta’s reply to you in an answer to you three days ago. Mind you, checking back, you never replied to that either. It might explain why you know squat about solar system dynamics though, your arithmomania leads you to ignore responses which don’t contain numerical information couched in terms which can be handled by the technique you think is best.

    Look, tallbloke, I told you I didn’t see it, so you can stuff your nastiness and your protesting ladies where the sun don’t shine. I’ve been going strong getting ready for this trip, so I didn’t see it—take a Prozac if it helps you handle my not seeing it, because it seems to be disturbing you greatly, but that’s the facts in the case.

    My bad for missing it. There’s an easy cure for that, however. You say “Hey, Willis, you missed it”, I say “OK, I’ll get to it as soon as I can,” and we move on.

    Or, on the other hand, you could be a total jackwagon and dump the contents of your diseased brain out for all to repulsed by as you have just done, with its dark suspicions and ugly accusations and your creepy fantasies about what goes on in other people’s minds.

    And unfortunately, there’s no cure for that, unless the person wants to be cured.

    So tallbloke, yes, I will answer Scafetta. When have you ever known me not to answer someone? I am one of the few people writing on the climate science who attempts to answer all serious questions.

    But at present I”m in the airport waiting for a flight, so you’ll just have to wait. I’m sure that you can pass the time by letting us know more of your bizarre fantasies about what I or other people are doing that don’t have the Tallbloke Stamp of Approval™, and spew more accusations of things like, what was it, “arithmomania” … or you could just STFU and wait, like any decent person would.

    Your choice …

    w.

  264. Willis Eschenbach says:
    August 3, 2011 at 9:12 am
    Look, tallbloke, I told you I didn’t see it, so you can stuff your nastiness and your protesting ladies where the sun don’t shine.

    Willis Eschenbach says:
    August 2, 2011 at 11:07 am
    And like I said, Geoff, when you do that folks just point and laugh at you.

    Willis,
    Most threads on possible solar cycles [and those were at the root of the L&S paper] end up being hijacked by tallbloke and Geoff [with occasional others] pushing with nastiness and insults their personal views way beyond what they are worth. No amount of sound counterarguments can restore some reasonableness into the ‘debate’ as we have seen.

  265. tallbloke says:
    August 3, 2011 at 8:02 am

    “The argument here is how good their evidence is that the observed cycle really is a cycle, and whether such supporting evidence as they do have from the paleo record is bolstered or not by cycles in planetary motions which may be affecting the Sun and Earth.”

    What I get from this is that Fourier analysis and Periodicity analysis may not be the right tools for analyzing cyclic but non-stationary processes. Apparently Scafetta has a better one.

  266. pochas says:
    August 3, 2011 at 10:09 am
    What I get from this is that Fourier analysis and Periodicity analysis may not be the right tools for analyzing cyclic but non-stationary processes. Apparently Scafetta has a better one.
    apparent from what? He doesn’t say he has a better one… Although I may have missed where he says that. Perhaps you could guide me to where.

  267. Leif Svalgaard says:
    August 3, 2011 at 7:31 am

    There is no 210 year gap in the recent barycenter distance: http://www.leif.org/research/Barycenter-Distance-1600AD-2100AD.png Your ‘signal’ has been marked with arrows.

    Yes you are right, I have the start of both grand minima at 210 years apart in my head. But you have demonstrated the variability of the 3 prongs and how they throw options up each cycle, the message is starting to get through. The current cycle has no third prong at all (looking at AM) which is unusual. I am now wondering where the De Vries cycle comes from.

    Your distance graph is different to the one Carl did back in 2008 and looks to show more detail, are you just using the JPL distance from SSB to Sun? I produced by accident an interesting distance graph a while ago that plots the difference between Sun to Jupiter and SSB to Jupiter, it also shows the extra detail.

    Carl’s distance graph with my annotation, he produced this graph after I pointed out to him the perturbations are the key not the zero crossings:

    Mine:

    I might need to extend mine out further. A point of interest, Landsch***t didn’t use any of the prongs but concentrated on the points where the graph goes below zero, this is why he was wrong with his 1990 prediction and a little late with the current minimum (if it comes to pass).

  268. @Richard Saumarez
    I really do not see the point in continuing this conversation. I am well aware that one can generate a filtered analogue waveform from a correctly digitised signal that approximates to the original waveform, provided one uses a linear phase shift filter.

    You’re still not getting the ‘perfect reconstruction’ part of Shannon’s theorem, are you? As a PhD you should be able to appreciate, mathematically, that a discrete set of samples from a ‘correctly digitized’ band-limited waveform contains _all_ of information available for that signal. There is no residual error, nothing’s missing. It’s _not_ an approximation!

    That’s why equation (7) in Shannon’s proof is so mind-bendingly amazing. First of all, it has an ‘equals’ sign, so it’s an exact expression, not an approximation (as you keep insisting). Secondly, it equates, on the left side, _any_ band-limited function of time f(t) with arbitrarily infinite resolution in time [down to yocto-seconds, or smaller if you wish] to, on the right side, a sinc-function interpolation formula that depends _only_ on the values of f(t) at a finite number of sample points x1,x2,..,xn etc.

    You should also (as a PhD) be able to distinguish this perfect representation in ‘theory’, from ‘practice’, where measurement noise (including quantization noise) does indeed create errors in communication (hence the name of the paper).

    It was this same 1949 paper, however, in sections III & ff (following section II, Sampling Theorem), where Shannon presented his thesis to the world, that these communication errors cannot be eliminated, but can be made arbitrarily small, by managing the information space in which the time signals are embedded.

    Best regards!
    John Day

  269. Geoff Sharp says:
    August 3, 2011 at 10:43 am
    Yes you are right, I have the start of both grand minima at 210 years apart in my head. But you have demonstrated the variability of the 3 prongs and how they throw options up each cycle, the message is starting to get through.
    You are too quick to jump to conclusions. The prongs do not ‘throw options’. That is your head only. You have no clear message, and if you compare with http://www.leif.org/research/Barycenter-Distance-240AD-590AD.png [green line] you see that it is very close to 1750-2100Ad, yet there are no grand minima in that interval and solar activity is very different in the two intervals 1750-2100 and 240-590. You are just chasing shadows.

    Your distance graph is different to the one Carl did back in 2008 and looks to show more detail, are you just using the JPL distance from SSB to Sun?
    Just use JPL with a step size of 100 days or less [I tried 30 days - didn't make any difference].

  270. Geoff Sharp says:
    August 3, 2011 at 10:57 am
    “And there is no correlation between the tridents and grand minima.”
    You might need to point this out?

    It is the one making the claim that there is who has that burden. This is why I ask you to annotate my graphs with what you consider Grand Minima.

    Anyway, I just did point this out:
    Leif Svalgaard says:
    August 3, 2011 at 11:06 am
    “if you compare with http://www.leif.org/research/Barycenter-Distance-240AD-590AD.png [green line] you see that it is very close to 1750-2100Ad, yet there are no grand minima in that interval and solar activity is very different in the two intervals 1750-2100 and 240-590. “

  271. phlogiston says:
    August 3, 2011 at 6:41 am

    So, just to be clear – this (below) is what Willis and his sagacious companions are describing as noise or an instrumental artefact:

    http://i53.tinypic.com/2s0g5te.jpg

    So, just to be clear, no, that is a graph of the AMO, and I didn’t talk about the AMO at all.

    This is why I ask that people quote exactly what I said that they are reacting to. phlogiston obviously thinks I said something about the AMO, or that I claimed the ~60 year cycles in the HadCRUT3 record are an “instrumental artifact”.

    I made no such claim. I said that in red-noise random datasets, that such long-period pseudo-cycles are quite common, and that as a result we don’t know if the ~60 cycle in the observational data is real or not.

    Quote what I said, phlogiston (and others). It will help prevent you from tilting at windmills, and will allow us to understand exactly where we may disagree.

    w.

  272. Leif Svalgaard says:
    August 3, 2011 at 10:31 am

    pochas says:
    August 3, 2011 at 10:09 am
    What I get from this is that Fourier analysis and Periodicity analysis may not be the right tools for analyzing cyclic but non-stationary processes. Apparently Scafetta has a better one.

    Leif Svalgaard:
    “apparent from what? He doesn’t say he has a better one… Although I may have missed where he says that. Perhaps you could guide me to where.”

    see above
    “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”

    As for myself, the 60 year cycle is easily visible to the unaided eye in the recent temperature record, although I certainly don’t expect you to agree :-)

  273. pochas says:
    August 3, 2011 at 10:09 am
    What I get from this is that Fourier analysis and Periodicity analysis may not be the right tools for analyzing cyclic but non-stationary processes. Apparently Scafetta has a better one.

    Spot on again. Fourier can be used, but from more than one angle is better. Hence the response from Scafetta which Willis tells us he will be replying to:

    nicola scafetta says:
    July 30, 2011 at 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, there is very little to question.

  274. Leif Svalgaard says:
    August 3, 2011 at 9:48 am
    tallbloke and Geoff [with occasional others] pushing with nastiness and insults their personal views way beyond what they are worth. No amount of sound counterarguments can restore some reasonableness into the ‘debate’ as we have seen.

    We learned at your feet master.

    Considering the amount of nastiness and insults you and Willis have dished out in the past, to see you girls whining about about it when a bit comes back your way is a hoot. Thanks for the laugh.

    As to the question of who’s counterarguments are sound and reasonable and worthwhile, I’m sure you feel right is on your side to be the arbiters of good taste and judgement there, as do we.

    Get a grip.

    And Willis: Have a great flight, I’m jealous.

  275. tallbloke says:
    August 3, 2011 at 12:32 pm
    Considering the amount of nastiness and insults you and Willis have dished out in the past, to see you girls whining about about it when a bit comes back your way is a hoot.
    You are still at it, it seems. It would be refreshing if you could get back to science, if possible.

  276. pochas says:
    August 3, 2011 at 11:59 am
    As for myself, the 60 year cycle is easily visible to the unaided eye in the recent temperature record, although I certainly don’t expect you to agree :-)
    The 60-yr is there [nobody says it isn't] but not quite stationary. It is the 20-yr cycle that is missing.

  277. @tallbloke
    Richard Saumarez and John Day,
    Please would you take a look at the DSP techniques employed in this post and leave some comment.

    http://tallbloke.wordpress.com/2011/07/31/bart-modeling-the-historical-sunspot-record-from-planetary-periods/

    I’d also appreciate any input you can give to the discussion about sampling rates for barycentric data towards the bottom of the comments in this thread too if you can spare the time

    http://tallbloke.wordpress.com/2011/07/25/ed-fix-solar-activity-simulation-model-revealed/

    Many thanks

    I don’t have much time available (and especially don’t want to get drawn into these long, heated discussions).

    But I would like to take a quick look at some of the data being discussed, e.g. the HadCRUT3 and barycentric datasets with the disputed decadal patterns and features. I kind of new around here and don’t know much about them.

    Does there exist a list of pointers to websites where I can download datasets like these?

    Thanks.

  278. John Day,
    The conversation on my site never gets heated, though occasionally long drawn out.

    Hadruct3 here. Click the raw data link at the bottom of the page

    http://woodfortrees.org/plot/hadcrut3vgl

    Data for the distance in xyz between Barycentre and solar centre is from JPL Horizons. Click [change] to set parameters Tip: Select Body Equator for reference plane:

    http://ssd.jpl.nasa.gov/horizons.cgi

    For other datasets, this site has reference pages with links to sources at the bottom.
    e.g.http://wattsupwiththat.com/reference-pages/global-temperature/

    Link to reference pages is up near top of page

    Hope that helps

  279. @tallbloke says:
    August 3, 2011 at 3:16 pm

    Hi tallbloke, daft question – why do you ref the varience adjusted HadCRUT3v rather than HadCRUT3?

  280. Leif Svalgaard says:
    August 3, 2011 at 12:35 pm
    It would be refreshing if you could get back to science, if possible.

    Gladly.
    Here’s more evidence of the Gas Giant Jupiter’s effect on solar activity.

    So, can we get real please.

  281. tallbloke says:
    August 3, 2011 at 3:35 pm
    Here’s more evidence of the Gas Giant Jupiter’s effect on solar activity.[...]
    So, can we get real please.

    You claim with your superior understanding of Newtonian mechanics that Newton’s laws are not valid for gases, because they are not elastic, so you are a bit off the reservation here. What happened to the barycenter idea? Why do you think a correlation is ‘real’ when the labels are so sloppy as they are? This is not science. Explain what you think this is. And what happened to all the other pieces: Saturn, Uranus/Neptune, etc

  282. tallbloke says:
    August 3, 2011 at 3:35 pm
    Here’s more evidence of the Gas Giant Jupiter’s effect on solar activity.[...]
    So, can we get real please.

    “Why do you think a correlation is ‘real’ when the labels are so sloppy as they are?”
    Perhaps that was hasty. It is possible you claim that when the Jupiter is closest to the Sun there are fewer sunspots, and that the farther away from the Sun Jupiter is, the more sunspots there are. Let us move Jupiter further out to increase solar activity [also increases its angular momentum]. Perhaps to infinity to really get the Sun going crazy :-)

  283. Leif Svalgaard says:
    August 3, 2011 at 3:56 pm
    Let us move Jupiter further out to increase solar activity [also increases its angular momentum]. Perhaps to infinity to really get the Sun going crazy :-)

    Well, we should remember Jupiter’s orbit is more eccentric than the other gas giants, and it’s bigger (much bigger) and closer. So gravitationally it creates big perturbances on the Sun because instead of the hypothetical ~1mm tide for an Earth like semi-rigid body, a largely inelastic body such as the gaseous Sun is going to get it’s interior directly beneath Jupiter stirred around quite a lot more than an average tidal force spread across the entire body. These disturbances will create the ‘suitable flows’ which release extra fusion energy from the Sun a la Wolff and Patrone. This will create hotspots above the convection cells, with vorticity, and so sunspots.

    So, why more sunspots when Jupiter is further away rather than closer to the Sun?
    Well, when Jupiter is further away, it exerts less gravitational pull on the Sun and so the barycentre moves closer to the solar core. If you study the Wolff and Patrone paper closely, you’ll find out where the ‘sweet spot’ is for maximising the fusion energy release.

    Of course, the other gas giants play a part in determining the barycentre, so that’s why the solar cycle doesn’t just follow the Jupiter orbital period, though it’s more often close to it than the average cycle length, just as it’s more often close to half the Jupiter-Saturn synodic period length than the average cycle length.

  284. http://wattsupwiththat.com/2011/07/30/riding-a-pseudocycle/#comment-710197

    http://wattsupwiththat.com/2011/07/30/riding-a-pseudocycle/#comment-710275

    http://wattsupwiththat.com/2011/07/30/riding-a-pseudocycle/#comment-711511

    Leif – Is this where you’re getting your ideas that molecules of oxygen and nitrogen in our atmosphere are elastic, i.e., ideal gas?

    [And that because of this they move through the atmosphere as if ideal gas molecules without properties except for elasticity – i.e. as hard dots randomly moving at vast speeds through empty space bouncing off each other with no volume, etc. http://wattsupwiththat.com/2011/06/30/earths-climate-system-is-ridiculously-complex-with-draft-link-tutorial/#comment-706716%5D

  285. Myrrh says:
    August 3, 2011 at 5:26 pm
    Leif – Is this where you’re getting your ideas that molecules of oxygen and nitrogen in our atmosphere are elastic

    One can actually easily see that from the link you provided:
    Myrrh says:
    August 1, 2011 at 3:50 am
    http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/circulation/air_pressure_p_1.html
    Look at all that empty space between the molecules in Figure 6.1

    randomly moving at vast speeds through empty space bouncing off each other with no volume
    No, it is wrong that they have no volume. I have shown you many times that the volume of all the Nitrogen molecules in one cubic meter of [atmospheric pressure and density] Nitrogen gas is 0.00175 cubic meter, so that 1 – 0.00175 = 0.99825 cubic meters are not occupied by any molecules or by anything else, i.e. is empty space as you showed so nicely in your link. You can see them bounce around elastically here http://upload.wikimedia.org/wikipedia/commons/6/6d/Translational_motion.gif where the speed is slowed down two trillion times [otherwise their vast speeds would just look like a blur].

  286. Willis,

    The comment editor is really balky online tonight, so I’ll try to resolve our points of disagreement by typing something up in the next day or two. In the meantime you might ponder the legitimacy of periodicall extending the average waveform computed by the algorithm when the underlying data is aperiodic.

  287. Leif Svalgaard says:
    August 3, 2011 at 11:06 am

    You are too quick to jump to conclusions. The prongs do not ‘throw options’. That is your head only. You have no clear message, and if you compare with http://www.leif.org/research/Barycenter-Distance-240AD-590AD.png [green line] you see that it is very close to 1750-2100Ad, yet there are no grand minima in that interval and solar activity is very different in the two intervals 1750-2100 and 240-590. You are just chasing shadows.

    Leif, there is a MAJOR difference between the 2 time periods. Your plot is really too small to appreciate the differences but I can see it immediately. If I can make some suggestions, the distance plot needs to be widened and scaled up, the solar proxy chart should be increased in the vertical plane.

    The major difference is in the type of perturbation which is crucial. In my paper you will see Type A and Type B perturbations (AMP). Type B is much weaker than type A. Type B is perturbing at the end of the inner loop, Type A is perturbing at the start of the inner loop. Type B is always on the upslope of the sine wave and Type A is on the downslope. I would expect much weaker solar disturbance during the 240-590 period. Follow the colored annotations for both periods and you will see the difference in the strength of perturbance.

  288. Geoff Sharp says:
    August 3, 2011 at 9:37 pm
    The major difference is in the type of perturbation which is crucial.
    How can such a minor difference be ‘crucial’? except in your eyes. I’ll expand the scales, but you should mark ahead of time on my solar plots where you think the Grand Minima are. For that you do not need the expanded scale. On your plot the scale is much too small and one can’t see the details. Perhaps on my plot you should also mark type A and type B.

  289. Leif Svalgaard says:
    August 3, 2011 at 11:06 am

    You are too quick to jump to conclusions. The prongs do not ‘throw options’. That is your head only. You have no clear message,

    You will see in time that the Holocene solar proxy record follows the perturbation strength of the AM or distance charts. You have not got your head around the quantification method. The prong options are clearly labelled via the colored dots. You will need to apologize for your comments soon.

  290. tallbloke says:
    August 3, 2011 at 4:52 pm
    Well, we should remember Jupiter’s orbit is more eccentric than the other gas giants, and it’s bigger (much bigger) and closer. So gravitationally it creates big perturbances on the Sun because apart from the hypothetical ~1mm tide for an Earth like semi-rigid body
    that tide is calculated for a completely non-rigid body [a perfectly deformable body]. You are still hung up on the rigid/gaseous thing. Newton’s laws are equally valid for both, and, anyway, the tides are calculated under the assumption that the matter is allowed to move freely under the gravitational tidal influence. With a perfectly rigid body [which are the only ones that obey Newton's laws according to you] there would be no tides.

    largely inelastic body such as the gaseous Sun is going to get it’s interior directly beneath Jupiter stirred around quite a lot more than an average tide spread across the entire body.
    No, the tides depends on the diameter of the region. As you go inwards, the tides shrink away to nothing [proportional to distance from the center]. And the tides are calculated for a gaseous sun, anyway.

    These disturbances will create the ‘suitable flows’ which release extra fusion energy from the Sun a la Wolff and Patrone.
    It takes 200,000 years for the energy created by that extra fusion to randomly diffuse to the convection zone, so any 11-yr signal is completely lost. This is another flaw in the W&P paper.

    If you study the Wolff and Patrone paper closely, you’ll find out where the ‘sweet spot’ is for maximising the fusion energy release.
    It takes 200,000 years for the energy from the ‘sweet spot’ to get out, so any 11-yr signal is completely lost.

    And the analysis you have chanced upon is seriously flawed. To ‘get real’ one must perform a real analysis, like this one: http://www.leif.org/research/Jupiter-Distance-Monthly-Sunspot-Number.png
    It shows first the distance as a function of the sunspot number for every month since 1749. You can see immediately by eye that there is no correlation. Instead you see a concentration [for all sunspot numbers] towards the bottom [smallest distance] and the top [largest distance]. This is purely a selection effect from the fact that there are many more months near the smallest and largest distance than at the average distance 5.2 AU, so you get many more monthly values [data points] of the sunspot number around perihelion and aphelion. This is because the distance changes less when Jupiter rounds the two ‘blunt’ ends of the orbit than at other times. There is another effect: as Jupiter moves more slowly at aphelion, the distribution will be ‘top heavy’, as you can clearly see on the graph. Finally, almost all the very high values of the sunspot number [in the oval] occurred at the maximum of solar cycle 19, so these points are not independent. The plot also shows the distribution for every bin of 10 sunspot numbers. The first one from 0 to 10, the next from 10 to 20, and so on. For every bin, you can see that there is no correlation. You can even now and then see the expected ‘top heaviness’.
    So, there is nothing ‘real’ there. Don’t fall for any old correlation that you stumble upon. Confirmation bias is strong here.

  291. Geoff Sharp says:
    August 3, 2011 at 10:34 pm
    You will see in time that the Holocene solar proxy record follows the perturbation strength of the AM or distance charts. You have not got your head around the quantification method.
    The quantification is a posteriori: you label as it fits.
    The prong options are clearly labelled via the colored dots.
    Where are the A and B types?
    You will need to apologize for your comments soon.
    One does not apologize. The correct attitude is that one concedes something. Apology has nothing to do with it. Your attempts of personalize everything are misplaced.

  292. Leif Svalgaard says:
    August 3, 2011 at 11:19 pm

    And the analysis you have chanced upon is seriously flawed. To ‘get real’ one must perform a real analysis, like this one: http://www.leif.org/research/Jupiter-Distance-Monthly-Sunspot-Number.png Confirmation bias is strong here.

    First of all, thanks for taking the time to do the analysis. You are right about this, and if I’d thought about it more before posting I’d have realised that the effect on barycentric distance of the eccentricity of Jupiters orbit is small compared to the effect of the Jupiter-Saturn synodic cycle. I admit the confirmation bias, someone posted the graph on my blog last night and I threw it into this discussion without enough consideration. I’ve posted your excellent analysis and comment there in full.

    that tide is calculated for a completely non-rigid body [a perfectly deformable body]. You are still hung up on the rigid/gaseous thing. Newton’s laws are equally valid for both, and, anyway, the tides are calculated under the assumption that the matter is allowed to move freely under the gravitational tidal influence. With a perfectly rigid body [which are the only ones that obey Newton's laws according to you] there would be no tides.

    Yes, Newton’s laws are equally applicable, all of them. This means that we need to consider the extent to which bodies are elastically deformable and plasticly deformable, and realise that in the case of a gaseous body like the Sun, that plastic deformation can appear to be elastic deformation due to the centre of gravity pulling the body back to sphericity. The key point in what I’ve been saying all along is that this won’t be done without non-reverting internal redistributions of matter as a result of the action of the perturbing force.

    Perfectly elastic (not necessarily rigid but they tend towards it) bodies will perfectly transmit force as resultant motion vestors in collision with other perfectly elastic bodies (pool ball experiment), inelastic bodies won’t (ball of putty or gas). This is what I meant by elastic bodies obeying Newton’s (idealised) laws of motion. In the context of our discussion, it was clear that I was getting at the difference between that idealised perfectly elastic object and the big wobbly mass of plasma and gas called the Sun. You have deliberately mis-contextualised what I said in order to distract attention from my correct characterisation of the Sun as being composed of largely inelastic material and it’s about time you put that canard down because no-one else is falling for it and it just reduces my trust in you as a fair person to debate with.

    the tides depends on the diameter of the region. As you go inwards, the tides shrink away to nothing [proportional to distance from the center]. And the tides are calculated for a gaseous sun, anyway.

    The major difference between the gas the sun is composed of and the tidal oceans on Earth is that water is incompressible and gas isn’t. So whereas Earth’s tides are raised on both sides of the planet because of the near perfect transmission of tidal force, on the Sun they won’t be. The effect of the gravitationally perturbing body will be more localised and therefore more concentrated.

    TB: These disturbances will create the ‘suitable flows’ which release extra fusion energy from the Sun a la Wolff and Patrone.
    LS: It takes 200,000 years for the energy created by that extra fusion to randomly diffuse to the convection zone, so any 11-yr signal is completely lost. This is another flaw in the W&P paper.

    Read the paper! They state that the effect will occur at various levels in the Sun from around 0.15r all the way to the top of the convection zone dependng on the barycentre-solar core radius . So yes, where the effect occurs at deeper levels (“carrying fresh fuel to deeper levels” as they put it) it will take a long time (there doesn’t seem to be a consensus on exactly how long), for the knock on effect to surface. But it will still happen in cyclic waves. This is probably where the longer periods in solar activity arise from, the barycentric motion has strong cycles at ~172, 934, 2250, 4500 years and who knows which longer periods.

    Thanks again for sitting back and taking a while before replying, I really get a lot out of our discussions when they happen at a more leisurely and considered pace.

  293. Leif Svalgaard says:
    August 3, 2011 at 10:03 pm

    Geoff Sharp says:
    August 3, 2011 at 9:37 pm
    The major difference is in the type of perturbation which is crucial.
    ————————————–
    How can such a minor difference be ‘crucial’? except in your eyes. I’ll expand the scales, but you should mark ahead of time on my solar plots where you think the Grand Minima are. For that you do not need the expanded scale. On your plot the scale is much too small and one can’t see the details. Perhaps on my plot you should also mark type A and type B.

    So you say a minor difference?, its only in my eyes? Let’s try to keep to the science.

    The perturbation is taking place in a completely different part of the inner loop on the solar path. Type B take place after the Jupiter/Saturn opposition, the majority of the cycle is done with and already in its acceleration phase ready to go into the next loop. These are solid physical attributes that coincide with much smaller solar disturbance observed across the Holocene during Type B.

    It is not hard to differentiate between the two types as already outlined plus the appropriate strength is shown with the color code which you seem to have ignored. Marking grand minima is as stated pointless, you will see when we get to the BC record that there can be long periods of Type B activity which displays a high plateau of sawtooth type trends, these plateaus are not grand minima but still important and coincide with the Roman and Minoan warming periods.

    As a rough guide you could look at my original graph which raises the Usoskin bar but it is still very arbitrary. What matters is the strong AMP events coincide with large troughs with weaker troughs coinciding with weak Type A and Type B events. Once you can identify the quantification process it will become clear. I think there is still scope to improve in this area..

    I have raised the bar to the Dalton Minimum height.

    I noticed you have not compared the AMP events (prongs) with the sunspot record.

  294. Geoff, keep going, I can see what you’re driving at.

    future.png gets a 404

    On your other chart, would a poly fit be more useful than a flat ‘bar’? It might bring out the effective-peak trough shifts more clearly. Not strictly following the barycentric data, but I doubt the proxy is a correct representation anyway.

  295. Leif Svalgaard:

    At August 3, 2011 at 9:04 pm you reply to sky who said (at August 3, 2011 at 7:45 pm)
    “you might ponder the legitimacy of periodically extending the average waveform computed by the algorithm when the underlying data is aperiodic.”
    by saying;
    “This is what L&S did
    http://wattsupwiththat.files.wordpress.com/2011/07/loehle-scafetta_fig3.png?w=640&h=494

    Yes!
    And that is a major part of the real problem with the L&S analysis; please see my comment in this thread at July 30, 2011 at 4:06 pm.

    All this debate about planets, the Sun and the barycenter may be important and may interest you guys, but it is mere fluff in the context of the L&S analysis.

    Richard

  296. tallbloke says:
    August 4, 2011 at 1:41 am

    Geoff, keep going, I can see what you’re driving at.

    future.png gets a 404

    On your other chart, would a poly fit be more useful than a flat ‘bar’? It might bring out the effective-peak trough shifts more clearly. Not strictly following the barycentric data, but I doubt the proxy is a correct representation anyway.

    I am not sure about the ploy fit, the record is leveled to allow for geomagnetic variance. The grand minima line by Usoskin is derived to maintain the illusion the Sun only enters grand minima occasionally and not on a regular basis, so the crap shoot mechanism of the Babcock theory is maintained. I am happy to raise the bar to the Dalton Minimum level for one sound reason. Grand minima in my view is about “phase catastrophe”. If the Hale cycle breaks down as we might witness for the first time in history it is worthy of attaining the Grand Minimum tag. For a second cycle to be killed because the preceding is violated is substantive.

    I also have some doubts on the proxy records once we get back far enough, the first part(oldest) of the INTCAL98 record is via coral samples and then moves over to tree rings, the break is clearly visible. We need to keep in mind I am trying to match to a record that is not exactly a true representation of solar activity, the solar wind speed/density does have a coronal hole component. I also have some questions on the accuracy in the timeline once we get back around 5000 years ago…this will come out when we get to the BC records.

  297. Richard S Courtney says:
    August 4, 2011 at 2:51 am

    All this debate about planets, the Sun and the barycenter may be important and may interest you guys, but it is mere fluff in the context of the L&S analysis.

    You are missing the core of the L&S paper. The 60 year cycle in the temp record and PDO record is tied to the 60 year cycle in the solar velocity record about the SSB, via an unknown mechanism. The authors acknowledge the longer solar cycles aka solar forcing is not fully included in their results when determining the gap between the temp record.

    Scafetta is 100% behind planetary influences being the controller of solar modulation and climate drivers, that is why the discussion is focused on these issues. Willis has tried to derail this area of science by applying one form of analysis….but unfortunately he failed and in the process showed us more of his character.

  298. tallbloke says:
    August 4, 2011 at 12:48 am

    First of all, thanks for taking the time to so the analysis. You are right about this, and if I’d thought about it more before posting I’d have realised that the effect on barycentric distance of the eccentricity of Jupiters orbit is small compared to the effect of the Jupiter-Saturn synodic cycle.

    Props for that, at least on this side of the fence we can admit when we are wrong.

  299. Geoff Sharp says:
    August 4, 2011 at 4:26 am
    ” Willis has tried to derail this area of science by applying one form of analysis….but unfortunately he failed and in the process showed us more of his character.”

    I have no right to an opinion in this area due to the lack of technical knowledge but this seems to be a comment one would see at RC rather than here.

  300. Geoff Sharp says: “You are missing the core of the L&S paper. The 60 year cycle in the temp record and PDO record is tied to the 60 year cycle in the solar velocity record about the SSB, via an unknown mechanism.”

    The 60-year cycle in the PDO appears in the paleoclimatological reconstruction referenced by L&S but it does not appear in all reconstructions of the PDO. On the earlier thread about L&S here at WUWT, I asked L&S a number of questions about the reconstructions they referenced.

    http://wattsupwiththat.com/2011/07/25/loehle-and-scafetta-calculate-0-66%c2%b0ccentury-for-agw/#comment-705914

    I wrote:

    Craig and Nicola: You’ve presented a very limited number of paleoclimatological reconstructions to confirm a 60-year cycle, which appears to be the backbone of this paper. Do other paleoclimatological studies support a 60-year cycle or is the 60-year cycle limited to the handful of studies presented? Does the “PDO” in the referenced paleoclimatelogical paper represent the SST of the North Pacific or the PDO as defined by JISAO?

    It was a loaded question since I knew one of the answers. I had written a post about the lack of a 60-year cycle in the PDO reconstructions:

    http://bobtisdale.wordpress.com/2010/03/15/is-there-a-60-year-pacific-decadal-oscillation-cycle/

    L&S also referred to a Black et al (1990) Cariaco Basin Sea Surface Temperature reconstruction for the 60-year cycle in the AMO. But the Black et al (2007) reconstruction, which is based on the same cores, does not show 60-year cycles. And that was the basis for the second part of my question:

    Also the Black et al (2007) Cariaco Basin Sea Surface Temperature reconstruction data…
    ftp://ftp.ncdc.noaa.gov/pub/data/paleo/contributions_by_author/black2007/black2007.txt
    …(which is based on their 1990 samplings) does not appear to bear any similarity to the data from Black et al (1990) you’ve presented in your Figure 4a. Why?

    L&S never bothered to answer those questions or the one that followed about their use of HADCRUT data:

    Your model appears to be very dependent on the spatially incomplete sea surface temperature dataset (and soon to be obsolete) HADSST2. (Land surface data between suppliers is basically the same for the latitudes of 60S-65N.) How would the results differ with the interpolated SST products from the Hadley Centre (HADISST) and NOAA/NCDC (ERSST.v3b)?

    Some paleoclimatological studies show a 60-year cycle, while others do not. Why? Do the proxies that show a 60-year cycle share a common factor that has no relationship to temperature? Are they in error because of it? Or are the numerous other studies that do not show a 60-year cycle in error? There are similar questions about the ICOADS, HADSST2, HADSST3, HADISST, ERSST.v3b, and Kaplan Sea Surface Temperature datasets, which serve as the backbone of the 60-year cycle assumption over the past 150 plus years. Some support a 60-year cycle; others do not. Which ones are right and which are wrong?

  301. Tom in Florida says:
    August 4, 2011 at 4:42 am
    this seems to be a comment one would see at RC rather than here.

    Knowing what he has said about what he has been through in the past, I pretty much forgive Willis his irascible behaviour, as he is always willing to quickly forgive in return. The substantive objections Scafetta and others raise to the technique Willis applies in this article are that which is important, not the personal diatribe anyone indulges in, colourful though it can be.

    I must admit that every now and then I just can’t resist winding up those who love to dish it out, but can’t take it back. :-)

  302. Bob Tisdale says:
    August 4, 2011 at 5:32 am

    The 60-year cycle in the PDO appears in the paleoclimatological reconstruction referenced by L&S but it does not appear in all reconstructions of the PDO.

    Granted, proxy records do that.

  303. @ John Day
    Thank you for your education. I wonder, if I could ask you a very simple question, which might clarify your thinking and aid your understanding of the Shannon theorem.
    If you take a signal and sample it between times T0 and T1, consider the interval between T0 and the first sample. With a sinc reconstruction, (which I am aware is a continuous function except for a limit at t=0), a point at T0 +dt is the sum of a(n)*sinc(n*sample period+dt) where n ranges from +- infinity. I agree that this calculation can be performed for any value of dt and the error can can be made arbitarily small by restriction on n.

    However, what value of a(n) do you use when n is negative? If you do a DFT and perform an interpolation by expanding the spectrum, the values for a(n), when n is negative, are a(t1-n), which is a circular convolution. This is correct, only if you have an absolutely periodic signal and your sample period is exactly that period. Any other signal will give incorrect results.

    So my question is how do you calculate the value of the function at T0+dt? If you can answer the question correctly, which I used to pose when teaching post-graduates, I might begin to believe that you have some understanding of the subject rather than simply producing ranting posts.

  304. Geoff Sharp says: “Granted, proxy records do that.”

    Then, basically, many of the discussions taking place on this thread are based solely on assumed, very possibly nonexistent, 60-year cycles in the surface temperature record, in the PDO record, and in the AMO record.

  305. Leif Svalgaard says:
    August 3, 2011 at 11:19 pm

    And the analysis you have chanced upon is seriously flawed. To ‘get real’ one must perform a real analysis, like this one: http://www.leif.org/research/Jupiter-Distance-Monthly-Sunspot-Number.png

    Hi Leif, further investigation reveals another graph from the same source, which on the face of it, doesn’t seem to be so easily explained. Please would you take a look:

    The curious thing is the period over which the sunspot number is averaged, 7.5 months. I’ll explain the oddity when you’ve given me an opinion.

    Thanks

  306. Bob Tisdale says:
    August 4, 2011 at 6:55 am
    Then, basically, many of the discussions taking place on this thread are based solely on assumed, very possibly nonexistent, 60-year cycles in the surface temperature record, in the PDO record, and in the AMO record.

    Bob, would you agree that they equally ‘very possibly existent’, as they are ‘very possibly non-existent’?

    Have we got a statistical test for that? ;-)

  307. tallbloke says:
    August 4, 2011 at 12:48 am
    I admit the confirmation bias, someone posted the graph on my blog last night and I threw it into this discussion without enough consideration. I’ve posted your excellent analysis and comment there in full.
    Confirmation bias is a powerful force

    Perfectly elastic (not necessarily rigid but they tend towards it) bodies will perfectly transmit force as resultant motion vestors in collision with other perfectly elastic bodies (pool ball experiment), inelastic bodies won’t (ball of putty or gas). [...]
    The major difference between the gas the sun is composed of and the tidal oceans on Earth is that water is incompressible and gas isn’t. So whereas Earth’s tides are raised on both sides of the planet because of the near perfect transmission of tidal force, on the Sun they won’t be. The effect of the gravitationally perturbing body will be more localised and therefore more concentrated.

    This is totally off the charts. Study http://www.astro.uni-bonn.de/~izzard/doc/lectures/binary_stars/3/slides_3.pdf There are two bulges on each side of the star or the Sun. This has nothing to do with your elastic problem. Perhaps ask W&P if they believe there is only one bulge on the sun.

    where the effect occurs at deeper levels (“carrying fresh fuel to deeper levels” as they put it) it will take a long time (there doesn’t seem to be a consensus on exactly how long), for the knock on effect to surface.
    All estimates are from tens of thousands to even millions of years which will wash out any short-term periods.

    Geoff Sharp says:
    August 4, 2011 at 1:06 am
    So you say a minor difference?, its only in my eyes? Let’s try to keep to the science.
    Science says there is no spin-orbit coupling

    These are solid physical attributes that coincide with much smaller solar disturbance observed across the Holocene during Type B.
    Such as?

    It is not hard to differentiate between the two types as already outlined plus the appropriate strength is shown with the color code which you seem to have ignored. Marking grand minima is as stated pointless
    If one has to decide whether your cycles coincide with Grand Minima, knowing where you put them is essential.

    I noticed you have not compared the AMP events (prongs) with the sunspot record.
    I notice that you ignore http://www.leif.org/research/Solar-Activity-vs.Barycenter-Distance-Annotated.png

    So, annotate my plots, please.

  308. tallbloke says:
    August 4, 2011 at 7:16 am
    Hi Leif, further investigation reveals another graph from the same source, which on the face of it, doesn’t seem to be so easily explained.
    Same thing: http://www.leif.org/research/Jupiter-Distance-Monthly-Sunspot-Number2.png
    Note the clustering of points at both aphelion and perihelion. If you ignore that and calculate a correlation anyway R^2 is 0.0262, i.e. not significant.

    The curious thing is the period over which the sunspot number is averaged, 7.5 months. I’ll explain the oddity when you’ve given me an opinion.
    As there is no correlation, the oddity is not of interest.

  309. Bob Tisdale:

    Sincere and heartfelt thanks for your comment at August 4, 2011 at 6:55 am which says;

    “Geoff Sharp says: “Granted, proxy records do that.”

    Then, basically, many of the discussions taking place on this thread are based solely on assumed, very possibly nonexistent, 60-year cycles in the surface temperature record, in the PDO record, and in the AMO record.”

    I am sure all the astronomical discussions in this thread have great importance in their own right, and possibly warrant a thread on WUWT that specifically addresses them. But they are NOT the subject of this thread.

    This thread is about the validity of the L&S determination of climate sensitivity based on the assumed invariance of two cycles (i.e. of 20 years and 60 years length) and the assumed irrelevance of all other cycles.

    So, Geoff Sharp is plain wrong when (at August 4, 2011 at 4:26 am ) he asserts the astronomical considerations are “the core of the L&S paper. The L&S paper merely provides a conjecture as to the causes of the cycles which it assesses. And, importantly, the paper and its analysis are not affected in any way by whether or not that conjecture about cause is correct.

    This thread is supposed to be discussing the above essay by Willis that argues there is insufficient evidence in the data for the existence – never mind the invariance – of the assessed two cycles. And I have repeatedly gone further than that.

    Simply, in the context of the L&S determination of climate sensitivity, it does not matter one jot as to the causes of the cycles.

    I again stated the real issue in my own post in this thread at July 30, 2011 at 4:06 pm . And I quote it here to save others finding it.

    “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.”

    The astronomical considerations are not relevant to any of that, but they have side-tracked the thread from discussing any of that. The best that could be said of the astronomical considerations is that they relate to some possible causes of the cycles assessed by L&S: but so what?

    Richard

  310. Leif Svalgaard says:
    August 4, 2011 at 7:55 am
    tallbloke says:
    August 4, 2011 at 7:16 am
    Hi Leif, further investigation reveals another graph from the same source, which on the face of it, doesn’t seem to be so easily explained. http://www.bnhclub.org/JimP/jp/xyss.JPG

    Same thing: http://www.leif.org/research/Jupiter-Distance-Monthly-Sunspot-Number2.png
    Note the clustering of points at both aphelion and perihelion. If you ignore that and calculate a correlation anyway R^2 is 0.0262, i.e. not significant.

    The curious thing is the period over which the sunspot number is averaged, 7.5 months. I’ll explain the oddity when you’ve given me an opinion.

    As there is no correlation, the oddity is not of interest.

    Hmmmm, I need to give this some thought. Thanks for the quick response, I’ll take a timeout to have a think on this. It seems odd that such a good correlation appears when the data is averaged at that timescale of 7.5 months. I think I might know why though, and it’s to do with interaction between Jupiter and another planet.

    Thanks as always for your time.

  311. @Richard S Courtney
    > The best that could be said of the astronomical considerations is that they relate to
    > some possible causes of the cycles assessed by L&S: but so what?

    … because some of the [C]AGW arguments run like this: “We’ve detected some correlations with CO2 in the data, so CO2 must be cause. What else could it be?

    The astronomical findings may provide some “what else’s”

    BTW, excellent summary and assessment of this thread. Thanks.

  312. tallbloke:

    At August 4, 2011 at 8:05 am you ask me:

    “Richard, I’m not stopping you discussing the aspects you want to discuss, so what’s the problem?”

    I answer that there are two problems.

    Firstly, the Off Topic astronomical considerations have deflected this thread from discussion of its topic. Trolls often use such deflection as a deliberate tactic to inhibit discussion of a topic in a thread. In this case it has happened inadvertently (i.e. not deliberately and not by action of trolls).

    Secondly, it HAS inhibited the discussion of the subject of this thread (i.e. discussion of the argument presented by Willis as to the validity of the L&S method). But that subject is worthy of discussion.

    As I said;
    “I am sure all the astronomical discussions in this thread have great importance in their own right, and possibly warrant a thread on WUWT that specifically addresses them. But they are NOT the subject of this thread.”

    Richard

  313. Leif Svalgaard says:
    August 4, 2011 at 7:46 am

    notice that you ignore http://www.leif.org/research/Solar-Activity-vs.Barycenter-Distance-Annotated.png

    So, annotate my plots, please.

    Your analysis is lousy Leif, no grouping, no recognition of AMP strength etc. It would be better if you plotted all of my annotations on the 10Be record using their respective colors (strength).

    I am on the road for a few days and will address when I return. In the meantime ponder my graph again which shows the AMP strength as annotated on your graph summed to each 172 year centre.

  314. tallbloke says: “Bob, would you agree that they equally ‘very possibly existent’, as they are ‘very possibly non-existent’?”

    Regardless of how we present them, very possibly existent or very possibly nonexistent, the 60-year cycles in the temperature record are still an assumption. The appear in some records but not others. They are not a hard fact as portrayed by many on this thread.

  315. @Richard Saumarez
    [Re: Shannon sampling],…, what value of a(n) do you use when n is negative? If you do a DFT and perform an interpolation by expanding the spectrum, the values for a(n), when n is negative, are a(t1-n), which is a circular convolution.

    The value of n is strictly for indexing through your set of finite temporal samples x1, x2, … , xn etc. for the purpose of summation. So, any sequence of integers will be fine. Recall that Shannon pointed out that sequences don’t have to start out at zero.

    The sinc() reconstruction has nothing to do with DFT’s. That is a separate, unrelated indexing scheme.

    Of course, the existence of the Fourier transform for the sequence is absolutely critical for Shannon’s proof. But not required for actual implementation, which again is simply a summation of sinc() function values over a set of samples at some precise time t.

  316. @Richard Saumarez
    [Re: Shannon sampling],

    … forgot to add an additional requirement for the sequence indexing is that the expression (2Wt-n) evaluate to zero somewhere in the support range of the interval, such that sinc() can act as a sifting function, while interpolating the exact value of f(t).

    I’ll add that the first time I read this theorem I was highly skeptical too. What if f(t) peaks between samples? How can it possibly predict that?

    So I wrote a little program in Turbo Pascal to generate arbitrary band-limited functions from weighted sinusoids. Then the program would take equally spaced samples at arbitrary offsets and reconstruct them and plotted them superimposed on the original waveform. (You should try this too.)

    I was amazed that the reconstruction faithfully found all the peaks and valleys between the sampling points. It was indeed ‘perfect reconstruction’, except for some minor endpoint effects at the first and last sample points.

  317. Richard S Courtney says:
    August 4, 2011 at 8:30 am
    tallbloke:

    At August 4, 2011 at 8:05 am you ask me:

    “Richard, I’m not stopping you discussing the aspects you want to discuss, so what’s the problem?”

    I answer that there are two problems.

    Firstly, the Off Topic astronomical considerations have deflected this thread from discussion of its topic. Trolls often use such deflection as a deliberate tactic to inhibit discussion of a topic in a thread. In this case it has happened inadvertently (i.e. not deliberately and not by action of trolls).

    Since Loehle and Scafetta are relying to a large extent on the astronomical phenomena to support their contention of the existence of a repeating quasi cycle in temperature variation, the astronomical aspect of the debate is decidedly not off topic in my opinion. The question of causation has been a vexing issue for a long time and that rumbles on through many solar related threads. This thread isn’t the only one to have that issue as one of its dominant themes. Given the number of other threads which come to be dominated by issues such as polar ice or greenhouse effect radiative physics I don’t see that we can be fairly singled out. I did at one point on the original Loehle and Scafetta thread say that the argument shouldn’t be about causation on a thread discussing cycles in solar and terrestrial phenomena, but it will not be allowed to rest by certain parties who wish to discredit cyclic research by pointing to the lack of proven physical mechanism.

    Secondly, it HAS inhibited the discussion of the subject of this thread (i.e. discussion of the argument presented by Willis as to the validity of the L&S method). But that subject is worthy of discussion.

    Actually, no-one has talked much about their method. Scafetta’s own contribution went uncontested and undiscussed, for whatever reason, and this thread was all about Willis’ method, not L&S’. Willis’ null result does not prove the L&S method invalid. Compare the several studies which say “We find no causal link between Forbush decreases and cloud cover, and the CERN CLOUD project.

    As I said;
    “I am sure all the astronomical discussions in this thread have great importance in their own right, and possibly warrant a thread on WUWT that specifically addresses them. But they are NOT the subject of this thread.”

    If you look at the content of the graphs WIllis created, half were to do with astronomical phenomena, and half were to do with random datasets representing surface temperature. Maybe there just aren’t enough interested parties who want to discuss random datasets representing surface temperature, so by default the debate has become one about real celestial phenomena, because many here are very interested in that on topic part of the issues raised by Willis’ analysis..

  318. Leif – I’d been trying to work out where your ideas had come from as you know, and Tallbloke’s mentioning Newton knowing his equations were for idealised bodies is the first thing that makes sense of it,

    [Tallbloke: “Newton knew his equations of motion and kinematics applied to idealised bodies with perfect elasticity.

    Leif: “Complete nonsense. Newton’s laws are universal and apply to all bodies, whatsoever.”

    So I think I might have another go …, but I’ll take this back to the other thread. Over the weekend.

  319. tallbloke says:
    August 4, 2011 at 8:12 am
    It seems odd that such a good correlation appears when the data is averaged at that timescale of 7.5 months.
    It is not a good correlation. You have been taken in by the same sleight of hand [often used by enthusiasts] as on the first version. They quote R^2 of 0.9776 and 0.952, but that is not for the correlation [that has R^2=0.026, i.e. not significant] but for the fit of the polynomial to their data points.

    Geoff Sharp says:
    August 4, 2011 at 8:58 am
    Your analysis is lousy Leif, no grouping, no recognition of AMP strength etc.
    It is not me trying to convince the world of anything. The null-hypothesis is that there is no correlation. You could improve things by providing a table [easier than a plot] that for each of your perturbation you give the time, the ‘strength’ [whatever you think it is], and its type. Then in another table the time of the central point of each grand minimum you think there is. That will put the whole thing on a numerical footing so it can be analyzed properly [and get you away from mere hand waving].

    tallbloke says:
    August 4, 2011 at 1:13 pm
    The question of causation has been a vexing issue for a long time and that rumbles on through many solar related threads.
    No, it not is vexing at all [there isn't any - that may be vexing for people who want there to be such causation] and that it rumbles on is only because the threads get hijacked by people [misusing the hospitality of WUWT] to push their own theories [in spite of having their own blogs for such].

  320. Myrrh says:
    August 4, 2011 at 1:30 pm
    Leif: “Complete nonsense. Newton’s laws are universal and apply to all bodies, whatsoever.”
    So I think I might have another go …, but I’ll take this back to the other thread. Over the weekend.

    I think you have already embarrassed yourself enough…

  321. Leif Svalgaard says:
    August 4, 2011 at 3:39 pm

    tallbloke says:
    August 4, 2011 at 1:13 pm
    The question of causation has been a vexing issue for a long time and that rumbles on through many solar related threads.
    No, it not is vexing at all [there isn't any - that may be vexing for people who want there to be such causation] and that it rumbles on is only because the threads get hijacked by people [misusing the hospitality of WUWT] to push their own theories [in spite of having their own blogs for such].

    Seriously out of order statement. Anyway, Wolff and Patrone are published, whereas your ramblings on the non-existence of causation are not. How’s the rebuttal coming along by the way?
    You seemed to think there was something amiss with equations 2a 2b and 4. I look forward to your full rebuttal paper, if it ever gets written.

  322. Leif Svalgaard says:
    August 4, 2011 at 3:39 pm
    You have been taken in by the same sleight of hand [often used by enthusiasts] as on the first version. They quote R^2 of 0.9776 and 0.952, but that is not for the correlation [that has R^2=0.026, i.e. not significant] but for the fit of the polynomial to their data points.

    I haven’t been taken in this time round Leif. I said I’d think about it, and having thought about it, I’ve come to the same conclusion. The data points are averages of averages.

  323. FTA: “While Fourier analysis is very useful, it has a few shortcomings. First, it can only extract sinusoidal signals.”

    That is incorrect. Power spectral density analysis is a mature field which is widely used in system identification. It can identify standard rational processes which describe the evolution of linear or linearized systems. Since every smoothly evolving system can be linearized about a particular operating point, the method has wide, virtually universal, applicability.

    All this “periodicity analysis” does is apply a not-very-good bandpass filter to each periodicity bin. It is an unsophisticated analysis technique.

  324. tallbloke says:
    August 4, 2011 at 4:54 pm
    “No, it not is vexing at all” [...] because the threads get hijacked by people [misusing the hospitality of WUWT] ”
    Seriously out of order statement.

    But true

    whereas your ramblings on the non-existence of causation are not.
    Lots of papers already on that. You might enjoy my upcoming presentation at AGU Fall Meeting in December:
    “Is Solar Activity Modulated by Astronomical Cycles?”
    ABSTRACT BODY: When Rudolf Wolf devised the sunspot number he noted [1859] that the length of the cycle was close to the orbital period of Jupiter. He even constructed a formula involving the periods of Jupiter, Saturn, Venus, and Earth that reproduced the sunspot numbers
    1826-1848. Unfortunately the formula failed for subsequent cycles and Wolf concluded at the end of his life that the attempts by himself and others to ‘explain’ solar activity by planetary influences had really never yielded any satisfactory result. Nevertheless, the hypothesis rears it head from time to time, even today. I review several recent attempts, both proposed correlations and mechanisms. The recent discovery of exoplanets and the possibility of detecting magnetic
    cycles on their host stars offers a near future test of the hypothesis, based on more than the one exemplar, the solar system, we have had until now.

    tallbloke says:
    August 4, 2011 at 4:57 pm
    I haven’t been taken in this time round Leif. I said I’d think about it, and having thought about it, I’ve come to the same conclusion. The data points are averages of averages.
    If you keep taking averages of averages of averages of …, eventually the number of degrees of freedom dwindles to zero. I showed in my second plot that there is no correlation.

  325. tallbloke says:
    August 4, 2011 at 4:57 pm
    I haven’t been taken in this time round Leif. I said I’d think about it, and having thought about it, I’ve come to the same conclusion. The data points are averages of averages.
    Another point that complicates this is the uneven quality of the sunspot number series. Early on many values were interpolated [creating false linear correlations]. From 1882 to today [including the 20% Waldmeier jump ~1945], the record is thought to be of higher quality [no longer based solely on Wolf’s small telescope http://www.leif.org/research/Wolf-37mm.jpg ]. Using the higher-quality series 1882-2011 completely removes even the spurious correlation: http://www.leif.org/research/Jupiter-Distance-Monthly-Sunspot-Number3.png
    Averages of averages will not restore a meaningful result, where there is none.

  326. @John Day
    There is a very precise relationship between the sinc function and the properties of the DFTs. When you take two sampled functions and convolve them by multiplication of their discrete spectra, what you doing is equvalent to the time domain convolution of two infinite series. This is because the DFT is a true fourier transform of an infinite signal multiplied by a a rectangular window, and multiplyied by a train of Dirac functions. The method of interpolation using a Fourier series, i.e.: a DFT, requires that the coefficients are computed correctly and to do so, the sampling period must be equal to the fundamental frequency of the signal. If this is the case, frequency domain interpolation, by taking a DFT, expanding the the spectrum with zeros above the Nyquist frequency and inverse transformation will give exact results (to numerical accuracy). This is a well known result. However, this is a convolution in frequency domain in which the spectum of the signal is multiplied by a “filter” that has a brick wall cutoff above the Nyquist Frequency. This is directly equivalent to a time domain convolution between two infinite series, both of which we know because the signal is periodic and the inverse Fourier transform of the “reconstituting filter” is the impulse response of the filter: sinc(t).

    This has a number of idea has a number of implications. The first is that if you want to filter a signal, you take the signal, the impulse response of the filter, perform a DFT, multiply their spectra, perform an inverse DFT and quite possibly get the wrong result. This is because you are convolving two infinte series and the response to the earlier cycles will appear in the signal after you have convolved them – known as wrap around. If the arrays contining the data are ” padded” with zeros to over twice the sample period, this problem is eliminated although only the results within the original sample period will be meaningful. This is also extremely important from the point of view of signal interpolation. If the sampling period is not exactly the fundamental period, you are convolving an infinites series of a signal containing a discontinuity with sinc(t). Consider a sine wave that is well sampled but the sampling period is not the period of the sine wave. There is a “jump” between the first an the last sample. The next sample in the Fourier series is predictable from Taylor’s theorem. However, the derivative of the signal in the last point in the sampled signal is band limited, since the differentiation in the frequency domain is simply multiplication by -jw. Thus the derivative in the signal exceeds that which it can be due to bandwidth and the signal is discontinuous. When Fourier reconstruction is attempted, this results in a Gibb’s phenomenon and the reconstruction oscillates between samples. In a real signal, containing many different frequencies, this is likely to occur for at least some Fourier components.

    You should try the following:
    Compute an array containing a sine wave whose frequency is exactly 2*pi/N where N is the array length. Perform a Fourier reconstruction and calculate the error between the reconstructed signal and the true signal. The result will be exact except for small numerical error. Now increase the frequency of the sine, by say 5%, without changing the length of the aray and repeat the procedure. Repeat this by increasing the frequency in 5% steps until it is double the starting frequency. I think that you will be surprised by the results.

    I’m so glad that you have attempted a sinc reconstruction in the time domain but I am not surprised by errors at the end of signal. More points at either end will impove the reconstruction, but how many points are needed? Will the solution converge to the correct value before resolution is degraded by numerical accuracy? Actually, I use both these methods all the time. In practice, by allowing a start-up and tail off at either ends of the signal, one can quite easily interpolate to the resolution of the ADC but the solution is not exact.

  327. Leif Svalgaard says:
    August 4, 2011 at 6:53 pm
    tallbloke says:
    August 4, 2011 at 4:54 pm
    “No, it not is vexing at all” [...] because the threads get hijacked by people [misusing the hospitality of WUWT] ”
    Seriously out of order statement.
    But true

    You are entitled to your opinion. I can understand why you’d want to exclude those who show your rhetoric to be empty and your position untenable.

    You might enjoy my upcoming presentation at AGU Fall Meeting in December:
    “Is Solar Activity Modulated by Astronomical Cycles?”
    ABSTRACT BODY: When Rudolf Wolf devised the sunspot number he noted [1859] that the length of the cycle was close to the orbital period of Jupiter. He even constructed a formula involving the periods of Jupiter, Saturn, Venus, and Earth that reproduced the sunspot numbers
    1826-1848. Unfortunately the formula failed for subsequent cycles and Wolf concluded at the end of his life that the attempts by himself and others to ‘explain’ solar activity by planetary influences had really never yielded any satisfactory result. Nevertheless, the hypothesis rears it head from time to time, even today. I review several recent attempts, both proposed correlations and mechanisms. The recent discovery of exoplanets and the possibility of detecting magnetic
    cycles on their host stars offers a near future test of the hypothesis, based on more than the one exemplar, the solar system, we have had until now.

    Excellent. Great to see you’ll be giving the topic an airing. Will you be making the rest of the presentation available in advance of the meeting so we can offer some constructive critique?
    :-)

    Will there be a panel discussion or just a brief Q&A afterwards?

  328. By the way Leif, I’ve made a discovery about your 10.8 year period that you believe to be the fundamental period (along with 121 years) which is the expression of the “solar dynamo” and can explain the other periods which you claim are only coincidentally related to Jupiter and Saturn.

    It is itself, apart from being a ‘sideband’ of those planetary periods, directly related to fundamental physical attributes of the solar systems planetary orbits. The whole system is tied together as a real system, and instead of arguing about the direction of causation, we need to be discussing the feedback mechanisms which must be in operation.

    I’ll be putting a new post up later which will make these relationships clear. Today, I’m filming.

  329. tallbloke says:
    August 5, 2011 at 12:26 am
    By the way Leif, I’ve made a discovery about your 10.8 year period that you believe to be the fundamental period (along with 121 years) which is the expression of the “solar dynamo” and can explain the other periods which you claim are only coincidentally related to Jupiter and Saturn.
    The dynamo period is not constant 10.8 but varies with time. It was 11.3 when Wolf did his compilation and has been 10.6 the past ~100 years [both with the usual fluctuations between cycles]. So is not ‘fundamental’ in the sense of being invariant [as it would be if astronomical].

    It is itself, apart from being a ‘sideband’ of those planetary periods, directly related to fundamental physical attributes of the solar systems planetary orbits. The whole system is tied together as a real system, and instead of arguing about the direction of causation, we need to be discussing the feedback mechanisms which must be in operation.
    At the time in the 1880s when the period was believed to be 11.3 years, Charles Harrison showed that if you insert the periods p, masses m, and distances from the Sun d for the eight planets in the formula P = sum (p*m/d^2)/sum(m/d^2) you get 11.29 years, so you see, numerology was going strong even back then [unfortunately the formula doesn't hold any longer - as is so often the case with numerology].

  330. Heh, no. It’s much simpler than that. The factors affecting variation in the solar cycle length either side of the background main driver are a bit more complex, but we already got that worked out last year. This is deliciously direct.

  331. tallbloke says:
    August 5, 2011 at 8:56 am
    solar cycle length either side of the background main driver
    You mean the solar dynamo, of course.
    BTW, the Harrison formula can also be expressed as P =sum(A)/sum(A/p) where A is the angular momentum. Numerology is fun at times, but ultimatlely unproductive.

  332. nicola scafetta says:
    July 30, 2011 at 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 tecniques, 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.

    Are there quasi 20 year and 60 year cycles in the temperature data? Certainly.

    Are they real cycles? My Monte Carlo analysis, which you have not commented upon, shows that such long-period pseudo-cycles are very common in random autocorrelated datasets. So there is no reason to believe that the 60-year cycle in the temperature record are real. They may be real, but we have no reason to believe they are, and plenty of reason to believe they an artifact.

    (In passing, I love it when people say things like “Moreover similar cycles have been found by numerous other people in numerous climatic data and published in numerous data.” Citations are your friend, Nicola, that’s just handwaving.)

    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 [would] present such a perfect repetition of cycles that would be possible only if the temperature were made of cycles with perfect periods of: 20, 10, 5, 4, 2.[years]

    What Willis did is simply to calculate a single average cycle and then he plotted this same cycle many times in a consecutive way.

    Well, yes, that’s what I did, and it’s what I said I did, it’s called “Periodicity Analysis” and it is a recognized technique. All your objection proves, Nicola, is that you did not read the paper I cited on Periodicity Analysis.

    Like all other techniques, it has its strengths and weaknesses … so? Does repeating the average cycle somehow make the average cycle incorrect? This is a trivial objection.

    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.

    Nicola, I fear I don’t follow you here. Periodicity analysis finds the actual 20 year cycle. If I make up a sequence made of 2 cycles, periodicity analysis can find one and subtract it out. And yes, it will extract the 20 and 15 year cycles. So I don’t understand your objection, except that it appears to show that you don’t understand periodicity analysis. It can do exactly what you say it can’t do. For example, I use periodicity analysis on the barycentric data in Figure 6, and extract the largest components. These allowed me to reconstruct the barycentric data to good accuracy using just those major cycles. If periodicity analysis doesn’t work (as you claim), then how can it deconstruct and reconstruct the barycentric data?

    But in any case, my statements regarding the problems in the L/S analysis do not depend in any sense on periodicity analysis. I use periodicity analysis because it gives me different understandings of the data, but that is a personal preference. The issues I raised with the L/S analysis are underlying problems which have nothing to do with periodicity analysis.

    Now, tallbloke had excoriated me for not answering Nicola. Drawing on his experience of his own actions, I suppose, tallbloke maliciously assumed that there was a good chance that I was trying to dodge Nicola, saying:

    I hope Willis is taking his time to consider Nicola Scafetta’s response, and is carefully formulating a well considered reply. Because if not he is just ignoring Scafetta’s criticism, having written a post which purports to rebut Loehle and Scafetta’s paper.

    That Scafetta took the time to answer Willis should be regarded as a compliment, even though he is critical of the analysis technique employed to rebut the L & S 2011 paper.

    Hack and run tactics will not enhance the reputation of open peer review. I think Willis owes it to the open science community as well as to Craig Loehle and Nicola Scafetta to respond to the criticism.

    First, accusing me of “hack and run” tactics is a joke. I am one of the most responsible climate bloggers on the web regarding answering any and all scientific objections to my claims and ideas.

    Second, it is not a “compliment” for someone to answer scientific objections to their ideas, that simply shows that tallbloke misunderstands the scientific process. It is a scientist’s obligation to answer reasonable scientific objections to his theory. And indeed, he would be a fool not to answer them, as if he does not do so, people may not believe his ideas.

    I have made several objections to the L/S paper, none of which have been refuted, or even disputed in some cases:

    1. While there are ~20- and ~60-year quasi-cycles in the temperature data, the ~20 year cycles barely rise out of the noise. Does anyone dispute this?

    2. Monte Carlo analysis shows that the ~60-year quasi-cycles in the temperature data have a very good chance of being merely an artifact of the length of the record. Does anyone dispute this? If so, present your code, I’ve shown mine.

    3. The size of the two cycles is inverted between the barycentric and the temperature records, with the ~60 year cycle being about a tenth of the size of the ~20 year cycle in the barycentric data, and the reverse size relationship (sixty-year much larger than twenty-year cycles) holding in the temperature data. Does anyone dispute this?

    4. The null hypothesis in the L/S analysis is that the temperature will continue to rise at 0.15°C per century. There is nothing in their analysis to substantiate or justify this choice, other than that it is the trend of the first 2/3 of the observations. Since the historical trend is around 0.5C per century, the choice of this null hypothesis needs to be vigorously established. Instead, it is not established at all.

    5. If you are going to claim that barycentric variations affect the climate, you have to use the actual amplitude, phase, and cycle of the barycentric observations. You can’t just say “well, there’s a quasi-20-year cycle in the data” and give it your own phase and amplification to match it to another dataset. If you’re going show the barycentric data affects the climate, you need to use the actual barycentric data. You can’t just pick two underlying cycles, adjust their phase and amplitude to fit the temperature, and say “TA-DA!”.

    Note that none of this has anything to do with the type of signal analysis used. I could have used Fourier, or wavelet, or periodicity analysis. They’re all analyzing the same thing, and their results are largely similar. Use any of them and you’ll find that the ~60 cycle in the barycentric data is tiny compared to the 20 year cycle, yet Loehle/Scafetta claims that the reverse is true in the temperature data.

    How does that work again? …

    w.

    (Written from the Kaladi Brothers coffee shop on the Kenai River, it’s a beautiful day, I’m headed outside. My best to all.)

  333. Leif Svalgaard says:
    August 5, 2011 at 10:29 am
    Numerology is fun at times, but ultimatlely unproductive.

    Except when it fits with observations, and creates predictions which turn out correct for long enough to be treated as usefully reliable.

    Newtons gravitational equations for example…

    Willis Eschenbach says:
    August 5, 2011 at 10:57 am
    First, accusing me of “hack and run” tactics is a joke.

    Willis, reread the first sentence of my comment and then take note of the if-then clause the later part is predicated on. Thanks, and apologies for getting you riled.

    Regarding your reply, I’m in agreement with you regarding much of what you say. There are a couple of things I’d like to comment on.

    [Periodicity analysis] Like all other techniques, it has its strengths and weaknesses … so?

    You were in transit when this reply from Bart came in:
    Bart says:
    August 4, 2011 at 5:23 pm
    FTA: “While Fourier analysis is very useful, it has a few shortcomings. First, it can only extract sinusoidal signals.”

    That is incorrect. Power spectral density analysis is a mature field which is widely used in system identification. It can identify standard rational processes which describe the evolution of linear or linearized systems. Since every smoothly evolving system can be linearized about a particular operating point, the method has wide, virtually universal, applicability.

    All this “periodicity analysis” does is apply a not-very-good bandpass filter to each periodicity bin. It is an unsophisticated analysis technique.

    Regarding you point 3: While it’s true the 20 year Jupiter-Saturn synodic cycle dominates the x-y barycentric data, Scafettas analysis isn’t completely predicated on the barycentric motion. It may be (or may not be) important that every sixty years, the J-S conjunction takes place at the same place relative to the galactic centre and/or the bowshock of th heliosphere. Also, your reply to me regarding the z-axis didn’t take into account the tilt of the Sun wrt the plane of invariance. This also may be important. Hopefully, the publication of the Loehle-Scafetta paper may raise awareness and create research interest in these questions. As the saying goes – Further research required. A bit of funding heading in this direction may well be better spent than paying people to fly around Alaskan coasts in choppers counting polar bears floating belly up in the briny, as I’m sure you’d agree.

    Cheers

    tb

  334. Willis
    stuff here which may be of interest

    http://tinyurl.com/4ya5qkj

    some of the early posts use a narrow band filter manually scanned over centre frequencies from a few months to 150 years looking for peak amplitude outputs (there was NO 60 year cycle found)
    The latter posts adjust these frequencies and manually adjust phase and amplitude for best fit. Further frequencies of 60 years and 118 years were added to further improve the fit. 6 frequencies and a trend are all that is required to produce a good fit.
    10.1y
    the TSI
    14.9y
    21y
    59.7y
    118.5y
    +Trend
    There is No justification for any of these frequencies!
    The spreadsheets are available if required

  335. Willis Eschenbach says:
    August 2, 2011 at 5:56 pm

    As a follow up to my earlier response, there are two major issues that divide us. The first is role of intuition in mathematical analysis and the second is the adequacy of red noise models and periodicity analysis in dealing with real-world data.

    In your post you state: “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.”

    Then is your reply you claim that intuition proves “historically” correct.

    No doubt, intuition often is inspiring. Yet in matters mathematical
    conjecture does not suffice. While highly informed intuition led Fermat to
    a correct conclusion that escaped proof for a very long time, that is an
    exceptional case. For us mere mortals, proof is necessary.

    The developers of periodicity analysis intended the algorithm to be used on
    data known A PRIORI to be strictly periodic. There’s not a whiff of any
    suggestion of applying it to random data to detect imbedded periodicities.
    The only random data components S&S consider are gaussan white noise. I
    believe the authors know full well that in strongly time-limited data the
    mathematical conflation of very narrow-band components and strictly
    periodic ones is great. The unproven conjecture that the algorithm
    extracts “real” cycles in such cases is entirely yours.

    Red noise is the very simplest of random processes that generates
    autocorrelated ones from white noise. Unfortunately, low-order ARIMA
    processes are that only ones that i.i.d-oriented statisticians seem familar
    with. While the low-frequency spectral content of red noise indeed produces
    long-term wanderings that may appear over short stretches similar to
    band-limited processes, the latter have a distinctly oscillatory, rather
    than monotonically decaying autocorrelation function (acf). That structure
    is what produces oscillations in the records of typical real-world
    processes. With short records, the sample autocovariance cannot be
    accurately computed over lags long enough to fully capture the process
    888888888structure. Decades ago, Burg developed a “maximum entropy” spectral
    estimation algorithm that in effect extends the lag-range by fitting a
    HIGH-order AR approximation to the available acf estimates. That algorithm,
    rather than periodicity analysis, is what professional signal analysts
    employ. They do not rely on intuition alone.

    To bring home the reality of random cycles in every-day terms, consider
    ocean surface waves. They are never strictly periodic and in a raging sea
    not even very narrow band. Yet their forces have sunk ships large and
    small. That should be real enough for anybody.

  336. tallbloke says:
    August 5, 2011 at 1:55 pm
    Newtons gravitational equations for example…
    For all your superior intuition and in-depth knowledge of Newtonian Mechanics you fail to see the important point: Newton was able to deduce Kepler’s laws, tides, and flattening of the Earth from a few fundamental concepts. No curve fitting or numerology there.

    tallbloke says:
    August 5, 2011 at 3:29 pm
    Here you go Leif, you’re going to love this.
    All this is old hat and actually serves to debunk the whole thing. Here is an old blog post [from 2009] about this: http://www.leif.org/research/Vuk-SAM.pdf but this conclusion is actually 111 years old.

  337. Leif Svalgaard says:
    August 5, 2011 at 9:41 pm
    No curve fitting or numerology there.

    Gravitational anomalies are an interesting subject. So is tides.

    tallbloke says:
    August 5, 2011 at 3:29 pm
    Here you go Leif, you’re going to love this.
    All this is old hat and actually serves to debunk the whole thing. Here is an old blog post [from 2009] about this: http://www.leif.org/research/Vuk-SAM.pdf but this conclusion is actually 111 years old.

    Old truths bear repeating when continually ignored or misrepresented. There are a couple of new things I have updated the post with since you looked at it. One being a possible explanation of your 17 year solar cycle. By The way, I acknowledged your Brown 1900 reference, thanks again for that. Please come over and tell us more about the 17 year cycle. Have any careful studies been done on the appearance of opposite polarity spots which would give me curves for their appearance in schwabe cycles?

    Leif Svalgaard says:
    August 5, 2011 at 9:54 pm
    Here is a non-technical description of how the solar cycles are generated

    http://arxiv.org/abs/1103.3385

    Chouduri is always good for light fiction reading. :-)

  338. tallbloke says:
    August 6, 2011 at 3:23 am
    Please come over and tell us more about the 17 year cycle.
    Slide 40 ff of http://www.leif.org/research/SHINE-2011-The-Forgotten-Sun.pdf have something on the ‘extended cycle’.

    Have any careful studies been done on the appearance of opposite polarity spots which would give me curves for their appearance in schwabe cycles?
    Richardson studied this very carefully in the late 1940s [newer studies does not alter his conclusions]. The opposite polarity spots occur at random. Some 3% of all spots are ‘reversed’ with no systematic behavior. They are most likely just ordinary regions that have rotated as all regions do to some degree.

  339. Leif Svalgaard says:
    August 6, 2011 at 5:20 am
    The opposite polarity spots occur at random. Some 3% of all spots are ‘reversed’ with no systematic behavior. They are most likely just ordinary regions that have rotated as all regions do to some degree.

    OK, thanks. I must have misunderstood your basis for the ‘extended solar cycle’. I’m waiting for the pdf to load so I can view slide 40

    Ah. there we go, how did I know the tandem sketch would be included? :-)
    Small typo bottom of 47 Unexpected[ly] early

    Thanks, it’s a great pdf.

    FYI 17 years is the harmonic mean of the motions of Jupiter and Saturn.

  340. Hello,
    Sorry for my very bad English, I am French and I don’t speak English.

    Willis, I understand the process ARMA to generate the series of temperatures with this red noise, but I don’t understand how we can see, if this red noise and the autocorrelation has not been created by the cycles (of 60 years and/or all the other cycles).

    For example here in Excel, the white noise for 160 years ( with SD 0.09° and a trend 0.16°/dec) :

    In the same data, I add a cycle of 60 years ( 0.2°, 0.4° peak to peak), now the noise is red. In this perfect case, it is only this cycle of 60 years that generate autocorrelation and this red noise :

    Thank for yours explanations and your very pedagogique post.

  341. Leif Svalgaard says:
    August 3, 2011 at 9:04 pm
    sky says:
    August 3, 2011 at 7:45 pm
    you might ponder the legitimacy of periodically extending the average waveform computed by the algorithm when the underlying data is aperiodic.
    This is what L&S did
    ====================================================================

    And I criticized them for this oversimplification on their original post.

  342. tallbloke says:
    August 5, 2011 at 1:55 pm

    Willis Eschenbach says:
    August 5, 2011 at 10:57 am
    First, accusing me of “hack and run” tactics is a joke.

    Willis, reread the first sentence of my comment and then take note of the if-then clause the later part is predicated on. Thanks, and apologies for getting you riled.

    Gosh. So I can say “If tallbloke didn’t read one of my posts, that’s understandable. But if he read it and didn’t reply, he’s a scummy bicycle-seat sniffing coward who is terrified to actually stand behind his words” and that’s acceptable?

    That kind of use of the “if/then” clause is just a cheap way of making a mean, nasty accusation that you can dodge responsibility for, tallbloke. So re-reading it changes nothing, it’s just as unpleasant as it was the first time. If you want to accuse me of something, at least have the stones not to hide behind an “if-then” construction.

    That said, I do appreciate the apology, that is a measure of your strength. Regarding your other point:

    Regarding your point 3: While it’s true the 20 year Jupiter-Saturn synodic cycle dominates the x-y barycentric data, Scafettas analysis isn’t completely predicated on the barycentric motion. It may be (or may not be) important that every sixty years, the J-S conjunction takes place at the same place relative to the galactic centre and/or the bowshock of the heliosphere. Also, your reply to me regarding the z-axis didn’t take into account the tilt of the Sun wrt the plane of invariance. This also may be important. Hopefully, the publication of the Loehle-Scafetta paper may raise awareness and create research interest in these questions. As the saying goes – Further research required.

    So if it’s not based on the barycentric cycle, and it may depend on which direction the bowshock of the heliosphere is pointing … how does that differ from just picking cycles at random?

    Part of the problem is that the motion of the sun, eight planets and an ex-planet, and a host of asteroids is very, very complex. As a result, it contains just about any cycle that you might care to name. Need 10.6, or 11.3, or 20, or 183, or 60-year cycles? No problem. For the 60 years we have which way the galactic center interacts with the heliosphere, or something like that … I’m sure you see the problem. It is ex post facto cycle fitting.

    As I demonstrated before, I can get about as good a fit using 60- and 40- year cycles as they got with 60- and 20-year cycles. And I’m certain I could find a forty year cycle somewhere in the great solar orrery … but so what?

    And as I have said many times and people (including yourself) keep ignoring, if you are going to say that barycentric motion is important to the climate, then you have to use the actual barycentric motion to compare with the climate. You can’t say oooooh, I see a tiny 60 year cycle in the z-axis, so I can change the phase and make it larger and fit it to the temperature data and get meaningful results. That way lies the madness of curve fitting.

    A bit of funding heading in this direction may well be better spent than paying people to fly around Alaskan coasts in choppers counting polar bears floating belly up in the briny, as I’m sure you’d agree.

    Heck, I’m in Alaska right now, I’ll go count dead polar bears by helicopter, that sounds like an excellent use of funds to me …

    Should there be more research on the question? Well, perhaps, but before I said “Yes” there would have to be some kind of solid preliminary findings … and the L/S analysis is a long ways from that. For starters, their null hypothesis is that the underlying rate of natural warming for the entire 20th century is 0.15C/century.

    Until you (or someone else) comes up to defend and explain that choice, I wouldn’t put another penny into that line of research. And to say well, we need more funding to determine the exact cycles, I’m sorry but that’s not either an excuse for a bad paper or a reason to give more funding.

    Again, let me be clear. I find the barycentric hypothesis to be definitely possible, which means that (afaik) it doesn’t break any physical laws. What I don’t find is any solid research showing that the barycentric movement is related to much of anything … sure, there are cycles in the barycentric movement, all kinds of cycles. And there are cycles in various aspects of climate. But finding two cycles that happen to appear in both means nothing.

    w.

    PS – I have also commented several times that it is extremely common for a tuned cycle analysis to start going off the rails as soon as it leaves the calibration data and enters the unseen data. Most people look at that and conclude the model is flawed. L/S make the outrageous claim that the model is not flawed but human interference with the climate is why their model ran off the rails … right, pull the other one.

    Explaining the most common failure mode as being a result of human effect on the climate, without a scrap of evidence to back them up, is something I would expect from Gavin Schmidt or one of the GCM modelers. Perhaps while you are explaining their null hypothesis choice you could explain why Occam’s razor wouldn’t say that by far the most probable explanation is … well … that their model is not ready for prime time …

  343. ChristianP says:
    August 6, 2011 at 9:41 am

    I am glad you put the graphs to illustrate a key issue. Allow me to point out, however, that the sample acf in the second graph–which generically resembles many regional temperature indices–is NOT an example of red noise. The acf of red noise decays exponentially and does not exhibit persistently negative values at long lags. Only the acf of truly oscillatory signals does that. That persistent feature is what distinguishes such signals from red noise.

  344. sky says:
    August 5, 2011 at 5:23 pm

    Willis Eschenbach says:
    August 2, 2011 at 5:56 pm

    As a follow up to my earlier response, there are two major issues that divide us. The first is role of intuition in mathematical analysis and the second is the adequacy of red noise models and periodicity analysis in dealing with real-world data.

    In your post you state: “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.”

    Then is your reply you claim that intuition proves “historically” correct.

    Regarding the first issue, come back when you are willing to quote my statements about intuition, so I can see what you are on about. I was responding to a claim that Periodicity Analysis appeals to “primitive intuition”, when in fact it is a recognized analysis method.

    I despise this kind of thing. You have it in your mind that I said something or other about intuition, so you spend lots of time attacking it. QUOTE MY WORDS if you disagree with them, not just one word out of context. All you have done is to prove beyond a doubt that you don’t have a clue what my position on intuition really is.

    w.

  345. sky says:
    August 5, 2011 at 5:23 pm

    The developers of periodicity analysis intended the algorithm to be used on
    data known A PRIORI to be strictly periodic.

    And you know this how?

    There’s not a whiff of any
    suggestion of applying it to random data to detect imbedded periodicities.
    The only random data components S&S consider are gaussan white noise. I
    believe the authors know full well that in strongly time-limited data the
    mathematical conflation of very narrow-band components and strictly
    periodic ones is great. The unproven conjecture that the algorithm
    extracts “real” cycles in such cases is entirely yours.

    I make no assumption that the algorithm extracts “real” cycles, that’s my whole point. Again you are off attacking straw men. QUOTE WHERE I SAID that every cycle that any analysis detects is real, much less that every cycle that periodicity analysis detects is real. You truly need to work on your reading skills. My point is that the 60-year cycles in the temperature data are very likely not real, despite being detectable by anything from Fourier analysis to the unaided eye. Perhaps you could discuss that.

    Gotta run, I’ll respond to the rest of your post on red noise later.

    w.

  346. Hey Willis,
    Given that all they need is a fast PC and some grey matter between their ears, funding several whole roomfuls of solar system dynamics researchers wouldn’t cost anything like as much as gets wasted sending Lonnie up Kilmanjaro and the Karakorum every year. Then at least we’d get some people who would know what they were talking about when criticising other team’s results.

    Scafetta agreed with me that this was a first foray which required a lot of following studies to resolve the linear trends they used in their simple upper bounding analysis. It seems pretty obvious to me that they included the 0.66C GHG warming as a way of getting it into the literature, as we’ve seen with so many other studies paying lip service to AGW to get past the gatekeepers.

    It’s a trojan horse which can later be superceded, now they are through the gate, with another better analysis which accounts for longer term cycles, which is probably their intention. I think they were just being too subtle for you, and the reviewers. Which means that they did a good job.

  347. tallbloke says:
    August 6, 2011 at 2:24 pm
    I think they were just being too subtle for you, and the reviewers. Which means that they did a good job.
    Huh? being obscure is doing a good job?
    This is a poor paper.

  348. tallbloke says:
    August 6, 2011 at 2:24 pm

    Hey Willis,
    Given that all they need is a fast PC and some grey matter between their ears, funding several whole roomfuls of solar system dynamics researchers wouldn’t cost anything like as much as gets wasted sending Lonnie up Kilmanjaro and the Karakorum every year. Then at least we’d get some people who would know what they were talking about when criticising other team’s results.

    I’d prefer to have someone who wouldn’t make ridiculous assumptions about the null hypothesis, and then refuse to defend it, but that’s just me.

    Scafetta agreed with me that this was a first foray which required a lot of following studies to resolve the linear trends they used in their simple upper bounding analysis.

    In other words, you’re not going to answer any of my scientific questions or address any objections. Instead, you’re going to say it doesn’t matter if it’s a piece of junk, it just requires “following studies”?

    And you call this science?

    It seems pretty obvious to me that they included the 0.66C GHG warming as a way of getting it into the literature, as we’ve seen with so many other studies paying lip service to AGW to get past the gatekeepers.

    So you are saying that the main conclusion of their study, the subject they discuss in their abstract, the claimed GHG warning, has no support in the study itself but was just included so they could get it published? Putting a totally false claim into your paper just to get it published? I expect that of the Hockey Team. But on the our side of the discussion?

    And you call this science?

    It’s a trojan horse which can later be superceded, now they are through the gate, with another better analysis which accounts for longer term cycles, which is probably their intention. I think they were just being too subtle for you, and the reviewers. Which means that they did a good job.

    Oh, right, they’re too subtle for me … subtle like a two by four across the head. According to you, they’ve included total bullsh*t just to get their garbage analysis published, in order to come back later with an actual analysis … that’s far too subtle for me, all right. I mean, once they’ve besmirched their reputation by pushing junk, just to get a paper published … do you really think a better paper will repair the damage?

    Why is it so hard for folks to understand that once you have lost people’s trust, it is very difficult to regain it? Since as you claim they’ve misrepresented their results just to get their paper published, didn’t you ever consider that now that they’ve deceived people once, who is going to pay any attention to them next time? I mean, other than you?

    Because “includ[ing] the 0.66C GHG warming as a way of getting [their paper] into the literature” is so far from science as to be actively deceptive. I find it repugnant myself, and I would not dream of misrepresenting results in order to get them published. That way lies chaos.

    w.

  349. sky says:
    August 5, 2011 at 5:23 pm

    Red noise is the very simplest of random processes that generates autocorrelated ones from white noise. Unfortunately, low-order ARIMA processes are that only ones that i.i.d-oriented statisticians seem familar with.

    Well, that’s good. Start with an insult, and move on from there.

    While the low-frequency spectral content of red noise indeed produces long-term wanderings that may appear over short stretches similar to band-limited processes, the latter have a distinctly oscillatory, rather than monotonically decaying autocorrelation function (acf). That structure is what produces oscillations in the records of typical real-world processes.

    It might help your understanding if you looked at the acf of the HadCRUT3 data. If you can find a “distinctly oscillatory” nature to that acf, you’re not looking at the HadCRUT3 data, which has NO SUCH OSCILLATORY STRUCTURE.

    Which means, of course, that all of your claims about that structure being what “produces oscillations in the real world” must be wrong, since the HadCRUT3 data doesn’t have that structure, and yet it produces oscillations in the real world … go figure.

    In fact, the HadCRUT3 data has an acf structure which is quite similar to the low-order ARIMA random data that I used … WHICH IS WHY I USED THAT LOW ORDER DATA. Had I used your recommended high-order option, the acf of the random data would have been completely different from the acf of the actual data that I was trying to simulate, and as a result the random data would have been meaningless in this context.

    You really should look at the data first, sky, before getting all huffy about your superior theoretical knowledge. You’ve run aground on the reef of ugly facts.

    With short records, the sample autocovariance cannot be accurately computed over lags long enough to fully capture the process structure. Decades ago, Burg developed a “maximum entropy” spectral estimation algorithm that in effect extends the lag-range by fitting a HIGH-order AR approximation to the available acf estimates. That algorithm, rather than periodicity analysis, is what professional signal analysts employ. They do not rely on intuition alone.

    First, what is it with you and “intuition”? I made no claims that intuition alone could solve mathematical conundrums, nor that mathematicians relied on intuition alone, that’s your fantasy.

    Second, you claim that professional statisticians use “maximum entropy spectral evaluation” instead of periodicity analysis. Since I doubt you’d even heard of periodicity analysis until this post, how do you know what might be used in its place? And professional signal analysts apply, not “that algorithm”, but hundreds of algorithms depending on the situation. Saying that they use one algorithm “instead” of another is a huge oversimplification of the process of choosing an algorithm for a problem. Finally, one analyst may well choose a different algorithm than another for a given problem, making your claim, well, … I’ll just call it unlikely.

    Third, my claims do not rest on periodicity analysis. They can be substantiated by the spectral analysis of your choice.

    Fourth, if you have a better way to estimate whether the apparent 60-year cycle in the temperature data is real or not, bring it on. Among professional signal analysts, saying you know all about a subject and then not providing data, code, examples, or your own analysis has a specific technical term. It’s called “hand-waving”. Scientific analysis, rather than hand-waving, is what professional signal analysts employ.

    To bring home the reality of random cycles in every-day terms, consider ocean surface waves. They are never strictly periodic and in a raging sea not even very narrow band. Yet their forces have sunk ships large and small. That should be real enough for anybody.

    Thanks, sky. If you hadn’t told me that ocean waves aren’t periodic and can actually sink ships, I’m sure I would never have realized that despite being a seaman and a commercial fisherman for a good chunk of my life and sailing across the Pacific and …

    This is supposed to bring home “the reality of random cycles”? Did I or anyone say that random cycles aren’t real? QUOTE MY WORDS, I’m getting tired of folks reading their own brand of nonsense into what I said. In any case, what does the “reality of random cycles” have to do with this discussion? That example makes no sense at all, it is totally unrelated to the topics in question.

    w.

  350. sky says:
    August 6, 2011 at 2:02 pm

    Allow me to point out, however, that the sample acf in the second graph–which generically resembles many regional temperature indices–is NOT an example of red noise. The acf of red noise decays exponentially and does not exhibit persistently negative values at long lags. Only the acf of truly oscillatory signals does that. That persistent feature is what distinguishes such signals from red noise.

    Yes that’s right, my simulation is too simple with only one cycle + white noise and no other oscillations / variabilities that are capable to generate a real red noise as in reality.

  351. Willis Eschenbach says:
    August 7, 2011 at 12:32 am

    Because “includ[ing] the 0.66C GHG warming as a way of getting [their paper] into the literature” is so far from science as to be actively deceptive.

    It no doubt seems too low for the warmista, and too high for the hardline sceptics. You can’t please everyone. Seems to me they did a pretty good job defining an upper bound at 0.66C/century and managing to get it past the gatekeepers. Well done Craig and Nicola!

    I find it repugnant myself, and I would not dream of misrepresenting results in order to get them published.

    I think their conclusion is reasonable given the current state of knowledge. And the current state of knowledge is why more study is needed. Not just in solar system dynamics either, as I’m sure you’ll agree.

    I’d prefer to have someone who wouldn’t make ridiculous assumptions about the null hypothesis, and then refuse to defend it

    Scafetta defended his and Craig’s paper the day you attacked it. It’s not his fault you now have the floor to yourself four days later. You think he should keep coming back and refreshing this page on the offchance you might get around to replying to him? Maybe you should have done better research on Scafetta 2010, taken some time to think, and put your post up when you weren’t about to jet off to Alaska. That way you’d have been around to reply to the physicist you mis-aimed your blunderbuss at. Barn door at five paces. Whoosh. Dead pigeon.

    According to you, they’ve included total bullsh*t just to get their garbage analysis published, in order to come back later with an actual analysis … that’s far too subtle for me, all right. I mean, once they’ve besmirched their reputation by pushing junk, just to get a paper published … do you really think a better paper will repair the damage?

    …And you call this science?

    You call this potty mouthed rant scientific discourse?

  352. Leif, in your world you debunked it. I note Willis missed that thread, or gave it a miss.

    Abstract of Scafetta 2010
    We investigate whether or not the decadal and multi-decadal climate oscillations have an astronomical origin. Several global surface temperature records since 1850 and records deduced from the orbits of the planets present very similar power spectra. Eleven frequencies with period between 5 and 100 years closely correspond in the two records. Among them, large climate oscillations with peak-to-trough amplitude of about 0.1 $^oC$ and 0.25 $^oC$, and periods of about 20 and 60 years, respectively, are synchronized to the orbital periods of Jupiter and Saturn. Schwabe and Hale solar cycles are also visible in the temperature records. A 9.1-year cycle is synchronized to the Moon’s orbital cycles. A phenomenological model based on these astronomical cycles can be used to well reconstruct the temperature oscillations since 1850 and to make partial forecasts for the 21$^{st}$ century. It is found that at least 60\% of the global warming observed since 1970 has been induced by the combined effect of the above natural climate oscillations. The partial forecast indicates that climate may stabilize or cool until 2030-2040. Possible physical mechanisms are qualitatively discussed with an emphasis on the phenomenon of collective synchronization of coupled oscillators.

  353. tallbloke says:
    August 7, 2011 at 2:57 am

    I’d prefer to have someone who wouldn’t make ridiculous assumptions about the null hypothesis, and then refuse to defend it

    Scafetta defended his and Craig’s paper the day you attacked it. It’s not his fault you now have the floor to yourself four days later. You think he should keep coming back and refreshing this page on the offchance you might get around to replying to him?

    Scafetta is free to do what he wants. I think if he doesn’t defend his paper, he will lose credibility, so it is in his interest to defend it.

    However, your claim that he defended the null hypothesis in his post is plain, flat out not true. I challenge you to show me where he defended his choice of a null hypothesis in that response. Again you bring up your claims without any facts to back them up.

    So … just where did Scafetta defend his null hypothesis on this thread, or respond to any of my objections to the paper? Because as near as I can tell, he has made exactly one and only one response in this thread, he did not answer any of my questions or objections, and he did not defend his choice of a null hypothesis in that response.

    Perhaps on your planet that constitutes defending your paper, tallbloke. I find it sadly inadequate.

    w.

    PS – on their previous thread, the only thing that Scafetta said in defense of the null hypothesis that the natural portion of the global warming is 0.15 degrees per century was this:

    We clearly state in the paper that there are other cycles such a the millennial one explaining the MWP and LIA. However, in this paper we are dealing only with the data since 1850. The first approximation that can be done with this data is a linear one which yields to an upper estimate for our 21st forecast.

    Maybe you consider that an explanation and defense of the choice of null hypothesis, tallbloke. For me it’s just industrial strength tap-dancing. What does the choice of 0.15° per century have to do with the start of the dataset? If it’s 0.15° per century, it is 0.15° per century no matter when the dataset started. That’s just fast and furious tapdancing to cover up a totally arbitrary choice of null hypothesis.

  354. Willis Eschenbach says:
    August 7, 2011 at 9:47 am
    ….

    Hi Willis,

    I didn’t say he defended the null hypothesis, I said he defended his paper.
    The first mention of the Null Hypothesis on this thread is in your reply to Geoff Sharp at
    http://wattsupwiththat.com/2011/07/30/riding-a-pseudocycle/#comment-710885 on August 2nd, long after Scafetta left his response to the original post which you didn’t reply to until yesterday, August 6th. (UK time).

    However I see that you raised the null hypothesis issue several times on the original thread and didn’t get a reply. Looks to me like they generalised it from the Loehle non-tree ring proxy. These are rough heuristics we’re dealing with. Still better than the IPCC assumption of no long term underlying trend at all IMO.

    My personal opinion is that they oversimplified the situation, but Ive stopped trying to second guess their thinking.

  355. Thanks, tallbloke.

    To recap, my objections to the paper were:

    1. They have made an assumption that the period 1850-1942 represents a constant unchanging “natural” upward trend, with a rate of increase of 0.15°C per century. They have not justified this choice. When they don’t justify and explain their null hypothesis, their study is done before it starts—without a clear null hypothesis the whole thing goes directly to the circular file.

    2. They have assumed that the signal can be meaningfully decomposed by assuming two linear trends. There is no evidence to substantiate this.

    3. They have not compared the statistics for the fit of the two situations, one with two trends and one with one trend.

    4. In fact, they have not provided statistical backup nor shown statistical significance for their various curve fits. This may be a result of the fact that the autocorrelation of their cyclical reconstruction is extremely high, so that as a result the fits are not statistically significant.

    5. They have not used the barycentric data at all.

    6. They have said that their 20 and 60 year cycles are present in the barycentric data, which they are. However, they have not used the actual phase and amplitude of those cycles. Instead, they have substituted their own phase and amplitude simply because they provide a better fit. Cute, but not science.

    7. You say “I think their conclusion is reasonable given the current state of knowledge.” I say that estimating the human contribution in their manner is totally unsupported given the current state of knowledge, and that claiming it can be estimated to the nearest hundredth of a degree in this manner is un grán chiste.

    8. I have shown that in very similar random ARIMA datasets, spurious artifacts in the form of what look like long period cycles appear quite frequently. However, there are no cycles in those datasets, they are random. As a result, we have no reason to believe that the 60 year cycle in the HadCRUT data is real, and good reason to believe it is an artifact.

    I have raised these issues several times, and provided my data and code. Scafetta has not explained or defended a single one of these points. As far as I’m concerned, the discussion is done unless Scafetta actually wants to stand behind what he wrote and explain and defend it. As Leif commented, the study is cyclomania at its worst.

    w.

  356. Leif Svalgaard says:
    August 4, 2011 at 3:39 pm

    Geoff Sharp says:
    August 4, 2011 at 8:58 am
    Your analysis is lousy Leif, no grouping, no recognition of AMP strength etc.
    ——————–
    It is not me trying to convince the world of anything. The null-hypothesis is that there is no correlation. You could improve things by providing a table [easier than a plot] that for each of your perturbation you give the time, the ‘strength’ [whatever you think it is], and its type. Then in another table the time of the central point of each grand minimum you think there is. That will put the whole thing on a numerical footing so it can be analyzed properly [and get you away from mere hand waving].

    A table has been available since Jan 09 which shows the position of each perturbation group with the central perturbation’s planet angles also supplied. This table is compared with the Solanki/Usoskin proxy record. It is difficult to place every solar downturn into a table and of little value IMO. I have given you weighted individual AMP events that you can plot directly onto the Steinhilber graph, this will show directly the correlation if you plot the relevant color codes.

    At present you are doing the handwaving, making statements that the correlations are weak or non existent without showing any examples of your claims (or those shown actually proved my case). My graphs already show the correlations.

  357. Geoff Sharp says:
    August 7, 2011 at 11:46 pm
    It is difficult to place every solar downturn into a table and of little value IMO. [...]
    My graphs already show the correlations.

    Why is it difficult to make a table of what you consider to be a ‘downturn’?
    Sorry, the graphs do not show any convincing correlation.

  358. Leif Svalgaard says:
    August 8, 2011 at 3:34 am

    Why is it difficult to make a table of what you consider to be a ‘downturn’?

    Because they all vary in length. I have updated my Solanki graph back to to around 1150BC showing the same color coding as before. The AMP events are entered correctly via the spreadsheet. I cannot see how you would require any more information.

    Sorry, the graphs do not show any convincing correlation.

    This is hardly a scientific assessment and expected as I stated earlier. There is only one area around 600BC that could be questioned with the probable result being influenced by “Wilsons Law”. I am comparing a detail dataset with a proxy record spanning 3200 years, the proxy record is only a close approximation of the solar record derived from solar wind that is not a true representation of actual solar output. Even so the match is very close with all 5 MAJOR downturns coinciding with strong AMP events with the rest matching the strength of the AMP events of the day. The MWP is also correlating with some precision. The obvious feature is that no large grand minima coincides with weak AMP events.

    The sunspot record is also a very close match with individual events like SC20 and SC24 matching with precision. I think you are living in denial.

  359. Geoff Sharp says:
    August 8, 2011 at 4:30 pm
    “Why is it difficult to make a table of what you consider to be a ‘downturn’?”
    Because they all vary in length.

    So you just give the [deepest] year of the Grand Minimum. What is difficult about that?

    I cannot see how you would require any more information.
    The information may be there scattered about on several graphs. This makes it hard to do anything with it. So it is up to you to make a [new - if need be] table with the years, quantification, type, whatever and which Grand Minimum you think is related to your ‘perturbation’.

    I think you are living in denial.
    Personal comments like that does not belong in reasonable discourse. Stick to the data.

  360. Leif Svalgaard says:
    August 8, 2011 at 6:08 pm
    So you just give the [deepest] year of the Grand Minimum. What is difficult about that?

    Your method is not satisfactory. For a start not every downturn is a grand minimum, plus each downturn has different period lengths. Giving one date would not be sufficient to match against multiple strong AMP events when they occur. One date also does not convey the depth of the downturn.

    Personal comments like that does not belong in reasonable discourse. Stick to the data.

    You have more than enough data, you are now procrastinating. All the data required is available in the one graph, I can send the spreadsheet if required. If you cannot find fault with the data provided I will have to assume your correlation statements are without supporting evidence.

  361. Geoff Sharp says:
    August 9, 2011 at 12:26 am
    One date also does not convey the depth of the downturn.
    Doesn’t matter as I have solar data. I just need to know which of the wiggles you consider grand minima.

    If you cannot find fault with the data provided I will have to assume your correlation statements are without supporting evidence.
    You have this backwards. It is you trying to convince the world, not me. Provide the data in full 3000BC-3000AD as I originally suggested by annotating my graph or providing the tables.

  362. Willis,

    The deterioration of communication and analytic insight in the ongoing discussion that I found upon returning from my trip is dismaying. I’ll look past the personally-directed remarks to sharpen the focus on signal structure.

    If the sample acf you compute from the HADCRUT3 series doesn’t show very significant NEGATIVE correlation at multidecadal lags, then obviously the series trend and mean were not properly removed before that computation. This basic blunder introduces a systematic POSITIVE BIAS in the results. Conclusions about signal structure drawn from such grossly faulty estimates are mathematically baseless.

    Because you’re an extraordinary guy, Willis, I’ll take extraordinary means to clear the communication channel and attempt to clarify this and other isuuse, whenever I find the free time. Pressing matters will occupy me today.

  363. sky says:
    August 9, 2011 at 4:07 pm

    Willis,

    The deterioration of communication and analytic insight in the ongoing discussion that I found upon returning from my trip is dismaying. I’ll look past the personally-directed remarks to sharpen the focus on signal structure.

    If the sample acf you compute from the HADCRUT3 series doesn’t show very significant NEGATIVE correlation at multidecadal lags, then obviously the series trend and mean were not properly removed before that computation. This basic blunder introduces a systematic POSITIVE BIAS in the results. Conclusions about signal structure drawn from such grossly faulty estimates are mathematically baseless.

    Because you’re an extraordinary guy, Willis, I’ll take extraordinary means to clear the communication channel and attempt to clarify this and other isuuse, whenever I find the free time. Pressing matters will occupy me today.

    Thanks, sky. I didn’t understand that you were talking about long-term oscillations, I was speaking of the first twenty years or so of the ACF which don’t oscillate. However, that makes no difference, as my ARIMA datasets have variations of the same ACF structure as the HadCRUT data whether you look short or long. If you think I’m wrong about the ACF of the HadCRUT3 data then you should indeed post up the graphs to support your claim. I detrended both the HadCRUT data and the random pseudotemps. The ACFs are indistinguishable both in the short and long term autocorrelation, which, as I said before, is why I used the low order ACF — because it matched the data. My code for the generation of the pseudodata is above, please demonstrate (not claim but demonstrate) that the ACFs of the pseudodata are somehow fundamentally different from those of HadCRUT3, because I sure can’t find it. FOr example, which of these is the HadCRUT3 data and which are pseudo-data?

    Finally, yes, things tend to go pear-shaped when, as in the example above, you accuse me of a “basic blunder” when you haven’t provided a scrap of evidence that I actually am wrong. If you accuse people of being blunderers making stupid mistakes and you provide nothing to support that accusation, sky, surely you can’t be surprised if they snap back at you.

    And then you wanted to school me that ocean waves can actually be destructive … but I’ve spent a large part of lifetime at sea, and I doubt if you have. Can you teach me something about ocean waves? Quite possibly … but not by acting like I don’t understand them at all and you are going to show me the error of my ways.

    Do you see why you might be seen as arrogant?

    Likely you are not arrogant at all in real life, sky … but you really should tone down the accusations of “basic blunders” and your assumption that you have the stature to lecture a seaman on ocean waves …

    All the best,

    w.

  364. Willis,

    My (unprovoked) comments on WUWT are always about the technical issue, rather than the person. I write formally, with logical thinking foremost. Please note the if-then construction of my statement about HADCRUT3 at multidecadal lags. Failure to properly remove the mean and trend is a frequently made basic blunder, of which I did not accuse you .

    Since WUWT is an open forum, rather than a private exchange, I do keep the comprehension of the general reader in mind in choosing my examples. That is the reason I chose random ocean waves as an example of a real, oscillatory process that is aperiodic. I wasn’t lecturing you at all.

    Although ACF estimation algorithms differ in results, my choice for HADCRUT3 is #3. But that is NOT an example of red-noise, commonly modeled in discrete time by x(n) = r(1)*x(n-1) + g(n), where r(1) is the value of acf at lag 1 and g(n) is gaussian white noise. Red noise has an exponentially decaying NON-negative acf (aside from sampling fluctuations) characteristic of diffusion-type processes. Once you get into higher-order ARIMA processes with oscillatory acfs , you have real, albeit random, cycles instead of mere wandering. Cycles are not an artifact of autocorrelation , they are its expression.

    Because this is an important topic, I want clear up. with your indulgence, other issues as well in the coming days.

    Cheers.

  365. Thanks, sky, apologies for my misunderstanding.

    Since you say that the cycles in higher-order ARIMA processes are “real but random”, I fear that you’re going to have to post up some examples and code to show what you are talking about, as I’m not sure what you mean by that. Do you mean that real cycles come and go at random times, or that there are real cycles with random phase and period, or what?

    If you’d post some R code (or even pseudocode) so I could play with what you are talking about, that’d be great. Because at present, I see nothing that invalidates my claim that random ARIMA datasets (either low or high-order) with N=158 show different apparent cycles in different sections of the same dataset. That is to say (as is exemplified in my figure above) the first 158 datapoints show one cycle, the next shows another, the next might show only small cycles, and so on.

    So if you could post an example of a high-order ARIMA dataset in which the same long-period cycles (greater than say a third of the record length) appear in every 158-year segment of the ARIMA random dataset. I have not been able to reproduce your ideas, whenever I do it I get different cycles in different segments of the same dataset. Likely that means I’m not understanding exactly what you are saying.

    w.

  366. Willis,

    Can’t really help you with R code, because I’m not adept at it. The signal analysis and time-series modeling software I use is the property of our research and consulting firm and the results often belong to clients. I can try to explain, however, an analytic concept that many Ph.D. scientists in various fields have a difficult time in wrapping their heads around. That concept is the linear superposition of many band-limited random-phase oscillations covering a broad range of frequencies. That’s the structure manifested by most most real-world signals not produced by periodic astronomical forces (such as tides). Think of swell from a distant fetch. The apparent wave height and period varies from wave to wave within a wave group, and there’s can be abrupt transitions of phase btween wave groups. Now, instead of wave periods being confined to generally less than 20sec as in the ocean, imagine entirely separate processes that produce swell-like waves at widely seperated frequency bands to complete the conceptual picture.

    To get away from the information limitations of short duration temperature records, we have to turn to proxy data. The GISP2 del18-O isotope data, whose acquisition benefitted greatly from a signal-savvy instrumentation engineer on the team, provides perhaps the best available proxy indication of multidecadal, quasi-centennial and much longer random temperature variations.

    Power spectrum analysis of the entire Holocene portion of GISP2 data provides frequency resolution two orders of magnitude greater than is available from most instrument records.
    It reveals a rich superposition of fairly narrow-band multidecadal and quasi-centennial oscillations, which form a very complex, unpredictable interference pattern in time. The most powerful component in this range, however, has a pronounced spectral peak at ~62 yrs. The Lohle non-dendro series similarly shows, inter alia, a prominent peak at ~59yrs. These oscillations, which cry out for a physical explanation, are not the impersistent wanderings of red noise or the the oscillations of low order ARIMA processes.

    I’ll have time again tomorrow to remark upon the pitfalls of modelling. After a long break, pigskins are flying in the air tonight.

    Cheers.

  367. sky, I found the GISP2 data here. Is that what you are referring to?

    If so, where can I find the corresponding power spectrum analysis of the data which you discuss? You say that a spectrum analysis shows a “very complex, unpredictable interference pattern in time”, and also that it contains a “pronounced spectral peak” at ~62 years. Not sure how that can be both, if you’d provide a citation to the power spectrum analysis you are referring to that would be great. Right now, I have virtually no information on what you are talking about. How was the analysis done, what method was used, was the data partitioned and analyzed, did the analysis of the various partitions contain the same or different cycles, it’s all questions and no answers at this point …

    So far all you’ve done is tantalize me. When are you actually going to provide us with some meat? To date, no citations, no graphs, no data, no code … I’m sure you see the problem.

    Thanks,

    w.

  368. The GISP2 isotope data I refer to is not the core profile data that you link
    to, but the bidecadal series available from NCDC paleoclimate link. Simple
    plotting of that data shows the complex superposition pattern of MANY
    oscillations, that I speak of. To obviate the need for accurate
    detrending, always a problematic task, I spectrum analyzed the bidecadal
    ROC, which applies an analytically well-known high-pass filtering to the
    data. Due to sampling uncertainty and mild non-stationarities, there are
    the expected differences, of course, in the power densities of the
    bi-sectioned data. The pronounced ~62yr peak in the spectral estimate for
    entire Holocene, shows up closer to ~65yrs in the early Holocene portion
    and there are other differences as well. A ~44-yr oscillation is more
    precisely common to both sections. But that’s what real-world random
    signals that are not very narrow-band do: they vary from section to
    section. And thats what makes thier predicatiability over long time
    horizons virtually nil. Pronounced peaks in the power spectrum are not at
    all imcompatible with unpredicatabilty in complex cases.

    Since you are championing the idea on this post that real-world temperature variations are explained by red-noise aor ARIMA processes, it should be your burden to provide compelling evidence. My problem is that I have not seen anything that would convince anyone competent in signal analysis that such is the case. I’ve already explained why no code will be forthcoming from me. I’m further handicapped by lack of web-surfing skills. I don’t even know how to provide a link, let alone post a graph for everyone to see. That’s why in a disupte at CA with Koutsoyannis about the adequacy of the red-noise model he champions, I could only post the numerical values of the sample acf for a representative set of vetted USA stations. But I’d be happy to e-mail you any results that I’m free to divulge. Hope that helps mutual understanding.

  369. sky says:
    August 12, 2011 at 5:20 pm

    … I’m further handicapped by lack of web-surfing skills. I don’t even know how to provide a link, let alone post a graph for everyone to see.

    Fortunately for all of us, either one is quite easy to do. To provide a link, merely copy it and paste it into a message, like this

    http://wattsupwiththat.com

    and the hosting service (WordPress) does the rest. For images, post it to a free online graphics hosting service like http://photobucket.com or http://flickr.com and then post a link to it as above.

    I await your examples, as what you say is quite interesting and I’m always ready to learn.

    All the best,

    w.

  370. Dear Willis,
    let me send you 2 pages from my book (ISBN 978-3-86805-604-4) to show a historical
    comparison of the “Net Solar-irradiation Gain (NSG)” and the “Hadley-staircase, the GMT
    (Global Mean Temp). I will sent them separately to you, since someone has to paste the
    page into here:
    ……. 2 graphs here……

    Comment: The “Hadley Staircase” -GMT- is the previous HadCRUT2 curve, used
    until 2005, from which the staircase form can be more easily detected than from
    HadCRUT3.
    If you subject HadCRUT3 to your mathematical approach , you are blurring the
    staircase form, thus not very helpful. The staircase steps are detected and talked
    about in the L&S-paper as 60 year cycles (one step surface plus one step height)!

    But, always a but in life, L&S include 2 mistakes 1. The first step (1850-1910) is longer in flat
    surface, due to crossing the NSG-line (60 years are one flat surface plus one step height),
    thus is longer than 60 years, and the 2. and most important, there cannot be an additional
    step upward (as L&S predict) and therefore also no 0.66 C man made additional warming
    in the 21.Century, because we reached the NSG top limit and the NSG constitutes
    nothing less than the “mysterious ” heat for global warming since the LIA… From year
    2000 onwards, the GMT temps will stay flat as “plateau” , as you can also see…..

    Both graphs show: We have reached the top of the NSG-cycle [790 year
    Earth orbit multicentennial cycle, so far widely unknown, due to the IPCC silence
    about it (grounds for my ongoing AR4-error complaint this month). If you like, I will
    copy my complaint to you….., if you want….
    Furthermore, the Net Solar-irradiation Gain (which has risen since middle of the LIA
    by 2.17 W/m^2) will peak at the year 2045 and will decrease from thereon into the
    coming LIA, 395 years further ahead……
    The booklet calculates transparently all mentioned figures of this natural astronomic
    cycle, no simulations, no assumptions, only straightforward calculations,
    for everyone, and impossible to refute….
    Please give it a thought, if I can get the IPCC into looking at the Earth’s orbit, then
    a great leap forward has been made……..
    Regards Your JSei.
    PS to Geoff: My reply to your question at the end of the L&S blog..

  371. Willis Eschenbach says:
    August 12, 2011 at 6:16 pm

    I’ll try posting some graphs to illustrate the issue next week, when I return from yet another assignment. In the meantime, I prepared some remarks on the pitfalls of discrete-time modeling. They may help to bridge the gap between what I’m saying and what your numerical simulations show.

    The commonly used model in red-noise simulations produces an overlay of
    white noise. To obtain pure red noise, as in Gauss-Markov processes, the
    last term in the recursive equation I gave should contain the factor (1 -
    r(1)) to rein in the overlay of gaussian white noise. The generating
    equation then is an exponential filter, with white noise input. After the
    initial transient settles down, it will produce a series whose power
    density is the circular Cauchy distribution. Even this, however, is not
    quite the analytic f^(-2) spectrum of white noise integration in continuous
    time that consitutes the red noise in some physical systems.

    Success in discrete-time simulations meeting various analytic expectations
    depends strongly upon how well the random number generator produces truly
    uncorrelated numbers, without any cyclical components. Many library
    routines are deficient in that respect, producing rythmic ripples in the
    sample acf as seen in Christian P’s first graph.

    While band-limited random signals can be obtained by band-passing true
    white noise, this requires mastery of digital filter design, involving the
    complex-valued discrete shift-operator z. The approach is entirely AR,
    without any IMA. The coefficients in a power series of various orders in z
    are used to control the bandwidth and roll-off rate. It isn’t just any
    high-order AR process that produces narrow-band series. BTW, Burg’s MEM
    spectral estimation algorithm determines those coefficients optimally from
    a sample acf for any chosen order of analysis.

    A simplified approach to emulating narrow-band random signals is to
    superimpose a handful of sinusoids with INCOMMENSURABLE periods unevenly
    clustered around the target peak frequency. Each sinusoid is assigned a
    random phase drawn from a UNIFORM distribution in the range 0 to 2pi, which
    remains CONSTANT throughout the simulation. It varies only from realization
    to realization in an ensemble of simulations. Assigning smaller amplitudes
    to the flanks of the cluster helps emulate roll-off and varying the spread
    in the cluster regulates bandwidth.

    Hope this helps. Let’s enjoy the weekend.

  372. Can’t take any more time today to fix the size problem in the Spectral Graphs. Hope to fix that and provide a succinct write up in the next day or two.

  373. I have time today only for a brief note on the power spectrum estimates shown by the above link . They were obtained from the bidecadal GISP2 isotope series of only the first 408 data points, covering the age range from 10-8150BP. This truncation was necessary to avoid a severe non-stationarity in the data from the preceding century. The truncated series is weak-sense stationary and is virtually trendless. The sample acf through lag 50 (1000yrs) of both the data series and of the bidecadal ROC (first difference) series was computed by a robustly unbiased algorithm. The cosine transform was then applied and the resulting raw power density estimates were “hanned.”

    This classic estimation procedure was chosen not only because of the flexibility it provides for handling any record length, but because it avoids the substitution of the CIRCULAR acf implicit in psd estimates produced from raw FFT periodograma either by decimation in frequency or in time algorithms. The present estimates, which have ~15 degrees of freedom, show peaks and valleys that are appreciably less sharp than would be obtained by either of the FFT algorithms, and far less sharp than could be obtained using Burg’s algorithm. This constitutes a very conservative approach to identifying signal structure, giving the maximum benefit of doubt to smoothly varying academic models.

    Since, at the lowest frequencies, first differencing is a close approximation to continuous differentiation, which has a power transfer proportional to f^2, it’s apparent at a glance at the first graph that the physical process that produced the GISP2 data is NOT the integration of white noise. The latter would produce a sample psd that is FLAT at the lowest frequencies. Instead, we get a sample psd that RISES nearly linearly with frequency and showws significant peaks and valleys at the higher frequencies.

    Hope to find more time tomorrow to discuss other salient differences wrt the red-noise model provided by Gauss-Markov proceeses.

  374. Having seen that the GISP2 data is not at all the integrated white noise of
    the Wiener process (aka “drunkard’s walk”), let’s examine its resemblance
    to the red noise model of Gauss-Markov processes. The comparison is based
    on the data sample value of r(1) =.197. This low value tells us mmediately
    that the data is very noisy or the signalis very wide-band–or both.
    Indeed the red noise model spectrum shown in the second graph differs
    little from the flat spectrum of white noise. But the always monotonically
    declining red noise model denies any possibility of significant spectral
    peaks and valleys, which are amply evident in the GISP2 spectrum at widely
    separated frequencies 3, 12, 33, with a double peak at 44 and 47. These
    spectral features indicate the presence of band-limited signal components
    whose power density rises above the noise.

    Because the spectral densities have been normalized by their total
    variances, the plotted FRACTIONAL power density values add up to unity in
    each case. Thus adding the ordinates from frequency 0 through 8 tells us
    that 30% of the total variance of GISP data is due to multi-centennial and
    quasi-millennial oscillations; correspondingly the red noise model would
    allow only 21% in that range. Frequencies 9-16 show 18% and 30-36 show
    12%, while 42-50 shows 14%. Thus the four spectral bands account for 74%
    of the GISP2 total variance. While other spectrum analysis schemes may
    increase the peakedness and change the peak frequency somewhat, the latter
    result should not change materially.

    It is not noise alone, but the very wide frequency range covered by various
    signal components that produces the low absolute value of r(1) for the
    GISP2 data. First differencing narrows the effective signal bandwidth
    considerably, producing the sample value r(1) = -0.47 for the ROC series.
    Such large NEGATIVE correlation, which is virtually unattainable by differencing red noise, provides further confirmation of oscillatory
    signal components in the multi-decadal range. Whatever broad-brush resemblence red noise may have to real-world signals manifesting low r(1) values, that resemblence disappears as r(1)increases to the positive levels often shown by vetted station data.

    To be sure, low-order ARIMA models are capable of producing non-monotic spectra and oscillating behavior that qualitatively resembles instrument measurements. But close QUANTITATIVE agreement is the province of high-order AR or random phase models.

    I’ll try to wrap up my comments tommorrow.

  375. The spectral signature of GISP2 Holocene data is quite instructive. It
    reveals the presence of oscillatory signal components in widely separated
    freuency bands from the quasi millennial to the multi-decadal, which are
    obscured by considerable noise. These signal components make any concept of
    linear trend over quasi-centennial time-scales or less quite chimeral. The
    apparent linear trend will oscillate in response to the trans-centennial
    and multidecadal oscillations.

    What Lohle&Scaffeta did wrong was to idealize the multidecadal oscillations
    as STRICTLY periodic cycles and treat the apparent trend as a SECULAR one,
    rather than the product of trans-centennial oscillations. This entirely
    deterministic model is grossly unrealistic, because it ignores the very
    limited predictability of random oscillations.

    I’ll check back for any questions next Tuesday.

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