In a recent post here on WUWT, someone yclept “Javier” has written about the Bond Rafted Ice data. In a comment, he said:
This is a frequency spectrum from Bond data. It shows the 980-year Eddy cycle, and the 2400-year Bray cycle I have written so much about.
Well, that looks like it establishes the existence of the 960-year cycle in the Bond data beyond any doubt …
Intrigued by that, and knowing next to nothing about the Bond data or the “980-year Eddy cycle” referred to by Javier, of course, I had to go take a look at it. Javier provided a link to the paper by Debret et al. he was discussing, entitled “The origin of the 1500-year climate cycles in Holocene North-Atlantic records“
The abstract of the Debret et al. paper says:
Since the first suggestion of 1500-year cycles in the advance and retreat of glaciers (Denton and Karlen, 1973), many studies have uncovered evidence of repeated climate oscillations of 2500, 1500, and 1000 years. During last glacial period, natural climate cycles of 1500 years appear to be persistent (Bond and Lotti, 1995) and remarkably regular (Mayewski et al., 1997; Rahmstorf, 2003).
Hmmm … however, I was interested in the data itself, so I dug around and found out that it’s available here.
I found out that what the paper analyzed was called the “stacked ocean record”. What does that mean? Well, they combined a record of hematite grains with two records of Icelandic glass from different drill cores and one record of detrital carbonate … add them together, divide by four, and presto! A “stacked” record.
So I did a Complete Ensemble Empirical Mode Decomposition (CEEMD) analysis of the stacked record. I used the “CEEMD” function in the R package “hht” for the analyses. To begin with, I found what the authors found about the “Eddy cycle”. Their comment was
… the application of a 1000-year filter to the composite series of IRD does not provide very conclusive correlation during 0–5000 years, …
Now, here is the periodogram of the CEEMD analysis:
This shows the strengths of the cycles in each of the empirical modes. It sure looks like there is a 960-year cycle in there in empirical mode C3, along with strong cycles at about 2300 and 7000 years, and a weaker cycle at around 1,300 years in length. And this is what we saw in the periodogram provided by Javier above.
But a look at the individual empirical modes gives a deeper understanding of the situation with the 960-year cycle. These empirical modes are the actual signals that when added together recreate the original raw data signal shown in the top panel below.
As the authors found, the putative 960-year cycle in empirical mode C3 only has significant strength in the earliest 6,000 years of data. On the other hand, it weakens and nearly disappears in the most recent 5,000 years. As I’ve said many times, this kind of appearance and subsequent disappearance of “cycles” is quite common in natural datasets.
More to the point, however, upon learning that it was a “stacked” record, my further thought was “Wait a minute, whenever you add different records you can get all kinds of artifacts from constructive and destructive interference”. So I did a CEEMD analysis of the four individual underlying Bond datasets. Here are the pairs of CEEMD graphs for each of the four individual datasets that make up the “stacked” dataset. In each case, as in the “stacked” data, the putative 960-year Eddy cycle is in empirical mode C3. First, the hematite stained grains dataset. Click on the graphic if you’d like a larger image.
Curious. In this one, there is no clear peak in C3. There’s still a peak at ~2,300 years, in empirical mode C5, but the 7,000-year cycle is much weaker. And there’s a wide peak around 1,400 years in empirical mode C4. This is very different from the stacked data.
Next, here’s the first of the two Icelandic Glass datasets.
In this one, the 7,000-year cycle is back … but there’s even less sign of the putative 960-year cycle in empirical mode C3. However, the previous cycle in C4 has moved down to a weak peak near 1000 years.
Then we have the second Icelandic Glass dataset, from a different drill core.
Once again, there is no 960-year cycle. It’s smeared out from 500 to 1,500 years, basically non-existent, but the 7,000-year cycle is strong. Overall, the two Icelandic Glass datasets are nearly identical, which increases the confidence in these results.
Finally, here’s the detrital carbonate data.
Most interesting. Almost no sign of the 7,000-year cycle, and once again there’s only a weak 960-year cycle. However, in empirical mode C4, there is a small peak around 1,500 years in length.
So … what have we learned?
Well, the first thing I learned is that the putative 960-year “Eddy Cycle” only exists in the “stacked” dataset. There is little sign of it in the four underlying datasets. It is an artifact of the averaging process was used to stack the four datasets.
Next, Debret et al. say that there is a 1,500-year cycle in the Bond data … however, although it appears to show up in the “stacked” data, it is only found in one of the four individual datasets. Again, this appears to be an artifact.
Next, the 7,000-year cycle is strong in the Icelandic Glass datasets, weak in the hematite data, and basically non-existent in the detrital carbonate data. Go figure.
Next, there is a cycle in all four of the datasets at somewhere between 2,200 and 2,600 years. This is the “Bray Cycle” referred to by Javier. Since it appears in all four datasets, can we believe that it is real?
Well, not so fast. Here’s empirical mode C5 for all four of the datasets:
At about 5,500 years BP, they all line up. And moving towards the present, the adjacent cycle is almost exactly 2,500 years long.
But the next cycle nearer to the present is quite different. For the first three datasets, it’s only about 2,000 years long … and for the detrital carbonate, a bit longer than that. Also, all of the cycles are disappearing as we get nearer to the present.
Going back in time from the 5,500-year peak, however, things get worse rapidly. The correlation of the data falls apart, and by the time we’re back to 10,500 years before present, it’s all over the map. The datasets are completely different. However, instead of decreasing in size as they did near to the present, they maintain their amplitude back to the earliest part of the record.
Note, however, that the two Icelandic Glass datasets (blue and red) stay in very tight lockstep over the whole dataset. This is not good since they are both given equal weight in the “stacked” dataset … meaning that the Icelandic Glass data gets counted twice and thus is given twice the weight of the other two datasets. This is bad practice because it distorts the end result.
So … is there actually a 2,500-year cycle as claimed by Debret et al.?
Well, it’s possible, but the evidence is far from clear. There’s only one 2,500-year complete cycle in the data, from ~ 3,000 to 5,500 years BP … but before and after that, the cycles vary in both length and amplitude in the four datasets.
I see this as yet another cautionary tale of expert analysis gone wrong. Here are the cautions, in no particular order:
• As Richard Feynman observed, “Science is the belief in the ignorance of experts”. I can’t tell you how many times I’ve looked at some paper like this one, written by experts, only to have it fall apart under closer examination.
• Periodograms and Fourier Analyses are limited in that they can be fooled by a signal that only appears in part of the record, and then disappears.
• What I call “pseudocycles” are quite common in nature. These appear to be real cycles, but over time they get larger, or get smaller, or disappear altogether, only to be replaced by some other pseudo cycle.
• The fact that four datasets all show say a ~ 2,500-year cycle does not mean that the cycles are in phase.
• Using “stacked” datasets can easily create artifacts through both constructive and destructive interference.
• Using two basically identical datasets in a “stack” of four datasets will overweight that data, leading to incorrect conclusions.
• Humans are very good at detecting patterns and cycles, even where none exist. For example, almost all cultures see “constellations” in random groupings of stars. I hold that this is a result of using our eyes to find predators—there is no penalty for seeing a pattern of stripes that is not there, but there is a huge penalty for not noticing the pattern of stripes that is a tiger. And as a result, we tend to see patterns everywhere, including cycles in natural climate datasets, even though they may not exist at all.
• This implies that all such claims of cycles in natural climate datasets need to be investigated very, very carefully. For example, if you are using a periodogram or doing a Fourier analysis, at a minimum it is imperative to divide the dataset in two and see if the claimed cycle exists in both halves. Or, as I have done, you can use a CEEMD analysis to investigate the nature and changes in the cycle visually. However, I see experts all the time do one Fourier analysis on a full dataset and declare victory …
My best wishes to you for all the good things—laughing with your family, walking in the rain, sunlight far-reaching on the sea, gentle breezes …
w.
MY USUAL REQUEST: Please, when you comment, QUOTE THE EXACT WORDS YOU ARE DISCUSSING so that we can all understand who and what you are talking about. In addition, it’s not possible to refute someone’s claim unless you quote it first. Note that while this request is polite, I am likely to get grumpy and say inappropriate things about your ancestry and personal habits if you repeatedly refuse to identify what you’re talking about.
In support of that, I’ve posted this graphic before, and I’ll post it again. Please structure your comments to keep them up near the top of the pyramid.
The graphic is based on How to Disagree by Paul Graham, which is well worth reading.
One thing I’d like to highlight is that in the linked article the author says (emphasis mine):
DH5. Refutation.
The most convincing form of disagreement is refutation. It’s also the rarest, because it’s the most work. Indeed, the disagreement hierarchy forms a kind of pyramid, in the sense that the higher you go the fewer instances you find.
To refute someone you probably have to quote them. You have to find a “smoking gun,” a passage in whatever you disagree with that you feel is mistaken, and then explain why it’s mistaken. If you can’t find an actual quote to disagree with, you may be arguing with a straw man.
I saw the graph titled “Empirical Mode C5 Four Bond Ice Rafting Datasets”, and so I did my own overlay of all of the empirical modes. One thing I saw is that the two glass ones are practically identical and that it could be useful to combine them into one dataset. Another thing I saw is that C3 lined up well in all four datasets for most of the past 5,000 years, impressively well for nearly 7.5 cycles, and C4 lined up impressively well for the past nearly 6,000 years or 5 cycles. For that matter, C4 lines up well through the past nearly 9,000 years or nearly 9 cycles in all four datasets, except for the hematite dataset missing one positive peak around 6500 years ago. I see this as some evidence that a periodic item in C4 with a period close to 1,000 years is for real.
As for 9,000 to 12,000 years ago, it appears to me that the ~1,000 year cycle is shifted from C4 to C3 for the glass and hematite datasets, so it mostly exists in all datasets for the full 12,000 years with the main exception being the hematite dataset missing one positive peak. I wonder if this is related to C5 having phase disagreement in the datasets around and before 7,000 years ago, with either C3 or C4 being temporarily or intermittently a harmonic of C5. If the fundamental waveform of the solar cycles is not a sinusoid but a distorted one with faster risetime and slower falltime as is the case with the 11-year cycle, then I think CEEMD being modified to consider this could make it more clearly separate and identify any actual longer period solar cycles. Another thing I noticed is that the carbonate dataset has an irregularity a little over 9,000 years ago that is mostly in C1 and C3 and the C3 component of this irregularity just happened to be pretty much in phase with the ~1,000 year cycle, so I wonder if the ~1,000 year cycle itself got temporarily misidentified as something else because of this nonperiodic irregularity.
Something else I noticed: The squiggle in C1 around 3,000 years ago shows up in all of the datasets. That was something that held up well as periodic for about 1.5 cycles or a little more with agreement in all of the datasets, but is obviously not an ongoing oscillation.
One more thing: The ~11-year solar cycle is an obvious ongoing oscillation that does not have steady frequency or amplitude, and even looked close to nonexistent in the sunspot record during the Maunder Minimum. Any longer period cycles modulates the ~11-year cycle, and I wonder if CEEMD has trouble distinguishing harmonics and/or modulation of one cycle by another.
You could do the world a favor by studying the AMO cycles with modern data combined with USGS drill core data from coral reefs. We need some answers and not modeler simplifications with averages.
We need to decide why we are doing so much of this expensive research.
We need to set objectives that are more important than satisfaction of intellectual curiosity.
How important are cycles to our present well being and quality of life?
I propose them as irrelevant. Geoff
You could do the world a favor by studying the AMO cycles with modern data combined with USGS drill core data from coral reefs. We need some answers and not modeler simplifications with averages.
You could do the world a favor by providing links to the “AMO cycles with modern data” and the “USGS drill core data” you’re babbling about. I’m happy to look at most anything, I’m a curious guy, but I’m not going to try to guess what the heck it is you are referring to. I don’t go on a snipe hunt for any man … or woman, if that’s what you are, don’t want to make sexist assumptions …
Finally … what do you expect to find? That temperatures in the AMO are somehow related to temperature proxies in the drill core data? And if they are … so what? What new insights do you think it will provide?
w.
I have 2 comments that are unrelated so will treat them separately.
Although I appreciate that this post is of scientific interest, is it relevant to ongoing CAGW debate? The cycles being discussed appear to be over periods long enough that we might not observe them over the 30 year period from 1989 to present.
Thanks, pmh. It is relevant to the ongoing debate because the underlying paper is a good example of the kind of sketchy science that goes on in the field. As I said, it is a cautionary tale to encourage people to be skeptical, not only of alarmist claims, but even more so of claims that agree with our preconceptions.
w.
I much appreciate the time, dedication, and sacrifice Mr. Watts has made with this blog. I have nothing original to contribute and have learned much. My problem is that if my comments/questions are not in the first 12 hrs (or so) from when the post appears, everyone has moved on the to the next post and subsequent comments/questions are either ignored or lost. Not having spent my life in this field, what is lost to me is the educational aspect. But, perhaps that is not one of the purposes of the blog. In any event Wattsupwiththat is still the go-to blog on climate related issues and I offer my thanks and appreciation.
Not true for comments on my posts. I subscribe to each of them so I get an email whenever someone comments. I reply to as many of them as seem relevant.
w.
Frank
March 15, 2018 3:54 pm
Thanks for doing this analysis, Willis. Very educational. Especially some of the comments on anonymity.
Quasi-periodic data that breaks down over time may be due to earth dynamics interfering with more regular solar events. The Pleistocene Ice Age began when continents assumed their modern placement and caused major changes in ocean currents and atmospheric circulation.
Milankovic Cycles were highly likely to have been active before this time but to smaller effect, perhaps causing a globally moderate cooling. The much more disruptive Pleistocene Ice Age resulted from concentration of the cooling in the polar regions, particularly in the NH because of the concentration of land that inhibited distribution of heat by ocean currents.
Major events like collision of bolides with earth could also interrupt whatever “cycles” were in play. A giant one could probably end a glacial maximum and a Yellowstone grade volcanic blowup could bring one on early.
That quasi-cycles aren’t enduring shouldn’t discourage their investigation. They could still be quite useful for forecasting. An intelligent humanoid understanding Milankovic Cycles 2.5 mya would have had a good long run forecast going!
Today’s 60ish year cycle of warming and cooling seems to have arrived on schedule to give us the dreaded Pause and with it, given the great over estimation by CAGW proponents, support for the recent warming having had a substantial boost by the rising phase of this cycle. IIRC, someone in the early years of the new millennium predicted the cooling going forward. I myself cautioned about 5 years ago here on WUWT that instead of crowing about the hurricane drought, sceptics should pre-empt the certain exploitation of renewed major hurricane activity to come – a repeat of the busy 1950s hurricane cluster- by forecasting the return in a few years. By golly I went and predicted Harvey, Maria and friends on schedule, and, of course the doomsday crowd’s rejuvenation. IIRC, I threw in the ending of the Texas drought as a bonus. This cycle may end eventually but might be useful for a few centuries.
Another possibility I have never seen ruled out is a slowly decreasing sea level atmospheric pressure (SLAP). A slow secular decline in SLAP over millions of years would eventually make ice ages begin as the weakening warm attractor would allow the climate trajectory to veer toward Ice Age attractor under the Milakovitch INSOLATION cycling. Chaotic, but stochastic.
Thanks for the idea, Joel. I find this from Science magazine, which says the opposite … but who knows?
w.
Germonio
March 16, 2018 12:19 am
Willis, A couple of points – Firstly Fourier transforms do not get confused – if you want to reconstruct a signal as a sum of complex exponential then the coefficients you need are those you get from a Fourier transform anything else would not give the correct signal.
On the other hand Fourier transforms do not tell you what frequency components are present at which moment in time. For that you need to calculate the instanteous frequency. This is not what the empirical mode decomposition does although it is a step on the way. To do that you would need to take the Hilbert transform then get the analytic signal, calculate the phase and then take the derivative of the phase. Simply eyeballing the amplitude of empically calculated mode and claiming that it seems to grow or decay is like finding patterns in stars. It is just not good enough.
I am also slightly skeptical about the modes you show. I downloaded the data from the website ran it through two different programs to calculate the empirical mode decomposition and got very different results. Firstly they both found 9 modes not 6 and also the 2nd mode is very different. The issue is that the empirical mode decomposition is not unique and so different methods for calculating them will find different modes and also find different Fourier coefficients for each mode.
Willis, A couple of points – Firstly Fourier transforms do not get confused –
I didn’t say Fourier transforms get confused, that’s just some random fantasy of yours. QUOTE WHAT YOU ARE DISCUSSING!
– if you want to reconstruct a signal as a sum of complex exponential then the coefficients you need are those you get from a Fourier transform anything else would not give the correct signal.
I love folks like you who want to lecture people on things you don’t understand.
Fourier transforms are only one of a number of ways to completely decompose a signal. Periodicity transforms can do it. SubBandAnalysis can do it. PCA can do it. Tensor decomposition can do it. Low frequency PCA can do it. S-Transforms can do it. A Non-Uniform Filter Bank can do it. Wavelets can do it. Your idea that “anything else would not give the correct signal” is a joke.
And more to the current point, the “Complete” in Complete Ensemble Empirical Mode Analysis (CEEMD) means that unlike EEMD, it contains all of the information necessary to give what you call “the correct signal”. When you add up all the different empirical modes together (C1 through C6 plus the residual) you reconstruct the original signal perfectly.
So no, my friend, I fear you truly don’t grasp the underlying idea of decomposing signals into simpler signals. You’ll have to go lecture someone else. I’m not interested in being talked down to and patronized by you, that’s no fun at all.
Please address future comments to anyone but me, thanks.
w.
Willis,
You said that Fourier analyses get “fooled” I wrote confused. I am happy to go with fooled. But the same
point applies. Taking a Fourier transform of a sympony will tell you whether or not you need a piccolo player but not whether they can go home after the first five minutes. Fourier analysis tells you one particular thing – namely the amplitude of the complex exponential that you need to reconstruct the signal. Changing the amplitudes of those exponential will give you a different answer when you reconstruct the signal.
Of course you can write a signal as a sum of polynomials or any other set of orthogonal functions. Each
decomposition tells you different things about the signal. CEEMD does not tell you about what periods are
present – they do not give you a spectrogram. For that you still need to calculate the instanteous frequency
of each mode. Looking at it by eye is not good enough – the brain sees patterns everywhere as you have pointed out.
Germonio, was I truly that unclear in my last post? I’ll give it another shot.
Go away. Slope off. Not interested. You’re addressing the wrong man. Talk to the hand, the head ain’t listening. You’re too stupid to quote my words despite being asked to do so both here and in other threads. You tried to stuff words in my mouth. Disappear. Try your schtick on someone else. Go bother yer momma, she might not be able to see through you. You’ve burnt your bridges with me. I’ve been through this movie with you both here and elsewhere, not interested in re-runs.
You getting the picture?
w.
Germonio writes “Which level of the pyramid of refutation does your response fit with?”
Communication happens best, IMO, when participants speak similar languages and use similar styles. It really doesn’t work for one person to use formal language while the other uses vernacular. Being able to wrestle in the mud is at times a useful skill if that is where everyone happens to be.
I wonder about your choice of handle or online name; it could be a clever reference to the book Guns, Germs and Steel, about forces that civilized such places as are civilized, or it could be a misspelling of “Geronimo”.
i love how geronimo tells you how to do it.
then claims to have done it.
then….
doesnt show his work.
geronimo.
you cannot refute willis with words about methods.
you have to show your work.
numbers
data
code.
or no cookie.
Germonio writes “Firstly Fourier transforms do not get confused – if you want to reconstruct a signal as a sum of complex exponential”
Fourier transforms do not use exponentials; but rather sines and cosines harmonically related and in varying amplitudes.
Confusion in this case is “aliasing” or violation of the Nyquist Theorem.
Thank you for showing me the existence of Fourier Transform as an integral; I now agree it contains an exponential (or it can do so as one representation). I have used Fourier Transform as shown as figure 1 of https://en.wikipedia.org/wiki/Discrete_Fourier_transform which is a way to actually implement DFT in a computer using sines and cosines.
While I’ve known a relationship exists between “e” and sine and cosine, until today I haven’t focused my attention on that interesting phenomenon.
From wikipedia:
Euler’s formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler’s formula states that for any real number x
e^( i x) = cos x + i sin x https://en.wikipedia.org/wiki/Euler%27s_formula
Willis – love your work – just wondering, however:
Would you consider some day looking into the “sudden stratospheric warming events”? We just had one, as you’re undoubtedly aware, and I think I noticed something that might be interesting:
During this latest event it stood out to me: Where the stratosphere warmed pressure at the surface increased, and where it cooled the pressure was lowered. Now I know you are interested in the tropical management of temperatures, so here’s the hook:
The lower stratosphere cooled in the tropics as the warming in the Northern hemisphere progressed. The response was immediate and fairly radical: Tropical SST rose under the cooling umbrella while Arctic SST cooled under the warming umbrella.
Now I think, that these phenomena can be seen as signs of suppressed/enhanced convective regimes governed by the lower stratospheric density/temperature – acting as a radiative filter where convective processes end at the tropopause. Essentially: back-radiation seem to be highly sensitive to density witch would make physical sense.
Interestingly these stratospheric warming events seem to have absented themselves prior to the major warming event of the late nineties during a period of high solar activity.
Dispensing with a fruitless debate whether cycles can be identified or not, we might make some headway into the mechanisms of short term temperature variation. I am convinced that you are the guy who could do that – would you? please…
Per
lloydr56
March 16, 2018 5:28 am
Speaking for myself, I have enjoyed and learned from both Javier and Willis over the years. As far as I know, Javier has done some great work on major Holocene events, and beyond that the Pleistocene, especially glaciation and de-glaciation. My sense as a lay person is that it is difficult to identify any one “external” factor that “caused” massive (to us) climatic changes, but there are three things that change with the earth in relation to the sun: axial tilt or obliquity, orbital precession, and eccentricity. There is reason to think that while any of these alone might have little effect, two (or more) together could have been the main drivers of significant climate change.
Willis, as far as I know, has focussed more on short-term solar changes, and whether they can be linked to short-term temperature or climate change. He keeps saying no, as he does in this post and comments. He teaches us to be skeptical about leaps from small amounts of data, which only speak clearly when they are treated in a specific way, to big picture explanations. If four smaller data sets do not support a conclusion, but support for the conclusion suddenly appears when you stack the data sets, there is still a problem with your conclusion. I enjoyed Javier’s recent work on the northern hemisphere cryosphere (not “the globe”); noticeable or significant temperature increase, low humidity/water vapour; ice loss. Judith Curry weighed in with soot/albedo. I can’t resist adding: no known harm so far to any living species, including homo sapiens.
The warmists have made big careers out of saying they have identified the one critical man-made factor that causes blah blah blah. There is a temptation to jump in and say something like “no you idiots; here is the one critical factor”; water vapour or sun or whatever. Maybe every “symptom” that is being discussed is quite complex (I won’t annoy Mosher by saying “part of a chaotic system”); maybe sea level, for example, is affected by additions of water from deep underground–small changes from year to year, but with a significant long-term effect, including a surprising stability as opposed to dramatic or frightening changes (Jim Steele on Curry’s site). One thing I like in Willis’s work is the reminder that the climate system, assuming that phrase even conveys much meaning, is remarkably stable, and short-term events that are quite dramatic from a human perspective generally come to an end with a return to a status quo we are used to. There is an overall resiliency in nature, and of course we are the species that can adapt to change better than any other. We are supposed to prove we are good people by saying “I believe climate change is real” (today’s profession of faith, without which persecution may be in order); the consensus doesn’t want us to say “I believe climate stability and resiliency are real.”
Anyway, keep up the good work.
William Astley
March 16, 2018 6:36 am
Willis, This is boring. What the heck are you trying to do? The rock crystals are from glacial advances in the middle of a interglacial period.
Did you forget about the ocean sediment analysis that you presented in this forum? (O16/O18 ratio in the shell of a marine animal that is deposited in the ocean sediment is analyzed to determine past surface temperatures.) The ocean surface temperature cools up to 10C, cyclically.
Do you know what a Bond event is? Have you heard of the super large Bond event that is called a Heinrich event?
Have you heard about the Younger Dryas (12,900 year abrupt cooling event) or the 8,200 year cooling event? The observations are real.
The glacial/interglacial cycle is real. It physically happened.
It is a fact, that there are periods of millions of years in the paleo record when atmospheric CO2 has been high and the planet is cold and vice versa. There is not even correlation of atmospheric CO2 levels and planetary temperature in the paleo record.
It is a fact that the planet’s climate changes cyclically both poles. It is a fact that after 30 years there is no mechanism, no physical explanation to explain the past cyclic climate change. http://www.agu.org/pubs/crossref/2003/2003GL017115.shtml
of abrupt climate change: A precise clock by Stefan Rahmstorf
Many paleoclimatic data reveal a approx. 1,500 year cyclicity of unknown origin. A crucial question is how stable and regular this cycle is. An analysis of the GISP2 ice core record from Greenland reveals that abrupt climate events appear to be paced by a 1,470-year cycle with a period that is probably stable to within a few percent; with 95% confidence the period is maintained to better than 12% over at least 23 cycles. This highly precise clock points to an origin outside the Earth system (William: Solar magnetic cycle changes cause the warming and cooling); oscillatory modes within the Earth system can be expected to be far more irregular in period.
Davis and Taylor: “Does the current global warming signal reflect a natural cycle”
…We found 342 natural warming events (NWEs) corresponding to this definition, distributed over the past 250,000 years …. …. The 342 NWEs contained in the Vostok ice core record are divided into low-rate warming events (LRWEs; < 0.74oC/century) and high rate warming events (HRWEs; ≥ 0.74oC /century) (Figure). … …. "Recent Antarctic Peninsula warming relative to Holocene climate and ice – shelf history" and authored by Robert Mulvaney and colleagues of the British Antarctic Survey ( Nature , 2012, doi:10.1038/nature11391),reports two recent natural warming cycles, one around 1500 AD and another around 400 AD, measured from isotope (deuterium) concentrations in ice cores bored adjacent to recent breaks in the ice shelf in northeast Antarctica. ….
then comes the question and the point of the article: why does the bond event sometimes just get supressed?
the Bond events are called Oescher Dansgaard events during glaciations and here you see how irregular they appear http://1.bp.blogspot.com/_tG8JCC_Tnp0/TK3hw4fmpOI/AAAAAAAAAFo/oJUYikI5zuQ/s1600/Pleistocene_Holocene.JPG
that’s also why they called it “events” not a cycle as they don’t appear like clockwork but they seem to appear in bundles
William Astley
March 16, 2018 8:24 am
Nothing has changed since Wally Breocker’s Model’s to the rescue paper.
Wally’s comment below comment is correct, that climate scientists do not have a first order idea (do not have a clue) what causes abrupt climate change such as the Younger Dryas or 8200 BP cooling event and almost no one can imagine the planet’s climate during the 100,000 year glacial phase.
Wally Broecker, GSA January, 1999
MODELS TO THE RESCUE?
But wouldn’t predictions based on conveyor shutdowns carried out in linked ocean-atmosphere climate models be more informative than analogies to past changes? I would contend that to date no model is up to the task. No one understands what is required to cool Greenland by 16 °C and the tropics by 4 ± 1 °C, to lower mountain snowlines by 900 m, to create an ice sheet covering much of North America, to reduce the atmosphere’s CO2 content by 30%, or to raise the dust rain in many parts of Earth by an order of magnitude. If these changes were not documented in the climate record, they would never enter the minds of the climate dynamics community.
Models that purportedly simulate glacial climates do so only because key boundary conditions are prescribed (the size and elevation of the ice sheets, sea ice extent, sea surface temperatures, atmospheric CO2 content, etc.). In addition, some of these models have sensitivities whose magnitude many would challenge. What the paleoclimatic record tells us is that Earth’s climate system is capable of from one mode of operation to another. These modes are self-sustaining and involve major differences in mean global temperature, in rainfall pattern, and in atmospheric dustiness.
In my estimation, we lack even a first order explanation as to how the various elements of the Earth system interact to generate these alternate modes.
Why the magnetic fields at the solar south(?) pole when the field switches polarity at the end of cycle!
That, and the big iron core, and large magnets that are waved around in the Suns magnetic field.
I believe we’ve discussed that the next solar cycles was strongly influenced by the residual magnetic field, I think at the south pole, when that field switches polarity.
Do I remember that correctly?
Lief your comment concerning a lack of physical evidence to solve the problems is incorrect.
There are piles and piles of independent physical evidence, in peer reviewed papers, to solve the problems.
The trick to solving the problems was following the different fields, pulling out the anomalies and paradoxes, organizing them, and then looking for possible solutions.
But what is the point in arguing without looking at the observations in question?
Up above, Andy May claimed that “the solar/climate connection investigation is just getting started”. I replied:
This whole area has been closely looked into since at least the early 1800s, when William Herschel wrongly claimed that sunspots affected wheat prices. As evidence of the effect of Hershel’s claims on the field, a search on Google Scholar for “sunspots and wheat prices” yields over 5,000 results, and a search for “sunspots and temperature” yields over 33,000 results … so no, the investigation is not “just getting started”, it’s been going on for two centuries.
Inspired by Andy’s comment, I thought I’d take a look at the wheat data. I went to the excellent UN Food and Agriculture Organization (FAO) dataset, and got the wheat yield for all countries for the years of record, 1961 – 2016. There are 85 countries which have complete records for all of those years. I looked to see the p-value of the correlations, using the method of Koutsoyiannis to adjust for autocorrelation.
The result? Out of the 85 countries with complete records of wheat yields, not one showed a p-value less than 0.05, the usual threshold in the climate field. Minimum p-value for the 85 countries is 0.16, far from significant. Nor do things get better when I look at the cross-correlation between sunspots and any country’s wheat yield.
So … once again I’ve looked for a connection between sunspots and a surface dataset, in this case wheat yield, and found nothing. And although as I’ve said many times this doesn’t prove anything, because you can’t prove a negative, it is one more in the increasingly long list of places that I’ve looked for such a connection and found nothing.
Best to you all,
w.
1sky1
March 17, 2018 3:21 pm
What I call “pseudocycles” are quite common in nature. These appear to be real cycles, but over time they get larger, or get smaller, or disappear altogether, only to be replaced by some other pseudo cycle.
Irregular natural cycles come in a great variety of bandwidths, which dictate the degree to which they resemble the behavior of strictly periodic cycles. That’s why power spectra (F. transforms of autocovariance functions) are used in serious signal analysis of random geophysical time-series. There are trade-offs to be made in such analysis between the confidence limits and the frequency-resolution of the spectral estimates.
While raw periodograms, such as employed here, are useful in analyzing strictly periodic time-series, they provide notoriously unreliable, asymptotically inconsistent estimates of the spectral density that characterizes the underlying random process. It’s a grave mistake to conclude on that basis that the natural oscillations are “pseudocycles,” as if their unpredictable irregularity makes them physically less real.
This is for Andy:
You have in recent posts expressed several misconceptions about TSI [PMOD in particular]. I don’t think you inventted those yourself, so I am interested in where you got them from.
I saw the graph titled “Empirical Mode C5 Four Bond Ice Rafting Datasets”, and so I did my own overlay of all of the empirical modes. One thing I saw is that the two glass ones are practically identical and that it could be useful to combine them into one dataset. Another thing I saw is that C3 lined up well in all four datasets for most of the past 5,000 years, impressively well for nearly 7.5 cycles, and C4 lined up impressively well for the past nearly 6,000 years or 5 cycles. For that matter, C4 lines up well through the past nearly 9,000 years or nearly 9 cycles in all four datasets, except for the hematite dataset missing one positive peak around 6500 years ago. I see this as some evidence that a periodic item in C4 with a period close to 1,000 years is for real.
As for 9,000 to 12,000 years ago, it appears to me that the ~1,000 year cycle is shifted from C4 to C3 for the glass and hematite datasets, so it mostly exists in all datasets for the full 12,000 years with the main exception being the hematite dataset missing one positive peak. I wonder if this is related to C5 having phase disagreement in the datasets around and before 7,000 years ago, with either C3 or C4 being temporarily or intermittently a harmonic of C5. If the fundamental waveform of the solar cycles is not a sinusoid but a distorted one with faster risetime and slower falltime as is the case with the 11-year cycle, then I think CEEMD being modified to consider this could make it more clearly separate and identify any actual longer period solar cycles. Another thing I noticed is that the carbonate dataset has an irregularity a little over 9,000 years ago that is mostly in C1 and C3 and the C3 component of this irregularity just happened to be pretty much in phase with the ~1,000 year cycle, so I wonder if the ~1,000 year cycle itself got temporarily misidentified as something else because of this nonperiodic irregularity.
Something else I noticed: The squiggle in C1 around 3,000 years ago shows up in all of the datasets. That was something that held up well as periodic for about 1.5 cycles or a little more with agreement in all of the datasets, but is obviously not an ongoing oscillation.
One more thing: The ~11-year solar cycle is an obvious ongoing oscillation that does not have steady frequency or amplitude, and even looked close to nonexistent in the sunspot record during the Maunder Minimum. Any longer period cycles modulates the ~11-year cycle, and I wonder if CEEMD has trouble distinguishing harmonics and/or modulation of one cycle by another.
I immediately thought of this:
Penguin In Bondage
https://youtu.be/FWqWI5diKPA
You could do the world a favor by studying the AMO cycles with modern data combined with USGS drill core data from coral reefs. We need some answers and not modeler simplifications with averages.
resource guy.
looking at data requires models.
typically statistical models.
We need to decide why we are doing so much of this expensive research.
We need to set objectives that are more important than satisfaction of intellectual curiosity.
How important are cycles to our present well being and quality of life?
I propose them as irrelevant. Geoff
ResourceGuy March 15, 2018 at 12:53 pm
You could do the world a favor by providing links to the “AMO cycles with modern data” and the “USGS drill core data” you’re babbling about. I’m happy to look at most anything, I’m a curious guy, but I’m not going to try to guess what the heck it is you are referring to. I don’t go on a snipe hunt for any man … or woman, if that’s what you are, don’t want to make sexist assumptions …
Finally … what do you expect to find? That temperatures in the AMO are somehow related to temperature proxies in the drill core data? And if they are … so what? What new insights do you think it will provide?
w.
I have 2 comments that are unrelated so will treat them separately.
Although I appreciate that this post is of scientific interest, is it relevant to ongoing CAGW debate? The cycles being discussed appear to be over periods long enough that we might not observe them over the 30 year period from 1989 to present.
Thanks, pmh. It is relevant to the ongoing debate because the underlying paper is a good example of the kind of sketchy science that goes on in the field. As I said, it is a cautionary tale to encourage people to be skeptical, not only of alarmist claims, but even more so of claims that agree with our preconceptions.
w.
I much appreciate the time, dedication, and sacrifice Mr. Watts has made with this blog. I have nothing original to contribute and have learned much. My problem is that if my comments/questions are not in the first 12 hrs (or so) from when the post appears, everyone has moved on the to the next post and subsequent comments/questions are either ignored or lost. Not having spent my life in this field, what is lost to me is the educational aspect. But, perhaps that is not one of the purposes of the blog. In any event Wattsupwiththat is still the go-to blog on climate related issues and I offer my thanks and appreciation.
Not true for comments on my posts. I subscribe to each of them so I get an email whenever someone comments. I reply to as many of them as seem relevant.
w.
Thanks for doing this analysis, Willis. Very educational. Especially some of the comments on anonymity.
Quasi-periodic data that breaks down over time may be due to earth dynamics interfering with more regular solar events. The Pleistocene Ice Age began when continents assumed their modern placement and caused major changes in ocean currents and atmospheric circulation.
Milankovic Cycles were highly likely to have been active before this time but to smaller effect, perhaps causing a globally moderate cooling. The much more disruptive Pleistocene Ice Age resulted from concentration of the cooling in the polar regions, particularly in the NH because of the concentration of land that inhibited distribution of heat by ocean currents.
Major events like collision of bolides with earth could also interrupt whatever “cycles” were in play. A giant one could probably end a glacial maximum and a Yellowstone grade volcanic blowup could bring one on early.
That quasi-cycles aren’t enduring shouldn’t discourage their investigation. They could still be quite useful for forecasting. An intelligent humanoid understanding Milankovic Cycles 2.5 mya would have had a good long run forecast going!
Today’s 60ish year cycle of warming and cooling seems to have arrived on schedule to give us the dreaded Pause and with it, given the great over estimation by CAGW proponents, support for the recent warming having had a substantial boost by the rising phase of this cycle. IIRC, someone in the early years of the new millennium predicted the cooling going forward. I myself cautioned about 5 years ago here on WUWT that instead of crowing about the hurricane drought, sceptics should pre-empt the certain exploitation of renewed major hurricane activity to come – a repeat of the busy 1950s hurricane cluster- by forecasting the return in a few years. By golly I went and predicted Harvey, Maria and friends on schedule, and, of course the doomsday crowd’s rejuvenation. IIRC, I threw in the ending of the Texas drought as a bonus. This cycle may end eventually but might be useful for a few centuries.
Another possibility I have never seen ruled out is a slowly decreasing sea level atmospheric pressure (SLAP). A slow secular decline in SLAP over millions of years would eventually make ice ages begin as the weakening warm attractor would allow the climate trajectory to veer toward Ice Age attractor under the Milakovitch INSOLATION cycling. Chaotic, but stochastic.
Thanks for the idea, Joel. I find this from Science magazine, which says the opposite … but who knows?
w.
Willis, A couple of points – Firstly Fourier transforms do not get confused – if you want to reconstruct a signal as a sum of complex exponential then the coefficients you need are those you get from a Fourier transform anything else would not give the correct signal.
On the other hand Fourier transforms do not tell you what frequency components are present at which moment in time. For that you need to calculate the instanteous frequency. This is not what the empirical mode decomposition does although it is a step on the way. To do that you would need to take the Hilbert transform then get the analytic signal, calculate the phase and then take the derivative of the phase. Simply eyeballing the amplitude of empically calculated mode and claiming that it seems to grow or decay is like finding patterns in stars. It is just not good enough.
I am also slightly skeptical about the modes you show. I downloaded the data from the website ran it through two different programs to calculate the empirical mode decomposition and got very different results. Firstly they both found 9 modes not 6 and also the 2nd mode is very different. The issue is that the empirical mode decomposition is not unique and so different methods for calculating them will find different modes and also find different Fourier coefficients for each mode.
Germonio March 16, 2018 at 12:19 am Edit
I didn’t say Fourier transforms get confused, that’s just some random fantasy of yours. QUOTE WHAT YOU ARE DISCUSSING!
I love folks like you who want to lecture people on things you don’t understand.
Fourier transforms are only one of a number of ways to completely decompose a signal. Periodicity transforms can do it. SubBandAnalysis can do it. PCA can do it. Tensor decomposition can do it. Low frequency PCA can do it. S-Transforms can do it. A Non-Uniform Filter Bank can do it. Wavelets can do it. Your idea that “anything else would not give the correct signal” is a joke.
And more to the current point, the “Complete” in Complete Ensemble Empirical Mode Analysis (CEEMD) means that unlike EEMD, it contains all of the information necessary to give what you call “the correct signal”. When you add up all the different empirical modes together (C1 through C6 plus the residual) you reconstruct the original signal perfectly.
So no, my friend, I fear you truly don’t grasp the underlying idea of decomposing signals into simpler signals. You’ll have to go lecture someone else. I’m not interested in being talked down to and patronized by you, that’s no fun at all.
Please address future comments to anyone but me, thanks.
w.
Willis,
You said that Fourier analyses get “fooled” I wrote confused. I am happy to go with fooled. But the same
point applies. Taking a Fourier transform of a sympony will tell you whether or not you need a piccolo player but not whether they can go home after the first five minutes. Fourier analysis tells you one particular thing – namely the amplitude of the complex exponential that you need to reconstruct the signal. Changing the amplitudes of those exponential will give you a different answer when you reconstruct the signal.
Of course you can write a signal as a sum of polynomials or any other set of orthogonal functions. Each
decomposition tells you different things about the signal. CEEMD does not tell you about what periods are
present – they do not give you a spectrogram. For that you still need to calculate the instanteous frequency
of each mode. Looking at it by eye is not good enough – the brain sees patterns everywhere as you have pointed out.
Germonio, was I truly that unclear in my last post? I’ll give it another shot.
Go away. Slope off. Not interested. You’re addressing the wrong man. Talk to the hand, the head ain’t listening. You’re too stupid to quote my words despite being asked to do so both here and in other threads. You tried to stuff words in my mouth. Disappear. Try your schtick on someone else. Go bother yer momma, she might not be able to see through you. You’ve burnt your bridges with me. I’ve been through this movie with you both here and elsewhere, not interested in re-runs.
You getting the picture?
w.
Hi Willis,
Which level of the pyramid of refutation does your response fit with? Name calling i.e. “too stupid”
or something lower?
Germonio writes “Which level of the pyramid of refutation does your response fit with?”
Communication happens best, IMO, when participants speak similar languages and use similar styles. It really doesn’t work for one person to use formal language while the other uses vernacular. Being able to wrestle in the mud is at times a useful skill if that is where everyone happens to be.
I wonder about your choice of handle or online name; it could be a clever reference to the book Guns, Germs and Steel, about forces that civilized such places as are civilized, or it could be a misspelling of “Geronimo”.
i love how geronimo tells you how to do it.
then claims to have done it.
then….
doesnt show his work.
geronimo.
you cannot refute willis with words about methods.
you have to show your work.
numbers
data
code.
or no cookie.
Germonio writes “Firstly Fourier transforms do not get confused – if you want to reconstruct a signal as a sum of complex exponential”
Fourier transforms do not use exponentials; but rather sines and cosines harmonically related and in varying amplitudes.
Confusion in this case is “aliasing” or violation of the Nyquist Theorem.
Michael you are wrong when you say: “Fourier transforms do not use exponentials”
..
Here is the definition of a Fourier transform: https://wikimedia.org/api/rest_v1/media/math/render/svg/97ad0938a279c4846d42a4bbd212f6a1f0ca4c0f
…
That little “e” in the formula is an exponential.
Thank you for showing me the existence of Fourier Transform as an integral; I now agree it contains an exponential (or it can do so as one representation). I have used Fourier Transform as shown as figure 1 of https://en.wikipedia.org/wiki/Discrete_Fourier_transform which is a way to actually implement DFT in a computer using sines and cosines.
While I’ve known a relationship exists between “e” and sine and cosine, until today I haven’t focused my attention on that interesting phenomenon.
From wikipedia:
Euler’s formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler’s formula states that for any real number x
e^( i x) = cos x + i sin x
https://en.wikipedia.org/wiki/Euler%27s_formula
Willis – love your work – just wondering, however:
Would you consider some day looking into the “sudden stratospheric warming events”? We just had one, as you’re undoubtedly aware, and I think I noticed something that might be interesting:
During this latest event it stood out to me: Where the stratosphere warmed pressure at the surface increased, and where it cooled the pressure was lowered. Now I know you are interested in the tropical management of temperatures, so here’s the hook:
The lower stratosphere cooled in the tropics as the warming in the Northern hemisphere progressed. The response was immediate and fairly radical: Tropical SST rose under the cooling umbrella while Arctic SST cooled under the warming umbrella.
Now I think, that these phenomena can be seen as signs of suppressed/enhanced convective regimes governed by the lower stratospheric density/temperature – acting as a radiative filter where convective processes end at the tropopause. Essentially: back-radiation seem to be highly sensitive to density witch would make physical sense.
Interestingly these stratospheric warming events seem to have absented themselves prior to the major warming event of the late nineties during a period of high solar activity.
Dispensing with a fruitless debate whether cycles can be identified or not, we might make some headway into the mechanisms of short term temperature variation. I am convinced that you are the guy who could do that – would you? please…
Per
Speaking for myself, I have enjoyed and learned from both Javier and Willis over the years. As far as I know, Javier has done some great work on major Holocene events, and beyond that the Pleistocene, especially glaciation and de-glaciation. My sense as a lay person is that it is difficult to identify any one “external” factor that “caused” massive (to us) climatic changes, but there are three things that change with the earth in relation to the sun: axial tilt or obliquity, orbital precession, and eccentricity. There is reason to think that while any of these alone might have little effect, two (or more) together could have been the main drivers of significant climate change.
Willis, as far as I know, has focussed more on short-term solar changes, and whether they can be linked to short-term temperature or climate change. He keeps saying no, as he does in this post and comments. He teaches us to be skeptical about leaps from small amounts of data, which only speak clearly when they are treated in a specific way, to big picture explanations. If four smaller data sets do not support a conclusion, but support for the conclusion suddenly appears when you stack the data sets, there is still a problem with your conclusion. I enjoyed Javier’s recent work on the northern hemisphere cryosphere (not “the globe”); noticeable or significant temperature increase, low humidity/water vapour; ice loss. Judith Curry weighed in with soot/albedo. I can’t resist adding: no known harm so far to any living species, including homo sapiens.
The warmists have made big careers out of saying they have identified the one critical man-made factor that causes blah blah blah. There is a temptation to jump in and say something like “no you idiots; here is the one critical factor”; water vapour or sun or whatever. Maybe every “symptom” that is being discussed is quite complex (I won’t annoy Mosher by saying “part of a chaotic system”); maybe sea level, for example, is affected by additions of water from deep underground–small changes from year to year, but with a significant long-term effect, including a surprising stability as opposed to dramatic or frightening changes (Jim Steele on Curry’s site). One thing I like in Willis’s work is the reminder that the climate system, assuming that phrase even conveys much meaning, is remarkably stable, and short-term events that are quite dramatic from a human perspective generally come to an end with a return to a status quo we are used to. There is an overall resiliency in nature, and of course we are the species that can adapt to change better than any other. We are supposed to prove we are good people by saying “I believe climate change is real” (today’s profession of faith, without which persecution may be in order); the consensus doesn’t want us to say “I believe climate stability and resiliency are real.”
Anyway, keep up the good work.
Willis, This is boring. What the heck are you trying to do? The rock crystals are from glacial advances in the middle of a interglacial period.
Did you forget about the ocean sediment analysis that you presented in this forum? (O16/O18 ratio in the shell of a marine animal that is deposited in the ocean sediment is analyzed to determine past surface temperatures.) The ocean surface temperature cools up to 10C, cyclically.
Do you know what a Bond event is? Have you heard of the super large Bond event that is called a Heinrich event?
Have you heard about the Younger Dryas (12,900 year abrupt cooling event) or the 8,200 year cooling event? The observations are real.
The glacial/interglacial cycle is real. It physically happened.
It is a fact, that there are periods of millions of years in the paleo record when atmospheric CO2 has been high and the planet is cold and vice versa. There is not even correlation of atmospheric CO2 levels and planetary temperature in the paleo record.
It is a fact that the planet’s climate changes cyclically both poles. It is a fact that after 30 years there is no mechanism, no physical explanation to explain the past cyclic climate change.
http://www.agu.org/pubs/crossref/2003/2003GL017115.shtml
Greenland ice temperature, last 11,000 years determined from ice core analysis, Richard Alley’s paper. William: As this graph indicates the Greenland Ice data shows that have been 9 warming and cooling periods in the last 11,000 years.
http://www.climate4you.com/images/GISP2%20TemperatureSince10700%20BP%20with%20CO2%20from%20EPICA%20DomeC.gif
http://wattsupwiththat.files.wordpress.com/2012/09/davis-and-taylor-wuwt-submission.pdf
then comes the question and the point of the article: why does the bond event sometimes just get supressed?
the Bond events are called Oescher Dansgaard events during glaciations and here you see how irregular they appear
http://1.bp.blogspot.com/_tG8JCC_Tnp0/TK3hw4fmpOI/AAAAAAAAAFo/oJUYikI5zuQ/s1600/Pleistocene_Holocene.JPG
that’s also why they called it “events” not a cycle as they don’t appear like clockwork but they seem to appear in bundles
Nothing has changed since Wally Breocker’s Model’s to the rescue paper.
Wally’s comment below comment is correct, that climate scientists do not have a first order idea (do not have a clue) what causes abrupt climate change such as the Younger Dryas or 8200 BP cooling event and almost no one can imagine the planet’s climate during the 100,000 year glacial phase.
Wally it is the sun.
Wally it is the sun.
You have no evidence for that. And what made the Sun vary. The sun is a million+ times bigger than the Earth.
Why the magnetic fields at the solar south(?) pole when the field switches polarity at the end of cycle!
That, and the big iron core, and large magnets that are waved around in the Suns magnetic field.
I would like to respond, but your comments make no sense. Try again.
I believe we’ve discussed that the next solar cycles was strongly influenced by the residual magnetic field, I think at the south pole, when that field switches polarity.
Do I remember that correctly?
I am not sure what you are hinted at. You may find your answer here:
http://www.leif.org/research/Super-Synoptic-Maps-and-Polar-Fields.pdf
Lief your comment concerning a lack of physical evidence to solve the problems is incorrect.
There are piles and piles of independent physical evidence, in peer reviewed papers, to solve the problems.
The trick to solving the problems was following the different fields, pulling out the anomalies and paradoxes, organizing them, and then looking for possible solutions.
But what is the point in arguing without looking at the observations in question?
Up above, Andy May claimed that “the solar/climate connection investigation is just getting started”. I replied:
Inspired by Andy’s comment, I thought I’d take a look at the wheat data. I went to the excellent UN Food and Agriculture Organization (FAO) dataset, and got the wheat yield for all countries for the years of record, 1961 – 2016. There are 85 countries which have complete records for all of those years. I looked to see the p-value of the correlations, using the method of Koutsoyiannis to adjust for autocorrelation.
The result? Out of the 85 countries with complete records of wheat yields, not one showed a p-value less than 0.05, the usual threshold in the climate field. Minimum p-value for the 85 countries is 0.16, far from significant. Nor do things get better when I look at the cross-correlation between sunspots and any country’s wheat yield.
So … once again I’ve looked for a connection between sunspots and a surface dataset, in this case wheat yield, and found nothing. And although as I’ve said many times this doesn’t prove anything, because you can’t prove a negative, it is one more in the increasingly long list of places that I’ve looked for such a connection and found nothing.
Best to you all,
w.
Irregular natural cycles come in a great variety of bandwidths, which dictate the degree to which they resemble the behavior of strictly periodic cycles. That’s why power spectra (F. transforms of autocovariance functions) are used in serious signal analysis of random geophysical time-series. There are trade-offs to be made in such analysis between the confidence limits and the frequency-resolution of the spectral estimates.
While raw periodograms, such as employed here, are useful in analyzing strictly periodic time-series, they provide notoriously unreliable, asymptotically inconsistent estimates of the spectral density that characterizes the underlying random process. It’s a grave mistake to conclude on that basis that the natural oscillations are “pseudocycles,” as if their unpredictable irregularity makes them physically less real.
This is for Andy:
You have in recent posts expressed several misconceptions about TSI [PMOD in particular]. I don’t think you inventted those yourself, so I am interested in where you got them from.