Guest Post by Willis Eschenbach
I hear a lot of folks give the following explanation for the vagaries of the climate, viz:
It’s the sun, stupid.
And in fact, when I first started looking at the climate I thought the very same thing. How could it not be the sun, I reasoned, since obviously that’s what heats the planet.
Unfortunately, the dang facts got in the way again …
Chief among the dang facts is that despite looking in a whole lot of places, I never could find any trace of the 11-year sunspot cycle in any climate records. And believe me, I’ve looked.
You see, I reasoned that no matter whether the mechanism making the sun-climate connection were direct variations in the brightness of the sun, or variations in magnetic fields, or variations in UV, or variations in cosmic rays, or variations in the solar wind, they all run in synchronicity with the sunspots. So no matter the mechanism, it would have a visible ~11-year heartbeat.
I’ve looked for that 11-year rhythm every place I could think of—surface temperature records, sea level records, lake level records, wheat price records, tropospheric temperature records, river flow records. Eventually, I wrote up some of these findings, and I invited readers to point out some record, any record, in which the ~ 11-year sunspot cycle could be seen.
Nothing.
However, I’m a patient man, and to this day, I continue to look for the 11-year cycle. You can’t prove a negative … but you can amass evidence. My latest foray is into the world of atmospheric pressure. I figured that the atmospheric pressure might be more sensitive to variations in something like say the solar wind than the temperature would be.
Let me start, however, by taking a look at the elusive creature at the heart of this quest, the ~11-year sunspot cycle. Here is the periodogram of that cycle, so that we know what kind of signature we’re looking for:
Figure 1. Periodogram, showing the strengths of the various-length cycles in the SIDC sunspot data. In order to be able to compare disparate datasets, the values of the cycles are expressed as a percentage of the total range of the underlying data.
As you’d expect, the main peak is at around 11 years. However, the sunspot cycles are not regular, so we also have smaller peaks at nearby cycle lengths. Figure 2 shows an expanded view of the central part of Figure 1, showing only the range from seven to twenty-five years:
Figure 2. The same periodogram as in Figure 1, but showing only the 7 – 25 year range.
Now, there is a temptation to see the central figure as some kind of regular amplitude-modulated signal, with side-lobes. However, that’s not what’s happening here. There is no regular signal. Instead of there being a regular cycle, the length of the sunspot cycle varies widely, from about nine to about 15 years, with most of them in the 10-12 year range. The periodogram is merely showing that variation in cycle length.
In any case, that’s what we’re looking for—some kind of strong signal, with its peak value in the range of about 10-12 years.
As I mentioned above, when I started looking at the climate, like many people I thought “It’s the sun, stupid”, but I had found no data to back that up. So what did I find in my latest search? Well, sweet Fannie Adams, as our cousins across the pond say … here are my results:
Figure 3. Periodograms of four long-term atmospheric pressure records from around the globe.
There are some interesting features of these records.
First, there is a very strong annual cycle. I expected annual cycles, but not ones that large. These cycles are 30% to 60% of the total range of the data. I assume they result in large part from the prevalence of low-pressure areas associated with storms in the local wintertime, combined with some effect from the variations in temperature. I also note that as expected, Tahiti, being nearest to the equator and with little in the way of either temperature variations or low-pressure storms, has the smallest one-year cycle.
Other than semi-annual and annual cycles, however, there is very little power in the other cycle lengths. Figure 4 shows the expanded version of the same data, from seven to twenty-five years. Note the change in scale.
Figure 4. Periodograms of four long-term atmospheric pressure records from around the globe.
First, note that unlike the size of the annual cycle, which is half the total swing in pressures, none of these cycles have more than about 4% of the total swing of the atmospheric pressure. These are tiny cycles.
Next, generally there is more power in the ~ 9-year and the ~ 13-14 year ranges than there is in the ~ 11-year cycles.
So … once again, I end up back where I started. I still haven’t found any climate datasets that show any traces of the 11-year sunspot cycles. They may be there in the pressure data, to be sure, it is impossible to prove a negative, I can’t say they’re not there … but if so, they are hiding way, way down in the weeds.
Which of course leads to the obvious question … why no sign of the 11-year solar cycles?
I hold that this shows that the temperature of the system is relatively insensitive to changes in forcing. This, of course, is rank heresy to the current scientific climate paradigm, which holds that ceteris paribus, changes in temperature are a linear function of changes in forcing. I disagree. I say that the temperature of the planet is set by a dynamic thermoregulatory system composed of emergent phenomena that only appear when the surface gets hotter than a certain temperature threshold. These emergent phenomena maintain the temperature of the globe within narrow bounds (e.g. ± 0.3°C over the 20th Century), despite changes in volcanoes, despite changes in aerosols, despite changes in GHGs, despite changes in forcing of all kinds. The regulatory system responds to temperature, not to forcing.
And I say that because of the existence of these thermoregulatory systems, the 11-year variations in the sun’s UV and magnetism and brightness, as well as the volcanic variations and other forcing variations … well, they make little difference.
As a result, once again, I open the Quest for the Holy 11-Year Grail to others. I invite those that believe that “It’s the sun, stupid” to show us the terrestrial climate record that has any sign of being correlated with the 11-year sunspot cycles. I’ve looked. Lots of folks have looked … where is that record? I encourage you to employ whatever methods you want to use to expose the connection—cross-correlation, wavelet analysis, spectrum analysis, fourier analysis, the world is your lobster. Report back your findings, I’d like to put this question to bed.
It’s a lovely Saturday in spring, what could be finer? Gotta get outside and study me some sunshine. I wish you all many such days.
w.
For Clarity: If you disagree with someone, please quote their exact words that you disagree with. It avoids all kinds of pernicious misunderstandings, because it lets us all know exactly where you think they went off the rails.
Why The 11-year Cycle?: Because it is the biggest cycle, and we know all of the other cycles (magnetism, TSI, solar wind) move in synchronicity with the sunspots. As a result, if you want to claim that the climate is responding to say a slow, smaller 100-year cycle in the sunspot data, then by the same token it must be responding more strongly to the larger 11-cycle in the sunspot data, and so the effect should be visible there.
The Subject Of This Post: Please do not mistake this quest for the elusive 11-year cycle in climate datasets as an opportunity for you to propound your favorite theory about approximately 43-year pseudo-cycles due to the opposition of Uranus. If you can’t show me a climate dataset containing an 11-year cycle, your hypothesis is totally off-topic for this post. I encourage you to write it up and send it to Anthony, he may publish it, or to Tallbloke, he might also. I encourage everyone to get their ideas out there. Here on this thread, though, I’m looking for the 11-year cycle sunspot cycle in any terrestrial climate records.
The Common Cycles in Figures 3 and 4: Obviously, the four records in Figs. 3 & 4 have a common one-year cycle. As an indication of the sensitivity of the method that I’m using, consider the two other peaks which are common to all four of the records. These are the six-month cycle, and the 9-year cycle. It is well known that the moon raises tides in the atmosphere just as it does in the ocean. The 9-year periodicity is not uncommon in tidal datasets, and the same is true about the 6-month periodicity. I would say that we’re looking at the signature of the atmospheric tides in those cycle lengths.
Variable-Length Cycles, AKA “Pseudocycles” or “Approximate Cycles”: Some commenters in the past have asserted that my method, which I’ve nicknamed “Slow Fourier Analysis” but which actually seems to be a variant of what might be called direct spectrum analysis, is incapable of detecting variable-length cycles. They talk about a cycle say around sixty years that changes period over time.
However, the sunspot cycle is also quite variable in length … and despite that my method not only picks up the most common cycle length, it shows the strength of the sunspot cycles at the other cycle lengths as well.
A Couple of my Previous Searches for the 11-Year Sunspot Cycle:
Looking at four long-term temperature records here.
A previous look at four more long-term temperature records.
Atmospheric Pressure and Sunspot Data:
Tahiti to 1950 and Tahiti 1951 on (note different units)
Darwin to 1950 and Darwin 1951 on (note different units)
Sunspots These are from SIDC. Note that per advice from Leif Svalgaard, in the work I did above the pre-1947 values have been increased by 20% to adjust for the change in counting methods. It does not affect this analysis, you can use either one.
For ease of downloading, I’ve also made up a CSV file containing all of the above data, called Long Term Atmospheric Pressure.csv
And for R users, I’ve saved all 5 data files in R format as “Long Pressure Datasets.tab”
Code: Man, I hate this part … hang on … let me clean it up a bit … OK, I just whacked out piles of useless stuff and ran it in an empty workspace and it seemed to fly. You need two things, a file called madras pressure.R and my Slow Fourier Transform Functions.R. Let me know what doesn’t work.
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RACookPE1978 : By eye (which may or may not be an effective tool!) it is not a 11-year simple cycle beat, but a pattern of 3 cycles high, 3 cycles lower, 3 cycles higher, 3 cycles lower of sunspot activity that repeats regularly.
There no 60 in the SPD . The data is 80y and I’m using window fn that flat for 80% and cosine tapers each end.
http://climategrog.wordpress.com/?attachment_id=949
However, having noted the quadrature, if I do it the other way in integrate SSN, everything rises and correlates with sizeable 30 and 60y peaks.
Bearing in mind the window fn and the data length you may get something of that with a straight line so don’t make too much of it. In short it’s +ve around zero lag and -ve at each end which makes for some kind of 60y component.
The most significant correlation is +0.2 at zero lag, so there is a definite direct correlation between the integral of SSN and SST in Tahiti.
[30/60 or 33/66? .mod]
From LT on May 27, 2014 at 6:23 am:
I quickly found out you have a problem.
While RSS goes from 1979, and PMOD TSI from just a few months before that, the SIDC SSN goes back much further, to 1749. From 1979 is barely three sunspot cycles, hardly enough.
So as a quick check, I switched to HADCRUT4 for surface temps, and set from:1850 (start of HADCRUT4) except TSI where I just took the from out.
It’s not pretty. The SSN highest peak is at 15, twice as high as the 1 peak. 11 is the low point before the sharp upturn to 15.
And for some reason HADCRUT4 shows not only the expected 1 (annual) peak, but a 3 peak which is easily 5x higher than any others.
Using your call-out without the normalize, SSN only, and from 1749 to 2014, the very big peak shifts to 24.
The 11-yr cycle is in the sunspot data. Yet by doing what you’re doing but adding more of the data, the location of the peak keep shifting to a larger period.
This strongly suggests what you are doing is wrong.
Here’s what SST and MAT look like for the 5×5 grid around Tahiti:
http://climategrog.wordpress.com/?attachment_id=953
What is notable is that there seems little justification for the post war meddling that the Met Office gets up to. Sure, there is an anomalous jump up in 1940 but if anything this seems to be bringing it back into line with MAT. If there was an “anomaly” it was BEFORE 1941.
There was an interesting treatment of the idea of integrating SSN, done in a more sophisticated way:
http://montpeliermonologs.wordpress.com/author/jpat34721/
http://montpeliermonologs.files.wordpress.com/2013/10/gregssag.png
I think he got bore or ran out of time, so it did not go as far as it could but the method was interesting.
From LT on May 27, 2014 at 8:59 am:
NO. SSN and HADCRUT4SH from 1850 still shows the peak shifted to 15-yrs, and nothing special happening to HADCRUT4SH.
From LT on May 27, 2014 at 12:13 pm:
DOUBTFUL. Going to 1900, start of the PDO dataset, SSN is still peaking at 11, and there is a PDO dip at 11. But there are many other more-severe drops, from 13 to 14 the PDO drops about twice as much, 20 to 21 is about 2.5x. Thus the significance of a possible solar connection look very small, and likely not significant at all.
And of course the cycle peak still shifts to 15 if the SSN data goes from 1850. I’m not aware of the Sun dramatically changing its cycles between 1850 and 1900, nor 1750 to 1850. So something is still wrong in your method.
From LT May 27, 2014 at 12:38 pm (now comparing with NH sea ice extent):
Large plate of Crow Quiche and an opportunity to try harder. Bon appetit!
Good heavens shawnhet, the fact that the ITCZ moves seasonally within the year is an intrinsic Earth factor! Hello!
“So something is still wrong in your method.”
I’m not surprised trying to use a tool like that to do it.
When I saw what an unintelligible mess the Fourier option was on WTF.org , I thought WTF ?!
That’s pretty typical. The only filter for years was the dreaded runny mean and super functions like “isolate” which subtracts the runny mean and tells what distortion you have left.
You cant even subtract two time series.
It’s not much good for anything beyond fitting linear models to data that has nothing linear about it.
That’s why I call it WTF.org , it’s not dyslexia, it’s like: WTF ??
kadaka, may 27,5:45pm…..really, not aware of cycles dramatically changing between 1750 to 1850….HELLO…what about SC4 to SC5, 18yrs from peak to peak!!Better save some of that Crow. And, oh yea, the earth experienced a cooling spell, but we all know it could absolutely not be the sun.
Gray et al 2013
A lagged response to the 11 year solar cycle in observed winter Atlantic/European weather patterns
[1] The surface response to 11 year solar cycle variations is investigated by analyzing the long-term mean sea level pressure and sea surface temperature observations for the period 1870–2010. The analysis reveals a statistically significant 11 year solar signal over Europe,[1] The surface response to 11 year solar cycle variations is investigated by analyzing the long-term mean sea level pressure and sea surface temperature observations for the period 1870–2010. The analysis reveals a statistically significant 11 year solar signal over Europe, and the North Atlantic provided that the data are lagged by a few years. and the North Atlantic provided that the data are lagged by a few years.
Pamela Gray says:
May 27, 2014 at 6:13 pm
“Good heavens shawnhet, the fact that the ITCZ moves seasonally within the year is an intrinsic Earth factor! Hello!”
Well, you’re half right. It is an Earth factor that changes *where and how solar energy hits the Earth*. As such, solar energy (distribution) effects where the ITCZ ends up. Hello?
Since we can now agree that solar energy changes can change the location of the ITCZ and that you have no response to the data that shows the ITCZ tracks solar proxies, I believe it is still game set and match to me.
I would hazard a guess than any and all of these lagged responses to an 11 year solar cycle could also be lagged to any other kind of event that is intrinsic to Earth. For example, one could back-track-lag temperature anomalies in Golf Stream coastal areas to an El Nino/La Nina series of events in the Pacific. Lagging seems to be the darling of all things solar. If you a looking for a solar signal, I am betting you will find it. Doesn’t mean your result is robust instead of spurious.
Shawnhet, you do no justice to your speculation when you move the cheese. The amount of solar energy that affects the Earth on a year to year basis is entirely an intrinsic factor. To hedge your bet on that one is silly.
Shawnhet, I have given you a well done study on intrinsic factors that affect the movement of the ITCZ that did not use solar variables in order to come to their conclusions. I believe this to be the superior hypothesis. The energy available to shift this zone around is clearly in intrinsic factors without the need of a yet to be discovered amplifying solar factor. I have postulated nothing else as you well know. To say in contrary to the written evidence that I now agree with you is a weak debating trick easily identified by debate judges and given low marks.
Kadaka,
I see what you mean, its impossible to know for sure what is going in the normalization of the FFT of different lengths with the woodfortrees software. It is intriguing enough for me to write a quick program to do the FFT. The satellite data should show the signal if it is there, particularly the stratosphere. I keep hearing little bits that 35 years is not enough data to see an 11 year cycle, and I know that is absolutely not true. I will write a program and see what I come up with. Willis’s program on the RSS shows a bump the is very close to the 11 year cycle, it looks encouraging to me. The Enso repsonse should have a complex periodicity that has side lobes that will interfere with the SSN cycle with only three cycle, but it still should show something. I know because I have used the sliding short window FFT many times to generate energy attenuation anomalie. The power spectrum will show energy of a partial sin wave, you just cannot filter it out without aliasing it, if you are using the FFT as a filtering operation.
Pamela Gray says:
“Shawnhet, you do no justice to your speculation when you move the cheese. The amount of solar energy that affects the Earth on a year to year basis is entirely an intrinsic factor. To hedge your bet on that one is silly.”
Look up the definition of intrinsic. The solar energy that hits the Earth is due to both extrinsic(the sun’s energy) and intrinsic(the shape of the Earth) factors.
“Shawnhet, I have given you a well done study on intrinsic factors that affect the movement of the ITCZ that did not use solar variables in order to come to their conclusions. I believe this to be the superior hypothesis. The energy available to shift this zone around is clearly in intrinsic factors without the need of a yet to be discovered amplifying solar factor. I have postulated nothing else as you well know. To say in contrary to the written evidence that I now agree with you is a weak debating trick easily identified by debate judges and given low marks.”
Unfortunately, for you, Pamela (and I mean this respectfully) your position is just not logical. Regardless of how well you think that the ENSO explains current, short term changes in the ITCZ (and I agree that it does so well), the ENSO cannot explain the long term(ie thousands of years) pattern of movements of the ITCZ. That is just a fact. Since a complete understanding of the climate needs to explain both short and long term changes in it, your theory is sadly lacking.
I was being a bit tricky in my language I suppose but clearly you are too. When you claim that the amount of solar energy that affects the Earth is (ie must be) intrinsic to Earth you are abusing the language to avoid dealing with the issue. That is why I used the language I did, so as to deny you these rhetorical tricks to hide behind.
IMVHO, Pamela, you should take this as a learning experience. It is quite clear that you have no way of addressing the long term changes in climate that certainly appear to be closely correlated with changes in solar proxies. Instead of hiding behind the definition of “intrinsic”, try to figure out what the link I gave you earlier was telling you. Maybe when you do understand that you might be able to rescue your ideas in some form but right now all you are doing is displaying the worst characteristics that you criticised in others throughout this thread. The long term data is not going to go away because you ignore it.
Cheers, 🙂
Shawnhet “IMVHO, Pamela, you should take this as a learning experience.”
Our Pam sounds like a member of the teaching profession. They are intrinsically refractory to learning, what they do is teach.
Once again, the changes in solar parameters are trivial compared to changes in Earth’s intrinsic variables. Comparatively speaking, those who propose solar sources of Earth temperature trends have a much harder case to prove in terms of energy available from relatively small solar variations and have yet to present plausible mechanisms compared to those of us who propose intrinsic variables that vary the amount of solar insolation at the surface, both in terms of long term and short term time spans. There are several well-done articles that demonstrate plausibility and mechanism going through the Little Ice Age and further back in time. I have posted many here over the years.
Wriggle matching and cylcomania are not at the same level as the papers I have often linked to in terms of exposing the sources of present and past temperature trends. It has nothing to do with me. It has much to do with which side is more thoroughly investigated, vetted with peer review, and plausibly explained. Intrinsic factors hold the upper hand in plausibility, and noisy short and long term temperature data and its proxies bury tiny mathematical solar forcings.
Shawnhet, unless you have another link for me, the paper you referred to is behind a paywall but attributes the cause of the proxy trends they uncover to decreasing solar insolation (which can happen even when the Sun is rock steady). The Earth is quite good at doing that. Volcanologist are now able to calculate aerosol load thus calculate solar insolation. Ash veils from super eruptions (along with their habit of continuing to burp and belch through their active stage) can explain reduced solar insolation. Oscillations in terms of increased cloud cover regimes are also very good at reducing solar insolation. And certainly going further back, changes in continental arrangements most definitely change weather and climate. All of these variables are intrinsic and calculably powerful enough to swamp solar variations.
Really, Pam, the above position remains illogical based on what we know of the history of the Earth’s climate. You cannot logically postulate that something that doesn’t change (what you call the “intrinsic” mechanisms) is solely responsible for something that does change (ie the long-term climate of the Earth). No amount of shucking and jiving will alter that at all.
You can claim that your data is better than other data presented here but, in truth, it is just more convenient for you to ignore other data. You cannot point to any actual flaws in my link (and don’t forget that their results are entirely with the entirely independent measurements of ice cores).
Pamela Gray says:
May 27, 2014 at 10:01 pm
Actually, it only talks about decreasing solar insolation for part of the record for some of the record the insolation is increasing. IAC, volcanism will not rescue your theory. If there was constant enough volcanism over the last 50,000 to explain these records, we would have plenty of independent evidence of that. We don’t have such evidence so we have to assume that there was no such persistent increase in volcanism.
Anyways, I applaud you for finally trying to figure out what the relevant paper says. I believe the following link should get you a free copy.
http://www.researchgate.net/publication/222398528_A_high-resolution_absolute-dated_deglacial_speleothem_record_of_Indian_Ocean_climate_from_Socotra_Island_Yemen/file/72e7e51837d0b5661e.pdf
If that doesn’t work just go to Google Scholar and search for “Holocene ITCZ and Indian monsoon dynamics recorded in stalagmites from Oman and Yemen (Socotra)”
That should get you started with the long term side of the issues.
LT says:
I see what you mean, its impossible to know for sure what is going in the normalization of the FFT of different lengths with the woodfortrees software. It is intriguing enough for me to write a quick program to do the FFT.
Changes in the stratosphere are causing waving, which changes the circulation in the troposphere. Just to see the strength of the winter polar vortex. Small its disruption causes a strong reaction on the surface. You should not focus on the temperature on the surface, but in the stratosphere, and changes in the UV.
http://earth.nullschool.net/#current/wind/isobaric/10hPa/orthographic=-260.78,-21.07,319
Regarding Willis Eschenbach says:
May 27, 2014 at 12:08 pm
======================================
I think Willis missed the implications (to the searched for 11 year cycle) of important observations regarding the seasonal changes. Willis correctly asserted that the earth spends less time when it is closest to the Sun in the SH summer. However the earth still rotates at the same rate. The difference in time has the affect of shortening the summer by two days, but each day is still 24 hours. During the ENTIRE SH summer, the earth is significantly COOLER despite the rate of energy input increasing from 1.321 kW/m² to 1.412 kW/m² at the closest approach to the Sun. (My earlier link showed insolation charts for both hemispheric summers.)
How is this cogent to the 11 year solar cycle? Well if about 90 w/m2 INCREASED insolation for several months is undetectable to the GAT, except in the fact that the GAT DROPS every time, then one might expect that a change of insolation of about 1 to 2 W/m2 over part of 11 years would likely be hard to detect. However, just as the much greater SH summer insolation fails to manifest as an increased GAT within the atmosphere, so might the highly active solar cycles SW energy bypass the atmosphere, and enter the long residence time oceans. It may take a 1/2 century or so of above active solar cycles, daily pouring their SW energy into the oceans, for the atmosphere to consistently register the heat energy that was pumped into the oceans for many thousands of successive days, 24 hours a day.
Not all watts are equal. The WL is critical to the heating potential.
1. Only two things can affect the energy content of any defined system in a radiative balance; either a change in input, or a change in some aspect of the residence time of the received energy.
2. The residence time of the energies involved is determined by the WL of the input, and the materials encountered. (It is the materials encountered that produce the surprising bi-annual changes discussed)
As an exercise in thinking about the above two laws please consider how differently the earth would respond if the SH summer had a TOA increase of 91 W/m² LWIR verses the total TSI spectrum. ( Some thoughts jump out. The ocean surface skin would absorb far more insolation, but the ocean depths. far less. The insolation would reach the atmosphere far quicker, but the residence time, and therefore heat capacity receiving that insolation would be far shorter, allowing much less accumulation.) I am certain other will have far more educated thoughts on this, but the lesson is in thinking about how all climate responses following the two laws.
Dominic Manginell said on May 27, 2014 at 6:45 pm:
Well, the peak between 1800 and 1810 is pretty jagged, and who would be foolish enough to think the highest monthly value must be the peak? So I’ll apply 5yr+1mo running mean smoothing for a better view.
Huh. The biggest peak-to-peak is only about 13 yrs. There is no “18yrs from peak to peak” anywhere here. Did someone do something amateurish like looking for max values around the peaks and finding the duration between, before looking at the data and seeing its shapes?
From Greg [Goodman] on May 27, 2014 at 6:34 pm:
Thankfully, as seen at WFT when you hit “Software” in the top toolbar:
And the ISO C++ source code is right there for the downloading.
So instead of merely loudly complaining about a free service, provided out-of-pocket by a private individual without government funding, YOU CAN CONTRIBUTE your great knowledge of mathematics and write better code and more functions, and make the entire site better.
Don’t just talk about change when YOU CAN BE THE CHANGE!
Wills, re: “I tried that equation and it didn’t do anything like what you said.”
See Chapter 2 of Robert Gilmore’s book:
http://einstein.drexel.edu/~bob/PHYS750_NLD/ch2.pdf
I got the above link from the links for his class on nonlinear dynamics (471/571 at Drexel):
http://einstein.drexel.edu/~bob/Physics-750_13.html
The logistics map is extremely important in chaos theory because it is so simple and yet it shows all the behavior of chaos seen in chaotic differential equations. But since it is iterative, it computes much much faster than a set of PDEs. And it’s simple to control (one variable) so it will be a nice workhorse for generating sequences of chaotic but deterministic data. By changing the value “a” in Gilmore’s chapter (or the value “r” in the wikipedia article) you can make the system exhibit any of the many types of chaotic behavior. You’ll have a blast playing with it. One of the things I did as a physics grad student at U. Cal., Irvine was to wire up some electronics that implemented the map. The result was that I was able to put the “spiderweb diagrams” (see figure 2.3, 2.4) onto an oscilloscope. By the way, it is possible to rewrite the logistics equation as a set of continuous differential equations, at least to any given degree of accuracy; thus the behavior seen in it is not unique to this being a simple iterative equation. Sets of partial differential equations do the same thing.
If you have any problems with this, send me an email carl at sign brannenworks dot com, this is a subject I’ve done some stuff in and can help. I prefer to use java as a programming language (hence I like to use math techniques that are computationally friendly).
I’ve given some (not a lot) of thought to the cross-correlation plots.
http://climategrog.wordpress.com/?attachment_id=952
Firstly the magnitudes are very small but due to the integrating capacity of the oceans this may be expected. As noted there is more than a passing resemblance between the cumulative sum of SSN and global temps. Correlations on intSSN are much more significant : 0.2
So could it be random? If you take while noise and CC with a signal that has one major peak it could produce something of this order. So perhaps the SST line is just that. Though I don’t see a reason why it would have a phase which is orthogonal. Perhaps some Monte Carlo tests would shed light.
However, the clear onset of a causal response in MAT and SLP does not seem to fit that kind of explanation even though the amplitude is small.
Now if there is a strong atmospheric feedback, acting to counter changes in SST, this may tie in with what is found.
My hands on knowledge of tropical climate is somewhat limited and I’ve never lived there long enough to get an understanding of the climate. I suspect Willis is much better equipped to comment on all this.
What seems clearest in all this is the anti-phase between SST,MAT and SLP. In temperate climates, high pressure is generally associated with clear sunny weather and a drop in surface pressure presages rain or stormy weather. The tropics may well be very different, I don’t know.
However, if SLP drops with higher temps, this seems like observational numerical evidence of Willis’ regulator hypothesis. That needs someone with a knowledge of the meteorology of the tropics.