NEW An update to this has been made here:
Part II
By Basil Copeland and Anthony Watts
In Part I, we presented evidence of a noticeable periodicity in globally averaged temperatures when filtered with Hodrick-Prescott smoothing. Using a default value of lambda of 100, we saw a bidecadal pattern in the rate of change in the smoothed temperature series that appears closely related to 22 year Hale solar cycles. There was also evidence of a longer climate cycle of ~66 years, or three Hale solar cycles, corresponding to slightly higher peaks of cycles 11 to 17 and 17 to 23 shown in Figure 4B. But how much of this is attributable to value of lambda (λ). Here is where lambda (λ) is used in the Hodrick-Prescott filter equation:
The first term of the equation is the sum of the squared deviations dt = yt − τt which penalizes the cyclical component. The second term is a multiple λ of the sum of the squares of the trend component’s second differences. This second term penalizes variations in the growth rate of the trend component. The larger the value of λ, the higher is the penalty.
For the layman reader, this equation is much like a tunable bandpass filter used in radio communications, where lambda (λ) is the tuning knob used to determine the what band of frequencies are passed and which are excluded. The low frequency component of the HadCRUT surface data (the multidecadal trend) looks almost like a DC signal with a complex AC wave superimposed on it. Tuning the waves with a period we wish to see is the basis for use of this filter in this excercise.
Given an appropriately chosen, positive value of λ, the low frequency trend component will minimize. This can be seen in Figure 2 presented in part I, where the value of lambda was set to 100.
Figure 2 – click for a larger image
A lower value of lambda would result in much less smoothing. To test the sensitivity of the findings reported in Part I, we refiltered with a lambda of 7. The results are shown in Figures 3 and 4.
Figure 3 – click for a larger image
As expected, the smoothed trend line, represented by the blue line in the upper panel of Figure 3, is no longer as smooth as the trend in the upper panel of Figure 1 from Part I. And when we look at the first differences of the less smoothed trend line, shown in Figure 4, they too are no longer as smooth as in Figure 2 from Part I. Nevertheless, in Figure 4, the correlation to the 22 year Hale cycle peaks is still there, and we can now see the 11 year Schwabe cycle as well.
Figure 4 – click for a larger image
The strong degree of correspondence between the solar cycle peaks and the peak rate of change in the smoothed temperature trend from HadCRUT surface temperature data is seen in Figure 5.
Figure 5 – click for a larger image
The pattern in Figure 4, while not as eye-catching, perhaps, as the pattern in Figure 2 is still quite revealing. There is a notable tendency for amplitude of the peak rate of change to alternate between even and odd numbered solar cycles, being higher with the odd numbered solar cycles, and lower in even numbered cycles. This is consistent with a known feature of the Hale cycle in which the 22 year cycle is composed of alternating 11 year phases, referred to as parallel and antiparallel phases, with transitions occurring near solar peaks.
Even cycles lead to an open heliosphere where GCR reaches the earth more easily. Mavromichalaki, et. al. (1997), and Orgutsov, et al. (2003) contend that during solar cycles with positive polarity, the GCR flux is doubled. This strongly implicates Galactic Cosmic Ray (GCR) flux in modulating global temperature trends. The lower peak amplitudes for even solar cycles and the higher peak amplitudes for odd solar cycles shown in Figure 4 appears to directly confirm the kind of influence on terrestrial climate postulated by Svensmark in Influence of Cosmic Rays on Earth’s Climate (1998)From the pattern indicated in Figure 4, the implication is that the “warming” of the late 20th century was not so much warming as it was less cooling than in each preceding solar cycle, perhaps relating to the rise in geomagnetic activity.
It is thus notable that at the end of the chart, the rate of change after the peak associated with solar cycle 23 is already in the negative range, and is below the troughs of the preceding two solar cycles. Again, it is purely speculative at this point, but the implication is that the underlying rate of change in globally averaged temperature trends is moderating, and that the core rate of change has turned negative.It is important to understand that the smoothed series, and the implied rates of change from the first differences, in figures 2 and 4, even if they could be projected, are not indications of what the global temperature trend will be.
There is a cyclical component to the change in global temperature that will impose itself over the underlying trend. The cyclical component is probably dominated by terrestrial dynamics, while the smoothed series seems to be evidence of a solar connection. So it is possible for the underlying trend to be declining, or even negative, while actual global temperature increases because of positive cyclical factors. But by design, there is no trend in the cyclical component, so that over time, if the trends indicated in Figures 2 and 4 hold, global warming will moderate, and we may be entering a phase of global cooling.
Some are probably wondering which view of the historical correspondence between globally averaged temperatures and solar cycles is the “correct” one: Figure 2 or 4?
Such a question misconstrues the role of lambda in filtering the data. Here lambda is somewhat like the magnification factor “X” in a telescope or microscope. A low lambda (less smoothing) allows us to “focus in” on the data, and see something we might miss with a high lambda (more smoothing). A high lambda, precisely because it filters out more, is like a macroscopic view which by filtering out lower level patterns in the data, reveals larger, longer lived processes more clearly. Both approaches yield valuable insights. In Figure 2, we don’t see the influence of the Schwabe cycle, just the Hale cycle. In Figure 4, were it not for what we see in Figure 2, we’d probably miss some similarities between solar cycles 15, 16, and 17 and solar cycles 21, 22, and 23.In either case, we are seeing strong evidence of a solar imprint in the globally averaged temperature trend, when filtered to remove short term periodicities, and then differenced to reveal secular trends in the rate of change in the underlying long term tend in globally averaged temperatures.
At one level we see clear evidence of bidecadal oscillations associated with the Hale cycle, and which appear to corroborate the role of GCR’s in modulating terrestrial climate. At the other, in figure 4B, we see a longer periodicity on the order of 60 to 70 years, correspondingly closely to three bidecadal oscillations. If this longer pattern holds, we have just come out of the peak of the longer cycle, and can expect globally average temperature trends to moderate, and increased likelihood of a cooling phase similar that experienced during the mid 20th century.
In Lockwood and Fröhlich 2007 they state: “Our results show that the observed rapid rise in global mean temperatures seen after 1985 cannot be ascribed to solar variability, whichever of the mechanisms is invoked and no matter how much the solar variation is amplified.” . Yet, as Figure 5 demonstrates, there is a strong correlation between the solar cycle peaks and the peak rate of change in the smoothed surface temperature trend.
The periodicity revealed in the data, along with the strong correlation of solar cycles to HadCRUT surface data, suggests that the rapid increase in globally averaged temperatures in the second half of 20th century was not unusual, but part of a ~66 year climate cycle that has a long history of influencing terrestrial climate. While the longer cycle itself may be strongly influenced by long term oceanic oscillations, it is ultimately related to bidecadal oscillations that have an origin in impact of solar activity on terrestrial climate.
We are continuing to look at different methods of demonstrating a correlation. Please watch for future posts on the subject.
NEW An update to this has been made here:
References:
Demetrescu, C., and V. Dobrica (2008), Signature of Hale and Gleissberg solar cycles in the geomagnetic activity, Journal of Geophysical Research, 113, A02103, doi:10.1029/2007JA012570.
Hadley Climate Research Unit Temperature (HadCRUT) monthly averaged global temperature data set (description of columns here)
J. Javaraiah, Indian Institute of Astrophysics, 22 Year Periodicity in the Solar Differential Rotation, Journal of Astrophysics and Astronomy. (2000) 21, 167-170
Katsakina, et al., On periodicities in long term climatic variations near 68° N, 30° E, Advances in Geoscience, August 7, 2007
Kim, Hyeongwoo, Auburn University, “Hodrick-Prescott Filter” March 12, 2004
M. Lockwood and C. Fröhlich, Recent oppositely directed trends in solar climate forcings and the global mean surface air temperature, Proceedings of the Royal Society of Astronomy doi:10.1098/rspa.2007.1880; 2007, 10th July
Mavromichalaki, et. al. 1997 Simulated effects at neutron monitor energies: evidence for a 22-year cosmic-ray variation, Astronomy and Astrophysics. 330, 764-772 (1998)
from Chile (AD 1587–1994)
, Planetary and Space Science 55 (2007) 158–164Svensmark, Henrik, Danish Metorological Institute, Influence of Cosmic Rays on Earth’s Climate, Physical Review Letters 15th Oct. 98
Wikipedia, Hodrick-Prescott Filter January 20, 2008
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Gary,
So the question goes to you as well; what in Taminos analysis is wrong in you opinion? Keep to the question, or don’t comment on my comments. At least stay close to polite.
With respect to automatic writing, count the number of comments here saying something along the lines “I don’t know much math, but this seems convincing to me”.
And the phase has everything to do with the present analysis since it’s correlating the timing of two oscillating signals.
And to be very picky: second derivative is normally written d^2T/dt^2. Being even more picky, DT/Dt (note big letters) is normally reserved for the substantial derivative.
Bill Illis:
If your scatter analysis comes out with clusters both before and after the timing of the temp, then you have no causality. I could of course be very wrong in that, if so, please explain why.
I am not of the Sun school. However, if you want to acertain the sun’s influence you have to figure a way of getting volcanic forcing ( at least) out of the record
volcanoes are basically shot noise. I think Tammy had a post on how to back their contribution out of the time series. So back out ( remove) the volcano jolts and then see what you have.
REPLY: They won’t just show up as “shots” or spikes in the temp record, more like the pulse followed by the right side trailing slope of a gaussian curve as particulates settle.
To Onanym, ideally the scatter would produce solar cycles which lead the temperature cycle by a short period of time. But the climate is also randomly variable and the sunspot solar cycle does not always equate directly with total solar energy received by the Earth so there is likely to be both positive and and negative lags in the two maximums.
Anthony,
The Institute of Physics has published a short paper this week that argues there is weak or no statistical confirmation of the link between cosmic ray ionization (due to reduced solar flux) and low-level cloud formation.
Paper here
REPLY: Thanks Peter, I was aware of it but had not hunted down the PDF just yet. I appreciate you providing it and saving that trouble. I’ve briefly scanned it, and I have a couple of problems with it and the author, Sloan.
1) In this is the paper’s conclusion:
On the surface it seems the time scales of the effects they looked at and what Svensmark proposes are vastly different. They are looking at Forbush decrease for the signatures, but they are short period events (hours/days) compared to the much longer GCR modulation by long period changes in the suns’s magnetism, which is said to be the driver.
It just seems disconnected. Maybe I’m missing something, but it seems to me that you can’t draw a conclusion about something that operates on timescales of years to short period events lasting hours or days.
2) In the interview Sloan gave to BBC he said:
Now I don’t know if he was misquoted or not, but particle bursts/CME’s (and resulting Forbush decrease) from the sun are an entirely different thing than GCR modulation by the suns magentic change over a long period.
Asked to comment, Svensmark said in the BBC article:
If Sloan was looking for correlation between charged partcle bursts instead of GCR’s I’d have to agree with Svensmark. We’ll see how it all shakes out. Maybe the BBC just did another crappy job of reporting a science interview and that’s not what he said at all, but it sure seems odd.
Here’s another paper that looks at the much larger view of GCR modulation:
http://www.griffith.edu.au/conference/ics2007/pdf/ICS176.pdf
Yes. Spike followed by a fall off. These events pin the negative
excursions. Not sure what that does. just an observation.
Onanym
“it shred(s) the correlation between soalr cycles and temp. rise to pieces.”
Bold words. My wife has the mathematical nouse in this household; she understood Tamino’s rebuttal; she didn’t like his George Clooney attitude, but that goes with the territory. I’m just a humble lawyer trying to make a killing from the carbon-trading gravy train before Joe Public realises he has been sold a pup and the whole thing goes belly-up.
Fourier can still be useful; Watts have concentrated on 2 cycles, Schwabe and Hale, with a nod at a 60-70 year periodicity; they have used Javaraiah’s work on the Hale cycle, but Javariah has also done a paper on a 17 year solar cycle; since the solar influence is variably constant, any analysis should cover all cycles, with a reasonable assumption being that climatic discrepancies that statistically fall outside those periods are the result of either lag or unknown cycles or combinations. The Watts’ analysis was brave but deficient in content perhaps.
I posted this also on the sunspot page. Take a look at this link:
http://www.griffith.edu.au/conference/ics2007/pdf/ICS176.pdf
This predicts that the next minimum period is imminent and may be as pronounced as either the Daulton or Maunder.
This is a totally different approach than the solar scientists have used to predict an unusually/unprecedented low level of activity in cylce 25 – but both forecasts are pointing to the same result.
Basil and Anthony great work. The results are astounding. As an electrical engineer I fully appreciate what you have done, it’s what we have been doing with signal analysis for years. A really ground breaking application of the technology.
Output the temperature with a DSP and do a Fourier transform analysis on the signal. Never know what you might find … If anyone has a copy of Mathematica, I believe it will do the work for you.
oops – didn’t realize that was previously posted. Sorry
Mosher’s comment re “shot” has to do with the incidence of the actual explosions themselves. That they happen irrespective of the sun or of AGW. Modelling the temp effect as a trailing off from the events is fine. But the attempted correction to Mosh’s point is off.
Basil (several posts back):
A. I’m not sure of the semantics. In any case, my sense is that correlation analysis and your choice of axes and such is off. I think this has been well pointed out to you by now by others with more description. I’m not a “jock”, but I could sense right away that there was a fundamental flaw in your method.
B. I don’t know a better method of comparing cyclicality. I have asked this question as well. I think you should research this in books and with experts. I’m sure that it is a type of problem that has been thought about and that there are some good methods and caveats on usage and stuff. Your work to date is obviously very preliminary and the comments on publishing, etc. were “off”. It’s fine to “doodle”. But at least appreciate that you are doodling when you do so. And then go and learn the basics of what techniques are needed to use on your particular problem. Do that before publishing or even before overly promoting your work. (BTW: you worry me a bit with some of your tone. You seem to be a bit pompous in language, etc. but not to really be a critical thinker. Please work on that.)
C. ‘the peaks are interesting but come out with higher level filtering’.
1. Well, in the filter you DID use, the peaks were there. So they should be included in figure 5.
2. Why the comment on filters in commentary, but not in the initial headpost (draft publication)? Do you appreciate that points like this should be raised as part of the publication itself?
3. It just scares me to hear things like use more filtering to remove peaks.
4. Doing numerical correlation analysis on smoothed data is a dangerous thing. One that we criticize AGWers for.
REPLY: TCO, using a better “wrapper” these days I see. Good on you!
I was kinda iffy on Tammy’s raleigh R. Ah well first off I liked the measure
but I was not so sure how a spatial measure did in the temporal domain. That’s not a criticism just a quizicism. It would be good to test if that method was robust in this kind of application. Open question.
The entire issue of “correlating” through whatever measure, the sunspot maximum with the surface temp dt, seems on reflection to be a snipe hunt of sorts.
Surface temps ( as collected by Jones and cru and hansen and crew) are noisy bits of the record. If you think that SSN correlates in some way to the HEAT of the planet, then look at SST. It’s a big old capacitor and all the high freq crap is filtered out.
Looking at hadcrude or gimptemp ( jokes intended) you are just introducing unnecessary noise.
Look at SST. a thought.
AW here is a thought.
Do a reconstruction.
Gary, you said: “There is no pertinence to the term ‘phase shift’ in the present context, Basil and Anthony are measuring the departure in time at SSN max of DT/dt^2 = 0 at the positive extrema.”
However the following quote shows that B & A are indeed trying to assert that the two curves are in phase.
“The strong degree of correspondence between the solar cycle peaks and the peak rate of change in the smoothed temperature trend from HadCRUT surface temperature data is seen in Figure 5.”
However the form of plot they used hides the actual lack of correlation between the timings of the peaks.
“One should be careful to analyze for oneself and not depend too closely on gadflies like Hansen’s Bulldog; his enthusiasm outstrips his talent.”
Some of us are able to think for ourselves Gary!
Phil and Mosher:
I’m at best a jack of all trades and master of none and am obliged to defer to those like Mosher who obviously work often in the area.
My abiding belief here is that stats are inappropriate (ICA excepted) for the determination and evaluation of causation, and I believe Phil, J, and Tammy are expecting Basil and AW to prove that to which they do not aspire, a correlation of cyclic phenomena tantamount to causation.
A couple of relevant observations of current practice:
MBH98 proposed to combine temperature proxies, e.g., the Bristlecone series, by means of PCA, to replace existing proxies with less precision, e.g., 10Be, and temperature data. The latter because the record was essentially NH only.
It would have been entirely plausible to do a PCA on the BC data, separating into factors (H20, C02, Temp), creating a polynomial fit and then doing phase analysis in a calibration of the resulting fit with the local temp.
This was not done or imagined. This despite the intent to recreate a reasonable facsimile of the temperature curve, a continous record!
Phase analysis wasn’t undertaken with the composite proxy! And some of the MBH98 supporters are here engaged.
Svalgaard and Cliver (2007?) have proposed correcting historic SSN data with Geomagnetic data. Neither are physical quantities, but statistics themselves. Indeed, SSN are discontinuous taking no value between 0 & 11.
The former are the direct result of torodial fields near the Suns surface, presumably bathed in the polodial field. The later are the effect at 93 million miles of the highly ‘twisted poloidal field’ of orginating some days earlier. In addition the Geomagnetic measure is highly effected by UV, a highly volatile factor.
It would have been perfectly plausible that the SSN and Geomagnetic data be evaluated for phase consistency since the object was to correct SSN data.
This was not done or imagined.
I’m not arguing against hypocrisy here. Basil and AW are measuring a feature of the data. Many of their critics are manifestly out of their depth in their analysis.
Just happened to have three annual mean temperature graphs of Mauritius, N. Colombia and Zinder, W. Africa from 1951 onwards; you would be surprised to see how closely the peaks and troughs match those on fig. 4!
Mosh, thanks for the suggestions.
Capacitor, indeed. I love capacitors. Especially those big honking 1 farad ones you can buy now.
aw the big issue with the gsmt record is the year to year noise. this will give you a very noisy estimate of dt. sst might be better, but check.
one way to think about it is this. if you had zero trend and noise with a 1 deg sig
your year to year delta can be huge. swinging from 1 sig down to one sig up would imply a rate of 2 times the 1 sig value.
Excellent work gentlemen! There is a wonderful elegance about using differentials. After all, weather and climates are not driven by absolutes but by differences, and it seems apropos that the sun’s relationship to our climate also be related in this manner.
Thanks again and Godspeed in getting this published!
[…] week, when Basil and I posted Part 2 of our series on seeing a solar imprint in the HadCRUT temperature record, it spawned a lot of interest, debate, replication, and criticisms. One of the criticisms from […]
Very good work.
Now if you can determine the extent of solar radiation on global mean temperatures you will be closer to testable predictions.
TCO:
“BTW: you worry me a bit with some of your tone. You seem to be a bit pompous in language, etc. but not to really be a critical thinker. Please work on that.”
Pot, kettle, … ?
I love following wherever the trail leads. I have no pre-conceived notion about warming other than the cancer scar on my lip. For that, I must admit, I have a bone to pick with the sun and its rays.
My first thought about global warming was the result of my skin heating up and burning (I am a redhead so I burn ALL THE FRIGGIN TIME) when the sun is shining bright. From there I naturally thought that when the sun was hot, I was hot. Therefore the temperature around me was hot. If the sun stayed hot with little time spent in slumber, I just figured that the temperature rise was due to a hot sun. However, if that were the case, we would have seen this simple relationship long ago and there would be no Al Gore movies.
Apparently this is not the case because we have Woody Al stiffly describing the devastating affects of the stuff we all breath out.
But at least I was given the opportunity to see peaks. . . .Then I started looking at valleys. From there I started looking at what the sun was doing during the valleys. Man, was I surprised. Here is what it is doing when it sleeps: It is NOT protecting us from some very damaging rays. Not only did I get a hole in my lip, but our blanket in the sky is being eaten alive by that seemingly quiet, passive sun. So I have come full circle. The scar on my lip can probably be blamed on solar MINIMUMS, not maximums. What else can we add to the rap sheet of the sun when it looks oh so peacefully quiet?
Hey Pamela, I’m sorry to read about your scar and I hope it goes okay for you (presumably it wasn’t malignant!). In your case, you could blame genetics as much as the sun ;).
It’s true this simple relationship hasn’t been seen before, more than likely because nobody bothered to look. But you know, apparently there is nothing new under the sun. So it goes.
[…] the reply from Svensmark Here’s another from Ken Gregory and here’s another from Anthony WattsObviously you won’t spend any time reporting on them, because life’s too short isn’t it […]
Frank Ravizza: Good post. I’m not much of a physicist, but when I took physics, we learned that moving a conductor in a magnetic field produced a current. The Earth’s core is a conductor, yes? Is there a pole-to-pole terrestrial dynamo current? If so, how large? And what part would the semi-conductive crust and the conductive oceans play in this?
Basil & Anthony: Interesting, but based on a friendly argument at SC24, I’m leery of H-P smoothing. I hope you find an appropriate [non-derivative-based] function set that will allow correlation, rather than peak matching.
Pamela Gray: My turkey cooling theory: Heat rises; cold doesn’t. A warm turkey in a cold box will set up a convection pattern with the hot turkey air rising and then being cooled and recycled back from bottom to top again. No such convection cell exists with a cold turkey in a 70°F room–the hot air will not come down from the ceiling and flow over the turkey. Makes sense?