Evidence of a Significant Solar Imprint in Annual Globally Averaged Temperature Trends – Part 2

NEW An update to this has been made here:

evidence of a lunisolar influence on decadal and bidecadal oscillations in globally averaged temperature trends

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.

UPDATE: We have had about half a dozen people replicate from HadCRUT data the signal shown in figure 4 using FFT and traditional filters, and we thank everyone for doing that. We are currently working on a new approach to the correlations shown in figure 5, which can yield different results using alternate statistical methods. A central issue is how to correctly identify the peak of the solar cycle, and we are looking at that more closely. As it stands now, while the Hodrick-Prescott filtering works well and those results in figures 2,3, and 4 have been replicated by others, but the correlation shown in figure 5 is in question when a Rayleigh method is applied, and thus figure 5 is likely incorrect since it does not hold up under that and other statistical tests. There is also an error in the data point for cycle 11. I thank Tamino for pointing these issues out to us.

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:

evidence of a lunisolar influence on decadal and bidecadal oscillations in globally averaged temperature trends


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)

Mavromichalaki H, Belehaki A, Rafios X, et al. Hale-cycle effects in cosmic-ray intensity during the last four cycles ASTROPHYS SPACE SCI 246 (1): 7-14 1997.
Nivaor Rodolfo Rigozo, Solar and climate signal records in tree ring width

from Chile (AD 1587–1994), Planetary and Space Science 55 (2007) 158–164

Ogurtsov, et al., ON THE CONNECTION BETWEEN THE SOLAR CYCLE LENGTH AND TERRESTRIAL CLIMATE, Geophysical Research Abstracts, Vol. 5, 03762, 2003
Royal Observatory Of Belgium, Solar Influences Data Analysis Center, monthly and monthly smoothed sunspot number. (Description of data here)

Svensmark, 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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Can someone check for an approximate 19 or 20 month periodicity in the 12-month-running mean for the period from start of 2000 to end of 2007 for the Hadley data at http://www.cru.uea.ac.uk/cru/data/temperature/hadcrut3gl.txt
I’m runing Gnumeric on linux at home, so Excel plugins don’t do me much good. I do notice that if I switch to a 19 or 20 month running mean (boxcar?) the sawtooth pattern (as seen in the 12-month running mean) disappears. So I assume I’m seeing a 19 or 20 month periodicity. I do know of one natural cycle that takes approximately that long, but I’d hold my nose when quoting it, unless I had damn good backup.
I’ve uploaded a spreadsheet, with a lot of tabs, at http://clients.teksavvy.com/~walterdnes/temperatures.zip to show what I mean. The zipped file is approx 1 and a quarter megs. Read the README tab for documentation. I’ve saved as Excel 2007 format, so most everybody should be able to handle it.

Mike Bryant

Thanks so much for your work on this project. These results are astonishing. I am no physicist, but I can certainly see that this should put to rest any doubts about the solar connection. I remember a simpler time when the sun was acknowledged as a force in weather. Warm was good and the chilling cold was the killer. The world of science has been turned upside down. Thanks again for your work in helping to right some terrible wrongs.
Mike Bryant


So, a conclusion of your analysis above would be that it’s important to look a short time scales versus the long time-scales that climate modelers have used (which they emphasize when skeptics bring up the effects of the sun on climate). In other words, the climate modelers have misinterpreted the effects of multiple short-time events as one long-time effect that they attribute to man-made warming caused by CO2. Thus, the fundamental difference in explaining the recent warm-up between the skeptics and climate modelers is essentially one of time scales (i.e., climatge modelers don’t recogonize the impact of the sun in the short term and as a result they are implementing a long-term model that is fundamentally flawed when compared against reality). As a result, too much weight is given to CO2 in their models. People only model what they know. If people don’t understand how the sun impacts the climate, it’s not going to be reflected in their models.

Steve Keohane

Nice work gentlemen. I notice in Fig. 4 that when the HADCRUT peak preceeds the peak solar cycle, it seems to indicate warming.

Jim B

It seems pretty conclusive and well referenced. Any chance of seeing this published in a Journal any time soon?
Anthony: Yes we hope to. I had a number of qualified people including a published climatologist, solar scientist, a statistician, and a certified consulting meteorologist (among others) look at this beforehand. We’ll see what new insight the comments bring.

Jim B

Well I unfortunately, have non of those credentials, I believe I am the ONLY one who has noticed fig 1, is the Batman Logo!
So There!

Frank Ravizza

Why didn’t you include plots of solar cycles along with the temperature data?
REPLY: Fugure 5 shows correlation between peak rate of change in the sunspot numbers and peak rate of change in the HadCRUT surface temp data. But, I’ll see if we can create an additional graph to post. Thank you for the suggestion.


I’ve asked (leif) today if he would be interested in commenting on these results at climateaudit (solar thread)
REPLY: Thanks

R John

Very nice work Anthony and Basil.
Now all of us flat earther’s and moon landing denier’s have more work to support our story.


From figure 2 it looks like the non-cyclic temperature increase from 1880 to 2000 is 0.15C, which I assume is the AGW forcing.

James Bailey

You have found a way to pull out of the temperature data, components of specific periodicity. Furthermore, you showed that there is a component whose rate of change is in sync with and proportional to a well known solar cycle.
Can you take the numerical analysis further?
How many degrees of warming would this component, by itself, give us?
Can you use this technique to decompose the magnitude of warming /
cooling by periodicity?
AGW is supposed to create a small but monotonically increasing component superimposed on all the other, wildly changing, components of temperature change. Can you use this technique to isolate such an aperiodic signal and determine its magnitude?
Can you take the science further?
You have isolated an effect and shown it is compatible with prior work on CGR based influences on temperature.
Can you develop a model for how this effect would work?
Is there some component of our atmospheric system that somebody has shown behaves like this model?
Can you use this model to bring to light features of this component?
Stepping back out into more generic issues, can this technique, coupled with a good model, be used to pull out generic features of the system or of the driving influences? Say time constants of various thermal reservoirs?
Have you thought about what it means when you look at a smoothed rate of change of a smoothed global average?
Anyways, my questions are meant to urge you to take this further, if possible.
thanks for sharing your work.

The Impact of Different TSI Time Lags on Average TSI?
The following is a graph of TSI data, where a second duplicate column of TSI data (Lean et al & ACRIM) has been lagged five years after the first, to simulate the difference in response times of land and oceans. The bold red line is their average.
The results mimic the global temperature record well.
To reproduce, simply copy the same annual TSI data onto two spreadsheet columns and shift one down five years. Then average the two. It’ll be interesting to see what happens when the two data sets are proportioned for the differences in land and ocean area, and when the lag average is created with monthly data, and when PMOD data is used in place of ACRIM. I’ll let you know.
What I thought was the best correlation of the whole thing: that downward spike in the latter half of the 20th century is at 1976, which is close enough to the Great Pacific Climate Shift and the change in the AMO to be significant.
Bob Tisdale

Bob B

Anthony, being an electrical engineer in RF and communications this makes perfect sense to me after you guys doing the math. I think the “CO2 Climate scientists” at RC will be smarting after this one.
Outstanding job!
REPLY: Actually I think they’ll either ignore it at RC or make a joke of it. They are clearly entrenched in “no solar correlations”. -Anthony

This is incredible information and a credit to both of you for pulling it all together. Someday soon (hopefully) I’ll be asking permission to post it on the svensmarkeffect.com website once I finish the design and get it up and running.
I just can’t imagine how many hours you guys put into this… any guesses on your part?
Jack Koenig, Editor
The Mysterious Climate Project


The connection between temperature and the solar cycle is complex, and non linear. There’s a connection, but it is not one that is easily presented visually. The solar cycle itself is a complex phenomenon to depict in a plot. What, exactly, is the “solar cycle” and how do you plot it? Sure, we could plot the sunspot cycle, but that’s not the connection we think we are seeing here, except in a very indirect way. The plot in Figure 4 correlates strongly with the timing of the solar cycle peak, as measured by sunspots, but not necessarily with the number of sunspots. But sunspots may be merely a proximate cause, and their number not a good indication of all that is taking place.
Figure 4 very strongly points to something that has to do with magnetic pole reversal. There is a very pronounced difference in the shape of GCR flux between odd and even numbered solar cycles. During even numbered solar cycles, it it peaks sharply. During odd numbered solar cycles, the “peak” is flatter, but longer in duration. If this is influencing earth’s climate through cloud cover formation, the effect is probably gradual and non linear. It probably causes the “core” trend in earth’s temperature to accelerate and decelerate with lagged influence. If all of this could be easily shown in a graph, it would have been done long before now.
Look at what we’re doing this way, if you can. There are lots of studies showing 22 year periodicities in climate proxies such as tree rings, drought indexes, etc. These implicate a solar climate connection even if they do not result in a plot against SSN’s. We’re seeing the same thing here, but with a twist. First, we’re seeing it in the instrumental record, which has only been rarely reported, that I can find, and second we’re seeing it in a way that is consistent with variations in GCR flux. It gives us some ideas on where to go next, in trying to establish a stronger statistical link. But the complexity of the relationships involved doesn’t reduce to something that can be easily plotted on a graph.

Nigel Calder

It’s very pleasing (though unsurprising) that Basil and Anthony’s remarkable analysis finds such a clear 22-year signal. That distinguishes the the climatic role of cosmic ray modulation by the Sun from the effects of the 11-year cycle in other solar mechanisms such irradiance.
Research on cosmic rays and climate has moved on a very long way since the rather elderly reference to Svensmark 1998. For a review article from last year see:
Henrik Svensmark, ‘Cosmoclimatology: a new theory emerges’, Astronomy and Geophysics, Royal Astronomical Society, London, Vol. 48, Issue 1, 2007
And Basil and Anthony’s rate-of-change analysis applied to Lockwood and Fröhlich provides valuable reinforcement to: :
Henrik Svensmark and Eigil Friis-Christensen, ‘Reply to Lockwood and Fröhlich – The Persistent Role of the Sun in Climate Forcing’, Danish National Space Center Scientific Report, 3/2007, September 2007
Downloadable from http://spacecenter.dk/publications/scientific-report-series/
As for the remark about possible global cooling — in an updated 2008 edition of our plain-language book The Chilling Stars (newly out with Totem in the USA, and Icon in the UK and Canada) Svensmark and I comment that we’ve been advising our friends to enjoy the global warming while it lasts.

Stan Needham

Basil and Anthony,
Thanks for putting this in language that an old Navy radio operator can understand. It will be interesting to see how the scientific community responds to this work.


Steve Keohane,
I haven’t looked at them all, but it certainly looks like that for cycle 23, where our rate of temperature change peaks in 1997, but the solar cycle, as measured by SSN’s, peaks in 2000. This may have to do with the way the GCR flux varies between odd and even numbered solar cycles.


Can you use this filtering method to determine how many independent cycles/harmonics are contributing to the overall temperature record?

I asked a PHD Economics Univ of (Name withheld to protect the innocent) to comment on the use of the filter and his response was:

Re the post — he uses Hodrick-Prescott filter, which is a two sided filter (uses data from both sides of the observation in question) that has a lot of problems as one gets near the end points.
There are other problems with the HP filter that are probably more serious in a macroeconometric context — as with the Baxter-King high pass band filter — tends to impart business cycle fluctuations into filtered series even when they don’t exist.

Which leaves me to ask is there another filter to use to confirm results? Just trying to forestall any criticisms.


The analysis is interesting but can’t be used as evidence of causality between solar activity and temperature increase. Temperature increase manifests itself as a trend in the original data. By differentiating the temperature you are reducing the trend contribution to a constant value.
For example, if:
By differentiation, the trend component (a*t+b) was reduced to a constant. So the cycles in figure 4 are independent of the existence of a trend. They come from d(cyclic_component)/dt. The only information in figure reminiscent of the trend is a constant value that is being added to the cyclic component.


ok, there has got to be an enterprising graduate student who will take this on as their thesis.
If I didn’t like not starving, i’d be back in graduate school doing this.
As I said before this most definately needs to be published.


B, that vitriol is like a cat hissing; it’s scared.


oh, i also see a correlation too, but I’d love to know the exact mechanism and how it all interacts.


Very interesting gentlemen. I can’t imagine the hate-mail Anthony is culling out of the comments section.
REPLY: The hate mail is nonexistant thus far. But having said that, I’m sure some will come any second now. -Anthony


Doesn’t what you are saying — about differencing reducing the trend component to a constant — apply only if the trend is linear? What if its non linear? What you see in the smoothed series — the blue lines in either figures 1 or 3, are not linear trends. They undulate, and differencing reveals a non random pattern of change in the rate of change. E.g., I’m questioning whether the “a*t” part of your question specifies the correct functional relationship, and that the resulting conclusion that dT/dt reduces to the constant “a” (plus the change in a cyclic component, but that’s already been removed from the data)). In effect, what you see plotted in Figures 2 and 4 are the “a’s” of your equation, and they are anything but constant.
As for causation, that’s always been the rub for studies which show 22 periodicities in climate metrics. When 22 year periodicities are found in tree rings, what does it prove? Many will say it shows a “connection” between solar activity and climate, but lacking an explanation of the actual physical basis for the connection, others will say that more is needed before claiming that the correlation proves causation.
That’s where the differing amplitude of the differenced “trend” between even and odd numbered solar cycles we are seeing here may prove important. Why would the signal be weaker in even numbered solar cycles than in odd numbered solar cycles? Well, there is a theory about that, having to do with the role solar magnetic pole reversals modulate cosmic ray flux. If you haven’t already, read Mavromichalaki, et al. Incidentally, I just now noted that Anthony has a difference Mavromichalaki, et al. paper than what I intended. The one I had in mind to cite is this one:
I hope that link comes out when this gets posted. A full cite would be
Mavromichalaki H, Belehaki A, Rafios X, et al. Hale-cycle effects in cosmic-ray intensity during the last four cycles ASTROPHYS SPACE SCI 246 (1): 7-14 1997.
Another useful read as to why 22 year periodicities may infer something about the physical mechanism involved is this one:

Chris Knight

Please could you include a plot of the 22year cycle (HadCRUT3 alone would be sufficient) filtered with lambda=100 and the 11 year cycle fltered with lambda=7 on the same graph for comparison?
Oh, and the Mauna Loa CO2 series might be interesting too!
REPLY: Actually you can do those yourself and easily. There is an HP filter plugin for Excel available here:


“oh, i also see a correlation too, but I’d love to know the exact mechanism and how it all interacts.”
See the two references in my reply to JM. In the first, pay close attention to how cosmic ray flux is modulated between even and odd solar cycles, and the role magnetic pole reversal plays. The lower amplitude we are seeing in the even numbered solar cycles, compared to the odd numbered solar cycles, fits this model of solar activity very well.

You are correct if the trend is modeled with a linear function. But once it is modeled with another function it will still be present to some degree in the first derivative. In fact, if the trend is modeled using an exponential function (e.g. – a hockey stick), then the trend will still be present in the derivative.


thank you, Basil for your reply. I am looking forward to seeing many others actually take an open minded look at this. I think you’ll have better luck with the graduate students then you would with the entrenched “senior-level” climatologists.


Hodrick-Prescott works like a high pass filter. Other smoothing techniques, such as the binomial filter used by HadCRUT to smooth the long term temperature trend. are low pass filters. In the latter, the trend is forced upon the data, and the residuals are treated as the cyclical component. In Hodrick-Prescott, the data is not so much smoothed, as de-trended, with the “smoothed” series being the residual, just the opposite. In economics, the interest is in the de-trended part. Here, we’re finding something in the “residual trend” after the stronger, shorter cycles have been removed, allowing longer term cycles to emerge. Because we are looking at the smoothed series, and that over a long time frame, I don’t think that the traditional concerns your source mentions apply.
But if someone can suggest another filter that works similarly to HP, and if they wish to see if it confirms what we’re seeing, then by all means, we’re open to that kind of exploration.
Actually, what we’re seeing here has, in some degree, already been found, using spectral analysis. See, for instance:
So, in a sense, the connection has already been found. We’re just seeing it in a different temperature record, using a different technique, that happens to show a variation between odd and even solar cycles that may well relate to current thinking about how solar activity would impact earth’s climate.
BTW, I could find no reference to those Brunetti papers in IPCC AR4 WG1, Chapter 3, which is where I would have expected them to be discussed. There’s reference to related research by Brunetti et al on precipitation, but not to the work on solar signals in the instrumental record. It sure looks like a case of special pleading on IPCC’s part.

Gary Gulrud

Basil, and Anthony: A veritable tour d’ force, congratulations. I agree with J.B., McG. and others, this is significant.
No doubt peer-review can offer some editor-friendly improvements, but my intuitive feel is that it is ready for such an endeavor.

Chris Knight

I asked nicely, I thought – I can’t post the plots here, they would strengthen your argument considerably, please, would you do it?
REPLY: Hi Chris, You did ask nicely, and I’m sorry if you thought the response was some sort of a brush-off, because that was not the intent. I just thought you and other readers might like to be engaged in the process a bit. We’ll have follow ups to this one where that and more can be posted. -Anthony


This may have to do with the way the GCR flux varies between odd and even numbered solar cycles.

Ah I see, it is like the flux between odd and even numbered Star Trek films. Now I get it.
j/k, nice work guys.


smart people man.

Chris Knight

Many thanks, Anthony (& Basil)

Pierre Gosselin (aka AGWscoffer)

Bob B / Anthony
Being entrenched does not bear any scientific fruit, now does it?
Just goes to show that the RC folks have no clue about how science works.


Leif Svalgaard points out alternating shapes to the peaks of solar activity, sharper alternating with rounder. Is there a connection?

Drew Latta

Nice work and very interesting analysis, though I certainly don’t know anything about data filtering and smoothing… Looking at your data in Figure 5, it is pretty astounding that you see almost no lag between peak solar cylce date and peak temperature date. Your correlation results seem to refute Scafetta and West’s (2007) hypothesis that there is an internal lag associated with changes in solar activity due to heat sinks in the earth system. Their response times are from 6-12 years, which would make sense to me. Any ideas why this might/might not be true? My guess would have been that the terrestrial realm might respond faster to insolation changes, but HadCRUT is both sea surface temperatures and terrestrial measurements, so that doesn’t seem to hold up.
I’m sure you know this, but some journals state that publishing on the internet is prior publication and disqualifies a paper for publication in their journal. I hope you don’t have problems with this, and I assume you have had some journals in mind that might not care either way.
Scafetta, N., and B. J. West (2007), Phenomenological reconstructions of the solar signature in the Northern Hemisphere surface temperature records since 1600, J. Geophys. Res., 112, D24S03, doi:10.1029/2007JD008437.

Paul Clark

I’m running to keep up here, but I think I’ve replicated your results using pure Fourier analysis with the (growing like Topsy!) C++ toolset I mentioned earlier.
Here is the raw HADCRUT3VGL monthly data with a low-pass filter which removes everything above the 15’th harmonic in frequency space – i.e., everything shorter than (150/15 = 10) years:
and here is the first derivative of that graph:
Basically the process is:
– DFT the raw data into frequency space
– Remove everything above the 15th harmonic (keeping 0..14 and (N-15)..(N-1))
– IDFT back to time space
– (Second graph): Take first derivative
That’s it. There is no other smoothing or filtering.
Please ignore the end-effects; that is an artefact of the DFT/IDFT process which I’m still trying to figure out. I’d hate someone to use this as evidence of massive cooling in the past decade! Nevertheless, the main part of the graph indicates the same 11 and 22-year cycles. Oh, and the time axis is in months from 1850 (haven’t corrected that back from the IDFT yet).
Sorry this is a bit messy – there will be a proper interactive way of driving this at http://www.woodfortrees.org (as in, “seeing the…”) Real Soon Now.
Hope this helps!
REPLY: Thanks Paul, Nice to see an alternate method replicate it. Thanks for doing that. The first derivative graph you posted matches ours in pattern pretty well, but has one less peak. It also appears to be a bit more smoothed. Do you think that missing peak is related to the end effects you mentioned or maybe one of the smaller peaks, like 18, got smoothed out? -Anthony

Basil, thanks for the response. Would the Baxter-King high band pass filter, just replicate the same effort? I am not a scientist/mathematician so am clueless?
Unless you guys say no, I will put Part II up at my clearinghouse site. I already have the first referenced, but not written an article, as of yet. I am assuming that since it is here it is public.
REPLY: It Is public, feel free to link to it or post excerpts. I’d ask that the graphs not be copied to secondary webservers though. -Anthony

Frank Ravizza

I agree that demonstrating the exact physical link between temperature and the sun will prove difficult.
With regard to the apparent connection between solar magnetic field polarity and temperature, and the connection to cosmic ray flux which you eluded too; has anyone tried examining the physical interaction of the cosmic ray flux direction with the solar and terrestrial magnetic field? It seems apparent to me that the solar and terrestrial fields sum to increase or decrease the deflection of cosmic rays dependent upon the polarity of the solar magnetic field.
To elaborate on my inquiry of graphing the local dT/dt max and solar cycle max together to demonstrate correlation, I believe the key feature will be to find which solar parameter is linked to temperature change. From my previous paragraph, this link could be the solar magnetic field intensity, and/or some linear combination of other parameters.
It’s probably that whatever the link, it’s going to be highly convolved, because if it is obvious, you would think it would have already been discovered. Although, to be an important discovery you don’t necessarily have to hit the homerun, which would be a deterministic relationship capable of prediction, which is what the AGW focus on at their peril; it could just be a step in that direction and be critical to enhancing our understanding the solar-climate connection.

Bob B

Anthony or Basil, is it possible to get a hold of tabularized data for Fig3b and Fig4?
Much appreciated


I wanted to give a kudos on temperature analysis in the derivative domain. A lot of people seem resistant, because they think that differentiating a noisy signal is always wrong.
But the important thing here is the extraction of meaningful features.
The errors in the surface temp series will occur as thermometers are moved, as site quality changes, or as stations are closed down. These changes are acyclic, and tend to dominate a signal over time.
By filtering out this “noise”, you get to see a whole new set of information encoded into the temp record. This is exactly what signal processing is for.
My signal processing is decent, but my statistics is rusty. Can anyone estimate the chances that this is just coincidence? It doesn’t look like it to me, but I have been fooled before.


Nice job Basil/Watts. Nothing that will not be derided by most groups that are entrenched in one way or another, but still it is a nice piece of work. I look forward to more on this subject.


Why don’t you send your work to Bob Hodrick at Columbia? he is a good guy and not a brain-dead liberal. This is a topic that according to the alarmists is a threat to our very existence. It would be a good application of the skills that Hodrick has.
Maybe he could be paired up with someone like Lubos Motl or Svensmark to publish a study.

Paul Clark

I think peak 18 disappeared from low-pass(15) because it’s very close to peak 19, so got suppressed by my right-on-the-edge filter. Moving the filter up to harmonic 18 generates this:

Paul Clark

[Damn, wrong button: Please combine these if you can!]

Paul Clark

OK, here’s another interesting Fourier example… This is a band-pass filter between harmonic 5 and 25 – in other words, selecting cycles roughly between 6 and 32 years long:
Note this is not differentiated. This simple shows the raw data with the long-term (more than 32 year) trend and the short term (less than 6-year) noise removed.
I’m now going to put this on a Web page where you can select filters to your hearts’ content… watch this space!
What I want to know now is, what was different about the 1930’s, solar wise?


Oh, great. just when we’ve got this neato cool 60-year PDO cycle that correlates, and now THIS?!
Curse you, Red Baron!