Solar Periodicity

Guest Post by Willis Eschenbach

I was pointed to a 2010 post by Dr. Roy Spencer over at his always interesting blog. In it, he says that he can show a relationship between total solar irradiance (TSI) and the HadCRUT3 global surface temperature anomalies. TSI is the strength of the sun’s energy at a specified distance from the sun (average earth distance). What Dr. Roy has done is to “composite” the variations in TSI. This means to stack them one on top of another … and here is where I ran into trouble.

I couldn’t figure out how he split up the TSI data to stack them, because the cycles have different lengths. So how would you make an 11-year composite stack when the cycles are longer and shorter than that? And unfortunately, the comments are closed. Yes, I know I could write and ask Dr. Roy, he’s a good guy and would answer me, but that’s sooo 20th century … this illustrates the importance of publishing your code along with your analysis. His analysis may indeed be 100% correct—but I can’t confirm that because I can’t figure out exactly how he did it.

Since I couldn’t confirm Dr. Roy’s interesting approach, I figured I’d take an independent look at the data to see for myself if there is a visible ~ 11 year solar signal in the various temperature records. I started by investigating the cycle in the solar variations themselves. The TSI data is here. Figure 1 shows the variations in TSI since 1880

total solar irradiance lean dataFigure 1. Monthly reconstructed total solar irradiance in watts per square metre (W/m2). As with many such datasets this one has its detractors and adherents. I use it because Dr. Roy used it, and he used it for the same reason, because the study he was investigating used it. For the purposes of my analysis the differences between this and other variations are minimal. See the underlying Lean study (GRL 2000) for details. Note also that this is very similar to the sunspot cycle, from which it was reconstructed.

If I’m looking for a correlation with a periodic signal like the ~ 11-year variations in TSI, I often use what is called a “periodicity analysis“. While this is somewhat similar to a Fourier analysis, it has some advantages in certain situations, including this one.

One of the advantages of periodicity analysis is that the resolution is the same as the resolution of the data. If you have monthly data, you get monthly results. Another advantage is that periodicity analysis doesn’t decompose a signal into sine waves. It decomposes a signal into waves with the actual shape of the wave of that length in that particular dataset. Let me start with the periodicity analysis of the TSI, shown in Figure 2.

periodicity analysis tsi leanFigure 2. Periodicity analysis of the Lean total solar irradiance (TSI) data, looking at all cycles with periods from 2 months to 18 years. As mentioned above, there is a datapoint for every month-by-month length of cycle. 

As you can see, there is a large peak in the data, showing the preponderance of the ~ 11 year cycle lengths. It has the greatest value at 127 months (10 years 7 month).However, the peak is quite broad, reflecting the variable nature of the length of the underlying sunspot cycles.

As I mentioned, with periodicity analysis we can look at the actual 127 month cycle. Note that this is most definitely NOT a sine wave. The build-up and decay of the sunspots/TSI occur at different speeds. Figure 3 shows the main cycle in the TSI data:

cycle length 127 months lean tsiFigure 3. This is the shape of the main cycle for TSI, with a length of 10 years 7 months. 

Let me stop here and make a comment. The average cyclical swing in TSI over the period of record is 0.6 W/m2. Note that to calculate the equivalent 24/7 average insolation on the earth’s surface you need to divide the W/m2 values by 4. This means that Dr. Roy and others are looking for a temperature signal from a fluctuation in downwelling solar of .15 W/m2 over a decade … and the signal-to-noise ratio on that is frankly depressing. This is the reason for all of the interest in “amplifying” mechanisms such as cosmic ray variations, since the change in TSI itself is too small to do much of anything.

There are some other interesting aspects to Figure 3. As has long been observed, the increase in TSI is faster than the decrease. This leads to the peak occurring early in the cycle. In addition we can see the somewhat flat-topped nature of the cycle, with a shoulder in the red curve occurring a few years after the peak.

Looking back to Figure 2, there is a secondary peak at 147 months (12 years 3 months). Here’s what that longer cycle looks:

cycle length 147 months lean tsiFigure 4. The shape of the 147-month cycle (12 years 3 months) in the Lean TSI data

Here we can see an advantage of the periodicity analysis. We can investigate the difference between the average shapes of the 10+ and the 12+ year cycles. The longer cycles are not just stretched versions of the shorter cycles. Instead, they are double-peaked and have a fairly flat section at the bottom of the cycle.

Now, while that is interesting, my main point in doing the periodicity analysis is this—anything which is driven by variations in TSI will be expected to show a clear periodicity peak at around ten years seven months. 

So let me continue by looking at the periodicity analysis of the HadCRUT4 temperature data. We have that temperature data in monthly form back to 1880. Figure 5 shows the periodicity analysis for the global average temperature:

periodicity analysis hadcrut4 satFigure 5. Periodicity analysis, HadCRUT4 global mean surface air temperatures.

Bad news … there’s no peak at the 127 month period (10 year 7 month, heavy dashed red line) of the variation in solar irradiance. In fact, there’s very little in the way of significant periods at all, except one small peak at about 44 months … go figure.

Next, I thought maybe there would be a signal in the Berkeley Earth land temperature data. The land should be more responsive than the globe, because of the huge heat capacity of the ocean. However, here’s the periodicity analysis of the Berkeley Earth data.

periodicity analysis berkely earthFigure 6. Periodicity analysis, Berkeley Earth global land surface air temperatures. As above, heavy and light red lines show main and secondary TSI periods.

There’s no more of a signal there than there was in the HadCRUT4 data, and in fact they are very similar. Not only do we not see the 10 year 7 month TSI signal or something like it. There is no real cycle of any power at any frequency.

Well, how about the satellite temperatures? Back to the computer … hang on … OK, here’s the periodicity analysis of the global UAH MSU T2LT lower tropospheric temperatures:

periodicity analysis uah msu t2ltFigure 7. Periodicity analysis, MSU satellite global lower troposphere temperature data, 1979-2013. 

Now, at first glance it looks like there is a peak at about 10 years 7 months as in the TSI. However, there’s an oddity of the periodicity analysis. In addition to showing the cycles, periodicity analysis shows the harmonics of the cycles. In this example, it shows the fundamental cycle with a period of 44 months (3 years 8 months). Then it shows the first harmonic (two cycles) of a 44-month cycle as an 88 month cycle. It is lower and broader than the fundamental. It also shows the second harmonic, in this case with a period of 3 * 44 =132 months, and once again this third peak is lower and broader than the second peak. We can confirm the 132 month cycle shown above is an overtone composed of three 44-month cycles by taking a look at the actual shape of the 132 month cycle in the MSU data:

cycle 132 months t2ltFigure 8. 132 month cycle in the MSU satellite global lower troposphere temperature data.

This pattern, of a series of three decreasing peaks, is diagnostic of a second overtone (three periods) in a periodicity analysis. As you can see, it is composed of three 44-month cycles of diminishing size.

So the 132-month peak in the T2LT lower troposphere temperature periodicity analysis is just an overtone of the 44 month cycle, and once again, I can’t find any signal at 10 years 7 months or anything like it. It does make me curious about the nature of the 44-month cycle in the lower tropospheric temperature … particularly since you can see the same 44-month cycle (at a much lower level) in the HadCRUT4 data. However, it’s not visible in the Berkeley Earth data … go figure.  But I digress …

I’m sure you can see the problem in all of this. I’m just not finding anything at 10 years 7 months or anything like that in either surface or satellite lower troposphere temperatures.

I make no claims of exhausting the possibilities by using just these three analyses, of the HadCRUT4, the Berkeley Earth, and the UAH MSU T2LT temperatures. Instead, I use them to make a simple point.

If there is an approximately 11 year solar signal in the temperature records, it is so small that it does not rise above the noise. 

My best wishes to everyone,


PERIODICITY THEORY: The underlying IEEE Transactions paper “Periodicity Transforms” is here.

DATA: As listed in the text

CODE: All the code necessary for this is in a zipped folder here.  At least, I think it’s all there …

USUAL REQUEST: If you disagree with something I said, and yes, hard as it is to believe it’s been known to happen … if so, please quote the exact words you disagree with. That way, everyone can understand your point of reference and your objections.



newest oldest most voted
Notify of

“it is so small that it does not rise above the noise”
I love this quote from Pielke Jr:
“My 2¢ on metaphysics: a signal that cannot be seen is indistinguishable from a signal that does not exist”

Lance Wallace

Link to IEEE paper didn’t work for me.


0.8C of warming in 150 years is only 0.00533C per year. If we wish to find if solar variation can cause that, we will have to wait for solar cycle 25 or later and review data from modern instruments.
There are several plausible explanations of possible solar connections to climate variability, but trying to find 0.00533C per year in “reconstructed TSI” or old thermometer readings from 1880 seems a stretch. The corollary of that is nor can we dismiss the possibility of solar influence on such records.

Lance Wallace

The 2nd harmonic (88 months) looks like it might be there in the HADCRUT4 data as well. Since Roy used HADCRUT3, which might be less diddled with than HADCRUT4, would it be worth looking at?

Dave N

“Polar vortex over the South Pole unabated.”
Wow! That is cool.. thanks!

Ren doesn’t understand what “off topic” means, just because something is cool, doesn’t give you a license to blurt it out on a totally unrelated thread. Had there not been a comment addressing it already I would have deleted it.
Please folks, use TIPS and NOTES

1) TSI is made up of UV, IR and visible light. How far can we go back with those as separate values?
2) I notice the pre-1950 TSI curves are shorter with more periods that are very low.

Willis Eschenbach

Lance Wallace says:
April 10, 2014 at 10:51 pm

Link to IEEE paper didn’t work for me.

My bad, it’s here. I also fixed the link in the head post.

Willie Soon claims to have identified a link between solar activity and important temperature metrics.


Hi from Oz. Interesting analysis (as usual), Willis – thanks. Following up on the comment from sunshinehours1, can you tell me what has the TSI measurement that you used actually measured, in terms of spectral range (width)? Does it include all the solar radiation that might have an effect on global surface temperature, or not (i.e. from the high UV to the low infra-red range, including of course all the visible spectrum). And if not, how much radiation might have been missed by this measure, and what effect might the “missing” energy / insolation have for instance on the sea temperature, noting that (AFAIK) some of the non-visible light spectrum has a far greater heating effect on (sea)water than the visible light spectrum?
Keep up the good work – for us all.
regards, J


Dr Lief Svalgaard has made a new Sunspot series where he has integrated the data from various data sets. He has also made a 21 year Running average of the graph. How well does that running average correlate to the temperature graph?


By inspection, TSI is clearly too flat to be a good candidate for temperature correlation. UV, on the other hand, varies much more. A lunar component might also be proposed, since there is a pronounced atmospheric ‘tide.’ Leif claims the thermosphere is too tenuous to have an effect on weather; I’m not so sure. It’s certainly low in density, but it’s thick, and the thickness varies considerably with incoming UV. The odds of a photon escaping from Earth without colliding with an atom or ion in the thermosphere is very small.

Yes, you can play interesting games with sunspots. For example, the following integrates sunspot count using a baseline of 40 – anything below 40 sunspots is considered a “cooling” event. I don’t know how valid it is from a scientific perspective.

I think this result of Willis is consistent with the claim that the oceans with their immense heat capacity act as heat sinks to average out the annual and sub-decadal temperature variations
I have read the claim that the oceans (PDP, AMO, NAO) “ate the heat” from about year 2000 and will continue to eat the heat during the 30 years or so after 2000 until about 2030.
If we projecting that claim backwards 30 years in time before 2000, the oceans were in their up phase–yielding up the heat to the atmosphere–which would account for the observed global warming between about 1970 to 2000.
The oceans with their immense heat capacity act as heat sinks to average out the annual and sub-decadal temperature variations but the up phase of the 60-year natural cycle from about 1970 to 2000 has been mistaken as a secular increase global warming caused by burning fossil fuels.
I think this explanation is consistent with what Willis shows here and what Kevin Trenberth has offered as an explanation of the “pause”.


Please repeat with ocean temperature data. I suspect you may be surprised!


Further to the above comment I believe you may see surprisinly short term ocean temperature signals i.e. nothing to do with Frederick Colbourne’s buffering directly although this is doubtless of significant truth.

Kelvin Vaughan

I used to work on Tropospheric Scatter radio systems where the radio signal was lost in the background noise. You could clearly see this on a spectrum analyser. We were amazed to see that phase correcting 4 different receivers and combining their signal cancelled out some of the noise but enhanced the signal. You could now see sitting well above the noise.

in my greenhouse if the sun comes out its an oven and at night its sun effects pretty instant and variable.
if i was looking for sun influence correlations then i would look at earth angle movements, earth sun distances , maybe moon influence, magnetosphere. This would set the the mood within which a lot of other variables would be fitted like volcanoes
in the past space rock hits and close fly bys seem to be the cause the ‘catastrophic’ element in past climate. Sumarians talked of earth being shifted on its axis and earth crust slides eg hudson bay 12,900 years ago, after being hit by debris [and close fly bys of planet sized rocks] from a supernova explosion that they then reported caused a 1000yr winter [ younger dryas].
space rock like the russian 1908 come every 100 years and if it had landed in belgium would have killed everyone in it. So the next one could be a ‘country killer’ if it lands near mass populations.Some say modern civilisation has only a 50 50 chance of making it thro any 100 year space rock hit period. But you can’t tax ‘human caused’ space rock so co2 deathstar is the fashion in the academic beerosphere.
the point being does the earth have a stable climate system that is subject to frequent shocks like space rock and volcanoes that create ‘oscillations’ which take it ages to rediscover the return to the mean? So the effects remain after the cause is long forgotten?
given the melting ice sheets are revealing buried forests then this current warming looks more like a return to the normal mean or at least the warm season in the ice age ‘year’.

charles nelson

Could you please detail the locations and the type of equipment used to measure TSI during the 1880s?


No signal? Gimme a break…
By just looking at this plot you will notice the solar cycle influence on mean temp.


According to this site the TSI measurement is integrated over the entire solar disc and over the entire spectrum:
This report came from this website:
Apparently there are other TSI measuring data sources as well, and apparently they don’t agree with each other as is evident from a plot on Greg Kopp’s web page:


What Dr. Roy has done is to “composite” the variations in TSI. This means to stack them one on top of another … and here is where I ran into trouble.
I have to admit I haven’t looked at Dr. Spencer’s article, but when you said he’d “‘composite’ the variations in TSI,” what came to mind was a composite of the variations in UV, IR, and so on.


There is a big connection between TSI and Global Temps. TSI drives the AMO in turn the AMO drives not only N hem temps and global temps also I find. Seems in the 1970’s they forgot to tamper with the AMO data?
AMO and Global Temps


W: “it is so small that it does not rise above the noise.”
That makes it tricky but not an insurmountable problem.
Have a read of
Where ‘Spread spectrum’ techniques are described.
It is common, (especially with satellite signals) to demodulate signals that are ‘below the noise floor’.
Sounds daft at first but the above link gives an exceptional description of the process.
How does this apply to spotting ‘signals’ in climate records?
As with spread spectrum, you have to know what signal (or pattern or key) you will be receiving so all we need to do is predict what sine waves made up our 100 year data set (f1 + f2 + f3 etc), sum them and check for correlation with the time series, if a poor match then change the sine wave set and repeat.
The chance of hitting on an educated guess giving a good correlation is slim so:
One could envisage thousands of PCs running R scripts, with pseudo random sine wave sets being compared to a time series. With only ‘reasonable’ matches being flagged up, it would take little time from humans.
Perhaps 5 pseudo random frequencies, with pseudo random start points (phase shift) with pseudo random amplitudes,
Generate f’s
Correlate with Ts
Write variable values and correlation value to text file
After a certain time, grep the text file for values greater than 0.95 or whatever would be helpful for further diagnosis and share with others.

Alan the Brit

Even the crazy UNIPCC admit & accept that the Sun drove past climate changes, but irrationally & illogically deny that the Sun has a significant influence on Climate today! I find it somewhat bizarre that the big shiny ball thingamajig in the sky that heats me up when the clouds are away, but cools me down when the clouds are present, possesses 99.9% of the mass of the Solar System, is 332900 times the mass of the Earth, is a vast fusion reactor converting hydrogen (the second most abundant element in the Universe) into helium (the first most abundant element in the Universe) its activity can take out power grids, satellites, & communications equipment, & disrupt tv viewing pleasure, doesn’t affect our climate one jot, not even an iota!!!! Strange, very strange! Ho hum.


Willis says: “The land should be more responsive than the globe, because of the huge heat capacity of the ocean”
Whereas njsnowfan shows us a chart (short on axis data but I presume temperature – unquantified) showing exactly the short term correlation I predict. This graph in its own right contradicts Willis’s assertion despite this being based on on an obvious and true (implied) heat capacity argument.
In fact the ocean is being very responsive and is heating up and down in synchronicty with the TSI. I cannot see much of a phase lag at all but note the upward trend in temperature underlying the fine structure which I certainly believe is due in part to buffering effect mentioned by others and implied by Willis.
The AMO temperature curve is in sync with the TSI curve in fine detail however this is a correlation. No causality is proved. Indeed the AMO curve in my opinion is not caused by the pitiful TSI variation (as is likely the opinion of most readers of this article). The TSI variation is far too small when quantified to account for the ocean temperature changes.
Thanks to njsnowfan for showing us this curve match I predicted some years ago (but didn’t know the data existed).
So help us out Willis. Do your stuff with the ocean data and if we see a positive result I will tell you all what is going on!


No you do not need to divide the TSI anomaly by 4 because the Earth does not receive it ALL OVER but on a hemisphere because we have day/night cycles. So divide by 2.
Your thinking is FLAT EARTH thinking.

cRR Kampen

“The land should be more responsive than the globe, because of the huge heat capacity of the ocean.”
Somewhat true, but actually the solar cycle temp signal will mainly be found (and is found) inside of the tropics. The signal is lost at higher latitudes, much like the EN/SO-signal.


In retrospect, INMHO, Willis periodicity analysis wouldn’t so much care about who was right with respect to a baseline TSI value as this type of analysis sees low frequency and baseline data as one component all the way to the right of the graph. Instead this analysis provides insight about what is happening over time, where the time scale is anything greater than 1 month. As long as the data sets haven’t been fudged up or down with some kind of predetermined periodic data that just happens to be at 10 years 7 months or “averaged” so greatly over vast regions to produce a monthly values that are mush (ie premasticated so as to be devoid of any meaningful taste-bud signal, Berkley’s data?) – then periodicity analysis like Fourier analysis should show up any signal that repeats. Finding such a signal should then prompt the question, What is causing it? Does the sun have it’s own internal “clock”? And analysis of the magnitude of the variability over the “entire spectrum” should also prompt interrogation of why the “spectrum” was integrated, instead of measured at each wavelength to ascertain the true solar irradiance power, and instead of just staring at the sun, perhaps have a look as well at the earths overall outer atmosphere from a distance to watch how solar flux influences the molecules it bombards, and does this then correlate to cloud formation or any other phenomena below etc.
Would someone be so devious as to “fudge” data so that it had periodicity? I don’t think so. But many well meaning folk could so badly masticate data so that any meaningful periodicity was averaged out. So, NOT finding a signal could have meaning, or it could just reflect on how bad the temperature series currently are in there current “post-adjustment” state at giving us any kind of meaningful energy balance information.

I’ve given up the TSI –temperature link idea few years ago.
North Atlantic SST ( AMO )and the 350 year long CET record are by no means metric of what the rest of the globe is/was doing at the time. However they may help understand possible input from the natural variability, Maximum insolation months Jun + July have near zero trend, while the minimum insolation months December (Y-1) + January(Y) have the strongest uptrend. Graphs includes relevant periodgrams.
One could speculate for reasons, but this would be OT. Climate science is fun.

D. Cohen

i remember decades ago back in grad school coming across articles about how sunspots affected the weather, using data claiming that wheat prices in 19th century England correlated with the 11 year sunspot cycle. Sure enough, this stuff can still be found on line. The correlation of the sunspot cycle to wheat prices in the middle ages is discussed here
and an analysis of sorts of modern data is here
It wouldn’t have to be temperature changes affecting the wheat crop. It could be something reacting to keep the temperature from changing — for example, more clouds and rain in response to a rise in sunshine, (already suggested and analyzed in earlier posts here by the author W. Eschenbach)
I have also sometimes wondered whether investigators calculating the TSI have taken proper account of how the time-averaged, effective size of the sun could change over the sunspot cycle as more (and larger) or fewer (and smaller) solar prominences erupt from the sun’s edge. Each solar prominence seen edge-on from the earth would contribute just that much more to the solar radiation reaching the earth — and a similar thing could be happening with more or fewer hot particles being ejected into the solar wind. I think this effect would be very difficult to measure accurately, and of course it wouldn’t have to be a very big effect to change by multiple tenths of a percent the solar radiation reaching the earth over the solar cycle.

Layman Lurker

If there is an approximately 11 year solar signal in the temperature records, it is so small that it does not rise above the noise.

I think it makes sense that global temp is not a direct linear response to solar variability. But global temp should reflect energy imbalance which is ultimately about how the system captures and releases energy from the sun. Because of ocean inertia and other climate system properties, I seriously doubt that the ebbs and flows of (solar) energy imbalance is a linear process.

Eric Worrall says:
April 11, 2014 at 12:28 am
Yes, you can play interesting games with sunspots. For example, the following integrates sunspot count using a baseline of 40 – anything below 40 sunspots is considered a “cooling” event. I don’t know how valid it is from a scientific perspective.
I don’t think it is valid, especially not the free parameter 40. What would make sense, perhaps, is to use the overall mean as the base, then you get this:


Thanks, Willis — easy to understand. Interesting about the seeming ~44 month periodicity. Some kind of ENSO effect?
One might assume that the 10.7 yr TSI variance is simply too small to have an effect.


This is a very good read that Joe D’Aleo wrote, I found awhile ago, Has info on TSI.
Solar Changes and Climate.


Not so fast Willis
Others have done this more accurately and found peaks close to 10, 11 and 12 years, very close to your Best and UAH.


” Since Roy used HADCRUT3, which might be less diddled with than HADCRUT4, would it be worth looking at?”
How about the CET temperatures in that case?


Or we could use a 200 yrs sliding window for the integral, remember?


So the 132-month peak in the T2LT lower troposphere temperature periodicity analysis is just an overtone of the 44 month cycle,

Here’s the Wikipedia definition of an overtone:

An overtone is any frequency higher than the fundamental frequency of a sound.

The 44 month signal has a higher frequency than the 132 month signal. (frequency = 1 / period) Thus the 132 month signal is, by definition, not an overtone of the higher frequency 44 month signal.
The term you were probably looking for is undertone (or subharmonic). In my experience, in unamplified systems, subharmonics are usually a lot weaker that their fundamental frequencies. In that light, the 44 month signal is more likely to be a harmonic of the 132 month signal.
Other possibilities:
1 – both signals are harmonics of another, lower frequency, signal
2 – one or both signals are bogus and are products of the analysis
I’m not familiar with periodicity analysis and don’t know what kind of pitfalls it presents. Fourier Analysis suffers from things like aliasing and spectral leakage. I would be surprised if periodicity analysis doesn’t suffer from something similar.

lgl says:
April 11, 2014 at 7:30 am
Or we could use a 200 yrs sliding window for the integral, remember?
That would be yet another free parameter. I’m sure we could find more and thus drive the correlation to any degree of ‘significance’.

Retired Engineer John

Willis, this is an interesting analysis. I am sitting here thinking about what it means. When the Sun is at Solar Maximum, there is approximately a 6 percent increase in ultraviolet radiation. The total TSI increases only .1 percent; so there is reduction in mid frequency radiation. It would appear that sunspots with their much lower temperature, several thousand degrees lower, combined with the fact that the radiation generated varies with the fourth power of the absolute temperature shifts their radiation to lower frequencies and emits smaller amounts. The power generation of the Sun does not slow down and the energy must find other places to escape. The probable areas are the plaque areas on the Sun. These hot white areas radiate the energy blocked by the Sunspots at a higher frequency. In short, the spectrum of the Sun changes and the energy contained in the wavelengths that are absorbed by the substances whose temperatures you are analyzing could actually be decreasing. Just thinking.

lgl says:
April 11, 2014 at 7:03 am
Others have done this more accurately and found peaks close to 10, 11 and 12
Willis found those same peaks for the SSN; they are simply the result of the long 100-yr period]. They are not there for the temperature.

Retired Engineer John

Another factor, when you look at Bob Tisdale’s temperature charts, the Ocean temperatures appear to change in discrete steps, not in a smooth manner, that your analysis would require.


Willis Eschenbach says:
lsvalgaard says:
I think this one to one mapping of TSI or Sunspots to temperature could be missing something. As long as the Sunspot activity stays within some band the whole chaotic climate system just sort of chugs noisily along, but if Sunspot activity either remains below or exceeds the band over a protracted period the climate changes. The recent warming may have occurred during a period where sunspots were greater than average. While there are reconstructions of Sunspot numbers going back millennia, we only have observations of 22 complete cycles starting at the end of the Little Ice Age. Our temperature data is pretty much limited to the same period.
I think we can safely say the Little Ice Age happened as there is just too much evidence to reason otherwise. So…how could it happen?
Either the Sun done it, the Clouds done it or the Oceans done it or they all contrived together to do it.
I think we can rule out the Oceans as the sole cause because they would need to stuff heat down for 350 years and while I guess it is possible for the NAO to stay negative for that long, it is unlikely and the LIA would have only been regional.
So by my reckoning Total Solar Radiation decreased, Albedo increased or there was a combination of the two. From what I’ve read from Leif and others it seems to me that over the long trek the photons make through the Sun they should be pretty homogenized, meaning Total Solar Radiation is probably constant over millennial timescales. So as Sherlock says whatever is left, that being Albedo, done it. So whatever caused the change in Albedo, be it GCR’s , Volcanos, Unicorns or Space Aliens flying rice sized ships, if we can solve that riddle, I think we will be on our way to predicting climate changes into the future. My best guess is that somehow low sunspot counts over protracted periods increase the Albedo of the Earth, ….somehow.

Thanks, Willis. Very good analysis.
I will ponder its consequences in my overall view of the possible influences on climate.


From a comment I posted on Dave Stockwell’s blog back in 2011.

This is what I found when I plotted integrated sunspot number against satellite TLT temperatures some time ago. At time I wasn’t aware of the phase lag relationship.
I had to lag the model temperatures by 36 months to make the solar influence visually evident.  Of course, signals from ENSO and volcanism are present as well, and can dominate.  Now that I know that the correct lag is 11 * 12  / 4 = 33 months, I take credit for a good guess!”

This quarter-cycle phase lag relationship is well known to EEs and signal processing experts.


OOPS! Armagh temperatures not satellite temperatures.


Willis found those same peaks for the SSN; they are simply the result of the long 100-yr period]. They are not there for the temperature.
That’s three sentences and three errors, congrats.
Willis did not find those same peaks, one of them is at 9 years. The 100-yr modulation is just speculation, (and wrong because the sidebands are not symmetrical and not of the same amplitude) and there are indeed periods around 10, 11 and 12 years in the Best and UAH data.