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
Figure 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.
Figure 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:
Figure 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:
Figure 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:
Figure 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.
Figure 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:
Figure 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:
Figure 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,
w.
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.
jorgekafkazar says:
April 11, 2014 at 12:26 am
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.
This may be very pertinent. Satellites are affected by thermosphere changes since a hotter states results in expansion and thus more drag on satellites placed in Low Earth Orbit. Cooling has the opposite effect. I’ve heard through grapevine sources that the last few years have seen unexpectedly low requirements for orbital correction maneuvers, meaning the “pause” has had genuine economic effects. Less maneuvering means that the satellite can remain in service longer before it ceases to be maintainable.
One could start with the basics. If we look at solar changes purely as a radiative forcing of 0.15 W/m2 (0.044%), one can calculate a no-feedbacks temperature change of 0.028 degK (using dW/W = 4*(dT/T). Multiple this whatever feedback amplification you prefer: The IPCC’s preferred value for TCR 1.8 degC is 1.5X greater than a no-feedbacks climate sensitivity of 1.2 degC, whereas Nic Lewis’s preferred TCR of 1.3 degC represents essentially no amplification. (For cycles of 11 years, TCR is a more appropriate metric than ECS.) From a purely forcing perspective, the amplitude of the temperature response to TSI forcing is likely to be about 0.03-0.05 degK.
Anyone proposing or finding changes bigger than this is looking for a mechanism that isn’t purely dependent on the change in total energy reaching the earth. The amplitude of the change in UV (about 10%) with the solar cycle is far greater than the amplitude of the TSI change (0.04%) and the change at even higher energies is greater – but these high energies don’t penetrate to the troposphere. The mechanism of their effect must be indirect. Trying to detect these indirect effects using TSI data reported units of W/m2 appears somewhat dubious, when we already know that radiant energy alone can’t produce large changes in temperature. Looking for correlations with some other proxy for solar activity besides TSI (sun spot number, C14, Be10, ?) might be more fruitful.
Willis, writes:
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.
++++++++++
I’m at work, but found this post’s introduction of interest. I look forward to reading it more thoroughly later on, so my input could be moot or incorrect.
It sounds like Roy integrated the rate of TSI over time. In controls, when we integrate, we add up rates over a millisecond time frame so we capture at that level of precision, the accumulation of the rate. So the sample changes from a rate to an accumulation of that rate, or the integral. Thus if we integrate power over time, we get energy. If we integrate speed, we get distance. I hope my input is not insulting, but if this is what was done, readers might find my post of interest.
Kindest regards,
Mario AKA fanboy 🙂
Willis
There is a paper by Dan Pangburn : The Time-Integral of Solar Activity explains Global Temperatures 1610-2012, not CO2
Calculated Mean Global Temperatures 1610-2012
http://hockeyschtick.blogspot.com/2014/04/the-time-integral-of-solar-activity.html
This paper considers the effects of solar magnetic cycles on long term ocean heat flux and ocean surface temperature oscillations. This takes into account the total solar effect – UV flux and frequency changes during cycles, ozone production and destruction and solar proton flow that affects ozone heating, hence surface pressures and of course through cosmic ray flux low level cloud formation:
http://climatechange1.wordpress.com/2011/09/19/climate-disaster-declining-rainfall-rising-sea-levels/
http://www.space.dtu.dk/upload/institutter/space/forskning/06_projekter/isac/wp501b.pdf
http://hockeyschtick.blogspot.com/2014/04/new-paper-corroborates-solar-cosmic-ray.html
Since it is recognized that global land temperatures largely reflect ocean surface temperatures and ocean heat capacity through heat distribution via the atmosphere and ocean currents this approach that ignores the deficiencies of the land series makes more sense. I would be interested in your take on the paper.
Nice work Willis.
people should do the following thought experiment.
Look at figure 1.
Imagine that Willis had labelled that C02.
Then imagine he had claimed that he could find no c02 effect in the temperature data.
would you accept this result.
Now lets look at the twists and turns. First lets look at them schematically
A) Theory “X” influences the climate.
B) hypothesis, if “X” influences the climate and “X” has property “Y” ( a peak at 11 years)
Then we should find “Y” in the climate.
C:test.
we look for “Y” in the climate and dont find it
D: interpretation
I’ll use this example to make the argument Ive made many times before. Nothing compels us to
“falsify” a theory. Step D is not a logical step or mathematically determined. It is an interpretation
step. It’s governed by pragmatics .
Here are some choices.
1. Falsify the theory?
2. you need to use a different method
3. you need to look at different data sets/ adjust data etc
4. you need to look for different effects in the climate/
5. its too small to see we will have to wait.
6. Stop investigating the theory, chances of it being true are low
Note that there is Nothing in math or logic that dictates what you should do ( 1 through 6)
It a choice. a pragmatic choice.
Folks looking for a big solar influence are wasting their time. That’s a pragmatic choice.
After looking at the off-topic antarctic polar vortex graphic and the D’Aleo paper posted, plus the other comments, with all the feedbacks in place can you really expect a peak anywhere?
My guess are trend changes at best. Changes in UV and solar wind result in changes in ozone and cloud formations which changes wind and frozen precipitation patterns which changes ocean temps which changes jet stream patterns which .. you get the drift. Throw in the thermal inertia of the oceans and it make it worse.
I know the intent of the article was to prove/disprove a statement by Roy Spencer and Willis presented his methodology and findings in his usual easy read and understand method. But if you are heating a large pot of water on the stove and turn the heat down suddenly, the water temperature in the pot will slowly cool. Turn the heat back up and it will slowly warm. I see peaks in the heat going in, but curves in the results.
wow.
I should have read all the excuses before I did my comments.
folks seem to be saying.. Forget feynman…….
What ever you do Willis, dont falsify the theory.. dont do that!!!
forget Feynman, forget Popper…
Instead…
is your data good, look at hadcrut3, look at land, look at ocean, look at CET, arrggg
look at lake levels, look at stream flows, look look look find that 11 years somewhere..
find that unicorn..
is your method right? oh use a different method, use method x, scale by z, integrate the signal,
detrend, then integrate, transform, flip, stretch… find that 11 year signal..it has to be there…
dont look at TSI, look at UV.. look here, look there, look everywhere
Here is the clue folks. When you believe it has to be the sun, there is NO END to where you can look and how you can look.
No end.
No mathematical end,
no logical end.
You can look for unicorns forever.
and the longer you look the higher your chance of finding a spurious result.
if your goal is actually understanding things.. you’d note that the sun supplies the power. the power doesnt vary much.. and you’d look at something else to explain the changes.
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.
###############
sun + volcanos is the standard theory. it works.
“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.”
Willis’s usual masterful analysis of TSI vs temperature quantifies long-held conclusions that variations in TSI are too small to correlate with global temperature changes. But that doesn’t necessarily mean that we should forget about solar variation related to global temperature. It isn’t mere coincidence that global cool periods correlate so well with times of low sunspot incidence (e.g., Maunder, Dalton, 1895-1915, 1945-1977 among others). The 11-year periodicity doesn’t correlate well with global temperature, but the number of sunspots in each cycle correlates very well.
Also interesting is the very good correlation of 10Be and 14C concentrations with sunspot number, which tells us that 10Be and 14C production rates in the upper atmosphere (which depend on radiation flux) are dancing in tune with solar variation and global temperature.
So my question, Willis, is what do the numbers show if you plot numbers of sunspots in each cycle with global temperature, rather than the periodicity?
Steven Mosher says:
April 11, 2014 at 9:40 am
…Folks looking for a big solar influence are wasting their time. That’s a pragmatic choice.
++++++++
Do you really conclude that the sun does not have a big influence on our climate? Riddle me this: What is the most influential source of energy that warms our planet?
I submit that the argument is whether or not relatively small changes in measured TSI could result in slightly higher variations in temperature of a complex system.
tolou says:
April 11, 2014 at 1:54 am
I looked at the plot. I don’t see any such influence. What next? Well, what would normally be next is a mathematical analysis of your data … I await your analysis.
w.
@njsnowfan says:
April 11, 2014 at 2:25 am
Thanks, snowfan. Unfortunately, your accompanying graph is useless, because you haven’t specified where you got your data, or how you have massaged it to get it to that form …
In any case, I just did a periodicity analysis on the AMO data. There is no peak of any kind near the 10 year 7 month period, and in fact the periodicity analysis of the AMO (as one would expect) looks very much like the periodicity of the HadCRUT data … no surprise there, because the AMO is just a detrended subset of the global temperature data.
w.
Kelvin Vaughan says:
April 11, 2014 at 1:35 am
Thanks, Kevin. You are right that kind of task is not too hard to do … if you already know the answer.
By that I mean that in your example you knew a) exactly what the signal looked like that you were searching for, and b) that it was in fact there, and c) you had scads of good clean data.
But as usual, “parallels” from the world of signal analysis don’t transfer all that well to the climate domain. Digging out a signal gets much harder when you don’t know if the signal is even there, or if it is, what it might look like, and when your data is really bad, with lots of gaps and variations in quality … in that kind of situation, you might find the signal and not recognize it, or not find it and think you recognize it.
When you solve that one, let me know. Until then, claims of success in some field other than climate like signal analysis don’t really mean much …
I don’t mean that climate scientists couldn’t learn from signal analysts, there’s much they could learn. But that doesn’t make the underlying problem more tractable.
w.
steverichards1984 says:
April 11, 2014 at 2:34 am
See my post immediately above …
So you are going to run a million possible scenarios, and grep for the extremes using a p-value of 0.95? … if you don’t see the problems with that procedure, I’m not going to try to explain them.
Finally, you ASSUME that the climate can be represented over some long period of time as a simple superposition of sine waves, and your method searches for them. If so … don’t you think a simple fourier analysis would be a better way to go about it? And don’t you think people might have tried that already?
w.
eco-geek says:
April 11, 2014 at 2:46 am
Dear heavens, njsnowfan’s graph shows NOTHING!.
We have no idea what was done to get those two lines to line up. eco-geek, I showed the actual TSI in Figure 1. When you figure out how njsnowfan converted that data to what you see in njsnowfan’s graph, you let us know, OK? Because njsnowfan’s data doesn’t contain an 11 year cycle. Look at Figure 1 before you sign up for njsnowfan’s uncited, unreferenced, and unexplained graph. Does his “TSI” data look like Figure 1? No. Can you explain why? No.
But SIMPLY BECAUSE IT FITS YOUR PREJUDICES, you want to pick up the snowfan’s uncited and unexplained, mystery graph and start bashing me with it? Sorry, my friend … here we do science.
w.
cRR Kampen says:
April 11, 2014 at 2:51 am
Science by unsupported assertion … wonderful. Come back when you actually have something to add to the discussion.
w.
D. Cohen says:
April 11, 2014 at 3:43 am
Yes, this claim can still be found online … so what? Even the most simplistic analysis of Herschel’s original claims about wheat prices and sunspots show that he was totally wrong. Heck, even your citation says Herschel was wrong …
And the citation you give? First off, it appeared in a Nature journal, so that means it’s got a good chance of being totally incorrect, as Nature has a long record of publishing bogus climate studies.
But setting that aside, did you bother to read the underlying document, or were you just fooled by the Nature article? Because the underlying document is a hoot. It’s here, and contains howlers like this one:
Oh, that’s wonderful. They simply throw out the data that doesn’t agree with their theory … and you believe them? Do your homework, friends. There is as much garbage about climate published in “scientific” journals like Nature as there is in the blogosphere … actually, often the quality of the science is much higher in the blogosphere.
I’m not sure why this kind of “science” is all too common in the field of solar studies. Perhaps people get sun-struck or something when they start their analysis …
w.
Steven Mosher says (elsewhere):
……… magic undetectable fairy dust (that) controls the temperature?
Not exactly, but close enough, it’s the flutter of its wings ; see bottom right hand corner,
lgl says:
April 11, 2014 at 7:03 am
Scafetta? If Scafetta told me it was raining, I’d look out the window. The document you cite closes by saying:
Couldn’t agree more …
w.
RobR says:
April 11, 2014 at 8:28 am
Really? And your evidence for this is … what?
Folks, “science by assertion” doesn’t work with me. If you want to make some claim like Rob’s claim, that the climate changes if sunspots go above or below a certain (unspecified) limit, you need more than your mouth to back that claim up.
w.
“Do you really conclude that the sun does not have a big influence on our climate? Riddle me this: What is the most influential source of energy that warms our planet?”
1. the sun supplies all the energy.
2. the variations in that power are small.
3. these variations do not influence the CLIMATE
4. climate is the long term average of weather.
There are exceptions. when we look over really long periods you will find evidence that orbital changes do influence the climate and that the faint young sun does as well.
But to the actual point. The changes from 1850 to today are not solar driven
A) the variations are small relative to the changes
B) there is no coherence between the TSI record and the temperature ( which is just PART OF the climate)
C) If you want to identify the cause of the change in temperature, you need to look at something else.
what is not a cause.
1. natural variation. natural variation doesnt explain natural variation.
2. ocean cycles. ocean cycles describe patterns in data they do not ’cause’
a good candidate for study?
well the intuition that the sun is the main cause is good one. the sun supplies the power received.
does anything else cause forcing or change forcing or modulate forcing.
yes: the atmosphere and what it is made of
Steven Mosher says:
April 11, 2014 at 9:55 am
” sun + volcanos is the standard theory. it works.”
Volcano: I do not thinks so, a big one would need to have gone off every couple of years for 350 years.
http://wattsupwiththat.com/2014/02/24/volcanoes-erupt-again/
Sun: This post is saying no.
pochas says:
April 11, 2014 at 9:08 am
Pochas, I can’t tell you how tired I am of people posting uncited, unexplained, unreferenced plots like yours on the web. The plot you gave is entitled ” ‘Lumpy’ vs Armagh Temps”.
Now, I’m immersed enough in this world to know that “Lumpy” is Lucia’s name for her simplified climate model. And Armagh is a monastery with a very long and very good temperature record.
But above you claim that the temperatures are lagged, saying you had to “lag the model temperatures” … what does that mean, particularly since on your plot it says “lag sunspot data 36 months”. And what “sunspot data” are you using? It’s obviously not the raw data, given the smoothed curve.
Finally, I don’t see any 11-year signal in the Armagh data … hang on, I have it on my computer … OK, here’s the predominant cycles in the Armagh temperatures:
The problem is that there are no predominant cycles in the Armagh data, 11 years or otherwise. So your claim that the Armagh temperatures have a solar component simply doesn’t stand up to examination.
Look, guys. I’m happy to be shown wrong … but waving your hand at some whiz-bang uncited unexplained unreferenced and mathematically unanalyzed graph on the web isn’t anywhere near enough to do it.
w.
PS—Curiously, the same 44-month cycle is the strongest cycle in the Armagh data … WUWT?
“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.”
You don’t hear the carrier signal on your AM radio either. If you hypothesize that the Earth’s climate response is dominated by processes with very long time constants, then that could be effectively what is happening – the 11 year “carrier” is filtered out, and you get the “signal” which is carried in the envelope of the rectified carrier.
However, there is another possibility. To appreciably affect the climate, you might hypothesize that you need to get substantial ocean mixing to store up the heat. That would suggest that perhaps the additional solar heating would be modulated by the sloshing of the oceans as forced by nutation of the Earth’s polar spin axis.
The Earth’s spin axis undergoes forced nutation, mostly from lunar influences, with a period of about 18.6 years. The radius of that motion varies in roughly a 3:2 ratio with a period of about half that at 9.3 years. Modulate an 11 year influence with a 9.3 year one, and you get periods of
T1 = 11*9.3/(11+9.3) = 5 years
T2 = 11*9.3/(11-9.3) = 60 years
These are, roughly speaking, evident in the data. I discuss this all here.
Steven Mosher says:
April 11, 2014 at 9:55 am
Thanks, Steven. I dealt with the “volcanoes caused the Little Ice Age” claim in my post “Dronning Maud Meets the Little Ice Age“. Short answer? Ice core data says volcanoes had nothing to do with it.
w.