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.
Bart, let me try this a different way.
I am well aware that in the lab, we can do lots of things with a signal. We can double the frequency, or halve it. We can heterodyne the signal with another signal, extract the resulting beat frequency, rectify it, and retrieve the signal that was riding on a carrier. We can amplitude modulate a carrier wave, pick one of the sidebands, throw away the carrier and the other sideband, and just broadcast the sideband. And on the other end, the receiving end, we can resupply the original carrier frequency and restore the original signal.
Your hypothesis is that an 11-year cycle can be transformed into say a 5 year and 60 year cycle, and giving me the math to prove it.
I know that. I know that in the lab, that 11 year signal could be doubled, or halved, or heterodyned, or rectified, the list is endless. You don’t have to demonstrate that, it’s obvious.
But the climate system is not the lab. There are no single-sideband radios, or any analogue of them, in the climate system. In fact, there’s a whole host of things that we can do to signals in the lab that just don’t seem to happen in the climate system.
So you can’t just point to the fact that you can take an incoming AM radio signal, heterodyne it, bandpass filter it to retrieve the frequency of interest, rectify it, and extract the news broadcast from the carrier wave DOESN’T MEAN THAT THE SAME THING IS HAPPENING IN THE CLIMATE SYSTEM.
That’s the missing link I keep pointing at. Be clear that I AGREE WITH YOU. You can do what you claim. You can transmute one signal into two signals at different frequencies than the original. Doing it on paper is no problem. Doing it in the lab is harder, but almost always possible for a given combination of one input and two output signals. So yes, Bart, I agree with the math and I agree with the lab results. It is possible.
But is it happening in the climate system? I am aware of no evidence that any transmutation of an input signal of that nature is happening in the climate system. For example, the annual variations in the strength of the sun are not somehow transmuted into a 3-month and a 10-year cycle.
The same thing is true of the daily cycle of forcing. It’s not transmuted into something else. We see the clear imprint of the 24-hour variation in total solar irradiation at a given location as a corresponding 24-hour variation in the temperature record.
And we also see the clear imprint of the seasonal variations in total solar irradiation in the corresponding seasonal temperature variations.
So why would we expect the 11-year variation in total solar irradiation to behave differently than the 24-hour and the seasonal variations in total solar irradiation? It’s possible, sure, I agree. You can do it with the math. You can do it in the lab. But you have yet to show the climate system is doing it, or anything like it.
However, yes, that may be possible. To show that it is anything more than a signal engineer’s fantasy, however, you need to show evidence that it is happening somewhere, anywhere in the climate system. I can do lots of things with math that will never happen in nature.
Let me recap the bidding:
• We agree a host of signal transformations can be done with math. Some, but not all of them can be translated into physical systems in the lab, and we are constantly learning how to do more.
• However there are no natural single-sideband signals in the climate system that I know of. Man does things with signals that simply do not occur in the climate system.
• You have no examples of your proposed effect occurring anywhere in the climate system.
• You haven’t even put forward an example of a similar effect occurring somewhere in the climate system.
• You have no proposed physical mechanism.
• Other variations in total solar irradiance behave as expected (cycles of input solar forcing reappear with the same period in the output temperature at all other timescales).
Given that, Bart, I’m not buying the idea that nutation ate the evidence …
I continue to say that IF there is an 11-year temperature signal corresponding to the ~ 11-year solar cycle, it is so small as to be lost in the weeds … and to me, than means the solar cycle doesn’t appear to be affecting the climate on a decadal scale.
Again, I make no overarching claims. I’m just saying, I can’t find evidence of the 11-year solar cycle in any of the temperature records I’ve examined to date. Doesn’t mean it’s not there. If you have such evidence, bring it forward.
I do think you understand signal anaysis, Bart. I just don’t think you considered the messy realities of climate.
w.
Bart, in writing that last comment, I got to thinking about why some kinds of signal transformations don’t seem to happen in natural systems like the climate.
What I realized was that many of the physical signal processing systems depend in some form on the concept of resonance. An oscillator naturally resonates at a certain frequency. Or a bandpass filter allows resonant frequencies.
I think the main issue is that natural flow systems are heavily damped. Curiously this is a result of the Constructal Law. The Constructal Law governs the direction of evolution of flow systems. It states that flow systems far from equilibrium (e.g. the climate) evolve to increase the size of the interface between the individual flows that make up the system.
One corollary of the Constructal Law is that natural flow systems evolve towards configurations which would stop the most quickly if the driving force is removed. This is because of the extensive contact between individual flows going in opposite directions.
As an example, consider the flow of the Hadley cells. At the surface, the air is moving constantly from about 30°N to the Equator. But just a few miles above the surface, the air is moving constantly from the Equator to about 30°N.
So we have a giant sheet of air about 2,000 miles long (Equator to 30°N) and a few miles thick going south, and directly above it the same thing going the other way …
Systems like that don’t “ring”. They don’t feature much in the way of overtones. There is too much turbulence and counterflow at the interface, and that interface covers the entire region 30N-30S.
Anyhow, that’s my guess about why we can do things with signals in the lab that don’t seem to occur in the climate system. It’s too heavily damped by turbulence and counterflow.
w.
Willis says:
“You seem to be claiming that the tides are a line-spectrum signal but that temperature or something else unspecified is a CONTINUOUS spectrum signal. I’ve provided periodicity analyses upstream for a number of datasets. Which of them are line-spectrum and which are CONTINUOUS, and how do you distinguish the two?”
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If the tides did not intrinsically consist of the superposition of a large number if pure sinusoids, they would not be predictable over the far time-horizons that they patently are. The tidal constiuents are indeed LINE spectra; see Fig. 17.12 in http://oceanworld.tamu.edu/resources/ocng_textbook/chapter17/chapter17_04.htm
The complicating factor is that many of the constituents are incommensurable in period; hence, they are smeared into adjoining frequencies, because they do NOT correspond to a harmonic set of frequencies as in FFT or “periodicity” analysis. Tides require special methods of analysis, outlined in Bruce Parkers monograph at http://tidesandcurrents.noaa.gov/publications/Tidal_Analysis_and_Predictions.pdf
Other geophysical variables, on the other hand, are not driven by a discrete set of periodic astronomical forces and manifest a CONTINUOUS power spectrum, characteristic of chaotic or random processes. This includes wind-stress-driven variations in water level that also register in tide-gauge records–adding another complication.
It’s a nice try to invite me to provide suitable analysis of the S.F. tide record. While I’m experienced in doing such analyses, I don’t do free consulting. You’ll have to learn enough to credibly analyze that data yourself.
Bart:
Outside of some coastal waters, the flow velocities in tidal streams are generally not fast enough to push the [ Reynolds number] into the turbulent range. The tidal flow field is usually irrotational. And not even the most funding-hungry academics claim that the lunar precession cycle, which modulates the diurnal tidal range by several centimeters, is what [produces] “tidal mixing.”
Willis Eschenbach says:
RobR says:
“Extended excursions below the LCL could result in high albedo making higher albedo and cold.”
Well I spent a lot of time trying to back up my idea. I thought if I plotted the trend of the temperature around high and low periods of sunspot activity, I would see a difference. So I downloaded the massive HadCruT4 and filtered it only to realize it only went back to 1850. I wanted to look at sunspot cycles around 5, 6, 7 and 8 so I downloaded the CET record. There is no trends I could tie to sunspots in the CET data. I messed with anomalies, raw, even plotted the moving slope for each month looking back 6 years and ahead 5. The slopes oscillated around but never in correlation with sunspots. I did trends and there were negative trends during high sunspots activity and positive trends during low. There was nothing, nothing, nothing to reinforce my idea.
While there may be something to my thoughts, I can not find any evidence. I think I thought what I thought because I always thought it, from stuff I heard or read. At this point, I have to grudgingly believe, based on the direct observation data (who knows about proxies and what) there is no correlation between sunspots and temperature as far as I can tell.
RobR
Moderator:
Please correct my last comment to read Reynolds number, instead of Richardson number.
In my comment to Bart, please read Reynolds number, instead of Richardson number.
1sky1 says:
April 17, 2014 at 5:19 pm
Well, that’s the last time I ever communicate with you on a scientific matter, 1sky1. You just burnt your bridges with me Your claim, that I’m asking you to do valuable consulting for free, is the most ludicrous excuse for not answering a simple question that I’ve heard in all my time blogging.
Look, 1sky1, if you don’t have the interest or the time or the balls or the smarts or the whatever it is to answer my question, that’s fine. You can bail on the challenge, you don’t need to explain why. Your explanation doesn’t matter, in any case—people see you running from the question in a cloud of dust, and none of your excuses will change that.
But claiming you are backpedaling because I’m trying to take commercial advantage of you? Did you really believe that would fly? Do you think the lurkers are blind?
I asked you to compare your analysis with mine in the spirit of friendly scientific inquiry, and anyone reading the thread knows that. To cast that as a “nice try”, to accuse me of trying to take commercial advantage of you is sick, my friend. That’s all you, not me.
I leave you to talk to the others if they can stomach you. I’m done with you.
w.
Bart says:
April 17, 2014 at 1:54 pm
Like I said, Willis. If you heat something with a T1 period cycle, and that something stores and releases heat on a T2 cycle, then the two cycles are going to modulate, and the amount of energy stored is going to evolve in periods of T1*T2/|T1 +/- T2|.
Think, maybe, of a heat source being alternatingly pushed toward a thermometer, and then pulled away. Now, move the thermometer back and forth, too, with a different period. What periods will show up in the temperature reading from the thermometer?
I’m tired, Willis. I’m tired of being attacked for saying things I know to be true, but without the means in this venue to demonstrate that I am right. I really don’t need this in my life. If you don’t get it, if you don’t believe it, then you don’t. The world will get along.
1sky1 says:
April 17, 2014 at 5:19 pm
There are no pure sinusoids in nature. Even our best crystal oscillators are merely the excitation of a high Q oscillating mode with a sympathetic input.
1sky1 says:
April 17, 2014 at 5:28 pm
Doesn’t have to be turbulent. Max effect is at the transition between steady and unsteady flow. But, it does not have to be at the max to have a significant effect on climate. Remember, we’re talking something on the order of 0.7 degC over 30 years.
And, I’m not talking about precession.
Bart says:
April 17, 2014 at 9:18 pm
Bart, I guess my last message didn’t get through. Let me try again. I agree that lots of things can happen IN THEORY, as in your theoretical example above. And I agree that lots of things can happen IN THE MATH. And I agree that lots of things can happen IN THE LAB.
What I don’t see, and have never seen, is a natural single-sideband signal in the climate. I use this as a simple example of a fairly simple signal transformation that happens in theory, in the math, in the lab, in radios around the world … but doesn’t appear in nature.
So what your theory needs, Bart, and what it doesn’t have, is a single real world example of what you claim is happening in the climate system. Let me give you a f’rinstance.
The earth moves closer to and further from the earth over the course of the year. This is exactly the situation that you describe above, with the “heat source being alternatingly pushed toward a thermometer, and then pulled away”
Now, I’ve never seen that 12-month cycle end up modulated into say a 5-month and a 60-month cycle, as you and I both agree can happen in the lab. But perhaps it is actually happening.
But until you find an actual example, Bart, it’s just a signal engineer’s fantasy. You need to go beat the bushes and show how the earth approaching and then receding from the sun creates an 18-month cycle somewhere.
Until you can show it actually happening, not in theory, not in the math, not in the lab, but in the real climate systems somewhere, anywhere, you have nothing but an unsupported theory.
Ding-burst it, how many times do I have to say it? I AGREE WITH YOU! The things you say are true. All of that stuff does work the way you say it does, in the lab and in the math and in theory.
And for all we know, they may be happening in the climate system … but until you can come up with one real-world example, you have nothing. Zip. Zero. Nada. Zilch. Nicht. Nulevoy.
The problem is, Bart, that theories about cycles are a dime a dozen … actually, that overvalues them. There are uncountable folks out there on the web, each with his own cycle theory, each as convinced as you are that they are right … and we know you can’t all be right.
What you theorize is a forcing at one frequency disappearing totally and being transformed into two widely separated resultant signals at very different frequencies.
I DO BELIEVE THAT IS POSSIBLE. I know all kinds of signal processing can happen in theory, in math and in the lab. Certainly it can happen.
What I have absolutely no evidence for is anything like you describe (the period of variations the forcing disappearing entirely and reappearing at other periods in the resulting temperature) happening anywhere in the climate system …
I don’t say it’s not possible. I don’t say it’s not happening.
I do say I’ve never seen evidence of it happening. And being a scientist, without evidence, I give your theory a pass.
w.
Bart says:
April 17, 2014 at 9:18 pm
“Now, move the thermometer back and forth, too, with a different period.”
Actually, that’s a bad example. A better one would be assume no motion, just that the power to the heat source is alternatingly ramped up and down with one period. Then, have a screen extend and retract between the source and the thermometer with some other period. Now, what periods will show up in the thermometer reading?
“But until you find an actual example, Bart, it’s just a signal engineer’s fantasy. You need to go beat the bushes and show how the earth approaching and then receding from the sun creates an 18-month cycle somewhere. “
It was a bad example. It is the unsteady mixing of the oceans storing heat, not the distance, which would create the modulation of the solar input. The new example I put in above, which oddly I wrote just before your new post flashed up, is much more representative.
“I don’t say it’s not possible. I don’t say it’s not happening. I do say I’ve never seen evidence of it happening.”
But, until you can say for sure it isn’t, then you cannot say that solar variation is not affecting the climate. That has been the point all along.
These things are in my favor, from my point of view:
1) The GHG theory has failed. It does not explain the trend and ~60 year periodicity, both of which have been in evidence since the end of the LIA. With just those two components removed from the observations, there is very little which needs to be explained or worried about.
2) The Sun and the Moon have known, large effects on the Earth’s climate. A mechanism involving them is really the first place that should have been looked to explain the observations. The temperature variations are really a fairly small. Second order lunar and solar effects are probably the cause.
3) There are known lunar/solar/terrestrial processes which would produce the observed periodicities if modulated together.
4) This looks suspiciously like this.
5) What other viable processes are there which could produce the observations?
I see no other viable competitor. I think this is it. Time will tell.
Willis says:
The SF tide data is here, monthly data 1850 to 2014 as a .csv file. Link to your graph of what you consider to be a proper signal analysis of that data, and we’ll go forwards from there.
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Throw whatever tantrum you want about my refusal to spend my day doing a proper signal analysis of the SF data, but anyone expert at that will recognize that it’s you who’s running away from the manifest inability to recognize what’s involved in such. You plainly failed to grasp my earlier analytic expanation about the continuing periodic acf of line-spectrum signals versus the decaying acf of continuous-spectrum signals. And you continue to believe that the wave form produced by “periodicity analysis” can be meaningfully extended as in your Figs. 3 &4. Try comparing that extension with the actual signal and you’ll find that works only if that signal IS periodic (such as the annual temp cycle), but not with narrow-band aperiodic signals (such as sunspot data).
Bart:
I only have time to say that pedantry about physical periodicities hardly conceals that you don’t know what you’re talking about in matters oceanographic.
1sky1 says:
April 18, 2014 at 5:22 pm
Whatever you say, 1sky1, say what you want, but I’m done with you. I told you in friendship to that it was difficult to understand your theoretical explanations. I asked you in friendship to show us a practical example of what you meant, by doing a simple analysis to compare to my analysis, so we could understand the differences.
You response was to accuse me of trying to slip something by you, to accuse me of sneakily trying to get you to reveal your infinite wisdom for free, when everyone knows that your time is oh-so-valuable …
Fine. You don’t want to play, that’s fine.
But I’m not interested in your further excuses for not doing it, no one is. Everyone sees you running from the challenge. No one cares what you are mumbling as you bolt for the door after refusing to provide a simple example.
As to your further claims that I don’t know what I’m doing, perhaps I don’t. But I’ve provided data, code, theoretical support, and an IEEE paper to back up what I said … you’ve not shown that anything I’ve done is wrong, even though you have to code to inspect. Instead, you’ve provided nothing but insults and opaque theory. I’m more than happy to let the lurkers decide who knows what here.
Address your further remarks to Brad, 1sky1, because as far as you’re concerned, I’ve left the building.
w.
1sky1 says:
April 18, 2014 at 5:25 pm
Meh. You have shown no particular acumen. You don’t even seem to know the difference between turbulent and unsteady flow, or precession and nutation.
lsvalgaard says:
April 14, 2014 at 12:24 pm
Thanks for that link, Leif. It’s a nice piece of work.
w.