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.
1sky1 says:
April 14, 2014 at 5:25 pm
Mmmm … not exactly sure what that means. The results produced by an FFT will not magically make the noise disappear either.
I guess my problem is not understand what you mean by “decompose a signal … in a variance-preserving way”. You can decompose a signal using either FFT or periodicity analysis. As you might expect, when you combine the underlying frequencies in either method, you reconstruction the original signal exactly.
The difference between the two is that the FFT decomposes the signal into an orthogonal set of waves. So the results are the same regardless of the order in which you remove the underlying sine waves.
In periodicity analysis, on the other hand, the signal is projected on to non-orthogonal periodic spaces. So the order in which you remove the underlying waves leads to different results.
Note, however, that I’m NOT trying to “decompose a more general signal in a variance-preserving way”, no matter what you might mean by that. I’m not trying to decompose the signal in any manner or form.
Instead, I’m using periodicity analysis to display the strength of the cycles at each underlying period. The huge advantage of periodicity analysis for this purpose is that periodicity analysis is linear in period, rather than being linear in frequency as is FFT. This lets me examine the question in detail.
The other advantage is that it doesn’t find just sine waves. Instead, you can examine the actual form of the 11-year or any other cycle, as in Figures 3 & 4.
More confusion. Don’t mistake me, I’m not saying you’re wrong. I’m saying it’s hard to understand your meaning. For starters, you were talking about periodicity analysis. Now you’ve shifted to discussing autocorrelation. I don’t understand the connection.
In any case, we are not dealing with strictly periodic cycles, nature is never that regular. For example, TSI / sunspot cycles vary between about 9 and 13 years … go figure. This is revealed quite clearly by the periodicity analysis. It shows up in the width of the peak in Figure 2.
Note that from about ten to about eleven and a half years we have increasing and then decreasing power in the various cycles. I assume that this is what you are calling “a spectral CONTINUUM in a narrow band of frequencies”.
Did you read the IEEE Transactions paper I referenced above? I think it might answer some of your questions.
Anyhow, thanks for your thoughts,
w.
lsvalgaard says:
“You make the same mistake as Bart, believing that there is a physical signal of that length. There is not. The ‘signal’ comes about because there are different physical reasons for the various peaks.”
Yes I do realise that there are “different physical reasons for the various peaks”, but the issue is here is simply about where they occur, not why they occur.
Ulric Lyons says:
April 15, 2014 at 6:18 am
but the issue is here is simply about where they occur, not why they occur.
But that is not an ‘issue’. The data themselves show us that: http://www.leif.org/research/Historical%20Solar%20Cycle%20Context.pdf
Geomagnetic activity, A, can be calculated from the contributions from the three parameters B, V, and n: A = k B V^2 n^(1/3) giving you the several bumps that we see.
sorry, wrong link. Should be:
http://www.leif.org/research/Climatological%20Solar%20Wind.png
Ulric Lyons says:
April 15, 2014 at 6:18 am
Yeah, well, Leif is also the author of such howlers as “everything on earth including the oceans and the atmosphere nutates the same amount.”
He does not understand the frequency response way of characterizing phenomenon. He does not understand functional bases and their usefulness.
There is a physical signal of that length, every bit (pun intended) as much as 101010 = 42.
Bart says:
April 15, 2014 at 7:46 am
He does not understand the frequency response way of characterizing phenomenon. He does not understand functional bases and their usefulness.
Whatever…
But I do understand the physics of the system
lsvalgaard says:
“Geomagnetic activity, A, can be calculated from the contributions from the three parameters B, V, and n: A = k B V^2 n^(1/3) giving you the several bumps that we see.”
Well thanks for that, but I’m only concerned with the frequency of the main Ap drops, not the bumps. Though would the periodicity analysis pick up such a signal?
Willis:
You say: “I guess my problem is not understand what you mean by “decompose a signal … in a variance-preserving way”. You can decompose a signal using either FFT or periodicity analysis. As you might expect, when you combine the underlying frequencies in either method, you reconstruction the original signal exactly.”
Because FFT uses orthogonal basis functions, it will reconstruct the discretely sampled finite RECORD–but not the entire signal–exactly in the general case. In non-orthogonal “periodicity analysis” you get entanglement of different frequencies of the continuum in the general case, and the signal reconstruction can be exact if and ONLY if that signal is strictly periodic. (In that case, noise is reduced by averaging of waveforms.) Otherwise, the periodic extension of the computed waveform becomes a grossly misleading artifact of analysis.
The structure of the acf, which is well-defined for all continuing (non-transient) signals, provides a means of discriminating between random signals and those with a deterministic periodic component. Upon Fourier integral transformation in accordance with the Wiener-Kintchine theorem, one obtains spectral continuums for random signals and discrete line spectra for periodic ones. BTW, SSN refers to sun-spot number, which is strongly coherent with TSI variations, not SST, which is not.
Hope this helps.
Ulric Lyons says:
April 15, 2014 at 1:04 pm
Well thanks for that, but I’m only concerned with the frequency of the main Ap drops, not the bumps. Though would the periodicity analysis pick up such a signal?
It all depends on what you trying to do [on the ‘functional bases’ so beloved by Bart; more formally treating the problem as a ‘field’, over a combination of functional bases, defining a ‘space’ containing all the statistical and physical properties of what you are investigating]. If you think that Ap [geomagnetic activity] directly is the driver, then you must consider the combined effect of B, V, and n. If you think only the solar wind velocity, V, directly is the driver, then only the V-signal is important, and so on. So, the ‘signal’ is different in each case. You cannot separate the signal processing from the physical understanding and make any real progress.
1sky1 says:
April 15, 2014 at 4:11 pm
I’m still not getting it. I take a discretely sampled finite record. I do a periodicity analysis. I decide how I want to decompose it and I do so.
To reconstruct the record, I just run the process in reverse. I add back in the frequencies that I took out. I get back to where I started.
So I’m not understanding why you think the reconstruction of a periodicity function can’t reconstruct the signal. The operations involved are all reversible.
However, again I don’t understand the underlying objection, because I’m NOT decomposing a wave form. I’m just checking the signal strength at the various cycle lengths.
Next, you talk about the “periodic extension of the computed waveform”. I assume you mean extending the waveform “out-of-sample”. My experience with this in the world of climate is that both FFT and periodicity analysis are pretty useless for that purpose.
But again, I’m not using periodicity analysis for that purpose either. I’m just using it as a tool to determine if there are any 10-11 year signals in the various temperature datasets. It happens to be very good at that. But you can use whatever you’d prefer for that analysis, FFT, wavelets, whatever. All I’m interested is whether the signal is actually there … and to date, I haven’t found it in any temperature datasets.
All the best, thanks for the response,
w.
Willis Eschenbach says:
April 16, 2014 at 3:02 am
“…and to date, I haven’t found it in any temperature datasets.”
There are two possibilities then:
1) variations in solar output cause no effect on Earthly climate
2) you are searching for the wrong observable
Instantaneous responses are typically weak. For long term climate effects, you should be looking for things which result from energy storage mechanisms. This is a weighted integration of the input, with the weighting being provided by the cyclical behavior of the storage medium, i.e., the oceans.
Nutation of the Earth does, indeed, cause the oceans to “slosh” with an 18.6 year periodicity, plus a strong 2X harmonic, and in the weighted integral, these would produce harmonics which match those evident in the PSD.
I only put quotations around slosh because it is a slow process to our immediate senses, and it would not be a turbulent flow, which is opposite to how a lay person might typically picture the word applying. But, speed up the film, and you would see the oceans tilting from one side of their basins to the other in time with the nutation, modulated of course by the diurnal motion of the tides.
Bart says:
April 16, 2014 at 9:01 am
Willis Eschenbach says:
April 16, 2014 at 3:02 am
I do love how you throw out claims like “Instantaneous responses are typically weak” without any attempt to substantiate them. In fact, at most points on the planet, the day-to-day changes are often larger than the month-to-month changes, and these are in turn often larger than the year-to-year changes. Does that sound like weak instantaneous response to you?
And while there is indeed a weighted integration of the input, that doesn’t make the input signal disappear. Perhaps you would be so kind as to tell the lurkers what the integral of a sine wave is, and whether integrating such a sine wave changes the cycle length …
Bart, so far your theory seems to be:
1. The moon causes tidal forces.
2. Inter alia, the tidal forces cause the oceans to “slosh” in their basins and also cause the earth to nutate.
THEREFORE …
3. There is no sign of an ~ 11-year cycle in the 10Be records, because the ocean sloshing has transmuted the 11-year cycle into two cycles with periods of “about” 5 and 60 years.
I’m sorry, but you’ll have to show me the math about how the THEREFORE part of your theory works. And not just hand waving math about here’s some cycles, you add them together, mix them up, subtract the synodic period of Jupiter and Saturn, and presto! the mystery number 11 disappears and is replaced by the numbers 5 and 60.
I mean real math, you know, the kind with UNITS.
As both Leif and I have both stated and provided evidence for, the nutation doesn’t “cause” the oceans to slosh. The tidal forces cause both the sloshing (which comes from a host of factors, not just nutations) and the nutations themselves.
What we are still missing is anything resembling a mechanism for your claimed actions, or any data showing the results you claim. For example, you say it’s nutation. Nutation has an 18.6 year period … and you claim that is supported by your graph showing the HadCRUT3 dataset with a 21-year period. How does that work, Bart? Does the sloshing of the oceans stretch the 18.6 year cycle to 21 years?
EVIDENCE! You can speculate and make your theoretical claims all day long … but where is your evidence? Here, for example, is the periodicity analysis of the San Francisco tides. There is a very weak cycle near to 18.6 … but I fear that near only counts in horseshoes. If you want to show say an annual cycle in the data, it’s no good showing an 11-month cycle, even though 11 months is assuredly “near” to 12 months.
Me, I employ people’s usage of the word “near” to separate the real cycles from the poseurs. If someone tells me that phenomenon A has cycles that are “near” to say the synodic period of Jupiter and Saturn, I just laugh. If phenomenon A were in fact driven by that synodic period, then the long-term average of phenomenon A would show a cycle that is within measurement error of the synodic period.
For example, in your citation above, you point to a 21-year period in some data or other as evidence in support of your claim of an 18.6 period … sorry, my friend. Doesn’t fly. Yes, 21 is indeed “near” to 18.6, as you point out.
But a 21-year cycle is NOT evidence of an 18.6 year forcing mechanism.
Regards,
w.
Willis Eschenbach says:
April 16, 2014 at 11:33 am
“I do love how you throw out claims like “Instantaneous responses are typically weak” without any attempt to substantiate them.”
Sorry. In the circles I travel in, this would not be particularly notable. Systems with long lag response time typically have higher dc gain.
“2. Inter alia, the tidal forces cause the oceans to “slosh” in their basins and also cause the earth to nutate.”
No. The Earth nutates independently of the ocean tides. If the oceans were not there, the Earth would still be undergoing forced nutation from the Sun and Moon. The tidal forces also cause the oceans to slosh, and that motion does affect the nutation. It’s a coupled system. But, the oceans are a small part of the mass of the Earth, and are not responsible for the lion’s share of nutation.
That lion’s share comes about because the Earth is an oblate spheroid, and has mismatched axial and transverse inertias. That creates a torque on the Earth via gravity gradient in the gravitational field of another body like the Sun or the Moon. Google “gravity gradient torque” to learn more.
“I’m sorry, but you’ll have to show me the math about how the THEREFORE part of your theory works. “
What do you get when you beat an 11 year sinusoid against a 9.3 year one? This.
Take two sinusoids, one with period T1, and another with period T2. Multiply them together, and you get components with periods T1*T2/|T1 +/- T2|.
“As both Leif and I have both stated and provided evidence for, the nutation doesn’t “cause” the oceans to slosh.”
You have not provided evidence, and you are both wrong. Nutation is an unsteady angular motion which produces accelerations which vary with distance from the center of rotation, and direction relative to the instantaneous axis of rotation. Acceleration times mass equals force. If you have a problem with that, take it up with Mr. Newton.
“…and you claim that is supported by your graph showing the HadCRUT3 dataset with a 21-year period.”
It’s an old plot. The annotation was simply pointing out the largest formations.
The nutation looks like this. It takes 18.6 years to complete a full circuit. It is elliptical, and the radius of motion has a 9.3 year period.
The solar cycle is dominated by peaks at frequencies corresponding to 10, 10.8, and 11.8 years. Beat those against the 18.6 and 9.3 year nutation harmonics, and you get terms close to the greater and lesser peaks in the temperature anomaly PSD.
“But a 21-year cycle is NOT evidence of an 18.6 year forcing mechanism.”
We’re not looking for 18.6. Nor 9.3, 10, 10.8, or 11.8. We are looking for the harmonics when you modulate the frequencies of the source with those of the energy storage mechanism.
“EVIDENCE! You can speculate and make your theoretical claims all day long … but where is your evidence?”
You misapprehend. I am not trying to prove anything here. I am showing that you have not proved anything. That there are possibilities which you have not explored, and you are not yet in any position to dismiss a solar variation to climate connection.
Longer response appears to be held up in the queue. But, another comment:
“If someone tells me that phenomenon A has cycles that are “near” to say the synodic period of Jupiter and Saturn, I just laugh.”
I don’t laugh. I was raised to be more polite than that when people are making an honest effort. I just don’t put much stock in it. Short of an unappreciated resonance phenomenon, there is no physically significant mechanism to connect the climate to planetary cycles, and the existence of a resonance condition which would tend to build up stored energy on the Earth from that source over a lengthy interval seems a long shot.
But, the Earth’s nutation is an observable quantity, and well known. The effect of tides on climate are significant. The solar cycles, again, just so. There are substantial connections to the Earth’s climate worthy of exploration in that mix.
Willis says:
“I’m still not getting it. I take a discretely sampled finite record. I do a periodicity analysis. I decide how I want to decompose it and I do so.
To reconstruct the record, I just run the process in reverse. I add back in the frequencies that I took out. I get back to where I started.
So I’m not understanding why you think the reconstruction of a periodicity function can’t reconstruct the signal. The operations involved are all reversible.
However, again I don’t understand the underlying objection, because I’m NOT decomposing a wave form. I’m just checking the signal strength at the various cycle lengths.”
===========================================================================
Getting back to “where I started” proves nothing relevant! It can be done with subtraction of ANY ARBITRARY time-function g(t) from a signal function f(t), as shown by the trivial equality f(t) = f(t) -g(t) + g(t). My objection is that obtaining g(t) as a periodic extension of the T-long average of the ASSUMED periodic signal form f(t) = f(t + kT) over all k doesn’t provide meaningful results, unless f(t) truly IS strictly T-periodic AND that period is an integer multiple of the data sampling period. Otherwise, you get a result that is NOT an orthogonal measure of “signal strength at the various cycle lengths.” In that general case, the summation of the “variance index” will not add up to the variance of the data!
Periodicity analysis offers the advantage of compact wave-form determination and noise suppression–but only when ALL the stringent prerequisites are strictly met. As your results for San Franciso tide data show, it fails to produce credible identification of tidal constituents even for a line-spectrum signal. It cannot be expected to provide anything better for geophysical signals caharcaterized by a CONTINUOUS spectral structure!
Bart:
Although the idea of tidal influence on climate via oceanic mixing crops up quite regularly when academic oceanographers seek NSF funding, no one has yet demonstrated any convincing connection. Nor does the 18.631yr lunar node precession cycle figure prominently in the long list of tidal constituents. It certainly does’nt create any “sloshing” in ocean basins, whose fundamental resonance modes are on the order of days in period, not decades.
1sky1 says:
April 16, 2014 at 7:11 pm
Exactly, which is why I didn’t understand your claim.
Not sure why the exclamation mark, but yes, I’m aware of that.
Again, we’re back into not clear. First, why on earth would you assume that the SF tidal data is a “line-spectrum signal”. Perhaps you could do what you think is the appropriate type of signal decomposition, and link to your results.
Provide anything better that what? I’m not clear what your argument is here.
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?
Be clear I’m not saying you’re wrong, 1sky1, and there’s always more for me to learn. I’m just not understanding your objections and your claims that some other method is better, or about the type of signals. I work better with real examples. So how about this:
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.
w.
Bart says:
April 16, 2014 at 6:48 pm
Sorry, in the cycles I travel in, people quote the relevant parts of the question. In this case I’d asked:
You have ignored the examples entirely, explained nothing, substantiated nothing, and merely replaced one unsubstantiated claim with another. This is one of the most frustrating aspects of discussing anything with you. Instead of providing anything solid, any real world examples, any math with UNITs, or responding to anything solid, you keep retreating to some theoretical world. Or as in this case you tell us what happens in your (unspecified) “circles” … circles of friends? Circles of people working in climate? Crop circles? Circles of theoretical climate scientists?
You seem to forget, you are ANONYMOUS. I have no idea what kind of work you do or what circles you move in … nor do I much care unless it is climate. You seem to think that anything you can do with a signal, the climate can do with a signal. But you haven’t given us ONE STINKING REAL WORLD EXAMPLE of whatever it is you are talking about when you claim that an 11-year solar signal can get transmuted by the freaking nutation into a 5-year and a 60-year signal. Heck, you haven’t even provided any data that your claimed 5-year signal EXISTS!
How about we start by you discuss each of my examples above in light of your claim that instantaneous responses (daily or monthly variations) are so much smaller than annual, decadal or century-long variations, and explain how the instantaneous response to changing forcings is so small … then we can move on to the next real, substantial question that you ignored.
That would be the question where I asked you for the math with the UNITS showing the transmutation of the 11 year solar signal into the other 5 and 60 year signals … to which you replied using math without a single unit. Again, Bart, I know you can do it with math. That’s the easy part of your cycle transformations. Any idiot can do things to theoretical signals with math.
What you’ve failed to show is that the climate system can do it with molecules …
w.
1sky1 says:
April 16, 2014 at 7:54 pm
“Although the idea of tidal influence on climate via oceanic mixing crops up quite regularly when academic oceanographers seek NSF funding…”
Well then, obviously, I’m not the only loon out here.
“It certainly does’nt create any “sloshing” in ocean basins, whose fundamental resonance modes are on the order of days in period, not decades.”
It’s not a question of resonance. It’s a question of mixing the heated surface waters into the depths. It’s a question of the dominance of inertial forces over viscous ones.
I think you guys perhaps are confused by the wording. “Slosh”, in my neck of the woods, means the second of the definitions here:
It does not mean foamy seas splashing up against cliff sides. It means it moves about. And when I say “it”, I don’t mean waves on the surface, but the entire mass of the oceans.
Nutation is a dynamic angular motion of a spinning body. It does accelerate, and put into motion, any flexible or fluid elements on the spinning body. The induced lunar/solar nutation for the Earth’s axis puts the oceans in motion, resulting in mixing, as well as viscous energy dissipation.
You can argue that you do not think it is significant, but that is just an expression of belief at this point in time. It’s a given that there is no known influence. Nobody knows the reason for the ~60 year periodicity in the climate. Obviously, it’s hiding where people haven’t yet discovered it. This is as good a candidate as any.
Willis Eschenbach says:
April 16, 2014 at 10:44 pm
“But you haven’t given us ONE STINKING REAL WORLD EXAMPLE of whatever it is you are talking about when you claim that an 11-year solar signal can get transmuted by the freaking nutation into a 5-year and a 60-year signal.”
Sure I have. 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|.
“Heck, you haven’t even provided any data that your claimed 5-year signal EXISTS!”
Five years is idealized, given the modulation of a perfectly synchronous 11 year cycle with a 9.3 year one. The reality is that the solar cycle is quasi-periodic, with several peaks near frequencies associated with 10, 10.8, and 11.8 years, and non-trivial bandwidth. The polar motion of the Earth is also not perfectly localized, either.
But, we do see some, at least superficial, similarities. Compare this with this. A perfect match? No, of course not. But, considering measurement error, random events, and the vast simplification of just an 11 year and 9.3 year cycle beating against each other, it’s rather suggestive if you ask me.
“…explain how the instantaneous response to changing forcings is so small…”
Energy storage is about accumulation, about integration over time. Take a sinusoid x(t) = cos(w*t) and integrate it. What do you get? sin(w*t)/w. It’s inversely proportional to the frequency. The accumulation of a yearly cycle versus a daily one is going to be amplified 365X. A 60 year cycle, 21,915X.
When you are dealing with quantities that integrate over time, a slow process can easily dominate a faster one, even if the driving forces appear instantaneously mismatched in favor of the faster one.
“What you’ve failed to show is that the climate system can do it with molecules.”
No, I’ve merely failed to show that it does do it. I don’t do this stuff for a living, you know. A proper analysis would be a major undertaking.
By the way, here’s something else you might want to consider. You know your period chart here? Where you’re looking for something at 18.6 years? What do you see at about 9.3 years? That is the period you should have been looking for.
Appropriate line above should have been “Compare this with this.”
Bart says:
April 16, 2014 at 11:20 pm
You seem to misunderstand the burden of proof here. I do not argue that nutation is not significant in the climate system. I argue that you have not demonstrated that it IS significant, and that’s your job, not mine.
To do that, you need to show the 18.6 year frequency of the nutation has an effect, not on the tides, but on some climate dataset. That’s the part that I have repeatedly pointed out is missing in your argument—evidence that nutation is doing something.
I don’t have to show that nutation is insignificant to the climate, Bart. It’s your theory, not mine. So it’s your job to provide EVIDENCE to show it IS significant … and to date, far from completing that task, as far as I know you have not even begun it.
w.
PS—Nobody knows if there even IS a 60 periodicity in the climate. Sure, it looks like there is … but there are big problems with that.
The first problem is that we really don’t have enough temperature or other climate data to show it. My own rule of thumb is that I don’t trust any apparent “cycle” that is longer than a third of the length of the dataset. With less than three full cycles, you may just be looking at a momentary disturbance in the force. So the maximum cycle we can detect in the HadCRUT data is about 50 years …
The second problem is that there is no clear cycle at 60 years. There is a very broad spread of power in the region, which stretches from about 50 to 70 years … which makes it very hard to say anything real about the purported “cycle”. Here’s a look at what I mean.
Willis Eschenbach says:
April 17, 2014 at 11:27 am
“I argue that you have not demonstrated that it IS significant, and that’s your job, not mine.”
That is not my purpose here. My purpose is to challenge the assertion that there is no evidence of solar variation driving the climate based on the lack of an observed 11 year periodicity in the temperature data. My point is that the influence on the climate would not necessarily manifest directly as an 11 year periodicity.
Other than that, I’d just like to get people thinking. The 9.3 year nutation amplitude is showing up in your own periodicity chart for the tides. Combine energy storage varying at 9.3 years, and the solar quasi-cycles, and you get something that looks very like the observations. I think it is significant. YMMV.
“To do that, you need to show the 18.6 year frequency of the nutation has an effect, not on the tides, but on some climate dataset.”
Or, somebody does. On a hunch, I went over to our friends at The Hockey Schtick and searched on “tides”. Interesting, the number of papers focusing on the 18.6 year cycle, like here, here, and and here. Lots of activity in this arena, it appears. Somebody will figure it out.
“With less than three full cycles, you may just be looking at a momentary disturbance in the force.”
Not with this kind of regularity. The odds against it are high. Two essentially uniform full cycles cannot, or should not, be blithely dismissed.
“The second problem is that there is no clear cycle at 60 years.”
Shows up pretty clear in my PSD. Of course, that’s because 60 years +/- 10 in period is 0.0167 years^-1, +0.0024/-0.0033 in frequency.
It is normal to have spreads of this kind. It isn’t a pure cycle. It’s a stochastic system, a series of lightly damped resonances being driven by random inputs. The energy is spread out. You’ve got the 18.6 year lunar forced nutation cycle, which is changing all the time as the Moon recedes in orbit. You’ve got the Solar cycle components, which are quasi-periodic. Nothing here is a pure sinusoid. There is a certain level of futility in trying to pin an exact number on it.
Bart says:
April 17, 2014 at 1:54 pm
My point exactly. YOU need to demonstrate that “the influence on the climate would not necessarily manifest directly as an 11 year periodicity”. It’s your claim, not mine.
So far, you’ve stated it over and over, waved your hands a whole lot, and shown that your hypothesis is possible in theoretical signal analysis. Yes, it’s theoretically possible … and no, I’m not impressed. Where are the observations to back up your claim that a strong ~ 11 driving signal will NOT have an 11-year component in the result, but will be mystically transmuted into ~5 and ~60 year cycles if we simply repeat the magic phrase “nutation, nutation, nutation”?
And where is the math with the units? I fear that math without units doesn’t impress me much either …
w.
Willis Eschenbach says:
April 17, 2014 at 3:25 pm
I cannot believe you are too dim to grasp what I have explained numerous times. Therefore, this is likely a tactic to avoid acknowledging the obvious.
“Yes, it’s theoretically possible … and no, I’m not impressed.”
OK, then. Willis is not impressed. I’ve done all I can with the time and resources available. Others, hopefully, will not be so obstinate.