Solar Periodicity

Guest Post by Willis Eschenbach

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

My best wishes to everyone,

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.

 

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1sky1
April 17, 2014 5:19 pm

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.

1sky1
April 17, 2014 5:28 pm

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.”

RobR
April 17, 2014 5:29 pm

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

1sky1
April 17, 2014 6:01 pm

Moderator:
Please correct my last comment to read Reynolds number, instead of Richardson number.

1sky1
April 17, 2014 6:08 pm

In my comment to Bart, please read Reynolds number, instead of Richardson number.

Bart
April 17, 2014 9:18 pm

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
April 18, 2014 12:07 am

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?

Bart
April 18, 2014 12:13 am

“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.

Bart
April 18, 2014 12:24 am

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.

1sky1
April 18, 2014 5:22 pm

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).

1sky1
April 18, 2014 5:25 pm

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.

Bart
April 18, 2014 6:40 pm

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.

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