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

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.