Tools to Spot the Spots

Guest Post by Willis Eschenbach

People have asked about the tools that I use to look for any signature of sunspot-related solar variations in climate datasets. They’ve wondered whether these tools are up to the task. What I use are periodograms and Complete Ensemble Empirical Mode Decomposition (CEEMD). Periodograms show how much strength there is at various cycle lengths (periods) in a given signal. CEEMD decomposes a signal into underlying simpler signals.

Now, a lot of folks seem to think that they can determine whether a climate dataset is related to the sunspot cycle simply by looking at a graph. So, here’s a test of that ability. Below is recent sunspot data, along with four datasets A, B, C, and D. The question is, which of the four datasets (if any) is affected by sunspots?

Figure 1. Monthly sunspot numbers, and comparison data.

If you asked me which of those look like they are related to the sunspot data at the top, I’d have to say “None”. Not one of them shows any obvious sunspot-related signature.

In fact, one of those datasets is strongly affected by sunspots, one is weakly affected, and two show no signs of being affected by sunspots. Here they are under their real names.

Figure 2. Monthly sunspots and UAH MSU atmospheric temperature anomalies.

From the bottom up, first we have the lower troposphere in violet. This is the part of the atmosphere nearest to the surface. Moving up we have the middle troposphere in blue.

Above that is the tropopause, which is the relatively thin layer that separates the troposphere from the overlying stratosphere. And finally, we have the lower stratosphere, the atmospheric layer just above the tropopause.

So let me start seeing just what periodograms and CEEMD analysis can show about these signals. I’ll start by looking at the periodogram of the sunspot cycles.

Figure 3. Periodogram, sunspot data.

As you can see, the ~ 11-year signal in the sunspot is quite large. It covers 60% as much as the total range of the sunspot data.

Having seen that, let’s see what the periodograms of the four levels of the atmosphere look like. Figure 4 shows all of them together.

Figure 4. Periodograms, sunspot data and UAH MSU atmospheric temperature anomaly data

Now, this is most interesting. In the lower stratosphere (red) there is a clear solar signal at the ~ 11-year mark. The signal even has the same shape as the solar periodogram, with a “shoulder” at around nine years. It is relatively strong, about a quarter of the size of the variations in the underlying lower stratosphere data.

This is not a surprise to me because I am a ham radio operator, H44WE. So I know that sunspots change the upper atmosphere, particularly the ionosphere, enough to mess with radio reception during parts of the sunspot cycle. And this lower stratosphere data confirms that the known solar effect from extends the upper reaches of the atmosphere down to the lower stratosphere.

Moving lower in the atmosphere, at the tropopause (orange), the boundary layer between the stratosphere and the troposphere, we can still see a weak solar signal. However, it is not as strong as the solar signal in the stratosphere. It is only about a tenth of the size of the underlying troposphere data.

Moving lower yet, there is a tiny hint of a hump in the middle troposphere periodogram (blue), at about 12 years. But by the time we get down to the lower troposphere, the sunspot signal has disappeared entirely. Instead, these signals are dominated by a cycle at about 3.8 years, which may or may not be related to El Nino changes.

Now, before I go on to look at the CEEMD analyses of these five datasets, I want to highlight a curiosity. People say that because we know that the sunspot cycle affects the upper atmosphere, that it is therefore likely that the sunspot-related solar variations also affect things at the surface like the ocean, or the river flow, or the like.

However, as this analysis shows, the effects of the solar variations are unable to even propagate from the lower stratosphere down to the lower troposphere, much less down to the surface. Go figure.

Next, I’ll turn to the CEEMD analysis. Here are the underlying empirical modes of the sunspots.

Figure 5. CEEMD empirical modes, sunspots 1987 – 2018

As you can see, the major empirical mode is mode C6, which contains the ~ 11-year main cycle. There is very little power in any of the other cycle lengths.

We can understand the actual empirical modes better by looking at the periodograms of each of the empirical modes. Figure 6 shows those periodograms.

Figure 6. Periodograms of empirical modes of the sunspot data.

As we saw above in the periodogram of the whole sunspot data, the sunspots have one major frequency, which peaks at around 11 years.

Now, let’s look at the CEEMD analysis of the lower stratosphere data. Here are the empirical modes, and their periodograms.

Figure 7. Empirical modes of the lower stratosphere UAH MSU temperature anomaly data.

Figure 8. Periodograms of the empirical modes, lower stratosphere UAH MSU temperature anomaly data

Here again, we have the clear sign of a solar signature, with a strong signal at the ~ 11-year period. However, there is some strength in shorter cycles.

For the next three datasets, I’ll just show the periodograms to show the decay of the sunspot-related signal as we move downwards towards the surface.

Figures 9. Periodograms of the empirical modes of the tropopause, middle troposphere,  and lower troposphere UAH MSU temperature anomaly data

You can see how as we get closer and closer to the surface, the sunspot signal gets weaker and then disappears entirely.

Finally, there is one more very valuable thing that we can do with CEEMD that we cannot do with an ordinary periodogram or Fourier analysis. This is to look at the actual empirical modes, the signals themselves. For example, Figure 10 shows a comparison of the ~11-year empirical modes of the sunspot data and the lower stratosphere.

Figure 10. Approximately eleven-year empirical modes of the sunspot data and the UAH MSU lower stratosphere temperature anomaly data.

As you can see, this provides a lot of support for the idea that we are looking at a common signal. In lockstep with the sunspot signal getting smaller and smaller over time, the response in the stratosphere is also getting smaller and smaller.

In addition, you can see that the two signals have the same phase structure, with the sunspots leading the stratospheric response by a generally stable amount of about a year and four months.

All of this taken together means that it is extremely likely that the changes in the stratosphere are a result of the changes in some parameter related to the sunspot cycles (e.g., TSI, solar wind, cosmic rays, far UV, heliomagnetic field, etc.).

CONCLUSIONS:

• Both the periodogram and the CEEMD analysis are quite capable of identifying a sunspot-related signal in a climate dataset.

• Both the periodogram and the CEEMD analysis are quite capable of distinguishing between a dataset which is even weakly affected by solar variations and a dataset which is not significantly affected by solar variations.

• The CEEMD analysis allows us to verify whether or not two signals which both contain an ~11-year signal are actually related. We can compare the actual signals in the two datasets to see if they agree in phase and in changes in amplitude.

• Although there is a clear solar signal in both the ionosphere and the lower stratosphere, for unknown reasons it does not propagate downwards to the lower troposphere.

Th-th-th-that’s all, folks. Sunshine to you all, unless you need rain, in which case make the obvious substitution. You are welcome to join me at my blog, or on Twitter @WEschenbach, for discussions on … well … lots of strange and interesting things.

w.

The Usual: I politely request that you quote the exact words you are discussing. I’m tired of people claiming I took a position I’ve never taken. Quote the words so we can all decide who is right. I ask politely, but I get crabby if people don’t follow my polite request. You are now forewarned, forewarned is forearmed, and forearmed is half an octopus, so please, quote the words you are referring to.

The Data: Sunspots, Lower Stratosphere, Tropopause, Mid Troposphere, Lower Troposphere