A Better Way to Eliminate Seasonal Variations – Speeding Up With That?

Guest posts by Willis Eschenbach

For no other reason than my unrelenting curiosity, I looked at Rutgers snow cover data from KNMI. Here is the full data as shown in the KNMI chart:

Figure 1. Rutgers snow cover. Note that prior to 1972 there were gaps in the data.

And here’s a KNMI chart of the same data with monthly variations removed.

Figure 2. Snow cover anomalies in Rutgers (i.e. seasonal variations removed).

When I saw that, I said “Hmmm. What’s with the picture?” Can you see what the challenge is?

(For what it’s worth, on my planet I don’t have a “problem.” Instead, I have a “challenge”… a small but important difference. But I digress…)

The challenge in Figure 2 above is that there are still very large annual fluctuations in some places. For example, they are clearly visible circa 1980 and can also be seen elsewhere in the record. I assume this is because in some periods the snow falls earlier and in some periods later. So the usual method of eliminating year-to-year fluctuations, by averaging each month and subtracting the monthly average of each month from the respective months of the raw data, simply doesn’t work. It does not properly eliminate annual fluctuations.

After pondering this for a bit, it occurred to me that I could do a better job using a mathematical technique with the unwieldy name Empirical Mode Decay of Entire Sets . For obvious reasons, it is often referred to as CEEMD.

CEMD “decomposes” any signal into a group of elementary signals that, when added together, will exactly reconstruct the original signal. It is similar to Fourier Analysis, but it has some advantages. I discussed the technique in my post.”Data analysis supports noise“. Then I wrote an article called “CEEMD and Sunspots” about how I use it regularly to see if there is an 11-year period in climate data that indicates whether sunspots can influence certain climate phenomena.

Here is the CEMMD decomposition of the snow cover data shown above:

Figure 3. CEEMD analysis, Rutgers snow data. The top panel shows the raw data. Tables C1 to C8 show different experimental mode individual signals plus residuals, which, when added together, reconstruct the raw data.

Obviously, Experimental Mode C3 is the sum of all elementary signals with a period of one year. However, it is not a simple ordinary sine wave. Instead, over time, each experimental mode changes slightly in phase and amplitude. The graph below shows the raw data (in blue) overlaid with C3 Experimental Mode data (in matte red) for the beginning of the record.

Figure 4. Rutgers snow data in blue, overlaid with CEMD C3 Empirical Mode in translucent red.

As you can see in the more detailed view above, the CEMD Empirical Mode C3 data varies in both amplitude and phase. This is because it is the sum of all the fundamental signals with a period of about one year.

And when I subtract CEMD C3 Experimental Mode from the raw data I get the following histogram. I have repeated Figure 2 above for comparison.

Figure 5. Comparison of the two annual cycle elimination methods. Since CEEMD can only operate on complete datasets with no gaps, I removed the beginning of the pre-1972 data.

As you can see, the CEEMD method does a much better job of eliminating the annual cycle. It no longer contains the large annual fluctuations shown in the standard method used by KNMI and it clearly shows the true underlying variations.

Why is it important? I learned early on the importance of sharp tools. My second real job, at age 13 at $0.30 an hour ($3.00 an hour in 2022 dollars), was digging the foundation for a new house with a hoe and shovel. And looking back, I was probably worth that much every hour.

In the pre-PC days, working with a shovel was called “Playing the Swedish Banjo”. Here’s a recent picture of me doing it:

And I’ve been playing the Swedish banjo for a much more reasonable salary many times since I was 13.

Perhaps due to my work history, I divide people into three groups:

  • People who used shovels.
  • People who made money with shovels.
  • Those who sharpened shovels.

So I consider this new approach to eliminating seasonal changes as honing a valuable tool that I use all the time. Now all I need to do is write code to automate the process… “SMOP”, we like to call it “small stuff of programming”.

Finally, by the way… it’s worth recalling the following prediction from 2000:

According to Dr David Viner, a senior research scientist at the University of East Anglia’s climate research unit, in a few years winter snowfall will become “a very rare and exciting event”. “Kids won’t know what snow is,” he said.

As the table below in Figure 5 clearly shows, that’s just one of the climate alarmists’ endless series of doom after failure predictions. The mystery to me is, why do people still believe in them?

But anyway, it’s my day. How is yours?


Postscript—I am still waiting for Twitter to lift my suspension. I assume they are testing blue and celebrities first. But if anyone on Twitter wants to remind @elonmusk that I was wrongly suspended, my Twitter address is @WEschenbach. Please include a link to my post”Open letter to @elonmusk” discussion of the crazy Twitter Rules. Thank you very much.

As usual: I asked that when you commented you quote the exact words you are answering. This avoids many of the misunderstandings that often cause discussions on internal web pages.


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