A Better Way to Remove Seasonal Variations

Spread the love

Guest Post by Willis Eschenbach

For no other reason than my unquenchable curiosity, I took a look at the Rutgers snow cover data from KNMI. Here’s the full data as shown in the KNMI graph:

Figure 1. Rutgers snow cover extent. Note that pre-1972 there are gaps in the data.

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

Figure 2. Rutgers snow cover extent anomalies (i.e., seasonal variations removed).

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

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

The challenge in Figure 2 above is that there are still very large annual swings in certain places. They’re clearly visible, for example, around 1980 and can also be seen elsewhere in the record. I assume that this is because in some periods the snowfall is earlier, and in some periods it’s later. So, the normal method of removing annual swings, by averaging each of the months and subtracting the monthly average of each month from the corresponding months of the raw data, simply isn’t working. It’s not properly removing the annual swings.

After pondering this for a bit, I realized that I might be able to do a better job by using a mathematical technique with the unwieldy name of Complete Ensemble Empirical Mode Decomposition. For obvious reasons, it’s usually referred to as CEEMD.

CEEMD “decomposes” any signal into a group of underlying signals which when added together reconstruct the exact original signal. It’s similar to Fourier Decomposition, but it has several advantages. I discussed the technique in my post “Noise Assisted Data Analysis “. I later wrote a post called “CEEMD and Sunspots” about how I use it frequently to see if there is an approximately 11-year cycle in climate data that would indicate if the sunspots might be affecting some given climate phenomenon.

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

Figure 3. CEEMD decomposition, Rutgers snow data. The top panel shows the raw data. Panels C1 through C8 show the various empirical mode individual signals plus the residual, which when added up will reconstruct the raw data.

Clearly, the Empirical Mode C3 is the sum of all of the underlying signals that have around a one-year cycle. However, it’s not a simple regular sine wave. Instead, over time each empirical mode varies slightly in phase and amplitude. The graph below shows the raw data (blue) overlaid with the Empirical Mode C3 data (translucent red) for the early part of the record.

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

As you can see in this more detailed view above, the CEEMD Empirical Mode C3 data varies in both amplitude and phase. This is because it’s the sum of all of the underlying signals with a period around one year.

And when I subtract the CEEMD Empirical Mode C3 from the raw data, I get the following graph. I’ve repeated Figure 2 above for comparison.

Figure 5. Comparing the two methods of removing the annual cycle. Since CEEMD can only work on complete datasets without gaps, I’ve removed the pre-1972 early part of the data.

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

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

In those halcyon pre-PC days, working with a shovel was called “Playing the Swedish banjo”. Here’s a recent picture of me doing that very thing:

And I’ve played the Swedish banjo for more reasonable wages a number of times since I was 13.

Perhaps as a result of my work history, I divide folks into three groups:

  • Those who have used a shovel.
  • Those who have made money with a shovel.
  • Those who have sharpened a shovel.

So, I consider this new method for removing seasonal variations as sharpening a valuable tool that I use all the time. Now all I need to do is write the code to automate the process … “SMOP”, we used to call it, a “small matter of programming”.

Finally, in passing … it’s worth recalling the following prediction from 2000:

According to Dr. David Viner, a senior research scientist at the climatic research unit of the University of East Anglia, within a few years winter snowfall will become “a very rare and exciting event”. “Children just aren’t going to know what snow is,” he said.

As the lower panel in Figure 5 clearly shows, that was just another one of the climate alarmists’ endless failed serials Doom casts. The mystery to me is, just why does anyone still believe them?

Anyhow, that was my day. How was yours?


PS—I’m still waiting for Twitter to work its way down to lifting my suspension. I assume they’re doing the blue-checks and the famous folks first. But if anyone who is on Twitter wanted to remind @elonmusk that I’ve been wrongly suspended, my Twitter handle is @WEschenbach. Please include a link to my post “An Open Letter To @elonmusk” discussing the crazy Twitter Rules. Many thanks.

As Usual: I ask that when you comment you quote the exact words you’re replying to. This avoids many of the misunderstandings that plague discussions on the intarwebs.

via Watts Up With That?

November 29, 2022

A Better Way To Remove Seasonal Variations — Watts Up With That?