Guest Post by Willis Eschenbach
Back in 2015 in a post called “Noise Assisted Data Analysis“, I described a way to decompose a signal into its underlying components. It’s known by the acronym “CEEMD”, hence the title of this post. The most common kind of signal decomposition is called “Fourier Analysis”. However, it decomposes a signal into regular sine waves, constant signals with no changes in strength or frequency over time.
CEEMD, on the other hand, decomposes a signal into empirically-determined groups of time-varying underlying components. “Empirically determined” means that the division of the groups is based on the nature of the signal itself. This lets us see how each group of underlying components varies in strength and frequency over time.
I find CEEMD much more useful than Fourier Analysis because among other reasons it lets me investigate the relationship between different climate datasets. To demonstrate how this is done, let me begin with a look at the result of a CEEMD decomposition. Here’s the CEEMD analysis of the El Nino index called the “ONI”, the Oceanic Nino Index.
Figure 1. CEEMD analysis of the Oceanic Nino Index (ONI). Units are standard deviations of the underlying ONI signal.
From the top to the bottom, first you have the raw ONI data. Then you have the underlying signals, from the shortest period (highest frequency) signal group shown as empirical mode C1, to the longest period (lowest frequency) signal group shown as empirical mode C7. At the bottom you have the “Residual”, which is what’s left over after the removal of empirical mode signals C1 through C7. And if you add together all of those, C1 to C7 plus the residual … you reconstruct the original ONI signal exactly
As you can see, the strongest part of the signal is in empirical mode C5. This is the part of the signal with periods from about two to five years in length.
One of the most powerful uses of the CEEMD analysis is that it lets us see if two or more signals are closely related to each other. For example, Figure 2 below shows the empirical mode C5 for a variety of datasets. They include three temperature-based El Nino indices—the NINO34, ONI (Oceanic Nino Index), and MEI (Multivariate Enso Index).
Then there is one sea-level atmospheric pressure based El Nino index, the SOI (Southern Ocean Index). It is built around the difference in sea level pressure between Tahiti and Darwin, Australia.
There is one atmospheric temperature dataset, the UAH MSU satellite-based tropical lower troposphere temperature.
Finally, there are two total precipitable water (TPW) datasets. One is the tropical (23.5°N – 23.5°S) portion of the full ECMWF TPW dataset. The other is the RSS (Remote Sensing Systems) 20°N – 20°S ocean only TPW dataset. Here are the empirical mode 5 CEEMD results for all of them.
Figure 2. CEEMD empirical mode 5 results for a variety of datasets.
Interesting result, huh? You can see clearly that all of these datasets are moving in close harmony.
I got to thinking about this because in the comments to my last post, A Chain Of Effects, Matthew Sykes pointed out that the ECMWF total precipitable water (TPW) data was unlike the NVAP TPW data. To see who the outlier is, here are the CEEMD empirical mode 5 results for three different TPW results—the ECMWF, the RSS, and the NVAP total precipitable water datasets. The NVAP dataset starts in 1988, so I’ve started the comparison there.
Figure 3. CEEMD empirical mode 5 results for three total precipitable water datasets.
From this, it seems clear that the NVAP dataset is the clear outlier. It goes into and out of sync with the other two, while the other two agree well throughout.
That answers the question that I came in on, as well as demonstrating the usefulness of the CEEMD analysis. And further deponent sayeth not.
Meanwhile, here on our Northern California coastal hillside with a tiny view of the ocean, we’re supposed to get big rain all week starting this morning (Tuesday) … fingers crossed. They say it will rain 2.7 inches (6.9 cm) today alone, which ain’t no ordinary rain, it’s a frog-strangler. But since we’ve only had about 40% of normal rain so far, I can only wish for a tropical downpour.
Best of this wondrous world to everyone,
PS—I am happy to discuss and defend what I’ve said. However, I cannot defend or discuss what you think I said. As a result, I ask that when you comment you quote the exact words you are discussing so that we can all be clear on both who and what you are referring to.