From Watts Up With That?

*Guest Post by Willis Eschenbach*

Over at Phys.Org, there’s a new article claiming the following:

*Order in chaos: Atmosphere’s Antarctic oscillation has natural cycle, discover researchers*

Climate scientists at Rice University have discovered an “internally generated periodicity”—a natural cycle that repeats every 150 days—in the north-south oscillation of atmospheric pressure patterns that drive the movement of the Southern Hemisphere’s prevailing westerly winds and the Antarctic jet stream.

Here, from the underlying study, are their Fourier analyses supporting their claim.

*“Hmmm”*, sez I, *“seems kinda unlikely”* … so I took a look at the study. For unknown reasons, the Antarctic Oscillation (AAO) is also called the Southern Annular Mode (SAM). The abstract says:

However, here we show using observational data, model data, and theory that SAM has an intrinsic 150-day periodicity arising from the internal dynamics of the extratropical atmosphere. This 150-day oscillation clearly influences the variability of the hemispheric-scale precipitation and ocean surface wind stress, suggesting broader impacts of this periodicity on the SH weather and climate.

We also found that many state-of-the-art climate models cannot faithfully reproduce this periodicity, providing an explanation for some of the previously reported shortcomings of these models in simulating SAM’s variability. Based on these findings, we propose new metrics and ideas for evaluating these models and understanding their shortcomings, and potentially, improving them.

*“Hmmm”*, sez I …

So what is the Antarctic Oscillation (AAO) when it’s at home? Well, it’s the difference in average sea level “zonal” pressure in the ring around the planet at 40° South latitude, and the corresponding zonal pressure at 60°S. Here’s a map of the area in question. 60°S is the dotted circle that goes between the tip of South America and Antarctica. 45°S is the next dotted circle outside of that one.

Original Caption, from the link below: *“Spatial pattern of the AAO.”*

A description of how the AAO is calculated, the above graphic, and daily data for the AAO, are available from NOAA here for the period 1871 to 2012.

And how many observations do we have of the daily zonal pressure around the planet at 60° South latitude from 1871?

Well … approximately none. No land there. And for 40°S, maybe a few 1871 observations from Tierra Del Fuego in South America, or Tasmania or New Zealand … or not. Seriously. Almost none.

But never fear, that’s why we have “reanalysis” climate models. These are climate models that are regularly kept from running too far off the rails by including whatever observations we do have.

So, we start with a disadvantage. We have almost no observational data, so we’re analyzing the output of a reanalysis climate model. Not auspicious.

Setting that aside for the sake of discussion, I did a CEEMD analysis of the entire NOAA AAO computer model results from the site linked above. And what, you might reasonably ask, is “CEEMD”?

CEEMD is *“Complete Ensemble Empirical Mode Decomposition”*. Similar to Fourier analysis, CEEMD is a way to “decompose” a complex signal into underlying “empirical modes” containing signals of various frequencies which, when added together, reconstitute the original signal. I describe the CEEMD analysis method in my post “Noise-Assisted Data Analysis“. Here’s one view of the CEEMD analysis of the full NOAA AAO results.

*Figure 1. CEEMD analysis, full NOAA AAO dataset. This shows the empirical modes C1 to C14. The colored lines show the strength of the underlying signals at various periods that combine to make up the original signal.*

This shows that the AAO is comprised of a variety of signals ranging in length from about 40 to 1,000 days. However, the strongest signal is not at 150 days. Here’s a closeup of the range of the above graphic from 100 to 200 days.

*Figure 2. As in Fig.1, but showing the range from 100 to 200 days. The peak showing the maximum value is at 183 days. There’s nothing of note at 150 days.*

Now, having looked at dozens and dozens of CEEMD analyses, I know that there are often what I call “pseudocycles” in natural datasets. These are cycles that appear at some given time, persist for some length of time, and then disappear. So before I declare that a real enduring cycle exists, I run the same analysis on subsets of the data. If there is a true persistent cycle in the data, it will show up in each of the subsets.

In this case, I divided the data into four quarters and analyzed each one separately. The results are shown below, starting with the earliest quarter of the data.

*Figure 3. As in Fig.2, but showing the first quarter of the data. As in the full dataset, the peak showing the maximum value is at 183 days. There’s nothing of note at 150 days.*

Now, the results are scaled so that the strongest cycle in the entire dataset has a value of 1.0. In the full dataset and the earliest quarter shown above, that’s been the 183-day cycle. But here’s the second quarter of the data.

*Figure 4. As in Fig.2, but showing the second quarter of the data. As in the full dataset, the peak showing the maximum value is at 183 days. There’s a smaller peak at 147 days.*

There are a couple of differences in the second quarter of the data. The 183-day cycle is not the strongest cycle in the dataset. That cycle is at 365 days, an annual cycle. The 183 and 147 day cycles are only about half the strength of the annual cycle. Here’s an expanded graphic with data out to 400 days showing the strongest cycle, the annual cycle.

*Figure 5. As in Fig.4, but showing the cycles out to 400 days. The largest peak is now at 365 days*.

*“Hmmm”*, sez I … moving on to the third quarter we find the strongest peak is again at 365 days, but …

*Figure 6. As in Fig.2, but showing the third quarter of the data. The peak showing the maximum value is again at 365 days (not shown). The largest peak in the 100-200 day range is at 153 days, the closest we’ve come to their value. However, there is another peak of nearly the same size, at 172 days.*

Curiouser and curiouser. Bear in mind that we’re moving from the computer reanalysis model output of the oldest quarter, the one with the least actual observational data, towards modern times when we actually at least have a few, however sparse, observations in the area of interest. Here’s the final quarter of the data.

*Figure 7. As in Fig.2, but showing the fourth and most recent quarter of the data. In this part of the data, the peak showing the maximum value is not at 365 days (not shown). Instead, it is at 144 days.*

*“Hmmm”*, sez I … *“not seeing it.*

Next, I thought I’d look at how big these underlying cycles are. One of the strongest ones is the 183-day cycle in the first quarter of the data … so here is the best fit of a 183-day and a 150-day sine wave to the first quarter of the AAO data.

*Figure 8. Best fits of 183-day (red) and 150-day (yellow) sine waves to the AAO first quarter data.*

Note that the largest regular cycle in the data, the 183-day cycle, is quite small … and the 150-day cycle is basically nonexistent.

There’s another way that we can verify all of this. Here’s a Fourier periodogram of the first quarter of the AAO.

*Figure 9. Fourier periodogram of the first quarter of the AAO data.*

Note that as in the CEEMD data, there are a whole host of cycles from around 40 days to 1,000 days. The 183-day cycle is the largest, and the cycles with periods around 150 days are far smaller.

And note also, Figure 9 shows the same result as Figure 8—the 183-day cycle is quite small, only 8% of the total range of the data.

**[UPDATE]** Bob Weber points out in the comments that they used a different dataset for their AAO data, available by FTP. I got that. It’s much shorter, only since 1979. Here are the relevant graphics of the FTP 1979-on dataset:

*Figure 10. CEEMD analysis, full NOAA AAO FTP 1979-on dataset. This shows the empirical modes C1 to C14. The colored lines show the strength of the underlying signals at various periods that combine to make up the original signal.*

Curiously, in this dataset the largest cycle is around 650-750 days.

Here’s the range from 100 to 200 days of the FTP 1979-on dataset.

*Figure 11. As in Fig.10, but showing the range from 100 to 200 days. The peak showing the maximum value is at 145 days. However, it’s quite small.*

Here’s the best fit of the 145-day sine wave to the FTP 1979 on dataset:

*Figure 12. Best fit of 145-day (red) sine waves to the AAO FTP 1979-on full data.*

And here’s the Fourier periodogram of the AAO FTP 1979-on data.

*Figure 13. Fourier periodogram of the first quarter of the AAO FTP 1979-on full data.*

The 145-day cycle is there, but it is tiny, only a bit more than 4% of the range of the data. As you can see, as far as finding a significant 150-day cycle, this FTP 1979-on data is even worse than the data I originally used.

What can we conclude from all of this? Well, I’d draw these conclusions.

- There is no regular 150-day cycle in this data as the authors claim.
- The analysis of the full dataset shows a clear peak, but it’s at 183 days, not 150 days.
- The analyses of the four individual quarters of the data disagree wildly with each other.
- Two of the quarters show a peak at around 183 days.
- One quarter shows a peak at 153 days, but it’s not large and has a peak nearly as large at 173 days.
- The most recent data shows a peak at 144 days.
- The four quarters of the data and the full dataset all show a peak at around one year, but it’s the strongest peak in only one of the quarters and the full dataset.
- Neither the full data nor any of the subsets show a 150-day cycle
- All of the cycles are quite small, with the peaks around 10% of the range of the data or less.
- Given the small number of sea level pressure observations made in the Southern Ocean, particularly in the earlier times and at 60°S latitude, be clear that we’re mostly not analyzing the real world—we’re mostly analyzing modelworld. Back in the sailing days and ever since then, those latitudes have been called the “Roaring Forties” the “Furious Fifties”, and the “Screaming Sixties” because of the strength of the wind. As a result, very few boats venture there even today, and sea-level pressure observations are infrequent and widely scattered in space and time.
**It’s extremely important to run a decomposition analysis, whether it’s a Fourier analysis as they used or a CEEMD analysis, on several subsets of the data before declaring that a true, permanent cycle exists. Any study that does not do this can likely be dismissed out of hand.**

*“Hmmm”*, sez I … at the end of the day, not seeing what the authors claimed at all.

The very best of life to everyone,

w.

**Coda:** The town nearest to where I live is named Occidental. The Thursday Farmer’s Market has just started up again. I live with my gorgeous ex-fiancée, our daughter and son-in-law, and two grandkids—a girl who’s “Almost four” and a two-year-old boy. So today we all went to the Occidental Farmers Market, where we danced to the band, saw rafts of folks we know, and the kids got to play with their friends in the sunshine.

Yes, the world does seem to be prancing down the primrose path to perdition … but family and friends and the sunshine are forever. Here, to give you a flavor of the town and the community, is a story about Occidental and a man named Ranger Rick.

**My Usual Request:** When you comment please quote the exact words you’re discussing. This lets us know just what you are referring to.

**A Reminder: **It’s important to keep in the forefront of any analysis of reanalysis “data” the fact that we’re looking at is not observational data of any kind. It’s the output of a computer climate model, with all of the advantages and the problems that entails. See my post “Meandering Through A Climate Muddle” for a discussion of some of those problems.

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