Digital Diatribes

A presentation of data on climate and other stuff

A Closer Look At Oceanic Oscillation Cycles

Posted by The Diatribe Guy on February 2, 2009

In the past, I’ve presented some charts on the different Oceanic Oscillations for PDO, AMO, and ENSO. I’ve started to take a look at these again with an eye towards running a correlation analysis. The initial work I’ve done today is something I considered somewhat interesting, so I thought I’d share it.

The first thing I’ll present is the chart for Arctic Ocean Oscillation Indices since 1950, smoothed at one year, 5 years, and 10 years. These are presented below:

1-year smoothed Arctic Oscillation Data since 1950

The overall Arctic Oscillation index data since 1950 - 1 year smoothing.

5-year smoothed Arctic Oscillation Data since 1950

The overall Arctic Oscillation index data since 1950 - 5 year smoothing.

10-year smoothed Arctic Oscillation Data since 1950

The overall Arctic Oscillation index data since 1950 - 10 year smoothing.

Unlike the AMO, PDO, and ENSO charts, there is no apparent cyclicality showing up in the Arctic Oscillation chart. There does appear to be a trend upward overall, and there are certainly ups and downs within that. The 1-year chart looks much like an ENSO chart would be. Unlike ENSO, though, I’m not picking up a longer cycle.

Well, I wanted to show that chart to start, since the Arctic seems to be the focus of a lot of attention. I guess it bears musing whether or not the Oscillation has a root cause from the Ocean itself, or the sun, or melting ice, or freezing ice, or other factors that override any cyclical nature that would otherwise be apparent.

That’s all I really did on that piece. But I’d like to move on to some work I did with the AMO, PDO, and ENSO (as well as a look at those Arctic Oscillations).

As I viewed these charts again, I fit a polynomial to the data and it really looked like the interior of the chart had a stable pattern from peak to peak and trough to trough. So, to me it looked as if I could introduce a sine wave. So I set scale parameters, offset parameters, and wave length parameters and solved for the best fit on a least-squares basis. I present the following three charts with the best-fit sine functions overlaid:

The raw Atlantic Multidecadal Oscillation Index Data with best-fit sine function

The raw Atlantic Multidecadal Oscillation Index Data with best-fit sine function.

The raw PDO Index Data with best-fit sine function

The raw Pacific Decadal Oscillation Index Data with best-fit sine function.

The raw ENSO Index Data with best-fit sine function

The raw ENSO Index Data with best-fit sine function.

I find these charts interesting, because it seems to my eye that the sine function is a fairly savvy estimator. PDO and AMO have much more history than ENSO. The ENSO period doesn’t cover a full period with the best-fit sine function.

If this is truly a good indicator, and making the assumption that we can extend it backwards and forwards, we can see the interplay between the different functions.

First, though, let’s take a look at each index’s cycle.

Starting with the AMO, the period in the sine function is shown by looking at the Maximums (or Minimums, if you wish): A peak occurred on May 1878 and November 1944. The next peak is forecasted to occur in April 2011. The last trough occurred in January 1978, and the next trough is expected to occur in June 2044. As we see here, the length of a complete cycle is about 66.5 years.

The PDO cycle is not quite as long as AMO. Because the periods differ, their peaks and troughs will vary relative to each other. This has an interesting long-term result in terms of warming and cooling that will be demonstrated later. The PDO had a peak in the function in October 1929 (about 15 years prior to AMO). The next peak occurred May 1990 (about 21 years prior to the anticipated AMO peak). The next peak in the PDO is not expected until November 2050 (only 6 years after the anticipated AMO trough). The period here is about 60.5 years.

The ENSO cycle isn’t as clear, since the data is only back to 1950. However, when I did the fit of the sine function, the results seemed to make sense relative to the PDO, so I have some level of confidence in them. Obviously, ENSO is most known for its short-term swings in temperature. However, the charts also indicate that there is a longer term cycle. The sine fit seems to support this conclusion. There was a trough in November 1958, and a peak in December 1990. (Now, I know there was that super El Nino a few years later – the peak of the function does not necessarily correspond to individual peak years, but the overall wave that these years “ride” and fluctuate around. In other words, 1998’s El Nino was not only a strong event in and of itself, but it was a strong event near the top of a cycle). We don’t have a complete period in the data, but the half-period is about 32 years, implying a full period of 64 years. The last peak corresponded well with the peak in the PDO. I suspect that more data would show that the long-term ENSO cycle would match up with the PDO, but I don’t know that as a certainty. So, for now let’s just go with the cycle as is.

Since I haven’t done a correlation analysis, I don’t have any kind of a conclusion at the moment on how much weight each of these indices should get in order to compare to temperature. That a ways down the road because I want to look at multiple other factors. But I can make a broad assumption simply to illustrate the effects of the interplay between these cycles. For this purpose, I’ll assume that ENSO and PDO each get 30% weight and AMO gets 40% weight.

The following result occurs:

The composite sine function

The composite sine function with 40/30/30 weight.

At first glance, you may say “big deal. It’s a sine wave.” Well, that’s true, sort of. But if you look closely, take note of the peak-to-trough periods and vice-versa. Also note that the cycle has dampened. This is due to the difference in length between AMO and the other two. The cycle with a PDO peak in 2110 will have an AMO trough that same year, and that would be the wave of least amplitude. The peak that occurred around 1810 was close to the highest magnitude possible.

A coouple things to note here: the composite chart may have more or less amplitude, or may shift one way or another depending on the actual weights that are appropriate. The above is for illustration, but I played with different weights and the chart more or less tells the same story, so we can still draw some general information from the chart. Also, depending on the impact of other ocean oscillation indices, the above chart may or may not change once those are taken into account. In addition, the chart shows the best fit overall index value for the three indices. It does not represent actual contribution to temperature or temperature changes. Only a correlation analysis will get us to that number. Finally, in no way do I intend to imply that these indices are the sole contributor to temperature changes. They are an important component, along with other considerations. I hope to look at some of these otehr factors, as well, when I get closer to my correlation analysis.

For the record, I did the best-fit sine wave to the Arctic oscillation data. It showed a best fit of a wave that is hundreds of years long. I’m not comfortable with drawing any sort of conclusion on that. For now, I will assume that there does not appear to be any significant cyclical aspect to the anomalies in the Arctic Ocean. That does not mean that the index is not correlated with global temeprature, however.

In the meantime, I have a number of other indices to look into. I will present them as I do them.

17 Responses to “A Closer Look At Oceanic Oscillation Cycles”

  1. Gardy LaRoche said

    Your curves vaguely reminded of some of Dr Theodor Landscheidt’s work.
    In case you’re interested, here’s a list of his papers available online.

    Landscheidt papers

    Click to access Mini-Crash_in_Tune_with_Cosmic_Rhythms_3_p_1989.pdf

  2. Layman Lurker said

    Very interesting work. Oceans store the heat from the sun and radiate it back in rythmic, cyclical patterns. But as you point out, the net ocean heat radiation is the sum of a number of regional oscilations. Sometimes these cycles converge near the peaks of heat radiation and sometimes in the valleys. Throw in the atmospheric factors and the feedback mechanisms: CO2, solar radiaton, humidity, clouds, ice cover, aeresols, etc. and you have the raw materials for oscilating climate variability. I think it makes sense that the arctic is not subject to the same patterns as other oceans because ice extent and albedo are so sensitive to the pushes and pulls of all of the ocean / climate variability. The artic then acts as an “amplifier” for warming or cooling determined by all of the other factors.

    ps – great game yesterday eh? 🙂

  3. The Diatribe Guy said

    Yes, great game from a fan point of view. I had a sentimental favorite in the Cards, but I congratulate Pittsburgh for pulling it out.

    I have a good feeling about the Pack next year, though. We’ll be back!

  4. […] Posted by Jeff Id on February 3, 2009 A Closer Look At Oceanic Oscillation Cycles […]

  5. Harold Vance said

    Would surface temperatures be expected lag the composite sine function by a number of years?

  6. […] A Closer Look At Oceanic Oscillation Cycles « Digital Diatribes […]

  7. The Diatribe Guy said

    #6: I would anticipate that this is the case. I have written before about the importance of persistency in the different metrics to generate a warming or a cooling trend. One could reasonably expect that it takes some period of consecutive cooler anomalies to start the trend, and the max depth of cooling probably corresponds more to the upslope of the sine curve rather than the trough.

    That said, it’s sort of conjecture on my part. These analyses are step one towards looking at a correlation analysis of the different oscillations, which naturally would attempt to determine optimum weight in the contribution of prior months/years in determining temperature changes. That’s a while in coming, though. I still have a number of data sets to get through and try and figure out the best way to handle all that.

  8. […] A Closer Look At Oceanic Oscillation Cycles « Digital Diatribes reddit_url=’’ reddit_title=’Website Directory – Cycles’ […]

  9. […] A Closer Look At Oceanic Oscillation Cycles […]

  10. s4caster said

    Just found your site and I like it. Have you visited at all? Thanks, Jim

  11. The Diatribe Guy said

    Yes, I have. It’s one of the sites I have bookmarked for occasional review, and I recommend it to anyone with an interest in the solar activity.

  12. […] Posted by Jeff Id on February 3, 2009 A Closer Look At Oceanic Oscillation Cycles […]

  13. If you want to read a reader’s feedback 🙂 , I rate this post for 4/5. Detailed info, but I have to go to that damn yahoo to find the missed parts. Thanks, anyway!

  14. […] sort of repeating what I did in this post. But it bears repeating. It seems fairly obvious to me, and it’s almost implausible to believe […]

  15. […] Century in the midst of 12 years where no warming has occurred. My own analysis here, here, and here leads me to believe that cooling is on the way. But in each of those analyses, it recognizes […]

  16. […] Posts Uh Oh… Does the plummetting ENSO Index portend a cold winter?A Closer Look At Oceanic Oscillation CyclesThe Ultimate Peer ReviewDeconstructing the HadCrut DataSome fun stats with Sunspots and how the […]

  17. etregembo said

    I’ve always assumed that the AO would typically peak when the PDO and AMO peaked (when coincident), and would hit null when the PDO and the AMO were both negative. Since both oceans seem to dump warmer water into the poles from each basin. Guess the null would be roughly 1960-1965, the peak roughly 1990-1995ish, the next null maybe 2020-2025…does seem to fit with your AMO+ENSO+PDO sinusoidal prediction. Doesn’t seem like rocket science, though for climate science it seems to be quite a leap!

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