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:
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:
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:
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.