Digital Diatribes

A presentation of data on climate and other stuff

September 2009 Update on the AMO

Posted by The Diatribe Guy on September 23, 2009

I’ve looked at the AMO data set to see what it’s been up to lately, and after a brief plunge into negative territory, it’s come back to a level in accordance with the current sine wave path of the cycle. If you recall, there was a period of 77 consecutive months of positive AMO anomalies, with January 2009 finally breaking that string of positives. We then had 5 consecutive negative anomalies. Historically, such a deviation is not necessarily unexpected, as can be easily enough seen from chart observation. However, it was not an expectation for a persistent state, and we’ve now seen the last three anomalies come in at 0.175, 0.282, and most recently 0.205.

While these are positive anomalies, viewing them relative to the red wave line on the chart shows us that they are right around what would normally be expected.

When looking at certain Oceanic oscillations, the cycle is very clear, and the strength of a given anomaly should be placed in the context of the overall wave path. Deviations from the wave are a stronger indication of the unusualness of an anomaly than the actual value of it.

As I’ve noted in my previous write-ups, we’re nearing the peak of the wave. We should expect many more positive AMO anomalies. In fact, we should expect more positive AMO anomalies for the next 20 years (well, sort of – I’ll explain why this is probably shortened artificially in a bit). Since the wave is at its peak, we will soon see continually cooler anomalies for the next 34 years or so. However, the next few years will still be positive, but dropping.

Here’s the chart:


Atlantic Multidecadal Oscillation Data as of 200908

Maybe it’s just me, but this is one of my favorite charts. Admittedly, the change in it is nearly imperceptible on a month-by-month or quarter-by-quarter basis. But one reason I present it occasionally is because I think it really tells a good story.

The story begins with the cyclicality, which is very evident. This, combined with ENSO and PDO (and I’ll keep looking at other indices) show a clear cyclicality in Ocean Temperatures. In my humble opinion, this should raise a red flag with regard to temperature correlations to anyone who even remotely wishes to get to the truth of what drives global temperatures. Making this cyclicality more clear is the fact that the Arctic and Antarctic Oscillations do not show this behavior at all. Click on the link related to the Arctic to read more about the PDO and ENSO cycles as well.

The next story is, where are we in the cycle? As I’ve alluded to, we are at the peak of the cycle. That means that the anomaly has, on average, risen continually for over the last 30 years. The most rapid point of acceleration of the wave occurs in the early-mid 1990s. Since then, it’s been increasing at a decreasing rate. In a couple years, it will start decreasing at an increasing rate for the next decade and a half.

The AMO is about a quarter-phase out of sync with the PDO (Again, see link above – click on the word “Arctic”). Thus, the PDO has been decreasing over the last number of years. As we’ve seen in the Temperature Charts we’ve been flat for about 12 years now, and we’ve actually seen decreasing temperatures over the last handful of years. This seems to correspond will with an AMO that is only slightly increasing and a PDO that is cooling off more rapidly.

The rest of the story can be told based on the parameters that determine the wave. The first thing to note is that the wave fitted is a sine wave. Whether or not this is the best fit, I don’t know. But it’s a pretty nice fit to the eye. It’s entirely possible that there is some other function out there that does better, but at first glance the sine wave appears to be a reasonable assumption.

The sine wave is adjusted as follows, to determine the minimum least squares value in the deviations in actual anomalies versus the wave values. Other fitting algorithms could be used, to be sure, but the minimum least squares method seems to have yielded satisfactory results.

The first determination is the starting point of the wave. If we consider a cycle, in degrees, to be 0 at the inflection point in the upward direction, then the peak of the wave is at 90 degrees, the inflection point on the way down is at 180 degrees, the trough is at 270 degrees, and it all starts over again at the inflection point on the way up. Our wave starts at 337 degrees in January 1856. We are currently at 73 degrees, and the peak of the AMO should occur around October 2012. At that point, we’ll see declining anomalies until the anticipated trough about 34 years later.

The second parameter to be determined is what I call the “Phase Reduction.” That’s probably a horrible parameter title, but at least I understand what I mean when I’m running the numbers. It determines the length of the wave. It is the amount per month that the wave advances in terms of 360 degrees. The value here is 0.4427, which if you do the math, implies a 67.7 year period for a complete cycle.

The next parameter is the “scale” parameter, which shrinks the peaks and troughs to the level that best accommodates the anomalies. The AMO doesn’t deviate wildly from zero, generally in the range from 0.6 to -0.6. The center of these values only swings +/0.18, which is the scale factor.

The next parameter is a vertical shift of the curve upward or downward. The overall AMO anomalies are actually biased a bit on the negative side, so the best fit curve is actually shifted down 0.0465. If this were correctly centered around zero, then, the current anomaly would be 0.252 instead of 0.205.

The final parameter is a measurement of linear trend that may be affecting the results. The best-fit model shows a near-zero trend. The value is only 0.0000417 per month. This implies that the chart is fitted about a linear trend of only 0.05 degrees Celsius per Century. So, if there is a linear trend in actual ocean temperature, the calculation of the anomalies has done a nice job of filtering that effect out, seemingly isolating only the cyclical nature of the oscillation pattern.

My conclusions: (1) Negative anomalies in early 2009 were significant deviations from expected; (2) current anomalies in the last three months are in line with expectations, (3) AMO will be at about current levels for the next 5-6 years, (4) starting in late 2012, a 34 year stretch of cooling anomalies will occur in the AMO. The most rapid decline will occur around 2030, with the period from 2020-2040 showing a rapid cooling similar to the period from 1952-1972. (5) The initial stretch of cooling over the next 20 years will correspond with a further decline in the PDO. (6) Buy wool.

I’ve also put together some smoothed charts that I’m including here. I don’t have much additional to say about them, but the smoothing sometimes helps clear up the picture. Personally, I think the raw chart is already pretty clear:


Atlantic Multidecadal Oscillation 12-month Smoothed Data as of 200908


Atlantic Multidecadal Oscillation 5-Year Smoothed Data as of 200908


Atlantic Multidecadal Oscillation 10-Year Smoothed Data as of 200908


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