It’s been a few months since I’ve taken a good look at the ENSO index, so I thought I’d check that out and provide some context for that data. First, let’s start with a couple nifty little charts (click on them for larger charts):

ENSO Chart One - Raw Anomalies with best-fit sine wave.

ENSO Chart Two - 5-year moving average of ENSO index readings.

I’ll discuss those in a moment. First, a little housekeeping on the data and the latest readings, and recent historical context.

First, keep in mind that the ENSO index is based on a two-month average. The data is released in terms of JanFeb, FebMar, MarApr, … So, by default, the “monthly” readings are really a two-month moving average. I don’t think that matters all that much to the analysis, but it’s worth noting. For simplicity in conversation, I’ll refer to the anomalies as “monthly” anomalies, but we all know what that means. (I’m lazy)

The current anomaly is -0.737, which is the fourth consecutive month where the reading is lower than the previous month. It is the seventh consecutive month where the reading is below -0.500, which is that point where they consider the period a “La Nina” period. It is the eighth consecutive negative anomaly. This stretch followed two readings that barely peeked above zero (0.050 and 0.028) after a previous period of 12 consecutive readings below zero. The prior stretch was colder (Spetember 2007 – December 2007 were all below -1.100).

The last time there was a stretch where 21 of the last 23 readings were below zero occurred during the period ending March 2002. However, the average anomaly during this stretch is a bit cooler than that one. The average of the last 23 readings is -0.703, and the last time we had 23 readings with at least that low of an average was the period ending September 2000.

Back to the charts…

Chart one shows the raw anomalies. We often hear of the ENSO index cycling in a somewhat irregular, short-term manner. It is evident from the chart that this is the case from a more short-term basis. However, I think we also need to recognize that there is also a longer-term cycle underlying the data. Admittedly, due to the paucity of the data period, this is based on what appears to be roughly one full cycle, and after another 200-300 years, we’ll know more. Since I won’t be around then, I can only work with what I have to work with.

The explanation makes some sense, though. Simple observation of the chart seems to indicate a general low phase and a high phase. If you look a the peaks and valleys from the zero anomaly only, recent spikes look like an aberration. If you look at them relative to the sine wave, it’s less of an aberration.

The sine curve was determined by utilizing the “Solver” add-in in Excel. It simultaneously solves for the parameter values that minimize the least square differences from the raw anomalies to the sine curve.

The sine curve was determined by solving for (1) point on the curve at January 1950, that optimally fits the rest of the data, (2) the scale of the wave, in magnitude (in terms of degrees Celisus), (3) the monthly phase reduction of the wave (basically this establishes the length of the optimal wave), and (4) vertical shift in the curve.

The results show an optimized sine curve fit that started 17.3% into its downward cycle as of January 1950, with a full (360 degree) cycle length of just over 61 years. This differs slightly from a previous analysis, and the main difference is that I did not consider a vertical shift in that previous analysis. But that needs to be considered because just because we’re told that there’s a zero anomaly for purposes of measurement doesn’t mean that it works that way in reality.

The scale of the long term curve is 0.4337. This may not seem overly large, but it is significant. From peak to trough, the difference is nearly 0.9 degrees. Consider an ENSO event that deviates in a given month positively by 2 degrees Celsius. At the trough of the longer-term cycle, this will be a 1.5-1.6 anomaly. At the peak of the cycle, it’s a 2.4-2.5 anomaly. The short-term event is no different, but it’s happening at a different point in the cycle, and the conclusions that may be drawn from it as a startlingly high event could be erroneous.

In addition to that, there is, in fact, a small bias towards higher anomalies in the data. One would expect all anomalies to balnce out to zero on a best-fit basis if there were no bias. I found that a vertical shift of 0.0325 degrees was needed in an upward direction to get the best fit of the sine wave. This is not a large amount, but in conjunction with the scale factor, it helps put the recent spikes in perspective.

Take, for example, the peak value in the index from 1997 (2.872). The sine curve vlaue at that point was 0.360, for a difference of 2.512. This is a significant deviation, to be sure. But if we review the data, is it completely out of the norm? I guess it depends on what one decides is out of the norm, but here are otehr months where the deviation was at least as large:

- April 1983 – 2.644
- March 1983 – 2.759
- February 1983 – 2.615

That’s it. So, that deviation was still pretty significant, although it was less that the deviation in each of those readings in 1983. However, it is still not quite as significant as it first appeared. Compare the raw anomaly of 2.872 (deviation from curve of 2.512) to a reading, for example, for the good old days of the cold and freezing 1970s. July, 1972 showed a raw anomaly of 1.816. That’s a decent anomaly, but it is more than a full degree less than the 1997 reading we just looked at. However, the sine curve in 1972 had a negative value of -0.091, creating a difference of 1.907. the gap in the difference is now only 0.6 degrees Celsius. This in now disregards the 1997 peak value as a significant deviation, but it mitigates the degree to what the actual deviation was, and helps put it in context.

There are very few of these data points to draw any kind of conclusion, but the peak positive deviations (+2.0 or more) do outweight the “peak” negative deviations (-2.0 or less). 1983 and 1997 experienced those peak positive deviations, while 1988 experienced the sole negative deviation of at least two degrees. Note that, while 1988 was in fact the largest negative deviation from the wave in the data, it is only the 5th lowest trough point on a raw basis.

As for Chart 2, it is simply a 5-year smoothed presentation of the ENSO data. Purely for observation, it basically corresponds to the idea that there is a longer-term cyclical nature to the ENSO index. Pre-1990, anomalies, on average, were negative. Post-1980, anomalies, on average, have been positive. It is much more akin to a step function, or what could be expected with a cycle, than any sort of linear trend. What is happening on the right hand side of the chart indicates a potential transition point, though one should be a little careful about declaring positive anomalies dead. On the left side of the chart, I don’t know how far back the actual anomalies fell below the zero line. Looking at the double peak in the periods ending 1960 and 1970 may have looked like a transition point at that time. But La Nina wasn’t quite done yet, giving us one last good blast in the mid 1970s. After that, there was a clear transition into a stronger El Nino phase. The 2003 and current dip looks similar in nature to me. However, the double maximum peak in 1983 – 1997 looks similar to the double negative trough in 1957 and 1976, as well. So, this is where I could go either way on whether or not the transition is now or in another 5-10 years. But if I consult Chart 1, 1976 was just entering the positive phase of the cycle, and we’re just now entering the negative phase. So if I had to wager my 3rd child, I’d go with “the transition is now.”

Of course, entering the cold phase doesn’t mean there will be no more El Ninos (or at the very least, positive deviations from the wave). They still occur, perhaps as frequently, but the deviations from a negative phase wave translates into a lower raw anomaly.

At least, that’s how I see it.