Curve-Fitting the ENSO Index Suggests We Have the Highest El Nino Event since 1998

ENSO Index and Fitted Curves @ 12/31/2009

I’ve continued to work, as I have the time to, on pulling the Oceanic Oscillation data, developing a fitting spreadsheet for each index, to get some idea of what the underlying cyclical nature of the oscillations may be.

I decided to post the above chart on ENSO, since I (a) completed it, (b) we’re currently in the midst of an El Nino, and (c) most amateur climatologists know about it and occasionally like to take a look at it.

The source for the data can be found on the right side of this page. The largest hurdle in the curve-fitting is that good(?) data only goes back to 1950. Even this may be a little questionable, and from what I’ve read, any proxied data prior to that is even less reliable. But, we’ll run with the data we have with the caveat that is always there about analysis only being as good as the accuracy of the data and all that.

I’ve been very interested in trying to understand the tendency of these oscillations to cycle (or not cycle, as the case may be). The ENSO index, in particular, can have the appearance of a random variation with no particular pattern.

At this point, I need to explain what I did here, and then I need to explain what I am saying and what I am not saying regarding the conclusions.

PROCESS

1) I have simultaneouosly fitted a long-period wave and a short-period wave to the ENSO data
2) The following elements have been fitted:

For the long period wave:

1.  Best fit sine wave with a period of at least 30 years
2. A scale factor to determine amplitude of the wave
3. A phase increment amount to determine the length of the wave
4. A starting point on the wave cycle to be fitted at the beginning of the data
5. A vertical shift, to account for bias in the zero-anomaly base assumption
6. A slope of linear trend

For the short wave:

1. Best fit sine wave with a period less than 30 years
2. A scale factor for amplitude
3. A phase increment amount to determine cycle length
4. A start point on the wave at the beginning of the data

There is no shift or trend determined on the short wave determination, since this will follow the path of the long wave.

Through a simultaneous and recursive process, all these elements are simultaneously solved to produce the minimum value of squared differences from the point on the short wave to actual ENSO index readings.   The ultimate solution is not necessarily incorporating the best-fitted long wave taken in isolation.   I initially ran the long-wave fit first, and then separately ran the best fit short wave along that curve.   Moving to running everything simultaneously helped the overall fit and actually reduced the length of the long-wave.    The difference is not huge, but since it is the best fit and the results appear reasonable, I went with that.

RESULTS

The results of this analysis show a 50.5 year ENSO cycle that underlies the shorter-term variations.   I have shown this before, and it is an interesting consideration in evaluating the relative magnitude of certain ENSO events, not so much as it relates to the zero value, but as it relates to the long-term wave.   The current long-term wave is on a decline, and may, in fact, be bottoming out in another four or five years.

The starting point is just past the halfway mark of the cycle, so we see a lower-index period at the beginning of the chart.  The amplitude of the wave is about 0.32 at its peak.   So, from top to bottom (with no linear trend) there is a difference of 0.64 in the magnitude contributed to ENSO events from one period to another, depending on where the long-term cycle is at.

There seems to be, in addition to the cycle, a linear trend in the data for which the long-term cycle moves along, at least since 1950.   It may be that there is a third cycle that is substantially longer that is being mistaken for a linear trend.   This may matter in the long run, but for a 60-year time period the linear approximation should suffice.   However, it may well be that we need a number of additional years of data to better fit this and judge whether or not there is a linear trend, or some other cycle at work.  For now, though, I go with the best fit, and for that the rate of change is 0.7 degrees Celsius per century.

This long wave is being fit simultaneously with a short wave placed on its path.   The period of this short wave is 4.93 years.  Its scale is 0.49.   So, at the top of this wave, plus the top of the long wave, we are adding 0.81 degrees to the ENSO index.   The first wave starts at about the 220 degree mark of a cycle.

Key Assumptions (What I’m doing versus what I’m suggesting)

There are a couple key assumptions here.  The primary assumption is the selection of a sine wave for fitting.  I am not saying this is the best assumption.  All I am saying is, given this assumption, there is a best fit.   As I look at the data, it actually doesn’t do too bad a job in aligning with peaks and valleys.  However, it is far from perfect.   There are other ways to manipulate this, if desired.  One can select a skewing assumption so that the wave peaks earlier or later in the cycle than at 90/270 degrees.   Or, once can assume that there is a factor that compresses or expands length over time (or both in some oscillating pattern over years).   Another thing to look at is to see if the length of sunspot cycles impacts the difference in timing of ENSO peaks/valleys, as I’ve seen suggested.

All these are potential refinements that could improve results.   However, all that said, I still think there are some interesting results here.   The most significant El Nino events do seem to correspond well with peaks in both waves.

The other assumption is that there are two cycles to consider.  A third assumption that can be questioned is the validity of a linear trend in the data.

DEVIATIONS

One may think that the waves represent the anticipated direction of the ENSO index.  That is actually not what the waves imply.  The red wave pattern marks the “starting point” for the current index.  From there, deviations may go up or down.    This may be the most confusing aspect on how to read the chart.   It’s not so much about predicting El Nino or La Nina, it’s about showing how the ultimate magnitude is affected.

Examples:

June 1955 ENSO index = -2.270; Wave value = -0.76.  Negative deviation = -1.51

September 1973 ENSO index = -1.71; Wave value = +0.20.  Negative deviation = -1.91.

One could argue that the 1973 event was substantially more profound than the 1955 event, even though the actual ENSO index reading was lower in 1955.

Likewise:

The most profound El Nino event, in terms of a deviation from the underlying wave, actually occurred in 1983 – not 1998.  The March 1983 reading = 3.11, and the wave value = 0.77, for a differential of 2.34.    The maximum deviation during the “Super El Nino” was actually August 1997 – a difference of 2.03.

In fact, we actually have a fairly significant event occurring right now.   The December 2009 deviation from the wave is +1.54, which is the largest difference since April of 1998!

Eastern Pacific Oscillation and Random Stuff – Believe it or not, a New Post…

Ah, it’s been a while, hasn’t it? My friend Jeff at The Air Vent asked me if I’m giving up. I understand the appearance of this, given my lackluster performance (or more accurately, zero performance) as of late.

Before I present a chart of the EPO Index, which most of us probably don’t care all that much about anyway (if we’ve even heard of it), I have a few random observations:

1) To Docattheautopsy: Ha! I told you! (Check out comment #6 here: https://digitaldiatribes.wordpress.com/2009/09/30/el-nino-is-back-with-the-fury-of-a-woman-scorned/#comments). Good thing, too, because I get enough spam. Anyway, as complex as climate is, it is actually kind of amazing that so much of the simplicity can be missed among the complexity. I know it doesn’t always hold, but there are some rules of thumb that stand up pretty well. La Nina in spring/summer ==> cold Wisconsing Winter. El Nino in Spring/Summer ==> mild Wisconsin winter. It’s not really rocket science. So, each of the last two years gave us frigid temps and lots of snow, and so far this year we have above average temperatures in November. It’s supposed to cool off soon, but nothing unusual. I admit I was nervous in October – it was a very cold and wet October, but November has been beautiful.

2) Climategate: I love it. I don’t “love it” in the sense that it should have ever happened. That part ticks me off, because it’s simply a blight on the scientific process and public trust, and a validation of the more underhanded aspects of the whole thing – it’s about money, politics, control and power. That’s a major shame. But I do “love” the fact that this has been exposed. It may well be true that much of their analysis doesn’t change, and they may actually believe their conclusions. But what is lost in making that simple argument of dismissal about the relevance of the situation is that there are other scientists who have reached different conclusions who were essentially shut of of the public debate, and in doing this it led to a global, incessant mantra that brainwashed policymakers and citizens alike. It’s not whether or not their studies are meritorious, it’s about the fact that the full debate and scientific process was not implemented, and the full range of views were shut out of attaining credibility through reprehensible methods of collusion and intimidation. And really, it just shows the overall poor character of the participants in these exchanges, which also leads to a lack of trust.

3) Where are the temperature charts? Well, I’ll get back to them. I really wanted to spend time on the Oscillation Data, so I’m continuing down that path at the moment. The trends don’t change so much from month to month, and I am in no way avoiding it due to recent uptick in temperatures. I don’t do that, even if Phil Jones and Michael Mann may suggest implementing a trick to disguise the uptick, if they were skeptics.

And so, with that, let me explain the following chart: The Eastern Pacific Oscillation Data are available since 1950 (link to the right) and is just another one of the Oceanic Oscillations. It’s not one we hear about much, and may well not be highly important in the climate discussion. That’s OK. By plowing through the different indices, I hope to isolate the ones that do have an apparent oscillation pattern, because it seems to me that this is an indication that the Oscillation is a driver of temperature, rather than the other way around. The interesting thing about most of the oscillation patterns is that they tend to cycle on a longer time period. Even ENSO, with its shorter term spikes (not on particularly predictable intervals, it seems) has a longer term cycle. The EPO index suggests something else – an 8.9 year cycle.

Caveat: there are no December values in the data set. I have adjusted this by using the average of the November and January values. I have sent an e-mail to NOAA seeking an explanation for this. If I receive a response, I’ll either comment about it or update the post.

EPO Data as of 200910

It’s hard to say how much impact this metric has on global temperatures, and I probably won’t know until I can do a full correlation analysis of all the oscillations, solar index, and CO2, at minimum. But it may have some impact. There is almost no linear trend whatever on this, and the index seems well-centered around a zero anomaly.

There also does seem to be a very shallow 40-year cycle, if I expand the analysis out to look at that, but nothing worth more than a note. The driving cycle is the shorter-term one.

Hope all is well with everyone. If I find I cannot get to data analysis, I will try to do better at posting some fluff just to let you know I’m still here ;).

A Closer Look At Oceanic Oscillation Cycles

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:

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

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

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).

Pacific Decadal Oscillation (PDO) Index – Back into the Negative

The PDO index is a measure of another one of those weird oceanic oscillation patterns.  The ENSO index is a shorter-term varying event, whereas the PDO index is considered a longer-term event.  Interestingly, however, when you collapse the ENSO index into longer average time periods, there does appear to be persistency in the ENSO index, as well. However, the short-term cyclical nature of the ENSO index is much more evident than the PDO index, even if the averages show similar persistency.

The PDO index is predominant in the Northern Pacific and secondarily evident in the tropics, whereas the ENSO index is the other way around. ENSO receives so much attention because of the large short-term cyclical variations, but the PDO has very significant swings as well, just usually over a longer period of time.

The index, however, is measured on a month-to-month basis and the data can be located here.

November has not yet been updated, but the October index value was -1.76. This was the single coolest reading in any month since November 1999, and was the 14th consecutive negative reading in a row. While there have been other stretches of 14 consecutive negative readings – the last being 1999-2000, it is interesting to note that the current streak of seven consecutive readings of less than -1 has not been seen since the period ending February 1976. That particular stretch ended at 7 months. If this month’s reading is below -1, it will mark the first time since the period ending June 1972. And that streak ended at 8. Beyond that point takes us to a streak in the early 1960s. So I’ll keep an eye on that.

As I did with the ENSO index, I collapsed the raw data into different average periods. Since the PDO does seem to vary over a longer period of time, I went up to a 10 year average. The persistency in the index is very clear once you take longer-term averages.

Below are a few charts of the PDO. The first is the raw data. Taking the edges off with 12-month smoothing follows that. I then present 5-year and 10-year averages.

The PDO monthly index has been negative for a bit already, as has the five-year average. But the 10-year average recently went negative, as well. Of course, all the same arguments apply as in the ENSO discussion – the persistence matters. You keep a heater running and the temperature gets warmer than the temperature an hour ago, depending on insulatory effects. Persistence in both ENSO and PDO correspond with the warming we see in the global temperature readings. The 10-year average PDO is slightly negative, and we’ve cooled slightly in the last few years. Coincidence?

The overall PDO index data since 1900.

The overall PDO index data since 1900 with 12-month smoothing.