## El Niño Project (Part 7)

So, we’ve seen that Ludescher et al have a way to predict El Niños. But there’s something a bit funny: their definition of El Niño is not the standard one!

Precisely defining a complicated climate phenomenon like El Niño is a tricky business. Lots of different things tend to happen when an El Niño occurs. In 1997-1998, we saw these:

But what if just some of these things happen? Do we still have an El Niño or not? Is there a right answer to this question, or is it partially a matter of taste?

A related puzzle: is El Niño a single phenomenon, or several? Could there be several kinds of El Niño? Some people say there are.

Sometime I’ll have to talk about this. But today let’s start with the basics: the standard definition of El Niño. Let’s see how this differs from Ludescher et al’s definition.

### The standard definition

The most standard definitions use the Oceanic Niño Index or ONI, which is the running 3-month mean of the Niño 3.4 index:

• An El Niño occurs when the ONI is over 0.5 °C for at least 5 months in a row.

• A La Niña occurs when the ONI is below -0.5 °C for at least 5 months in a row.

Of course I should also say exactly what the ‘Niño 3.4 index’ is, and what the ‘running 3-month mean’ is.

The Niño 3.4 index is the area-averaged, time-averaged sea surface temperature anomaly for a given month in the region 5°S-5°N and 170°-120°W:

Here anomaly means that we take the area-averaged, time-averaged sea surface temperature for a given month — say February — and subtract off the historical average of this quantity — that is, for Februaries of other years on record.

If you’re clever you can already see room for subtleties and disagreements. For example, you can get sea surface temperatures in the Niño 3.4 region here:

Niño 3.4 data since 1870 calculated from the HadISST1, NOAA. Discussed in N. A. Rayner et al, Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century, J. Geophys. Res. 108 (2003), 4407.

However, they don’t actually provide the Niño 3.4 index.

You can get the Niño 3.4 index here:

You can also get it from here:

Monthly Niño 3.4 index, Climate Prediction Center, National Weather Service.

The actual temperatures in Celsius on the two websites are quite close — but the anomalies are rather different, because the second one ‘subtracts off the historical average’ in a way that takes global warming into account. For example, to compute the Niño 3.4 index in June 1952, instead of taking the average temperature that month and subtracting off the average temperature for all Junes on record, they subtract off the average for Junes in the period 1936-1965. Averages for different periods are shown here:

You can see how these curves move up over time: that’s global warming! It’s interesting that they go up fastest during the cold part of the year. It’s also interesting to see how gentle the seasons are in this part of the world. In the old days, the average monthly temperatures ranged from 26.2 °C in the winter to 27.5 °C in the summer — a mere 1.3 °C fluctuation.

Finally, to compute the ONI in a given month, we take the average of the Niño 3.4 index in that month, the month before, and the month after. This definition of running 3-month mean has a funny feature: we can’t know the ONI for this month until next month!

You can get a table of the ONI here:

Cold and warm episodes by season, Climate Prediction Center, National Weather Service.

### Ludescher et al

Now let’s compare Ludescher et al. They say there’s an El Niño when the Niño 3.4 index is over 0.5°C for at least 5 months in a row. By not using the ONI — by using the Niño 3.4 index instead of its 3-month running mean — they could be counting some short ‘spikes’ in the Niño 3.4 index as El Niños, that wouldn’t count as El Niños by the usual definition.

I haven’t carefully checked to see how much changing the definition would affect the success rate of their predictions. To be fair, we should also let them change the value of their parameter θ, which is tuned to be good for predicting El Niños in their setup. But we can see that there could be some ‘spike El Niños’ in this graph of theirs, that might go away with a different definition. These are places where the red line goes over the horizontal line for more than 5 months, but no more:

Let’s see look at the spike around 1975. See that green arrow at the beginning of 1975? That means Ludescher et al are claiming to successfully predict an El Niño sometime the next calendar year. We can zoom in for a better look:

The tiny blue bumps are where the Niño 3.4 index exceeds 0.5.

Let’s compare the ONI as computed by the National Weather Service, month by month, with El Niños in red and La Niñas in blue:

1975: 0.5, -0.5, -0.6, -0.7, -0.8, -1.0, -1.1, -1.2, -1.4, -1.5, -1.6, -1.7

1976: -1.5, -1.1, -0.7, -0.5, -0.3, -0.1, 0.2, 0.4, 0.6, 0.7, 0.8, 0.8

1977: 0.6, 0.6, 0.3, 0.3, 0.3, 0.4, 0.4, 0.4, 0.5, 0.7, 0.8, 0.8

1978: 0.7, 0.5, 0.1, -0.2, -0.3, -0.3, -0.3, -0.4, -0.4, -0.3, -0.1, -0.1

So indeed an El Niño started in September 1976. The ONI only stayed above 0.5 for 6 months, but that’s enough. Ludescher and company luck out!

Just for fun, let’s look at the National Weather service Niño 3.4 index to see what that’s like:

1975: -0.33, -0.48, -0.72, -0.54, -0.68, -1.17, -1.07, -1.19, -1.36, -1.69 -1.45, -1.76

1976: -1.78, -1.10, -0.55, -0.53, -0.33, -0.10, 0.20, 0.39, 0.49, 0.88, 0.85, 0.63

So, this exceeded 0.5 in October 1976. That’s when Ludescher et al would say the El Niño starts, if they used the National Weather Service data.

Let’s also compare the NCAR Niño 3.4 index:

1975: -0.698, -0.592, -0.579, -0.801, -1.025, -1.205, -1.435, -1.620, -1.699 -1.855, -2.041, -1.960

1976: -1.708, -1.407, -1.026, -0.477, -0.095, 0.167, 0.465, 0.805, 1.039, 1.137, 1.290, 1.253

It’s pretty different! But it also gives an El Niño in 1976 according to Ludescher et al’ definition: the Niño 3.4 index exceeds 0.5 starting in August 1976.

### For further study

This time we didn’t get into the interesting question of why one definition of El Niño is better than another. For that, try:

• Kevin E. Trenberth, The definition of El Niño, Bulletin of the American Meteorological Society 78 (1997), 2771–2777.

There could also be fundamentally different kinds of El Niño. For example, besides the usual sort where high sea surface temperatures are centered in the Niño 3.4 region, there could be another kind centered farther west near the International Date Line. This is called the dateline El Niño or El Niño Modoki. For more, try this:

• Nathaniel C. Johnson, How many ENSO flavors can we distinguish?, Journal of Climate 26 (2013), 4816-4827.

which has lots of references to earlier work. Here, to whet your appetite, is his picture showing the 9 most common patterns of sea surface temperature anomalies in the Pacific:

At the bottom of each is a percentage showing how frequently that pattern has occurred from 1950 to 2011. To get these pictures Johnson used something called a ‘self-organizing map analysis’ – a fairly new sort of cluster analysis done using neural networks. This is the sort of thing I hope we get into as our project progresses!

### The series so far

Just in case you want to get to old articles, here’s the story so far:

El Niño project (part 1): basic introduction to El Niño and our project here.

El Niño project (part 2): introduction to the physics of El Niño.

El Niño project (part 3): summary of the work of Ludescher et al.

El Niño project (part 4): how Graham Jones replicated the work by Ludescher et al, using software written in R.

El Niño project (part 5): how to download R and use it to get files of climate data.

El Niño project (part 6): Steve Wenner’s statistical analysis of the work of Ludescher et al.

El Niño project (part 7): the definition of El Niño.

El Niño project (part 8): Berezin et al on the stability of climate networks.

### 9 Responses to El Niño Project (Part 7)

1. And no one noticed that Australia and New Zealand vanished entirely for the duration of the 97/98 El Niño?

2. Simplicio says:

I read the earlier posts, but am a little confused. Is the basic idea that there are two different states (El Nino and El Nina), or three (those two plus some “normal” average state that the other two are relatively rare deviations from).

The graph from Part II kind of makes it look like the former. But talk of “anomalies” and such make it sound like there’s three states: a usual state the system spends most of its time in, and that only occasionally does the temperature differential “jump” to one of the other two (or, I guess, maybe nine) different states.

• John Baez says:

Simplicio wrote:

But talk of “anomalies” and such make it sound like there’s three states…

Beware! In climate science, “anomaly” does not mean “unusual event”. It means “the temperature minus the average temperature for this time of year”. I explained this in the post here.

As to your actual question, the basic oversimplified idea is that there are 3 states: El Niño, La Niña and ‘in-between’. The El Niño and La Niña states are not very unusual. Here is a chart of the Oceanic Niño Index since 1950, showing these 3 states:

 Year DJF JFM FMA MAM AMJ MJJ JJA JAS ASO SON OND NDJ 1950 -1.4 -1.3 -1.2 -1.2 -1.1 -0.9 -0.6 -0.5 -0.4 -0.5 -0.6 -0.7 1951 -0.8 -0.6 -0.4 -0.2 0.0 0.4 0.6 1.0 1.1 1.2 1.1 0.9 1952 0.6 0.4 0.3 0.3 0.3 0.1 -0.1 0.0 0.2 0.2 0.2 0.3 1953 0.5 0.6 0.6 0.7 0.7 0.7 0.7 0.7 0.8 0.8 0.8 0.8 1954 0.7 0.5 0.1 -0.4 -0.5 -0.5 -0.6 -0.7 -0.8 -0.7 -0.7 -0.7 1955 -0.7 -0.7 -0.7 -0.8 -0.8 -0.8 -0.8 -0.7 -1.1 -1.4 -1.7 -1.6 1956 -1.1 -0.8 -0.6 -0.5 -0.5 -0.5 -0.5 -0.6 -0.5 -0.5 -0.5 -0.5 1957 -0.3 0.1 0.4 0.7 0.9 1.0 1.1 1.2 1.2 1.3 1.5 1.8 1958 1.8 1.6 1.2 0.9 0.7 0.6 0.5 0.3 0.3 0.4 0.5 0.6 1959 0.6 0.6 0.5 0.3 0.2 -0.1 -0.2 -0.3 -0.1 0.0 0.1 0.0 1960 -0.1 -0.2 -0.2 -0.1 -0.1 0.0 0.1 0.2 0.2 0.1 0.1 0.1 1961 0.0 0.0 0.0 0.1 0.3 0.4 0.2 -0.1 -0.3 -0.3 -0.2 -0.1 1962 -0.2 -0.3 -0.3 -0.3 -0.2 -0.2 0.0 -0.1 -0.2 -0.3 -0.4 -0.5 1963 -0.4 -0.2 0.1 0.3 0.3 0.5 0.8 1.1 1.2 1.3 1.4 1.3 1964 1.1 0.6 0.1 -0.4 -0.6 -0.6 -0.6 -0.7 -0.8 -0.8 -0.8 -0.8 1965 -0.6 -0.3 0.0 0.2 0.5 0.8 1.2 1.5 1.7 1.9 1.9 1.7 1966 1.4 1.1 0.9 0.6 0.4 0.3 0.3 0.1 0.0 -0.1 -0.1 -0.2 1967 -0.3 -0.4 -0.5 -0.4 -0.2 0.1 0.1 -0.1 -0.3 -0.3 -0.3 -0.4 1968 -0.6 -0.8 -0.7 -0.5 -0.2 0.1 0.4 0.5 0.5 0.6 0.8 1.0 1969 1.1 1.1 1.0 0.9 0.8 0.6 0.5 0.5 0.8 0.9 0.9 0.8 1970 0.6 0.4 0.4 0.3 0.1 -0.2 -0.5 -0.7 -0.7 -0.7 -0.8 -1.0 1971 -1.2 -1.3 -1.1 -0.8 -0.7 -0.7 -0.7 -0.7 -0.7 -0.8 -0.9 -0.8 1972 -0.6 -0.3 0.1 0.4 0.6 0.8 1.1 1.4 1.6 1.9 2.1 2.1 1973 1.8 1.2 0.6 -0.1 -0.5 -0.8 -1.0 -1.2 -1.3 -1.6 -1.9 -2.0 1974 -1.9 -1.6 -1.2 -1.0 -0.8 -0.7 -0.5 -0.4 -0.4 -0.6 -0.8 -0.7 1975 -0.5 -0.5 -0.6 -0.7 -0.8 -1.0 -1.1 -1.2 -1.4 -1.5 -1.6 -1.7 1976 -1.5 -1.1 -0.7 -0.5 -0.3 -0.1 0.2 0.4 0.6 0.7 0.8 0.8 1977 0.6 0.6 0.3 0.3 0.3 0.4 0.4 0.4 0.5 0.7 0.8 0.8 1978 0.7 0.5 0.1 -0.2 -0.3 -0.3 -0.3 -0.4 -0.4 -0.3 -0.1 -0.1 1979 -0.1 0.1 0.2 0.3 0.2 0.0 0.0 0.2 0.3 0.5 0.5 0.6 1980 0.5 0.4 0.3 0.3 0.4 0.4 0.3 0.1 -0.1 0.0 0.0 -0.1 1981 -0.4 -0.6 -0.5 -0.4 -0.3 -0.3 -0.4 -0.4 -0.3 -0.2 -0.2 -0.1 1982 -0.1 0.0 0.1 0.3 0.5 0.7 0.7 1.0 1.5 1.9 2.1 2.2 1983 2.2 1.9 1.5 1.2 0.9 0.6 0.2 -0.2 -0.5 -0.8 -0.9 -0.8 1984 -0.5 -0.3 -0.3 -0.4 -0.5 -0.5 -0.3 -0.2
• Simplicio says:

Ah, thanks. I was indeed misinterpreting “anomaly”.

I was also picturing that if I graphed the above table as a histogram it’d be tri-modal, but it turns out that’s not the case. The El Nino state doesn’t particularly stand out, warmer trends bleed more or less evenly into average and colder trends. (In retrospect, if that wasn’t the case, the definition of El Nino would be obvious and you wouldn’t need a blog-post talking about it).

I guess, then, that the different states aren’t set apart so much by being particularly much more frequent then the intermediate states between them, but that they tend to persist for solid blocks of time. So once the differential is warmer then .5 degrees above average, it tends to stay that warm or warmer for a many months at a time.

3. arch1 says:

FWIW (not much I realize) my general purpose neural network tells me 1) the “interesting” rectangle (7S to 7N x 175 E to 95 W) extends somewhat further E than the “Niño 3.4” rectangle, 2) some of the common patterns are linked (2&1, 4&3, 8&9 because the 1st member looks like a precursor or close cousin of the 2nd, 4&8 because they both make me apprehensive though I can’t put my finger on why:-).

• John Baez says:

Arch1 wrote:

1) the “interesting” rectangle (7 °S to 7 °N × 175 °E to 95 °W) extends somewhat further E than the “Niño 3.4″ rectangle,

Right! Ludescher et al try to predict El Niños by seeing how strongly the temperatures at the red dots (the “interesting rectangle” and two more dots) are correlated to the rest of the dots here:

but people say an El Niño is happening when the water is especially in one of these rectangles, especially the Niño 3.4 region:

some of the common patterns are linked (2&1, 4&3, 8&9 because the 1st member looks like a precursor or close cousin of the 2nd, 4&8 because they both make me apprehensive though I can’t put my finger on why:-)

I’m not sure what the numbers here mean.

• arch1 says:

Thanks for the extra info and rather charitable interpretation of my comment John.

The ambiguous numbers (sorry) refer to the “9 most common patterns of sea surface temperature anomalies” near the end of the post.

4. The Azimuth Code Project has been working on both predicting and understanding the El Niño phenomenon, along with writing expository articles. So far we’ve mostly talked about the physics and data of the El Niño […]