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This is a blog article in progress, written by John Baez. To see discussions of the article as it was being written, visit the Azimuth Forum.

If you want to write your own article, please read the directions on How to blog.

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 definitions

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 smart 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:

TNI (Trans-Niño Index) and N3.4 (Niño 3.4 Index), NCAR.

You can also get Niño 3.4 index 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.

It’s not particularly computer-readable.

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’re 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.

Here is 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, they say 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 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! It exceeds 0.5 starting in August 1976.

For further study

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!

category: blog