San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

Some Statistical Investigations of the
El Niño Southern Oscillation Phenomenon

From time immemorial the natives of the western coast of South America noticed that from time to time there was a distinct change in the weather. The weather changed from a normal cool dryness to warmer and rainier. Since rains were welcome this was looked upon as a gift of the gods. Since the rains came near the end of December, in Christian times they were associated with the baby Jesus, El Niño, the boy child.

It is one of the great successes of meteorology/climatology to have identified and explained the phenomenon of El Niño. The British meteorologist, Gilbert Walker, as a result of his study of the Indian monsoons identified the mechanism of the phenomenon. He called it the Southern Oscillation and now it is generally known as the El Niño-Southern Oscillation, ENSO for short.

The mechanism for the Southern Oscillation is the building up of mound of water in the western South Pacific as a result of the trade winds blowing from the east.

There are other effects of El Niño besides the rains. Under normal conditions there is an upwelling of cold water from the ocean's depths that brings mineral nutrients that feed the bottom levels of the marine ecology.

The pile of water to the east of the islands of Indonesia is only about 18 inches high but it extends thousands of miles. The surface of this water is warmed.

When the east winds fail this mound of water flows downhill to the east. It is like the wind blowing a barrel up an incline. As long as the winds are blowing the barrel stays at the top of the incline. If the winds fail the barrel rolls down the incline. The winds do not have to stop entirely for the barrel to roll down the incline. If they subside temporarily and the barrel starts rolling the winds cannot stop it even if they resume their normal strength. They cannot counter the momentum the barrel develops after it starts rolling. However once the barrel stops rolling on its own the winds can slowly push it back to the incline and up the incline for the process to start over again.

In the absence of the upwelling of cold water from the ocean depths the diminution in the lower levels of the food chain works its way up into the fish the human population depends upon.

The ENSO phenomenon has been found to produce climate effects globally. It not only affects the monsoons of South Asia but the weather in North America and perhaps beyond.

The Statistical Representation of ENSO

Since the ENSO phenomenon is tied to wind conditions and winds are determined by pressure differences the index for ENSO is based upon pressure differences in the South Pacific. The standard index is the pressure difference between Tahiti and Darwin, Australia.

The concept and name oscillation suggests a bimodal phenomenon. Once the term El Niño became common the term La Niña (the girl child) became common as a term for the absence of El Niño, or some polar opposite condition.

There would generally be a distribution of the index rather than just two states. A bimodal (two peaked) distribution could be something like the following.

Below are the histograms (frequency distributions) for the Southern Oscillation Index at different times.

The distribution for January is shown first.

The histogram for the July values is:

And finally the histogram of the annual averages:

The conjectured bimodality of the index is just not there.

If there were some persistence of state then a scatter diagram of the index plotted against its value some time previously would show a structure such as this one.

The sizes of the circles denote the frequencies of occurrence. Thus when in the lower state the system tends to stay in the lower state, but sometimes moves to the upper state. And likewise for the upper state.

The display of the December values versus the November values indicates that there is a persistence of state though the correlation of 0.58 is not extraordinarily high.

However that correlation of monthly values is enormous compared with the correlation of the year-to-year December values.

Correlation analysis is not indicating a longer term persistence of values. The alternative is to look for cyclic patterns over time.

The Time Patterns of the Southern Oscillation Index

The simple average of the monthly values of the SO index does not display any obvious cyclic pattern over time.

There is a great deal of year-to-year fluctuations in the data. Computing a moving average of the annual values will suppress the unsystematic variation. However care must be taken because the process of averaging can introduce a cyclic pattern in purely random values (white noise).

The five-year moving averages are shown below and they indicate a cyclic pattern, at least during some intervals.

The pattern becomes clearer with nine year moving averages.

The pattern is of short term cycles with longer term changes in the amplitude of those cycles.

(To be continued.)

HOME PAGE OF applet-magic
HOME PAGE OF Thayer Watkins