This graph relates to a graph of the cumulative values of the Southern Oscillation Index, posted earlier and copied below.
The graph above is in a more familiar form . It may help to explain what the earlier graph means. That is, that the SOI was dominated by positive values (towards La Niña) for about fifty-nine years before 1976, and was dominated by negative values (towards El Niño) for twenty-four years after that date. From 2000 the trend seems to be upward, showing La Niña dominance again. Broadly, these were straight-line CUSUM relationships throughout each of the periods, as shown by the coloured trend lines. Slopes on a CUSUM plot represent offsets of the mean monthly value: the mean SOI in the earlier period was +1.4 units, and that in the second period was -3.5 units. Since 2000, the mean monthly value is around +1.0 units.
These offsets are quite large, but not as large as the offsets that define El Nino and La Nina episodes. According to the Bureau of Meteorology,
* Sustained negative values of the SOI greater than -8 often indicate El Niño episodes.
* Sustained positive values of the SOI greater than +8 are typical of a La Niña episode.
Another definition uses SOI values in the first and last deciles, which are values greater than +/-13.
The trace of the raw monthly SOI values shown on this graph could be used as an example of random “white noise” as described in Wikipedia.
Like everybody else, I try to distinguish meaningful episodes with “sustained” high positive or negative values. The red line shows values smoothed by a Gaussian function of half-width six months. Many of the major El Niño and La Niña episodes can then be recognised.
I have transferred the trend-line construction from the earlier graph in the form of a blue line, with steps at changes in the trend. I could not have estimated the shape of the blue line without doing the CUSUM plot. After drawing the blue lines, however, one can see that the red lines do move up and down with the blue ones.
The CUSUM technique was invented to identify sudden large and persistent changes in a value. In climate, this has been called a “climate shift”. The SOI has suffered three climate shifts since 1876: in 1917, 1976, and 2000.
If the Southern Oscillation Index dates climate events without lead or lag, the highest peak on the SOI CUSUM graph places the great climate shift of 1976 precisely, within a week or so of the solstice on the 23rd of June.
I posted discussion of an earlier version of this graph in “Weatherzone” Forums >> Weather >> Climate and Climate Change >> ENSO Discussion 2012 Post #1105539. That thread was closed with all other threads relating to climate change on “weatherzone” forums.