21-C Rain ENSO IPO: Scatterplot

The anomaly of monthly rainfall at Manilla, NSW varied with that of ENSO for only a part of the 21st century to date.

Scatterplot Rainfall vs ENSO

This connected scatterplot relates the smoothed anomaly of the El Niño-Southern Oscillation (ENSO) to the smoothed and 2-month-lagged anomaly of monthly rainfall at Manilla, NSW. The earlier data, from September 1999 to September 2011, is plotted in blue, and the later data, from October 2011 to November 2018, in red.

The same data was displayed as a dual-axis line plot in an earlier post titled “21-C Rain-ENSO-IPO: Line graphs”. Data sources are linked there.

The line plot revealed two things: the relationship changed from earlier to later times, and there was a better match when the rainfall data was lagged by two months. To clarify, I prepared various scatterplots with fitted regressions.

Raw data scatterplots

Scatterplots of the raw data values yielded regressions with very low values of the coefficient of determination (R-squared). For the whole population, R-squared was 0.028. I then checked the coefficient when I lagged the rainfall by 1-, 2-, or 3-months. A 1-month lag almost doubled the coefficient to 0.041; a 2-month lag gave 0.055, and a 3-month lag gave 0.041 again.
My observation that Manilla rainfall typically leads ENSO by 2 months is confirmed.

Connected scatterplots of smoothed and lagged data

The smoothing function used in the dual-axis line plot of the earlier post makes a good visual match. That suggests that local rainfall and ENSO are physically related at a periodicity no shorter than 12 months.
Using the smoothed and 2-month-lagged data, I have made the scatterplots shown in the graph above.
The better-matched data from September 1999 to September 2011 (blue) has a satisfactory R-squared of 0.498, nearly 20 times greater than that of the raw data. The very poorly-matched data from October 2011 to November 2018 (red) has an R-squared value of 0.040, no better than the raw data.

Patterns in the sequence of rainfall and ENSO values

In the above graph, I have joined the consecutive smoothed data points to make a connected scatterplot. Because little noise remains, clear patterns appear.

Matched rainfall and ENSO

The pattern up to September 2011 (blue) is mainly a series of ellipses, some clockwise and some anti-clockwise. They are almost parallel to the regression line:

y = -0.047x-0.246

The blue point furthest to the top left is that for September 2002, a time of extreme drought and El Niño.
The blue point furthest to the bottom right is that for December 2010, a time of very high rainfall and La Niña.

Discordant rainfall and ENSO

The pattern from October 2011 (red) swings about wildly and does not repeat. The regression (with a trivial coefficient of determination) is nearly horizontal. Near its ends are the extreme drought of June 2018 and the deluge of January 2012, both at times when ENSO was near neutral. At the top of the graph is the Super El Niño of November 2015, when Manilla rainfall was normal.

Conclusion

Scatterplots, connected scatterplots and regressions confirm that a strong relation between rainfall at Manilla and ENSO failed in 2011 as the IPO was rising from a negative toward a positive regimen.

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