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.


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.

21-C Rain-ENSO-IPO: Line graphs

From 1999, rainfall at Manilla NSW matched ENSO only up to 2011, before the IPO became positive.

Manilla rain, ENSO, IPO

This graphical log compares the rainfall at Manilla NSW with the El Niño-Southern Oscillation (ENSO) and the Inter-decadal Pacific Oscillation (IPO) through the 21st century to date. Values shown are anomalies, smoothed. (See Notes below on “Data”, “Smoothing”, and “Lagged Rainfall”.)

Rainfall (black) uses the left axis scale; the ENSO (magenta) and the IPO (green) use the inverted right axis scale.

[21st century temperature and rainfall at Manilla are compared as smoothed data in the post “21-C Climate: Mackellar cycles”.]

Matches between rainfall and ENSO

There is an excellent match between the rainfall and ENSO values in the left part of the graph.
I improved the visual match by various means:
1. The ENSO scale (magenta) is inverted, because positive values of the ENSO anomaly relate to negative values of rainfall anomaly here.
2. The scales are harmonised: the zero values are aligned, and 20 mm of monthly rainfall anomaly is scaled to (minus) one degree of ENSO anomaly.
3. Smoothing is applied to suppress cycles shorter than 12 months.
4. Rainfall anomaly values are lagged by two months. (See the Note below.)
As lagged, most peaks and troughs of rainfall coincide with troughs and peaks of ENSO, and their sizes (as scaled) are often similar.

Failure to match rainfall and ENSO

In the right part of the graph, the match between rainfall and ENSO fails. There are extreme mismatches: the Super-El Niño of 2014-16 had no effect on local rainfall, the rainfall deluge of 2011-12 came with a mild and declining La Niña, and the extreme drought of 2018 came while ENSO was neutral.
By visual inspection, I judge that a close relation of rainfall to ENSO, which had applied for the twelve years up to September 2011, then failed for the following seven years.

Influence of the IPO

The inter-decadal Pacific Oscillation (IPO) affects the relation between ENSO and Australian weather. (See note below “Effect of the IPO”.)

Power et al.(1999) show that Australian seasonal weather and its prediction align with ENSO only when the IPO is negative. It follows that a good match between ENSO and Manilla rainfall was expected while the IPO (green) was negative from 1999 to 2013, and was not expected from 2014 to 2017. The trend of the IPO through 2016-17 makes it likely that the IPO continued positive through 2018, as the mismatch between rainfall and ENSO persisted.
Power et al. note that the relation is not sensitive to the width of a neutral zone chosen to separate the positive and negative regimens of the IPO. In this particular case, the rainfall/ENSO match failed as the IPO rose through minus one degrees. However, the rainfall/ENSO match began in 1999, much earlier than the time when the IPO fell through minus one degrees.

Scatter plots

In a following post I show scatter plots and regressions for the periods of match and mismatch on this graphical log.




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Hot Days and ENSO

Graphical log of max temps and hot days

More frequent hot days do not come in a three year cycle, but in a 1.5 year cycle related to ENSO.

The Hot Day data set

The graph of number of hot days per year

Log of annual hot days in 16 yearsThe graph on the left is one I posted earlier. The height of each data point represents the number of hot days in a year, plotted near January. The pattern of points led me to join them by a smooth curve. This curve swings up and down rather regularly, with five peaks and five dips in the fifteen years. That is, more frequent hot days seem to come in a three-year cycle.
Is this cycle “real”? Should we look for a cause? Will the cycle continue?
Probably not! The points of measurement are one year apart. Cycles that are only three years long may be “aliases” of different and shorter undetectable cycles. (See Note below on Nyquist frequency.)

More detailed hot day data

Other graphs already shown include further data: the number of hot days in each month, and the 13-year average number of hot days in each calendar month. From these I have calculated a relative frequency. That is, the ratio of the actual number to the average number for that month.
Only the months of November, December, January and February have enough hot days to calculate a relative frequency, but these can show changes within the hotter months of each year.

The daily maximum temperature data set

A graph that I posted in “El Niño and my climate” shows a curve of smoothed monthly means of daily maximum temperature anomalies. The yearly cycle of summer-to winter temperature has been removed. I have also applied a smoothing function, which makes the monthly points of measurement effectively two or three months apart. As a result, cycles longer than about six months can be detected.
There are about 10 peaks and 10 dips in the 15.5 year curve. They define a cycle of about 1.5 years wavelength. That cycle is so much longer than the minimum-detectable six month cycle that “aliasing” is not likely.
The reality of this temperature curve is supported by its close similarity to the recognised curve of the El Niño – Southern Oscillation (ENSO), as read from NINO3.4 Pacific Ocean sea surface temperature anomalies.

A combined graph of hot day and temperature data

The graph at the top of the page presents the monthly smoothed maximum temperature anomaly again, using the scale at the left. To this I have added data on the number and frequency of hot days.
The annual number of hot days is shown in blue, in blue boxes. The boxes are placed higher or lower according to the number, but the height is adjusted to match other data better.
A “Hot Day Index” is shown by blue diamonds. This index is based on the relative frequency of hot days in each month that has data.  I have re-scaled the values to improve the match. (See Note on Re-scaling below.)

Matching hot days with temperature

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El Niño and My Climate

ENSO and Manilla NSW temperature anomalies over sixteen years


The first graph shows that the temperature at Manilla NSW agreed very closely with El Niño and La Niña temperatures for a good part of the last sixteen years.
The El Nino – Southern Oscillation (ENSO) is shown by NINO3.4 monthly anomaly values, and temperature at Manilla, NSW is smoothed monthly mean daily maximum temperature anomalies. (See the Note below.)
Values of Manilla temperatures agree with those of ENSO through the major temperature peaks and troughs in the spring seasons of 2002, 2006, 2007, 2009, and 2010. In the two highest peaks of 2002 and 2009 and the deep trough of 2010, Manilla temperature extremes were more than a month ahead of ENSO temperature extremes.
Since mid-2011, the two curves do not agree well:
* A La Nina in summer 2011-12 that was very weak produced the deepest of all troughs in Manilla temperature.
* An El Nino in winter 2012 resulted in heat at Manilla, but not until four months later.
* In spring 2013, when there was no El Nino at all, Manilla had a heat wave just like those with the El Nino’s of 2002 and 2009, .
The record for ENSO since January 2013 is unlike that earlier this century: it flutters rather than cycles.
To show slower changes, I have drawn cubic trend lines for both of the variables. These also agree closely, with ENSO going from a maximum (2004) to a minimum (2011) seven years later. Manilla temperature trends remained ahead of ENSO temperature trends by one or two years.


ENSO and Manilla NSW rainfall anomalies over sixteen years.

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Manilla’s Hot Days to June 2015

Log of annual hot days in 16 years This post updates a similar one by including three more years to make a total of sixteen. It is in the same format as a recent post on Manilla’s frosts. Because the summer, which has the most hot days, crosses from one calendar year to the next, I have begun each year at July. I have called days warmer than 35° “hot days”, and days warmer than 40° “very hot days”.

Note added.

I have analysed the pattern of hot days in more detail in a later post “Hot days and ENSO”. By finding the relative frequency of hot days in all of the hotter months, I show that there is a cyclic variation related to ENSO. The cycle period is near 1.5 years, not 3 years as the log of annual frequency of hot days (above) suggests.

Graphical log of hot and very hot days

The first graph is a log of the number of hot and very hot days in each year. The three years with the most hot days had almost the same number: the year ’02-’03 had 41, the year ’09-’10 had 44, and the year ’13-’14 had 43. The two years with the fewest were ’07-’08 which had 5, and ’11-’12, which had only 4. The 13-year average is 26. Counting only the very hot days, ’03-’04 had the most (6), and four years had none at all. On the average, two days exceeded 40° in a year. (These are thirteen-year averages, not updated.) The number of hot days per year seems to have a cyclic pattern, with a period that increases from two years to four years during this short record. This is just a curiosity. The pattern of hot days has a lot in common with the pattern of smoothed monthly temperature anomalies for all months. These are plotted here, on a graph that relates them to ENSO. The relation of Manilla daily maximum temperature to ENSO was quite close from 1999 to 2011, but failed almost completely since mid-2011. In the earlier post on frosts, no cyclic pattern can be seen, nor any relation to ENSO.

New Record hottest days

In the sixteen years, there have now been 37 days hotter than 40 degrees: that is, 2.4 days per year. It remains true that December has fewer very hot days than November or February. A new record was set on 12/1/2013 by a daily maximum temperature of 43.2 degrees, beating the 42.6 degrees of 20/11/2009. This record was broken again on 3/1/2014, with 43.7 degrees. In the latest year, the hottest day (41.1 degrees) ranked only 12th, and it was not in summer, but in November.

Three new annual graphs

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