Rainfall kurtosis vs. HadCRUT4, revised

Patterns of rainfall kurtosis and global temperature.

The kurtosis of annual rainfall at Manilla NSW forms a time-series that matches the time-series of global surface temperature when detrended.

[REVISED:
Earlier posts were based on rainfall data sets that were too small. Estimates of kurtosis and skewness were unstable. For details please read “Rainfall kurtosis matches HadCRUT4” and “Rainfall kurtosis vs. HadCRUT4: scatterplots”.]

The variables

These two climate variables have little in common. Manilla, NSW, is a single station that has a 134-year record of daily rainfall only. That yields estimates of rainfall kurtosis, an indicator of the relative frequency of extreme values.
HadCRUT4 is one of several century-long estimates of near-surface temperature for the whole world. [See Note below: “Data Sources”.]

The visual match of the patterns

The first graph (a dual-axis line chart) shows that these two variables have similar patterns of variation over time.

I found the best visual match by:
* scaling 0.5 units of Manilla rainfall kurtosis to 0.1° of detrended HadCRUT4 temperature;
* aligning the kurtosis value of -0.3 units with the zero of detrended temperature;
* lagging the rainfall by two years.

Features that the two patterns have in common are:
* matching main peaks at 1897, 1942 and 2005, each higher than the one before;
* persistent low values in the 1910’s, 1920’s, 1950’s, 1960’s, 1970’s and early 1980’s;
*some matching minor peaks and troughs.

Regression rainfall kurtosis on HadCRUT4.

The correlation chart

The second graph is a correlation chart. The linear regression of kurtosis on detrended temperature has the reasonable R-squared value of 0.67.
As I have made it a connected scatterplot, you can see how the relation has changed through time. From the first data point in 1898 (in red) both variables decreased together to the lowest temperature in 1910. Both peaked in 1942, having risen since 1920, later falling until 1955-56. The final rise to the highest peak (2005) was continuous from 1984 for temperature, but the rise in kurtosis was not. It fell slightly in 1990, then remained static until 1998.
All rainfall figures actually came two years earlier. [See note below: “Manilla’s 2-year lead”.] The assigned two-year lag not only makes peaks match on the first graph. It sharpens the reversals on the second graph. On a trial connected scatterplot without lag, these reversals had been smooth clockwise curves.

What it means

As evidence of extreme behaviour in climate

It is said that more extremes in climate will occur as the world becomes warmer. The evidence is not strong. Most data sets are overwhelmed by noise, and “extreme” is seldom defined with rigor.
In the present case, I believe that the definition of “extreme” that I use is sound: that is, the kurtosis of a frequency-distribution. The instability of kurtosis when based on my small samples had been an issue. In this revision I have increased the sample population size from 21 to 125.

My rainfall data set that displays more and less extreme behaviour is not general but local. It can merely suggest that data elsewhere may reveal functional relationships.

De-trended global temperature

This strong link between local rainfall kurtosis and global climate has a surprising feature. Although this extreme behaviour seems to relate to global temperature, it does not relate to global warming! It relates to a temperature trace from which the global warming trend has been removed. Times of high kurtosis, denoting enhanced extremes, correspond to times when the global temperature was highest above trend. Such times occurred not only in the twenty-first century, but also in the nineteenth century. There was another (widely-known) peak in detrended global temperature near 1940: at that time also kurtosis was above normal.

Should global temperature remain static for a time, it would be falling rapidly below its rising trend. According to this data set, that should bring reduced extreme behaviour in annual rainfall at Manilla.


Data Sources

(i) Global temperature time-series

From the three available century-long time series of global near-surface temperature I have chosen to use HadCRUT4, published by the British Met Office Hadley Centre. The link is here.

I selected from the section: “HadCRUT4 time series: ensemble medians and uncertainties”.
From this, I downloaded two files:
(i) “Global (NH+SH)/2, annual”;
(ii) “Global (NH+SH)/2, decadally smoothed”.
[The “Decadally smoothed” data supplied is annual data smoothed with a 21-point binomial filter.]
From each data file, I used only the first column: the year date, and the second column: the median value.

I established the secular trend of global warming using the linear trend function in Charts for “Excel”. I found the linear trend of the whole HadCRUT4 annual series data (1850 to 2016) to be:

y = 0.005x – 0.52.

I then subtracted the annual value at the trend line from the decadally smoothed HadCRUT4 value to get the de-trended smoothed value shown on the first graph.

(ii) Kurtosis of Manilla annual rainfall

The rainfall data is that for Manilla Post Office, Station 055031 of the Australian Bureau of Meteorology. Station 055031 functioned without gaps from 1883 to March 2015. Since then, the official record is fragmentary.
For this revised analysis, I found kurtosis values for 12-monthly rainfall by using the (excess) kurtosis function in “Excel”. I used sub-populations of 125 successive months, referred to the median month. I smoothed these values with a 181-point Gaussian filter (yielding similar smoothing to that of HadCRUT4). Smoothing reduced the years that could be plotted to those from 1896 to 2004. From 12-monthly values for successive months, I selected those for June each year as annual values.

Manilla 12-monthly rainfall history: KurtosisI posted a line graph of this revised kurtosis data earlier, in “Moments of Manilla’s 12-monthly rainfall”.

 


 Note: Manilla’s 2-year lead

The match between Manilla rainfall data and global temperature is optimised by lagging the Manilla data by two years. That is to say, local climate events occurred at Manilla before corresponding events of global scope. This may be due to chance. However, this is not the only such occurrence.

In the post “El Niño and My Climate”,   I show that 21st century events in Manilla’s rainfall and temperature consistently led those of ENSO (El Niño-Southern Oscillation) in the central Pacific Ocean. Manilla’s seasonal anomalies preceded anomalies in NINO3.4 values by one month for temperature, two months for rainfall and three months for dew point. In longer term trends, Manilla led ENSO by one or two years in both temperature and rainfall.

 

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