I. Better graphs of Manilla’s annual rainfall and its scatter
The first two graphs are new versions of graphs in an earlier post, published also as an article in “The Manilla Express” (28/2/17) and in the “North West Magazine” (20/3/17).
In that article, I said:
“This Manilla rainfall record is one counter-example to the snow-balling catalogue of reported extreme climatic events.”
My claim was not well supported. While the two graphs showed that recent annual rainfalls have been normal, with little scatter, they do not show whether there were any extreme events.
However, Manilla’s annual rainfall record can be analysed to show extreme events. This post considers the Total Range within a 21-year sampling window as an indicator of extremes. A following post discusses kurtosis as another measure.
The two improved graphs
The re-drawn graphs of historical records in this post use a 21-year sampling window, as before. They now have an improved smoothing procedure: a 9-point Gaussian curve. (The weights are stated below.)
1. Yearly Rainfall Totals
The first graph (above) represents the normal rainfall as it changes. The earlier version showed the arithmetic mean. The new version uses the median value (the middle, or 50th percentile value) instead.
The new version is less “jumpy” due to better smoothing. The median varies much more than the mean does. All the same, most features of the shape are unchanged: very low annual rainfall from 1915 to 1950; very high rainfall from 1955 to 1982; normal rainfall since 1983. There are some shape changes: rainfall before 1900 does not plot so high; from 1911 to 1913 there is a respite from drought; the highest rainfall by far now appears from 1970 to 1980.
As before, one can say:
“Present rainfall will seem low to those who remember the 1970’s, but the 1970’s were wet times and now is normal. Few alive now will remember that Manilla’s rainfall really was much lower in the 1930’s.”
In addition, this new version makes the pattern of growth and sudden collapse obvious. Collapses amounting to 100 mm came within a few years after both 1900 and 1978. Growth in the 58 years from 1920 to 1978 came at the phenomenal and unsustainable rate of 33 mm per decade. By the 1970’s, elderly residents of Manilla would have seen rainfall increase decade by decade throughout their lives.
(I noted this pattern of growth and collapse in an earlier post about Manilla’s summer rainfall.)
2. Yearly Near-Mean Rainfall Scatters
The plot on this second graph is changed only by better smoothing. However, the titles are changed. I realised that the Inter-quartile Range is not a good general indicator of spread or, in this case, of reliability of rainfall (as I had assumed). Inter-quartile Range measures the scatter of values that are close the middle: just the middle 50%. My new title refers to “near-mean” scatter. Any values that could be called “extreme” fall very far beyond the Inter-quartile Range.
Two more measures of scatter
An alternative measure of scatter in data is the Standard Deviation. In normally distributed data, the Standard Deviation extends 34% each side of the median (and mean). The “Standard Deviation Range” then extends from the 16th percentile to the 84th percentile. It includes a much larger proportion (68%) of a population than the Inter-quartile Range (50%) does. However, it also says nothing about extremes, which will lie far out in the residual 32% “tails” of the data.
The broadest measure of scatter is the Total Range from the lowest to the highest value. This measure does include any extreme values that exist in the data.
In the present case, each calculation uses a sample that includes only 21 points. The lowest data point is close to the 5th percentile and the highest data point is close to the 95th percentile of a similar continuous curve.
All three measures of scatter graphed
The third graph shows the history of the three measures of scatter on a common scale of millimetres. The near-mean Inter-quartile Range is plotted in red, the conventional Standard Deviation Range in black, and the extreme Total Sample Range in blue.
To some extent, the measures moved together. There was low scatter in 1906 and 1934, and high scatter about 1948. The Total Sample Range disagreed with the others around 1920, when it was relatively lower, and around 1900 and 2000, when it was relatively higher.
Using Total Range to measure “extremes”
The 21-year Total Range in annual rainfall at Manilla, as plotted in blue can be taken as one measure of the presence of extremes of either excessive or deficient annual rainfall. In that case:
Annual rainfall showed very high extremes before 1900;
Annual rainfall showed high extremes 1942 to 1953;
Annual rainfall showed normal extremes from 1962 to the present;
Annual rainfall showed low extremes from 1902 to 1936.
The historical pattern of the three measures of scatter in annual rainfall values at this site seems to be coherent. However, no explanation of the pattern suggests itself.
If the 21-year Total Range does indicate the pattern of extremes in annual rainfall as an attribute of climate, then these particular extremes do not seem to relate to anthropogenic climate change, as quantified by records of global temperature. On the contrary, the data points that showed the greatest extremes were at the earliest dates, when the climate was cooler.
A following post will explore the use of kurtosis as an indicator of extremes in this data.
Note on smoothing
The weights for a 9-point Gaussian smoothing function are:
Date minus 4: 0.013
Date minus 3: 0.047
Date minus 2: 0.117
Date minus 1: 0.202
Actual Date: 0.242
Date plus 1: 0.202
Date plus 2: 0.117
Date plus 3: 0.047
Date plus 4: 0.013