## III. When extreme values were more or less extreme

#### This graph is based on applying a 21-year sampling window to each year in the Manilla rainfall record, then adding smoothing. *(See “Note about Sampling” below.)*

Back to the prelude **“Manilla’s Yearly Rainfall History”.**

Back to **Extremes Part I.**

Back to **Extremes Part II.**

Forward to **Extremes Part IV.**

Forward to **Extremes Part V.**

[In later work, I use kurtosis as a measure of extremes. For example, in **“Rainfall Kurtosis vs. HadCRUT4 revised”**.]

### Making the graph

For each year, I have identified the highest and lowest values of annual rainfall in its 21-year sample. I already know the long-term mean annual rainfall at Manilla: **652 mm**. From those values I have plotted the height of the maximum value above the mean **(red)** and the depth of the lowest value below the mean **(green)**. Both may be called “Extreme Values”.

The difference between the maximum value and the minimum value in each 21-year sample is the Total Range. That also is a measure of Extreme Value, which I graphed in **an earlier post.**

The Total Range is equal to the sum of the two Extreme Values that are plotted. To make it easy to compare the three measures, I have divided the Total Range by two. I have plotted that value in **blue**.

### Two discordant results

All three measures agree well except at two dates: **1897** and **1980**. On both occasions the Minimum Value **(green)** was not extreme at all, being only about 200 mm below the long-term mean. The Maximum Value in 1980 was rather extreme (about 330 mm above the mean). The Maximum Value in 1897 was **the most extreme value** that appears on this graph: 475 mm above the mean!

The pattern of this graph is dominated by this single feature. It is due to just one data item: the annual rainfall reading of 1129 mm in the year 1890, which was the highest ever.

### The pattern

For extreme annual rainfalls at Manilla, this graph suggests the following:

**They were more extreme than usual at the end of the 19th century and in the 1940’s.**

** They were less extreme than usual from the 1900’s through to the 1930’s.**

** They have been no more or less extreme than one should expect through all of the last five decades.**

### Comment

This graph depends on very simple statistics: the maximum, the minimum and the mean. Such a sparse data set is subject to the effect of chance. Also, although this is not obvious, this graph assumes that other features of the distribution of annual rainfall have not been changing, which is not true. See the post **“Moments of Manilla’s 12-monthly Rainfall”**.

I have more to say on this topic.

[In later work, I use kurtosis as a measure of extremes. For example, in **“Rainfall Kurtosis vs. HadCRUT4 revised”**.]

*Note about Sampling*

I chose a 21-year sampling window to be wide enough to contain enough points for analysis, without losing time-resolution, or losing too many years at each end of the record from 1883 to 2016.

The first mid-year of a sampling window was 1893 and the last, 2006.

To remove jumps in the trace on the graph, I then applied a nine-point Gaussian smoothing function. That further reduced the years that could be plotted to those from 1897 to 2002.