# Rainfalls: 8 in the 0.1th percentile

## Normal rainfall in November

Rainfall in November 2019 (40.2 mm) was near normal. That reduced shortages at durations from 2-months to 5-months. Otherwise it had little effect: fifteen of twenty longer durations remained extreme shortages.

## Values plotted in the 0.1th percentile

For simplicity, the bottom line is labelled with the 0.1th percentile value, and percentile values below 0.1% are plotted on the line. As there are 1600 months of record, both the 2nd-driest month (percentile value 0.063%) and the driest month, (percentile value 0.000%, by convention), which would plot below the line, are plotted on it.
Driest records have again been broken at durations of 12-months (270 mm), 24-months (611 mm), 30-months (834 mm), 72-months (2927 mm), and 96-months (4205 mm). The 96-month record had stood at 4405 mm since November 1919.
A value that equals an earlier record occurs at 84-months (3555 mm).
Values that are 2nd-driest occur at 36-months (1129 mm) and at 240-months (11816 mm). The 240-month (20-year) total is now only 50 mm more than the lowest-ever value of 11766 mm set in February 1931.

## How to read the graph

This graph shows all the present rainfall shortages at Manilla, short term and long term, as percentile values. The latest values, as at the end of October 2019, are shown by a thick black line with large circles. Those from one month earlier are shown by a thinner line with small diamonds. [The method is described in “Further Explanation” below.]

## Further Explanation

The following notes explain aspects of this work under these listed headings:

Data analysis

Cumulative rainfall totals
Percentile values
Severity of rainfall shortages

Limitations of this analysis

Monthly rainfalls form a single population
Observations are not retrospective
The rain gauge failed

## Data analysis

This graph is based on analysis of monthly rainfall totals from 1884. Using the spreadsheet application Excel, I calculate cumulative totals and their percentile values. Using these values, I identify rainfall shortages as serious, severe, or extreme .

### Cumulative rainfall totals

I prepare two tables. The rows in each table are serial months, more than 1600 in total. The columns in each table are headed by the selected number of months, n, as specified below. In the first table I cumulate the rainfall totals. First, I add each month’s rainfall total to that of the previous month for a 2-month total. Using the previous two months, I get a 3-month total, and so on. In this way, I get n-month rainfall totals from n = 1 up to n = 360 (30 years). However, I calculate for only the following 25 values of n:

n = 1, 2, 3, 4, 5, 6, 9, 12, 15, 18, 24, 30, 36, 42, 48, 60, 72, 84, 96, 108, 120, 144, 180, 240, 360

### Percentile values

In the second table, I convert values from the first table to percentile values by the function PERCENTRANK(). Each value in this table represents the percent of such observations in the historical record that have been lower. A 12-month rainfall value that falls at the 5th percentile (for example) is lower than all but 5% of all 12-month totals in the record.

### Severity of rainfall shortages

Percentile values are shown on the y-axis of the graph using a logarithmic scale.
I classify these percentile values of rainfall shortage using th. That is, “Serious shortage” between the 10th and the 5th percentile, and “Severe shortage” below the 5th percentile. Because the data demand it, I further classify as “Extreme shortage” those values that are below the first percentile.

Note. A given percentile value represents the same rarity of occurrence (say 5%) regardless of the duration of the shortage concerned. However, the rate of rainfall at a given percentile value rapidly approaches the normal rate as one considers longer durations. This accounts for long-term shortages being, in some cases, more severe than short-term shortages observed at the same date.

## Limitations of this analysis

### Monthly rainfalls form a single population

Percentile ranks have been calculated using the whole data record, in which the median monthly rainfall is 44 mm. No distinction has been made between calendar months. As a result, January months, which generally have the highest rainfall, (median value 75 mm) will be ranked here as rather less drought-prone than other months.
This limitation will not affect those n-month totals that comprise whole years, such as 24 months.
Since adjusting the analysis to account for the differing rainfall in calendar months is difficult, I am letting this simpler analysis stand.

### Observations are not retrospective

When a current month’s data shows (for example) an extreme rainfall shortage for a duration of 15 months, this graph will plot that 15-month extreme shortage at the current month. If the previous month did not have an extreme rainfall shortage of that duration, it will not have been recorded there. Logically, that 15-month extreme shortage must have commenced 14 months earlier. It began then, but the evidence for it has appeared only now.
The data for each current month must always be provisional concerning the drought status at durations longer than one month. I am preparing graphs that project shortages back to the date that they began, so as to show the onset, persistence, and breaking of droughts. [Such graphs are presented in the posts “Rainfall Shortage History: Manilla” and “Rainfall Shortage Jan 2000 – Mar 2019”.]

### The rain gauge failed

This analysis of rainfall shortage, with the resulting graphs, is vitiated by failure to maintain an official rain gauge at Manilla Post Office, Station 055031 for the the four years to July 2019. The last manual reading by the Postmaster was on 26 March 2015. After a gap of 13 months, the Bureau of Meteorology re-purposed an automatic gauge for flood analysis, installing it in the museum yard. It operated there under the same station number for four months from 23 May 2016 to 7 October 2016. After repair, the same gauge operated as Manilla (Museum), Station 055312 for six months from 17 March 2017 to 24 September 2017 and intermittently during the five months from 16 March 2018 to 26 August 2018, when it failed again.