More Droughts After Heavier Rains III.

Graphical log of errors when droughts are predicted from rains

Droughts and flooding rains at Manilla NSW were related in a way that is remarkable and unexpected.

Part III. Predicting drought from heavy rain

[Back to Part II: Scatter-plots]

The graph above is derived from the first graph in this series (copied here) by using the blue regression trend-line from the scatter plot of selected data (also copied here). (For data details, sLog of 1-year droughts and 5-year lagged heavy rainfallsee Note 1, below.)

The equation of the trend line, y = 0.030x is used AS IF to use the daily rainfall excesses to predict the drought frequency five years later. The graph shows the “error” of this “prediction”. (In Note 2, below, I concede that this data set could not support such prediction.)
As expected from the previous graphs, the “prediction” is accurate at most data points to 1975. It is correct to the nearest percentage whole number at nine of the eighteen points. From 1940 to 1955, droughts are uniformly more frequent than predicted. After 1975, the error curve swings wildly up and down.

Could droughts have been predicted from heavy rainfalls?

Scatter-plot 1890 to 1975

By about 1915, it is conceivable that this relationship could have been discovered, either by analysis of such data, or by modelling of the climate system. Then, the data for the next 20 years, up to 1935, would seem to confirm it. Data from 1940 to 1955 would cause doubts, but data from 1960 to 1975 would restore confidence. Then the utter failure of the model in the following four decades would have led to its abandonment, at least for the time being.

Climate shifts of 1975

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More Droughts After Heavier Rains II.

Scatter-plot 1890 to 1975

Droughts and flooding rains at Manilla NSW were related in a way that is remarkable and unexpected.

Part II. Scatter-plots

[Back to Part I: Graphical logs]

I have made scatter plots to see how much correlation there is between the two data sets: the frequency % of severe 12-month drought and the total decadal daily rainfall excesses over 50 mm, when lagged five years. (For data details, see Note 1, below.)

A. The first 70% of the data

The first scatter-plot includes only the first 70% of the data, from 1890 to 1975, which showed matching patterns on the graphical log copied below. I have broken the data points into two groups: the aberrant group 1940 to 1955 (red) and the fourteen best-matched points (blue). The trend line that best fits those fourteen points is y = 0.028x + 0.407, with R-squared = 0.898. However, I have been able to fit the trend line y = 0.030x, that shows y proportional to x, without making R-squared worse than 0.892.
Similarly, the four decades centred on 1940, 1945, 1950 and 1955, had y = 0.050x, with R-squared equal to 0.902.

Expressed in words: for fourteen of the first eighteen data points, the frequency % of severe 12-month droughts remained close to 0.03 times the decade total of daily rainfall (>50 mm/day) measured five years earlier. For the other group of four adjacent points, the number was not 0.03, but 0.05.

B. All the data

Scatter-plot 1890 to 2010

The second scatter plot shows data for all 25 (five-year overlapped) decades. There is a “shot-gun” pattern, as expected. Continue reading

More Droughts After Heavier Rains I.

Log of 1-year droughts and 5-year lagged heavy rainfalls

Droughts and flooding rains at Manilla NSW were related in a way that is remarkable and unexpected.

Part 1. Graphical logs

As the first graph shows, for most of the 130-year record year-long droughts came in direct proportion to very heavy daily rainfall five years earlier. (For data details, see Note 1, below.)
The match between these two variables is astonishing. Both are based on rainfall readings, but they are scarcely related. Excessive daily rainfalls are transient extreme weather events; 12-month droughts are an aspect of climate.

Mackellar’s “Droughts and flooding rains”

Dorothea Mackellar’s famous line * is more apt for this graph than for other graphs where I use “flooding rains” to mean periods unlike drought. (See Note 2. below.) The rains and droughts that I plot here both bring hardship. Severe droughts lasting one year are among the worst of droughts: long enough to use up reserves, and not so long as to be eased by periods of rain. The daily rainfall events plotted are the ones that cause damaging floods.

Features of the graphical log

Log of 1-year droughts and heavy rainfalls

This second graph shows the data at the actual dates. Although the data points for the decade excess of heavy daily rainfall and those for frequency % of 12-month droughts have a matching pattern for much of the record, the pattern is offset. Heavy rainfall points come five years earlier than corresponding drought points. Notice that the heavy rainfalls do not (except in 1980) come squarely in gaps between droughts.
Lagging the rainfall points by five years (as in the first graph) makes some matches almost exact. Such matches occur at all data points from 1890 to 1975, except those from 1940 to 1955, where drought frequencies are relatively higher. Both variables show a two-decade-long, slow decline from 1905 to 1925. At the chosen scales, the amplitude of corresponding rises and falls are usually similar as well.
After 1975, daily rainfall oscillates through a wide amplitude with a twenty-year period, while the frequency % of drought varies Continue reading

Rainfall Deficiencies III: 36-months Duration

Log of severe and extreme rainfall deficiency of 36-month duration at Manilla

This is the third of four graphs that show Manilla’s history of rainfall deficiencies (rainfall droughts), for periods of duration 3 months, 12 months, 36 months, and 120 months.

This third graph includes those periods of severe or extreme rainfall deficiency that last thirty-six months. They are rainfall droughts that affect about three successive years.
In Manilla’s climate, a time of severe 36-month rainfall deficiency has a rainfall total less than 1505 mm, when it normally would be 1940 mm. A time of extreme 36-month rainfall deficiency has a rainfall total less than 1380 mm.
Droughts of this duration have quite different effects to those that are much shorter.
While the 3-month drought that just qualifies as “severe” (by having rainfall in the fifth percentile) would have a rainfall total of 50 mm, in the similarly defined 36-month drought, each 3-month period within it would have, on average, a rainfall total of 125 mm (i.e. 1505*3/36). This 3-month rainfall total is only 25 mm less than the normal 150 mm total. It would scarcely be noticed if it did not persist for 36 months.
The importance of severe and extreme rainfall deficiencies of 36-month duration is that they use up the reserves that are held in surface and sub-surface water storage.

In the Manilla rainfall record, such three-year droughts were concentrated in just a few decades. They were very common around 1910-1915 and 1945 (in more than 12% of months) and in 1965 (in 9% of months). They were very rare or absent (less than 2% of months) before 1900, from 1925 to 1935, and in the entire forty years since 1975.
Extreme 36-month droughts generally comprised about one-fifth of the total, as one might expect (unlike the case for one-year droughts).

Areas shown on the graph

Rainfall deficiencies are called “severe” when they are lower than are recorded for five percent of the months. I have called deficiencies “extreme” when they are lower than are recorded for one percent of the months.
In this graph, I have coloured extreme deficiencies in blue. The maroon colour is deficiencies that are severe, but not extreme. The top edge of the maroon area marks the proportion of severe deficiencies including extreme deficiencies. As an average, this line is at five percent.

Data analysis

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Rainfall Deficiencies II: 12-months Duration

Log of severe and extreme rainfall deficiency of 12-month duration at Manilla

This is the second of four graphs that show Manilla’s history of rainfall deficiencies (rainfall droughts), for periods of duration 3 months, 12 months, 36 months, and 120 months.

This second graph includes those periods of severe or extreme rainfall deficiency that last twelve months. They are rainfall droughts that affect four successive seasons, sometimes making for two failures a year apart.
In Manilla’s climate, a time of severe 12-month rainfall deficiency has a rainfall total less than 400 mm, when it normally would be 640 mm.
The graph shows that such one-year droughts were very common around 1945-1950 and 1965-1970 (in 8% of months) and also 1905 (in 7% of months). They were not common (only 2% of months) around 1885, 1890, and 1980. Recently, around 2015, there have been none at all.
Remarkably, extreme 12-month rainfall droughts (in blue) were almost as common as severe ones in the long period from 1940 to 1975.

Note added June 2015

I have analysed a remarkable and unexpected relation between days of heavy rainfall and the frequency of year-long droughts at Manilla (as graphed here) in a series of posts:
More droughts After Heavier Rains I.
More droughts After Heavier Rains II.
More droughts After Heavier Rains III.

Areas shown on the graph

Rainfall deficiencies are called “severe” when they are lower than are recorded for five percent of the months. I have called deficiencies “extreme” when they are lower than are recorded for one percent of the months.
In this graph, I have coloured extreme deficiencies in blue. The maroon colour is deficiencies that are severe, but not extreme. The top edge of the maroon area marks the proportion of severe deficiencies including extreme deficiencies. As an average, this line is at five percent.

Data analysis

Continue reading