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. Recognising that matching patterns on the graphical log (copied here) are not present after 1975, I have broken the population into two: 1890 to 1975 (in blue), and 1980 to 2010 (in red), with a linear trend fitted to each. As expected, the second (red) population has a near-horizontal trend with a trivial value for R-squared.

Log of 1-year droughts and 5-year lagged heavy rainfallsThe trend for the earlier (blue) population, however, is rather convincing, with an R-squared value of 0.591. For this (blue) population, not many points are more than one percentage unit from the trend line. Points for 1940, 1945, 1950, and 1955 have higher drought frequency values than expected. They are identified on this scatter-plot by blue squares. The first scatter plot splits this 1890 to 1975 population into two.

Discussion

Taken together, the graphical log, with its remarkably good match and the scatter plots with their high R-squared values, indicate that there was, from 1890 to 1975, a phenomenon to be explained .

Continued in Part III: Predicting drought from heavy rain


Note 1. Data

A. “Droughts”
(See this earlier post.)

The graphical log of 12-month droughts shows the percentage of months in each decade that have a 12-month rainfall total below the 5th percentile. They have a median value of 5% but range above and below it. Values are plotted against the mid-year of each decade, with decades overlapped by five years. They have been smoothed (1:2:1)/4.

B. “Flooding Rains”
(See this earlier post.)

From the 130-year record of daily rainfalls at Manilla, NSW up to December 2014, I selected all 125 “very wet days” that have readings exceeding 50 mm. I listed them by date.
Since it is only the excess rainfall that runs off, leading to flooding, I have subtracted 50 mm from each rainfall amount. Then I have summed all such excesses for each half-decade. I summed these in pairs to give a decade sum (in mm) centered on the years 1885, 1890, 1895, etc.

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