Cumulative rainfall

 This post is an approach to stating the bleedin' obvious: 2022 was a very damp year.

On 31 December the ABC published an article showing the progress of rainfall year-to-date through 2022.  The driver of this was that for some locations 2022 ended with record rainfall.  This snip shows the chart for Melbourne.

A more spectacular, and thus more beloved by journalists, example is offered by the Chart for Sydney.

I have had an attempt at creating a similar chart for Mallacoota.  I have melded data from my weather station (WS) commencing in February 2019 with BoM data recorded at the Mallacoota Airport site for 39 years over the period  January 1975 to January 2019 (4 years in the 1980s are excluded due to missing data. In the past I have found the BoM data and my WS data to be highly correlated so believe this merger is acceptable, especially in view of the amount of 'fiddling about' that would be required to get the BoM data into the same format.

The basic approach was to assemble a table showing the rainfall for each day for each year and compile from this the cumulative rainfall for each year.  I then calculated the mean cumulative rainfall for each day and the standard deviation for that mean.  Consulting a table showing the areas under a normal curve showed that plotting the lines for Mean+/- (1.288 SD) would show a range equivalent to an 80% probability of the rainfall falling within that area. That is the space between the blue and orange lines in this chart. The grey line is the record for 2022, clearly above the upper bound of the 80% range from day 69 (8 March) onwards.  The big leap for 2022 is on days 93-94 (2nd and 3rd April).

A technical issue at this point is that the probabilities are based on the data showing a normal distribution - the famous bell shaped curve.  That is certainly not the case when looking at cumulative rainfall year to date.  So I go back to the (what I think is) ABC approach of looking at the values recorded in 80% of years: I assume they have removed the top 10% and bottom 10% of records.  Learning a few things about EXCEL along the way I applied the PERCENTILE function to plot the values the 90% and 10% percentiles giving the following chart.

I have added to the chart a maximum line plotting the highest cumulation recorded: this overlies the 2022 line for a couple of months but then the maximum line moves away due to heavier falls in June 1978 and October-November 1985.

My final chart includes the median cumulant for each day.  That measure is the value with half values above it and half below: it avoids the biasing impact of large outliers that boost the arithmetic mean, and is my preferred measure of "average" for rainfall.