Recently Melbourne has had a few recent unusually large maximum temperature increases from one day to the next, and I wanted to see how often this occurs. For example this year the city weather station had maximums of 19.8°C and 31°C on Nov 30 and Dec 1, 26.9°C and 39.9°C on Dec 18-19, 22.4°C and 36.5°C (Dec 27-28), and 25.5°C and 40.8°C (Jan 16-17). Similarly large decreases in temperature are more frequent due to cold fronts sweeping south-eastern Australia.
Firstly, the following boxplot illustrates the distribution of maximum temperature differences from one day to the next. In the summer months large increases occur more frequently than I had expected. (To interpret a box plot, the thick black line represents the median, the red boxes span the quartiles and the dashed lines extend 1.5 times the interquartile range in both directions. Outliers beyond this range are plotted separately.)
One data point that immediately stands out is at top left of the graph – it seems that in 1900 there was an increase from a maximum of 15.1°C to 40.3°C on 15-16 January 1900! This appears too large to be plausible.
As expected the temperature differences are negatively skewed in each month (lower tail fatter than the upper tail), with skewness values tabulated below.
Zooming in on the warmer months December-March we have the following histograms showing the fatter lower tail. However the upper tail is larger than I had anticipated.
Here are answers to some questions I had posed regarding this data.
How often is the maximum temperature above 30°C after failing to reach 20°C the previous day?
This has happened on average 1.2 times per year in Melbourne with frequency-by-month shown below.
There have in fact been 13 occasions (6 in January, 4 in November) where the maximum was above 35°C after being less than 20°C the previous day. This happened most recently in 1983 (35.0°C on 25/1 after 19.4°C on 24/1).
How often is the maximum temperature above 40°C after failing to reach 25°C the previous day?
This has happened 25 times (14 in January) with 24.4°C and 44.7°C on 9-10 Jan 1939, and 24.1°C and 43.3°C (23-24 Dec 1868) being two of the bigger increases. Most recently we had maximums of 24.2°C and 40.8°C on 15-16 Jan 2007. Melbourne has experienced 203 40+ days in the 159 years of records.
How often is there a day-to-day increase of at least 15°C?
This has happened on average 0.8 times per year in Melbourne, about half the time in January as shown below.
Finally, listed below are some notable events.
- The days 8-13 January 1939 (the 13th was Black Friday) had maximum temperatures of 43.1, 24.4, 44.7, 33.5, 25.6 and 45.6°C respectively, hence containing two 20-degree increases! The only other 20-degree increase was the anomalous 15.1°C to 40.3°C jump from 15-16 January 1900 mentioned earlier.
- 9-10 Jan 1877: 19.7°C and 38.1°C
- 9-10 Jan 1882: 19.9°C and 37.1°C
- 26-28 Feb 1865 had maximum temperatures of 20.3, 39.7 then back to 19.9°C.
- 1-3 Mar 1893 had maximum temperatures of 23.0, 40.8 then back to 22.1°C.
- 4-5 Apr 1888: 17.9°C and 30.1°C, the biggest increase in April
- 29-30 Oct 1919: 20.1°C and 34.7°C, the biggest increase in October
- 13-14 Nov 1878: 22.3°C and 39.4°C, the biggest increase in November
- 23-24 Dec 1868: 24.1°C and 43.3°C (mentioned earlier)
- 15-16 Dec 1897 : 22.3°C and 41.7°C