Heat waves and other extreme temperature phenomena

There seems to be a need for consistent terminology to cover extended periods of extreme temperatures in either directions.  This is most evident (in Australia) with periods of extreme heat leading to BoM issuing heat wave warnings.  However the same can apply to periods of very cold weather (noting that Australia's coldest recorded temperature - I think -22C - wouldn't cause people in Canada, Russia or most of the USA  to get their gloves out of the wardrobe, let alone put them on.)

High temperatures

The BoM definition, in their Glossary, of a heat wave is "A period of abnormally hot weather lasting several days."  I have in the past seen - somewhere - this expressed more precisely as "3 consecutive days of both maximum and minimum temperatures significantly above the long term mean".  The closest I have been able to locate to this definition is in a document by the Climate Council:

"In Australia, a heatwave is defined operationally as a period of at least three days where the combined effect of high temperatures and excess heat is unusual within the local climate (BoM 2012; Nairn and Fawcett 2013). Two aspects of this definition are important. First, a heatwave is defined relative to the local climate. That is, a heatwave for Hobart will occur at lower temperatures than one for Alice Springs. Second, the concept of excess heat is also important. Excess heat occurs when unusually high overnight temperatures do not provide relief from the daytime heat."

 My operational definition of a heat wave has had the following elements":

1. At least three days duration;
2. The days should be consecutive
3. Both minimum and maximum must be high;
4. "significant" means greater than 1 standard deviation above the long-term term mean for the month.

I usually record daily extremes in a spreadsheet, in which I use colour codes to indicate the status of the minima and maxima.  The graphic below shows the situation for the period 0000hrs 14 Sept to 0900hrs on 19 Sept

Blue is below the daily mean for that extreme, orange is above the daily mean for that extreme.  Text in bold red is >1SD above monthly mean (not shown below, but bold yellow is >1SD below monthly mean).  The horizontal hatching means >2 SD above!  A code of 1 is a summarising indicator showing both measures above the daily mean.

So for the 6 day period concerned (and by 0900 on 19/9 the maximum is already 27.7 and thus >2SD above the monthly mean) we have 4 days which satisfy most of the criteria.  However days 3 and 5 only have 1 extreme more than 1SD above the monthly mean, so we do not three consecutive days meeting the other three criteria.  So it hasn't been a heat wave according to my rules.  

This seems a bit 'odd', especially noting that the maximum on 18/9 only missed being 'significantly high' by 0.3C.  It can be overcome by some semantics!  I will define another term "hot spell" to refer to:

• a period of  consecutive days in which both minimum and maximum temperature are above the average temperature for the day, and 
• a majority of the days  are more than 1 SD  above the long term monthly average, which allows for a few readings to be 'warm' rather than 'hot'; and
• the period lasts at least 4 days (chosen to make it a little tougher than a 3 day run).

Going back to mid September 2023 here is another clip, showing final results.  The readings with horizontal black lines indicate reading >2SD above the long term mean.

There is not a heat wave  in this period as a few readings fail the 'significance' criterion.  However the period from 14 to 20 September is 7 days with both readings above the daily averages and 11/14 (79%)  readings more than 1 SD above the monthly average.  This counts as a 7 day hot spell.

I will also define a hot day as a day in which both extremes are more than 1 SD above the long term monthly average (for example 25 September).  This would allow the definition of a heat wave to become "3 or more consecutive hot days" but I am happy to stick with the more wordy definition which spells out the elements.  

I will also for completeness define: 

• a warm day as a day with both readings above the daily average but one or both by less than 1SD;  and 
• a warm spell as a period of at least 4 consecutive days with both readings above the daily averages but less than half more than 1 SD above.

Note that a heat wave can be embedded within a hot spell (or even a warm spell).  For example, in the example above, if the minimum on 16/9 had been 11.4C that would have given a 4 day heat wave within the 7 day hot spell.

Low temperatures

These are the equivalents to the periods above but going low rather than high.  In the second table image above both results for 23 September are filled blue (below daily average) with yellow text indicating >1SD below the monthly average.  As it's both readings, that is a cold day.

• Cool day: both readings < daily average;
• Cold day: both readings more than 1SD below the monthly average.
• Cool spell: at least 4 consecutive days with both readings <daily average, and <50% of readings more than 1SD below the monthly average.
• Cold spell: at least 4 consecutive days with both readings <daily average, and >50% of readings more than 1SD below the monthly average.
• Cold snap: At least 3 consecutive days with both readings more than 1SD below the monthly average