Average temperature: Difference between revisions

The average temperature for the day, is calculated by Cumulus using samples of the temperature taken at 1-minute intervals (sometimes called the 'integration method'). (This assumes Cumulus is running continuously, if it has just been restarted, for some station types Cumulus will use the temperatures stored at the console logging interval for the period since Cumulus previously ran).  Each minute the new measurement is added onto the accumulator ''Total'' and increments by one the counter ''Samples'' in the [[today.ini]] log file.  

The [https://library.wmo.int/doc_num.php?explnum_id=4166 WMO guidlines] say that for a climatic normal over an annual or seasonal period, the mean you quote should be the average of the monthly means you calculated for international exchanged products, but allow "National Meteorological and Hydrological Services [to] weight monthly normals by the number of days in the month when calculating the multimonth normal". In other words, within a nation you can report annual averages calculated using integrated daily means. If you are calculating climate norms for international publication you average the individual months. Put another way, within a nation you can add all the daily average temperature values you have and divide by the number of days (part or full year); for publishing climate norms you add all the monthly average temperatures you have for a past year and divide by 12.

For Cumulus users looking at complete ''past years'' the difference between the two approaches just sometimes shows small discrepancies, and those are mainly because of the way Cumulus does its rounding of each daily figure, rather than just rounding final figure. For the ''current year'', especially in Northern Hemisphere Spring, the difference between approaches is seen because February and April have fewer days than January, March, and May, and when you look at a report the current month may have even fewer days. e.g. on 7 March one approach divides by 3, the other by 66 in a non-leap year (31+28+6 completed days) leading to discrepancies, but in the same year on 1 April the first approach is still dividing by 3, but the second approach is dividing by 90. The latter shows little discrepancy because 30 (the 90 quoted divided by the 3 quoted) days is a reasonable average length for a month.

This offers an alternative to the simple mean of the highest and lowest temperatures of the day, and can give a 'better' average in cases where the high or low temperature occurred for a relatively short period, so could skew the simple average. To compare the two, select ''This period'' from the '''view''' menu and by default it will show both the integrated mean and simple mean temperatures for yesterday when you click '''Update display'''.

Note that statistically, a median temperature could be used to avoid such skewing, this would require holding all the individual measurements for a day, ranking them in order of magnitude and quoting the central value in that list - Cumulus does not retain the every minute individual values and cannot calculate median. If you wanted to compare daily median and daily mean, you would need to analyse the monthly log file with an external package.