Time in statistics

Many meteorological statistics are based on well defined observing processes that often need to be precisely described to avoid ambiguity and errors. For example:

• Wind Speed usually, but not always, means the horizontal wind speed at 10 metres above the surface, in a representative area, and averaged over the preceding 10 minutes, measured from 10 minutes before the hour until the hour, UTC.
• Daily rainfall means the amount of precipitation in the last 24 hours, measured between 09:00 and 08:59 UTC, or perhaps local time, or some other 24 hour range, such as 06:00 to 05:59.

So far, so good, but consider the important parameters: the climatological and actual monthly mean daily maximum temperatures. "Actual" is calculated by taking the arithmetic mean of the 28, 29, 30 or 31 values of daily maximum temperatures measured between each day of the month between 00:00 and 23:59 local time. The climatological value is calculated similarly, but normally for a period of 30 years -- say 1 Jan 1980 to 31 Dec 2010.

Many people have tried to produce statistical description languages, given a definitive list of known parameters, to avoid having a much longer lists of parameters and their statistical derivatives. I am wary of such an approach as there are at least a countably infinite number of statistics. Perhaps a pragmatic guideline is to state that as soon as a statistic of a variable becomes reasonably common, just declare it as a 'first class variable' too, and hide the time aspects in its definition. We used this approach for several WMO parameter lists.

-- PieroCampalani - 09 Apr 2013 (from Chris Little's email, 18 Mar 2013)