Probabilities of moving time averages of a meteorological variate

Abstract

A meteorological element, such as the surface air temperature, averaged over a given time interval, can serve as a measure of the persistence or duration of the condition over that time interval. To study the probability distribution of moving time averages involving both common and extreme averages, it was found necessary to use a Monte Carlo simulation technique. A simple Markov process generating a sequence of values of a normally distributed variate, characterized by a constant hour-to-hour correlation, has worked fortuitously well as a model of duration on the selected examples, for the number of hours ranging from one to 768. Charts have been prepared to give the probability distribution of the highest m-hour average in n hours, where n is equal to the number of hours in one day, 8 days or 32 days, and m is equal to 1, 3, 6, 12, 24, 48, 96, 192, 384 or 768 hours. The hour-to-hour correlation, in this study, ranges from zero to 0.999, with the usual value approximately 0.95.