Estimating the Joint Probability of a Weather Event at More Than Two Locations

Abstract

Hourly observations of precipitation, sky cover, ceiling, visibility, wind speed and temperature, taken over a 13-year period at nine locations along the east coast of the United States, were processed to obtain unconditional and joint relative frequencies of 10 weather events. The relative frequencies were used to develop a model for estimating joint probabilities of weather events from unconditional probabilities and a correlation parameter. The locations range from 9 to 431 mi apart. The probability estimates given by the model were compared with corresponding relative frequencies obtained from the data. The estimates were far superior to estimates based on the assumption that events are statistically independent. Hourly observations of the same weather elements taken over the same 13-year period at seven locations in the central United States were used to test the model. These locations range from 32 to 678 mi apart. The probability estimates given by the model in the test on independent data using correlation parameters developed from east coast data were also far superior to estimates made on the assumption of independent events. However, some of the estimates were biased. The bias would be eliminated if the correlation parameter for weather events in the central United States were accurately known.