Modeling daily precipitation occurrence process with Markov Chain

Daily precipitation records for 25 years at more than 100 stations in the conterminous United States have been analyzed. The order of the Markov chain representing the conditional dependence of precipitation occurrences at each station has been studied. This is done by using a decision procedure based on an extension of the principle of maximum likelihood. A loss function composed of a log‐likelihood ratio term and a degree‐of‐freedom term is used as the decision criterion. Among several competing Markov orders, the one that minimizes this loss function is selected. The results show that the order of conditional dependence of daily precipitation occurrences depends on the season and geographical location. There exists a prevalence of first‐order conditional dependence in summer and higher‐order conditional dependence in winter. An explanation based on meteorology is proposed. In both seasons, there are areas where the Markov order deviates from the prevalent patterns. If the record length is too short ( n ≪ 1000 days), there is a tendency for a low‐order chain to be misrepresented as the proper model. A specific example in which a third‐order model is required to depict the precipitation occurrence in winter is also given in some detail. Therefore the proper Markov order describing the daily precipitation occurrence process has to be determined and cannot be assumed a priori. The common practice of assuming that the Markov order is always 1 is unjustified.