Discrete-Time Point Process Models for Daily Rainfall

摘要

Several authors have recently had apparent success in applying continuous-time point process models to daily rainfall observation sequences. In this work it is shown that major problems arise when the observation sequence represents cumulative rainfall amounts over a period (e.g. one day) which is on the order of the process interarrival time. These problems have been illustrated by simulation and have been confirmed by the statistical analysis of six daily rainfall records from the states of Washington, Arizona, Texas, Florida, Pennsylvania, and Colorado. Several methods for fitting the semi-Markov model have been studied and two approximate maximum likelihood methods have emerged the best. The semi-Markov model was fitted to daily rainfall occurrences from Snoqualmie Falls, WA, and Roosevelt, AZ. It was seen that the fitted model coupled with a mixed exponential distribution for the non-zero rainfall amounts was successful in preserving the short-term structure, as well as the distributional properties of the cumulative rainfall amounts over longer periods of time, particularly for the Snoqualmie Falls station.