Analysis of periodic patterns of daily precipitation through simultaneous modeling of its serially observed occurrence and amount

Precipitation is of great importance to agriculture, environment and ecosystem as a regular precipitation pattern is usually vital to healthy plants; excessive or insufficient rainfall can be harmful. Periodic patterns of precipitation can be studied based on regularly observed data over time. Since regularly observed precipitation data are generally skewed with many zeros, two common analysis approaches have been proposed recently. One approach investigates precipitation using a two-part model where the occurrence and positive amount of precipitation are analyzed separately (Piantadosi et al. in Environ Model Assess 14:431-438, 2009), whereas the other approach handles occurrence and amount simultaneously using a Tweedie's compound Poisson model for independent observations (Hasan and Dunn in Int J Climatol 32:1006-1017, 2012). The former approach fails to maintain the regular temporal structure of serially observed precipitation, whereas the latter approach ignores serial dependence. As there is generally substantial serial correlation in the observed sequence of precipitation data over time, we introduce a compound Poisson state-space model with serially correlated random effects for daily precipitation data. This approach characterizes both occurrence and amount of precipitation simultaneously while accounting for the corresponding serial correlation. Our main results depend only on the first- and second-moment assumptions of unobserved random effects. We illustrate our method with the analysis of the daily precipitation data recorded at Mount Washington, NH, USA.