The Probability Distribution of Daily Rainfall in the United States

Choosing a probability distribution to represent the precipitation depth at various durations has long been a topic of interest in hydrology. Early study into the distribution of wet-day daily rainfall has identified the 2-parameter Gamma (G2) distribution as the most likely candidate distribution based on traditional goodness of fit tests. This paper uses probability plot correlation coefficient test statistics and Lmoment diagrams to examine the complete series and wet-day series of daily precipitation records at 237 U.S. stations. The analysis indicates that the Pearson Type-III (P3) distribution fits the full record of daily precipitation data remarkably well, while the Kappa (KAP) distribution best describes the observed distribution of wet-day daily rainfall. We also show that the G2 distribution performs poorly in comparison to either the P3 or KAP distributions.