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 L-moment 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.