1 The Probability Distribution of Daily Rainfall in the United States Lars S. Hanson 1 and Richard Vogel 2 1 GKY & Associates, 4229 Lafayette Center Dr., #1850, Chantilly, VA 20151, (ph) 703-870-7000 and Dept. of Civil and Environmental. Engineering, Tufts Univ., Medford, MA 02155 Email: lars.s.hanson@gmail.com 2 Dept. of Civil and Environmental Engineering, Tufts Univ., Medford, MA 02155 Email:.richard.vogel@tufts.edu Abstract: 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. 1. Introduction Establishing a probability distribution that provides a good fit to daily rainfall depth has long been a topic interest in the fields of hydrology, meteorology, and others. The investigations into the daily rainfall distribution are primarily spread over three main research areas, namely, (1) stochastic precipitation models, (2) frequency analysis of precipitation, and (3) precipitation trends related to global climate change. The first research area of interest is stochastic precipitation modeling. The purpose of such models is not so much to investigate the properties of rainfall, but instead to be able to produce artificially generated rainfall sequences that can be used as inputs in other models to explore the behavior of hydrologic systems (Buishand, 1978). A wide range of types of stochastic rainfall generators exist (see the introduction of Mehrotra et al., 2006 for a nice review). We are only concerned with the class of “two-part” stochastic daily precipitation models that utilize a probability distribution function to describe rainfall amounts on wet-days, while rainfall occurrence is separately described using a Markov model or alternating renewal process (Gabriel and Neumann, 1962; Buishand, 1978; Geng et al., 1986; among