Abstract. Choosing a probability distribution to represent daily precipitation depths is important for precipitation frequency analysis, stochastic precipitation modeling and in climate trend assessments. Early studies identified the two-parameter gamma (G2) distribution as a suitable distribution for wet-day precipitation based on the traditional goodness-of-fit tests. Here, probability plot correlation coefficients and L-moment diagrams are used to examine distributional alternatives for the wet-day series of daily precipitation for hundreds of stations at the point and catchment scales in the United States. Importantly, both Pearson Type-III (P3) and kappa (KAP) distributions perform very well, particularly for point rainfall. Our analysis indicates that the KAP distribution best describes the distribution of wet-day precipitation at the point scale, whereas the performance of G2 and P3 distributions are comparable for wet-day precipitation at the catchment scale, with P3 generally providing the improved goodness of fit over G2. Since the G2 distribution is currently the most widely used probability density function, our findings could be considerably important, especially within the context of climate change investigations.

Sizing storage for rainwater harvesting (RWH) systems is often a difficult design consideration, as the system must be designed specifically for the local rainfall pattern. We introduce a generally applicable method for estimating the required storage by using regional regression equations to account for climatic differences in the behavior of RWH systems across the entire continental United States. A series of simulations for 231 locations with continuous daily precipitation records enable the development of storage-reliability-yield (SRY) relations at four useful reliabilities, 0.8, 0.9, 0.95, and 0.98. Multivariate, log-linear regression results in storage equations that include demand, collection area and local precipitation statistics. The continental regression equations demonstrated excellent goodness-of-fit (R 2 0.96-0.99) using only two precipitation parameters, and fits improved when three geographic regions with more homogeneous rainfall characteristics were considered. The SRY models can be used to obtain a preliminary estimate of how large to build a storage tank almost anywhere in the United States based on desired yield and reliability, collection area, and local rainfall statistics. Our methodology could be extended to other regions of world, and the equations presented herein could be used to investigate how RWH systems would respond to changes in climatic variability. The resulting model may also prove useful in regional planning studies to evaluate the net benefits which result from the broad use of RWH to meet water supply requirements. We outline numerous other possible extensions to our work, which when taken together, illustrate the value of our initial generalized SRY model for RWH systems.

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.

Although rainwater harvesting (RWH) is gaining popularity as a sustainable water supply source in urban as well as rural areas, estimating required storage remains an important design challenge. This paper develops a robust, yet computationally simple equation for calculating required storage capacity for a RWH system, which is generally applicable in the United States (U.S.). A simulation model with a daily time step and a yield-after-spill algorithm is used to generate empirical Storage-Reliability-Yield (SRY) relationships for RWH systems at 232 U.S., first-order precipitation gaging stations with long daily precipitation records. A regional regression modeling approach is used to combine system parameters (daily yield, collection area, reliability) with climatic variables (e.g. standard deviation of daily rainfall) to predict required storage capacity. Nationwide regression models for fixed reliability cases (80, 90, 95, 98%) demonstrate good fits (R 2 > 0.95) between model predictions and simulated storage capacities. The fits improve (R 2 >0.97) when the nation is broken down into smaller, more climatically homogeneous regions.