Stochastic modelling of the hydrologic operation of rainwater harvesting systems

Rainwater harvesting (RWH) systems are an effective low impact development practice that provides both water supply and runoff reduction benefits. A stochastic modelling approach is proposed in this paper to quantify the water supply reliability and stormwater capture efficiency of RWH systems. The input rainfall series is represented as a marked Poisson process and two typical water use patterns are analytically described. The stochastic mass balance equation is solved analytically, and based on this, explicit expressions relating system performance to system characteristics are derived. The performances of a wide variety of RWH systems located in five representative climatic regions of the United States are examined using the newly derived analytical equations. Close agreements between analytical and continuous simulation results are shown for all the compared cases. In addition, an analytical equation is obtained expressing the required storage size as a function of the desired water supply reliability, average water use rate, as well as rainfall and catchment characteristics. The equations developed herein constitute a convenient and effective tool for sizing RWH systems and evaluating their performances.