This study investigated the sustainability of the rainwater harvesting system (RWHS) by analyzing six urban city sites with different rainfall statistics in the United States. We developed a new RWHS performance model by modifying a spreadsheet-based storage, treatment, and overflow runoff model (SS STORM) and verified its performance by comparing with another analytical RWHS model. The sustainability index (SI) evaluation method was used for a reservoir system and applied to the RWHS,

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... modified resilience and vulnerability evaluation methods due to the different characteristics of a reservoir and the RWHS. The performance of modified SS STORM is very similar to that of the analytical method, except in Los Angeles, which is characterized by long inter-event times and low rainfall event depths due to low annual rainfall. The sustainability indices were successfully evaluated depending on both RWHS size and water demand and vary over a wide range as annual rainfall increases. This study proposes a new RWHS performance model and sustainability index evaluation method. Further study should confirm the proposed approach in regions with widely different rainfall characteristics. 2 of 16 heterogeneous water use patterns. Their results showed that the total rain barrel size can be reduced without reducing RWHS reliability for heterogeneous users, but the same effect was not observed in the homogenous user group. Hanson and Vogel [15] applied the SRY relationship for dam behavior to RWHS performance. However, the SRY method only represented RWHS performance with a ratio model based on relative annual rainfall depth, and RWHS size should have been converted from a ratio of annual rainfall to a size unit. Thus, the SRY method did not show the effects of constant rain barrel sizes or water demand efficiency. Sample and Liu [16] evaluated the effect of water supply and runoff storage on RWHS performance under land use change conditions and for different locations in Virginia, USA, using the Rainwater Analysis and Simulation Program (RASP) model. They also estimated RWHS life cycle net benefits based on various types of land use from water supply to runoff capture reliability. However, most studies of RWHS performance do not include important multivariate effects, such as the combination of reliability, RWHS size, and water demand. Many sustainability indexes have been employed to evaluate water resource systems [17] [18] [19] [20] . Hashimoto et al. [17] proposed a sustainability evaluation for a reservoir water supply system using reliability, resilience, and vulnerability. Moy et al. [21] and Kundzewicz and Kindler [22] improved upon the sustainability evaluation method and suggested a different evaluation method for resilience and vulnerability using the maximum deficit period and value. Kjeldsen and Rosbjerg [18] compared various reliability, resilience, and vulnerability estimation methods and suggested that maximum values of deficit duration and volume show more consistent results than average values. proposed a geometric average of reliability, resilience, and vulnerability to evaluate the sustainability index (SI) and applied it to the Rio Grande basin water resources and environmental control system to verify the modified SI method. Asefa et al. [23] applied the SI to evaluate the Tampa Bypass Canal and Alafia River. However, these SI evaluation methods did not apply to RWHS performance; thus, it is necessary to investigate and confirm the applicability of current sustainability evaluation methods for RWHS. The objectives of this study are (1) to develop and verify an RWHS performance model; (2) to apply a SI including reliability, resilience, and vulnerability to the RWHS; and (3) to investigate the performance of the RWHS depending on storage capacity and water demand under different rainfall characteristics. This study applied the model to six cities in the US, with different rainfall characteristics [24] , and analyzed model performance indexes. Materials and Methods Analytical Approach This study employed Equations (1) and (2) to determine the reliability and rain barrel size of the RWHS, respectively. These equations are based on the assumption that distributions of event depth, inter-event time, and duration all follow one exponential distribution, as suggested by Adams and Papa [25] . Guo and Baetz [11] described the derivations in detail.