A stochastic rainwater harvesting system modeling (StRaHaS) method is developed to enhance both accurateness and applicability of hydrologic modeling in guiding extensive applications of individual rainwater harvesting (RWH) systems (especially over large data-scarce regions). The reliability of a RWH system is characterized as the fraction of time water demands being satisfied by a rainwater storage unit (RWSU). The variations of water balances, the post-rainfall RWSU full-storage probability, and the system reliability with random rainfall features, variable water demands, and the other RWH system characteristics are derived as analytical, accurate, and easily applied models through stochastic integration. StRaHaS is applied to three domestic RWH systems in Toronto, Canada. Due to high accurateness and low complexity in modeling, designing, assessing, and analyzing the RWH systems, StRaHaS outperforms existing methods (e.g., inaccurate water-balance estimation, complicated continuous simulation, and simplified stochastic simulation). Based on StRaHaS, we quantitatively expound the increases in the reliability of the systems with higher rainwater supplies (corresponding to higher rainfall depths, and lower rainfall losses and first-flush depths), lower water demands (in shorter wet and dry periods), and higher RWSU capacities. Long dry periods are lengthened by climate change and play dominant roles in low, spatially heterogeneous reliability of the systems. Synchronic changes and extremely high values of rainfall features do not significantly affect the reliability. Overall, StRaHaS is a promising method in modeling RWH systems, revealing RWH mechanisms, scientizing RWH applications, and facilitating the Sustainable Development Goals for addressing global water issues.

中文翻译：

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随机降雨特征和可变需水量下的随机雨水收集系统建模

开发了一种随机雨水收集系统建模 (StRaHaS) 方法，以提高水文建模的准确性和适用性，以指导单个雨水​​收集 (RWH) 系统的广泛应用（尤其是在大数据稀缺地区）。RWH 系统的可靠性被表征为雨水储存单元 (RWSU) 满足用水需求的时间分数。水平衡的变化、雨后 RWSU 满储概率以及随机降雨特征、可变需水量和其他 RWH 系统特性的系统可靠性通过随机积分推导出为分析、准确和易于应用的模型。StRaHaS 应用于加拿大多伦多的三个国内 RWH 系统。由于建模、设计、在评估和分析 RWH 系统时，StRaHaS 优于现有方法（例如，不准确的水平衡估计、复杂的连续模拟和简化的随机模拟）。基于 StRaHaS，我们定量阐述了具有更高雨水供应（对应于更高的降雨深度、更低的降雨损失和首次冲洗深度）、更低的需水量（更短的干湿期）以及更高的 RWSU 容量。气候变化延长了长时间的干旱期，并在系统的低、空间异质可靠性方面发挥主导作用。降雨特征的同步变化和极高值不会显着影响可靠性。总体而言，StRaHaS 是一种很有前景的方法，可用于对 RWH 系统建模、揭示 RWH 机制、科学化 RWH 应用、