The time distribution of extreme rainfall events is a significant property that governs the design of urban stormwater management structures. Accuracy in characterizing this behavior can significantly influence the design of hydraulic structures. Current methods used for this purpose either tend to be generic and hence sacrifice on accuracy or need a lot of model parameters and input data. In this study, a computationally efficient multistate first-order Markov model is proposed for use in characterizing the inherently stochastic nature of the dimensionless time distribution of extreme rainfall. The model was applied to bivariate extremes at 10 stations in India and 205 stations in the United States (US). A comprehensive performance evaluation was carried out with one-hundred stochastically generated extremes for each historically observed extreme rainfall event. The comparisons included: 1-h (15-min); 2-h (30-min); and, 3-h (45-min) peak rainfall intensities for India and (US) stations, respectively; number of first, second, third, and fourth-quartile storms; the dependence of peak rainfall intensity on total depth and duration; and, return levels and return periods of peak discharge when these extremes were applied on a hypothetical urban catchment. Results show that the model efficiently characterizes the time distribution of extremes with: Nash–Sutcliffe-Efficiency > 0.85 for peak rainfall intensity and peak discharge; < 20% error in reproducing different quartile storms; and, < 0.15 error in correlation analysis at all study locations. Hence the model can be used to effectively reproduce the time distribution of extreme rainfall events, thus increasing the confidence of design of urban stormwater management structures.

极端降雨事件的时间分布是控制城市雨水管理结构设计的重要属性。表征这种行为的准确性会严重影响水工结构的设计。用于此目的的当前方法要么趋于通用，从而牺牲准确性，要么需要大量模型参数和输入数据。在这项研究中，提出了一种计算有效的多状态一阶马尔可夫模型，用于描述极端降雨的无量纲时间分布的内在随机性。该模型已应用于印度10个站点和美国205个站点的双变量极值。对于每个历史观察到的极端降雨事件，均使用一百个随机产生的极端值进行了综合性能评估。比较包括：1小时（15分钟）；2小时（30分钟）；印度和美国站分别达到3小时（45分钟）的峰值降雨强度；第一，第二，第三和第四四分之一风暴的数量；峰值降雨强度对总深度和持续时间的依赖性；这些极端情况应用于假设的城市集水区时的返回水平和峰值排放的返回时间。结果表明，该模型有效地描述了极端时间的分布，其中：峰值降雨强度和峰值流量的纳什-萨特克利夫效率> 0.85；再现不同的四分位数风暴时，误差小于20％；并且<0。在所有研究地点的相关性分析中存在15个错误。因此，该模型可用于有效地再现极端降雨事件的时间分布，从而增加了城市雨水管理结构设计的可信度。