降雨强度-历时-频率模型的固有概率特征研究

Investigating Inherent Probabilistic Characteristics of Rainfall IDF Models

根据重现期与频率的关系，推导出了三类常用降雨强度－历时－频率模型所对应的概率分布函数及密度函数。经推导发现，为了保证模型的参数服从概率公理，每个模型的参数自身隐含一个约束。在估计模型参数时，必须考虑模型参数固有的隐含约束，否则将导致错误的结果。在应用香港特别行政区气象局年极大值降雨资料估计三类模型参数时，演示了这一重要的概率特征。

： In this paper， probability distribution functions corresponding to several commonly applied rainfall IDF models in hydrologic engineering are derived in terms of the relationship between return period and frequency． This leads to an important finding that， for each IDF model under consideration； there exists bounds on the model parameters that have to be satisfied in order to ensure model＇s compliance of probabilistic law． A numerical example is given to demonstrate the important implication of the inherent constraint on the fitted IDF model．