Abstract: Identification of the early warning indicators of flash flood disasters risk warning is a key technical issue in the flood control and disaster mitigation. However, because of the short time series and the small number of flash flood disasters, it is difficult to use the traditional statistical model to establish the flood disaster risk early warning method. An algorithm relates to relationships between inputs and outputs and the input-output relationship can be mathematically represented by functions. The function relationship can be established based on information matrix method which is able to get information from a small number of disaster samples. In this paper, a novel approach, called information matrix, is introduced to recognize the function relationship. Based on the rainfall and flow data of the 17 flash flood events between 2003 and 2012, the fuzzy relation matrix is constructed by learning from the samples of the antecedent soil moisture saturation, rainfall of five durations （1, 3, 6, 12, 24 h） before the occurrence of flash flood and the estimates of the peak flow of four return periods （＜5, ≥5, ≥20, ≥50 a）. The tests of the derived risk warning indicators in 40 independent historical flash flood events at different time steps have yielded a correct warning rate of over 70%, which demonstrates the feasibility of using the method for flash flood disaster warnings.

Key words: information matrix, information distribution, flash flood disaster, risk warning, Pihe basin

摘要： 山洪灾害风险预警指标的确定是防洪减灾工作中的关键技术问题，但由于山洪实测资料序列较短且山洪灾害样本量较小，难以采用传统的统计模型建立山洪灾害风险预警指标。任何统计模型其本质是建立输入-输出关系，在数学上可以用函数关系表达，信息矩阵方法能够从小样本获得信息并建立这种函数关系。利用淠河流域历史降水与流量极值资料，将2003—2012年17次典型洪水过程作为学习样本，构建流域前期土壤含水量饱和度、5个时间尺度（1，3，6，12，24 h）降雨量以及4个重现期（＜5、≥5、≥20、≥50 a）洪峰流量的模糊关系矩阵，进而建立山洪灾害风险预警不同等级组合指标。从2003—2012年洪水资料中选取未参与统计的40组独立样本，对不同时间尺度山洪灾害风险预警组合指标进行应用检验，总体预警合格率达到70%，表明该方法应用于山洪灾害风险预警是可行的。

关键词: 信息矩阵方法, 信息分配, 山洪灾害, 风险预警, 淠河流域