A TRIGGER TYPE CLUSTER MODEL FOR FLOOD ANALYSIS
Abstract
A two-level and two-dimensional non-homogeneous point stochastic process is developed to model the flood peak occurrences of a hydrograph. The model is a trigger cluster process of the Neyman-Scott type and presents the occurrences of flood generating mechanisms (FGM), at the precipitation level, as the triggers for clusters of flood peaks at the runoff level. The FGM's are studied in terms of the time of occurrence and the volume of what is called the cluster center of the FGM. These cluster centers form a two-dimensional point process N(,c)((tau)) with non-homogeneous rate of occurrence (lamda)((tau)). The cluster centers in turn generate a two-dimensional subsidiary process N(,s)(t(VBAR)(tau)), determined by the conditional rate of occurrence (mu)(t(VBAR)(tau)), in the runoff level and this process is characterized by the occurrences of flood peaks at time t with magnitude m, given a cluster center at (tau). The statistical properties of the cluster process N(t), defined as the total number of flood peaks, are found in terms of the probability generating functional of the process. A statistical methodology is developed to estimate the two-dimensional rate of occurrence of the process and the conditional rate of occurrence of the subsidiary process in the two-dimensions, time and magnitude. Data from several stations in the Ohio River Basin are used for that purpose. The theoretical rate of occurrence, the theoretical covariance density and the theoretical probability mass function of the process are compared to the empirical rate of occurrence, the empirical covariance density and the empirical probability mass function and a good fit is found for the analyzed stations.
Degree
Ph.D.
Subject Area
Hydrology
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