Stochastic trigger model for flood peaks: 1. Development of the model

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Abstract
The flood peak occurrences at a river cross section are treated as a two‐dimensional stochastic counting process in the time‐discharge plane. In order to gain insight into this process, statistical and conceptual analyses are performed on the flood peaks data of the Karahacili station on the Goksu River in the Mediterranean region of Turkey. On the basis of these analyses a two‐dimensional nonhomogeneous stochastic trigger model for the flood peaks is developed in terms of its univariate, bivariate, and multivariate probability generating functions. The first and second theoretical moments and the theoretical one‐ and two‐dimensional probability mass functions of the flood peak counts in the time‐discharge plane are derived from the probability generating functions. The trigger models have two levels. In the primary level the occurrence process of the flood trigger mechanisms (ftm's) takes place in the time dimension. This process is modeled as a one‐dimensional nonhomogeneous Poisson process. Each ftm at the primary level triggers a flood peak process at the secondary level. Each of these flood peak occurrence processes takes place in the time‐discharge plane and is modeled as a two‐dimensional nonhomogeneous Poisson process whose rate‐of‐occurrence function varies with time and discharge and depends on the starting time of the flood peak process. The mixing of the flood peak processes at the secondary level forms the complete process of the flood peak occurrences in the time‐discharge plane.Microfiche Appendix A and Appendix B are available with entire article on microfiche. Order from American Geophysical Union, 2000 Florida Avenue, N.W., Washington, D.C. 20009. Document J81‐001; $1.00. Payment must accompany order.

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