Mathematical model for flood routing based on cellular automaton

Abstract

Increasing frequency and severity of flooding have caused tremendous damage in China, requiring more essential countermeasures to alleviate the damage. In this study, the dynamic simulation property of a cellular automaton was used to make further progress in flood routing. In consideration of terrain's influence on flood routing, we regarded the terrain elevation as an auxiliary attribute of a two-dimensional cellular automaton in path selection for flood routing and developed a mathematical model based on a cellular automaton. A numerical case of propagation of an outburst flood in an area of the lower Yangtze River was analyzed with both the fixed-step and variable-step models. The results show that the flood does not spread simultaneously in all directions, but flows into the lower place first, and that the submerged area grows quickly at the beginning, but slowly later on. The final submerged areas obtained from the two different models are consistent, and the flood volume balance test shows that the flood volume meets the requirement of the total volume balance. The analysis of the case shows that the proposed model can be a valuable tool for flood routing.

Keywords

• cellular automaton
• flood routing
• mathematical model