Optimal Flood Mitigation over Flood Propagation Approximations

Globally, flooding is the most frequent among all natural disasters, commonly resulting in damage to infrastructure, economic catastrophe, and loss of life. Since the flow of water is influenced by the shape and height of topography, an effective mechanism for preventing and directing floods is to use structures that increase height, e.g., levees and sandbags. In this paper, we introduce the Optimal Flood Mitigation Problem (OFMP), which optimizes the positioning of barriers to protect critical assets with respect to a flood scenario. In its most accurate form, the OFMP is a challenging optimization problem that combines nonlinear partial differential equations with discrete barrier choices. The OFMP requires solutions that combine approaches from computational simulation and optimization. Herein, we derive linear approximations to the shallow water equations and embed them in the OFMP. Preliminary results demonstrate their effectiveness.