Active flood mitigation by boundary control

We develop a mathematical technique for active flood hazard mitigation. The procedure is based on the hypothesis that passive measures are not available or are inadequate, and a hazardous flood wave is already propagating in the river system. Specifically, a levee protecting a municipality has already been breached or its failure is imminent and real-time responses are needed to mitigate the impact of the flooding. The proposed method is also based on the assumption that there exist one or more alternative locations for emergency flow diversion, which can diminish the damages from the collapse of the levee, and even prevent its failure altogether.

The proposed method will scan the entire river basin in the vicinity of the endangered levee, identify the optimum location, if any, for a flow diversion, and provide the optimum time schedule for intervention. The decision is based on information derived from a two-dimensional, river-floodplain simulation model with a dynamic lateral flow withdrawal component. The optimum location and timing of this flow diversion is determined in real time by mapping the problem on the adjoint space, which determines the associated sensitivities and optimization gradients with just two runs of the model.

Special attention is paid to the derivation of non-reflecting boundary conditions for the adjoint equations by deriving approximate Riemann invariant relations for sensitivity waves and decoupling the adjoint variables for the flow rate and the depth of flow.

Examples are presented for bi- and omni-directional waves along with sensitivity maps for optimum intervention. It is found that the timing of active flood mitigation is the most sensitive parameter while the location is only moderately important. The sensitivity analysis, however, reveals certain counter-intuitive measures that are significantly more effective than methods currently used in practice.