Risk modeling for a system of levees under nonstationary conditions

The scale of the 1993 flood of the Mississippi and Missouri Rivers and large-scale flooding in Northern California have demonstrated that floodplain management should be conducted for regions rather than only for individual floodplains. In both the Mississippi and California regions, there is also evidence that climate variability or change and land use changes may be affecting flood risk. This dissertation develops models to characterize and improve dynamic decisionmaking for flood risk reduction over a large system of levees under non-stationary conditions. First, a model is developed to calculate the probabilities of flooding in a system of levees using the flood stages from a hydraulic model. Second, the secondary economic effects of flooding over a region are estimated by incorporating a Leontief economic input-output model with a probabilistic model of the potential flooding across a system of levees. Catastrophic losses would have significantly more secondary damage in the economy, an effect associated mathematically with a change in the basis of the solution in the input-output linear programming model. Third, a trend in climate or land use can affect flood risk; methods to model and manage this non-stationarity are discussed. The concept of the return period can be extended to non-stationary conditions by defining it as the “expected waiting time before failure.” The use of this definition as a design criterion and its implications for risk management under non-stationary conditions are explored. In addition, the use of extreme value distributions under non-stationary conditions is discussed. Fourth, a dynamic model of floodplain management is developed to address non-stationary conditions. The dynamic model is formulated as a Markov decision process. The optimal policy for levee building or replacement is found to depend on whether a flood has just occurred and on the costs of buying out property owners and rebuilding homes and levees.