Floodplain Planning with Risk-based Optimization

Economical integration of permanent and emergency flood control options is a long-standing problem in water resources planning and management. A two-stage linear programming formulation of this problem is proposed and demonstrated which provides an explicit economic basis for developing integrated floodplain management plans. The approach minimizes the expected value of flood damages and costs, given a flow or stage frequency distribution. A variety of permanent and emergency floodplain management options can be examined in the method, and interactive effects of options on flood damage reduction can be represented. The approach is demonstrated and discussed for a hypothetical example. Limitations of the method in terms of forecast uncertainty and concave additive damage function forms also are discussed, along with extensions for addressing these more difficult situations. INTRODUCTION The effectiveness of floodplain management options has long been recognized, and such options have come to be considered integral with classical structural options for addressing flood control problems (USACE 1976; White 1945; Wood, et al. 1985; Lind 1967). But integrated floodplain planning with probabilistic flood descriptions remains a problem. The most common economic framework for floodplain management is minimization of expected annual damages and flood management expenses (structural and non-structural flood control options) (WRC 1983; Goodman 1984). This form of probabilistic benefit-cost analysis largely has replaced older forms of economic analysis performed by examining only a particular design flood, such as a flood of record or an estimated 100-year event. Recently, more probabilistic approaches have become common, considering the damages that would result from a full range of probability-weighted flood events (Davis, et al., 1972; USACE 1996) and for long-term dynamic floodplain planning (Olsen, et al. 2000). This has improved the application of benefitcost analysis for flood control problems, although considerable work remains to be done. Within this newer form of analysis, a great deal of research has been devoted to the assignment of probabilities to the range of flood event discharges and flood stages (Cunnane 1978; USACE 1996). The assignment of probabilities in an expected damage evaluation framework has received considerable attention (Arnell 1989; Beard 1997; Goldman 1997; Stedinger 1997). Much of this controversy remains unresolved. The estimation of damages associated with inundation to a given stage/elevation also has received considerable attention (USACE 1988).