Mathematical Representation of an Urban Flood Plain

The computations of flood damages to an urban area have been formalized by using a mathematical model. The flood depth-damage relationship of a structure is written as the product of a unit damage function and an individual characteristic damage coefficient. The sum of such coefficients for all establishments within a small contour interval of the flood plain (the contour characteristic damage) denotes the damage susceptibility of that contour interval. The expected value and standard deviation of the present worth of a time series of damages can be expressed in terms of the current contour characteristic damages and a growth-discount factor that accounts for changes in the level of economic activity with time. A hypothetical example illustrates the application of these concepts to the determination of the optimal size of an upstream single-purpose flood control reservoir.