Risk Analysis and Uncertainty in Flood Damage Reduction Studies (2000) / Chapter Skim
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Risk Analysis Techniques
Risk Analysis Techniques
Pages 51-70
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From page 51... ...
Before starting a flood damage reduction study, it is important to differentiate between significant and insignificant factors. The following list addresses factors that are often important in determining flood risks.
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From page 52... ...
Seismic factors (on dams and leveesJ frequency and magnitude of earthquakes, fault and tectonic characteristics, earthquake-induced ground motion at the dam or levee site and liquefaction of foundation soil, and flooding probability associated with earthquake-induced dam or levee failure. Materials and construction factors type and quality of materials used for dams and levees, thermal and moisture variations affecting dam or levee quality during its service period and during its construction, and construction quality control.
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Sixth, an economic damage function of flooding is determined along with associated uncertainty. Finally, the failure probability and damage function are combined to yield expected annual damage.
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NATURAL VARIABILITY AND IMPERFECT KNOWLEDGE A risk analysis of flood hazards needs to address uncertainties associated with natural variability, engineering or economic models, and statistical relationships. Figure 4.1 provides a conceptual mode]
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For example, river stage as a function of floodflow is treated as statistical. The estimation error applied to the damagestage relationship mentioned previously is also modeled as a statistical error.
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The largest knowledge uncertainties are for uncommon, extremely large floods. The Corps's objective in flood damage reduction studies is to determine the expected annual damage (EAD)
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This curve is then integrated to give expected annual damage. In the Corps's method, annual exceedance probabilities of p = 0.5, 0.2, 0.1, 0.04, 0.02, 0.01, 0.004, and 0.002 are the values used in the computation.
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From page 58... ...
The computational procedure in the Corps's method uses Monte CarIo sampling to perform numerical integration of the damage exceedance probability curve for a damage reach. The damage-exceedance probability function is obtained from the discharge-exceedance probability, stage-discharge, and damage-stage functions.
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From page 59... ...
The Corps's approach is a reasonable risk analysis procedure that deserves consideration for wider adoption in the flood management community. It provides a mechanism for combining uncertainty in estimating flood discharge and stage with the inherent risk of different flood severities, to give overall risk measures of the system's engineering performance that are more complete than those customarily used.
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Risk analysis addresses such questions. Assume that the probability distribution capturing the uncertainty about the probability of exceedance of the peak flows at the potential damage site (as shown in the upper-right quadrant of Figure 4.2)
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From page 61... ...
result in a flood, · duration and distribution of rainfall on an area draining a potential flood damage site, and the precise rainfall-runoff and flow routing events (such as watershed topography, land use and cover, soil moisture content) that exist during such a storm, .
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MONTE CARLO SIMULATION Figure 4.4 shows a sequence of three graphs describing uncertainties in (lischarge, stage, and damage. The uncertainty in these quantities is signified by the probability distributions and dashed confidence-limit lines drawn around each curve and also by the dash~ot lines on each graph, which are possible alternative locations of the curves.
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From page 63... ...
The dotted lines show probability contours of the function f1 (A p) , which is the probability density function describing uncertainty in discharge for a given exceedance probability.
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ASSESSMENT OF ENGINEERING PERFORMANCE The engineering performance of a flood damage reduction project is measured by the probability that the land to be protected by the project will be flooded in any given year. Such probabilities are estimated for
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From page 65... ...
or dependent on the annual probabilities integrated over all the floods that could occur within a given year. In the Corps's method, the two main engineering performance measures combine the two sets of distinctions into the following measures: · annual exceedance probability the probability that the target stage will be exceeded in any year considering all potential floods and · conditional nonexceedance probability—the probability that the target stage will not be exceeded given a specific flood severity.
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, as shown in the third panel in Figure 4.7. The annual exceedance probability, Pe' is estimated from the stagefrequency curve as that probability corresponding to the target stage for the damage reach.
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After all the Monte Carlo simulations are complete, a set of N values of He exists, of which a subset, n, have stages not exceeding the target stage. The conditional nonexceedance probability of the target stage is given by n/N.
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The Corps's original geotechnical reliability model is a simple relationship based on two critical stage heights for the levee: the probable failure point (PFP) and the probable nonfailure point (PNP)
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The annual exceedance probability Pe including geotechnical uncertainty is then found in an analogous manner to the expected annual damage using Equation (4.31: l Pe = |R(P)
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ol ~ I.ll—* —l I, FIGURE 4.10 Computation of risk measures including geotechnical reliability.
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