Flood Risk Management and the American River Basin An Evaluation (1995) / Chapter Skim
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4 RISK METHODOLOGY
4 RISK METHODOLOGY
Pages 114-163
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From page 114... ...
because the ongoing evaluation of flood control alternatives for the basin by the Sacramento District is one of the first applications of the approach, and almost certainly the most complex application yet attempted by USACE. The risk and uncertainty methodology specifically addresses many assumptions in the 1991 ARWI that were subject to controversy, and which the committee was charged to review.
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From page 115... ...
However, it is often economically advantageous to provide protection from flood events that have a 1 in 50, 1 in 100, or a 1 in 500 chance of occurring in any year, depending on the value of the property at risk, the chance of loss of life, and the costs of flood risk reduction opportunities. Derivation of probability distributions to describe the possible magnitude of flood flows has been a practice in civil engineering since the early part of the century.
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From page 116... ...
. The USACE use of expected probability adjustments is one way to include parameter uncertainty in flood control project evaluation.
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From page 117... ...
For example, if levees can almost always pass flood flows that encroach within the specified design freeboard, they actually provide protection from larger floods than has been assumed in many analyses. However, the inclusion of safety factors in reservoir-levee system design to compensate for hydraulic uncertainty may not be sufficient to actually decrease the risk of levee system failure or levee overtopping.
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From page 118... ...
Safety factors are a reasonable way for designers of flood control works to ensure that over time a system can continue to pass the design flood without levee overtopping or breaching. However, it may not be immediately clear how safety factors included in different components of a reservoir-channel-levee system interact to affect overall system reliability.
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From page 119... ...
Of particular concern here with regard to the USACE risk and uncertainty methodology are: · models of natural and operational variability and randomness, including probability distributions describing flood flows, event-to-event variability in stage-discharge relationships and reservoir operations, and variability in flood damages due to factors not captured by flood stage, and . uncertainty representing limited understanding of system processes and the lack of accuracy with which the parameters in models describing natural processes can be specified, including the parameters of a probability distribution, the cross-sections used to derive a stage-discharge curve, and the value and the count of the number of dwellings in a protected portion of the floodplain.
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From page 120... ...
In this discussion, model prediction error is included with other parameter and model uncertainties. A FRAMEWORK FOR RISK AND UNCERTAINTY ANALYSES A framework is needed to understand the structure of risk and uncertainty analysis efforts for flood protection project evaluation and to understand the relative roles of the natural variability of flood volumes, reservoir operations,
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From page 121... ...
FIGURE 4.1 Deterministic and stochastic processes contributing to flood risk. Performance of a flood control system involving both reservoirs and downstream levees can depend on deterministic and stochastic components.
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From page 122... ...
Extreme variability results from the magnitude of the floods that may occur. Less important but still significant variability is introduced by flood hydrograph timing and shape, variations in reservoir operations, possible levee failure stage, and differences in the actual damages that would occur to a structure depending on the duration of flooding, wave attack, and differences in warning times; the effects of these factors are not captured by the specification of stage alone.
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From page 123... ...
However, there are often so many parameters in the models employed to evaluate flood protection projects that it would be difficult to integrate such one-at-a-time evaluations, or to decide how they should be incorporated into decisions (Moser, 1994~.
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From page 124... ...
over the probability distribution for co. The resulting descriptions of average flood risk and average economic losses are the average annual failure probability (denoted Avg~AFP]
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From page 125... ...
However, by including hydrologic uncertainty in its Monte Carlo evaluation of expected flood damages, USACE has implicitly introduced hydrologic parameter uncertainty (frequency-curve parameter-specification error) into the flood risk and expected damage calculations.
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From page 126... ...
If the flood damages corresponding to levee failure or overtopping are zero for flood peaks less than the fixed flow q, and have constant value D for flood peaks greater than or equal to q, then the true but unknown expected damages ED are ED = E{Damages} =DP[Q > q]
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From page 127... ...
For q0 002 and q0 00~ the bias is more severe, particularly for small n. Analysis Incorporating Hydrologic Uncertainty The new USACE risk analysis procedure proposes to include hydrologic
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From page 128... ...
analyzed both cases.) With the expected probability adjustment, the probability distribution describing the distribution of floods X is a Student t distribution with location M, scale parameter S(1 + 1/n)
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From page 129... ...
For every value of the sample mean and variance, the expected probability adjustment increases the estimated exceedance probability associated with the critical flow q. The estimators in Table 4.1 that ignored hydrologic uncertainty had some upward bias.
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From page 130... ...
provided a clear analysis of expected annual flood damage estimates obtained with (1) the conventional estimator without a correction for hydrologic uncertainty, (2)
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From page 131... ...
. The expected probability correction yields an estimator Xp of p for which the exceedance probability averaged over the distributions of M and S is indeed 1 - p.
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From page 132... ...
The conventional estimator without adjustment for hydrologic uncertainty can be thought of as a compromise. For designing a nationwide system of small structures, such as highway culverts, to meet mandated failure-rate criterion, the expected-probability adjustment can be appropriate.
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From page 133... ...
As a result, it is not surprising that the expected probability adjustment always yields an upward biased estimator of flood risk and damages. Recommendation To avoid the problem of bias in estimating expected annual damages, it seems most appropriate that the economic assessment and descriptions of the probability of flooding be based on best estimates of the parameters of models, AFP(cobes~)
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From page 134... ...
and EAD(cobes~) include expectations over the distributions of annual maximum flood events and perhaps also reservoir operation and levee failure stage.
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From page 135... ...
The uncertainty in the economic performance of a project depends largely on the uncertainty associated with flood flow frequency distributions, hydraulic relationships, specification of when levee failure occurs, and the economic value of
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From page 136... ...
The committee's task included looking carefully at the risk and uncertainty methodology used by the Sacramento District. The sections below first review the general approach USACE has adopted and then focus on the implementation of that philosophy in the American River basin.
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From page 137... ...
, · uncertainty in parameters describing hydrologic risk (hydrologic uncer · variability and uncertainty in stage-discharge (hydraulic) relationships, · levee performance variability, · variability and uncertainty in stage-damage (economic)
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From page 138... ...
Increasingly, USACE is confronted with severe budget constraints, new customer cost-sharing requirements, and concern among its customers and the public with project performance and reliability. System performance and planning uncertainties now need to be addressed more explicitly as part of the assessment of water resource investments.
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From page 139... ...
. The ability of the new planning procedure to better represent flood risk,
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From page 140... ...
For example, it will be hard to capture the effectiveness of flood-fighting efforts, and the feedbacks between system weaknesses and variations in reservoir operations to avoid failure. Nevertheless, ultimately the new methodology can provide a more accurate estimate of the true residual flood risk associated with a project and the uncertainty in average estimates of performance criteria due to unavoidable model specification errors.
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From page 141... ...
The two approaches in the statistical literature for representing such uncertainty are traditional confidence intervals, which are interval estimators that contain an unknown but fixed parameter with a specified frequency, and Bayesian inference, which describes the uncertainty in unknown parameters by a probability distribution. The USACE risk and uncertainty methodology employs a Monte Carlo procedure to generate alternative values of flood quartiles reflecting hydrologic uncertainty.
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From page 142... ...
At some locations the analysis may be plagued by complex hydraulics and junctions with other rivers and streams or with hydraulic control structures and weirs that divert flood flows. In such instances determination of the stage associated with a given flow may be difficult.
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From page 143... ...
Expected annual damages (EAD) and expected annual failure probability (AFP' are computed by repeatedly sampling from the dischargefrequency function and the levee stage-stability probability function, as well as the error distributions for frequency, stage-discharge, and stage-damage.
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From page 144... ...
SOURCE: USACE, Sacramento District, August 11, 1994.
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From page 145... ...
The Sacramento District considers variability in this transformation due to variations in initial storage, possible delays in making releases, use of a one- or two-wave model of the inflow hydrograph, outlet works operation, and spillway operation efficiency. The worst-case, most likely, and best-case values for operational performance and decisions were analyzed to determine for various inflow levels a possible distribution of peak outflow rates.
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From page 146... ...
Levee Performance Whether or not a levee fails is determined by the height of the water in the channel, though other factors such as the duration of flooding could be important. For the sixth step USACE (Engineering Technical Letter 1110-2-328 22 March 1993)
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From page 147... ...
In step 7, if a levee is overtopped or fails for other reasons, the error-affected stage, given levee failure stage S [o] determines the damages.
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From page 148... ...
. A similar simplification can be employed when calculating the expected annual levee failure probability.
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From page 149... ...
Examples can be found in the 1994 Alternatives Report (USAGE, Sacramento District, 1994a, Plate 12 and p. 57, Table III-1 and p.
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From page 150... ...
150 Cal Cal o = sin Cal V)
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From page 152... ...
. The calculated reliability includes hydrologic uncertainty, uncertainty in calculated stages given river discharge, and variability in levee failure stage.
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From page 153... ...
Use of critical historic flood events with known flood flow peaks would help resolve this conceptual vagueness.
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From page 154... ...
is due to hydrologic uncertainty, how much to stage-discharge uncertainty, and how much to variability in levee failure stage. It is not clear what this reliability calculation reflects.
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From page 155... ...
Table 4.4 and Figure 4.5 appear to reflect a desire to hold on to the old idea of "level of protection," expressed by the hydrologic return period T or exceedance probability for a design flood, while moving to a new risk analysis methodology that includes the idea of uncertainty and variability in other processes. Davis (1991)
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From page 156... ...
The "reliability of the system for a given inflow" is both simpler and more meaningful than the "reliability of the system for a given exceedance probability including our inability to determine the flow actually associated with that exceedance probability." In this regard, requiring reliability to remain the same for every hydrograph is a more demanding requirement than requiring that it not decrease for every median exceedance probability after averaging over hydrologic uncertainty in the frequency curve. The first approach requires that reliability not decrease at every flood flow; the second requires that reliability not decrease for averages over flow ranges.
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From page 157... ...
With the new risk and uncertainty methodology, estimates of flood risk are no longer tied to a single T-year design flood, but can depend on different combinations of flood flows, operating decisions, and levee performance. Instead of stating that a project has a 200-year "level of protection" or protection for the 200-year flood, the Sacramento District should instead indicate that the annual risk of flooding is 0.5 percent per year, or the annual risk of flooding is 1 in 200 (see Stedinger et al., 1993, p.
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From page 158... ...
The committee hopes that subsequent documents will more clearly describe how the analyses were conducted and will more clearly explain the basis for the risk and uncertainty analyses. THE PROMISE OF ECOLOGICAL RISK ASSESSMENT USACE has made a commendable effort to apply recently developed risk and uncertainty analysis to the engineering problems faced in minimizing the damage from floods.
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From page 159... ...
· The process can be tilted in favor of a particular action, given that uncertainty is great and the desired level of risk defined; the analysis may simply proceed until the desired endpoint is reached. In spite of these serious concerns, ecological risk analysis has had some success, leading to models that may provide templates for further development.
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From page 160... ...
Hence there is the potential for appropriate use of ecological risk analysis. Nonetheless, there is little likelihood that such an analysis would be accepted by the scientific and lay community at this stage in the development of flood control proposals for the American River.
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From page 161... ...
in the calculation of average flood risk and the average annual flood damages that might be averted by a project, inflates those estimates. This upward bias is a concern if the methodology is adopted nationwide because it could distort the economic evaluation of projects.
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From page 162... ...
· Measures of System Performance Reliability. Estimates of expected annual flood damages and economic benefits associated with different projects, and the probability of flooding at different locations, are likely to be the primary criteria describing flood risk and economic impacts.
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From page 163... ...
This terminology and phases appearing in the report fosters the erroneous idea that one and only one T-year flood occurs every T years. Moreover, with the new USACE risk and uncertainty methodology that was employed, failure is no longer related to a single T-year design flood being exceeded, but can depend on different combinations of flood flows, operating decisions, and levee performance.
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