1. Flood Risk Analysis – the USACE Approach
Professor Ke-Sheng Cheng
Dept. of Bioenvironmental Systems Engineering
National Taiwan University

2. The Levee Certification Program
Many flood damage reduction projects involve the construction of levees. The USACE’s (US Army Corps of Engineers) historical approach to coping with hydrological and hydraulic uncertainties of large floods was based on a best estimate of the levee height required to withstand a given flood, which was then augmented by a standard increment of levee height called “freeboard”.

3. The best estimate has traditionally been based on the expected height of a design flood (for example, the100-year flood).
A standard freeboard of 3 feet was then added above the expected height.
With the Corps adoption of risk analysis techniques in early 1990s, the freeboard standard for levee certification was abandoned in favor of the new risk analysis standard.

4. The new USACE approach was reviewed by the Committee on Risk-Based Analysis for Flood Damage Reduction of the National Research Council which is organized by the National Academy of Sciences and the National Academy of Engineers.

5. The committee recommends that the federal levee certification program focus not upon some level of assurance of passing the 100-year flood, but rather upon “annual exceedance probability” – the probability that an area protected by a levee system will be flooded by any potential flood.
How sure can we be that if we protect ourselves from a flow of 100-year return period, we will actually be protecting ourselves from all flows that occur less frequently, on average, than once in 100 years?

6. USACE Risk Analysis Techniques
The Corps’s objective in flood damage reduction studies is to determine the expected annual damage (EAD) along a section of river caused by possible floods, and to compare changes in those damages as a function of project alternatives.
For a flood of annual probability p (p=1/T, T: return period), a corresponding value of flood damage D(p) can be estimated.

7. The EAD is the average value of such damages taken over floods of all different annual exceedance probabilities and over a long period of years.
The current Corps method divides the calculation of EAD into three steps:
Determining flood frequencies, which describe the probability of floods equal or greater than some discharge Q occurring within a given period of time (usually 1-year).

8. Determining stage-discharge relations, which describe how high the flow of water in a reach of river (the stage) might be for a given discharge.
Determining damage-stage relations, which describe the amount of damage that might occur, given a certain height of flow.

9. Basis of the Corps’s EAD Computation
Annual exceedance probabilities of p = 0.5, 0.2, 0.1, 0.04, 0.02, 0.01, 0.004, and are used for EAD calculation.

10. There are uncertainties in
the probability of exceedance distribution of annual peak flows
the discharge-stage function
the stage-damage function
Stochastic simulation techniques are used to generate a single realization of each of the three relationships.

11. Uncertainty in annual peak flow

12. Peak flow records are commonly used to estimate the chance of a flood of a given or greater magnitude. But such estimates are uncertain due to
Limited number of observations of past peak flows
The changing and varying character of the drainage basin that influences the peak flow resulting from a specific rainfall.

13. Monte Carlo simulation is used to generate new realizations of each of the three curves using various exceedance probabilities.
The Monte Carlo simulation is repeated for a few thousand cycles of generating realizations and computing EAD.

14. Assessment of Engineering Performance
The target stage is defined as the water surface elevation in a reach at which significant economic damage occurs.
The 1% chance of flooding damage is found from the flood-frequency curve. A fraction of this damage (usually 10%) is taken and used to determine the corresponding stage from the damage-stage curve, which then becomes the target stage for the reach.

15. Engineering performance can be measured by conditional probabilities dependent on the occurrence of a flood of a given severity (e.g., the 100-year flood) or dependent on the annual probabilities integrated over all the floods that could occur within a given year.

16. Corps’s method for measuring engineering performance
Annual exceedance probability – the probability that the target stage will be exceeded in any year considering all potential floods.
Conditional nonexceedance probability – the probability that the target stage will not be exceeded given a specific flood severity.

17. In each cycle of the above Monte Carlo procedure, a new realization of the flood-frequency curve and the stage-discharge curve is generated. The flood-frequency is defined at discrete intervals of annual flood probability (p = 0.5, 0.2, 0.1, 0.04, 0.02, 0.01, 0.004, and 0.002).

18. Distribution of the target stage nonexceedance probability
Each cycle of the Monte Carlo procedure yields an estimate of the annual exceedance probability for the target stage.
N cycles of the Monte Carlo procedure are conducted to yield a distribution of the annual exceedance probability for the target stage.
The chance that the target stage will be exceeded at least one in n years is computed as , where pe is the expected annual exceedance probability.

19. Conditional nonexceedance probabilities at the target stage
For each value of p*, there corresponds an H*, determined in a similar manner.
After N Monte Carlo cycles are completed, a set of N values of H* 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.