This exercise involves simple exercises to demonstrate how flood risk (expected annual damage) and other risk metrics are computed. 

Part 1: Calculate Expected Annual Damage and Annual Exceedance Probability

Calculate expected annual damage and the annual exceedance probability for the without-project condition, with a levee, and with a reservoir. For calculations of AEP, the stage at which significant damage begins is 369ft. 

Hydrology

Below is a simple graphical peak unregulated discharge-frequency function with 5 coordinates. These 5 coordinates are chosen for ease of calculation on paper, which results in loss of some nonlinearity. Typically, graphical frequency functions used in HEC-FDA should have several more coordinates and should span the probability domain. 

Discharge Regulation

Below is an unregulated-regulated discharge transform function that represents the relationship between unregulated discharge into a reservoir and the regulated discharge out of a dam.

Hydraulics

Below is an example stage-discharge function, which transforms the peak discharge to stage of the river, also known as river elevation. 

System Performance

Below is a system response curve, which represents the expected system performance for a leveed impact area. The curve takes the form of a relationship between levee loading (stage in the river) and the probability of levee failure. The top elevation of the levee in this example is 377. 

Consequences

The consequences of flooding are modeled for many levels of flooding, from which we derive a relationship between peak stage and the consequences of flood inundation damage, as in the below example. 

Part 2: Calculate Levee AEP Statistics and Assurance

Below is example data from a risk compute with uncertainty. 19 realizations of AEP computed as a function of system performance and 19 realizations of the 0.1 AEP event. Use the weibull plotting position to calculate the cumulative probability of the equiprobable realizations. For this example, use the "default" system response curve which assumes that the levee has zero probability of failure to the top, after with probability of failure is 1. 

• Calculate the mean and median AEP.
• Calculate the AEP that has 90% assurance.
• Calculate assurance that the 0.1 AEP stage is below the top of levee elevation.