System performance metrics that describe the probability of flooding without explicitly including the consequences (i.e., economic damages) portion of the flood risk calculation are required risk reporting. System performance metrics include annual exceedance probability (AEP), long-term exceedance probability (LTEP), and assurance, a version of which is also known as conditional non-exceedance probability (CNP). AEP and LTEP can be calculated deterministically as described in the following sections, while assurance is a statistic that requires the incorporation of uncertainty into the risk assessment.

System performance is typically evaluated based on a threshold at a specific location, and should be representative of the weakest component of the system. Examples of locations at which to evaluate system performance include a consequence area index point, a specific grid cell, or a system response curve location. Typically, the threshold is a stage relevant to flooding. However, other examples of threshold variables include flow, duration and floodplain or flooding extent. The threshold variable and value are typically chosen based on local conditions. For example, when lateral structures such as levees or floodwalls are not considered, the performance of the system could be based on the stage that causes a damage value of interest. The default calculation for the without-project condition in HEC-FDA is the stage that causes 5% of the damage of the 0.01 AEP event. When a levee or similar structure is considered, evaluation of system performance depends on whether a system response curve is included. If a system response curve is not included in the assessment, then the top elevation of a levee can be used as a threshold. Alternatively, use of a system response curve would replace that fixed threshold by considering the joint probability of hazard loading and levee breach for the entire range of channel stages having a non-zero probability of breach.

Annual Exceedance Probability (AEP)

In situations where structural performance (i.e. system response curve) is not part of the assessment, AEP is the probability that a specific threshold at a given location is exceeded in any given year. For example, for a threshold defined as a stage of 20 feet, AEP is the annual frequency of stage reaching at least 20 feet at that location, and so the exceedance frequency of 20 feet on the stage-frequency curve. In situations where structural response is considered, AEP includes the probability of failure as described by the system response curve. AEP is the joint probability of hazard loading and structural failure.

Long-Term Exceedance Probability (LTEP)

LTEP is the probability of exceedance at least once within a given interval of time. For example, the 30-year LTEP refers to the probability that a threshold is exceeded in at least one year during a 30-year interval. LTEP accounts for the repeated annual exposure to flood risk over time. LTEP is calculated directly from an AEP estimate using a simplification of the binomial theorem, as follows:

LTEP = 1 – (1 – AEP)^N

where N is the number of years.  To illustrate, if the AEP of a levee is 0.01, the probability of exceedance during a thirty-year period is 1 – (1 – 0.01)30 = 0.26. Assuming in this example that the AEP of the levee includes the probability of levee failure, then so does the LTEP because LTEP is a direct function of AEP.


AEP with System Response 

AEP is also affected by including a system response curve.  In the Monte Carlo simulation approach to incorporating uncertainty, each AEP realization reflects the joint probability of loading and failure so that the system response curve is included at the realization level, rather than after all realizations are complete.  For AEP with system response, first find the average probability of failure for each stage quantile. Then calculate the incremental probability of stage exceedance for each quantile. After completing the incremental and average probability, sum the product for each stage exceedance quantile (see equation $ below). This sum of products represents AEP with system response for all stage exceedance quantiles.

AEP = \sum_{j\mathop=0}^1\left(P_{j+1}-P_j\right)\cdot\overline{P\left(F\right)}_{j+1,j}


\overline{P\left(F\right)} = The average probability failure for a stage quantile or computation interval

P= Probability of stage exceedance

j= A stage exceedance quantile