Scenario Results
For each impact area, there are two sets of results that come out of a scenario compute: expected annual damage outcomes and system performance statistics outcomes. All compute algorithms in HEC-FDA Version 2.0 are the same as those found in HEC-FDA Version 1.4.3, except those identified in the HEC-FDA Version 2.0 Release Notes.
The improvement removes bias from the mean expected annual damage estimate obtained from HEC-FDA Version 1.4.3. The bias was caused by a distributional assumption built into the HEC-FDA Version 1.4.3 implementation of the aggregated stage-damage algorithm. This algorithm is documented in Appendix E of the HEC-FDA Version 1.4.1 User's Manual. When computing aggregated stage-damage with uncertainty, HEC-FDA Version 1.4.3 computes damage for each stage many times, collecting a sample of damages for each stage until the sample satisfies convergence criteria. HEC-FDA Version 1.4.3 then calculates the mean and standard deviation of the sample, saves a Normal distribution based on that mean and standard deviation to the database, throws away the sample, and uses the Normal distribution of damage in the calculation of expected annual damage.
The HEC-FDA Version 2.0 development team designed an approach to implement the algorithm documented in Appendix E of the HEC-FDA Version 1.4.1 User's Manual without the need to assume that a sample of damage is Normally distributed. This approach takes the sample of damage to represent an empirical distribution. The team created tools to analyze an empirical distribution within the HEC-FDA Version 2.0 computational engine so that an empirical distribution has all of the same analytical capabilities as a Normal distribution. This technical innovation means that the software can save the sample as an empirical distribution to the database for use in the calculation of expected annual damage. In short, we do not throw away the sample.
It turns out that the shape of a sample of damage is very often very different from Normal. When you change the shape of the distribution by making a distributional assumption, the distribution becomes biased, biasing any estimate based on that distribution. The direction and magnitude will be different for every study because the sample of damage looks different for every study. The effect on differences in damage will also change from study to study as well as from plan to plan due to the strong heteroskedasticity in the aggregated stage-damage function. As a result, alternative ranking based on NED is subject to change.
The difference in EAD will occur when you need to re-compute stage-damage in HEC-FDA Version 2.0. If you transferred your Version 1.4.3 aggregated stage-damage functions into Version 2.0, then EAD calculated in Version 2.0 will match EAD calculated in Version 1.4.3 nicely. Once you use HEC-FDA Version 2.0 to compute stage-damage, this innovative approach comes into play, and your EAD estimate will be improved.
This approach is an improvement but is not without its weaknesses and requirements for assumptions, which we see as opportunity for further innovation. For HEC-FDA Version 2.0, we use very strict convergence criteria --- close to no variation in shape or 500,000 sample members, whichever comes first --- as a means of buying down model uncertainty. The point of contact for questions about this change is Dr. Richard J Nugent III, lead of the HEC-FDA development team: richard.j.nugent@usace.army.mil
Damage Outcomes
Two reports are available for damage outcomes: damage with uncertainty and damage by damage category.
Damage with Uncertainty
During the compute, HEC-FDA collects each expected annual damage realization in a histogram (empirical distribution). The damage with uncertainty report provides information on that empirical distribution of expected annual damage.
- On the left-hand side, we have a table with the first, second, and third quartiles of the expected annual damage distribution. Implicitly, each quartile is associated with an exceedance probability. For example, the first quartile (25th percentile) in the image below is $983.44. Thus, there is a 75% chance that expected annual damage exceeds $983.44.
- A plot of the histogram of expected annual damage is displayed on the right-hand side. The y-axis reflects the relative frequency and the x-axis reflects the level of expected annual damage.
Damage by Damage Category
Damage by damage category displays the mean expected annual damage for each damage category found in the selected impact area. Mean expected annual damage is $3,416.47 for residential structures. Note that the mean is greater than the median (second quartile) of expected annual damage. This is the expected behavior of a skewed-right distribution as can be seen in the image above.
System Performance Statistics
Three reports are available for performance outcomes: annual exceedance probability, long-term exceedance probability, and assurance of threshold. These reports are available for each impact area and optionally for each threshold. A default threshold will always be calculated and is calculated the same way as in HEC-FDA Version 1.4.3. As a friendly reminder, there are three possibilities:
- For impact areas without levees, the threshold is the stage at which 5% of the damage of the 1% event occurs. This is considered to be the stage at which significant damage begins.
- For impact areas with levees but without a system response curve, the threshold is the stage equal to the top elevation of the levee.
- For impact areas with levees and with system response curves, performance does not reflect a fixed threshold. Instead, performance considers the joint probability of hazard loading (e.g. stage) and levee breach for the entire range of stages for which there is a non-zero probability of breach.
Annual Exceedance Probability
In situations where structural performance (i.e. system response curve) is not part of the assessment, annual exceedance probability is the probability that a specific threshold is exceeded at a given location in any given year. For example, assume that the threshold has been identified as a stage of 20 feet. The annual exceedance probability is then the frequency of 20 feet on the stage-frequency curve. In situations where structural performance is considered, annual exceedance probability includes the probability of failure as described by the system response curve. Annual exceedance probability as a function of system performance is the joint probability of hazard loading and structural failure. During the compute, HEC-FDA collects each annual exceedance probability realization in a histogram (empirical distribution). The annual exceedance probability report contains three pieces of information:
- On the top left-hand side of the report, the mean and median annual exceedance probabilities are reported.
- Under the mean and median is a table that displays assurance of AEP. Observe in the table that there is a 1.02% chance that AEP will be less than 0.1.
- A histogram of the annual exceedance probabilities is displayed on the right-hand side of the report. Observe that the cumulative relative frequency of annual exceedance probabilities up to 0.1 is reasonably 1% - consistent with the assurance information in the table on the left-hand side.
Long-Term Exceedance Probability
Long-term exceedance probability reflects the probability that the threshold is exceeded at least once within a given interval of time. Three intervals are reported for the long-term exceedance probability report: 10yrs, 30yrs, and 50yrs.
Threshold Assurance
In cases where a system response curve is excluded, assurance reflects the chance that a random stage realization of a given flood event is less than the target stage. In the example of a levee, assurance is the chance that a random realization of channel’s water surface elevation does not exceed (overtop) the levee for a given flood event. When a system response curve is included in the assessment, then assurance reflects the chance that water does not move past the levee and inundate the floodplain, given the joint probability of hazard loading and structural failure or exceedance. Observe in the example below that there is a 4.12% chance that the threshold stage of 936.27 feet will not be exceeded among the 0.10 AEP flood events. Assurance is the term selected to replace “conditional non-exceedance probability” (CNP).
View Scenario Summary Results
To view summary results for more than one scenario at a time, right click on Scenarios and select View Summary Results... Check the box for all desired scenarios. See the image below.
