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## Section 2: Probability of Exceedance

The probability of exceedance describes the likelihood of a specified flow rate (or volume of water with specified duration) being exceeded in a given year. The probability of capacity exceedance describes the likelihood of the design flow rate (or volume of water with specified duration) of a hydraulic structure being exceeded in a given year.

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### Annual Exceedance Probability (AEP)

In this manual, the preferred terminology for describing the probability of exceedance is annual exceedance probability (AEP).

There are several ways to express AEP. The TxDOT preferred unit for expressing AEP is percent. An event having a 1 in 100 chance of occurring in any single year will be described in this manual as the 1% AEP event. Annual recurrence interval (ARI), or return period, is also used by designers to express probability of exceedance. A 5-year return interval is the average number of years between years containing one or more events exceeding the specified AEP. Lastly, AEP can also be expressed as probability (a number between 0 and 1), such as p = 0.01. Examples of equivalent expressions for exceedance probability for a range of AEPs are provided in Table 4-1.

Anchor: #i1080498Table 4-1: Three Ways to Describe Probability of Exceedance

AEP (as percent)

AEP (as probability)

Annual Recurrence Interval (ARI)

50%

0.50

2-year

20%

0.20

5-year

10%

0.10

10-year

4%

0.04

25-year

2%

0.02

50-year

1%

0.01

100-year

While AEP, expressed as a percent, is the preferred method for expressing probability of exceedance, there are instances in this manual where other terms, such as those in Table 4-1, are used. These instances include equation subscripts based on return period (e.g. Q10), plot axes generated by statistical software, and text and tables where readability was improved as a result.

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### Design AEP

The designer will determine the required level of protection to be provided by a hydraulic structure. The level of protection is expressed as the design AEP. The designer will apply principles of hydrology to determine flows and volumes corresponding to the design AEP. The purpose of most structures will be to provide protection against, or prevent, high stages; resulting from the design AEP event.

If stage is primarily dependent on flow rate, as is the case in a free-flowing channel, then the designer will estimate the peak flow value corresponding to the design AEP. If stage is primarily dependent on accumulated volume, as is the case with a storage facility, then the designer will seek to estimate the flow volume and duration corresponding to the design AEP.

Flows with computed AEP values can be plotted as a flood frequency curve as illustrated in Figure 4-1. In this example, the discharge is plotted on a logarithmic scale and AEP is plotted on a probability scale. As would be expected the curve indicates that flow increases as AEP decreases.

The AEP scale ranges from 100% to 0% (shown in Figure 4-1 as 1 to 0).

Figure 4-1. Typical flood frequency curve

Accuracy

The peak discharges determined by analytical methods are approximations. The drainage system will rarely operate at the design discharge. Flow will always be more or less in actual practice, merely passing through the design flow as it rises and falls. Thus, the design engineer should not overemphasize the accuracy of the computed discharges. The design engineer should consider a reasonable number of significant digits for each result based on the level of detail of each analysis. For example, flows computed for small areas like inlets should typically be reported to whole numbers for cfs values or at most tenths (e.g. Q10=14 cfs or 8.3 cfs rather than 14.39 cfs and 8.34 cfs). Whereas, flows for larger areas like streams may be reported by rounding off values produced in models (e.g. Q50=3,200 cfs rather than 3,217 cfs). Care should be taken to not allow rounding to create exaggerated results. For example, 1049 cfs for existing conditions and 1052 cfs for proposed conditions, should not translate to 1000 cfs and 1100 cfs respectively, which would then imply more difference than expected. Nor should both these values be rounded to 1050 cfs to imply parity in the results. In these cases, reporting more significant digits to show minimal change may be preferred. FEMA or other agencies may require reporting more significant digits than the accuracy of the computational method. When reporting to those agencies, to avoid minor disagreements, it is acceptable to follow their reporting preferences. The design engineer should emphasize the design of a practical and hydraulically balanced system based on sound logic and engineering.