# Relationship between exceedance probability and return period

### Three Key Statistical Concepts

Let's say the value "p" is the exceedance probability, in any given Relationship between return period adn annual. The probability that events such as floods, wind storms or tornadoes will occur is often expressed as a return period. The inverse of probability (generally. return period is the average time period between the occurrence of flood flows of probability is now expressed as the Annual Exceedance Probability (AEP).

Thus, if the period of record is only 40 years, there is a good chance that a flood like is not represented in the statistics. On the other hand, if the period of record is years, it is likely that more than one flood like is in the flood frequency statistics.

Thus, a longer period of record results in more representative flood statistics. For accurate and reliable statistical hydrologic guidance about possible events, it is necessary to use a dataset that includes a representative sample of as many different events as possible.

The longer the period of record, the better the likelihood of capturing the range of possible events.

- Fluvial Design Guide - Chapter 2
- Return period

There are several different return periods traditionally used by hydrologists. Common return periods include the 2-,, and even year flood. Values for each of these return periods can be calculated based on the statistics of the flow record.

However, there is a question of just how representative extreme values, such as the year flood value, might be. If possible, it is best to avoid estimating return period flood values that are greater than twice the record length.

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So you might not want to put much faith in your year flood estimate unless you have at least years of data. In an agreement was signed between seven states in the western United States governing the use of the water of the Colorado River.

This agreement calls for the river water as measured at Lees Ferry, Arizona to be distributed as follows: Over any ten year period, an average annual volume of 7. The Republic of Mexico has a separate allocation of 1. Together these water allocations total The problem is that studies have shown that the Colorado River long-term average is much less than the water allocation total.

In other words, the river usually does not have enough water for all the allocations. Original flow estimates were based on a very short period of record, during a relatively high period of flow. Actually the river's long term flow average is about 13 million acre-feet per year.

The result is that the river is over-allocated by about 4. Strictly speaking, this is the return period on the peaks-over-threshold POT scale.

The annual maximum return period is then the average interval between years containing a flood of flow at least Q.

The difference between the two definitions is only important at short return periods, less than about five years. Flood frequency can alternatively be expressed in terms of an annual exceedance probability AEPwhich is the inverse of the annual maximum return period. This is recommended when presenting results to non-specialists who may associate the concept of return period with a regular occurrence rather than an average recurrence interval. There are two common approaches to estimating the flood frequency curve: These are described below.

On many catchments, either approach can be applied and may give very different results.

## What is a return period?

Choosing between the approaches can be difficult, although in many cases the statistical analysis approach is preferable because it is more direct and is based on a larger dataset. The choice of method should be guided by a method statement that considers issues such as the needs of the study, the nature of the catchment and the type of data available. Refer to Section 4 of Flood estimation guidelines Environment Agency, for more information.

Single site and pooled analysis Flood frequency curves are best derived by analysis of flood peak data if available. FEH uses mainly annual maximum flows.

### Basic Hydrologic Science Course

Ideally, a long record of flood peaks is available at the site of interest, in which case the curve can be derived from single site analysis. More typically, there are no data or insufficient data at the site of interest. Pooled analysis generally reduces the uncertainty in design flows, but involves some assumptions that the catchments in the pooling group are representative of the subject site which can introduce errors.

In FEH, pooled analysis is carried out in two steps: It has a return period of two years. Estimating the growth curve which expresses design flows for other return periods as a ratio over QMED.

Note that the recommended procedures for flood frequency analysis could change as a result of further research since FEH was published. See Kjeldsen et al for further details. Design event approach Because rainfall records are more plentiful and generally longer than river flow records, flood estimation is often performed indirectly using a rainfall— runoff model.

An advantage of this approach over statistical analysis of flood peaks is that it produces a full flow hydrograph rather than just a peak flow. For this reason, the design event approach is often adopted when flood volumes or durations are important, for example in the design of flood storage areas or reservoir spillways.

For some exceptions, see Section 2.

For guidance on application of ReFH, refer to Section 5. The ReFH model transforms a design rainfall event into a design flood. It has three components: Loss model — removes losses such as those from evaporation and infiltration, leaving the net rainfall.