# Introduction to Flood Frequency Analysis

#### Introduction

## Conceptual Outcomes

- Students demonstrate a thorough understanding of flood frequency
- Students demonstrate an understanding of return period

## Practical Outcomes

- Students will be able to interpret the flood frequency curve and relate flood magnitude to return period.

## Time Required

## Computing/Data Outputs

## Hardware/Software Required

## Instructions

Flood frequency analysis is a technique used by hydrologists to predict flow values corresponding to specific return periods or probabilities along a river. The application of statistical frequency curves to floods was first introduced by Gumbel. Using annual peak flow data that is available for a number of years, flood frequency analysis is used to calculate statistical information such as mean, standard deviation and skewness which is further used to create frequency distribution graphs. The best frequency distribution is chosen from the existing statistical distributions such as Gumbel, Normal, Log-normal, Exponential, Weibull, Pearson and Log-Pearson. After choosing the probability distribution that best fits the annual maxima data, flood frequency curves are plotted. These graphs are then used to estimate the design flow values corresponding to specific return periods which can be used for hydrologic planning purposes. Flood frequency plays a vital role in providing estimates of recurrence of floods which is used in designing structures such as dams, bridges, culverts, levees, highways, sewage disposal plants, waterworks and industrial buildings . In order to evaluate the optimum design specification for hydraulic structures, and to prevent over-designing or under designing, it is imperative to apply statistical tools to create flood frequency estimates. These estimates are useful in providing a measurement parameter to analyze the damage corresponding to specific flows during floods. Along with hydraulic design, flood frequency estimates are also useful in flood insurance and flood zoning activities. Accurate estimation of flood frequency not only helps engineers in designing safe structures but also in protection against economic losses due to maintenance of structures.

In order to understand how flood frequency analysis works, it is essential to understand the concept of return period. The theoretical definition of return period is the inverse of the probability that an event will be exceeded in a given year. In general, return period, which is also referred as recurrence interval, provides an estimate of the likelihood of any event in one year. These events include natural disasters such as floods or earthquakes. Return periods are used to convey the risks of rate events more effectively that simply stating the probabilities.

For example, a 10-year return period corresponds to a flood that an exceedance probability of 0.10 or a 10% chance that the flow will exceed in one year. The most common misconception about return periods, for example, the 100-year return period is that the flood of this magnitude will only occur once in 100 years. It is essential to understand that if a flood with a 100-year return period occurs now, it does not mean that another flood of this magnitude will not occur in the next 100 years. Return period simply provides an estimate of the probability of exceedance of a given flow. For example, if the 100-year return period flow value for the Mississippi River is 5000 m^{3}/s, it means that there is a 1 in a 100 or 1% chance that this flow will be exceeded in the river in a given year.

The flood frequency curve is used to relate flood discharge values to return periods to provide an estimate of the intensity of a flood event. The discharges are plotted against return periods using either a linear or a logarithmic scale. In order to provide an estimate of return period for a given discharge or vice versa, the observed data is fitted with a theoretical distribution using a cumulative density function (CDF). This helps the users in analyzing the flood frequency curve.

As shown in the figure above, river discharge (flow in m^{3}/s or ft^{3}/s) is generally plotted on the y-axis using either a linear or logarithmic scale. Return period and/or exceedance probability are plotted on the x-axis. In the figure below, the x-axis scale is a modified probability scale, so that the resulting flood frequency curve appears as a straight line. Using this graph, the flow value corresponding to a 5-year return period event for the Wabash River near Lafayette, IN is approximately equal to 6200 ft^{3}/s.