# Overview of flood frequency analyses

Flood frequency analyses are used to predict the probability of occurrence of different magnitude floods. The USACE follows a flood frequency analysis method outlined in Bulletin 17B (last updated 1982), based on fitting a Log Pearson Type III (LP3) probability distribution to annual peak flow data. Many other sources detail the methods of fitting an LP3 distribution, including the interactive tutorial on the OSU Streamflow Evaluations for Watershed Restoration Planning and Design website. As such this module does not cover these methods in depth, but rather steps the user through the process of fitting an LP3 to gauge data from the American River at Fair Oaks, just below the Folsom Dam site.

# Folsom dam flood frequency (historical analysis)

The USACE began construction of Folsom Dam in 1948. Considering that gauge data beginning in 1905, the USACE had  a little over 40 years of daily discharge data (44 water years) available to base the dam's design and operations. Typically flood frequency analyses only consider the maximum discharge in a given water year, measured as a daily or multi-day average. For example, planners in California utilize the maximum 3-day average discharge for most flood frequency analyses. Figure 1.1 displays the maximum annual discharge recorded at Fair Oaks gauge from water years 1905-1948. What are some of your observations about the data?

Figure 1.1

## Exceedance probability and return interval

The exceedance probability, or probability that the event is equaled or exceeded in any given year, associated with each observed annual peak flow equals:

Equation 1:  m / (n+1)

where n = the number of values in the dataset and m = the rank (with the largest flow of the dataset ranked 1).

The inverse of the exceedance probability is the return interval (in years):

Equation 2(n+1) / m

Questions - Exceedance probability and return interval

Consider the dataset displayed in Figure 1, which contains 44 years of peak flows (n). Using Equations 1 and 2, above, answer the following questions.

• What is the probability of exceeding the largest flow on record in any given year?

• What is the expected return interval of the largest flow?   years.

• What is the probability of exceeding the smallest flow in any given year?   %

• What is the expected return interval of the smallest flow?   years

### Contact Info

116 Gilmore Hall Corvallis, OR 97331