The USGS Water Science School

# The 100-Year Flood—It's All About Chance (USGS)

by Robert R. Holmes, Jr.

## How accurate are estimates of the 1-percent Annual Exceedance Probability (AEP) Flood (also known as the 100-year flood)?

The accuracy of the 1-percent AEP flood varies depending on the amount of data available, the accuracy of those data, land-use changes in the river drainage area, climate cycles, and how well the data fits the statistical probability distribution. As a demonstration of the uncertainty in the estimates of flood probability, the flood probability relation for the Big Piney River near Big Piney, Missouri, is plotted in the figure below as the solid black line. Above and below that solid black line are two dashed lines that represent the 90-percent confidence intervals of this relation. These confidence intervals simply mean that we are 90-percent confident that the true flood magnitude for a particular AEP lies between the confidence limit lines; or, there is a 10-percent chance that the true value lies somewhere outside the confidence interval lines. The 1-percent AEP flood ("100-year flood") for the Big Piney River at this location has an estimated magnitude of 44,300 cubic feet per second (ft3/s). We know that 44,300 ft3/s is an estimate, but by looking closer at the graph, we can say that we are 90-percent confident that the true value of the 1-percent AEP flood is between 36,600 ft3/s and 56,400 ft3/s.

Most policy makers and water managers often are more concerned with the height of the water in the river (river levels) than the streamflow quantity. The uncertainty for the streamflow quantity of the 1-percent AEP flood for the Big Piney River can be translated into an uncertainty of the river level. A streamflow of 36,600 ft3/s corresponds to a river level of 20.6 ft, whereas a streamflow of 56,400 ft3/s corresponds to a river level of 22.85 ft. Stated another way, the flood probability analysis reveals that we are 90-percent sure that the river elevation will be between 20.6 and 22.85 on the Big Piney River at Big Piney for the 1-percent AEP flood.

## Speaking of chance...

The 1-percent AEP flood has a 1-percent chance of occurring in any given year; however, during the span of a 30-year mortgage, a home in the 1-percent AEP (100-year) floodplain has a 26-percent chance of being flooded at least once during those 30 years! The value of 26-percent is based on probability theory that accounts for each of the 30 years having a 1-percent chance of flooding.