Exceedance probability is used in planning for potential hazards such as river and stream flooding, hurricane storm surges and droughts, planning for reservoir storage levels and providing homeowners and community members with risk assessment. This probability gives the chance of occurrence of such hazards at a given level or higher.

#### TL;DR (Too Long; Didn't Read)

Exceedance probability can be calculated as a percentage of given flow to be equaled or exceeded. This probability measures the chance of experiencing a hazardous event such as flooding. Factors needed in its calculation include inflow value and the total number of events on record.

## Exceedance Probability Equation

Exceedance probability can be calculated with this equation:

If you need to express (*P*) as a percent, you can use:

In this equation, (*P*) represents the percent (%) probability that a given flow will be equaled or exceeded; (*m*) represents the rank of the inflow value, with 1 being the largest possible value. The (*n*) represents the total number of events or data points on record.

## Reservoir Planning

Exceedance probability is used to apprehend flow distribution into reservoirs. Reservoirs are used to regulate stream flow variability and store water, and to release water during dry times as needed. For planning construction of a storage reservoir, exceedance probability must be taken into consideration to determine what size of reservoir will be needed. This probability also helps determine the loading parameter for potential failure (whether static, seismic or hydrologic) in risk analysis.

## Streamflow Gauging

Scientists use historical streamflow data to calculate flow statistics. This data is key for water managers and planners in designing reservoirs and bridges, and determining water quality of streams and habitat requirements. Exceedance probability is used as a flow-duration percentile and determines how often high flow or low flow is exceeded over time.

## “100-Year Floods”

When hydrologists refer to “100-year floods,” they do not mean a flood occurs once every 100 years. This terminology refers to having an annual flood exceedance probability of 1 percent or greater according to historical rainfall and stream stage data. For example, if a river reaches a flood stage of several feet one time in 100 years, there is a 1 percent chance of such a flood in any given year. This information becomes especially crucial for communities located in a floodplain, a low-lying area alongside a river. In a floodplain, all locations will have an annual exceedance probability of 1 percent or greater. For more accurate statistics, hydrologists rely on historical data, with more years’ data rather than fewer giving greater confidence for analysis.

## The Importance of Calculating Exceedance Probability

Climatologists also use probability of exceedance to determine climate trends and for climate forecasting. With climate change and increased storm surges, this data aids in safety and economic planning. Calculating exceedance probability also provides important risk information to governments, hydrologists, planners, homeowners, insurers and communities.

#### References

- National Weather Service Climate Prediction Center: Understanding the "Probability of Exceedance" Forecast Graphs for Temperature and Precipitation
- U.S. Geological Survey: Floods: Recurrence Intervals and 100-Year Floods (USGS)
- Texas A&M Department of Geography College of Geosciences: Probability and Risk
- U.S. Geological Survey: Calculating Flow-Duration and Low-Flow Frequency Statistics at Streamflow-Gaging Stations
- USBR: II-1. Reservoir and River Stage Exceedance Probabilities
- Columbia University: Task 1: Flow-Duration Analysis and Reservoir Storage Allocation
- Oregon State University: Analysis Techniques: Flow Duration Analysis Tutorial