Flood Encounter Probability

This formula gives the probability of seeing at least one flood during a planning horizon of n years when the annual chance of that flood is treated as 1/T. It comes from taking the complement: first find the probability of no flood in a single year, raise that to n years assuming year-to-year independence, then subtract from 1 to get the chance of one or more floods. It is especially useful in risk analysis because a "100-year flood" does not mean "once every 100 years"; it means a 1% chance in any given year, which accumulates over time.

Use this when evaluating flood risk over the lifetime of infrastructure, property, or a project, such as levees, bridges, roads, dams, and building sites. It is also useful in insurance, emergency planning, and cost-benefit studies that need the probability of at least one exceedance over a design period.

• Confusing the return period T with a guaranteed recurrence interval; it is a probability-based average, not a schedule
• Using P = n/T for long time spans; that approximation can exceed 100% and becomes inaccurate as n grows
• Forgetting that the formula assumes independent yearly events and a constant annual flood probability