Flood Frequency – Exceedance in a Future Period from Return Period An annual maximum flood magnitude has a return period T = 8 years. What is the probability that this magnitude will be exceeded at least once during the next 5 years?

Introduction / Context:
Return period T relates to annual exceedance probability p by p = 1/T, assuming independence year to year. Hydrologists often need the probability of at least one exceedance over multiple future years for risk-informed design and communication.

Given Data / Assumptions:

• Return period T = 8 years ⇒ annual exceedance probability p = 1/8.
• Number of years n = 5.
• Events in different years are statistically independent.

Concept / Approach:

The probability of no exceedance in one year is (1 − p). Over n years, P(no exceedance) = (1 − p)^n. Therefore, P(at least one exceedance) = 1 − (1 − p)^n.

Step-by-Step Solution:

Verification / Alternative check:

Binomial distribution with parameters (n = 5, p = 0.125); summing probabilities of k ≥ 1 exceedances reproduces 1 − (1 − p)^n.

Why Other Options Are Wrong:

• 0.625 and 0.529: Do not correspond to the correct computation.
• 0.966: Would imply an extremely high risk inconsistent with p = 0.125.

Common Pitfalls:

Confusing return period with a guarantee of occurrence exactly once every T years; forgetting independence assumption when applying the formula.

Final Answer:

0.487