Interpreting a 5-year return period A storm of 20 cm depth has a recurrence interval (return period) of 5 years at a location. Which interpretation is correct?

Introduction / Context:
Return period (recurrence interval) is a probabilistic measure used in hydrology to characterize how often a given magnitude event is expected to be equaled or exceeded.

Given Data / Assumptions:

• Return period T = 5 years for a 20 cm storm depth.
• Events are modeled as independent from year to year for simple interpretation.

Concept / Approach:
The annual exceedance probability (AEP) is p = 1/T = 1/5 = 0.20 (20%) each year. The process is random; the interval between events varies. Multiple exceedances can occur in short spans, or none may occur over several years.

Step-by-Step Solution:

Verification / Alternative check:
The probability of at least one exceedance in 5 years is 1 − (1 − p)^5 = 1 − 0.8^5 ≈ 67.23%, not 100%.

Why Other Options Are Wrong:

• (a) treats return period deterministically.
• (c) forbids clustering, which is possible.
• (d) imposes a fixed count over 10 years, also incorrect.
• (e) is unnecessary since (b) is the correct probabilistic framing.

Common Pitfalls:
Assuming a return period guarantees timing. Design should consider AEP and the chance of multiple events within a project life.

Final Answer:
The storm will occur about once every 5 years on average, with an annual exceedance probability of 20%