Question

If \( n \) is the number of years, \( T \) is recurrence interval in years and \( m \) is ranking of rainfall event, then the recurrence interval given by Weibull formula is:

• A. \( m = \dfrac{T}{n+1} \)
• B. \( T = \dfrac{m}{n+1} \)
• C. \( n = \dfrac{m+1}{T} \)
• D. \( T = \dfrac{n+1}{m} \)

Hint:

The Weibull formula is one of the most important hydrology formulas: \[ \boxed{T = \frac{n+1}{m}} \] where:
• \( n \) = total number of observations
• \( m \) = rank of event Important observation:
• Larger rainfall events have smaller rank \(m\)
• Smaller rank gives larger recurrence interval Thus, extreme events occur less frequently and therefore have higher return periods.

Answer 1

The Correct Option is D

Concept: In hydrology and frequency analysis, the concept of return period or recurrence interval is extremely important for analyzing floods, rainfall events, droughts, and storms. The recurrence interval represents the average time interval within which a rainfall or flood event of a specified magnitude is expected to occur once. One of the most commonly used empirical formulas for recurrence interval is the Weibull Formula. The Weibull formula is given by: \[ T = \frac{n+1}{m} \] where:
• \( T \) = recurrence interval or return period
• \( n \) = total number of years of record
• \( m \) = rank of the event when arranged in descending order This formula is widely used in hydrology for flood frequency analysis and rainfall probability studies.

Step 1: Understanding recurrence interval. The recurrence interval indicates how frequently a particular hydrological event is likely to occur. For example:
• A 10-year flood means a flood having recurrence interval of 10 years.
• A 50-year rainfall event means such rainfall magnitude is expected once in 50 years on average. The Weibull formula helps estimate this recurrence interval from observed rainfall or flood records.

Step 2: Writing the Weibull formula. The standard Weibull formula is: \[ T = \frac{n+1}{m} \] where:
• \( n \) is the number of years of available data
• \( m \) is the rank assigned to the event This relation is directly used in hydrologic frequency analysis.

Step 3: Comparing with given options. Now compare the derived formula with the options:
• Option (A): \[ m = \frac{T}{n+1} \] Incorrect relation.
• Option (B): \[ T = \frac{m}{n+1} \] Incorrect because numerator and denominator are interchanged.
• Option (C): \[ n = \frac{m+1}{T} \] Incorrect expression.
• Option (D): \[ T = \frac{n+1}{m} \] This exactly matches the Weibull formula. Final Conclusion: The Weibull recurrence interval formula is: \[ \boxed{T = \frac{n+1}{m}} \] Hence, the correct answer is: \[ \boxed{(D)\ T = \dfrac{n+1}{m}} \]