Question

Determine the recurrence interval in years using Weibull formula if data is available for 16 years and 10 is the ranking of the particular event.

• A. 1.5 years
• B. 1.7 years
• C. 0.59 years
• D. 0.63 years

Hint:

The Weibull formula is easy to calculate:
Add 1 to the total number of years, then divide by the rank.
Here, \(\frac{16+1}{10} = 1.7\).
Always ensure that \(N\) represents the years of record and \(m\) represents the rank.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The recurrence interval (or return period, \(T\)) is the average time interval between occurrences of a hydrological event of a given magnitude or greater.
The Weibull plotting position formula is widely used in hydrology to determine the return period of historical events.
Key Formula or Approach:
The Weibull formula for the recurrence interval (\(T\)) is given by:
\[ T = \frac{N + 1}{m} \]
Where:
- \(N\) is the total number of years of record (sample size).
- \(m\) is the rank of the event when sorted in descending order of magnitude.

Step 2: Detailed Explanation:
From the problem statement, we have:
- Total number of years of data, \(N = 16\)
- Rank of the particular event, \(m = 10\)
Now, substitute these values into the Weibull formula:
\[ T = \frac{16 + 1}{10} \]
\[ T = \frac{17}{10} = 1.7 \text{ years} \]
Therefore, the recurrence interval of the event is 1.7 years.
This matches Option (B).

Step 3: Final Answer:
The correct option is (B).