Flood Series Return Period Calculation Explained

This explanation details how to calculate the return period for an annual flood series, focusing on the correct formula based on the event's rank and the total number of entries.

Understanding Annual Flood Series and Return Period

An annual flood series is a list of flood events recorded over consecutive years. These events are typically arranged in decreasing order of magnitude. This means the largest flood recorded in the entire series is ranked first (position m=1), the second largest is ranked second (m=2), and so on, up to the Nth flood.

The return period (often denoted as T) represents the average time interval, usually in years, expected between occurrences of a flood event of a specific size or greater. For example, a 50-year return period flood is a flood magnitude that has, on average, a 1-in-50 chance of being equaled or exceeded in any given year.

Calculating Return Period Using Plotting Position Formulas

To estimate the return period (T) for a specific flood event ranked 'm' in a series of 'N' total events, we use plotting position formulas. A widely accepted formula, particularly for annual series data, is the Weibull formula:

The formula is expressed as:

Where:

• T is the estimated return period in years.
• N is the total number of observed flood events (the count of entries in the series).
• m is the rank or position of the specific flood event when the series is arranged in descending order of magnitude (m=1 for the largest, m=2 for the second largest, etc.).

Analyzing the Options

Let's compare the given options with the standard formula:

• Option 1: m/N - This calculation relates more closely to the probability of exceedance for a specific rank but is not the standard return period formula.
• Option 2: m/(N + 1) - This is an inversion and modification of a probability calculation, not the correct return period formula.
• Option 3: (N + 1)/m - This formula directly matches the standard Weibull method for calculating the return period from an annual flood series ranked by magnitude.
• Option 4: N/(m + 1) - This is an alternative formula structure but not the conventionally used one for this scenario.

Conclusion

Based on standard hydrological practices for calculating the return period of flood events from an annual series ordered by magnitude, the correct formula uses the total number of entries (N) plus one, divided by the rank (m) of the event.