Chapter 13: Problem 13

There is a 65 -year record of peak annual discharges on the Ashnola River near Princeton, B.C. During this time, the second highest discharge was \(175 \mathrm{~m}^{3} / \mathrm{s}\). Based on this information, what is the recurrence interval (Ri) for that discharge level, and what is the probability that there will be a similar peak discharge next year?

Short Answer

Expert verified

The recurrence interval (Ri) for the second-highest discharge level of 175 m³/s on the Ashnola River is approximately 32.5 years. Therefore, the probability of a similar peak discharge occurring next year is approximately 3.08%.

Step by step solution

Understanding the Recurrence Interval (Ri)

Recurrence interval (Ri) is a statistical measurement used to estimate the likelihood of an event, such as a flood, occurring within a specified period. It is calculated by dividing the number of years of recorded data (n) by the rank of an event (m). In this case, the rank (m) for the second-highest discharge is 2. Ri = n/m

Find the Recurrence Interval (Ri) for the Second Highest Discharge Level

We have a 65-year record of peak annual discharges, and we want to find the recurrence interval for the second-highest discharge level of 175 m³/s Using the formula from Step 1, we have: n = 65 (number of years of recorded data) m = 2 (rank of the second-highest discharge) Ri = n/m = 65/2

Calculate the Recurrence Interval (Ri)

Now, we can calculate the recurrence interval (Ri) using the values from Step 2: Ri = 65/2 = 32.5 This means that the recurrence interval for the second-highest discharge level of 175 m³/s has an estimated occurrenceevery 32.5 years.

Understanding Probability

To find the probability of a similar peak discharge occurring next year, we must first recognize that the probability of an event occurring is the inverse of its recurrence interval. Probability = 1/Ri

Calculate the Probability of a Similar Peak Discharge Occurring Next Year

Using the values from Step 3 and the probability formula: Probability = 1/Ri = 1/32.5

Determine the Probability

Now, we can calculate the probability of a similar peak discharge occurring next year: Probability = 1/32.5 ≈ 0.0308 To express this value as a percentage, multiply by 100: Probability ≈ 0.0308 × 100 ≈ 3.08% In conclusion, the recurrence interval (Ri) for the second-highest discharge level of 175 m³/s on the Ashnola River is approximately 32.5 years. Therefore, the probability of a similar peak discharge occurring next year is approximately 3.08%.

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Short Answer

Step by step solution

Understanding the Recurrence Interval (Ri)

Find the Recurrence Interval (Ri) for the Second Highest Discharge Level

Calculate the Recurrence Interval (Ri)

Understanding Probability

Calculate the Probability of a Similar Peak Discharge Occurring Next Year

Determine the Probability

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