Question

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

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%.

Key concepts

Peak Annual Discharges

Peak annual discharges refer to the highest river flow rates recorded in a particular year. These measurements are crucial in hydrology, as they help in understanding the behavior of a river under extreme conditions. By analyzing yearly data, we can identify patterns and plan for events like floods. In the context of the Ashnola River, the peak discharge of 175 m³/s stands out as the second-highest-over-the-65-year-record.

• This data point is essential for calculating recurrence intervals, a measure indicating how often a similar magnitude of discharge can be expected.
• Such information aids in infrastructure planning and risk management.

Understanding peak annual discharges helps us predict future events, shaping the decisions we make to protect both lives and properties from potential flooding.

Flood Probability

Flood probability is a measure used to estimate how likely it is for a river to reach a certain discharge level in a given year. Knowing this probability allows us to assess the risk of flooding and make better-informed decisions about emergency preparedness and resource management. It's calculated as the inverse of the recurrence interval.
For instance, with a recurrence interval of 32.5 years from the Ashnola River data:

• Probability = 1/Ri = 1/32.5
• This translates to approximately a 3.08% chance of a similar event happening in any given year.

A clear understanding of flood probability helps communities prioritize investments in flood prevention and mitigation strategies. This ensures that sufficient attention is given to areas with higher chances of experiencing significant peak discharges.

Statistical Analysis in Hydrology

Statistical analysis in hydrology involves the examination of data related to water flow and its patterns over time. This discipline utilizes statistical tools to make sense of large datasets concerning river discharges and other hydrologic events. In our example of the Ashnola River, a 65-year dataset allows analysts to determine trends, calculate recurrence intervals, and evaluate probabilities.
Some important statistical techniques in hydrology include:

• Calculating recurrence intervals, which help in predicting the frequency of extreme events.
• Estimating flood probabilities, an indicator of future high-water events.
• Statistical modeling to assess the impact of climate changes on water systems.

These analyses play a critical role in designing and implementing policies and strategies aimed at managing water resources efficiently and sustainably. By understanding and utilizing statistical analysis, hydrologists can help safeguard communities against water-related hazards and ensure a resilient environment.