Exceedance Probability:

\\[ P_i = \frac{i}{n + 1} \cdot 100 \\]

Flow Duration Curve:

Sort flow rates \\( Q_1, Q_2, \ldots, Q_n \\) in descending order: \\( Q_{(1)} \geq Q_{(2)} \geq \ldots \geq Q_{(n)} \\).

Pair each \\( Q_{(i)} \\) with \\( P_i \\).

Plot \\( Q_{(i)} \\) (y-axis, m³/s) versus \\( P_i \\) (x-axis, %).

Where:

• \\( P_i \\): Exceedance probability for the \\( i \\)-th flow rate (%)
• \\( i \\): Rank of flow rate (1 for highest, 2 for second highest, etc.)
• \\( n \\): Total number of flow rate data points
• \\( Q_{(i)} \\): \\( i \\)-th sorted flow rate (m³/s)

Sorted Flows: 1.5, 1.3, 1.2, 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2

\\( n = 12 \\), so \\( P_i = \frac{i}{12 + 1} \cdot 100 = \frac{i}{13} \cdot 100 \\)

P1 = \\( \frac{1}{13} \cdot 100 \approx 7.69\% \\), Q1 = 1.5 m³/s

P2 = \\( \frac{2}{13} \cdot 100 \approx 15.38\% \\), Q2 = 1.3 m³/s

…

P12 = \\( \frac{12}{13} \cdot 100 \approx 92.31\% \\), Q12 = 0.2 m³/s

Q10: Flow exceeded 10% of time ≈ 1.3 m³/s (interpolated)

Q50: Flow exceeded 50% of time ≈ 0.8 m³/s (interpolated)

Q90: Flow exceeded 90% of time ≈ 0.2 m³/s (interpolated)

Sorted Flows (top 5): 3.5, 3.2, 3.1, 3.0, 2.9, …, (bottom 5): 0.8, 0.7, 0.6, 0.5, 0.4

\\( n = 30 \\), so \\( P_i = \frac{i}{31} \cdot 100 \\)

P1 = \\( \frac{1}{31} \cdot 100 \approx 3.23\% \\), Q1 = 3.5 m³/s

…

P30 = \\( \frac{30}{31} \cdot 100 \approx 96.77\% \\), Q30 = 0.5 m³/s

Q10: Flow exceeded 10% of time ≈ 3.1 m³/s (interpolated)

Q50: Flow exceeded 50% of time ≈ 1.9 m³/s (interpolated)

Q90: Flow exceeded 90% of time ≈ 0.6 m³/s (interpolated)

Sorted Flows (summarized): Max = 25.0, Min = 5.0

\\( n = 365 \\), so \\( P_i = \frac{i}{366} \cdot 100 \\)

Q10: Flow exceeded 10% of time ≈ 20.0 m³/s (interpolated)

Q50: Flow exceeded 50% of time ≈ 12.5 m³/s (interpolated)

Q90: Flow exceeded 90% of time ≈ 6.0 m³/s (interpolated)