1. **Problem Statement:** We have a 500 ha watershed with a Curve Number (CN) of 68 and initial abstraction ratio $I_a = 0.35$. We want to estimate runoff volume for two cases of rainfall considering antecedent moisture conditions. 2. **Formula and Important Rules:** The runoff depth $Q$ (in mm) is estimated using the SCS Curve Number method: $$Q = \frac{(P - I_a S)^2}{P + (1 - I_a) S}$$ where: - $P$ = rainfall depth (mm) - $I_a = 0.35$ (initial abstraction ratio) - $S = \frac{25400}{CN} - 254$ (potential maximum retention in mm) Antecedent moisture condition (AMC) affects CN: - Dormant season with 25 mm rainfall in past 5 days corresponds to AMC II (normal), so CN = 68 - For 35 mm rainfall in past 5 days, AMC is wetter, so CN increases. We adjust CN using: $$CN_{III} = CN_{II} + 0.2(100 - CN_{II})$$ 3. **Calculate $S$ for CN=68:** $$S = \frac{25400}{68} - 254 = 373.53 - 254 = 119.53 \text{ mm}$$ 4. **Case a: Past 5 days rainfall = 25 mm (Dormant season, AMC II), Rainfall $P=80$ mm** Calculate runoff depth $Q$: $$Q = \frac{(80 - 0.35 \times 119.53)^2}{80 + (1 - 0.35) \times 119.53} = \frac{(80 - 41.84)^2}{80 + 0.65 \times 119.53} = \frac{(38.16)^2}{80 + 77.70} = \frac{1455.3}{157.7} = 9.23 \text{ mm}$$ 5. **Convert runoff depth to volume:** Watershed area = 500 ha = 5,000,000 m² Runoff volume $V = Q \times \text{area} = 9.23 \text{ mm} \times 5,000,000 \text{ m}^2$ Convert mm to meters: 9.23 mm = 0.00923 m $$V = 0.00923 \times 5,000,000 = 46150 \text{ m}^3$$ 6. **Case b: Past 5 days rainfall = 35 mm (Wetter condition, AMC III)** Adjust CN: $$CN_{III} = 68 + 0.2(100 - 68) = 68 + 0.2 \times 32 = 68 + 6.4 = 74.4$$ Calculate new $S$: $$S = \frac{25400}{74.4} - 254 = 341.4 - 254 = 87.4 \text{ mm}$$ Calculate runoff depth $Q$: $$Q = \frac{(80 - 0.35 \times 87.4)^2}{80 + (1 - 0.35) \times 87.4} = \frac{(80 - 30.59)^2}{80 + 0.65 \times 87.4} = \frac{(49.41)^2}{80 + 56.81} = \frac{2441.1}{136.81} = 17.84 \text{ mm}$$ 7. **Convert runoff depth to volume:** $$V = 0.01784 \times 5,000,000 = 89200 \text{ m}^3$$ **Final answers:** - a) Runoff volume = 46150 m³ - b) Runoff volume = 89200 m³