Runoff using Horton's curve and pan data

The runoff is the rainfall minus infiltration and evaporation: $R = P - F - E$.

Given: $P = 10$ cm in 24 h; Horton: $f_0 = 0.8$, $f_c = 0.3$ cm/h, $K = 0.5$ h⁻¹; pan drop $= 0.5$ cm, $C_p = 0.7$; $A = 1$ km².

Step 1: Total infiltration in 24 h

Taking infiltration at capacity rate throughout, Horton's equation $f_p = f_c + (f_0 - f_c)e^{-Kt}$ integrates to

$$F = f_c t + \frac{f_0 - f_c}{K}\left(1 - e^{-Kt}\right) = 0.3\times24 + \frac{0.5}{0.5}\left(1 - e^{-12}\right) = 7.2 + 1.0 = 8.20\ \text{cm}$$

Step 2: Evaporation loss

$$E = C_p\times\text{pan} = 0.7\times0.5 = 0.35\ \text{cm}$$

Step 3: Runoff depth and volume

$$R = 10 - 8.20 - 0.35 = 1.45\ \text{cm}$$ $$V = 0.0145\ \text{m}\times10^6\ \text{m}^2 = 14\,500\ \text{m}^3$$

Answer: Runoff = 1.45 cm, i.e. 1.45 × 10⁴ m³ (14,500 m³) from the 1 km² catchment.