---
title: "Runoff using Horton's curve and pan data"
subject: "Engineering Hydrology"
chapter: 3
key: "semester_5/engineering_hydrology:horton-pan-runoff"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/horton-pan-runoff
site: BCT Engineering
---

# Runoff using Horton's curve and pan data

Engineering Hydrology · Chapter 3: Hydrological Losses

- Asked in: 2078 Bhadra, 5 marks
- Video: [Horton's infiltration equation parameters | Hydrology](https://www.youtube.com/watch?v=CXOPaeeWrmw) — The Study Sphere
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/horton-pan-runoff
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-3

## Question

Daily (24-hrs) rainfall observed over a catchment of 1 km$^2$ is 10 cm. A Horton's curve with a coefficient (K) of 0.5 hr$^{-1}$ indicated initial and final infiltration capacities of 0.8 cm/hr and 0.3 cm/hr, respectively. If an evaporation pan (pan coefficient = 0.7) installed in the catchment indicated 0.5 cm drop in the water level during the 24 hours of its operation, determine runoff from the catchment.

## Short answer

Infiltration from Horton's equation totals 8.20 cm, evaporation loss from pan is 0.35 cm. Runoff depth is 1.45 cm, giving 14,500 m³ from the 1 km² catchment.

## Answer

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.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Runoff here is:
   A. P + F + E
   B. P - F - E
   C. F - P
   D. P x E
   Answer: B. Runoff = rainfall - infiltration - evaporation. (Key point: Water balance)

2. Total infiltration in 24 h is:
   A. 8.20 cm
   B. 7.2 cm
   C. 10 cm
   D. 19.2 cm
   Answer: A. 0.3 x 24 + 1.0 x (1 - e^-12) = 8.20 cm. (Key point: Infiltration)

3. Evaporation loss is:
   A. 0.5 cm
   B. 0.35 cm
   C. 0.71 cm
   D. 0.7 cm
   Answer: B. 0.7 x 0.5 = 0.35 cm. (Key point: Evaporation)

4. The runoff volume is:
   A. 14,500 m3
   B. 1450 m3
   C. 145,000 m3
   D. 8,200 m3
   Answer: A. 0.0145 m x 10^6 m2. (Key point: Runoff)

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