---
title: "Energy budget method of lake evaporation"
subject: "Engineering Hydrology"
chapter: 3
key: "semester_5/engineering_hydrology:energy-budget-lake-evap"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/energy-budget-lake-evap
site: BCT Engineering
---

# Energy budget method of lake evaporation

Engineering Hydrology · Chapter 3: Hydrological Losses

- Asked in: 2072 Kartik, 8 marks; 2071 Chaitra, 6 marks (asked 2 times)
- Video: [Evaporation: energy balance method for evaporation](https://www.youtube.com/watch?v=3vn3a_WBlIU) — Tom Gleeson
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/energy-budget-lake-evap
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-3

## Question

Explain the energy budget method of estimating evaporation from a lake.

## Short answer

Apply energy conservation to the lake: net radiation equals heat used for evaporation, sensible heat, storage change, and advection. Sensible heat is obtained via Bowen ratio β, then evaporation from lake EL = (Qn - Qθ - Qv) / [ρL(1+β)]. It requires detailed radiation, temperature, and flow data.

## Answer

The energy budget method applies the law of conservation of energy to a lake over a period (usually a day or a week) to find the energy used in evaporation.

#### Energy balance
$$
Q_s - Q_r + Q_a - Q_{ar} - Q_{br} = Q_e + Q_h + Q_\theta + Q_v
$$

In short, $Q_n = Q_e + Q_h + Q_\theta + Q_v$, where

| Term | Meaning |
|---|---|
| $Q_s$ | incoming short-wave solar radiation |
| $Q_r$ | reflected short-wave radiation |
| $Q_a, Q_{ar}$ | incoming long-wave atmospheric radiation and its reflection |
| $Q_{br}$ | long-wave back radiation emitted by the water surface |
| $Q_n$ | net radiation energy received |
| $Q_e$ | energy used for evaporation $= \rho L E_L$ |
| $Q_h$ | sensible heat conducted to the air |
| $Q_\theta$ | change in heat stored in the water body |
| $Q_v$ | net energy advected by inflow/outflow |

#### Evaporation
Sensible heat is found by the **Bowen ratio** $\beta = Q_h/Q_e = \gamma (T_w - T_a)/(e_w - e_a)$. Substituting:

$$
E_L = \frac{Q_n - Q_\theta - Q_v}{\rho L (1 + \beta)}
$$

#### Data needed
- Radiation: from a pyranometer or computed from sunshine hours.
- Water temperatures at various depths (for $Q_\theta$), and air temperature and humidity (for $\beta$).
- Inflow, outflow and their temperatures (for $Q_v$).

#### Merits and demerits
- It gives accurate evaporation, can be used for any time period, and is the basis for calibrating other methods.
- It needs costly and detailed instruments, and each term is difficult to measure; $Q_v$ and $Q_\theta$ are especially hard to find. So it is used for research on large lakes rather than for routine estimation.

## Check yourself

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

1. The energy budget method is based on:
   A. Conservation of energy for the lake
   B. Conservation of mass of water only
   C. Wind speed relation
   D. Pan readings
   Answer: A. Energy received equals the energy used for evaporation, sensible heat, storage and advection. (Key point: Principle)

2. Q_theta in the energy balance represents:
   A. Heat advected by inflow
   B. Change in heat stored in the water body
   C. Reflected radiation
   D. Back radiation
   Answer: B. It is the increase of heat stored in the water. (Key point: Q_theta)

3. How is the sensible heat Qh handled?
   A. Measured by a pyranometer
   B. Eliminated using the Bowen ratio
   C. Ignored always
   D. Equal to Qe
   Answer: B. Qh = beta Qe with beta = gamma (Tw - Ta)/(ew - ea). (Key point: Sensible heat)

4. Why is the method used mainly for research on large lakes?
   A. It is inaccurate
   B. It needs costly detailed instruments and hard-to-measure terms
   C. It works only for one day
   D. It ignores radiation
   Answer: B. It is accurate but each term, especially Qv and Q_theta, is difficult and expensive to measure. (Key point: Limitation)

## Related in Engineering Hydrology

- [Methods of estimating lake evaporation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Alake-evaporation-methods) — Engineering Hydrology, chapter 3
- [Water budget and energy budget evaporation methods](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Awater-energy-budget-evap) — Engineering Hydrology, chapter 3
- [Lake loss from monthly pan evaporation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apan-evap-kathmandu-lake) — Engineering Hydrology, chapter 3
- [Daily lake evaporation by Penman, 30 N in April](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-lake-30n-april) — Engineering Hydrology, chapter 3
- [Energy balance and Bowen's ratio evaporation equation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Abowen-ratio-evap) — Engineering Hydrology, chapter 3, asked 2×

## Related in other subjects

- [Reservoir to lake channel with jump](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Areservoir-to-lake-channel-jump-profiles) — Hydraulics, chapter 8