---
title: "Water budget and energy budget evaporation methods"
subject: "Engineering Hydrology"
chapter: 3
key: "semester_5/engineering_hydrology:water-energy-budget-evap"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/water-energy-budget-evap
site: BCT Engineering
---

# Water budget and energy budget evaporation methods

Engineering Hydrology · Chapter 3: Hydrological Losses

- Asked in: 2075 Chaitra, 3+3 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/water-energy-budget-evap
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-3

## Question

Explain the water budget and energy budget methods for estimation of evaporation.

## Short answer

Water budget method uses continuity equation: evaporation = precipitation + net surface/groundwater inflow – outflow – storage change. Energy budget method uses energy conservation: evaporation = (net radiation – stored heat – advected energy)/[ρL(1+β)].

## Answer

#### Water budget method
Continuity equation applied to the lake over a period:

$$
P + V_{is} + V_{ig} - V_{os} - V_{og} - E_L - T_L = \Delta S
$$

so
$$
E_L = P + V_{is} + V_{ig} - V_{os} - V_{og} - T_L - \Delta S
$$

where $P$ = precipitation, $V_{is}, V_{os}$ = surface inflow and outflow, $V_{ig}, V_{og}$ = groundwater inflow and outflow, $T_L$ = transpiration loss, $\Delta S$ = change in storage (all in m³). It is simple, but seepage, groundwater flow and measurement errors make it inaccurate for short periods; it suits long periods.

#### Energy budget method
Conservation of energy for the lake: $Q_n = Q_e + Q_h + Q_\theta + Q_v$. Using Bowen's ratio $\beta = Q_h/Q_e$:

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

$Q_n$ is net radiation, $Q_\theta$ stored heat, $Q_v$ advected energy, $\rho$ density and $L$ latent heat. It gives accurate results for any period but needs costly instruments and many measurements.

## Check yourself

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

1. Water budget evaporation is:
   A. Outflow minus inflow
   B. P + inflows - outflows - T_L - change in storage
   C. P x area
   D. Pan x Cp
   Answer: B. From P + Vis + Vig - Vos - Vog - E - T = dS. (Key point: Water budget)

2. It is suited to:
   A. Short periods
   B. Long periods, seepage is hard to measure
   C. Hourly
   D. Only dry
   Answer: B. Errors are large for short periods. (Key point: Water budget limitation)

3. The energy budget method:
   A. Is accurate for any period but needs costly instruments
   B. Needs no data
   C. Is only for ponds
   D. Ignores Bowen ratio
   Answer: A. Accurate but demanding. (Key point: Energy budget)

## Related in Engineering Hydrology

- [Energy budget method of lake evaporation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aenergy-budget-lake-evap) — Engineering Hydrology, chapter 3, asked 2×
- [Water budget equation and its role](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Awater-balance-equation-processes) — Engineering Hydrology, chapter 1, asked 5×
- [Free water evaporation by Penman method, June](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-june-33n) — 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×
- [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

## Related in other subjects

- [Storm water estimation and its limitations](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Astorm-water-limitations) — Sanitary Engineering, chapter 2
- [Equivalent evaporation and boiler efficiency](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Aboiler-equivalent-evaporation) — Applied Thermodynamics, chapter 1