---
title: "PET versus AET, Penman's method"
subject: "Engineering Hydrology"
chapter: 3
key: "semester_5/engineering_hydrology:pet-vs-aet-penman"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/pet-vs-aet-penman
site: BCT Engineering
---

# PET versus AET, Penman's method

Engineering Hydrology · Chapter 3: Hydrological Losses

- Asked in: 2069 Chaitra, 2+4 marks
- Video: [Evapotranspiration | Potential Evapotranspiration | Actual Evapotranspiration | Hydrology (CE)](https://www.youtube.com/watch?v=58JiuyeCBV4) — ONLINETYARI CLASSES
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/pet-vs-aet-penman
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-3

## Question

What is the difference between potential evapotranspiration (PET) and Actual evapotranspiration (AET)? Explain the Penman's method for the estimation of PET from an area.

## Short answer

PET is maximum evapotranspiration from a well-watered crop, depending only on weather; AET is actual value limited by soil moisture, with AET ≤ PET. Penman's method combines energy balance (net radiation) and aerodynamic (drying power) terms to estimate PET from standard weather data.

## Answer

#### PET versus AET
| Point | PET | AET |
|---|---|---|
| Definition | Evapotranspiration from short, green, well-watered crop completely covering the ground | Actual evapotranspiration under the existing soil moisture |
| Water | Unlimited | Limited |
| Value | Maximum | $\le$ PET |
| Dependence | Weather only | Weather, soil moisture, crop |

#### Penman's method
Penman's method estimates PET by combining the **energy balance** (net radiation $H_n$) with the **aerodynamic** term $E_a$ (drying power of the air):

$$
PET = \frac{A\,H_n + E_a\,\gamma}{A + \gamma}
$$

- $A$ is the slope of the saturation vapour pressure curve at air temperature (mm Hg/°C), and $\gamma = 0.49$ mm Hg/°C is the psychrometric constant.
- Net radiation (mm/day):

$$
H_n = H_a(1-r)\left(0.29\cos\varphi + 0.52\frac{n}{N}\right) - \sigma T_a^4(0.56 - 0.092\sqrt{e_a})\left(0.1 + 0.9\frac{n}{N}\right)
$$

  where $H_a$ is the extraterrestrial radiation, $r$ the reflection coefficient, $n/N$ the sunshine ratio and $\sigma = 2.01\times10^{-9}$ mm/day/K⁴.
- Aerodynamic term: $E_a = 0.35(1 + u_2/160)(e_w - e_a)$ with $u_2$ in km/day and $e_a = RH\times e_w$.

**Steps:** (1) get $T$, RH, $n$, $u_2$, latitude; (2) read $e_w$, $A$, $H_a$, $N$ from tables; (3) find $e_a$; (4) compute $H_n$; (5) compute $E_a$; (6) compute PET. It is widely used because it needs only routine weather data and gives good results for daily and monthly periods.

## Check yourself

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

1. PET is
   A. Evaporation from bare soil only
   B. Rainfall minus runoff
   C. Maximum ET from well-watered short green crop fully covering ground
   D. ET under limited water
   Answer: C. PET assumes unlimited water. (Key point: PET)

2. AET relation to PET is
   A. AET = PET always
   B. Unrelated
   C. AET <= PET
   D. AET > PET
   Answer: C. Limited soil moisture keeps AET at or below PET. (Key point: AET vs PET)

3. Penman's method combines
   A. Energy balance and aerodynamic terms
   B. Infiltration and storage
   C. Temperature only
   D. Rainfall and runoff
   Answer: A. Net radiation Hn and drying power Ea. (Key point: Penman idea)

4. Penman is widely used because
   A. It ignores radiation
   B. It needs lysimeter
   C. It needs soil data
   D. It needs only routine weather data
   Answer: D. Routine weather data suffice. (Key point: Why used)

## Related in Engineering Hydrology

- [AET versus PET, field measurement of ET](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aaet-pet-measurement) — Engineering Hydrology, chapter 3
- [Actual versus potential evapotranspiration](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aactual-vs-potential-et) — Engineering Hydrology, chapter 3
- [PET by Penman method, Kathmandu in March](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-kathmandu-march) — Engineering Hydrology, chapter 3, asked 2×
- [PET by Penman method, Kathmandu in February](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-kathmandu-february) — Engineering Hydrology, chapter 3, asked 2×
- [PET by Penman formula, Dharan in April](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-dharan-april) — Engineering Hydrology, chapter 3
- [PET by Penman formula, Simara in April](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Apenman-simara-april) — Engineering Hydrology, chapter 3

## Related in other subjects

- [Potential evapotranspiration by Penman method](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Apenman-pet-steps) — Irrigation and Drainage Engineering, chapter 2
- [Potential difference versus emf](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Apotential-difference-vs-emf) — Basic Electrical Engineering, chapter 1
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- [Potential difference, emf, resistivity](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Aemf-pd-resistance-resistivity) — Basic Electrical Engineering, chapter 1