---
title: "Determining stability from temperature readings"
subject: "Environment and Pollution Control"
chapter: 2
key: "semester_7/environment_and_pollution_control:stability-from-lapse-rate-numerical"
source: https://www.bctengineer.com/q/semester_7/environment_and_pollution_control/stability-from-lapse-rate-numerical
site: BCT Engineering
---

# Determining stability from temperature readings

Environment and Pollution Control · Chapter 2: Metrological aspects of air pollution dispersion

- Asked in: year not given, 4 marks
- Video: [Understanding Atmospheric Stability](https://www.youtube.com/watch?v=TqsuD06INpY) — Bill Palmer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/environment_and_pollution_control/stability-from-lapse-rate-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_7/environment_and_pollution_control/chapter-2

## Question

The air temperature measured at 20 m above ground is 30.0 degrees C and at 270 m it is 27.9 degrees C. (a) Calculate the environmental lapse rate and state the stability condition. (b) A parcel of air at 20 m is lifted dry-adiabatically to 270 m. Find its temperature and show that your conclusion about stability holds. (c) What would the stability be if the temperature at 270 m was 26.7 degrees C?

## Short answer

Environmental lapse rate is 8.4 °C/km, less than dry adiabatic 9.8, so stable. A parcel lifted dry-adiabatically reaches 27.55 °C, colder than surrounding 27.9 °C, confirming stability. If 270 m temperature were 26.7 °C, ELR becomes 13.2 °C/km, unstable.

## Answer

Take the dry adiabatic lapse rate $\Gamma_d = 9.8\ ^\circ$C/km $= 0.98\ ^\circ$C/100 m.

#### (a) Environmental lapse rate
$$
\Gamma = \frac{T_1 - T_2}{z_2 - z_1} = \frac{30.0 - 27.9}{270 - 20} = \frac{2.1}{250}\ ^\circ\text{C/m} = 0.84\ ^\circ\text{C}/100\ \text{m} = 8.4\ ^\circ\text{C/km}
$$
Since $\Gamma = 8.4 < \Gamma_d = 9.8\ ^\circ$C/km, the atmosphere is **subadiabatic (stable)**.

#### (b) Parcel temperature
$$
T_p = 30.0 - 9.8 \times 0.25 = 30.0 - 2.45 = 27.55\ ^\circ\text{C}
$$
The surroundings at 270 m are 27.9 $^\circ$C. The parcel (27.55 $^\circ$C) is colder and denser than the surrounding air, so it sinks back to its original level. The atmosphere resists vertical motion, so it is stable.

#### (c) New reading
$$
\Gamma = \frac{30.0 - 26.7}{250} \times 100 = 1.32\ ^\circ\text{C}/100\ \text{m} = 13.2\ ^\circ\text{C/km} > 9.8
$$
The parcel would arrive at 27.55 $^\circ$C, warmer than the surroundings (26.7 $^\circ$C), so it keeps rising: **unstable (superadiabatic)**.

**Answer: (a) ELR = 8.4 $^\circ$C/km, stable; (b) parcel 27.55 $^\circ$C < 27.9 $^\circ$C, stable; (c) ELR = 13.2 $^\circ$C/km, unstable.**

## Check yourself

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

1. Temperature falls from 30.0 °C at 20 m to 27.9 °C at 270 m. The environmental lapse rate is:
   A. 0.84 °C/km
   B. 8.4 °C/km
   C. 84 °C/km
   D. 9.8 °C/km
   Answer: B. 2.1 °C over 250 m = 0.0084 °C/m = 8.4 °C/km. (Key point: ELR calculation)

2. Since ELR = 8.4 °C/km is less than 9.8 °C/km, the atmosphere is:
   A. Unstable
   B. Neutral
   C. Subadiabatic (stable)
   D. An inversion
   Answer: C. ELR < DALR means subadiabatic, which is stable. (Key point: Stability decision)

3. A parcel at 30.0 °C lifted dry-adiabatically 250 m has temperature:
   A. 27.9 °C
   B. 27.55 °C
   C. 26.7 °C
   D. 30.0 °C
   Answer: B. 30.0 - 9.8 x 0.25 = 27.55 °C, colder than the 27.9 °C surroundings, so it sinks back. (Key point: Parcel temperature)

4. If the temperature at 270 m is 26.7 °C, the atmosphere is:
   A. Stable, ELR 8.4 °C/km
   B. Unstable, ELR 13.2 °C/km
   C. Neutral
   D. Inversion
   Answer: B. ELR = 3.3/250 = 13.2 °C/km > 9.8; the parcel (27.55 °C) is warmer than surroundings and keeps rising. (Key point: Changed reading)

## Related in Environment and Pollution Control

- [Lapse rates and atmospheric stability](https://www.bctengineer.com/question.md?key=semester_7%2Fenvironment_and_pollution_control%3Alapse-rates-atmospheric-stability) — Environment and Pollution Control, chapter 2
- [Gaussian plume model and ground concentration](https://www.bctengineer.com/question.md?key=semester_7%2Fenvironment_and_pollution_control%3Agaussian-plume-ground-concentration) — Environment and Pollution Control, chapter 2

## Related in other subjects

- [Temperature for 30% occupation 0.75 eV above](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Afermi-temperature-30-percent) — Electrical Engineering Material, chapter 1
- [Single point ground above 1 MHz](https://www.bctengineer.com/question.md?key=semester_5%2Finstrumentation_ii%3Asingle-point-ground-high-freq) — Instrumentation II, chapter 6
- [Delta load 20∠60° power and wattmeter readings](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_engineering%3Adelta-load-20-60-440v-two-wattmeter) — Basic Electrical Engineering, chapter 8
- [Compatibility condition; portal frame temperature variation](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Acompatibility-condition-portal-temperature) — Theory of Structures II, chapter 2