--- title: "Lapse rates and atmospheric stability" subject: "Environment and Pollution Control" chapter: 2 key: "semester_7/environment_and_pollution_control:lapse-rates-atmospheric-stability" source: https://www.bctengineer.com/q/semester_7/environment_and_pollution_control/lapse-rates-atmospheric-stability site: BCT Engineering --- # Lapse rates and atmospheric stability Environment and Pollution Control · Chapter 2: Metrological aspects of air pollution dispersion - Asked in: year not given, 8 marks - Video: [Meteorology: What is the Dry and Wet Adiabatic Lapse Rate?](https://www.youtube.com/watch?v=nS5ReAWncHc) — MS Meteorology - 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/lapse-rates-atmospheric-stability - Whole chapter: https://www.bctengineer.com/md/semester_7/environment_and_pollution_control/chapter-2 ## Question Define environmental lapse rate and adiabatic lapse rate. With neat sketches of temperature against height, explain the superadiabatic, neutral, subadiabatic and inversion conditions and their effect on atmospheric stability. ## Short answer Environmental lapse rate (ELR) is the actual temperature decrease with height; dry adiabatic lapse rate (DALR) is 9.8 °C/km. Superadiabatic (ELR > DALR) causes strong vertical mixing (unstable), neutral (ELR = DALR) moderate mixing, subadiabatic (ELR < DALR) weak mixing (stable), and inversion (temperature increases with height) traps pollutants near the ground. ## Answer **Environmental (ambient) lapse rate (ELR, $\Gamma$)** is the actual rate at which air temperature falls with height at a given place and time, $\Gamma = -dT/dz$. **Dry adiabatic lapse rate (DALR, $\Gamma_d$)** is the rate at which a rising parcel of dry air cools because it expands in the lower-pressure air, without exchanging heat with its surroundings: $$ \Gamma_d = \frac{g}{c_p} = \frac{9.81}{1005} \approx 9.8\ ^\circ\text{C/km} \approx 1\ ^\circ\text{C}/100\ \text{m} $$ (The saturated adiabatic rate is lower, about 4-6 $^\circ$C/km, because latent heat is released.) #### Stability principle A parcel displaced upwards cools at $\Gamma_d$. If it becomes warmer than its surroundings, it is lighter and keeps rising (unstable); if it becomes colder, it sinks back (stable). In each sketch, `\` is the DALR line (temperature of a rising parcel), `.` is the ELR (actual air temperature) and `x` is the starting point at ground level. ```text (a) Superadiabatic (b) Neutral ELR > DALR ELR = DALR z z | . \ | \ | . \ | \ | . \ | \ | .\ | \ | x | x +---------------> T +---------------> T (c) Subadiabatic (d) Inversion ELR < DALR T rises with z z z | \ . | \ . | \ . | \ . | \. | \ . | \. | \ . | x | x +---------------> T +---------------> T ``` - (a) The air cools faster than the parcel, so the lifted parcel is warmer than its surroundings and keeps rising: unstable. - (b) The two lines coincide, so the parcel is always at the same temperature as its surroundings: neutral. - (c) and (d) The air is warmer than the lifted parcel, so the parcel sinks back: stable, and very stable in an inversion. | Condition | ELR compared with DALR | Stability | Effect on dispersion | |---|---|---|---| | Superadiabatic | ELR > 9.8 $^\circ$C/km | Unstable | Strong vertical mixing, rapid dilution; looping plume | | Neutral | ELR = 9.8 $^\circ$C/km | Neutral | Moderate mixing; coning plume | | Subadiabatic | 0 < ELR < 9.8 $^\circ$C/km | Stable | Weak vertical mixing; coning to fanning plume | | Isothermal | ELR = 0 | Very stable | Poor mixing | | Inversion | ELR < 0 (temperature increases with height) | Very stable | Pollutants trapped near the ground; fanning plume | Unstable conditions occur on sunny days with light winds; stable ones on clear, calm nights. Pasquill classes A (very unstable) to F (stable) express the same idea. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The dry adiabatic lapse rate is about: A. 0.98 °C/km B. 9.8 °C/km C. 4-6 °C/km D. 98 °C/km Answer: B. DALR = g/cp = 9.81/1005, about 9.8 °C/km or 1 °C per 100 m. (Key point: Dry adiabatic lapse rate) 2. Which condition corresponds to an unstable (superadiabatic) atmosphere? A. ELR < DALR B. ELR = 0 C. ELR > DALR D. Temperature increasing with height Answer: C. If ELR exceeds DALR a lifted parcel stays warmer than its surroundings and keeps rising. (Key point: Condition for instability) 3. An inversion layer is characterised by: A. ELR greater than 9.8 °C/km B. Temperature increasing with height, making it very stable C. ELR equal to DALR D. Rapid vertical mixing Answer: B. In an inversion temperature rises with height (ELR < 0), so pollutants are trapped near the ground. (Key point: Inversion) 4. A parcel lifted in a stable atmosphere: A. Becomes warmer than surroundings and keeps rising B. Becomes colder and denser than surroundings and sinks back C. Stays at the same level as ELR changes D. Cools at the saturated rate always Answer: B. In stable air the displaced parcel cools at DALR to below surrounding temperature and returns downward. (Key point: Stability principle) ## Related in Environment and Pollution Control - [Determining stability from temperature readings](https://www.bctengineer.com/question.md?key=semester_7%2Fenvironment_and_pollution_control%3Astability-from-lapse-rate-numerical) — Environment and Pollution Control, chapter 2 - [Temperature inversions: types and effects](https://www.bctengineer.com/question.md?key=semester_7%2Fenvironment_and_pollution_control%3Atemperature-inversions-types-effects) — Environment and Pollution Control, chapter 2 ## Related in other subjects - [Adiabatic diffuser: exit temperature and pressure](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Aadiabatic-diffuser-air-exit-temp-pressure) — Fundamental of Thermodynamics & Heat Transfer, chapter 4 - [Adiabatic saturation and wet bulb temperature](https://www.bctengineer.com/question.md?key=semester_3%2Fapplied_thermodynamics%3Aadiabatic-saturation-wet-bulb) — Applied Thermodynamics, chapter 4 - [Importance of rate analysis; how rates taken](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Arate-analysis-importance-rates-taken) — Estimating and Costing, chapter 4 - [Hot and cold working; temperature and strain rate](https://www.bctengineer.com/question.md?key=semester_4%2Fmanufacturing_and_production_processes%3Ahot-cold-working-friction-strain-rate) — Manufacturing and Production Processes, chapter 5