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Temperature lapse rates
The document discusses temperature lapse rates and atmospheric stability, emphasizing the impact of altitude on temperature changes and the dispersion of pollutants. It details the difference between dry and wet adiabatic lapse rates and their effects on atmospheric stability and pollution concentration. Additionally, it explores the conditions leading to various types of atmospheric inversions and their implications for air quality.
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Temperature lapse rates
- 1. TEMPERATURE LAPSE RATES AND STABILITY 18TE710- ENERGY AND ENVIRONMENT Arjun P | BL.EN.P2TSE19002
- 2. Temperature Lapse Ratesand Stability Air pollutants (Anthropogenic) Physical – Photo Chemical Transformation Receptors • Pollutant concentration → Dangerous Level → Near the source • So we should transport and dilute the pollutants before getting modified. • Stability of atmosphere = f(Rate of change of temperature with altitude)
- 3. Variation of temperaturewith altitude 1. 𝑑𝑝 𝑑𝑧 = -ρg 2. 𝑝 = ρRT (Assumption : Air is an ideal gas) 3. 𝑑𝑝 𝑑𝑧 = - 𝑝𝑔 𝑅𝑇 𝑑𝑝 𝑝 = - 𝑔∗𝑑𝑧 𝑅𝑇 ln(p) =ln(p0) - 𝑔𝑧 𝑅𝑇 ln( 𝑝 𝑝0 ) = - 𝑔𝑧 𝑅𝑇 4. p = p0 * exp(- 𝑔𝑧 𝑅𝑇 ) (Assumption : Isothermal atmosphere). • Pressure is reducing exponentially. • But observation is having some discrepancy with the modal Assumptions were wrong (:p) – stripes having uniform thickness but different temperature
- 4. Most general case: -Assume polytropic atmosphere 1. 𝑑𝑝 𝑑𝑧 = -ρg 2. 𝑝 = ρRT (Assumption : Air is an ideal gas) 3. 𝑑𝑝 𝑑𝑧 = - 𝑝𝑔 𝑅𝑇 4. ( 𝑇 𝑇𝑂 ) 𝑛 𝑛−1 = 𝑝 𝑝𝑜 5. (𝑇) 𝑛 𝑛−1 = p* C Substitute eqn (5) for p in eqn (3) 𝑑 𝑑𝑧 ( 𝑇 𝑛 𝑛−1 ) = - 𝑔 𝑅𝑇 ∗ 𝑇 𝑛 𝑛−1 ( 𝑛 𝑛−1 ) 𝑇 𝑛 𝑛−1 −1 ∗ 𝑑𝑇 𝑑𝑧 = - 𝑔 𝑅 ∗ 𝑇 𝑛 𝑛−1 −1 6. 𝒅𝑻 𝒅𝒛 = - ( 𝒏 𝒏−𝟏 )* 𝒈 𝑹 ➔ Temperature Lapse Rate. Up to 10 km – Temperature variation is found to be linear = 6.5 degree Celsius per kilometre 6.5 1000 = (𝑛/(𝑛 − 1)) ∗ 𝑔/𝑅 ➔ n = 1.23 Occurs in lower atmosphere
- 6. At lower stratosphereiso thermal modal is valid.
- 7. ◦While considering thevertical movement of pollutants adiabatic temperature change is important. ◦Air Parcel – (a tiny spherical control system) ◦Consider a air parcel moving upwards ◦pressure reduces ◦Volume increases → air parcel expands ◦Does some work on the surroundings Adiabatic Lapse Rate
- 9. If air containsmoisture ◦ In the presence of moisture in the atmosphere a rising air parcel may cool until the partial pressure of water vapour becomes equal to saturation pressure of water. ◦ If sufficient nucleation sites are present water will get condensed, and heat will be liberated 𝑑𝑄 = − ⅆ𝑄 = −𝜆𝑚 ⅆ𝜔 𝜆 → latent heat per gram m → mass of dry air in air parcel in gram 𝜔→ 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑣𝑎𝑝𝑜𝑢𝑟 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑑𝑟𝑦 𝑎𝑖𝑟 Q -dW = dU 𝜆ⅆ𝜔 + pdv + CvdT = 0 𝜆ⅆ𝜔 + (Cv+ R)*dT = vdp 𝑑𝑇 𝑑𝑧 = −𝑔 𝐶 𝑝 - 𝜆 𝐶 𝑝 𝑑𝜔 𝑑𝑧 - Wet adiabatic laps rate
- 10. ◦ 𝑑𝑇 𝑑𝑧 = −𝑔 𝐶 𝑝 - 𝜆 𝐶 𝑝 𝑑𝜔 𝑑𝑧 ◦Condensing water is having negligible effect - 𝑑𝜔 𝑑𝑧 is +ve ◦ Last term of the equation is +ve ◦ Temperature drop of moist air will be less than that of dry air as the altitude increases. ◦ Saturation vapour pressure of water increases rapidly with temperature → 𝑑𝜔 𝑑𝑧 depends on temperature → WALR is not a constant, and independent of altitude. ◦ In warm tropical region the wet adiabatic laps rate is one third of dry adiabatic laps rate.
- 11. Environmental and Adiabaticlapse rates ◦ The environmental lapse rate - temperature drop with altitude - in the troposphere; that is the temperature of the environment at different altitudes. ◦ It implies no air movement. ◦ Adiabatic lapse rate is associated only with ascending air, which cools by expansion.
- 12. Atmospheric stability ◦ Dispersionof pollutants in the atmosphere is a function of stability. ◦ Comparison between adiabatic and environmental lapse rate → stability ◦ When both of them are equal air parcel and its surroundings will be having same pressure temperature and density → no buoyant force → neutrally stable.
- 13. ◦ If environmentallapse rate > dry adiabatic lapse rate ➔ Super adiabatic ◦ Rising Air parcel will be hotter than surroundings → more buoyant force → moves further upwards → unstable. ◦ Instability increases ➔ vertical movement increases ➔ enhanced mixing➔ reducing concentration ➔ Pollution intensity is reduced. ◦ If environmental lapse rate < dry adiabatic lapse rate ➔ Sub adiabatic ◦ Rising Air parcel will be cooler and dense than surroundings → tend to fall back → unstable. ◦ Limited vertical mixing ➔ enhances the rate of pollution.
- 14. ◦ Consider saturatedatmosphere – stability and instability → neutrally stable atmosphere. ◦ Absolute instability → environmental laps rate > dry adiabatic laps rate ◦ Absolute stability → environmental laps rate < wet adiabatic laps rate ◦ Conditional stability →WALR < ELR < DALR ◦ Inversion → extreme case of stability → 𝑑𝑇 𝑑𝑧 > 0 → negative lapse rate ◦ Atmosphere → stable → no mixing
- 15. Inversions • Inversion preventsmixing → increased chance of pollution Inversions Subsidence Inversion Radiational Inversions Advective Inversions Subsidence Inversion • Associated with sub-tropical anti cyclone → stability → air parcel will be moving down→ air get warmed by compression→ achieve temperature higher than air underneath
- 16. • If ΔTis sufficient → Inversion. • Subsidence is caused by air flowing down to replace air which has flowed out of the high pressure region
- 17. Radiational Inversions • Resultsfrom Diurnal cooling cycle. • After sunset ground cools quickly by radiational HT • Lowest layer of atmosphere loses sensible heat (Conduction and low level mixing)→ temperature inversion → first few hundred meters • Valleys and low lying areas • Next sunny day inversion is destroyed
- 18. Advective Inversions • Whenwarm air moves over a cold surface (ground based) or cold air (elevation based). • Elevated Advective Inversions eg: when a hill range forces a warm land breeze to flow at high levels and a cool sea breeze flows at low levels in opposite direction Inversion spokes only about vertical mixing, in a very stable atmosphere there may be strong horizontal wind
- 19.