Adiabatic Lapse Rate Inversion Stable and Unstable Adiabatic

Adiabatic Lapse Rate Inversion , Stable and Unstable

Adiabatic Lapse Rate • The First Law of Thermodynamics can be expressed as: d. U = dq + dw where d. U is the change in internal energy, dq is the heat supplied to the system, and dw is the work done on the system. • Raise a parcel of air there is no heat input, hence dq=0 (adiabatic) and dw=pd. V.

Adiabatic Lapse Rate • The heat capacity of a gas at constant pressure, Cp, is defined as (d. H/d. T) so that Cp d. T= Vdp • From the hydrostatic equation we get dp = -g σ dz • Hence Cp d. T = -V g σ dz • For a unit mass of gas V=1/σ and we get ( d. T/dz)adiabatic perfect gas = - (g M/ Cp) T = temperature z = vertical distance g = acceleration due to gravity M = molecular weight of air Cp = heat capacity of the gas at constant pressure

• For Venus, Earth, Mars and Jupiter the calculated values of Γd are 10. 7, 9. 8, 4. 5 and 20. 2 K per kilometer. • The dry adiabatic lapse rate plays an important role in atmospheric stability.

Lapse Rates and Stability • Lapse rate is the rate at which the temperature decreases with altitude – the environmental lapse rate. • (Lapse rate is the negative of temperature gradient) • This should be compared with the dry adiabatic lapse rate of 10 ºC. • If the environmental lapse rate is less than 10 ºC, then the atmosphere is absolutely stable • If greater than 10 ºC, it is absolutely unstable

Wet adiabatic lapse rate • The presence of condensable vapors, such as water vapor, complicates the process. • As the parcel of air ascends it cools at the dry adiabatic lapse rate until the water vapor reaches saturation – then condensation takes place. • This releases latent heat – which can raise the temperature of the air parcel. • Now the lapse rate depends on the amount of water vapor wet adiabatic lapse rate.

Adiabatic expansion/compression: no heat exchange. Adiabatic lapse rate Dry adiabatic lapse rate ~ 10 K/km Moist adiabatic lapse rate ~ 6 K/km Remember: Dry > Moist always Environmental lapse rate. Atmospheric stability: Absolutely stable atmosphere Absolutely unstable atmosphere Neutrally stable atmosphere Conditionally unstable atmosphere • Stability on skew T – ln p charts • Stable, neutral, unstable, conditionally unstable • Stable atmosphere – Inversions – fog/air pollution • Unstable atmosphere – Convection – Thunderstorm development

Role of atmospheric stability Temperature inversions produce very stable atmospheric conditions in which mixing is greatly reduced. There are two general types of inversions: surface inversions and inversions aloft. v Surface inversions are the result of differential radiative properties of the Earth’s surface and the air above. The Earth is a much better absorber and radiator of energy than air; thus, in the late morning and afternoon hours the lower atmosphere is unstable. The opposite is true in the evening; a stable atmosphere with little vertical mixing prevails.

The Nocturnal Inversion • On clear nights, a temperature inversion develops near the surface. - Air temperature usually decreases with height. An inversion is a layer of air where temperature increases with height. - Because the layer of air in the inversion is warmer than the air below it, the cooler air below the inversion cannot rise above it. Pollutants near the surface are therefore trapped below the inversion in the overnight hours.

Fig. 3. 18

Role of Atmospheric Stability Inversions aloft are associated with prolonged, severe pollution episodes. These types of inversions are caused by the sinking air associated with the center of high pressure systems (subsidence). As the air sinks it is warmed adiabatically. Turbulence at the very lowest part of the atmosphere prevents subsidence from warming that portion of the atmosphere. Los Angles pollution episodes as well as those over the Mid-Atlantic region are the result of inversions aloft associated with strong high pressure systems.

Real lapse rate, Γ > Γd What happens to air at ‘O’ that is displaced upwards by a disturbance? And what happens if it is displaced downwards? Real lapse rate, Γ is less than the DALR, Γd What happens to air at ‘O’ that is displaced upwards by a disturbance? And what happens if it is displaced downwards?

Stability on skew T-ln p diagram

Q / How does the Stability of the Atmosphere Change During the Day? • Daytime: – The sun heats the ground. – The boundary layer is heated from below. – The environmental lapse rate is steep. – The atmosphere can become unstable. • Morning and evening hours: – Radiation cooling results in temperature inversion. – The boundary layer is cooler than the air above. – The environmental lapse rate becomes less steep. – The atmosphere is stable.

DAY NIGHT Air Stability The ground is warm IR cooling Environmental lapse rate Altitude Solar radiation Adiabatic lapse rate 20 30 Temperature [C] The ground is cool

Formation of Convective Clouds • The surface air temperature is 35 C and the dew point is 25 C

Stability and cloud thickness A conditionally unstable atmosphere allows for saturated air to keep propagating upwards

STABLE UNSTABLE