1. Lapse Rate
Poisson equation:
d ( )

2. Lapse Rate For an air parcel, going though dry adiabatic process,
So, is the dry adiabatic lapse rate when parcel moving up and down.
There are three different lapse rates:
(Environmental) lapse rate,
Dry adibatic lapse rate,
Moist adiabatic lapse rate,

3. Stability p Unstable Stable Neutral no tendency to no tendency to
displacement
no tendency to
no tendency to
displacement
displacement
continue or to return
continue or to return
tendency
tendency p
Stable (oscillating)? or
unstable (going away)?
displacement X

4. Dry Static Stability
Oscillation due to the restoring force after displacement in a stratified stable atmosphere.
Starting from the vertical momentum equ.
Displacement
Environment
environment

5. Dry Static Stability In the air parcel (density)
P adjusted to the environment immediately
Assume environment is hydrostatic balance

6. Dry Static Stability Back to the RHS of the momentum equation.
In the air parcel, d
From ideal gas law and Poisson equation, one can get:

7. Dry Static Stability Therefore
In troposphere, the average of N is about 1.2 X 10-2 s-1. So, the period
implying that the parcel oscillating one cycle needs about 10 min.

8. Dry Static Stability So the atmosphere is statically stable
Environment lapse rate So
the atmosphere is statically stable
the atmosphere is statically neutral
the atmosphere is statically unstable
(super adiabatic lapse rate)
This is for dry atmosphere. The moist atmosphere will be more sophisticated!

9. Sounding
Potential temperature
(superadiabatic)

10. Skew-T Log-P diagram q q T T Temperature Water vapor mixing ratio
Potential
Temperature or
Dry adiabat
Wet-bulb Potential
Temperature or
Moist adiabat T q

11. Instability
Superadiabatic
(unstable)

12. Instability

13. Conditionally Unstable
When the environment is unsaturated, it is stable.
When the environment is saturated, it is unstable.
colder
warmer
Environment

14. Potential Instability
(Also called convective instability, thermal instability.) The state of an unsaturated layer or column of air in the atmosphere with a wet-bulb potential temperature (or equivalent potential temperature) that decreases with elevation.
If such a column is lifted bodily until completely saturated, it will become unstable (i.e., its temperature lapse rate will exceed the saturation-adiabatic lapse rate) regardless of its initial stratification.
From AMS

15. Potential Instabilityq T
LCL
After lifted (dp)
Unstable
Absolutely
Stable
Air Layer dp
LCL T Td

16. Inversion Subsidence inversion Radiative inversion
Mixed layer inversion
Frontal inversion

17. Subsidence Inversion

18. Subsidence Inversion
High pressure systems

19. Subsidence Inversion

20. Mixed Layer Inversion Shear instability When there is no wind shear,
When there is shear
Ri < Shear instability (unstble)

21. Mixed Layer Inversion

22. Mixed Layer Inversion

23. Subsidence Inversion
High pressure systems

24. Radiative Inversion

25. Frontal Inversion

26. Frontal Inversion

27. Frontal Inversion
LCH
GGG
OUN
DOC

28. Frontal Inversion

29. Frontal Inversion

30. Frontal Inversion

31. Frontal Inversion