Atmospheric Stability

Science 123		Spring 2026
	Atmospheric Stability

Parcel Thermodynamics (video)
- Ideal Gas Law : relating temperature, pressure and density
  
  - $P = 2.87\rho T$
  
  - $T = am_wv^2$ temperature is directly related to the kinetic energy of the molecules
  
  - $P = \frac{\mbox{force}}{\mbox{area}} \sim \frac{\mbox{mass} \times \mbox{velocity} \times \mbox{frequency}}{\mbox{area}}$ exerted on the "walls" of the parcel
  
  - $\rho = \frac{\mbox{mass}}{\mbox{volume}}$
- Potential Temperature $\Theta = T\left(\frac{1000}{P} \right)^{R/C_p}$ is used to determine the temperature
  of the parcel as it moves off the surface of the earth into lower pressure $P$ with no phase change of water within the parcel.
- Figure of $\theta$ as a function of altitude and latitude.
- adiabatic process - no exchange of energy between the parcel and its environment.
- Potential temperature, $\theta$, is conserved when no moisture phase change occurs within the parcel.
- rising parcel of air cools - molecular KE is decreased as the parcel constituents expand the parcels by pushing against the parcel "walls"
- sinking parcel of air warms - molecular KE is increased as the parcel walls contract and impart energy to the parcel constituents
- Equivalent Potential Temperature, $\Theta_e$, accounts for difference of pressure and the thermal energy "potential" of the parcel due to the mass of water vapor of the parcel.
  The formula is
  
  $\Theta_e = T_e\left(\frac{1000}{P} \right)^{R/C_p} = \left(T + \frac{L_v}{C_p} \cdot W \right) \left(\frac{1000}{P} \right)^{R/C_p}$
  
  where $L_v$ is the latent heat of vaporization (condensation), $C_p$ is the heat capacity of dry air, and $W$ is the mixing ratio of the parcel in kg/kg or gm/gm.
  The quantity $T_e = T + \frac{L_v}{C_p} \cdot W$ is referred to as the equivalent temperature of the parcel.

Lapse Rates (video)
- environmental : $\Gamma_e$ = 6.5 degrees C per 1000 m
- dry adiabatic : $\Gamma_d$ = 10 degrees C per 1000 m
- moist adiabatic : $\Gamma_m$ = 6 degrees C per 1000 m

Atmospheric Stability (video)
- stable : $\Gamma_e \lt \Gamma_m \lt \Gamma_d$
- conditionally stable : $\Gamma_m \lt \Gamma_e \lt \Gamma_d$
- unstable : $\Gamma_m \lt \Gamma_d \lt \Gamma_e$

Stabilizing Events
- upper levels of the atmosphere warm
  
  - warm advection
- lower levels of the atmosphere cool
  
  - radiational cooling
  
  - cold advection
  
  - air moving over a cold surface
- subsidence inversions
  
  - top of the subsiding layer sinks more than the bottom of the layer

Destabilizing Events (video)
- cooling aloft
  
  - cold advection
  
  - short wave
  
  - radiational cooling (cloud tops or air)
- warming at the surface
  
  - solar radiational heating
  
  - warm advection
  
  - air moving over a warm surface
- mixing
- lifting of an entire layer
- convective instability

Cloud Development (video)
- lifting mechanisms
  
  - convergence
  
  - frontal
  
  - topography
  
  - convection
- layered clouds
- convective clouds

Thermodynamic Chart : Skew T - Log P (video)

Example Exercises
- Exercises 1a and 2a (video)
- Exercise 3 (video)
- Exercises 5 and 6 (video)