* Reading Assignments: All Sections

8. Hydrostatic Stability Describe the states of vertical stratification of atmosphere: * Stable equilibrium * Unstable equilibrium * Neutral equilibrium

8.1 Parcel method

The vertical acceleration of a unit mass air parcel is proportional to its displacement and the difference between the parcel and environmental lapse rates.

8.2 Stability Categories Stability in terms of temperature lapse rate

* For unsaturated air * For saturated air

* For both unsaturated and saturated air 1)Absolute unstable 2) Absolute stable 3) Conditionally unstable Stable for unsaturated air Unstable for saturated air Moisture Dependence

8.2.3 Stability in terms of potential temperature * For unsaturated air * For saturated air

8.3 Implications for vertical motion The vertical momentum equation for an unsaturated air parcel N is called the Brunt-Väisäillä frequency. If the atmospheric stratification is stable, N > 0.

Meteorology 341 Homework (8) 3. An air parcel, which has LCL (Lifting Condensation Level) at height of h c, ascends in a conditionally unstable environment, show the height of LFC (Level of Free Convection) h f are constants. 1.Problem 8 on page Problem 15 on page 201

8.4 Conditional instability Potential Energy : Convective Available Potential Energy: the total potential energy available for conversion to kinetic energy Kinetic Energy:

Potential Energy: :

Conditional instability is classified into three types: 1) Stable type: no positive area 3) Pseudo latent type: negative area is larger than positive area 2) Real latent type: positive area is larger than negative area

1)

2)

3)

When the height is used as the vertical coordinate, the kinetic energy for the air parcel within a layer is defined as where and are the air parcel’s temperature and vertical velocity, respectively. If the temperature lapse rate of the environment is 12 o C/km from surface to 500m and the surface temperature is 27 o C, find the kinetic energy for an unsaturated air parcel in this layer.

The lapse rate is 12 K/km from surface to 500m, and 8 K/km between 500m and 3000m. The surface temperature is 27 o C. Calculate the kinetic energy from surface to 3000m. The condensation level is above 3000m.

8.5 Effect of entrainment on ascending parcels is the ratio of entraining mass per unit height over the air mass. is defined as the mass entrainment height.

8.6 Modification of stability due to the displacement of layer * Potential Instability

* Vertical compression and expansion Stability decreases Instability decreases No change For

8.7 Layer (slice) method One assumption in the parcel method is that the environment remains undisturbed. The layer method removes this assumption by allowing the compensatory subsidence for the ascent of an air mass.

The stability criterion:

* Both ascending and descending air is unsaturated

* Ascending air is saturated and descending air is unsaturated

8.8 Stabilizing and destabilizing effects * External heat transfer