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## PowerPoint Slideshow about 'Lecture 10: Atmospheric Stability' - kolton

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Outline

- Dry adiabatic lapse rates
- Moist adiabatic lapse rates
- Conditional instability
- Buoyancy and CAPE
- Parcel theory

Introduction

- Not all important weather phenomena fit into the assumptions of quasigeostrophic theory
- Supercell thunderstorms
- Mesoscale convective systems
- Tornadoes
- The dominant energy source for mesoscale disturbances is convection.
- In this section we examine the types of mesoscale instabilities that lead to convection and examine the role of atmospheric stability in mesoscale weather systems.

Rising Air Parcels

- As the parcel rises, it will adiabatically expand and cool
- Adiabatic: a process where the parcel temperature changes due to an expansion or compression
- No heat is added or taken away from the parcel
- The parcel expands since the lower pressure outside allows the air molecules to push out on the parcel walls
- To compensate, they use up some of their internal energy in the process parcel cools

Sinking Air Parcels

- As the parcel sinks, it will adiabatically compress and warm
- The parcel compresses since it is moving into a region of higher pressure.
- Due to the parcel compression, the air molecules gain internal energy.
- Therefore, the mean temperature of the parcel increases.

Dry Adiabatic Lapse Rate

- Recall that the thermodynamic energy equation can be written in terms of potential temperature
- For an adiabatic process, we have
- How does the temperature change with height in a dry adiabatic atmosphere?

Dry Adiabatic Lapse Rate

- Taking the logarithm and differentiating with respect to height gives
- Using the ideal gas law and the hydrostatic equation, we obtain
- If is constant with height then

Dry Adiabatic Lapse Rate

- is referred to as the dry adiabatic lapse rate
- Note that the dry adiabatic lapse rate is a constant, independent of height or temperature
- gives the rate of change of temperature of a dry air parcel that is being raised (cooling) or lowered (warming) adiabatically in the atmosphere.

Dry Adiabatic Lapse Rate

- When is nonzero, we can write the above expression as
- is referred to as the environmental adiabatic lapse rate
- represents the vertical temperature profile observed in the environment at any particular location and time.
- is measured using radiosonde observations in the atmosphere.

Lapse Rates and Stability

- There are three types of stability conditions for dry, unsaturated environments.
- Case 1:
- Dry air parcel is always cooler than environment
- This is characteristic of a stable environment
- Case 2:
- Dry air parcel has same temperature as environment
- This is characteristic of a neutrally stable environment
- Case 3:
- Dry air parcel is always warmer than environment
- This is characteristic of an absolutely unstable environment

Moist Adiabatic Lapse Rate

- As an air parcel rises, it cools dry adiabatically until it becomes saturated.
- Further ascent results in condensation.
- Latent heat is released and the parcel cools at a rate that is less than
- How does the temperature change with height in a moist adiabatic atmosphere?

Moist Adiabatic Lapse Rate

- It can be shown that the moist adiabatic lapse rate is given as
- is the change in saturation mixing ratio with temperature.
- increases as temperature and the amount of water vapor increases.
- Values of range from 4 K/km near the ground in warm, humid air to 6-7 K/km in the middle troposphere.

Equivalent Potential Temperature

- As we showed earlier, potential temperature is conserved for dry adiabatic processes.
- Using classical thermodynamics, it can be shown that there is a variable that is conserved for moist adiabatic processes called the equivalent potential temperature.
- The equivalent potential temperature is defined as
- is the temperature a parcel of air would reach if all the water vapor in the parcel were to condense, releasing its latent heat, and the parcel was brought adiabatically to a standard reference pressure, usually 1000 hPa.

Equivalent Potential Temperature

- can be used to compare both moisture content and temperature of air parcels at different elevations and the trajectory air parcels will take.
- is used operationally to map out which regions have the most unstable air.
- Areas of relatively high are often the formation points for thunderstorms and other convective storms.

Dew Point Lapse Rate

- As an air parcel rises, the moisture content remains the same but the pressure of the parcel varies.
- This will cause the dew point to gradually decrease with height, producing a dew point lapse rate.
- Dew point lapse rate ranges from 1.6°C to 2°C/km.
- Once a parcel is saturated, the dew point lapse rate is equal to the moist adiabatic lapse rate.
- Variations in dew point lapse rate with height affects the location of the LCL.

Absolute Stability

- Notice that Tenv will always be greater than the temperature of a given air parcel.
- Therefore, an air parcel will always be cooler than the environment and will sink back down to the ground.
- This is an example of absolute stability.
- The condition for absolute instability is

Absolute Stability

- Absolutely stable layers in the atmosphere can form by
- Radiative cooling
- Cold air moving at low-levels
- Warm air moving over cold ground

Absolute Instability

- Notice that Te will always be less than the temperature of a given air parcel.
- Therefore, an air parcel will always be warmer than the environment and will sink back down to the ground.
- This is an example of absolute instability.
- The condition for absolute instability is

Absolute Instability

- 1. Cold air moving is aloft
- This often occurs when an extra-tropical cyclone passes over head
- 2. Surface heating
- This suggests that the atmosphere is most unstable in mid-afternoon
- 3. Warm air moving in at low levels
- This often occurs ahead of a cold front
- 4. Cold air moving over a warm surface
- An example of this is lake-effect snow

Conditional Instability

- Note that an unsaturated (saturated) parcel will be cooler (warmer) than the environment
- This implies that the unsaturated (saturated) parcel will sink (rise).
- This is an example of conditional instability.
- The condition for absolute instability is
- For conditional instability, the parcel is unstable if it's saturated

Conditional Instability - Example

- Consider a parcel with a surface temperature and dew point of 30 °C and 14 °C.
- The parcel is initially forced to rise in an environment where the environmental lapse rate is 8 °C/km up to 8 km.
- 1 km: The parcel is rising dry adiabatically since it is unsaturated.
- 2 km: The parcel has just become saturated. This is called the lifting condensation level (LCL).

Conditional Instability - Example

- 3 km: The parcel is now rising moist adiabatically.
- 4 km: The parcel is still rising moist adiabatically. What happens if the parcel is pushed upward just a little?
- 5 km and above: The parcel will rise on its own since it is less dense than the surrounding environmental air.
- This height is called the level of free convection (LFC).
- The parcel will rise until Tp = Te. This is often referred to as the equilibrium level (EL).

Stability of the Environment

- To determine the environmental stability, one must calculate the lapse rate for a sounding.
- Since the environment is often composed of layers with different stabilities, it is useful to identify these layers and then calculate their lapse rates.
- Stable dry environment
- Stable moist environment
- Unstable dry environment
- Unstable moist environment

Summary of Lapse Rates

- Environmental Lapse Rate: The rate at which temperature decreases with height in the environmental air.
- Dry Adiabatic Lapse Rate:The rate at which temperature decreases with height in an unsaturated, dry air parcel.
- Moist Adiabatic Lapse Rate:The rate at which temperature decreases with height in a saturated air parcel.
- Dew Point Lapse Rate: The rate of at which the dew point temperature decreases with height in an unsaturated parcel.

Stability and Cloud Development

- The cloud base is where the parcel reaches saturation, i.e. the LCL
- The cloud top is where the parcel will no longer be able to rise, i.e. the EL.
- An estimation of the base of a convective cloud is given by:

Lifting Mechanisms

- Q: How can an air parcel be lifted up to the LFC in a given environment?
- There are three basic lifting mechanisms
- Frontal lifting
- Surface convergence
- Topographic lifting

Frontal Lifting

- Another lifting mechanism is by fronts.
- If air is lifted into a stable layer:
- Stratus or Nimbostratus clouds often results (common along warm fronts).
- If air is lifted into a conditionally unstable layer:
- Cumulus or Cumulonimbus often result (common along cold fronts)

Surface Convergence

- Another lifting mechanism is due to convergence of air near the surface.
- If air converges to a given location near the surface, it must go up.
- This is common at the center of an extra-tropical cyclone.

Topographic Lifting

- If air being forced over a topographically barrier is stable, then wave clouds often form.
- Lenticular clouds are an example.
- Wave clouds are often aligned in “waves” and are often visible in satellite imagery.

Buoyancy

- One way to assess static instability is to begin with the vertical momentum equation
- Defining a horizontally homogeneous base state pressure and density field that is in hydrostatic balance, we can rewrite the above equation as
- Rearranging terms gives

Buoyancy

- The first term on the RHS is the vertical perturbation PGF.
- The second term on the RHS is the buoyancy force
- The buoyancy force is what causes the static instability of air parcels and drives the vertical circulation.
- The buoyancy force is attributable to density variations within an atmospheric column.

Buoyancy

- The buoyancy force can be approximated by
- Thus, when an air parcel is warmer (cooler) than its environment, a positive (negative) buoyancy force exists, resulting in upward (downward) acceleration.

CAPE and CIN

- Another way to assess the static stability in the atmosphere is through the convective available potential energy (CAPE).
- CAPE is the amount of energy an air parcel would have if lifted a certain distance vertically through the atmosphere.
- We define CAPE as

CAPE and CIN

- The amount of energy needed to lift a parcel to its LFC is called convective inhibition.
- CIN is the amount of energy required to overcome the negative buoyant energy that the environment exerts on an air parcel.

CAPE and Vertical Velocity

- To relate CAPE to the updraft velocity of a parcel, let’s assume that
- The air parcel is thermally insulated from its environment
- The air parcel remains at the same pressure as the environmental air
- These assumptions reduce the vertical momentum equation to

CAPE and Vertical Velocity

- Multiplying both sides by gives
- Integrating over the time required to travel from the LFC to the EL gives
- As CAPE increases, buoyancy does work on a given air parcel, causing it to increase its kinetic energy.

Limitations of Parcel Theory

- The above expression is an overestimation of the actual speed of air parcels because parcel theory neglects three basic processes
- Vertical perturbation pressure gradient force
- Entrainment and mixing
- The effects of condensation

The Effects of the Vertical Perturbation PGF

- Generally speaking, the vertical perturbation pressure gradient is not negligible in the vertical momentum equation and tends to offset the acceleration induced by the buoyancy force.
- An upward-directed (downward-directed) buoyancy force associated with (cold air) warm air tends to be associated with a downward-directed (upward-directed) perturbation pressure gradient.
- Thus, air parcels tend not to rise as fast as one would expect based on the consideration of the buoyancy force alone.

The Effects of Entrainment

- Mixing of environmental air into a rising air parcel slows the parcel by reducing its buoyancy and upward momentum.

The Effects of Condensation

- Parcel theory also neglects
- The presence of hydrometers or condensate (parcel theory assuming pseudoadiabatic ascent)
- The effects of freezing
- The effects of compensating subsidence
- For these reasons, the approximate vertical velocity of the updraft is

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