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Home , Atmospheric instability

MTO 412E Physics of and Objectives

• Be able to provide the definition of stability Static Stability and Cloud • Be able to describe the two methods by Development which air is displace • Be able to identify the types of that form during either forced ascent or auto - convective ascent • Be able to determine if the atmosphere is potentially unstable

Static Stability and Environmental Lapse Why is stability important? Rate (ELR) • Vertical motions in the atmosphere are a critical • Static Stability part of transport and strongly influence the • Absolutely Unstable Air hydrologic cycle • Absolutely Stable Air • Without vertical motion, there would be no precipitation, no mixing of pollutants away from • Conditionally Unstable Air ground level - as we know it would simply not exist. • There are two types of vertical motion: – forced motion such as forcing air up over a hill, over colder air, or from horizontal convergence – buoyant motion in which the air rises because it is less dense than its surroundings - stability is especially important here

Static Stability Stability in the atmosphere

• Static stability – The air’s susceptibility to lift. – Unstable – Air will continue to rise if given an initial upwards push – Stable – Air resists the upward displacement An Initial Stable Unstable Neutral and sinks back to original level. Perturbation – Neutral – Air will neither rise on its own or sink back to its original level. If an air parcel is displaced from its original height it can: Return to its original height - Stable Accelerate upward because it is buoyant - Unstable Stay at the place to which it was displaced - Neutral

1 Buoyancy Buoyancy Static Stability is Related to Buoyancy Parcel of Air • An air parcel rises in the atmosphere when it’s density is Less dense Than Surrounding Air: Positive Buoyancy less than its surroundings Tends to Rise (Warmer) • Let ρenv be the density of the environment. From the More dense Than Surrounding Air: Negative Buoyancy Equation of State/Ideal Gas Law Tends to Sink if Not Lifted(Colder) ρenv = P/ RT env A Rising Parcel of Air • Let ρparcel be the density of an air parcel. Then Stops Rising When It Cools to Surrounding Air ρparcel = P/ RT parcel • Since both the parcel and the environment at the same Sinks When It Becomes Colder Than Surrounding Air height are at the same This Suppresses Uplift

– when Tparcel > Tenv ρparcel < ρenv (positive buoyancy )

– when Tparcel < Tenv ρparcel > ρenv (negative buoyancy )

Rising Air What is ? Cools

The lapse rate is the change of • The lapse rate is the change of temperature with • Rising air with altitude. parcels expand height in the atmosphere • Work done by The atmospheric dry • There are two kinds of lapse rates: adiabatic air molecules in – Environmental Lapse Rate the parcel lapse rate is ~ • What you would measure with a weather balloon pushing 5.4 F/1000 ft outward or – Parcel Lapse Rate consumes 10 C/1000 m • The change of temperature that an air parcel would experience energy and when it is displaced vertically The actual, • This is assumed to be an (i.e ., no heat lowers the environmental lapse parcel rate may be greater exchange occurs across parcel boundary) temperature or smaller than this

Lapse Rates Trading Height for Heat

Lifted Parcel of Air There are two kinds of “static” energy in the Cools at One of the Adiabatic Lapse Rates Air Around it Maintains Its Original Temperature Profile parcel: potential energy (due to its height) and enthalpy (due to the motions of the molecules Relative Density 1. Depends on Unsaturated or Saturated that make it up) DALP or SALP 2. Environmental Lapse Rate (ELP) ∆S = c ∆ T +∆ gz Three Types of Static Stability p 1. Absolutely Unstable Air Change in Change in Change in 2. Absolutely Stable Air gravitational static energy enthalpy 3. Conditionally Stable Air potential energy

2 Trading Height for Heat (cont’d) • Suppose a parcel exchanges no energy with Lapse Rates its surroundings … we call this state adiabatic, meaning, “not gaining or losing • Dry adiabatic lapse rate (DALR) –Rate at which rising parcel of unsaturated air cools. (1.0°C/100 energy” 0 =c ∆ T + gz ∆ m) p • Saturated adiabatic lapse rate (SALR) - Rate at c∆ T =− gz ∆ which rising parcel of unsaturated air cools. p (0.5°C/100 m) ∆T g • lapse rate – Rate at which dew point = − decreases with height. (0.2°C/100 m) ∆z c p • Environmental lapse rate (ELR) – Vertical change in temperature profile through still air. “Dry adiabatic lapse rate”

Lapse Rates Lapse Rates

• Difference between ELR and DALR/SALR

Stability and the Reversible Process dry adiabatic lapse rate • Atmospheric stability depends on the environmental lapse rate – A rising unsaturated air parcel cools according to the dry adiabatic lapse rate – If this air parcel is • warmer than surrounding air it is less dense and buoyancy accelerates the parcel upward

• colder than surrounding air it is more dense and buoyancy forces oppose the rising motion

3 A saturated rising air parcel cools Stability and the less than an moist adiabatic lapse rate • Atmospheric stability unsaturated parcel depends on the environmental lapse rate • If a rising air parcel becomes saturated – A rising saturated air parcel cools according to the moist occurs adiabatic lapse rate • Condensation warms the air parcel due to the – When the environmental lapse release of latent heat rate is smaller than the moist adiabatic lapse rate, the • So, a rising parcel cools less if it is saturated atmosphere is termed dry absolutely stable • Define a moist adiabatic lapse rate • Recall that the dry adiabatic – ~ 6 C/1000 m lapse rate is larger than the – Not constant (varies from ~ 3 -9 C) moist – depends on T and P – What types of clouds do you expect to form if saturated air is forced to rise in an absolutely stable atmosphere?

Factors Influencing the Heating or Cooling of the Lower Environmental Lapse Rate Atmosphere

The Average Environmental Lapse Rate (ELR) -0.65 °C / 100 meters ( -6.5 °C / km) Highly Variable in Space and Time Both Surface Air Temperature Vertical Temperature Profile Influences 1. Heating or Cooling of the Lower Atmosphere. Atmosphere Is Heated From the Surface 2. of Cold or Warm Air at Different Levels. ELR Is Steeper (More Change in Temperature) at Mid -day 3. Advection of a Different Air Mass with a Different ELR. Greatest on Clear Days Least at Night Inversion - If Air at Surface Gets Colder Than Aloft Positive ELR

Advection of Cold or Warm Air at Advection of a Different Air Mass Different Levels with a Different ELR

Air Mass Large Area Distinguished From Its Neighbors by Differences i n Advection or Can Be Different at the Surface From That Alof t 1. Temperature ELR Can Be Different If Are Different 2. Water Content () Example Same Direction: -0.5°c/100m Maintain Their Identity (1 & 2) Perpendicular : -1.0°c/100m Air Masses Can Migrate Into Other Large Areas Changing ELR Idealized Example As Winds Gradually Change With Height (A takes the place of B) Seen by Cloud Movement

4 Limitations on Lifting Unstable Air Advection of Cold and Warm Air Stable

Unstable

Unstable Air Can Not Lift Forever Braking Mechanisms 1. Ascent Into Layer of Stable Air 2. Entrainment (Advection of Warmer Air)

Advection of Cold and Warm Air Static Stability

Static Stability Air’s Susceptibility to Uplift. Statically Unstable Air Continues to Rise If Given an Initial Upward Push Statically Stable Air Resists Upward Displacement and Sinks Back to Original Level Statically Neutral Air Will not Rise or Sink After Its Initial Upward Push Comes to Rest Where It was Displaced

Stability Psychological

• Psychological Stability • Results From Stress • Meteorological Stability – Too many Exams – Too Much Homework – Poor Grades – Too Much Alcohol • Example

5 Meteorological Stability Stability

• The ability of the air to return to its origin • Depends on the after displacement thermal structure of the atmosphere

Stability Stable

• Can be classified into 3 categories • Returns to original position after – Stable displacement – Neutral – Unstable

Neutral Unstable

• Remains in new position after being • Moves farther away from its original displaced position

6 Stability Forced Ascent

• How is air displaced? • Some mechanism forces air aloft – Two methods – Usually synoptic scale feature 1.) Forced Ascent 2.) Auto -Convective Ascent

Cold air Warm air Cool Air

Forced Ascent Auto-Convective Ascent

• Type of clouds • Air becomes buoyant – Depends on stability by contact with warm ground – Usually microscale or mesoscale

Stable - Stratus Unstable - Cumulus Cool Hot Cool

Auto-Convective Ascent Parcel Theory

• Type of Clouds • Assumptions T ,P T ,P – Cumulus – Thermally insulated from its e p environment – Temperature changes w adiabatically – Always at the same pressure as the environment at that level

7 Parcel Theory Stability

• Assumptions • As parcel rises T ,P T ,P – Hydrostatic equilibrium e p 1.) Parcel Temperature – Moving slow enough that its Changes kinetic energy is a negligible w • Unsaturated? – Dry Adiabatic Lapse Rate

Stability Stability Pseudo - Adiabat Mixing Ratio line • As parcel rises 4 1.) Parcel Temperature Unsaturated Changes 3 Parcel • Saturated? Temperature 2 – Pseudoadiabatic Lapse Dry Rate 1 Adiabat Height (km) Height Height (km) Height 0 -20 -10 0 10 20 Temperature (°C)

Stability Stability Pseudo - Adiabat Mixing Ratio line • As parcel rises 4 2.) Environmental Saturated Temperature Changes 3 Parcel • Environmental Lapse Rate Temperature 2 (Γe) Dry 1 Adiabat Height (km) Height Height (km) Height 0 -20 -10 0 10 20 Temperature (°C)

8 Stability Stability Pseudo - adiabat (ΓΓΓs) Mixing Ratio line • Environmental temperature profile depends 4 on many factors Parcel Parcel – Advection 3 Temperature – Sinking Air 2 Environmental Warm Air Advection Dry Temperature ( ΓΓΓe) 1 Adiabat (ΓΓΓd) Height (km) Height Height (km) Height 0 -20 -10 0 10 20 Cold Air Advection Temperature (°C)

Stability Stability

• Environmental • Stability depends on Temperature – Temperature Te Tp – Measured by rawinsonde • Environment • Parcel – Condition of Parcel • Unsaturated Te Tp

Te Tp

Unsaturated Unsaturated -Unstable

Dry Adiabat Γ • Unstable ΓΓΓd (Parcel Temperature) – Once displaced, continues 4 3 ΓΓΓe > ΓΓΓd 2 Environmental Lapse Rate ( ΓΓΓ ) 1 e Height (km) Height Height (km) Height 0 -20 -10 0 10 20 Temperature (°C)

9 Unsaturated Unsaturated -Neutral

Dry Adiabat Γ • Neutral ΓΓΓd (Parcel Temperature) – Once displaced, stays 4

3 ΓΓΓe = ΓΓΓd 2 Environmental 1 Height (km) Height Height (km) Height Lapse Rate ( ΓΓΓe) 0 -20 -10 0 10 20 Temperature (°C)

Unsaturated -Stable Unsaturated

• Stable – Once displaced, returns 4 ΓΓΓe < ΓΓΓd 3 Dry Adiabat ΓΓΓd 2 (Parcel Temperature) Environmental 1 Height (km) Height Height (km) Height Lapse Rate ( ΓΓΓe) 0 -20 -10 0 10 20 Temperature (°C)

Stability Stability

• A real environmental • Stability depends on sounding sometimes Γ – Condition of Parcel Te Tp combines all three ΓΓΓe • Saturated • Evaluate each layer

ΓΓΓd Te Tp

Te Tp

10 Saturated-Unstable Saturated-Neutral

Pseudoadiabat (ΓΓΓs) Pseudoadiabat (ΓΓΓs)

4 4

3 3 ΓΓΓe > ΓΓΓs ΓΓΓe = ΓΓΓs 2 Environmental 2 Lapse Rate ( ΓΓΓ ) Environmental 1 e 1 Height (km) Height (km) Height Height (km) Height (km) Height Lapse Rate ( ΓΓΓe) 0 0 -20 -10 0 10 20 -20 -10 0 10 20 Temperature (°C) Temperature (°C)

Saturated-Stable Stability

Environmental • Dry (or Unsaturated) Lapse Rate ( ΓΓΓe) 4 e

3 Height Height Height Height Height Height 2 ΓΓΓ < ΓΓΓ e s Temperature Temperature Temperature 1 Pseudoadiabat Height (km) Height Height (km) Height ΓΓΓe > ΓΓΓd ΓΓΓe = ΓΓΓd ΓΓΓe < ΓΓΓd (ΓΓΓs) 0 -20 -10 0 10 20 Dry Unstable Dry Neutral Dry Stable Temperature (°C)

Stability Stability

• Saturated • Combine to simplify – Absolutely Unstable t t – Dry Neutral Height Height Height Height Heigh Heigh – Conditionally Unstable – Saturated Neutral Temperature Temperature Temperature – Absolutely Stable ΓΓΓe > ΓΓΓs ΓΓΓe = ΓΓΓs ΓΓΓe < ΓΓΓs

Saturated Saturated Saturated Unstable Neutral Stable

11 Stability Height Height Height Height Height Height Saturated Environmental • Conditional Adiabatic Temperature Temperature Temperature Lapse Rate ( Γ ) Γe Lapse ΓΓΓe > ΓΓΓd ΓΓΓe = ΓΓΓd ΓΓΓe < ΓΓΓd ΓΓΓe > ΓΓΓs Instability Rate ( ΓΓΓ s) 4 Absolutely Unstable Dry Neutral Conditionally Unstable – Depends upon whether the parcel is 3 dry or saturated 2 Dry Adiabatic 1 Adiabatic Height (km) Height 1 Height (km) Height Lapse Rate ( ΓΓΓd ) Height Height Height Height 0 -20 -10 0 10 20 Temperature (°C) Temperature Temperature

ΓΓΓe = ΓΓΓs ΓΓΓe < ΓΓΓs Saturated Neutral Absolutely Stable

Stability Stability

Saturated Saturated Environmental Environmental • Conditional Adiabatic • Conditional Adiabatic Lapse Rate ( ΓΓΓ ) Lapse Rate ( ΓΓΓ ) ΓΓ e Lapse ΓΓ e Lapse Instability Rate ( ΓΓΓ ) Instability Rate ( ΓΓΓ ) 4 s 4 s – Unsaturated Parcel 4 – Saturated Parcel 4 3 3 • Stable • Unstable 2 Dry 2 Dry Adiabatic Adiabatic 1 Adiabatic 1 Height (km) Height 1 (km) Height 1 Height (km) Height (km) Height Lapse Rate ( ΓΓΓd ) Lapse Rate ( ΓΓΓd ) d 0 0 -20 -10 0 10 20 -20 -10 0 10 20 Temperature (°C) Temperature (°C)

Other Types of Stability Stability

• Static Stability • Static Stability • Potential (or Convective) Instability – The change of potential temperature with height

∂∂∂θθθ ∂∂∂z

12 Static Stability Static Stability

0 0 0 0 4 3 0 -6 -5 - - -2 200

• Atmosphere is said to be statically stable if 0 Bigger θθθ 1 potential temperature increases with height - ) ) 300 0 mb mb

0 400 1

∂∂∂θθθ 0 >>> 0 500 2 0 Pressure ( Pressure Pressure ( Pressure 3 ∂∂∂z 600 0 700 4 – Typical of atmosphere 800 Smaller θθθ 900 1000 Temperature ( oC)

Static Stability Static Stability

0 0 0 0 4 3 0 -6 -5 - - -2 200 Bigger θθθ • Large 0 Strong Static -1 – Tropopause ∂∂∂θθθ Stability ) >>> 0 ) 300 0 mb – ∂∂∂z mb

0 400 1

0 500 2 0 Pressure ( Pressure Pressure ( Pressure 3 600 0 700 4 800 Strong Static 900 Smaller θθθ Stability 1000 Stability Temperature ( oC)

Potential Instability Potential Instability

• The state of an unsaturated layer (or • Also Called column) of air in the atmosphere ∂∂∂θθθ ∂∂∂θθθ • Either w <<< 0 e <<< 0 ∂z ∂z – Wet bulb potential temperature (θw) or ∂∂ ∂∂

– Equivalent potential temperature (θe) • Decreases with elevation

13 Potential Instability Potential Instability

• Common when dry • Lifting Destabilizes Layer layer tops a warm, humid layer – Low level southerly flow – Upper level southwesterly flow

Warmer & Dry Cold air Warm air Warm & Moist Cool Air

Stability Stability

• Now the math! • During displacement – Let’s lift a parcel – Changes of state of parcel – Changes of state of environment

Stability Stability

• During displacement • During displacement – Pressure of parcel is the p-∆∆∆p p-∆∆∆p – Density of parcel is ρρρ’-∆ρ ’ ρ -∆ρ same as pressure of different than density of environemnt z environment z • Parcel Theory Assumption • Why? – Cools at a different rate p p ρρρ’ ρρρ

14 Stability Stability

• What is the equation for momentum balance • The atmosphere on average is balanced of the environment? d2z 1 ∂p Vertical Acceleration = PGF + g = − + g dt 2 ρ ∂z Vertical Equation of Motion No Acceleration

d2z 1 ∂p 1 ∂p = − + g 0 = − + g dt 2 ρ ∂z ρ ∂z Hydrostatic Balance

Stability Stability

• The equation of motion of the parcel • Equations of motion for parcel & environment

2 2 ρρρ’-∆ρ ’ 1 ∂p d z 1 ∂p d z 1 ∂p 0 = − + g = − + g 2 = − + g dt2 ρ' ∂z ρ ∂z dt ρ' ∂z z Hydrostatic Balance Parcel is accelerating

ρρρ’

Absolute instability Absolutely Unstable Air • The atmosphere is absolutely unstable if the environmental lapse rate exceeds the moist and dry adiabatic lapse rates • Dry Adiabatic Lapse Rate - DALR • This situation is not long -lived • DALR = 10o C/1000 m – Usually results from surface heating and is confined to a shallow layer near the surface • ELR > DALR – Vertical mixing can eliminate it

• Tenvironment < Tparcel • Mixing results in a dry adiabatic lapse rate in the • Parcel will rise away from original mixed layer, unless condensation (cloud formation) position occurs (in which case it is moist adiabatic)

15 Absolutely Unstable Air Absolutely Unstable Air

• Once a parcel is lifted it continues to move upward regardless of saturation. • Whenever the ELR exceeds the DALR -1.0°C (1°C/100 m) the air is absolutely unstable.

-1.5°C

ELR = -1.5°C / 100 m Unsaturated DALR = -1.0°C / 100 m Will Keep Rising - Cooling Slower than Surrounding Air

Absolutely Unstable Air Absolute instability (examples)

-0.5°C

-1.5°C

ELR = -1.5°C / 100 m Saturated SALR = -0.5°C / 100 m Will Keep Rising - Cooling More Slowly than Surrounding Air

Absolutely Unstable Absolutely Unstable Air

For Absolutely Unstable Air ELR Exceeds the DALR ELR Exceeds the SALR Parcel of Air will continue to Rise Faster IF the Temperature Difference Increases Slower IF the Temperature Difference Decreases

95

16 Absolutely Stable Air Absolutely Stable Air

• Air parcel returns to its original location • Saturated Adiabatic Lapse Rate - SALR after being displaced. • ELR < SALR • When ever the ELR is less than the SALR

• Tenvironment > Tparcel (0.5°C/100 m), the air is absolutely stable. • Parcel will sink back to original position

Absolutely Stable Air Absolutely Stable Air

-1.0°C -0.5°C

-0.2°C -0.2°C

ELR = -0.2°C / 100 m Unsaturated DALR = -1.0°C / 100 m ELR = -0.2°C / 100 m Saturated SALR = -0.5°C / 100 m Will Not Rise - Cooling Faster than Surrounding Air Will Not Rise - Cooling Faster than Surrounding Air

Absolutely Stable Absolutely Stable Air

For Absolutely Stable Air ELR Does NOT Exceed the DALR ELR Does NOT Exceed the SALR Parcel of Air will NOT Rise The Larger Temperature Difference the MORE Stable

101

17 Conditionally unstable air

Conditionally Unstable Air • What if the environmental lapse rate falls between the moist and dry adiabatic lapse • Conditionally Unstable Air rates? – The atmosphere is • SALR < ELR < DALR unstable for saturated air • depends on whether or not the rising air parcels but stable for unsaturated air parcels parcel is saturated – This situation is termed conditionally unstable • This is the typical situation in the atmosphere

Making Conditionally Unstable Air Conditionally Unstable Air Air is Warmer Rises Freely

S Dew Point

ELR = -0.7°C / 100 m Unsaturated DALR = -1.0°C / 100 m Will Keep Rising - Cooling Faster than Surrounding Air ELR = -0.7°C / 100 m Unsaturated: DALR = -1.0°C / 100 m UNSTABLE Saturated: SALR = -0.5°C / 100 m

Conditionally Unstable Growth of a

107 108

18 Stability Rules #1,#2, & #3 Limitations on Lifting

1. Absolutely Unstable Air • What causes air to quit rising? Whenever the ELR Exceeds the DALR or SALR – Stable air (Positive Buoyancy) • Inversions 2. Absolutely Stable Air Whenever the ELR Is Less Than the DALR or SALR – Entrainment (mixing) (Negative Buoyancy) 3. Conditionally Unstable Air Whenever the ELR Is Between the DALR and SALR

Inversions Layer of Stable Air

• Layer of the atmosphere where temperature of the air increases with altitude • Makes the air extremely stable • Types of Inversions • Radiation inversion • Frontal inversion • Subsidence inversion

Inversions: Extremely Stable Air Inversions: Extremely Stable Air

1. Radiation Inversion Cooling of Surface Develops at Ground Level Radiation If Cools to Dew Point Crop Damage If Cold enough - Frost

3. Subsidence (Sinking) Inversion Compressed Gas 2. Frontal Inversion Warms 100s km long Top Sinks and Warms Most Cold Enough - Sleet or Develops Well Above Surface Freezing Rain Hawaiian High Caps Air Above Los Angeles Heavy Pollution

19 Entrainment

• When air rises considerable turbulence is A Conditionally Unstable Air Mass generated. This entrainment draws in Rises Above the Level of Free Convection environmental air into the parcel and Must be Lifted Then Can Rise on Its Own suppresses further growth. LFC Clouds Increase in Depth (Thickness) Yield Precipitation

Factors Influencing the ELR Limitations on the Lifting of Unstable Air • Heating or cooling of the lower • A layer of stable air above the atmosphere unstable layer • Advection of cold and warm air at • Entrainment different levels •Mixing with surrounding • Advection of an air mass with a unsaturated air, causing evaporation different ERL and cooling of the borders of the cloud

What conditions enhance What conditions contribute to a atmospheric instability? stable atmosphere? • Cooling of air aloft • Radiative cooling of – Cold advection aloft surface at night – Radiative cooling of air/clouds aloft • Advection of cold air • Warming of surface air near the surface – Solar heating of ground • Air moving over a – Warm advection near surface cold surface – Air moving over a warm surface (e.g., snow) (e.g., a warm body of water) • Adiabatic warming • Contributes to lake effect snow due to compression • Lifting of an air layer and from subsidence associated vertical “stretching” (sinking ) – Especially if bottom of layer is moist and top is dry

20 Fair weather cumulus Fair weather cloud development development schematic

• Air rises due to surface heating • RH rises as rising parcel cools • Cloud forms at RH ~ 100% • Rising is strongly suppressed at base of subsidence inversion produced from sinking motion associated with high pressure system • Sinking air is found between cloud elements – Why?

What conditions support taller cumulus development ?

Stability and Cloud Development

• A less stable atmospheric (steeper lapse rate ) profile permits greater vertical motion • Lots of low-level moisture permits latent heating to warm parcel, accelerating it upward

Determining Convective

Cloud Bases Dry adiabats • Dry air parcels cool at the dry adiabatic rate d (about 10 oC/km) • Dew point decreases at a rate of ~ 2 oC/km • This means that the dew point approaches the air parcel temperature at a rate of about 8 oC/km d • If the were 4 oC at the surface, a cloud base would appear at a height of 500 meters – Cloud base occurs when dew point = temp (100% RH) • Each one degree difference between the surface temperature and the dew point will produce an increase in the elevation of cloud base of 125 meters Drier air produces higher cloud bases; moist air produces lower cloud bases

21 Determining convective cloud top

• Cloud top is defined by the upper limit to air parcel rise • The area between the dry/moist adiabatic lapse rate, showing an air parcel’s temperature during ascent, and the environmental lapse rate, can be divided into two parts – A positive acceleration part where the parcel is warmer than the environment – A negative acceleration part where the parcel is colder than the environment • The approximate cloud top height will be that altitude where the negative acceleration area is equal to the positive acceleration area

Dry Adiabatic Processes Dry Adiabatic Processes It is also possible for a parcel of air to change temperature The strength of the change in temperature is related to the without a change in the overall level of energy. This is change in volume according to the relation: referred to as an adiabatic process.

p· ∆α = - cv·∆∆∆T Think back to basic chemistry with Charles Law and Boyles Law. Temperature is related to pressure and volume through p - pressure the ideal gas law. ∆α - the change in volume

cv - the specific heat of air (assuming constant volume) Dry air can undergo an adiabatic change in temperature. For the ∆T - the change in temperature temperature to change, however, we require the parcel of air to change its volume and/or pressure. This is a form of the first law of thermodynamics .

Dry Adiabatic Processes Dry Adiabatic Processes The DALR (ΓΓΓd) is The temperature of The rate at which the constant the parcel of air temperature decreases is throughout the will drop called the dry adiabatic atmosphere. according to the lapse rate (DALR .) DALR. The DALR (ΓΓΓ ), d The surrounding air The DALR (Γ ) is by itself, does d will normally be approximately 1 degree not tell us the equal to or greater for every 100 meters. temperature of than that the air at a prescribed by the ∆T / ∆z = Γd given height. DALR. Consider lifting a This is a stable parcel of air. situation.

22 Dry Adiabatic Processes Moist Adiabatic Processes

The atmosphere is almost A parcel of air may experience an adiabatic change always stable to dry in temperature through moist processes. adiabatic processes. in temperature through moist processes. The only time that one can find the atmosphere to be Consider water undergoing a phase change, ie unstable is at the surface when water vapour condenses in a parcel of air. on hot days. The air warms, but this didn’t require any Convection happens in such exchange in solar or terrestrial radiation. The net instances to quickly energy is conserved. make the atmosphere stable again.

Phase changes of water Moist Adiabatic Processes

ICE/LIQUID (freezing/melting) 3.3 J/kg (x 10 5) Consider lifting a parcel of air even further. It will ICE/VAPOUR (sublimation) 28.3 J/kg (x 10 5) VAPOUR/LIQUID(condense/evaporate) ~25 J/kg (x 10 5) continue to cool according to the DALR. At some height, the parcel will cool enough so that the air will reach its saturation point.

This height is called the lifting condensation level (LCL). Typically this is the height of the base of convective clouds.

Moist Adiabatic Processes Moist Adiabatic Processes

If we were to raise the air above this height, then Γw is not constant throughout the atmosphere. It can vary the excess vapour would condense. considerably with temperature and pressure. Energy is released when the water vapour A typical value may be roughly 6 K per kilometer. This Energy is released when the water vapour will always be less than the dry adiabatic lapse rate of condenses. 10 K per kilometer.

The parcel of air will now cool at a different rate ΓΓΓw < ΓΓΓd than the DALR. Air cools LESS quickly when rising along Γw instead of Γd The air cools at the saturated (or wet ) adiabatic because it is receiving latent energy from the lapse rate (SALR or Γw). condensation.

23 Moist Adiabatic Processes Convection - part 2

Let ’s review this diagram As the air rises, we considering the DALR know that it will (Γ ) and the SALR (Γ ). d w eventually reach the In the lowest 100 hPa , the lifting condensation dry air roughly follows a dry adiabat . This suggests level. the air is well mixed. If the cloud air is pushed Above this region , the air up higher, it will cool roughly follows a along a saturated saturated adiabat for suggesting the air is adiabat . saturated in this layer.

Convection - part 2 Convection - part 2

The air is no longer cooling as quickly as along a dry adiabat . It is possible that the cloud air will actually be warmer than the air surrounding it. This situation is Stable to dry Unstable to moist unstable. adiabatic lifting adiabatic lifting

Convection - part 2 Convection - part 2

The warm cloudy air will want Deep convection is critical to continue to rise, and deep process in the is likely to occur. circulation as it mixes vapour, energy and momentum The air will continue to rise throughout the . until it reaches a level where the surrounding air is once Representing convection in again warmer than the numerical models is still a cloudy air. challenging research topic.

24 Summary Summary Conditions for a Stable Atmosphere 1. Environmental lapse rate is small - i.e. the difference in Conditions for an Unstable Atmosphere temperature between the surface air and the air aloft is relatively small. Unstable atmosphere is characterized when the air Air aloft warms - how? Warm Air Advection temperature drops rapidly with height or surface air cools - how? Radiational Cooling Cold Air Advection Air moving over a cold surface Air aloft cools how? Cold Advection 2. Another way the atmosphere becomes more stable is Radiational cooling from clouds when an entire layer of air sinks (subsides)

Example: Large layer of air 1000 m thick subsides, the entire layer will warm due to Surface air warms how? Daytime solar Heating compression. As the layer subsides, it is compressed by the atmo spheric pressure and Warm surface advection shrinks vertically. Actually, the upper portion sinks farther and warms more than the Air moving over a warm surface lower portion. The upper portion will become warmer than the bottom forming an inversion. This type of inversion is known as a Subsidence Inversion And now ...

Summary Summary

1. Instability implies that if a parcel is given an initial boo st 5. Environmental lapse rates vary not only through time, but also upward, it will become buoyant and continue to rise. On with elevation. Thus, a column of atmosphere might be the other hand, if the air is stable, a parcel displaced unstable at one level but stable aloft. vertically will tend to return to its original position. 2. Static stability or instability is determined by the air column' s 6. No matter what the condition of the troposphere, the rate of temperature decrease with altitude. When the stratosphere is always statically stable and thereby limits temperature lapse rate is less than the saturated adiabatic the maximum height of updrafts. rate, the air is statically stable; when it exceeds the dry adiabatic lapse rate, it is unstable. Conditional instability 7. Inversions are a special case in which the temperature arises when the lapse rate is between the two adiabatic increases with altitude. Because of their strong static rates. When the air is conditionally unstable, a lifted stability, inversions suppress the vertical motions parcel will rise on its own accord only if it is lifted above a necessary for cloud formation and for the dispersion of certain critical point called the level of free convection. . Inversions are formed by subsidence 3. Three processes modify the lapse rate: the inflow of warm and (sinking air), the emission of longwave radiation from the cold air at different altitudes, the advection of a different surface, and the presence of fronts. air mass, and heating or cooling of the surface.

Review Questions Review Questions Reading

• Hess – Chapter 7 After lifting a parcel of air to a new level, if the parcel’s temperature equals that of the surrounding environment, • pp 92 - 106 what type of stability is characterized? • pp 110 - 112

25