PHSC 3033: Meteorology Stability

Equilibrium and Stability • Equilibrium’s 2 States:

– Stable – Unstable

Perturbed from its initial state, an object can either tend to return to equilibrium (A. stable) or deviate away (B. unstable).

Environmental Lapse Rate (ELR) Γ = - ∆T/∆z Measured change in Temperature with Altitude Radiosondes yield information about the environmental lapse rate. It is what it is…on average ~ 6.5oC/1000m. This lapse rate can be equal to, less than, or greater than either the dry adiabatic lapse rate or moist adiabatic lapse rate. Determining stability involves asking what happens to a parcel of air if there is a small perturbation (vertical motion). What is its equilibrium like, stable or unstable?

Figure 6.4

Figure 6.3

Rising and Sinking Air Rising air expands and cools. Sinking air contracts and warms.

Adiabatic Process • Expansion and cooling or compression and heating without

any thermal exchange with the environment is an adiabatic process.

Adiabatic Lapse Rates ΓDry = - ∆T/∆z = -g/Cp { ~10oC/1000m } = -9.8 m/s2 ÷ 1004.67 J/kg/K ΓWet = - ∆T/∆z { ~ 6oC/1000m }

Eureka! In air, scale reads the weight W = T1. Immersed in water, the additional buoyant force reduces the objects weight T2 = W-Fb

Displaced fluid weight = ρfVo g = Fb (Archimedes’ Principle)

T1

W

T2

W

Fb

Buoyancy • Archimedes Principle: The buoyancy force is equal to the

weight of the volume of fluid displaced.

Weight of the volume of fluid* displaced ρfVog

Weight of the object ρoVo g

The net force on an object is its weight minus the buoyancy F = ρo Vo g - ρfVog *The environmental air is treated as a fluid in which a parcel of air is immersed.

Buoyancy and Acceleration Acceleration = Force/mass F = Weight - Fb F = ρo Vo g - ρfVog Acceleration = g(ρo Vo - ρfVo)/m = g(ρo - ρf)/ρo

Replacing densities using the ideal gas law P = ρ k T, yields an equation for the acceleration of the air parcel, given the temperature of the parcel (To) and the environment (Tf). Acceleration = g(Τo - Τf)/Τo Large temperature differences favor acceleration. a ~ ∆T

Environmental lapse Rate (ELR) is black unsaturated adiabatic parcel path (blue) saturated parcel path (red)

A) unstable parcel in unsaturated environ B) stable parcel in unsaturated environ C) unstable parcel in saturated environ D) stable parcel in saturated environ

Summary of categories of atmospheric layer stability

Environmental lapse rate ( Γ = ELR) Stability Γ = ELR > 10°C/km Unstable

Dry Adiabat Wet

Adiabat

Summary of categories of atmospheric layer stability

Environmental lapse rate ( Γ = ELR) Stability Γ = ELR > 10°C/km Unstable 6°C/km < ELR < 10°C/km Conditionally unstable (Unstable if saturated, stable if unsaturated) ELR < 6°C/km Stable ELR = 10°C/km Neutral if unsaturated, unstable if saturated ELR = 6°C/km Neutral if saturated, stable if unsaturated

Stability Conditions An atmosphere with an environmental lapse rate (ELR) will be... Always Stable if ELR < ΓDry ELR < ΓWet Always Unstable if ELR > ΓDry ELR > ΓWet

Absolute Stability (Dry) The parcel of air is cooler and heavier than the surrounding air around it at all levels. Γ < Γdry When perturbed it will tend to return to its original position.

Absolute Stability (Wet) The atmosphere is always stable when the environmental lapse rate is less than the moist adiabatic rate. Γ < Γwet

Convective Uplift Vertical Motion via Convection: exchange of thermal energy by mass motion. Hot air rises because it is less dense. Lifting a parcel of air to a height where condensation occurs, releases the latent heat stored in the water vapor as clouds form.

Lifting Mechanisms in the Atmosphere

Frontal Uplift Vertical Motion via Frontal Uplift: a cold air mass encounters warm air or a warm air mass encounters cooler air. Since colder air is more dense, it displaces the warm air upward in a cold front or a warm front along the air masses boundary.

Orographic Uplift Vertical Motion via Orographic Uplift: air that encounters steep topography is forced to rise.

Convergence Uplift Vertical Motion via Convergence: advection winds that encounter each other force rising motion away from the surface. Air rises because there is nowhere else to go.

Absolute Stability

A Stable Atmosphere • Stability favors a small environmental lapse rate. • Ways to make the lapse rate small….

– Warm the air aloft (Inversions)

• warm advection (warm front) • slowly sinking air (high pressure)

– Cool the air near the ground (Fogs) • calm night radiative cooling • cold advection (cold front) • air moving over a cold surface

Absolutely Unstable (Dry) The atmosphere is always unstable when the environmental lapse rate is greater than the dry adiabatic rate. Γ > ΓDry > ΓWet

Absolutely Unstable (Wet) The parcel of air is warmer and lighter than the surrounding air around it at all levels. When perturbed it will tend to accelerate away from its original position.

Absolutely Unstable

Conditional Stability (Dry) In this example the dry air is cooler and heavier than the air around it at all levels. It is stable. The environmental lapse rate is less than the dry adiabatic lapse rate. But, ΓDry > Γ > ΓWet

Conditionally Unstable (Wet) A saturated parcel is warmer than the surrounding air at all levels. It is unstable. With an environmental lapse rate between the dry and moist adiabatic rates, stability depends upon whether the air is saturated or not.

Conditional Stability If air can be lifted to a level where it is saturated, instability would result.

Figure 6.7

Table 6.2

Table 6.2 Stability categories and likelihood of severe convective storms for various ranges of the Lifted Index (LI), Showalter Index (SI), Convective Available Potential Energy (CAPE), Total Totals (TT) index and SWEAT index.

Stability LI SI CAPE TT SWEAT Very stable > +3 (no significant activity) Stable 0 to +3 > +2 < 0 (Showers possible; T’showers unlikely) Marginally unstable −2 to 0 0 to 2 0 - 1000 45 - 50 (T’showers possible) Moderately unstable −4 to –2 −3 to 0 1000 - 2500 50 - 55 250 -300 (Thunderstorms possible) Very unstable −6 to –4 −6 to –3 2500 - 3500 55 - 60 300 -400 (Severe T’storms possible) Extremely unstable < −6 < −6 > 3500 > 400 (Severe T’storms probable; tornadoes possible)

Figure 6B

Conditional Stability

Conditional Stability

Instability Causes • Instability favors a large environmental lapse rate. • Ways to increase the lapse rate large….

– Cool the air aloft • cold advection (jet stream) • radiative cooling (emitting IR to space)

– Warm the air near the ground • warm advection • daytime solar heating of the surface

Mixing Instability

Mixing may occur via convection or turbulence.

Stratocumulus

Stratus Formation Mixing stable air close to saturation can cause stratus-type clouds. The upper layer cools and saturates while the lower layer warms and dries out, increasing the environmental lapse rate.

Rising Instability • As a stable layer rises, the change in density spreads it out.

If it remains unsaturated, the top cools faster than below.

Convective Instability An inversion layer with a saturated bottom and an unsaturated top. The top cools at ΓDry

while the bottom cools at ΓWet because of latent heat release. This leads to absolute instability associated with severe storms.

Cumulus Convection A warm wet bottom and a cool dry top. Convection leads to large vertical development while the sinking air in between the clouds is clear.

Cumulus Conditions

Cumulus Development Instability may reach to the top of the troposphere where cumulonimbus clouds “anvil” out in response to the stable inversion layer of the stratosphere.

Mountain Rain Shadow Orographic lifting, adiabatic cooling, heating and loss of moisture content.

Adiabatic Chart (Rain Shadow Example)

Summary • A parcel of air in stable/unstable equilibrium will return/depart its

original position. • A rising parcel of unsaturated air will cool at the dry adiabatic rate of

(~ 10oC/1000m); a descending unsaturated parcel warms at this rate. • A rising parcel of saturated air will cool at the moist adiabatic rate of

(~ 6oC/1000m); a descending saturated parcel warms at this rate. • The environmental lapse rate is the rate that the actual air temperature

decreases with increasing altitude. Γ = - ∆T/∆z • Absolute Stability: Air at surface is cooler than air aloft (inversion), or

the environmental lapse rate is greater than the dry adiabatic rate. • Instability can be initiated if surface air warms, air aloft cools, or

vertical lifting occurs (convection, convergence, fronts, topography). • Conditional Instability: Environmental lapse rate is between the moist

and dry adiabatic rates. Unsaturated air is lifted to a point where condensation occurs and becomes warmer than the surrounding air.

Relative Humidity The relative humidity can be calculated from the vapor pressure (e) and saturation vapor pressure (es) and/or the mixing ratio (w) and saturation mixing ratio (ws) RH % = 100 (e/es) = 100 (w/ws)

Temperature

Vapor Pressure (mb)

or Mixing Ratio

(g/kg) (T,e) or (T,w)

(T,es) or (T,ws)

Dew Point The dew point temperature (Td) can be taken from the temperature and saturation vapor pressure (es) and/or the saturation mixing ratio (ws). RH % = 100 (e/es) = 100 (w/ws)

Temperature

Vapor Pressure (mb)

or Mixing Ratio

(g/kg) (T,e) or (T,w)

Td

Wet-Bulb Temperature At a given pressure level, do the following: •From the temperature, proceed up along a dry adiabat. •From the dew point proceed up along a mixing ratio line. •At the intersection, proceed down the saturation adiabat to the original level. In this example, air at 850 mb with T = 20°C and Td = 0°C has a wet-bulb temperature of 10°C.

Lifting Condensation Level (LCL) The LCL is located on a sounding at the intersection of the saturation mixing-ratio line that passes through the surface dew point temperature with the dry adiabat that passes through the surface temperature. In this example, air at the surface with T=9°C and Td=0°C will become saturated if lifted dry adiabatically to 870 mb.