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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)
Fb
T1
T2
W
W
Buoyancy
• Archimedes Principle: The buoyancy force is equal to the
weight of the volume of fluid displaced.
Weight of the volume of fluid* displaced
ρ f Vo g
Weight of the object
ρ o Vo g
The net force on an object is its weight minus the buoyancy
F = ρ o Vo g - ρ f Vo g
*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)
Γ = ELR > 10°C/km
Dry
Adiabat
Stability
Unstable
Wet
Adiabat
Summary of categories of atmospheric layer stability
Environmental lapse rate ( Γ = ELR)
Γ = ELR > 10°C/km
6°C/km < ELR < 10°C/km
Stability
Unstable
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
Very stable
(no significant activity)
> +3
SI
CAPE
Stable
(Showers possible;
T’showers unlikely)
0 to +3
> +2
<0
Marginally unstable
(T’showers possible)
−2 to 0
0 to 2
0 - 1000
Moderately unstable
(Thunderstorms possible)
−4 to –2
−3 to 0
Very unstable
(Severe T’storms possible)
−6 to –4
−6 to –3
Extremely unstable
(Severe T’storms probable;
tornadoes possible)
< −6
< −6
TT
45 - 50
1000 - 2500 50 - 55
2500 - 3500 55 - 60
> 3500
SWEAT
250 -300
300 -400
> 400
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)
(T,es)
or
(T,ws)
Vapor Pressure
(mb)
or
Mixing Ratio
(g/kg)
(T,e)
or
(T,w)
Temperature
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)
Vapor Pressure
(mb)
or
Mixing Ratio
(g/kg)
(T,e)
or
(T,w)
Td
Temperature
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.