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Chapter 5
Atmospheric Stability
© TAFE MECAT 2008
Introduction

In Chapter 4, we examined the concept of horizontal
and vertical atmospheric motion, and how pressure
differences create the winds that form on a variety of
different scales.

In this chapter, we examine the consequence of the
vertical lifting of air; atmospheric stability.
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Introduction

As you could predict from the terms, an atmosphere
that is stable will usually bring fine weather, and one
that is unstable may produce stormy weather.

This chapter answers the questions of what
constitutes a stable atmosphere and what changes
cause a stable system to decompose to an unstable
one.
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Equations of State

We now need to apply all of the physical aspects of
meteorology that we have learnt from the previous
chapters.

We will observe how buoyancy (which creates
convection) and the horizontal pressure gradient force
(hPGF), which creates advection) work together with
pressure, temperature and density to create the stable
and unstable weather we observe.
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An Equation of State
Where, at sea level;

=
atmospheric density in kg/m3
P
=
atmospheric pressure in kPa
R
=
gas constant
T
=
atmospheric temperature in K
(or virtual temperature)
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Equation of State

Using this equation we can determine the unknown
parameter by solving with the three known
parameters.

In the equation given, we are obviously solving for
density, but we can easily rearrange to solve for
pressure and temperature.
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Exercise

You would probably have encountered equations
similar to this in the laboratory calculations unit. Use
the skills you have learnt to solve the following
problems.

Solve the above equation for density given a pressure
of 99.4 kPa, and a temperature of 306 Kelvin.

Rearrange the equation of state above to solve for
pressure given a density of 1.18 kg/m3 and
temperature of 303 Kelvin.
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Equation of State

But what does all this mean?
 The
fact that these parameters are related means that if we
change one variable, we will change all the others as well
 We
therefore need to have a thorough understanding of how
they work
 For
example, if we change the temperature, does that
change the density of the air?
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The Gas Laws

The gas laws describe the relationships between all of
the physical variables that the atmosphere (or gases
in general) exhibit.

We cannot explore the behaviour of the atmosphere
without understanding the basics of how gases work.

Some of the relationships have been explored already,
but now we need to understand the mechanisms of
change by examining some of the calculations.
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Boyles Law
P1V1  P2V2

Boyles law states that;
 If
mass and temperature are kept constant, pressure and
volume are inversely proportional to each other

What this means is;
 if
we increase the volume, we decrease the pressure
 if
we increase the pressure we decrease the volume
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Charles Law
V1
V2

T1
T2

Charles Law states that;
 Under
constant pressure and mass, volume and
temperature are directly proportional to each other

This means that;
 if
we increase the temperature, we increase the volume
 if
we increase the volume we increase the temperature
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Gay-Lussac law
P1
P2

T1
T2

The Gay-Lussac Law states that;


Under constant mass and volume, temperature and pressure are
directly proportional to each other
This means that;

If you increase the temperature, you increase the pressure

If you increase the pressure you increase the temperature
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Avogadro’s Law
V1
V2

n1
n2

Avogadro’s Law states that;


Under constant pressure and temperature the volume is directly
proportional to the number of moles
This means that;

If you increase the volume you increase the number of moles

If you increase the number of moles you increase the volume

This law is the part that allows us to convert between mass and moles
and therefore is responsible for the density part of equations of state
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The Combined Gas Law

As the name suggests, it combines various part of the other
four laws.

The common form is seen as;
P1V1
P2V2

T1
T2

This contains Boyle’s, Charles and Gay-Lussac Laws, but derivations of
the Ideal gas Law are far more appropriate for mass / mole relationships
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The Ideal Gas Law

Scientist have found a better way to express the gas laws in
a more universal (thermodynamic) way, called the Ideal Gas
Law;
PV  nRT

This equation can solve for almost anything, assuming you
now where to put the formula weight of a compound! (with
the moles of course!)
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The Ideal Gas Law

This law can solve for the following;
 Pressure
 Volume
 Temperature
 Moles

But, apply a formula weight, it will solve for;
 Molar
mass
 Mass
 Density
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Exercise 5.2

This is a appropriate time to perform the gas laws
task found in the Ch 5 tab of the MetExplore
spreadsheet.

There you will find a variety of gas laws and other
interactive material that will shed light on this tricky
subject!
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The Pressure / Height Relationship

The second significant relationship we need to be
reminded of is the pressure/height relationship.

The pressure through a vertical slice of the
atmosphere is not the same – it follows a curved
pattern that decreases with altitude as seen in Figure
5.1 below.
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Plot of altitude versus pressure
Altitude (km)
40
35
30
25
20
15
10
5
0
0
200
400
600
Pressure (hPa)
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800
1000
The Pressure / Height Relationship

This is due to the compressibility of air (which creates
a pressure gradient), the gravitational force, as well as
the pressure gradient force.

As you could imagine, physicists have created many
formulas for calculating the change in pressure for any
given height (MetExplore spreadsheet Ch5).
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The Effect of Water

You should know by now that water has some very unique
properties;

a high specific heat capacity, found in all three states of matter,

highest density is at 4°C,

can easily sublimate under the right conditions, and there are many
more.

What you may not know is that water plays an enormous role in
determining the stability of weather,

This implies that measuring the relative humidity is important for
things other than knowing how comfortable (or uncomfortable)
the weather will be tomorrow!
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The Effect of Water

Let’s begin by understanding how water changes its
physical state, i.e. solid, liquid and gas (vapor).

The change of state is controlled by temperature,
obviously,
 solid
ice melts to become liquid water at 0°C (the melting
point),
 which

boils to become a gas at 100°C (the boiling point).
Figure 5.2 below shows the states of matter
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The Effect of Water

What you may not know is that water not only changes
state from liquid to gas at 100°C but also everywhere
in-between

Solid ice can change into gaseous water vapour
without first becoming a liquid!

This process is called sublimation
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Changes of State
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The Effect of Water

But you already new this, because this non-boiling
change of state is called evaporation!

This vaporisation of water produces a small partial
pressure which is added to all of the other partial
pressures exerted by the gases in the atmosphere

The pressure exerted by vaporised water in the
atmosphere is called the vapour pressure of water,
and is immensely important parameter in meteorology.
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The Effect of Water

Water evaporates at all temperatures, but obviously
more so at higher temperatures

The vapour pressure of water can have many units, a
common one being kPa or some other derivative.
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The Effect of Water
Pressure (mm Hg)
Plot of vapor pressures for liquid water
760
660
560
460
360
260
160
60
-40
274
294
314
334
Temperature (Kelvin)
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354
374
The Effect of Water

One derived unit of measure that you would be very
familiar with is called the relative humidity (% RH).
 The
% RH value is a measure of the moisture content as
vapour in the air.
 It
can be calculated directly from various equations, but most
people are familiar with looking the % RH value up from a
humidity table (MetExplore spreadsheet under the ‘Humidity
Table’ tab).
 Just
like vapour pressure, the % RH increases with
increasing temperature.
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The Effect of Water

We can start to look at the reverse situation in which
we see water vapour condense out of the air into liquid
water.

When vapor condenses to gas we call the air
saturated

Obviously we need a reduction in temperature for this
to occur, and the temperature at which this occurs is
called the dewpoint temperature.
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The Dewpoint Temperature

The dewpoint temperature effectively asks the
question

“to what temperature will we need to reduce a parcel of air in order to
achieve 100% RH (assuming a given temperature and relative
humidity <100 %)”.

We do this by calculating the dewpoint temperature.

To understand exactly how the air temperature,
dewpoint temperature and relative humidity are
related, it is best to view a graph
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Dewpoint vs dry bulb Temp
Relative Humidity (%)
Plot of T-T d versus % RH
120
100
80
60
40
20
0
0
5
10
15
20
Difference between Air & Dewpoint Temp (T - Td)
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25
The Moisture Density

Finally we need to look at

how air containing moisture exhibits a change in density

and how this density changes the buoyancy of an air parcel, which will
eventually lead to the rising or falling of an air parcel.

Figure 5.4 below shows how the density of air decreases as the
vapour pressure of water increases, but why is this so!

It is due to the fact that the molar mass of air is ~29, but that of
water is only 18, so the more water vapor you add, the less
dense the air becomes, the more buoyant air becomes.
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Plot of density versus vapor pressure
1.4
1
0.8
0.6
0.4
0.2
Vapor pressure (Pa)
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10
00
00
80
00
0
60
00
0
40
00
0
20
00
0
0
0
Density (kg/m 3)
1.2
Lifting Mechanisms in the Atmosphere

Applied to the atmosphere, the term ‘stability’ simply
means ‘resistant to change’.
 Any
upwards motion causes turbulence in the air
 To
achieve this turbulence we need to start ‘lifting’ the air, by
one (or more) of four mechanisms;

orographic lifting,

convergence,

diabatic heating and

frontal systems.
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Orographic Lifting

Orography is a concept in geography (specifically
topography) that deals with the height of land.
 Mountainous
terrain (can) provide a natural barrier to
horizontal winds, the consequence of which is the vertical
motion of air as the wind hits the mountain; it is forced to go
upwards (unless is can go around).
 The
process of a parcel or layer of air rising as a result of the
topography is referred to as orographic uplifting.
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Orographic Lifting

If the parcel or layer of air contains moisture then the
following sequence occurs as air rise’s up the side of a
mountain,

the pressure and temperature decrease adiabatically
until it reaches the lifting condensation level (LCL)
 The
LCL is that point in a parcel of air when the pressure
and temperature has dropped to the point were relative
humidity approximates 100 %, and clouds start to form
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Convergence

Convergence is another mechanism that can force air near the
surface to rise.

If winds blowing in different directions meet each other, the different
moving air masses become an obstacle to one another.

The air converges and has no place to go but upwards.

At the surface air flows inward to the center of low pressure where it
converges and then rises.

Convergence also occurs when air flowing over a smooth surface
suddenly hits a rougher surface and slows due to increased friction.

The air piles up at the rough surface where the friction is greater, and this
causes some of the air to move in a vertical direction.
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Convergence Lifting
Air is forced to lift
Advecting air
Advecting air
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Diabatic Heating

The radiation emitted by the earth (which comes from
the Sun) heats the air at the surface.
 Air
that is relatively warm compared to its surrounding rises,
and it can (and usually does) cool adiabatically.
 As
a result, the temperature drops in response to the change
in pressure as per the laws of adiabatic expansion and
compression.
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Diabatic Heating

Heating that occurs via the sun’s radiation as diabatic
heating, which is the opposite of adiabatic.
 The
suns radiation energy is absorbed by matter (air, land,
water etc), which results in the convection of warm air which
expands the air, creating a parcel that is of lower density and
therefore able to rise vertically through the atmosphere, and
is therefore a form of lifting.

You can safely assume that this is the most common
form of atmospheric lifting.
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Diabatic Heating
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Frontal Systems

The final lifting mechanism which we will discuss is the
overriding of air at frontal boundaries.

Moist air, because it is less dense, will override dry air. But how is this
different from convergence?

In the case of convergence, the lifting results from air molecules pushing
one another upward, like pushing two small piles of sand together with
your hands, forcing a larger pile to form.

When two frontal boundaries meet, the lifting that occurs is due to the
relative buoyancy of the two air masses.

The more buoyant air mass will override the lesser buoyant air mass.
The buoyancy is determined by the characteristics of the air masses (i.e.
temperature and moisture content).
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Frontal Lifting
Cold Front
Warm Front
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Adiabatic Processes

Think about where we are up to.

We now know all of the significant behaviours of the
atmosphere;


pressure changes,

temperature changes,

density changes,

and the relationships between these three variables;

the fact that air is convecting and advecting,

as well as the laws of buoyancy and adiabatic expansion and contraction.
Of all of these behaviours, the most important or ‘keystone’
variable behaviour is temperature.
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Adiabatic Processes

When air rise and cools (assuming adiabatically), it doesn’t just
get suddenly colder, the temperature changes by a certain
degree per unit of altitude, which we call a rate.

Because we talk about the temperature getting cooler, we refer
to the rate of change as the lapse rate, of which there are four
key rates to consider;

Dry

Saturated

Environmental, and

Dewpoint
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Adiabatic Processes

The key thing to remember here is that knowing the
rate at which rising air cools is vital in determining
the stability of the atmosphere.

One important distinction should be made at this time;
if a lapse rate increases, then the temperature gets
colder as an air parcel rises and vice versa.

To avoid confusion, we shall suggest in these notes
that parcels of air rise and fall, but lapse rate increase
or decrease.
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Dry Adiabatic Lapse Rate (DALR)

When a parcel of air rises, it expands, and the
temperature decreases.

Likewise, when air sinks, it compresses, and the
temperature increases.
 When
a parcel of air, either dry or containing water vapour
(<100%), rises or sinks without the addition or extraction of
heat, that process is said to be a dry adiabatic process.

Scientists have determined that this ‘theoretical’ lapse
rate is equal to 9.8°C/km (-9.8 if the parcel rises, + 9.8
if it falls).
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DALR
Plot of the Dry Adiabatic Lapse Rate
9.8 OC/km
12
Altitude (km)
10
8
6
4
2
0
-80
-60
-40
-20
Temperature (OC)
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0
20
40
Saturated Adiabatic Lapse Rate (SALR)

Note that the saturated adiabatic lapse rate (SALR) is
also called the moist (MALR), wet (WALR) (sometimes
even called pseudo) adiabatic lapse rate.

Colder air contains less water vapour due to the
adiabatic and gas laws,

When a parcel of air reaches its saturation point
(dewpoint), condensation begins and eventually
clouds will form.
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Saturated Adiabatic Lapse Rate (SALR)

As water vapour condensed to liquid water at the
dewpoint, latent heat is given off back to the air
parcels environment, thus warming the air.

In the reverse process, evaporation, we find that latent
heat is taken up from the air parcel, thereby cooling
the parcel of air.

Since no heat is exchanged between the parcel and
the environment, we still refer to this heating and
cooling as an adiabatic process.
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Saturated Adiabatic Lapse Rate (SALR)

However, during the processes of condensation and
evaporation, the cooling and heating of the saturated parcel
varies somewhat from the purely dry adiabatic process we
discussed above.

A rising saturated parcel cools at a slower rate due to the
release of latent heat, and a sinking saturated parcel heats
more slowly due to the conversion of heat energy during
evaporation.

This cooling of a rising (or heating of a sinking) saturated parcel
is called the saturated adiabatic process which has been
calculated to be an average of 6.5°C/km.
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DALR & SALR
Plot of the DALR (9.8OC/km) & SALR (6.5OC/km)
note that SALR is atmospheric average
12
Altitude (km)
10
8
DALR
6
SALR
4
2
0
-80
-60
-40
-20
Temperature (OC)
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0
20
40
Environmental Lapse Rate

So, the DALR is a sort of theoretical, calculated
‘moistureless’ lapse rate equalling 9.8°C/km,

and the SALR is a warmer lapse rate due to moisture
levels approximating 6.5°C/km.

So what do we get if we raise a weather balloon in the
air and measure the actual temperature of the
atmosphere?

The easy answer is environmental lapse rate (ELR).
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Environmental Lapse Rate

The problem is that the atmosphere can really be
doing three things when it comes to temperature. The
temperature at any point can be in a state of;
 Lapse
 Isothermal
 Inversion
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Environmental Lapse Rate

We already know that a lapse means a decrease with altitude,
so the environmental, or real, atmosphere is getting colder
(indicated by a negative slope on a graph).

Isothermal means ‘staying the same’, or ‘paused’, and so the
temperature remains constant with altitude (indicated by a
vertical line on the graph).

Yet sometimes we can see an increase in temperature with an
increase in altitude, and this is called a temperature inversion.

These three states can be seen on the hypothetical plot in
Figure 5.12 below.
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ELR
Lapse
Inversion
Isothermal
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Dew-point Adiabatic Lapse Rate

Even though a parcel of air may contain moisture, if
the parcel is rising, then it cools according to the dry
adiabatic lapse rate until it reaches the dew point
temperature, Td.

We refer to the pressure where the actual temperature
equals the dew point temperature as the Lifting
Condensation Level (LCL).

At the LCL, the cooling process becomes a moist or
saturated adiabatic process.
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Stable, Neutral and Unstable Atmospheres

The stability of the atmosphere is basically determined
by comparing the lapse rate of a parcel of air to the
lapse rate of the surrounding air

If we know the temperature and dew point of the air
parcel before it begins to rise, then we can pretty
accurately determine the temperature change as it
rises.

Measurement data provides us with a profile of the
environment with which to compare our rising air.
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Stable, Neutral and Unstable Atmospheres

We have found that there are three basic categories in
which the atmosphere or a layer in the atmosphere
can be classified in terms of stability. These
categories, which we discuss next, are stable,
unstable and conditional.
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The Stable Atmosphere

As previously mentioned, a stable atmosphere is
strongly resistant to changing its vertical position
(regardless of the height of the atmosphere)
 If
there was some force trying to push the air up or down, in
a stable atmosphere this ‘push’ would be resisted
 If
pushed, the parcel would move back to where it came
from.
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The Stable Atmosphere

Reference 2 states that “In a stable atmosphere, if
you lift a parcel of air, the temperature of the rising air
will decrease fast enough that its temperature will
always be colder than the temperature of the
environment. Colder air sinks. If the force pushing the
air up suddenly disappeared, the parcel would sink
back down to its original position where its
temperature and pressure would be in equilibrium with
the environment.” This is indicated by figure 5.13
above.
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
Absolute stability occurs when ELR is less than
SALR (and therefore less than DALR). This means
that ELR must be lower than SALR (which varies
between 3.9ºC/1km and 7.2ºC/1km) which will never
be more than 7.1ºC/1km (if SALR is at its maximum).

Neutral stability occurs when ELR and DALR are
equal. That is, when ELR is 9.8ºC/1km. It is called
'neutral' because the thermal keeps its initial
momentum and does not accelerate or slow down.
This is not indicated in figure 5.13.
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The Unstable Atmosphere

An unstable atmosphere is one where a parcel or
layer of air is encouraged to rise or fall. In an unstable
layer, the lapse rate of a rising parcel is less than the
lapse rate of the environment. Because the parcel is
warmer than the environment, the parcel has positive
buoyancy and continues to rise on its own.2
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The Unstable Atmosphere

Absolute instability occurs when ELR is greater than
DALR. We have learned that DALR is 9.8ºC/1km,
therefore we can conclude that absolute instability
exists when ELR is 9.9ºC/1km or greater.
Meteorologists call this a "super-adiabatic lapse rate"
since heat loss with elevation is so rapid.4
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Conditional Instability

To determine if the atmosphere is conditionally
unstable, we compare the lapse rate of a parcel to the
environment as it passes through the LCL.

The atmosphere is described as conditionally unstable
if the environmental lapse rate is less than the dry
adiabatic lapse rate beneath the LCL and greater than
the saturated adiabatic lapse above the LCL.

So, conditional instability can be easily determined by
making a comparison of all three lapse rates.
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Conditional Instability

Conditional Instability occurs when ELR is less than
DALR but more than SALR.

In other words, it is when ELR is between SALR
(which varies between 3.9ºC/1km to 7.2ºC/1km) and
DALR (which is 9.8ºC/1km).

The 'condition' for instability is only when the thermal
becomes saturated, not before.
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Conclusion

Atmospheric stability is not an easy concept to absorb.

Overall, meteorologists use weather balloons to
measure the vertical layers of the atmosphere for
many parameters including temperature and pressure.

From this data they produce one of four common
thermodynamic diagrams to examine the atmospheres
stability (SkewT-LogP, Tephigrams, Stuve Diagrams
and Emagrams).
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© TAFE – MECAT 2008