Download Chapter 4. Atmospheric Temperature and Stability

Chapter 4. Atmospheric Temperature and Stability
4.1 The temperature structure of the atmosphere
Most people are familiar with the fact that the temperature of the atmosphere decreases
with altitude. The temperature outside a commercial airliner at 12 km (36,000 ft) is
typically -40°C or colder. Mountains are often capped with snow and ice, while adjacent
valleys are green and lush. In this section we introduce students to the physical principles
that explain the decline of atmospheric temperatures aloft and examine the condensation
process in clouds and its effects on atmospheric temperature. We then study the concept
of stability: what determines whether air is buoyant and convection can take place, or
whether the atmosphere is stable and air parcels tend to return to their original altitude
when displaced. The circulation in the atmosphere, which is driven to a large extent by
convective motions, is discussed in Chapter 5; radiative processes (absorption and
reflection of sunlight, thermal radiation (radiant heat)), which also play important roles in
determining temperature and climate, are discussed in Chapter 6.
60
Latitude=30N
50
mesosphere
30
20
Altitude (km)
40
stratosphere
Fig. 4.1 Average observed
temperature distribution with
altitude. The temperature of the
atmosphere on average in
summer is shown for 30° N
latitude, along with the names
given to the major regions of the
atmosphere (troposphere,
stratosphere, mesosphere). The
upper boundaries of the
troposphere and stratosphere
("tropopause", "stratopause",
respectively) are indicated as
horizontal lines.
0
10
troposphere
220
240
260
280
300
T (K)
The lowest region of the atmosphere, up to the first temperature minimum at 12 - 16 km,
is known as the troposphere, a name derived from the Greek words tropos, turning, and
spaira, ball. The troposphere is relatively unstable because of the decrease of temperature
with altitude. Air in the troposphere is poised to over-turn (to convect) much like water in
1
a kettle heated from below. Most of the weather of the planet is confined to the
troposphere. The upper boundary of the troposphere, the altitude corresponding to the
temperature minimum, is known as the tropopause.
Temperature increases with altitude in the stratosphere (tropopause to 45 km), from the
Latin word stratus meaning stretched out or layered. Vertical motions are strongly
inhibited in the stratosphere as a consequence of the increase of temperature with altitude;
an air parcel that is pushed upwards becomes denser than the air it seeks to displace and is
driven back to its point of origin as we discuss below. The temperature maximum near 45
km (the stratopause) marks the upper boundary of the stratosphere. As we shall see,
most of the world's ozone (O3) is contained in the stratosphere. Stratospheric ozone is
vitally important to life because it absorbs harmful ultraviolet light from the sun,
preventing it from reaching the earth's surface. Stratospheric ozone has been studied
intensively for the last 30 years, reflecting concerns that global-scale changes have been
caused by human activities (Chapter 7).
The region of decreasing temperature above the stratopause is known as the mesosphere
(from the Greek word mesos, middle). Above the mesopause (85 km) there is a region of
very rapidly increasing temperature called the thermosphere (not shown in the figure),
which attains the highest temperatures observed anywhere in the atmosphere. Densities
are extremely low, and satellites orbit Earth for extended periods of time in the
thermosphere. Thousands of kilometers above the surface, the atmosphere merges slowly
with the interplanetary medium.
4.2 Displacement of an air parcel with altitude: work done by an air parcel on the
atmosphere
We now examine one of the basic factors causing atmospheric temperatures to decrease
with altitude in the troposphere: work must be done on the atmosphere by a rising air
parcel. (The other major factor, atmospheric radiation, is discussed in Chapter 6).
Consider taking a parcel of air and moving it vertically from altitude Z1 to Z2 (see Fig.
4.2), not allowing heat or mass to exchange between the parcel and the environment. If we
initially keep the volume fixed, then the pressure remains equal to P1. From the barometric
law, we know that the ambient pressure P2 at Z2is lower than the initial pressure P1 that
the parcel had at Z1, and we therefore allow the parcel at Z2 to expand until the pressure
inside is equal to the ambient pressure.
As the air parcel expands, it pushes against the force due to the pressure of the
surrounding atmosphere, doing work (Chapter 2). To do this work, the parcel requires
energy, but we have not allowed heat to be added to the parcel. Where does this energy
come from? The only source is the kinetic energy of the molecules inside the air parcel.
We know from Chapter 2 that this internal energy is related directly to temperature, E =
3/2 kT. Since energy is conserved ("1st Law of Thermodynamics") the work done by the
parcel on the atmosphere must be accompanied by a drop in temperature. This is a
fundamental reason why atmospheric temperature decreases with altitude.
2
We can determine the temperature change of an air parcel with altitude when the parcel
moves verticall without exchanging any heat with its surroundings. This quantity, ∆T/∆Z,
is called the adiabatic lapse rate. (The term adiabatic refers to the fact that the parcel is
not permitted to exchange heat with the atmosphere.) Consider an air parcel with mass m
15
Pressure and work on a vertically-displaced air parcel
Z (km)
10
The parcel
does work on
the atm
expanding from
P1->P2 at Z2
P2,Z2
P1,Z2
P1,Z2
P1,Z1
P1,Z1
0
5
P2,Z2
0.0
0.4
0.8
Figure 4.2 Vertical
displacement of an air parcel.
This diagram illustrates
schematically the upward
displacement of an air parcel in
the atmosphere, from altitude Z1
to Z2.. No exchange of heat or
mass is allowed with the
environment. Since pressure
decreases with height (left panel,
barometric law), the parcel will
expand in volume and pressure
will drop inside; in the process,
the parcel does work on the
atmosphere at Z2, and the
temperature of the parcel
decreases by an amount given by
the adiabatic lapse rate.
P (bar)
that is raised distance ∆Z, for example, due to the wind blowing over a mountain. As our
parcel goes up the mountain, another parcel goes down. Let us suppose that the
distribution of temperature and pressure in the atmosphere is so arranged that no energy
has to be supplied to effect the switch--the parcel that is falling gains just enough energy
to pull the other parcel up, like a perfectly matched pair of cable cars. What will be the
relationship between temperature and pressure, given that pressure and altitude obey the
barometric law? Since no energy needs to be supplied to exchange the parcels, and work
is done against gravity by the rising parcel, there must be an exact trade between internal
energy and gravitational energy. That means that the sum of these two is same in all
parcels with the same mass at any altitude. The work done against gravity (mg∆Z, see
work defined in Chapter 2) must exactly balance the amount of energy extracted from
the internal kinetic energy of the air molecules in the air parcel. The extracted energy
is defined as -m cp ∆T, where cp is the specific heat of air, the amount of energy required
to raise the temperature of 1 kg of air by 1°C (cp 1005 J/kg). We therefore know that the
two quantities are equal (work against gravity and energy extracted from molecules):
mg ∆Z=-m cp∆T
Eq. 4.1a
which can be re-arranged to yield the remarkably simple
∆T / ∆Z = -g / cp = -9.8° C / km.
Eq. 4.1b
∆T / ∆Z, the adiabatic lapse rate, is the temperature change for an air parcel (cools if it
moves up, warms if it moves down) when it suddenly moves from one altitude to another.
3
Our special atmosphere, where all parcels move up or down freely without exchanging
energy with the environment, is said to be neutrally stable as discussed below.
There are many ways that an air parcel can be forced to move adiabatically in the real
atmosphere. If the air blows over an obstacle, such as a mountain, the upward motion on
the front side and downward motion on the rear side occur too rapidly for heat or mass to
be exchanged with the surroundings. If air near the ground is heated, for example by
absorption of sunlight by the ground, then the scale height H increases and the whole air
column will be pushed upwards. Air parcels forced to move in this way have no way to
know if their motion is balanced by that of other air parcels, or if they are being push up or
down some other way.
Therefore, air parcels forced to move up or down adiabatically and which maintain
pressure equal to the surrounding atmosphere, change temperature with altitude as
given by the adiabatic lapse rate (Eq. 4.1b). Note that the ambient atmosphere need
not have this lapse rate (usually the atmosphere is not neutrally stable), so the parcel that
has moved will usually be at a different temperature than the surrounding air. It will
therefore have a different density (Perfect Gas Law).
This distinction, between the temperature change in a parcel forced to move vertically and
the temperature change with altitude in the ambient atmosphere, represents a key concept
in the discussion that follows.
10
4.3 Stability
adibatic
4
6
Fig 4.3 Ambient lapse rates and parcel
temperature changes. Schematic diagram
showing stable (Curve A) and unstable (Curve B)
temperature profiles for the ambient atmosphere,
compared to the lapse rate followed by a parcel
subjected to adiabatic vertical displacement.
0
2
Altitude (km)
8
A
stable
B
unstable
200
220
240
260
280
300
T (Kelvin)
Figure 4.3 shows the adiabatic lapse rate and two hypothetical profiles for atmospheric
temperature. In profile A, the atmosphere cools with altitude at a rate ∆T/∆Z= -6.5 K/km, less
rapidly with altitude than the adiabatic lapse rate. Suppose an air parcel is moved adiabatically
upwards a short distance in this atmosphere. The pressure decreases according to the barometric
law and temperature decreases according to the adiabatic lapse rate. The temperature of the air
parcel will therefore be lower than the temperature of the surrounding atmosphere. The parcel
will therefore be denser than the surrounding air. It is negatively buoyant and will tend to sink
back to where it came from. The atmosphere in profile A is stable, i.e. parcels given a little push
4
up or down return to where they started. If we wanted to take a parcel to a higher altitude in this
atmosphere, we would have to warm it, i.e. supply heat.
In profile B, the atmosphere cools with altitude at a faster rate, ∆T/∆Z=-10 K/km, than the
adiabatic lapse rate. An air parcel moved upwards will warmer than the surrounding atmosphere,
therefore less dense and thus buoyant. The parcel will tend to continue to rise due to buoyancy,
and the atmosphere is unstable.
If the atmospheric temperature profile were the same at the adiabatic lapse rate, an air parcel
moved up or down would have the same density as the surrounding air and have zero buoyancy,
the case of neutral stability discussed above.
Exercise: explain why a parcel given a push down in a stable atmosphere will return to its
original altitude.
Exercise: Consider an atmosphere with a lapse rate of -10 K/km. Show that an air parcel
displaced downward 100m is negatively buoyant and will be accelerated downwards. Find the
magnitude of the acceleration. Estimate the velocity of this parcel when it has descended 200m,
if the acceleration stayed constant. Do you expect that it would actually be moving faster, or
slower, when it reaches this level?
4.4 Convection
Dry Convection
In class we observe a demo in which a tank of water is heated on one side and allowed to return
to room temperature on the other. Small particles are suspended in the water so that we can
observe the motion of the fluid. The warm water rises in a column, then spreads out horizontally
as it cools off, descends on the cooler side, and flows back towards the heated side to make a
loop. Where the water is heated, buoyancy is generated, since the density of the warmer water is
lower than the density of the rest of the water in the tank. The rising column of fluid moves mass
into the upper part of the tank on the heated side, slightly increasing the depth of the column of
water, and thus the pressure, on the heated side. The water spreads horizontally pushed by this
pressure gradient, forming the circulation loop (see further discussion of pressure forces in
Chapters 5 and 6).
The experiment is the analogue of the sea breeze: the heating is provided by sunlight over the
land, warming the surface and raising air temperatures. The atmosphere over the land on a sunny
afternoon has typically been stirred sufficiently to reach a state where the lapse rate is
approximately adiabatic (Eq. 4.1b) through the lowest 1-3 km, i.e. the atmosphere is neutrally
stable. Additional heating of the ground raises the temperature and makes the local lapse rate
unstable, allowing air parcels to rise rapidly in what is called the atmospheric mixed layer. Over
the sea, the surface hardly warms, setting up a situation analogous to that in the tank.
5
Planetary boundary layer
During the daytime, solar heating develops a planetary boundary layer over land, in which dry
convection vigorously stirs the atmosphere from the ground to altitudes of 1 - 3 km, as illustrated
in Figure 4.4a. Suppose that, at sunrise, the atmosphere initially has a stable lapse rate of -6.8
K/km. Solar heating warms air near the ground rapidly, until the lapse rate reaches -9.8 K/km.
Convection then begins, and the warm air parcels mix with the ambient atmosphere until a neutral
condition is reached where the lapse rate is approximately adiabatic. As the day progresses, the
convective mixed layer, also called the planetary boundary layer, gets deeper and deeper. As day
ends, the atmosphere gradually cools by emitting infrared (heat) radiation, restoring a stable lapse
rate through the night. The process can then repeat the next day.
Figure 4.4a. Schematic diagram of the lapse rate
just before sunrise (stable) and in mid-afternoon
(neutral or slightly unstable). Dry convection driven
by solar heating stirs the lower atmosphere, creating
the planetary boundary layer or mixed layer during
daytime over land.
The convection in the mixed layer rapidly redistributes gases such as water vapor or
pollutants that are emitted from the earth's surface.
Figure 4.4b. Convection in the
atmospheric mixed layer.
Photograph showing puffy little
clouds, called fair weather
cumulus, occurring over land on a
typical afternoon. The lapse rate
in the mixed layer is approximately
adiabatic, and air parcels heated
near the ground are buoyant. Each
little cloud represents the top of a
buoyant plume.(Photograph
courtesy University of Illinois
Cloud Catalog).
The generation of convective plumes by solar heating of the ground is often apparent in
the afternoon when weather is fine. Little puffy clouds develop at the top portion of these
plumes, all with the same altitude at the bottom. Air parcels moving up cool off according
to the adiabatic lapse rate, -9.8°K/km, and therefore the cloud bottom is determined by the
altitude where the water content of the air brings the relative humidity (Chapter 3) to
6
100%. The association between convection and these "fair weather cumulus clouds" is
apparent to the air traveler, since the air is always rough in the mixed layer and the pilot
asks passengers to buckle their seat belts shortly before entering the cloud layer. When the
plane passes through a cloud, the ride can be very bumpy indeed, because the plane is
sampling the core of convection plumes. The air is moving downward between the clouds,
as it must to keep the mass balanced, just as it did in the "sea breeze" demo, but the
location of the rising and descending motions are distributed over the landscape, not lined
up along the beach.
Wet convection
Wet convection occurs when condensation of water in a rising air parcel adds enough heat
to make air parcels significantly more buoyant than they would have been if they were dry.
An unstable situation may be created when a parcel moves up, cooling causes
condensation, and the latent heat release raises the temperature of the parcel. If the
amount of condensation is sufficient, the parcel may become buoyant relative to the
surroundings just due to the release of latent heat. In this case the release of latent energy
would accelerate the upward motion, leading to more condensation. Wet convection can
produce a deep cloud with rain or snow. It is quite typical for the atmosphere to be stable
for small displacements of an air parcel, but for condensation that occurs with larger
displacements to add enough additional heat to make the parcel buoyant. This situation is
called conditional instability, indicating that a given finite displacement is needed to make
air parcels buoyant.
We examine the effects of condensation of water on atmospheric temperature and
buoyancy in two examples--the first representing a relatively dry atmosphere, the second a
moist summer day or a day in the moist tropics.
4.5 Conditional Stability
We start with a parcel of air at the surface that has a given amount of water vapor, relative
humidity less than 100% (see Fig. 4.5). Since the parcel is undersaturated, it cools at the
dry adiabatic lapse rate if forced to rise and no condensation occurs. But as the
temperature continues to decrease, the temperature may reach the condensation point as
given by the Clausius-Clapeyron equation, i.e., the relative humidity of the parcel will
reach 100%. Condensation will start at this point, and the parcel will cease cooling at the
dry adiabatic rate. Latent heat is being released, thus the process in no longer adiabatic.
Addition of heat makes the parcel cool at a slower rate. The resulting lapse rate is called
the "moist adiabatic lapse rate", because the heat comes from condensation within the
parcel, not from the external environment. This moist lapse rate (or "pseudo-adiabat",
since the process is not truly adiabatic) depends on temperature and water vapor content,
unlike the dry adiabatic lapse rate that is the same everywhere in the atmosphere.
7
5
5
Conditional instability: deep convective clouds (rain)
Tg 308, dewpt 305 [RH84%], atm lapse -8.5K/km
5
5
Conditional stability: fair weather clouds (no rain)
=> Tg 303, dewpt 290 [RH 45%], atm lapse -6.5K/km
Parcel
no cond.
atm.
T(Z)
atm.
T(Z)
satd
actual (w/cond)
4
3
1
1
2
dry
adiabat
(parcel)
ALTITUDE (km)
3
4
wet parcel
pseudoadiabat
2
ALTITUDE (km)
4
3
2
1
2
3
ALTITUDE (km)
dry
adiabat
(parcel)
1
ALTITUDE (km)
4
wet parcel
pseudoadiabat
Parcel
no cond.
Cloud
base
satd
270
280
290
T (K)
300
0
10
20
30
40
0
0
0
0
actual (w/cond)
270
Water Vapor Pressure
(mbar)
Figure 4.5 Rising air parcel, low water vapor
content. Bold red line shows the trajectory of an
air parcel forced to rise ("pseudoadiabat"). Also
shown are the dry adiabat and the atmospheric
profile (upper curve).
280
290
300
T (K)
0
10
20
30
40
50
Water Vapor Pressure
(mbar)
Figure 4.6 Rising air parcel, high water vapor
content. Bold red line shows the trajectory of an
air parcel forced to rise ("pseudoadiabat"). Also
shown are the dry adiabat and the atmospheric
profile (middle curve).
Convective cloud over Amazonia
3
Z
km
latent heat
release
2
1
Tdew
cloud base
Tdew = Tair
0
283 293 303
Temperature
K
Figure 4.7. An example of a cloud similar to the diagram in Figure 4.5, showing the updrafts in the
center (left panel) and the distribution of temperature and dew point in the interior of the cloud
(right panel). The billowing shape, but limited size, indicates that the cloud is probably slightly
buoyant. (Photo: © Steven C. Wofsy, Manaus, Brazil, 1987.)
8
In the examples in Figures 4.5 - 4.7, we have atmospheres with stable lapse rates, less
negative than the dry adiabatic lapse rate (curve labeled "atm"). In Fig. 4.5, let us examine
what happens if we displace an air parcel from the surface with a specific humidity of
about 0.016 kg of water vapor per Kg of air. From the plot of the saturated specific
humidity on the right we see that at surface temperatures the parcel is undersaturated.
Let's raise the parcel to 5 km above the surface. Initially, the parcel cools at the dry
adiabatic lapse rate. Near 2 km above the surface condensation begins and the parcel
thereafter cools more slowly, at the moist lapse rate. If we take this parcel all the way to 5
km, the parcel remains cooler than the surrounding air, and most of the water has been
condensed. Therefore the atmosphere is stable, even for finite displacements of air parcels.
Fair weather cumulus will form at about 1.7 km altitude, which will be the cloud base.
There will not be any rain showers.
Figure 4.6 shows a similar example, but with higher initial temperature and more water
vapor in the air parcel. Red lines show the trajectory of the air parcel. We have also
assumed a somewhat steeper lapse rate in the atmosphere (less stable, -8°/km vs. -6.5° in
Fig. 4.5; this would be typical of the tropics in the Amazon Basin, as illustrated in the
photo of a real cloud in Figure 4.7). The parcel starts with a specific humidity of 0.022 kg
of water vapor per Kg of air (relative humidity xx%). By the time the air parcel reaches
500 m above the surface, condensation begins. Since we have so much water vapor
available for condensation, a lot of heat is added to the parcel the moist lapse rate is only a
few degrees per km. By the time the air parcel reaches 5 km, it is warmer than the
surrounding air and is thus unstable. In this example, the parcel is stable for small
displacements (i.e. less than 500 m), but for larger displacements, it is conditionally
unstable. Strong convective rain showers (thunderstorms) could develop in the
atmosphere used in this example, reflecting the less stable ambient temperature profile and
the high humidity at the ground. The slightly unstable case, pictured in Fig. 4.7, actually
developed weak rain showers.
4.6 Main points of Chapter 4
Lapse rates
• The adiabatic lapse rate (-9.8 K/km) is the temperature change that takes place in an
air parcel displaced vertically in the atmosphere, where pressure vs. altitude follows
the barometric law. The temperature decline represents the source of energy for the
parcel to expand as it goes up, doing work on the surrounding atmosphere. The
reverse occurs when an air parcel descends.
• The moist or saturated lapse rate is the temperature change that takes place in an air
parcel with 100% humidity displaced vertically, with condensation maintaining 100%
humidity, as the parcel rises. Release of latent heat causes this lapse rate to have
smaller magnitude (usually -3 to -7 K/km) than the adiabatic lapse rate. The process
may be called pseudo-adiabatic since no heat enters from the environment, but heat is
generated by condensation.
9
Stability, instability, and conditional instability
• The adiabatic lapse rate defines neutral stability (neither stable nor unstable). If the
atmospheric lapse rate has smaller magnitude than the adiabatic lapse rate (e.g. -6 K
/km), a parcel that is displaced upwards has lower temperature than the surroundings,
therefore higher density: parcels tend to fall back where they started and the
atmosphere is stable.
• If the atmospheric lapse rate has larger magnitude than the adiabatic lapse rate (e.g.
-10 K /km), a parcel that is displaced upwards has higher temperature, therefore lower
density, than the surroundings. Parcels are buoyant when they start to rise (negatively
buoyant when they start to descend) and will be accelerated by buoyancy forces. The
atmosphere is unstable.
• The motion of buoyant parcels in an unstable atmosphere tends to bring the ambient
temperature gradient to neutral.
• If parcels contain high amounts of condensable water vapor, the atmosphere may be
stable for small displacements of air parcels, but conditionally unstable for larger
displacements: a large vertical displacement may release sufficient latent heat to make
the parcel warmer than the surroundings and therefore buoyant.
• When the atmosphere is conditionally unstable, rain showers (often thunderstorms)
may occur as heating of the ground causes parcels to rise above the level of
conditional instability. Conditional instability is a factor in many weather forecasts.
Note
You may note that condensation in the first example (Fig. 4.5) does not occur at the dew point of
the parcel (295 K) but at a lower temperature, 287 K. As the parcel rises, its pressure goes down
(barometric law), and the partial pressure of water also goes down. In this example, at 1.7 km
where our parcel started to condense water, atmospheric pressure was .78 bar and the partial
pressure of water had been reduced from 16 mb to 16 × 0.78 = 12.5 mb, corresponding to a dew
point of 287 K. Thus, even though water condenses when the partial pressure of water in a
parcel (pressure in mb) equals the saturation pressure (in mb) over liquid or solid water; and the
saturation vapor pressure depends on temperature only, the partial pressure of water changes as
the parcel rises and expands. Specific humidity, defined as the number of kg of water per kg of
air, does not change unless condensation occurs. The calculation of the exact altitude at which a
parcel becomes saturated with water vapor is consequently rather complicated and lies beyond
the scope of this course. Students are expected to understand the underlying process and to be
able to perform simple computations where the condensation altitude is supplied.
4.7 Demonstrations
1. Expansion, compression, and temperature in a gas #1. In the first demonstration
we compressed air in a pump (syringe), and observed a rise in temperature. The
10
temperature increased when we pushed on the plunger, representing conversion of
mechanical work to heat (temperature change), and decreased when we allowed the
gas in the syringe to do work on the plunger as we pulled it back. Quite large
temperature changes were obtained, up to 100°C!
2. Expansion, compression, and temperature in a gas #2. In the second demo a
member of the class discharged a CO2 fire extinguisher. The expansion of highpressure CO2 through the nozzle did work on the atmosphere (part was converted to
sound, that's why the device makes such a loud noise) and got cold enough to form
solid CO2 (dry ice, -78°C).
3. Buoyancy and circulation in a fluid. We observed a tank of water heated on one
side and allowed to return to room temperature on the other. Small particles were
suspended in the water so that we could observe the motion of the fluid. The warm
water rose in a column, then spread out horizontally as it cooled off, and descended on
the cooler side, and flowed back towards the heated side, effectively making a loop.
Where the water was heated, buoyancy was generated, since the density of the warmer
water is lower than the density of the rest of the water in the tank. Since this process
moved mass into the upper part of the tank on the heated side, the column of water
increased slightly there and thus the pressure increased there; water spread
horizontally pushed by this pressure gradient. As this flow added mass to the upper
part of the cooler side, this induced an additional pressure gradient and led to the
formation of the circulation loop that you could see.
This experiment is the analogue of the sea breeze, where the heating is provided by
sunlight over the land, which raises air temperatures there. The sea breeze really does
consist of a loop circulation, it does not go very far inland or over the sea (1-10 km)
and it does not go very high (about 1 km). Thus when you stand on the beach in Los
Angeles and note the wind blowing from the sea, it may be recycled from the city. The
sea breeze is one of the simplest examples of convection generated by buoyancy in the
atmosphere.
CHAPTER 4. ATMOSPHERIC TEMPERATURE AND
STABILITY
4.1 The temperature structure of the atmosphere
4.2 Displacement of an air parcel with altitude: work done by an air parcel on the
atmosphere
4.3 Stability
4.4 Convection
Dry Convection
Wet convection
4.5 Conditional Stability
Note
4.6 Main points of Chapter 4
Lapse rates
Stability, instability, and conditional instability
1
2
4
5
5
7
7
10
9
9
10
11
4.7 Demonstrations
10
12